Introduction
One of the credible threats of warming of the Earth’s surface is a rise in sea level. If of sufficient size and rate, future increases in sea level could cause substantial economic and social disruption by inundating many low lying regions. It is important to note that both the magnitude and rate of future rise need to be known to evaluate the potential cost/disruption, since economic costs and social disruption very far in the future may have very little current economic value.
Sea level rise is reasonably well documented from about 1870 to 1993 based on tide gauges, and since 1993 based on a combination of tide gauges and satellite altimetry; the total rise since 1870 is about 225 mm (~8.9 inches). But estimates of future rise vary widely. It is common to consider sea level to at least the year 2100 in discussing sea level rise, and estimates of rise to year 2100 range from as low as ~175 mm (~7 inches), at the low end of the IPCC AR4 range to as high as 1500 mm (~62 inches); even higher estimates (2+ meters, ~79+ inches!) are routinely suggested by people like James Hansen. Sea level increases in the upper range of currently published estimates would indeed be very disruptive in many regions, requiring large Netherlands-like dike projects and/or abandoning many coastal regions to the sea. So sea level increase is of considerable interest.
Some Earlier Studies
Many studies of sea level increase have focused on whether or not the rate of sea level rise is accelerating or is reasonably constant. The work of Church and White (2006, hereafter C&W) suggested considerable acceleration in the rate of rise between 1870 and 2001, but other authors (eg. Houston and Dean, 2011, hereafter H&D) have suggested that the rate of rise is not accelerating, at least not since 1930, although acceleration prior to 1930 seems clear from the available data. Vermeer and Rahmstorf (2009, hereafter V&R) proposed a “semi-empirical†model, where they fitted the historical data from C&W (with some adjustments), and concluded that future acceleration of sea level increase would be very high, leading to most probable estimates of 1 to 1.4 meters by 2100, depending on which IPCC emissions scenario is assumed.
This post was motivated by my dissatisfaction with the quality of analyses of both V&R and H&D; I found neither very credible, though for very different reasons. As Vermeer and Rahmstorf pointed out in a recent published refutation of H&D (as well as in a very critical post at RealClimate) the appearance of no acceleration was the result of a “cherry pick†of starting date (1930), which seemed designed to minimize the appearance of acceleration. It is a valid critique, although I would not accuse the authors of ‘cherry picking’; they were, however, a lot less than complete in their analysis.
V&R suffers from a different kind of problem. Their semi-empirical model does yield extreme rates of sea level rise, but it uses what seems like an odd combination of one physically justifiable, but incorrectly formulated function, and one physically unreasonable function, to generate that very high projected rate. V&R assume that the rate of sea level rise consists of two components, the first is that the rate of net melt of land-locked glaciers/ice sheets will increase in proportion to the rise in temperature over that temperature where glaciers/ice sheets would be in equilibrium (neither net melt nor accumulation). This is then the mass component of the increase in sea level. At any constant temperature above the equilibrium temperature, there should be a fairly constant rate of melt for a very long time (since glaciers/ice sheets hold a lot of ice and are expected to melt only very slowly).
But V&R appear to include thermal expansion (due to warming) with the increase in mass (due to melting of landlocked glaciers and ice sheets), which strikes me as simply incorrect, and bound to lead to errors. An increase in melt rate due to an increase in temperature ought to continue to have approximately constant continuing influence, since ice will keep melting unless the temperature falls. Thermal expansion is limited in contribution; once the temperature of the upper layers of the ocean increase in response to surface warming, thermal expansion should slow rapidly. These two factors can reasonably be expected to behave quite differently over time, yet V&R appear to have not attempted to separate their effects.
The second component in V&R’s semi-empirical model is the first derivative of temperature with time. Now you might expect that an increase in the rate of warming (positive first derivative) would have some positive impact on sea level rise, though it is not immediately obvious to me what the magnitude of that effect would be. But it is certainly reasonable to expect an increase in warming rate would cause an increase in rate of sea level rise. In fitting their semi-empirical model to historical data, V&R concluded that the best fit corresponds to the first derivative of the temperature with time having a strongly negative effect on the rate of sea level rise. In other words, an increase in the rate of warming will tend to reduce the rate of rise. I found that to be a remarkably non-physical result, and one which is contrary any reasonable expected behavior of warming water and melting ice. V&R noted that it was indeed unexpected, and offered a few possible explanations. I found none of them even slightly convincing; had it been me, I would have concluded that the approach was not connected to reasonable physical behavior, and tried to determine what was wrong.
At the time I read V&R, I expected that they would be criticized widely by the climate science community for proposing a model which was so physically unreasonable (and so contrary to common sense!).
Getting Started
As far as I know, that did not happen. Perhaps my expectations were too high. But it motivated me to start thinking about a physically sound way to model sea level rise.
My “A-ha!†moment came a few weeks back when I noted that the physically reasonable part of the V&R model (ice melting increases in proportion to temperature rise over an equilibrium value) was a good starting point; all that was needed was a way to quantify the ocean heat content over the past 140 years or so, and use that to estimate how the average density of water in the ocean has decreased (warming) or increased (cooling) over the past 140 years, and into the future. In other words, if a reasonable estimate of the steric (density change) contribution to the sea level could be developed, then that contribution could be subtracted from the measured historical sea level trend, to yield an isolated glacier/ice sheet melt contribution trend. Once so isolated, the melt-only curve could then be fitted (like V&R) to the known temperature history, yielding an explicit function for how the melt contribution can be expected to change under any assumed warming projection. But how to estimate past (and future!) ocean heat content (OHC), when the only good data available (Levitus et al) cover just 1955 to present? Clearly a model relating sea surface temperature (with data available starting 1850) to OHC was needed.
Modeling Ocean Heat Uptake
It has been recognized for some time that an adjustment following World War II was made in the Hadley SST2 data set to try to account for an assumed sudden decrease in the fraction of ship engine intake readings of temperature and simultaneous increase in bucket sampling, following the war. It has recently been concluded that this adjustment was not accurate. The most recent Hadley data set (SST3) has an off-set of ~+0.3C after WWII (compared to SST2) which decreases linearly to 0C by ~1970. Since I did not have the SST3 data set available, I manually adjusted the SST2 set to reasonably match the new data set.
ENSO causes confusion when trying to connect changes in ocean surface temperature to changes in heat content, because ENSO appears to mainly move ocean surface heat around, not increase or decrease it, while at the same time causing significant changes in the measured average sea surface temperature. ENSO therefore adds a lot of noise to the analysis. Many have noted that average sea surface temperature rises about 1 year following an El Nino event, and falls about 1 year following a La Nina event. A correlation of the one-year lagged Nino 3.4 value against the trend in sea surface temperature showed that an increase of 1C in the Nino 3.4 value corresponds to an increase of about 0.08 -0.1C in the average sea surface temperature 1 year later. (La Nina does approximately the same but in the opposite direction.) So I made a further adjustment in the ocean surface temperature to account for the ENSO (using an assumed constant of 0.1C per C in Nino 3.4). Both of these adjustments are shown in Figure 1.
The Nino 3.4 adjustment is a short-term adjustment in SST, because the Nino 3.4 index varies between positive and negative values, but averages out to near zero. Long term (decadal and more) changes in OHC should not be influenced much by the Nino 3.4 adjustment, but short term changes in OHC will be influenced.
To model heat diffusion into the ocean, I set up a series of 21 spread sheet columns, each column representing ~56 meters of ocean depth, with the temperature value in the first cell of the first column being the Nino-adjusted surface temperature in 1850, the second cell in that column being the Nino-adjusted surface temperature in 1851, so forth down the column until reaching 2010. The first cell in every other column (corresponding to the temperature at that corresponding depth in 1850) was set to -0.4 C (these are anomaly values like the Hadley SST’s, not absolute values!), which was my estimate of the approximate 1850 average temperature anomaly.
The second cell in the second column was calculated by averaging the first cell in the first column with the first cell in the third column. The second cell in the third column was calculated by averaging the first cells in the second and fourth columns, and so forth. Each step downward then represents a 1 year step forward in time, and changes in surface temperature (first column) are damped as their influence migrates and is “averaged†into the columns which represent deeper water. (A very small amount of damping, giving slightly slower response than simple averaging, was needed to reduce the tendency for the calculations to oscillate.) The resulting trends in temperature at several different depths are shown in Figure 2.
Note in Figure 2 that the variation in surface temperature year-on-year is rapidly damped at greater depths; indeed, there is only a very modest change in temperature between 1850 and 2010 at the maximum depth of 1120-1176 meters. The final step in developing the steric part of the model was running a regression between the measured changes in 0-700 meters OHC (Levitus et al) and the average temperature of the first 13 columns (nominally, 0-728 meters). This yielded the model equation:
OHC = 90.05(+/- 3.7) * (average temperature) + 19.8 (+/- 0.8) (Eq. 1)
The regression gives an R^2 value of 0.918. Figure 3 shows the modeled trend back to 1871, along with the measured trend from 1955 to 2011.
The calculations of heat diffusion started in 1850, but I treated the 1850 to 1870 period as a “windupâ€, because choosing an assumed initial temperature (-0.4C) could lead to significant inaccuracies in calculated heat, especially in the first two decades. Once the calculations have been based on actual surface temperatures for a couple of decades, the influence of any inaccuracy in the assumed initial temperature is greatly reduced. Figure 4 shows the scatter plot of the OHC model against the measured OHC.
While the fit is by no means perfect, it is at least reasonable, and gives a first order estimate of ocean heat content before 1955. The same combination of heat diffusion calculation and an assumed future surface temperature trend can (of course) be used project the trend in future OHC.
Figure 3 also shows the estimated steric contribution to sea level change based on the total change in heat from the surface to the deepest water (~1150 meters). The pattern of oscillation in ocean heat and the resulting contribution to steric sea level change is clear. The estimate of steric contribution is a little uncertain because the coefficient of expansion of sea water changes substantially with temperature; colder water expands less for a given temperature change than warmer water. A more exact calculation would require knowledge of the absolute temperature profile in addition to how the profile changes with time.
Determining the Mass Contribution
Subtracting the calculated steric contribution from the historical measured sea level should yield a much improved estimate of the true mass increase (increase due to melting of glaciers/ice sheets). The steric contribution from Figure 3 was subtracted from the C&W sea level data. The Ho, A, and To parameters in the following equation were then hand optimized to give a reasonably good match to the curve for level increase due to increasing mass:
H(t) = Ho + A* ∫ (T(t) – To) ∂t (Eq. 2)
Where: t is time
H(t) is mass related sea level as a function of time
Ho is a constant
A is the “melt rate constantâ€
T(t) is the average ocean surface temperature over time
To is the “equilibrium†(no melt) temperature
Integration is from 1870 to time t, with t between 1871 and 2001 (the period covered by C&W data).
The resulting fit values were:
A = 2.30 mm/deg-yr
Ho = -49.3 mm
To = -0.722
Note that the above equation says the “no-melt†average sea surface temperature is 0.722C below the zero point of the Hadley SST2 data (or about 0.722C below the temperature in 1980), which seems a reasonable value. The results are shown graphically in Figure 5, where the upper curves are the melt model and the steric adjusted measured sea level from C&W.
The lower curves in Figure 5 show the original C&W data along with the combined model: mass contribution model plus the steric contribution from the SST model. The fit appears quite good. The model estimate of sea level trend from 1993 to 2010 is almost exactly the trend independently measured by satellite altimetry. The quadratic fits for the mass increase part of the model and the mass portion of the C&W data are essentially identical. The mass increase portion of the model clearly shows net acceleration (0.0106 mm/yr^2), contrary to the claim of no acceleration by H&D.
Figure 6 is a scatter plot of the C&W data against the combined model. The fit is quite good. This suggests that the model is capable of simulating sea level changes with reasonable accuracy.
Future Sea Level Projections
(Drum roll please…)
Figure 7 applies the complete model (mass and steric contributions) to several assumed constant warming rates, ranging from 0.05C per decade (which should please folks like Roy Spencer and Richard Lindzen) to 0.30 C per decade (which should please folks like Gavin Schmidt and Tamino) in steps of 0.05C per decade, all taken to year 2100. Warming of 0.05C to 0.2C per decade yields sea levels within the range of IPCC AR4 estimates, while 0.25C and 0.3C per decade yield sea levels above the IPCC AR4 range.
The highest assumed trends (0.25 and 0.3C per decade) give 600 to 700 mm increases (~24 to ~28 inches) in 2100. One interesting result is that even no additional warming (a constant temperature from 2011 to 2100) would be expected to produce ~250 mm (~10 inches) of sea level increase (not shown on graphic). So at least 250 mm increase seems essentially unavoidable.
Figure 7 also shows the calculated result of a hypothetical global “crash program†to drastically reduce CO2 emissions. This is shown by the dashed green trend line. This trend is based on warming of 0.15C per decade over 20 years, 0.1C per decade over 10 years, 0.05C per decade over 10 years, constant temperature for 10 years, and then falling at 0.05C per decade until 2100 (or 40 years of falling temperatures). The result of such a “crash programâ€, an increase of 340 mm (~13 inches), seems modest, unless you assume that very rapid warming (0.25C or 0.3C per decade) would otherwise happen.
My personal take on these results is that sea level will probably increase somewhere between 380 and 500 mm (~15 to ~20 inches), a little over the mid-range of the IPCC AR4 projections, since I expect warming over the next 89 years to be between 0.10C and 0.15C per decade. Much lower or much higher sea levels in 2100 seem to me unlikely.
Figure 8 overlays the projections from V&R and these results. The difference is large. The lowest V&R projection lies well above the highest projection from this model. The short red line (the satellite trend from 1993 to 2010) shows that the V&R projected slope is already diverging from the measured slope. According to V&R, the slope in 2011 should be substantially higher than what it actually is. By 2020-2025, the V&R projected slope rises to almost double the current slope. I am reasonably sure this is not going to happen.
Recent ‘Deceleration’
Many have noted that the satellite altimetry trend shows recent ‘deceleration’ in the sea level rise. This is correct, but it is due to the nearly flat sea surface temperatures since 1998.
Figure 9 shows what the model ‘predicted’ for the trend during the satellite era. There is nothing inconsistent between the observed short term deceleration and predictions of longer term net acceleration when shorter term (steric) effects are considered, as done in the model. Indeed, if the model did not suggest the recent deceleration, that would indicate something was terribly wrong with how the model was formulated. The argument that a lack of recent acceleration is inconsistent with longer term acceleration is simply mistaken. The C&W data show substantial swings between periods of acceleration and deceleration, which seem driven by changes in the ocean surface temperature trend; there is nothing at all unusual in the recently observed deceleration.
General Comments (warning, some political content)
I am very happy that V&R was published, because it is one of the few cases I know of where a well known projection from climate science will actually be tested in a meaningful way within the possible remainder of my lifetime. I predict that by 2025, or possibly sooner, it will be clear to most everyone (OK, maybe not V&R and James Hansen, assuming he is still around) that the V&R projections of extreme sea level rise are just wrong. I believe their projections are badly distorted by the use of an obviously incorrect (not physically reasonable) semi-empirical model.
Substantial sea level rise will almost certainly take place between now and 2100, and the rate of rise is very likely to increase during most of that period due to rising CO2 levels and the associated increase in radiative forcing. But the magnitude of that rise will depend on the rate of warming…. showing (once again) how important it is to accurately know climate sensitivity to radiative forcing. Rationally evaluating the potential economic and social risk due to sea level rise, and justifying costly changes in energy infrastructure, production, and use to reduce that risk, are essentially impossible in the absence an accurate value for climate sensitivity (both “immediate†and “equilibriumâ€).
The uncertain future trajectory of CO2 emissions further complicates the estimation of sea level rise, since the substitution of nuclear, solar and wind energy for fossil fuels (primarily coal) depends on several imponderables, the most important of which is the future cost for fossil fuels; scarcity of fossil fuels, and/or falling prices for nuclear/solar/wind could reduce fossil fuel use and significantly reduce future CO2 emissions, independent of any orchestrated public action.
Strengths and Weaknesses of the Model
I agree with George Box, the great statistician, that all models are wrong, but that some are useful. The utility of a model of a physical system is not ever proven until and unless it makes substantially accurate predictions over a reasonable period (and I specifically define “prediction†as “what happens in the futureâ€, not what happened in the past). But it seems to me that any model based upon a poorly reasoned physical representation of a system is much less likely to be useful than one based on a well reasoned physical representation. For example, a model of a physical process based on a 5th order polynomial fit to observational data may very well not be at all useful (it may make predictions which are terribly wrong!), even though it matches currently available data almost perfectly. You disconnect your model from physically sound reasoning at your peril.
The most important strength of this model is that it is built upon three simple concepts, each of which appears physically reasonable:
1. The total rise in sea level due to warming is the sum of thermal expansion and melting of land supported ice (glaciers and ice sheets), and these two processes have very different temporal trajectories.
2. Warming of the ocean below the surface layer is a function of warming of the surface layer (that is, overall warming depends on diffusion of heat from the surface to deeper water).
3. The rate of melting of land supported ice should be approximately proportional to the rise in temperature over that temperature where there would be no net year-on-year change in the total.
It is mildly encouraging that the model (which is based mostly on data from before 2002), closely matches the measured sea level (satellite altimetry) through 2011. A more substantive test will be the performance of the model over the next 10-15 years.
The model has several weaknesses or, perhaps more accurately, areas where it could be more robust:
1. The expectation that melting will be proportional to temperature increase over an equilibrium temperature may not be accurate. For example, when mountain glaciers melt, the glacier’s melting front may “retreat†to a higher elevation, where the temperature is reduced due to the atmospheric lapse rate… so the “no net melting†equilibrium temperature would then be higher. The base of the melting front of an ice sheet may or may not move to higher elevation with warming (depending on local geography), but the top of the melting front for sure moves to higher elevation with warming temperatures, so the total length of the melting front may or may not grow significantly, and the equilibrium temperature may or may not increase with melting. Finally, the rate of ice flow (both glaciers and ice sheets) may increase in response to warming temperatures, which would tend to accelerate melting.
2. The diffusion model used here is very simple, and may not produce an accurate representation of the evolution of the ocean temperature profile over time. The diffusion model does yield a reasonable match to the measured OHC, but the model may diverge from measured OHC before or after 1955 to 2011. A more detailed and higher resolution heat diffusion model, one that matches both the measured changes in temperature profile with depth and the total OHC, would be more robust.
3. Uncertainty in the model’s projections is difficult to evaluate, in part because the final model (combined steric and mass contributions) depends on the “hind-cast†of the ocean heat model from 1955 back to 1870 to determine the steric adjustment to the measured sea level. Potential error in the ocean heat model hind-cast to 1870 adds uncertainty to the mass model parameters, and so adds considerable uncertainty in the overall 2011 to 2100 forecast. An improved ocean heat diffusion model would therefore reduce uncertainty in both the steric and mass contributions to future sea level rise.
4. Some authors have suggested that water accumulation in reservoirs and water pumped from aquifers for irrigation (“water miningâ€) have made significant contributions to the measured change in sea level. Since these factors were not included in my calculations, they represent potential error. From what I have been able to gather, the confidence in these contributions is low, so it is difficult to assess how important these factors might be.
I am sure there are other weaknesses which I have not thought of.
Blog Comments
I will address reasonable comments and questions, and especially reasonable technical questions, about the model. But I will not address comments like: “0.04% CO2 can’t possibly warm the Earthâ€, “Radiative forcing by CO2 violates the second law of thermodynamics.â€, “Nobody knows what the ocean surface temperature trend was.â€, “All the warming has been caused by changes in the sun.â€, “You deniers are destroying the Earth and endangering our grandchildren.â€, “Why should I believe you instead real climate scientists like Vermeer and Rahmstorf?â€, etc, etc, etc. Addressing these kinds of comments will only waste my time and yours, and life is too short for that.
References:
Vermeer and Rahmstorf (2009) www.pnas.org/content/early/2009/12/04/0907765106.full.pdf
Church and White (2006) www.agu.org/pubs/crossref/2006/2005GL024826.shtml
Houston and Dean (2011) www.jcronline.org/doi/abs/10.2112/JCOASTRES-D-10-00157.1?prevSearch=[AllField%3A+houston+dean]&searchHistoryKey=
Tom Moriarty has spent quite a bit of time dissecting Rhamstorf’s model and his refinement with Vermeer. He confirms many of your points although he does not attempt to create a “more reasonable model”, you can find his series of posts here:
http://climatesanity.wordpress.com/critique-of-a-semi-empirical-approach-to-projecting-future-sea-level-rise-by-rahmstorf/
http://climatesanity.wordpress.com/critique-of-global-sea-level-linked-to-global-temperature-by-vermeer-and-rahmstor/
However, a few of the issues he raises apply to your work, as well. For one thing, the Church and White paper from 2006 is out of date, they now have a paper at least as late as 2009 and the results are somewhat different.
Additionally, he proposes a potential groundwater depletion factor to combine with the impoundment data to further factor these non-climatic effects out.
Elegant that you conceive of your model in terms of physical processes, and work from there. Using water depth to predict change in seawater density seems adequate. On the other had, the response of glaciers looks to be complex, as you point out. Where would most of the frozen water come from: Greenland and Antarctica? Would it be practical to consider the likely physical effects of rising T on each of these reservoirs, and model them separately?
(Just thinking out loud… that might overcomplexicate the model, for no gain in predictive power.)
While mountain glaciers can retreat to higher elevation and find a new equilibrium, the opposite is true for Antarctica. Because the surface under the ice cap has been depressed below sea level, a retreat of the ice cap exposes more surface area to the ocean rather than less. I think this is the rationale behind some of the more catastrophic sea level rise predictions.
Steve F: “One interesting result is that even no additional warming (a constant temperature from 2011 to 2100) would be expected to produce ~250 mm (~10 inches) of sea level increase (not shown on graphic).”
That rate would be higher that the trend shown by the second half of the satellite data.
SteveF: “At any constant temperature above the equilibrium temperature, there should be a fairly constant rate of melt for a very long time (since glaciers/ice sheets hold a lot of ice and are expected to melt only very slowly).”
But the surface of the earth does not have a constant temperature. Only a portion of the earth’s ice would be exposed to temperature above the equilibrium given constant temperature. As that disappears, the rate of meltwater that will be added to the oceans will drop. This makes the first argument above seem implausible.
Some parts of the earth are above equilibrium temperature part of the year and below it other parts of the year. During the part where they are below it, they are adding snow that eventually becomes ice with compression. So ice leaves and is restored in those areas. This yields no change for the sea level. So if you don’t have more warming, the areas that are in annual equilibrium – or even adding, will not change. And the ones that are in a melting state will disappear and give no further ocean rise.
So considering the fact that sea level rise is already below what you compute for a no change situation, and considering the other elements that I stated, I doubt your computation of 10 inches from 2011 to 2100 with no temperature change.
DeWitt Payne: “Because the surface under the ice cap has been depressed below sea level, a retreat of the ice cap exposes more surface area to the ocean rather than less.”
I’m sorry, I’m not getting this.
SteveF: “One interesting result is that even no additional warming (a constant temperature from 2011 to 2100) would be expected to produce ~250 mm (~10 inches) of sea level increase (not shown on graphic). So at least 250 mm increase seems essentially unavoidable.”
This rate is higher than the measured rate for the second half of the available satellite data.
SteveF: “At any constant temperature above the equilibrium temperature, there should be a fairly constant rate of melt for a very long time (since glaciers/ice sheets hold a lot of ice and are expected to melt only very slowly).”
But only a portion of the earth’s ice is above the equilibrium temperature. So if there is no change in temperature, only that part can be expected to continue to decrease. And since it is a decreasing amount that is available to melt, then it must add less water to the oceans as time goes by. Do you know how much of the earth’s ice is above equilibrium temperature at this point. Remember that some of it melts during the summer and is restored by falling snow in the winter. So not all ice that melts for some period of the year is decreasing ice.
Given that the current rate of sea level rise is below your estimate for a constant temperature going forward, and given that the ice that is above the melting equilibrium is only a fraction of the total – and a shrinking fraction at that, I doubt your 10 inch estimate.
I think that alarming projections of future sea level rise are crucially dependent on the contribution of melt/loss from continental ice sheets growing ever faster. I believe that this is erroneous.
According to:
Nick, F.M., A. Vieli, I.M. Howat, and I. Joughin. 2009. Large-scale changes in Greenland outlet glacier dynamics triggered at the terminus. Nature Geoscience, 2, 110-114.
There were recent years with fairly large ice loss events, but these were transient:
“From our numerical modelling, we conclude that Greenland tidewater outlet glaciers are highly sensitive to changes in their terminus boundary conditions and dynamically adjust extremely rapidly, providing an explanation for their almost synchronous behaviour to short-term fluctuations in climate. This implies that discharge changes near the glacier terminus reflect short-term dynamical adjustments, and do not provide a reliable measure for the longer-term mass balance of an ice sheet. We predict that longer-term rates of mass loss, at least for Helheim Glacier, may be less marked than observed in recent years…Our results imply that the recent rates of mass loss in Greenland’s outlet glaciers are transient and should not be extrapolated into the future.”
The current contribution of Greenland and Antarctica is six inches per century, and it is likely higher than what one can reasonably extrapolate out to the future:
Velicogna, I., 2009. Increasing rates of ice mass loss from the Greenland and Antarctic ice sheets revealed by GRACE. Geophysical Research Letters, 36, L19503, doi:10.1029/2009GL040222.
The fact that one could not extrapolate the high rates before recent years is shown in that the rates returned to what they were in 2000 from previous highs:
Kerr, R. A., 2009. Galloping glaciers of Greenland have reined themselves in. Science, 323, 458.
That these ice sheets are more stable than many believe is not surprising when you consider that the Arctic was warmer than now by several degrees in July between about 8000 and 3500 years before the present, but there was no collapse of Greenland, not even an anomalously higher sea level early in the Holocene.
In the Antarctic, total melt has gotten slower in the last about thirty years:
Tedesco M., and A. J. Monaghan, 2009. An updated Antarctic melt record through 2009 and its linkages to high-latitude and tropical climate variability. Geophysical Research Letters, 36, L18502, doi:10.1029/2009GL039186.
These ice sheets will contribute some to sea level rise, but not nearly as much as alarmists fervently believe.
SteveF: “The argument that a lack of recent acceleration is inconsistent with longer term acceleration is simply mistaken. The C&W data show substantial swings between periods of acceleration and deceleration, which seem driven by changes in the ocean surface temperature trend; there is nothing at all unusual in the recently observed deceleration.”
Saying that it’s “driven by changes in the ocean surface temperature trend” doesn’t help. To say that the ocean surface temperature trend has some natural variation doesn’t help. Unless you can identify the source of the natural variation, you cannot say that the current deceleration is a part of a longer term acceleration because you don’t know the cause of the deceleration and so you have no basis for claiming that it will become an acceleration.
Quite informative, thank you very much.
DeWitt Payne said in Comment #79625
“While mountain glaciers can retreat to higher elevation and find a new equilibrium, the opposite is true for Antarctica. Because the surface under the ice cap has been depressed below sea level, a retreat of the ice cap exposes more surface area to the ocean rather than less. I think this is the rationale behind some of the more catastrophic sea level rise predictions.”
___________
Does this raise a question about how “land Ice” is defined? Is the Antarctic ice that lies on land below sea level considered land ice or sea ice?
Sea water getting under Antarctic ice that lies above sea level could cause it to break away and float out to sea, according to recent research reported in sciencedailey.com.
http://www.sciencedaily.com/releases/2011/06/110601134253.htm
I don’t really understand what is what in Fig. 8, but what I read on it worries me a bit.
.
Are you saying that your model does not take into account reservoir accumulation, and thus only reproduces sea level change minus whatever has flown into manmade reservoirs?
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Also:
.
I think you will need more than an argument from incredulity to refute the “time lag” explanation that they develop. The negative weight on rate of warming is not an independent physical process, it is the mathematical expression of a time lag in the response of the ice to warming.
.
Not saying they’re right, just that I’d like to know why you think they’re wrong.
SteveF,
Nice article. I will reread with some care this evening.
I note that you don’t treat isostatic contribution. This seems OK if you are comparing OHC data, but are your sea-level comparisons apples-to-apples?
Paul
Paul_K,
Thanks.
I believe Church and White data is already corrected for rebound (I will look to confirm), so I think only apples are being compared. The rebound effect would reduce net shore-line projections of level change in 2100 by about 27 mm.
Tilo Reber,
The significance of second half of the satellite record is almost certainly less than you imagine. The model projection is based on the behavior over a longer period; a short term trend is not a reliable indicator of longer term behavior. I hope you noted that the model does in fact predict a recent deceleration.
Your other comments do not make any sense to me. Of course most ice is not currently melting; that ice makes no contribution to sea level rise. Only the “melting front” contributes.
The model makes no prediction about what future warming (if any) will take place, it predicts sea level change based on surface temperature trend. If you don’t believe there will be any future warming (or even future cooling), that is OK with me, but I think you will find that very few people will agree with you. I would argue that both the temperature trend over the last 100+ years and the radiative effects of GHG’s are consistent with some future warming. How much is a subject of debate.
toto (Comment #79636),
Figure 8 shows a pasted overlay of the V and R 2009 projection with the graphic from my model. If you read V and R, the graphic I used is their “Figure 6”.
WRT reservoirs and groundwater mining: I used neither effect, because both seem quite uncertain. V and R choose to use only reservoirs (which increases the projected rise) and ignore groundwater effects (which would reduce projected rise). I think using only the effect which increases projected rise is inappropriate.
V and R combine the independent steric and mass effects (which evolve very differently over time) into one, and use the derivative term to make it all fit the data. If you don’t see why this is not a sensible approach, I am not sure I can explain any more clearly why.
AndrewFL,
I will look for the more recent Church and White data. I would need it in a down loadable form. My understanding (though this could be wrong!) is that the more recent data is mostly an extension of the earlier work to be more up to date, not a major change in earlier analysis.
DeWitt Payne (Comment #79625),
I think you are right that major changes in ice sheet melt mechanism (like ocean undermining of Antarctic ice) are involved in some of the more catastrophic projections of future rise. However, this is not the case with V and R: they based there projection on the more conventional “glacial melt front” analysis, as I did.
SteveF
Do sea level increase predictions reflect incremental (geometric?) increases in the basin volume as the level goes up? I would think that the basin volume described by present level and level in 2100 is knowable and since it is undoubtedly larger than say the increment from 1880 level to present level, should be a component of level estimates.
Maybe more clearly, the next meter in sea level will have much more water in it than the previous meter.
Great analysis Steve.
Just an aside first – the biggest component of sea level rise currently is ice sheet melt which is 0.5C. I imagine the ocean could be warming faster than it is cooling due to the 0.5C ice sheet melt being added to it, but I just thought that should be raised.
How much did the ocean warm from 20Kya to 5Kya when 120 metres of 0.5C water was added to it.
This would also be moderate-density water and would sink to about 3000 metres before it encountered more dense water.
—-
In addition, there is a point in the data where sea level rise begins to decelerate (it is hard to tell but it could be around 1950 or 1980 but certainly in the last 20 years).
If temperature increases to +3.0C by 2100 I’m sure there will be a renewed acceleration, but generally it has been decelerating for the past 60 or 30 or 20 years.
If anyone has any thoughts on possible “black swan” events that could influence sea level rise by 2100, please share them with me off-list at huntjanin@aol.com.
The biggest component of sea level rise is artificial adjustments added to satellite measurements.
As the earth continues to cool, sea level drop will accelerate.
SteveF: “The significance of second half of the satellite record is almost certainly less than you imagine.”
You seem to have misunderstood me on both of my major points, Steve. How significant I think it is that the satellite record shows a deceleration is not what you imagine that I imagine. How significant I think it is is dependent upon the physical explanation that you can give for the deceleration. If you can show that the deceleration is due of cyclic natural variation that will reverse itself as the cycle changes, then the deceleration is, indeed, not important. But if you cannot explain the decelertion in such terms as ENSOs or volcanaoes or some other physical explanation that is likely to reverse itself, then I have no confidence in your assertion that the short term deceleration is simply a part of a longer term acceleration. In the history of climate all and every long term trend (however you define long term) has reversed itself. So hand waving about long term trends does nothing for me. Long term trends are not forever in climate.
SteveF: “The C&W data show substantial swings between periods of acceleration and deceleration,”
This is true of the tide guage data, which is very coarse compared to the satellite data. The satellite data is of a finer resolution, and so far it shows a deceleration, nothing else.
SteveF: “If you don’t believe there will be any future warming (or even future cooling), that is OK with me, but I think you will find that very few people will agree with you.”
In this case, this has nothing to do with what I was talking about. I was making no predictions about the warming trend. I was simply using your own assumption when you said: “One interesting result is that even no additional warming (a constant temperature from 2011 to 2100) would be expected to produce ~250 mm (~10 inches) of sea level increase”
I’m saying that, based upon your own scenario of no warming, that the 10 inches seems unreasonable. First it is unreasonable because the current rate is already below that, second it is unreasonable because “the melting front” as you call it, will not move under such a scenario, and the amount of ice that is covered by that melting front will decrease as it melts – meaning that each year there would be less ice included in the melting front that could contribute to sea level rise.
Thanks for the analysis, Steve. Just a quick comment: I would expect to see components in a full model with response times on the order of hundreds of years (via long term mixing of the oceans via circulation driven events) and because that is the general consensus on how long it takes for the ice to reach an equilibrium with a constant temperature. For example, a total 3°C of global warming, then constant temperature, probably eventually leads to 5 meters of total seal level change, most of it from melt water of course.
I’ll see if I can dig up the IPCC description (if you aren’t already aware of it). I believe they leave out certain contributions as being too uncertain, that may explain why your numbers are slightly higher than yours.
Steve,
Have you compared your thermal expansion and volume change numbers with those of Cazenave, et. al. for 2003-2008?
SteveF, I have not had time to go over your analysis in sufficient detail to comment on the technical aspects of it at this time. I do, however, want to express my gratitude to posters like yourself who do these kinds of analyses derived from the content of a published paper or two. The value of these discussions is not so much that an unalterable truth has been found or even whether the models and/or theories put forth are without weaknesses, but rather that the ensuing discussion can add to my knowledge bank (I am selfish in that regard) and enlightened/inform my view of the subject.
In my view some of the best blog discussions on climate science related subjects have resulted from a non-partisan critique of a paper that’s conclusion/evidence supported more the skeptics view of AGW and its consequences and combined with a critique of that same paper’s criticism from consensus leaning scientists – as was the case here. The Douglass and Santer paper debates on the tropical troposphere to surface warming trend ratios was another such illuminating discussion.
I think we often do not appreciate the uncertainty of projections and models until we see a full debate from countervailing viewpoints. Your latching onto a model finding of V&R that would appear to be unphysical and (in my view of what you commented) hand waved away would be a prime example of these uncertainties and how the importance of the issue is ignored or paid lip service to. I would appreciate your recounting of the rationale used by V&R for this surprising find.
I have been going back over Mann (98), Mann(08) and Mann (09) in my ongoing attempts to model the proxies used in these reconstruction and determine how well they can be approximated by white and red noise. In doing so I was reminded that the Mann authors in Mann(98) waved off the issue of unrealistic TRW growth in the high elevation proxies by invoking anthropogenic CO2 fertilization for a period toward the end of the proxy series and then a leveling off of that accelerated growth by further invoking a saturation effect. They pointed to a reference and after stating that regardless the effect was not natural they adjusted those series to another series where they claimed the effect was not present.
In Mann (08) the authors invoked another hand wave by eliminating the MDX proxy series back to 1960 (for divergence, I think, which, of course, would be opposite to the accelerated growth adjustment in Mann (98)) by eliminating that data and in filling it with data from other series.
SteveF (Comment #79643)-the data here:
http://www.psmsl.org/products/reconstructions/church_white_new_gmsl.lis
is updated through 2007, from Church and White’s newer paper. It looks significantly different from the original in the early part of the record:
http://climatesanity.files.wordpress.com/2010/04/church-and-white-original-and-updated-data.png
DeWitt,
I had not compared to Cazenave, et al. They suggest about 0.37 +/- 0.1 mm/yr steric contribution from 2004 to 2008. My model suggests ~0.69 mm/yr for that period. My guess is that the heat diffusion part of the model is a bit too sluggish, and is a little behind the actual OHC content trend (you can see this discrepancy in Figure 3 of the post, where the Levitus data rises rapidly, then levels out in ~2004, while my model makes a more gradual transition). My guess is that a better diffusion model would help with the fidelity of the shorter term response.
Andrew_FL (Comment #79671)
Thanks for the link. I will take a look at the updated Church and White data in the next few days.
It occurs to me that the volume of water on the beach, so to speak could be very small as a part of whole. sorry for the noise.
Tilo,
The deceleration is the result of the lack of warming in recent years. The assumption of the model is that the overall rise has two components: steric and mass. The rate of absorption of heat (thermal expansion component) declines over a period of a couple of years to many decades if the surface temperature is constant.
The observed deceleration is the direct result of little recent warming, independent of why there has been little recent warming. From a historical perspective, there does appear to be a 60-70 year pseudo-oscillation in the temperature of ~+/- 0.1C around the overall trend (this is pretty widely recognized); the peak in this pseudo-oscillation should have been somewhere near 2003. My guess is that the near lack of recent warming is at least in part due to being on the declining side of the pseudo-oscillation (similar to ~1944 to ~1978). The low level of solar activity (and slightly lower total solar intensity) over the last 3 years may also have something to do with it.
But your quarrel seems to be more with the possibility of future warming, not with sea level rise as a result of warming. If there is significant future warming, then there will almost certainly be an acceleration in sea level rise. The data seem pretty clear: there has been a significant amount of sea level increase, and that continues (albeit at a slightly slower rate than a few years ago… which is not at all a surprise according to my model).
So let me ask you two simple questions: a) do you or do you not think that the measured rise since ~1870 is due to past warming, and b) do you think future warming (if that happens, for whatever cause) will cause accelerated sea level rise?
Please let’s not confuse two very different issues. I really do not want to argue with you about whether or not there will be significant future warming, since I believe that would be a waste of time for both of us.
“Houston and Dean rightly point out that one should likewise correct for the water mined from deep groundwater sources for irrigation purposes. However, no suitable time series of twentieth-century groundwater mining is available. Neverthe- less, Vermeer and Rahmstorf (2009) performed a sensitivity study of this effect, and Rahmstorf, Perrette, and Vermeer (personal communication) included the very high estimate of Wada et al. (2010) and assumed that water mining is propor- tional to global population (to extend it back in time before groundwater extraction data are available). The result is that groundwater mining only has a minor effect on semi-empirical sea-level projections: Inclusion of this effect only lowers pro- jected future sea level by a few percent. …” – VR rebuttal to H&D, JCR
@Lucia
Can you please provide the historic average of sea level height? My guess is no because we are below average sea level height and so you won’t provide it.
Carrick,
The response time of the steric portion of the model is indeed very long…. several hundred of years for the 0-1150 meter depth to approach equilibrium with a step change in surface temperature. If you assume warming of the entire ocean, then the time is thousands of years. But two points I think of interest:
1) The long term steric contribution is very modest compared to the long term ice melt contribution, and
2) The form of my model does not anticipate ice reaching equilibrium with an increase in temperature… and this is one of the limitations of a simple model, as I described in my post.
Which not to say that such an equilibrium could not/would not be reached at some higher temperature, only that the model assumes that in the foreseeable future you can approximate melt rate as proportional to the difference between the actual average temperature and a hypothetical equilibrium temperature (where there would be no year-on-year net melt or accumulation). If there is a model which describes an equilibrium level of ice as a function of surface temperature, then I have not heard of it.
JCH
I guess that pretty well sums it up. You can always arm-wave an explanation in the absence of data.
Thanks, Steve. That’s pretty much what I was thinking too…you are developing a model that only addresses short-term climate response to warming.
Refining the “fast term” may have a significant effect on your results (my intuition is it would tend to push the projected sea level rise down slightly). It would be interesting to see a quantitative revised model.
What you’ve done here illustrates what so many others do wrong—namely they hand-wave about relative importance of different contributions, instead of constructing an analytic model to explore what happens under different scenarios.
Just to clarify the no warming projection in sea level rise:
http://i54.tinypic.com/2lbp7j7.jpg
The lowest line is the assumed no warming projection. The projected average rate of increase in the absence of additional warming is ~2.8 mm/yr.
This does not mean that there may not be other factors which will cause variation from that projected trend, especially over relatively short periods.
j ferguson (Comment #79646)
The “basin volume” that you talk about would appear to be the same as the glacial rebound adjustment (basin volume grows as Earth’s mantel slowly rebounds from the loss of ice weight during the transition from the last ice age to the Holocene). This adjustment is expect to be essentially constant, at about 0.3 mm per year (about 27 mm total from now to 2100). This is not very large compared to the projected total sea level rises. The rate of rebound was almost certainly similar from before 1870 until now, so the “last meter” and the “next meter” will be pretty much the same in volume.
SteveF. Thank you so much. I was warming up (so to speak) to roughing out the beach volume myself to see if it could be significant, but I would not have thought of the rebound figure nor have had any idea how to derive it. I had supposed the issue might have been not unlike flood-plain volumes upstream from dams or hydraulic constrictions. It’s interesting that landmasses are resilient and rise if significant loads are removed.
thanks again, john
JCH (Comment #79682)-They are not entitled to ignore a factor because they think it doesn’t matter. As for their “sensitivity test” that says it doesn’t matter, I’ll believe it when I see it. Analysis I have seen suggests it’s effect is as large as the reservoir correction that they thought should be included. See this graph that uses an estimate from the Wada et al data and an exponential fit (which would be similar to proportionality with global population) for extrapolation, the effect it has is to essentially undo the reservoir correction that was so crucial that it had to be included:
http://climatesanity.files.wordpress.com/2010/10/church-and-white-with-wada-groundwater-depletetion-and-chao-reservoir-correction.png
j ferguson (Comment #79691),
The land masses, composed mainly of relatively low density rock, actually “float” on more dense mantle rocks. The mantle is at great depth and is “plastic”… it flows very slowly in response to an applied force. So when a weight is removed (melting ice sheets) the mantle “recovers”, at first relatively quickly, but gradually more slowly as it returns to closer to equilibrium. We are currently in the “very slow” portion of the rebound, and the rate changes so slowly that on century time scales we can assume that it is approximately constant.
SteveF: “The deceleration is the result of the lack of warming in recent years.”
Yes, I know that. But that’s not the question. The question is, what is the cyclic cause, and will it reverse itself. I don’t think that a 60 to 70 year pseudo ocillation is the answer, since a .1C ocillation over that period of time would not be able to overcome even the lowest CO2 climate sensitivity numbers. Solar, if it is the answer, means that we have no way of knowing when the warming will continue. But the point here is that there is no clear know cause for 13 years of no warming. All that we know is that some cause must exist. So as long as we don’t clearly know the cause, we can’t predict how long or strong the current cause will be.
SteveF: “So let me ask you two simple questions: a) do you or do you not think that the measured rise since ~1870 is due to past warming, and b) do you think future warming (if that happens, for whatever cause) will cause accelerated sea level rise?”
Yes, I think that the measured rise since 1870 is due to past warming. I think that there will be future warming, but I see no reason to believe that it will be “accelerated” warming and I see no reason to believe that there will be accelerated sea level rise. I think that we can have future warming and that this warming can be decelerated. Remember, the effects of CO2 are logarithmic. And I likewise think that we will continue to have sea level rise, but that rate of sea level rise will also be decelerated. I think that if you kept the temperature constant, that you would experience a falling rate of sea level rise – in fact, that is what is happening now. So just to maintain a given rate of rise you need to have rising temperatures. To have an accelerated rate of sea level rise you need, not just increasing temperatures, but an acceleration in temperature rise. I see no evidence for a scenario of accelerating temperature rise. To me, these curves with their sharp and ever increasing rate of sea level rise are absurd. And in my opinion, V&R’s numbers are comic.
Speaking of comic, here is a nice one:
http://i.minus.com/idFxzI.jpg
SteveF, I did not see a link in your post to the 2011 Rahmstorf and Vermeer (V&R) paper critiquing Houston and Dean’s paper so I posted it below.
http://www.pik-potsdam.de/~stefan/Publications/Journals/rahmstorf_vermeer_2011.pdf
In that paper from Figure 1 it is obvious that the uncertainty of determining the acceleration/deceleration is large from any starting point after 1930. Also the (V&R) model does not perform well compared to the observed data prior to 1935. Of course, after 1935 the uncertainty limits for acceleration are so wide that model fitting to the observed data must be considered problematic.
Another reminder of the Santer and Douglass debate where the uncertainty of the model and observed data by Santer showed a very similar problematic issue of contending (with a straight face) that the model was within the limits of the observations when both ranges of measurements were shown to be huge. Even that was not correct if the comparison period was extended forward in time and satellite data were used.
The V&R 2009 paper is linked below:
http://www.pnas.org/content/106/51/21527.full.pdf+html
The V&R model is a fitted one using observed data. Without out-of-sample testing I cannot be too impressed with this model or others like it that have not been tested.
The rationalization in the paper of a negative b, that you referenced as unconvincing, is listed below. It would appear that the answer to the parameters of fitting not being sufficient is to find more parameters.
“Remarkably, the value we find for b is negative. We can think of two possible physical explanations. The first is that the initial rapid sea-level response to a warming is indeed negative. A possible mechanism for this is higher evaporation from the sea surface and subsequent storage of extra water on land, e.g., in form of soil moisture (19, 20). Note, however, that such a negative effect would have to be large: it would need to compensate the b of 2.5 cm_K_1 found earlier for thermal expansion and thus would need to be three times as large as this to cause the overall negative b value we found. It is hard to see how the very large amount of water needed to be stored on land could remain inconspicuous.
The second possibility is of a positive, but time-lagged, sea level response. That a negative b corresponds to a lag is easily seen for the example of a steady linear temperature rise with rate c starting at time t _ 0. The solution then is H _ 1/2 a c t(t 2b/a). This is the same parabola as for the R07 model (H _ 1/2a c t2), except that its origin is shifted by (b/a, b2c/2a) (see Fig.5). For c _ 0.01 K_a_1 (i.e., an idealized 20th-century warming) and the parameter values found above, this shift is 12 years and _0.25 cm. The short transient sea-level offset of a maximum of _2.5 mm is too small to measure and of no consequence on the longer time scales (_15 years) considered here. However, the implied time lag of 12 years in this idealized case is permanent and significant. We tested this idea by implementing a time lag directly in Eq. 2: dH_t_/dt _ a_T_t _ __ _ T0_ _ b dT_t _ __/dt. [3] and subsequently finding the best fit for T0, a, b, and _. When the resulting Pearson correlation is plotted as a function of b and _(see Fig. 2), a linear dependence between the two is seen, with two optimal solutions: one for zero _ and b _ _5 cm_K_1, and another one b_4.5 cm_K_1 and _ _13 years. Choosing the value b _ 2.5 cm_K_1 from our model simulations for the thermal expansion effect corresponds to _ _ _11 years, close to this optimum. The two parameters b and _ cannot be unambiguously separated by the statistical fit because their effect on H is so similar. Thus, the most plausible physical interpretation of our statistical fit is that the negative value of b results from a positive ocean mixed layer response combined with a lag of over a decade in the response of the ocean-cryosphere system. Several mechanisms could be envisaged for a delayed onset of sea-level rise after warming. For example, mass loss of ice sheets can be caused by warm water penetrating underneath ice shelves, triggering their collapse and subsequent speed-up of outlet glaciers banked up behind the ice shelf (21). We cannot explore the causes of delay in more detail here, but note that the statistical result is robust irrespective of its causes.”
This may be inconsequential or even naive: Let R(V) = ave global sea level where V = volume of water of oceans. Think of R as an effective, idealized radius of the Earth. As R increases then subsequent equal increases in V will result in smaller increases in R. I am too lazy to compute this and maybe the effect is miniscule. If not is this taken into account in models?
Kenneth Fritsch,
I do have the web page with the V and R listed at the bottom of the post.
I find the V and R explanations for negative b just as unconvincing the second time through as the first. Fortunately, this is one case where the resulting projection is so outlandish that I believe data will refute it within about a decade. The odd combination of steric and mass components implicit in the V and R approach remains in my mind the primary problem. When you remove the steric component, the estimation of the mass component is more rigorous… and the calculated future warming trend is reduced. The addition of reservoir accumulation (which further increases the projected rise), but no groundwater use for irrigation (which would reduce the projected rise) is an added “What the…?” factor about the paper. They are going to look real bad real soon (well, real soon for climate science).
Tilo Reber (Comment #79695),
I provided a wide range of possible warming rates. I did not make any specific projection of future warming within the model…. that is a whole different question. If you think there are problems with the formulation of the model, that is fine, but I think it would be better if you focused on those problems rather than focusing on whether or not we know what future warming will be. The analysis I did is a good faith effort to show where I think V and R are deficient and what a more rigorous analysis should look like. The results are the results. If you think those results are incorrect, for the several different assumed warming rates, please tell me why you think they are incorrect.
jack mosevich (Comment #79697)
The effect you are talking about is smaller than minuscule. If the sea level were to rise by 1 meter, the last 1 cm of that change would represent about 1.5 * 10^(-7) more water than the first 1 cm. It is insignificant.
SteveF
You wrote, “One interesting result is that even no additional warming (a constant temperature from 2011 to 2100) would be expected to produce ~250 mm (~10 inches) of sea level increase (not shown on graphic). So at least 250 mm increase seems essentially unavoidable.”
Three questions. Is the ~250 mm sea level increase the increase until equilibrium? And when might equilibrium occur based on your model?
Second, many think that carbon soot plays an important or dominant role in northern hemisphere melt where the melt rate is higher than in the southern hemisphere. Does the melting effect of carbon soot make a difference, and is it a factor in your and other models. Unlike CO2, we could probably eliminate most anthropogenic black carbon without great cost and social change.
SteveF: “If you think those results are incorrect, for the several different assumed warming rates, please tell me why you think they are incorrect.”
I believe that I already did, Steve. But I will try to be clearer.
Taking all of the available sea level data from the University of Colorado and splitting it in two equal halves we get the following result.
First half rate = 14 inches/century
Second half rate = 8.6 inches/century
Splitting the second half again we have.
Last quarter rate = 8.3 inches/century
And sea level rise has actually gone negative for the last year.
Now, why are we having this deceleration in sea level rise? To put it in your own words: “The deceleration is the result of the lack of warming in recent years.â€
And I agree with this. The temperature trend has been flat, and the rate of sea level rise has decelerated.
So, let’s start with our current rate of 8.3 inches per century, and, knowing that we decelerate when the temperature is flat, let us look at your scenario where the temperature continues to be flat from here until 2100. In that case, you model predicts that we will have 10 inches of rise in 89 years. How is that possible? When we are already down to 8.3 inches per century and when flat temperature is causing a deceleration of the rate, how are you going to get another 10 inches in just 89 years with no further temperature increase. The logial thing is to expect that 8.3 inch/century rate to decelerate further with the possibility of the rate being zero by 2100 (using your flat temp scenario). This means that the flat temperature outcome should be far below 7 inches for 89 years. Obviously your flat temperature scenario does not pass the sanity test. You would need to get acceleration as opposed to deceleration using the same flat temp trend that we have so far seen causing only deceleration. And since the same model that is producing the unreasonable flat temperature scenario of 10 inches by 2100 is also producing the other scenarios, those are also likely to be incorrect as well.
Note: The data I used was GIA corrected. So the actual sea level rise rate is even less than shown by the UC data.
Furthermore, if Livingston and Penn’s work presages a Grand Minimum, and if temperatures stabilize or drop for a century, where’s the sea to go?
=========
steveF.
Nice:
lets see, if you can deduce the sea level rise from the temperature, can you work it in reverse and an make a seamometer?
that is given a sea level ( say in the past) deduce a temperature?
AndrewFL: I do not trust the climatesanity guy (YMMV), so I went and looked at the actual Church&White data, which are officially hosted there (both the 2006 and the 2011 version).
.
When I plot both versions, after subtracting their respective means over the common 1880-2004 period, I get this (I don’t know how to make an inline picture):
.
http://drvdo.free.fr/ChurchWhite2006-2011.png
.
Notice the difference with the climatesanity graph.
Tilo Reber (Comment #79703)
Short term trends (decadal) can be substantially different from the longer term trend. Look at the Church and White data; it is clear that the trend accelerated and decelerated over time. If you say “I don’t believe the tide gauge data is correct”, then there is nothing more to discuss, since the model is based on the tide gauge data. If you think the tide gauge data is correct, then you need to say exactly where you think where the model is incomplete or wrongly implemented, and better, offer an alternative model of sea level rise which is 1) physically reasonable and 2) which explains the available data better. I am virtually certain that you are not able to do this, but I would sure like to see you try.
The simple model I developed does not include other potential factors which very well might change that short term rate (like say the PDO, solar cycle, even weather patterns, and/or combinations of those and other things). Perhaps you could find some consistent pattern of influence from other factors which would make the model projection more accurate.
But you seem to mostly be saying that since the model does not exactly predict the short term trend NOW that it can’t possibly be close to correct in long term projections. Well, I think you are simply mistaken about this. Look at the model fit to all of the data and ask yourself if that fit is credible. Figure 6 from the post shows that there is modest deviation between measurements and model, but the key word is modest. Projections you don’t like (for whatever reason) are not automatically proven incorrect by your dislike. The burden is on you to show why those projections are not credible.
steven mosher (Comment #79705),
Well I suppose so, but I think you would need pretty good sea level data pre-1870. I don’t think anything close to the quality you would need is available.
Doug Allen,
The model does not pre-suppose the existence of an equilibrium (which is one of it’s limitations). If you look at teh “no-warming” projection graphic in one of mu comments above, you can see that the projection does not show any tendency toward equilibrium. The model is based on the assumption that the quantity of ice is so large that there is no significant approach toward equilibrium during the period examined. The limitations of the model (see post) include the potential inaccuracy of the melt model.
The model does not address the issue of soot and it’s contribution to melting. There has been much more melting in the northern hemisphere than in the southern, but there are lots of potential reasons for this, the most important of which is that there is much more ice which can possibly melt with modest warming in the north than in the south. I just do not know what the contribution of soot might be.
SteveF–
We’ll have to keep track now!
lucia (Comment #79711),
I guess I will have to make sure I don’t lose the calculations.
.
Actually, with the range of warming projections (Figure 7, 0.05 to 0.3C/decade) I suspect my projections will cover whatever warming actually happens over the next 15 years. And, it is the V and R projections that I think are going to be in deep trouble very soon, not mine! 😉
toto (Comment #79706)-Whether you trust him or not, I care not. However, I notice the same vague differences between Church and White 06 and 09 (not 2011?) in your graph as his (if Church and White have updated their data again, all the more reason to consider using their updated data!) namely that the early data are lower. The other differences appear to be that Tom has, I think, smoothed out the annual noise in the updated data, and not removed their long term means. Your plot probably offers a better comparison, however, it does not look inconsistent with Tom’s graph to me. What exactly do you insinuate that he did? At any rate, the new data is still noticeably different from the old.
SteveF–
You can upload stuff and store them on the server. If they involve excel files, you need to email them to me so I can get around the ‘protection’ by using ftp instead of using WordPress’s auto upload feature which only permits .jpg, .png, .txt and some subset.
SteveF: “Short term trends (decadal) can be substantially different from the longer term trend.”
Oh, lord, here we go again. Yes, yes, yes, short term trends can be different from longer term trends. But not without a reason! The trend doesn’t float around randomly, even in the shorter term. As you said, and now seem to deny, the short term trend, which is deceleration, has a reason. It is the flat temperature that we have had for the past 13 years. But starting from the current point, you would need to get acceleration from a flat trend to reach your 10 inches in 89 years. Show me any evidence of accelerating sea level rise during a period of flat temperature.
Your 10 inches in 89 years for a continued flat temperature is clearly wrong. So the model doesn’t work. It’s as simple as that. Ignore the physical evidence if you like. Hand wave it away in order to suit your desired result – I don’t care. Pretend that you don’t understand what I have very clearly explained – I don’t care. But your model is wrong.
SteveF–
I should add: I figure we should test both. 🙂
Tilo Reber (Comment #79716),
No need to get nasty. I assure you that I am at least as frustrated with you as you seem to be with me. I am not pretending to not understand what you say. You have clearly explained over and over the same argument that a short term trend proves the model is wrong. My answer is as before: the short term trend does not prove that the model projections are incorrect in the long term, because there can be other factors (not included in the model) which can cause short term differences between the model and the data. You need only look at the data from Church and White and the model trend and you can see lots of places where there is a similar (or larger!) discrepancy between the model and the data. I am not saying that the model is for certain correct (note my discussion of substantive doubts/uncertainties in the post). What I am saying is that IMO your objections amount to rubbish.. that is my honest technical evaluation, and I most certainly am not ‘pretending’ about that.
.
Once again, I challenge you to develop an alternative model which is:
1) Physically reasonable, and
2) Better explains the available data.
.
I don’t believe you can do it; I don’t think you will even make an attempt. Try to produce a better model if you want, but please don’t waste my time by repeating the same nonsense argument about a short term trend proving the long term model projections are incorrect.
Adeus.
lucia (Comment #79718),
I sure will be looking at the sea level trend in the future… and comparing to V and R; I suspect lots of people will. I will also be plugging the sea surface data into my model to see how the model does compared to the measured trend. Sometime in the next few weeks I will substitute the updated Church and White data to see if that changes the results significantly; I have lots of other stuff to do now.
Tilo
Why do you think this is clearly wrong? I’m trying to understand your argument: Is it that sea levels seem not to have risen for 2 years? Because sea level been mostly rising during the past decade while the surface temperatures have been at least moderately stable.
http://sealevel.colorado.edu/files/2011_rel2/sl_ns_global.png
SteveF
“Well I suppose so, but I think you would need pretty good sea level data pre-1870. I don’t think anything close to the quality you would need is available.”
I was thinking about the Kemp paper.
steven mosher (Comment #79725),
Do you have a link?
SteveF: “but please don’t waste my time by repeating the same nonsense argument about a short term trend proving the long term model projections are incorrect.”
Please don’t waste my time pretending that the 18 plus years of deceleration that is shown by the satellite record is just an accident without a reason.
And please don’t waste my time with a projection of 10 inches in 89 years when you would have to get acceleration from a flat temperature trend in order to produce it.
And of course I’m not going to produce a model. I’m not a mathematician. But I don’t care if you are the best mathematician in the world; your model defies both the evidence and common sense.
SteveF– No hurry. Obviously, testing of forecasts will have to take time. I figured we can plan to compare next year, the year after and so on. I plan to still be alive in 2025, so we can keep checking.
Tilo Reber,
For sure. And I suspect also not a physical scientist, nor an engineer. Which is probably why you are not able to see that your argument about the implications of a short term trend is nonsense. There are lot of legitimate uncertainties in my simple model. There may indeed be significant deficiencies and inaccuracies (remember the George Box observation about models). But your argument is not among them.
lucia, using 11th measurement in year (Colorado data)
2004.3074 34.114
2005.2847 39.085
2006.2892 38.983
2007.2937 41.711
2008.2981 37.564
2009.2755 40.497
2010.2800 44.219
2011.2844 45.041
11mm over 7 year … 1.55mm/year
6mm over 6 years … 1.0mm per year
7mm over 5 year … 1.4mm
3.3mm over 4 years … ,85mm
7.55m over 3 years … 2.5mm
4.5mm over 2 year … 2.25mm
.8mm over 1 year … .8mm
The best it has done is 2.5mm per year and the average is way less.
Best = 222mm over 89 years = 8.7 inches
Worst = 106mm over 89 years = 4.2 inches
Lucia: “Why do you think this is clearly wrong? I’m trying to understand your argument: Is it that sea levels seem not to have risen for 2 years? Because sea level been mostly rising during the past decade while the surface temperatures have been at least moderately stable.”
Lucia, it’s not sea level rising that we are arguing about. It’s acceleration in sea level rise. I agree that sea levels have been rising for the past decade and for the entire period of the satellite data (except possibly the last year or two). But the rate of sea level rise has also been decelerating for the period of the satellite data. As I said before, and using the data for the exact chart that you show above, the first half of the satellite data had a rise rate of 14 inches per century. The second half of the satellite data had a rise rate of 8.6 inches per century. The last quarter of the satellite data had a rise rate of 8.3 inches per century. So there has been a clear deceleration over the period of the satellite data.
This deceleration corresponds to a period of flat temperatures since 1998. So, what I am saying is that flat temperatures give you deceleration in the rate of sea level rise.
Now, note, that I am not predicting flat temperature in the future. I am only using SteveF’s own modeled case which says that if we did have flat temperatures from now until 2100 we would get 10 inches of sea level rise in 89 years. This corresponds to a rate of 11.23 inches per century. So, while the current flat trend has decelerated us to 8.3 inches per century, and if it were to continue would likely decelerate even further, SteveF’s model says that we will experience acceleration, even if the flat trend continues, because we would have to have acceleration in order to reach his result.
So, what we have is this, the satellite record has shown us that flat temperatures produce deceleration. This makes sense. One wouldn’t expect sea levels to rise indefinitely if there is no temperature rise. SteveF’s scenario, on the other hand, would demand a counter intuitive result. Starting at the roughly current rate of 8.3 inches per century, SteveF’s scenario would demand that the melt rate increase to give us 11.23 inches per century while the temperature stays dead flat. This is why I say that his model is clearly wrong. But Steve wants to use the long term trend with the tide guage data as the only acceptable place for extracting information. In other words, he is claiming that the deceleration that corresponds to the current flat temperature trend is some kind of fiction or random accident. He wants to believe that whatever he chooses as a long term trend is what will continue forever – even though it never has in climate history. And with regard to the longer term data set he wants to believe that you can get acceleration in sea level rise while the temperature is constant, even though he cannot show a case of this happening in his longer data set.
Aviso
OK … Aviso
http://www.aviso.oceanobs.com/fileadmin/images/news/indic/msl/MSL_Serie_EN_Global_IB_RWT_NoGIA_Adjust.gif
SteveF: “And I suspect also not a physical scientist, nor an engineer.”
I knew that it would come to that kind of cheap nonsense eventually. I’m a aerospace software engineer. But I’ve also had two years of undergraduate physics, four semesters of calculus, two semesters of differential equations, and a large number of other math and science courses. But non of that matters. Your model would be wrong if I were a janitor with an elementry school education. All it takes is the ability to think in order to see that.
Tilo
I don’t think he’s saying that. I think he’s saying that the period of flat temperatures is relatively short and he is fitting his semi-empirical model to a longer period of data.
There aren’t many long periods where temperature is actually constant. But even if there were, if I understand Steve’s model correctly, whether you tend to get melting or re-freezing will depend on whether the the flat temperature is above or below the temperature corresponding to equilibrium temperature for the current amount of ice. You’d expect this feature to propagate into whether you expect acceleration or deceleration.
So, I agree that the most recent short term data has a lower melt rate than required to reach Steve’s equilibrium level, I’m not sure your argument shows his model is obviously wrong as a first order estimate.
It strikes me that 11″ is all that far from 8″, so might need to focus on uncertainty intervals for his fitting parameters anyway.
Tilo-
Also note:
If this observation of physical properties is correct, I think it could hypothetically result in the acceleration a period of constant temperature above the ocean under some circumstances. Whether or not it did would depend on the distribution of temperature in the water itself and the temperature increment between the top of the water and the air.
Steve
Is it possible to separate out the part of the steady state effect that is due to the steric contribution and the melting?
Tilo Reber,
It takes that and some experience working with noisy data (and trying to understand the underlying physical processes) to appreciate that short term variation in noisy systems is sometimes is very misleading.
Look at this comparison graphic and ask yourself if you think the difference between those two trends means the model is ‘wrong’. http://i56.tinypic.com/34spb9i.jpg
The graph shows the 12-month centered rolling satellite average and the model projection for the same period, with the absolute level of the model output adjusted to change from the Church and White basis to the satellite basis.
Lucia: “I think he’s saying that the period of flat temperatures is relatively short and he is fitting his semi-empirical model to a longer period of data.”
The satellite data is more than 18 years long. And it is less noisy than the tide guage data. For me, the length argument only has relevance if one can explain why the shorter period went counter to the longer trend. In other words, the satellite data gives us a clear picture of what happens when we have a flat temperature trend. Unless I see some reason why this correlation between flat temperature and deceleration is caused by some other explainable physical cause, I’m going to assume that the relationship is meaningful – especially in the absence of any counter examples.
To me this makes physical sense as well. If the temperature is above equilibrium, then only a fraction of the ice on the planet will be above equilibrium. As the temperature remains the same the border for the ice that is at equilibrium will not change. However, the amount of that ice that is above equilibrium will shrink as the ice disappears. This means that you have less melting ice to contribute to sea level rise, and concequently a deceleration in sea level rise. Eventually, all the ice that is above equilibrium disappears and non of the remaining ice will melt because it is not above equilibrium. This may in fact be one of the problems with SteveF’s model, when he says this:
SteveF: “If you look at teh “no-warming†projection graphic in one of mu comments above, you can see that the projection does not show any tendency toward equilibrium. The model is based on the assumption that the quantity of ice is so large that there is no significant approach toward equilibrium during the period examined.”
So, while the total quantity of ice may be very large, the actual quantity that is above equilibrium may be very small and therefore it’s disappearance with time can severly effect the accuracy of the model.
Lucia: “It strikes me that 10″ is all that far from 8″, so might need to focus on uncertainty intervals for his fitting parameters anyway.”
Two points here Lucia. The 10 inches is for 89 years. So what we are actually comparing is an 11.2 inches per century rate versus an 8.3 inches per century rate. But, still, I agree that this is not huge. But we have to consider that the current 8.3 inches per century is still decelerating. And if we used Steve’s flat temperature case, it would be reasonable to believe that it would continue to decelerate. So the actual increase in sea level rise over a hundred years would be much less than that 8.3 inches. And that would give us a large difference in results.
I like your analysis. It does seem to be more statisitcally and physically valid than previous work.
Two elements seem to be missing to me:
1. Sea level rise should not be linear to increased mass, or to thermal expansion. As the surface rises, the surface area increases, much like a cone. Hence the rise should be proportional to the square root of the increased volume. Unless I’m missing something that seems to be missing.
2. Isostatic effects do not seem to be accounted for. As ice melts form the land masses they rise and the ocean floor sinks. U Colo recently had to adjust their sea level measurments to accont for this.
lucia,
The steric effect is essentially an exponential decay response to any change in temperature. There is only a stead state steric contribution long after the surface temperature is constant. This link shows the evolution of the steric portion of the model assuming a fixed temperature after 2010.
http://i54.tinypic.com/w7ea1j.jpg
As you can see, the model says it would take hundreds of years to approach equilibrium.
Tilo:
That’s just a fancy title for “software implementer”, right?
In any case, a few introductory courses on calculus and differential equations isn’t even the right background needed to understand how to do this type of analysis. (Nor does parallelizing code using MPI.)
You need training/experience in signal processing and analysis, and it is increasingly obvious you don’t have this background nor understand the issues with short period fluctuation.,
In any case, here’s an estimation of sea level trend uncertainty as a function of integration period. This is for single station data, but it makes clear the dangers in trying to compute trends when you have long-period correlations in the measurement noise.
Re: lucia (Jul 28 11:18),
In case anyone is interested, the physical properties of sea water, including a density calculator app can be found on this page.
Pure water has a density max above the freezing point. At a salinity of 2.47%, the density max is at the freezing point. Sea water has a salinity of ~3.5% so the density max is below the freezing point.
John Vetterling (Comment #79741),
1. The effect of the “cone-shape” of ocean basins is most likely very small, because even a very shallow shore inclination (say 1 meter in 500) would only expand the surface of the ocean a small fraction of the total existing area for a 1 meter sea level rise. Most shorelines have much steeper inclines than 1 meter in 500 meters.
2. IFAIK, the glacial rebound adjustment is already included in all data.
SteveF: “It takes that and some experience working with noisy data (and trying to understand the underlying physical processes) to appreciate that short term variation in noisy systems is sometimes is very misleading.”
I don’t believe in 18 year measurement noise. A climate pattern that continues for 18 years must have an underlying physical reason. And since a deceleration correlating to a constant temperature makes perfect sense, I see even less reason to assume that what the satellites are showing us is noise.
Concerning the physical process, I think that you fail to understand it. A movement in the direction of an equilibrium point will naturally decelerate the closer it gets to that equilibrium point. If your equilibrium point is a constant temperature and some amount of ice melt that is moving towards it, then it will decelerate as it get’s closer to that point. And that doesn’t even consider that there will be less ice to move towards that equilibrium point as time goes on, since only a fraction of the total ice is effected by that equilibrium point to begin with.
A. I can’t see the acceleration for the line that represents your model in your chart.
B. I can see the deceleration for the satellite era in my own chart very clearly when I plot and trend the data in two pieces.
SteveF, why did you not graph the actual satellite sea level rise since it is available?
Tilo
Sure. But we haven’t had flatish temperatures for 18 years. I thought you were discussing flattish temperatures?
It shows us what happened during a recent shorting flatish temperature trend. And what we see is sea level rose, it’s somewhat noisy. Also, the rate of rise was slower during the recent period with a flatish temperature trend and faster while the temperature was rising rapidly. That said: the sea level still rose while the temperatures remained flatish.
No one has suggested that the relationship has nomeaning.
This is somewhat similar to this by SteveF
But I guess your difference is that SteveF isn’t considering that the equilibrium temperature depends on the amount of ice left and so, parametrically the sea level. That might be something that needs to be considered. Whether it’s “first order” or “second order” I don’t know. (Vemeer and Rahmstorf do similar types of reasoning about limiting cases in their analysis– though their limits may be different.)
Carrick/SteveF
Stop arguing about credentials. I think you have a strong point about short term trends. But I think at least at this point, I understand Tilo’s concern. I do think that– while it might be 2nd order– not treating the ice as infinite might affect SteveF’s values. In which case, it might be that the first order method happens to give results correct to leading order, but the 2nd order effect of accounting for the fact that ice is not infinite might result in reducing the projected values.
This would still make Tilo’s diagnosis of obviously wrong incorrect since a first order model is necessary before we move to 2nd order. But it might just mean that the 2nd order effects are noticeable over decades.
Dewitt
Thanks for the link. I was pretty confident SteveF would be correct that the rate of expansion is a function of temperature. But I do want to point out to Tilo that there might be some phenomnological effects that could do ‘weird’ seeming things.
Tilo:
Whether you believe in it or not, it exists, and certainly does so for a “reason”. It goes under the rubric “coupled atmospheric-ocean oscillations”. Things that give rise to long period fluctuations includes (but is not limited to) thermohaline circulation which boasts overturn time scales as long as 300 years
Regardless of where it arises, it is still measurement noise if it is corrupting the physical quantity you are trying to measure (temperature or sea level trends in this case).
Bruce,
Because the satellite data includes a very strong annual cycle which only masks the underlying trend. Since the model produces only annual average data, I wanted an apples to apples comparison.
Lucia:
This relates to my previous question on what time intervals SteveF is trying to model. If you only want to do e.g. project forward circa 80 years (as SteveF agrees is the case), that’s small compared to the estimated timescales for saturation of ice loss, which is measured in thousands of years. Assuming a 1000-year 1-e folding time for ice loss, the second order contribution that Tilo is bringing up would represent roughly a 2% contribution to the model…
That is buried well inside of the noise.
lucia,
Sure, and that is why I said in the post:
My objection to Tilo’s comments is NOT that there may be legitimate issues WRT the assumptions that go into the model… I already laid a bunch of them out in the post… it is that his claim that the last decade trend in the satellite data proves (in his words) the model is obviously wrong about long term projections. This is nonsense.
.
I generally tell people that propose nonsense that what they say is in fact nonsense; it appears Tilo takes offense at this. I can’t help that.
.
WRT to credentials: I know people with lots of credentials who know very little, and others who know a great deal, but who have few credentials. My point was that Tilo’s experience seems to lead him to not understand the issue of short term noise. Most anybody with some experience in physical science or engineering learns (often through the painful experience of getting things way wrong) to be suspicious of short term noise when evaluating data.
Carrick: “You need training/experience in signal processing and analysis, and it is increasingly obvious you don’t have this background nor understand the issues with short period fluctuation.,”
I don’t need training or experience in anything in order to see when a model is diverging from reality. And I don’t need anyone to give me bull about 18 years of satellite data being noise or being meaningless.
On top of that, the people with all the training that you claim is needed to understand this stuff don’t agree on squat. Witness the differences between Houston and Dean on the one hand, Rahmstorf and Vermeer on the other, and SteveF on the third. The examples of Phd’s with the right experience producing garbage models are countless. Look at the last round of solar cycle predictions from all of the qualified experts. They varied by a factor of 4. And they covered everything in between. Some claimed to have 98% accuracy and ended up being dead wrong. So thump your chest about qualifications if you like. It doesn’t impress me at all.
SteveF after a more detailed reading of your modeling I have some added appreciation for what you have done here. I would , however be interested in a result if you split the 1955 to present time for your model into calibration and verification periods. It is what is done in climate science circles and while not as satisfying as true out-of-sample testing it is better than no testing (of this type) at all.
Are you sure that the uncertainty limits of observations will be sufficiently small over the next 25 years to determine whether the V&M model exceeds them? It is the acceleration factor that needs long time periods to even out periodic excursions – isn’t it? That various locations in the ocean/coast of the world can have significantly different sea levels was something that surprised me and went against a simple-minded view of what I Intuitively would have expected. The spatial infilling thus presents a significant uncertainty that would affect sparse tide gauge sampling going back in time, but is that overcome with the more recent measuring procedures?
As for the links to the pertinent papers that I missed in your original post, I can only ask that you do not put them in such plain view that I do not see them.
SteveF: “Because the satellite data includes a very strong annual cycle which only masks the underlying trend. ”
But Colorado says the seasonal signal has been removed.
And you left the Church and White data to go up and down instead of just drawing a straight line.
Looks misleading to me.
Lucia: “Sure. But we haven’t had flatish temperatures for 18 years. I thought you were discussing flattish temperatures?”
We have had them for 13 of those 18 years, and they showed a deceleration in sea level rise.
“That said: the sea level still rose while the temperatures remained flatish.”
This was never under debate. The deceleration in the rate of that rise is the point that I’m trying to make. It is the rate of rise that we have achieved that is below SteveF’s projection for a flat temperature. That combined with further deceleration will make his flat temp projection wrong.
Carrick: “Whether you believe in it or not, it exists, and certainly does so for a “reasonâ€. It goes under the rubric “coupled atmospheric-ocean oscillationsâ€. Things that give rise to long period fluctuations includes (but is not limited to) thermohaline circulation which boasts overturn time scales as long as 300 years.”
We are not talking about things that can make it warmer or cooler here. The temperature that gives us a correlation with the satellite sea level data is a known flat temperature that we have seen effecting the sea level rise rate for 13 years. And that effect has been deceleration. I see no evidence or reasoning for flat temperature to produce anything other than deceleration.
Carrick: “Regardless of where it arises, it is still measurement noise if it is corrupting the physical quantity you are trying to measure (temperature or sea level trends in this case).”
In that case, all of the changes in the “physical quantity you are trying to measure” can be called noise. There is no inherent, forever, temperature or sea level trend that you can extract that would not be effected by what you are calling noise. My interpretation of measurement noise is that which is produced by errors in the instruments and methods that you are using to measure the data with. The rest of what you call noise I call inadequate modeling.
Bruce (Comment #79757),
You are right, the annual trend was already removed (I thought it was still included). The 12 month rolling average still suppresses short term noise. If you prefer to see the short term noise:
http://i55.tinypic.com/2yov393.jpg
.
The best apples to apples comparison is yearly average from the satellite measurements with the output of the model (which is also annual):
http://i52.tinypic.com/b8qphf.jpg
.
There is no church and white data on the graphic; it is model output versus satellite. In any case, why would I want to use a straight line?
Misleading? I have no idea what you are talking about.
Some back of the envelope calcs:
tidal shoreline of NA = ~500km
area of NA = ~25,000 km^2
so if a 1m rise encroaches 5m (angl of repose of 20deg) that equals 2,500 km^2 of a 10% reduction in surf area.
A 10% reduction in the area of land =~ 4% increase in the surface of ocean so i see your point. The uncertainty in sea level rise is much greater.
Kenneth Fritsch,
I have compared the calculated ocean heat model constant based on the second half of the Levitus et al data to the constant calculated for the entire data set and for the constant calculated form the first half of the data set. The constant for the whole set is 9.0 * 10^23 joules per degree (+/-0.74 two-sigma), while that calculated for the second half of the data set is 9.6 * 10^23 joules per degree (+/- 1.12 two sigma), and for the first half 8.4 * 10^23 joules per degree (+/- 4.7 two sigma). The uncertainty ranges overlap a lot, so there does not seem to be any meaningful discrepancy. The first half of the Levitus data has a lot of relatively short term shifts (limited/uncertain data for the early data?), and this is reflected in wider uncertainty for the constant calculated form the first half of the data.
Tilo
I was giving a description which I think was required to see if we agree on what the data look like.
I concur that SteveF’s projection for a flat temperature is high relative to what we’ve seen. Nevertheless, his model physics could be correct as a first order model (meaning capturing leading order phenomenology) and it could have the correct parameters to leading order.
The fact is: no matter what data we had, getting the parameters by fitting data was bound to either result in projections that are a bit too high or too low. This is always the case. We can’t begin to say “wrong” until we at least know uncertainty intervals from the statistical fit.
Also, by definition, the first (or leading) order will leave out some phenomena. That’s what first or leading order means. A good long term model will try to capture the physics that that prevail over long periods– not shortish periods. We can argue which is which, but simply saying that you or I or Joe thinks N years is “long” isn’t the way to do it.
Anyway, since his model is leading order, his model giving a higher melt rate relative to current could either be because the current melt rates is due to a short term phenomema not captured by the leading order model, or because the errors (or noise) in the data resulted in the parameter estimates being higher than the “true” values or, possibly, his model is wrong.
But it seems to me that given his model, his parameters may be the best based on the data we have — which begin in 1875. You however are seem very focused on since 1990 — which is fine. But even if satellite data give good resolution quickly, that doesn’t mean we need to insist the fit be tuned for post 1990 rather than earlier periods.
That said: I do think that it maybe that SteveF should think about how he might correct for finite ice volumes in a way that might capture response to a step function in equilibrium temperature of the surface. But before he can think about the 2nd order terms in the physical model, he needs to capture the 1st order terms. So, I think it’s worth while discussing this and talking about what this particular phenomenological model — which differs from V&R’s– might tell us.
John Vetterling (Comment #79761),
You are multiplying meters by kilometers. The correct increase in ocean area would be shore line length in Km multiplied by sea level rise in Km times the inverse of the slope (in your example that is 5).
So ocean area increase for 1 meter rise is: (Shore line length in Km) * 5 * (sea level rise in meters)/1000. The factor of 1000 should make this pretty insignificant.
Tilo:
Absolutely we are. If there is a steric response to changes in mean ocean temperature associated with atmospheric ocean oscillations, that will show up as a fluctuating component to sea level rise.
Not if they are what you are measuring. If what you are measuring is secular variation, oscillatory components are “noise”.
Well yes, to some degree. But SteveF isn’t trying to model short period climate fluctuations, nor should he, unless he is interested in how these influence the long-term trend.
Hmmm. Looking at the first measurement of the year of satellite data.
I see an El Nino signal (with some lag) but no CO2 signal.
Date Level Change
1993.0138 -8.999
1994.0182 -6.094 2.8
1995.0227 3.402 9.3
1996.0000 3.174 -0.23
1997.0045 2.737 -0.44
1998.0090 4.620 1.9
1999.0135 8.368 3.7
2000.0180 18.665 10.3
2001.0225 19.267 0.4
2002.0269 18.194 -1.1
2003.0043 24.375 6.2
2004.0087 30.725 6.3
2005.0132 36.111 5.4
2006.0177 35.233 -0.9
2007.0222 34.269 -1.0
2008.0267 38.302 4.0
2009.0040 41.231 2.9
2010.0085 48.856 7.6
2011.0130 43.738 -5.1
Lucia:
If Tilo just wants to criticize SteveF, this is the low hanging fruit. I’m sure SteveF knows that any model projection is incomplete if you can’t publish CLs associated with it.
It’d be interesting to see how one would go about obtaining that.
Another thing I commonly see are error budgets for the parts of the system that don’t get modeled.
I estimated the error from assuming an infinite ice resource to be 2% over 100 years. I’d like to see other people’s estimate too, since my number is at least 50% SWAG. In a peer reviewed pub, as opposed to a blog post, I’d expect to see a table with that in it, were I a reviewer.
Bruce:
The signal associated with anthropogenic CO2 increase is very weak over periods of less than 30 years. You’d need to pull out then ENSO signal in particular (as Lucia does using MEI) if you want any hope of measuring it.
lucia,
I might think about it, but I believe it would take a lot of data to figure out exactly how mountain glaciers and ice sheets actually melt (which from what I can gather in limited reading is not at all well known), as well as some very solid numbers for reservoir accumulation and groundwater depletion.
I really don’t want to become a glaciologist (or any other type of climate scientist! 😉 ).
My objectives were 1) to point out that the V and R approach seemed not very well grounded in physical reasoning, 2) that SOME of the V and R reasoning made some sense, and 3) building on the sensible part from V and R gives sea level projections which are not much different from the IPCC AR4, while V and R suggest truly frightening sea level increases.
carrick, as we’ve discussed, there is no CO2 signal in long term tide gauge data either.
By the way, does anyone know which tide gauges Church and White actually looked at? I keep forgetting that all AGW claims must be verified quite carefully before considering that they may actually be telling the truth.
Stevef, if the model used El Nino / La Nina it might be more accurate.
And SteveF, any chance of using the non-GIA data. It’s bogus.
Bruce, saying whether or not there is a signal in tidal gauges involves an analysis of the sort that SteveF has done. You’d have to separate the steric, isostatic volumetric, and melt-water contributions to say whether or not there’s a signal.
(In other words, it’s an inverse problem. You can’t just look at data that support a particular conclusion in the absence of analysis.)
Carrick,
I recognize this is a problem. But this is a blog post, not a publication in GRL. It is easy to generate confidence limits for the ocean heat model versus Levitus. It is easy to generate confidence intervals for the final model versus the Church and White data. But since the uncertainty in the OHC part of the model influences the accuracy of the calculated steric adjustment to the Church and White data, I see no easy way to propagate that uncertainty in the final model… especially since the uncertainty in the ocean heat calculated by the model almost certainly increases the further back in time you go. If you have some suggestion, let me know.
Bruce:
I agree he could include MEI as an input (and have a OLS fit parameter associated with it), and that would improve the short-period fidelity of the model, as would accounting for other sources of autocorrelation in the data. I’m not sure looking at short-period changes in sea level was an objective of his modeling though.
For my perspective it only matters if this short period fluctuation causes long term changes in sea level rise (it can, through parametric nonlinearities, but that’s a discussion for another day).
Bruce (Comment #79772),
If you don’t like the rebound adjusted data, just subtract 0.3 mm/year from the projections… about 1 inch in 2100. Since the adjustment is constant, it does not change the projected increase at all, except for that ~1 inch by 2100.
SteveF–
Fair enough. I know dealing with the infinite reservoir assumption is difficult.
I don’t have a problem with leading order models. I think it’s fair to discuss whether your leading order model fits better than a different leading order model.
Like Carrick, I’d be interested in an estimate of how much the infinite ice assumption might affect the result. Unlike Carrick I don’t even have a swag.
Carrick: “Absolutely we are.”
You missed the point. We don’t care about a warming or cooling effect in determining what happens during a flat trend because there is no warming or cooling during a flat trend regardless of how such warming or cooling may be caused at other times. Unless I am mistaken here and you are trying to say that sea level rise decelerated while the temperature was constant because the oceans cooled and the water compressed during the same period of time that the surface temperature was flat. Is that what you are trying to say?
Carrick: “If what you are measuring is secular variation, oscillatory components are “noiseâ€. ”
There is no such thing as secular varitation in climate. It’s all made up of oscillatory components until you go out hundreds of thousands of years. And if you go back to the 1870’s for tide guage data, you don’t even have a meaningful AGW component.
Carrick: “But SteveF isn’t trying to model short period climate fluctuations,”
An 18 year “fluctuation” should agree with the model unless there is a physical reason not to. Considering that most of the phyiscal reasons would effect temperature and considering that the temperature during recent deceleration was flat, then the model should produce deceleration for flat temperatures. It doesn’t.
Probably the reason so many of these models are so wrong is because their originators gloss over the causation of periods of time that disagree with their models and put it down as “noise in the long term trend”.
SteveF:
The most straightforward way would be to estimate the short-period noise, then use that to perform a Monte Carlo analysis.
I have this little comment over at ScienceOfDoom discussing the breakdown of the central limit theorem when you have 1/f^nu noise. It includes some code for generating a random series from a 1/f^nu spectrum using the FFT method.
You could do the same thing if you had an estimate of the spectral content of the noise in your model. Start with the power spectrum, use it to create multiple instances of your fit parameters. This will generate a family of curves that would allow you to generate 95 CL bounds.
The other thing I would do is replace OLS with a maximum likelihood analysis, to reflect the growing uncertainty in the measurements as you go further backwards in time. That would yield a central value plus (probably a small) formal uncertainty associated with it.
Then just add these errors in quadrature.
SteveF
Although I didn’t mention it before, I very much appreciated the modesty of your “A First Order Estimate of Future Sea Level Rise.”
I’m presently rereading Darwin’s “The Origin of Species.” My undergraduate and graduate science course work is mainly field biology which requires little math, and regrettably, I have little. After following the “climate change wars” on the blogs these past 3 1/2 years, Darwin’s modesty and willingness to write about the weaknesses in his theory is a breath of fresh air compared to the blog and journal slug fests which include many of the IPCC principals. I was reminded of Darwin’s modesty when I read your paper. I was sorry to see you lose patience with Tilo. I think his main misunderstanding is how noisy short term trends are, but I also think he has made a valid point about your model requiring accelerating sea level rise during the next 89 years of modeled flat temperatures. That is certainly not intuitive, and I wonder about it, too. Because I am not able to appreciate the mathematical elegance and usefulness of sophisticated models, I think my comments are usually ignored, but like Tilo I think I bring a type of criticism that needs to be repeated over and over again. You and others have put blood sweat and tears into creating models that you all fervently want to approximate the variables that force warming. I am impressed, but very skeptical. I don’t think temperature trends are a random walk, and I doubt that turbulence (chaos) will prevent understanding of variables and eventually creating useful models, but I don’t think we’re there yet. You and the others are pioneers, and I wish you well. For the present, I think both alarmists and skeptics give far too much weight to models. From my perspective, we are just barely beginning to learn enough about climate to attempt hypotheses and predictions and should be far more modest than the IPCC and many others in selling our brand whether it be catastrophic warming or negative climate sensitivity. Darwin was a genius at observation. He was able to connect the dots after years of observation and study. I wish in climate science we had more emphasis on observation and a little less on modelling.
lucia,
My swag for the finite available ice volume goes like this: If we limit ourselves to mountains and Greenland (Antarctica remains far too cold for much melting outside the peninsula), and if we assume 100% of that ice melting would raise sea levels by 10 meters. Then I would expect the melt rate (all else being equal) to gradually decline until all the ice was gone. So a mass based sea level rise of 450 mm would tend to reduce the rate constant by a factor of about (10 – 0.450)/10 = 0.955, so maybe a 4% to 5% reduction in the rate constant by 2100; so maybe not important. Of course this ignores a multitude of factors, like albedo decreases from loss of ice increasing warming rate. But what the heck, you said ‘swag’.
Carrick,
Thanks for the suggestions on uncertainty, but it all sounds like a lot more work than I want to do.
Tilo:
There’s two parts to this story, one is the rapid temperature response of the ocean sea level to temperature change, and the other is the slow (hundreds of years). Both are important in modeling the instantaneous change of sea level.
It’s not exactly what I’m trying to say, but it’s getting closer. The past history of surface temperature changes together with the current one combines to affect the current measurement of sea level.
You can’t argue what is important or not important in the absence of a model that characterizes (as Steve has done) the various contributions to the current measured sea level from the current and historical temperature.
Anthropogenic CO2 forcings (see e.g. the Keeling curve) is most certainly a secular (non oscillatory) change. I’d be interested in what frequency you fit the long-term trend in that curve to. LOL.
How does that observation contribute to the discussion of whether there are secular components? If anything, it shores it up.
If what they are modeling is “long term trend” rather than short period fluctuation, wouldn’t “wrong” be defined as a statistically significant deviation from the “long term trend”? So how do you know they are “wrong”? I suppose, in the same way you know “there is no such thing as secular variation in climate.
SteveF:
Yes, I understand. I wouldn’t do it myself unless I wanted to submit it for publication. You asked, so I just wanted to make it clear it is possible to do.
(That and the error budget table estimating the effects of various things not included in your model are the only things missing before this could be written up, IMO.)
SteveF
I realize I speak of modelling warming in the above post, and that’s not what you’re doing. My comments are more generic-about modelling and creating hypotheses when the variables are poorly understood, so my comments of appreciation apply- your modesty- and my comments of caution a little less so,
SteveF
http://www.realclimate.org/index.php/archives/2011/06/2000-years-of-sea-level/#more-7947
Read The SI. You’ll note that they suggest (Mann and Vermeer) That the sea level reconstruction indicates that Mann 2008 might need a correction in early years. I dont want to get into that fight. rather, I think it would be interesting to look at what a seamometer would produce as a temp proxy. curious is all.
Shore,
Not multiply km by m, just dropped a 10^3. The correct NA shoreline is ~500,000 km. Which should be obvious since the distance from Maine to Fla >> 500km.
Still only has a 4% effect on surface area.
John Vetterling :
Another datum for the error budget. 😉
Carrick: “So how do you know they are “wrongâ€?”
Between D&H, R&V, and SteveF, two thirds have to be wrong. So my statement stands. And if you were able to think instead of just bragging about your qualifications, it would have occured to you that the wide variety of results that are produced by models in all areas of climate science means that many, if not most of them, have to be wrong.
Carrick: “How does that observation contribute to the discussion of whether there are secular components? If anything, it shores it up.”
Obviously, again, it should have occured to you that I put that in as a possible secular trend. But not one that you could use since 1870. In other worlds, if you are searching for a secular trend that goes all the way back to 1870, it’s not AGW based. Again, try to think instead of just reacting. Also, the Keeling curve is a reflection of man made action, not a nature based secular trend. As such, that curve could change at any time and certainly will change as we run out of fossil fuels. That “secular” trend may well end up being shorter than many natural cycles.
Carrick: “There’s two parts to this story, one is the rapid temperature response of the ocean sea level to temperature change, and the other is the slow (hundreds of years). Both are important in modeling the instantaneous change of sea level.”
Again, you are babbling about something that is irrelevant to what we are talking about. SteveF’s model shows no deceleration during a flat temperature period. The only available real world data that we have to check that against that does show deceleration during a flat temperature trend. The rest of what you are talking about is so much BS.
SteveF: “If we limit ourselves to mountains and Greenland (Antarctica remains far too cold for much melting outside the peninsula), and if we assume 100% of that ice melting would raise sea levels by 10 meters.”
I don’t think that we can assume that all of Greenland is above the threshold. What if only 2 or 3% is above threshold. The rest may simply have melting in the summer that is repalced by snowfall in the winter. In that case, a flat temperature scenario would definitely decelerate. To get the rest above the threshold would require further warming. But the question is, how much before all of Greenland was above the threshold.
Tilo:
Which 2/3s? Most of what you’ve said has been palpably wrong, I’d hardly say you are much of a judge.
Where have I “bragged about [my] qualifications”? I also though Lucia had asked us not to continue that OT thread.
Completely ambiguous. I have no idea what you are referring to. This reminds me of some other bloggers here who make broad assertions and expect us to fill in the blanks.
It couldn’t possibly have occurred to me because I can read and interpret English and you had said previously:
That’s pretty unambiguous. So you admit you contradict yourself within the same comment now?
Not relevant. Anthropogenically driven climate change is still climate change, and this is an example of a secular variation, hence your claim “there is no such thing as secular variation in climate” is falsified.
Purely speculative. The data we have at this point in our hand is secular (non-oscillatory).
Only to people like yourself who don’t understand basic inverse theory and modeling of data.
I download the Church and White 2011 Station Data (just the annual)
I looked at stations with data from 1999 to 2009 (the last year of C&W data)
Looking at 1999 to 2009
199 Stations / .876mm per year average
53 > 3mm/year
48 0 to 3mm/year
98 < 0
Carrick: “Which 2/3s?”
Who cares. What I said was this:
“Probably the reason so many of these models are so wrong is because their originators gloss over the causation of periods of time that disagree with their models and put it down as “noise in the long term trendâ€.”
That statement doesn’t depend on a “which”.
Carrick: “Completely ambiguous. I have no idea what you are referring to.”
Well, I will agree that you are trying very hard not to have an idea. I already mentioned the solar cycle models with their variation by a factor of four. And everything between the extremes is covered. We have climate sensitity models producing numbers from .5C for 2X CO2 to 6C for 2X CO2. Most of them are wrong. My statement about the failures of “qualified” people doing modeling stands despite your effort at not understanding it.
Carrick: “So you admit you contradict yourself within the same comment now?”
No, I’m telling you that I brought up the possible exception in the same comment. Again, if you are determined to misunderstand that for the sake of your ego, then be my guest.
Carrick: “Most of what you’ve said has been palpably wrong, I’d hardly say you are much of a judge.”
Your failure to understand the explanations given you doesn’t make them wrong or make you much of a judge.
Carrick: “Only to people like yourself who don’t understand basic inverse theory and modeling of data.”
More BS to support the original BS.
Sea level was about 5 metres higher at the end of the last interglacial in which temperatures were about 2.25C higher than today/pre-industrial. The glaciers never melted out in southern Greenland.
But the southern third of Greenland was deglaciated in the interglacial at 400,000 years ago. It was an especially long interglacial lasting 40,000 years although temperatures were lower than the Eemian interglacial at about 1.0C higher than today.
By itself, southern Greenland is too far south to have continental glaciers since the solar insolation in the summer is more than high enough to melt the snow and ice (even in low Milankovitch cycle conditions). The glaciers wouldn’t be there if there wasn’t a 3 km high glacier in the centre north of the Island.
It just takes a long interglacial to melt out southern Greenland so I imagine it has been continuously adding to sea level since 10,000 years ago.
Bruce: “I download the Church and White 2011 Station Data (just the annual)”
I’ve been thinking about doing the same thing. Tell me, how far does the tide guage data go and do they show the same trend after 1992 as the satellites?
Tilo:
And I pointed out why this was wrong and based on a lack of understanding of the problem on your part.
Sigh. You don’t even know what “wrong” means in context of comparison of data to model. It’s when there is a statistically significant disagreement between the two. If the uncertainty supports a value 0.5 to 6 °C/doubling of CO2, then the models aren’t “wrong” in the statistical sense.
This is a waste of time. You don’t even know when you don’t know.
Carrick: “And I pointed out why this was wrong and based on a lack of understanding of the problem on your part.”
You have a vivid imagination.
Carrick: “If the uncertainty supports a value 0.5 to 6 °C/doubling of CO2, then the models aren’t “wrong†in the statistical sense.”
There is your problem. Your definitions are so tied to statistical definitions that you have no concept of what wrong means to the rest of the world. Let me help you. A climate sensitivity of .5C means that absolutely no actions is required regarding AGW. A climate sensitivity of 6C means that we better spend trillions and begin drastic action immediately. So if you have models that are centered on .5C and models that are centered on 6C and you claim that all of them can be right, then your statistics is worse than useless and I will always call the majority of those models wrong.
Carrick: “This is a waste of time.”
At least you have that right. I’m tired of you. Adios.
SteveF:
By far the best study of impoundment issues and their effect on sea levels that I’ve found is:
Impact of Artificial Reservoir Water Impoundment on Global Sea Level
B.F. Chao, et al.
Science 320, 212 (2008);
DOI: 10.1126/science.1154580
It’s behind a paywall, but might be worth the $18 to you. In the (free) supplemental materials available on-line, they list the nearly 30,000 reservoirs created in the last 110 years and their capacities.
http://www.sciencemag.org/cgi/content/full/1154580/DC1
Materials and Methods
Table S1
Their basic conclusion is that the rate of impoundment peaked around 1970, reducing sea level rise in those years by about 0.75mm/year. Since then it has declined quite steadily to about 0.25mm/year in the past decade.
If you accept these figures and take them into account, an “acceleration” in sea level rise over the past 40 years or so of 0.5 mm/year does not indicate an increased rate of melt or steric expansion.
Carrick,
Amen. Usually rational people come to similar conclusions when confronted with overwhelming evidence. I reached that point on this tread several hours ago. The issue is if someone is willing to listen to reason or not. Sadly, many are not. I have added one new name to my “never respond, never reply” list (AKA, “not worth the effort” list.) I suggest you consider doing the same.
Curt (Comment #79800),
Thanks for the link. I will read the abstract and SI, though I’m not wild about spending $18 for a look-see at their argument.
Well, the rate in the 1960 to 1980 period was about 1.6 mm per year (if I have done my math right) and about 3.2 mm per year from 1992 to present, a difference of about 1.6 mm per year. I am not sure how a change from 0.75 mm per year (in 1970) to 0.25 mm per year (last decade) accounts for more than about 1/3 of this difference. But in any case, if someone wants to look at other factors, then it would be prudent to include both reservoir accumulation and ground water pumping.
Tilo, 1992 to 2009
Avg 2.18
80 > 3
52 0 to 3
52 < 0
mm/yr Station
13.18 POSIDHONIA
13.06 GUAM
11.00 WEST CHANNEL PILE
11.00 ISLAY (PORT ELLEN)
11.00 QUEENSCLIFF
11.00 HOVELL PILE
9.82 PORT HEDLAND
9.35 DARWIN
9.29 ILFRACOMBE
8.53 PORT LOUIS II
8.35 SUVA-A
8.00 LA CORUNA I
8.00 CARNARVON
8.00 GEELONG
7.82 WEIPA
7.59 LUCINDA
7.18 SANDY HOOK
7.06 KWAJALEIN
6.88 CHESAPEAKE BAY BR.
6.88 CAPE MAY
6.82 KO LAK
6.71 HAMPTON ROADS
6.53 LE CONQUET
6.47 PHILADELPHIA (PIER
6.29 FREMANTLE
6.29 LEWES (BREAKWATER H
6.24 MONTAUK
6.18 ALBANY
6.00 PAGO PAGO
5.71 TOWNSVILLE I
5.65 NEW LONDON
5.53 SHIMIZU-MINATO
5.47 CHICHIJIMA
5.41 MIYAKO II
5.24 PORT DOUGLAS 2
5.24 CAMBRIDGE II
5.24 REEDY POINT
5.18 BREST
5.12 PORT ISABEL
5.12 KIPTOPEKE BEACH
4.94 NANTUCKET
4.94 MIDWAY ISLAND
4.82 WASHINGTON DC
4.71 TANJUNG GELANG
4.71 SPRING BAY
4.59 PENSACOLA
4.59 FORT MYERS
4.47 BALTIMORE
4.47 VIGO
4.41 ATLANTIC CITY
4.41 NEWPORT
4.41 CAIRNS
4.41 LAUTOKA
4.41 BUNBURY
4.41 REYKJAVIK
4.24 PORTLAND
4.24 ANNAPOLIS (NAVAL AC
4.18 NEWHAVEN
4.12 EASTPORT
4.06 NAPLES
4.00 SAKAI
3.94 XI SHA
3.88 PORTLAND
3.76 VLISSINGEN
3.76 PORT PIRIE
3.65 HACHINOHE II
3.65 ABASHIRI
3.59 WAKKANAI
3.53 PROVIDENCE (STATE P
3.53 SHUTE HARBOUR 2
3.53 LOWESTOFT
3.53 DOVER
3.35 PULAU PINANG
3.35 TAGO
3.29 SASEBO II
3.24 MONTEVIDEO (PUNTA L
3.18 NAHA
3.18 NISINOOMOTE
3.12 CUTLER II
3.12 LEITH II
2.94 FORT PULASKI
2.88 KUCHINOTSU
2.88 ZHAPO
2.82 HAKATA
2.82 HAY POINT
2.82 MACKAY
2.76 MISUMI
2.71 HOEK VAN HOLLAND
2.65 KUKUP
2.59 BRIDGEPORT
2.59 VICTOR HARBOUR
2.59 PULAU LANGKAWI
2.53 NAGASAKI
2.53 HARLINGEN
2.41 OKINAWA
2.41 STAVANGER
2.35 TANJUNG KELING
2.29 BAR HARBOR, FRENCHM
2.29 SAIGO
2.29 TAJIRI
2.29 CEDAR KEY II
2.18 OURA
2.18 WILMINGTON
2.18 CHARLESTON I
2.06 ROOMPOT BUITEN
2.06 LUMUT
1.88 IZUHARA II
1.88 TREGDE
1.76 WEST-TERSCHELLING
1.71 IJMUIDEN
1.65 TOBA II
1.65 WAJIMA
1.65 SUMOTO
1.65 YAIZU
1.53 KARIYA
1.41 KEY WEST
1.41 KANMEN
1.41 DELFZIJL
1.41 ODOMARI
1.29 SYDNEY, FORT DENISO
1.29 AKUNE
1.24 TAPPI
1.24 NEZUGASEKI
1.18 MAASSLUIS
1.12 BROUWERSHAVENSE GAT
1.12 MOOLOOLABA 2
0.82 OSHORO II
0.71 DEN HELDER
0.71 PORT LINCOLN
0.41 BERGEN
0.35 SPRINGMAID PIER
0.29 OMAEZAKI II
-0.06 BUNDABERG, BURNETT
-0.12 TAN-NOWA
-0.12 KLAGSHAMN
-0.24 KO MATTAPHON
-0.29 N. SPIT, HUMBOLDT B
-0.41 MAGUEYES ISLAND
-0.76 GOTEBORG – TORSHAMN
-0.82 FERNANDINA
-1.12 GIBARA
-1.12 KOMATSUSHIMA
-1.41 SHIRAHAMA
-1.47 TAKAMATSU II
-1.47 SMOGEN
-1.53 HAKODATE I
-1.65 SAN DIEGO (QUARANTI
-1.82 OWASE
-1.88 LOS ANGELES
-1.94 BAMFIELD
-2.00 SOUTH BEACH
-2.35 MAISAKA
-2.35 VANCOUVER
-2.41 VICTORIA
-2.41 NAGOYA II
-2.41 MOKUOLOE ISLAND
-2.53 HONOLULU
-2.71 KUNGHOLMSFORT
-2.82 SAN FRANCISCO
-2.82 WINTER HARBOUR
-2.88 POINT ATKINSON
-3.00 HILO, HAWAII ISLAND
-3.00 POINT LONSDALE, POR
-3.06 ALAMEDA (NAVAL AIR
-3.12 PORT SAN LUIS
-3.18 SEATTLE
-3.18 FRIDAY HARBOR (OCEA
-3.24 KAHULUI HARBOR, MAU
-3.76 CAMPBELL RIVER
-3.82 SANTA MONICA (MUNIC
-3.88 KAINAN
-4.12 WAKAYAMA
-4.82 ONISAKI
-4.88 PRINCE RUPERT
-5.00 OLANDS NORRA UDDE
-5.53 BELLA BELLA
-5.71 PORT HARDY
-6.06 NEAH BAY
-6.12 QUEEN CHARLOTTE CIT
-6.24 KETCHIKAN
-6.35 TOFINO
-6.59 CRESCENT CITY
-7.06 LANDSORT
-7.06 STOCKHOLM
Bruce: “Tilo, 1992 to 2009 Avg 2.18 ”
Thanks Bruce. This is well below the Satellite trend by about 1.1 mm/year. It’s interesting because one of the people on Realclimate mentioned that he thought that part of what was being counted as acceleration in the historic data was simply a transition from tide guages to satellite records. Meaning that the tide guages had a lower level of sea level rise and continued to have a lower level of sea level rise after the beginning of satellite data. But the combination of the two, where the tide guage data was dropped after the satellite data began, then gave the appearance of an acceleration that really wasn’t there. Thanks for the result. I’m going to have to look at that a little closer now.
Tilo wrote:
“We have climate sensitity models producing numbers from .5C for 2X CO2 to 6C for 2X CO2. Most of them are wrong. ”
#############################
We have models ranging from 2.1 to 4.4C per doubling.
The mean of all the models is around 3.2
ModelE is about 2.7
To date, the models that have sensitivities less than 3 are doing better on certain metrics than those that are higher than 3.
no GCM used by the IPCC has a sensitivity less than 2.1
Tilo can you say you are wrong about this, simply and directly. We all make mistakes:
“Contents88.68.6.28.6.2.2
8.6.2.2 Why Have the Model Estimates Changed Since the TAR?
The current generation of GCMs[5] covers a range of equilibrium climate sensitivity from 2.1°C to 4.4°C (with a mean value of 3.2°C; see Table 8.2 and Box 10.2), which is quite similar to the TAR. Yet most climate models have undergone substantial developments since the TAR (probably more than between the Second Assessment Report and the TAR) that generally involve improved parametrizations of specific processes such as clouds, boundary layer or convection (see Section 8.2). In some cases, developments have also concerned numerics, dynamical cores or the coupling to new components (ocean, carbon cycle, etc.). Developing new versions of a model to improve the physical basis of parametrizations or the simulation of the current climate is at the heart of modelling group activities. The rationale for these changes is generally based upon a combination of process-level tests against observations or against cloud-resolving or large-eddy simulation models (see Section 8.2), and on the overall quality of the model simulation (see Sections 8.3 and 8.4). These developments can, and do, affect the climate sensitivity of models. “
Stevef
Can you separate out what your model projects for the steric component only?
i’m thinking that with current observations, given that GRACE could measure the mass component and other sats give you altimetry you could attempt to isolate the steric component.. er sumtin like that
Steven Mosher,
Do you mean the forecast going forward from today (based on a specified warming rate) or do you mean the model calculation up until now? I can do either, I’m not sure which you want.
Heh, Tilo’s probably right that the satellite record links flat temperatures and deceleration, but can’t prove it. I expect we’ll get more clarity as the temperature flattens enough to begin to decline.
=====================================================
Steven Mosher: We have models ranging from 2.1 to 4.4C per doubling.
Who is “we”. I’m not using only IPCC models. And I didn’t say that I was only using GCMs.
“I have compared the calculated ocean heat model constant based on the second half of the Levitus et al data to the constant calculated for the entire data set and for the constant calculated form the first half of the data set. The constant for the whole set is 9.0 * 10^23 joules per degree (+/-0.74 two-sigma), while that calculated for the second half of the data set is 9.6 * 10^23 joules per degree (+/- 1.12 two sigma), and for the first half 8.4 * 10^23 joules per degree (+/- 4.7 two sigma). The uncertainty ranges overlap a lot, so there does not seem to be any meaningful discrepancy. The first half of the Levitus data has a lot of relatively short term shifts (limited/uncertain data for the early data?), and this is reflected in wider uncertainty for the constant calculated form the first half of the data.”
I guess I was expecting a model derived from 1st half or 2nd half of the observed and then a correlation calculated for the observed with the modeled result for the other half. I am not sure what your comparison does, but it would appear to be a valid alternative. That the uncertainties overlap does not guarantee that the derived constants are not significantly different. Can you tell me what is the basis of the calculation made above: monthly or annually and if you have calculated AR1 for the series?
The uncertainty problem that you run up against with the first half of the data is not unusual when one divides the already short calibration period into a calibration and verification periods.
Okay, so I decided to download the Church and White data this morning and see what it really looked like.
First I plotted all of the data and ran both a trend line and a 2nd order poly through it. There was definite acceleration in the sea level rise. But I noticed that there seemed to be 2 inflection points where most of the acceleration was coming from. One of those inflection points happened around 1930. The other looked like it happened about the time that the satellite data was joined to the tide gauge data.
So I decided to see what was happening between the two inflection point. First I plotted the period from 1930 to 1992 and again ran a trend line and a second order poly through it. The result showed that in that 62 year period, there was some deceleration of the trend.
So I decided to “uncherrypick” the 1930 starting point and start in 1920. Again I ran a trend line and a 2nd order poly through it. The result was a nearly dead flat trend. When I laid a ruler across the second order poly I could not see a bend. So, this seems pretty important to me. Prior to attaching the satellite data we get zero acceleration in sea level data for 72 years, and over that time period, the temperature was definitely rising strongly.
Next I plotted only Church and White’s satellite period. It showed some acceleration. But the interesting thing is that the satellite trend was immediately steeper than the tide gauge trend. I also returned and plotted the CU satellite data for the same time period – 1993 through 2009. It looked similar, but the acceleration was barely there. And using the CU data, when you took it through the latest availabe, it has definite deceleration.
So, here is the problem. When you take satellite data that is by itself not accelerating and attach it to tide gauge data that is also not accelerating, you suddenly get acceleration in the combination.
It looks like there was some real acceleration that happened around 1930 as an inflection point. And the acceleration that started around 1992 looks more like a product of joining two different data types than a real acceleration.
Oh, and I did one other thing, I also ran a third order poly through the 1920 to 1992 tide gauge data. Interestingly it started out with acceleration and then turned to deceleration. This seemed to go counter to the R&V and SteveF idea that we should get more acceleration as it gets warmer.
Having looked at the data, I can’t see how SteveF or R&V could possibly be right.
If someone will point me to directions for attaching charts, and if anyone is interested, I can put up another post with some of the charts that I was talking about attached.
Geographical parsing by longitude is interesting as well.
If there was a seamometer, the west coast of NA would be freezing to death.
1992 to 2009
longitude mm/year
0 to 90 1.30
91 to 180 3.13
181 to 270 -2.70
271 to 360 4.37
SteveF, “Well, the rate in the 1960 to 1980 period was about 1.6 mm per year (if I have done my math right) and about 3.2 mm per year from 1992 to present”
Where do you get 3.2mm?
last entry 1991 to last 2001
1991.9583 90.52
2001.9583 110.85
20.3/10 = 2.03mm
Global Mean Sea Level (GMSL) reconstruction for the period 1870-2001 by John Church and Neil White
http://www.psmsl.org/products/reconstructions/church.php
http://www.psmsl.org/products/reconstructions/church_white_grl_gmsl.lis
Bruce: I think he is basing it on a trend line, instead of the end points. And he is probably using CU data for that 3.2 mm.
It’s interesting, when I plot the C&W satellite era data from 92 to 09 it shows a trend of 2.8 mm/year. The tide gauge data just before then shows a trend of 1.72 mm/year, and it is dead flat for 72 years. Quite a jump for just moving to satellites.
Steve:
Here is a link to a free source of the Chao impoundment paper:
http://www.clas.ufl.edu/users/rrusso/gly6932/Chao_etal_Science08.pdf
I see they use the Church & White data for the “uncorrected” sea level rise.
Ok Tilo:You Said “WE have models running from .5C to 6c
And you used that “fact” the argue that the models are wrong.
I point out the IPCC has a range from 2.1 to 4.4.
YOU refered to WE. So, for some strange reason you point to models that fall outside the consensus, and then disparage them
Ok: Which model shows .5C. Which shows 6C. YOU referred to them, so you must know what you refering to.
I understand SteveF and carrick now
SteveF
I think Both before and after would be nice.
http://grace.jpl.nasa.gov/data/steric/
It would seem to me that from the Time grace started and going forward you have an observation to test/refine your model since it breaks out a mass related and steric related component.
Not sure what do you think
Carrick (Comment #79779)-If the variables are i.i.d. then the general sense of the central limit theorem, that they should converge on an “attractor” distribution should still be true. It’s just that that distribution is only the normal distribution if the variance is finite (the mean must also be finite but distributions where that isn’t true are, shall I say, in the area of mathematical curiosity at best) So which one of these things is going on with 1/f^nu noise? I will assume i.i.d. still applies, since you wouldn’t be talking about the central limit theorem “breaking down”…so it’s because 1/f^nu noise has an infinite variance? If that’s the case, technically CLT still holds, just not in the classical sense that the distribution being converged to is the normal distribution. Otherwise CLT in the sense of any of a set of weak-convergence theories still holds.
Fun stuff! I hope you write it up and submit it. You should lose some of the obvious factual errors and fallacies, but once you do that, it’s really an interesting approach.
Another interesting paper:
http://sciences.blogs.liberation.fr/files/calottes-fondent.pdf
My quick take: Right now we are seeing a doubling time from the ice sheets of less than ten years. All hopes for a sub-meter sea level rise depend on that acceleration dramatically slowing even as we force the climate in the other direction. So while we could certainly have less than a meter, you need some pretty wild optimism to imagine it. But we’ll see (sea?)
Robert, the only thing “wild” is the extrapolation of acceleration far into the future from little data. According to:
Nick, F.M., A. Vieli, I.M. Howat, and I. Joughin. 2009. Large-scale changes in Greenland outlet glacier dynamics triggered at the terminus. Nature Geoscience, 2, 110-114.
“Our results imply that the recent rates of mass loss in Greenland’s outlet glaciers are transient and should not be extrapolated into the future.”
In other words, the recent elevated rates of mass loss are not an indication of long term continuous acceleration. The results of the study you reference not only depend on assuming the current rates are permanent, rather than transient, it also supposes that those rates will continue to rise indefinitely. That cannot be expected to give reasonable results for the future.
Steve Mosher: “Ok Tilo:You Said “WE have models running from .5C to 6c”
Yes, Steve, and if you had looked at the origin of the discussion you would have seen that we were talking about people who were qualified to understand SteveF’s math and produce models. So my “we” was the grand we, as in what is available for all humanity from all of the scientists that Carrick would consider to be qualified by educatation and profession to comment on SteveF’s work.
“YOU refered to WE. So, for some strange reason you point to models that fall outside the consensus, and then disparage them”
I refer to models produced by people that Carrick considers to be “qualified”. But I find your concept of the IPCC being “the consensus” and your “we” being the IPCC as being hilarious.
“Ok: Which model shows .5C. Which shows 6C. YOU referred to them, so you must know what you refering to.”
Since you are stuck on the IPCC, try AR4, WG1, Chapter 9, Table 9.3. Also, I remember that Spencer had a model that produced a climate sensitivity of .6C and I believe Lindzen had one that produced .5C.
“I understand SteveF and carrick now”
First of all, don’t blame me for your faulty assumptions, and second of all, same to you.
Andrew_FL: :
It’s one that depends on nu, so I’m not sure what the utility of the theorem is, in that case.
For the CLT to converge to a normal distribution, you need two things: 1) uncorrelated noise, 2) constant variance.
For S(f) = 1/f^nu, the first assumptions breaks down. As I said on the SOD thread, the reason I get the “double peaked” distribution is a pretty technical, but if you want me to try and explain it, I will.
What you said is also technically correct about infinite variance and is related, at least for nu > 0, and I can explain how this relates too if you want.
(I don’t mind doing it, but don’t want to waste my time if nobody is going to read it.)
Tilo Reber (Comment #79876)-“Also, I remember that Spencer had a model that produced a climate sensitivity of .6C and I believe Lindzen had one that produced .5C.”
Those are from the observed satellite radiation budget data, not models.
Carrick (Comment #79877)-I would in fact appreciate your writing on this topic. I can’t promise it won’t go over my head. So far it sounds like 1/f^nu noise violates i.i.d. in which case CLT just does not apply. Can noise be “correlated” but still independent and identically distributed? My (limited) understanding suggests not. I also suspect that changing variance is also contrary to the i.i.d. condition.
Robert: “My quick take: Right now we are seeing a doubling time from the ice sheets of less than ten years. ”
Where is the water?
OK, here goes (sure wish Lucia had a sandbox, it’d make this less hectic). Let’s call $latex S(f)$ the power spectra associated with a random process $latex x(t)$ which we are measuring in an interval $latex [0, T]$. For the sake of convenience, we will always use the “zero subtracted” version of $latex x(t)$ in this interval:
$latex \tilde x(t) = x(t) – {1\over T}\int_0^T x(t) dt$,
and we’ll drop the ~ symbol over the x. What this reduces to is a distribution $latex S(f) = 1/f^\nu$ for $latex f \ne 0$ and $latex S(0) = 0.$
[It’s a “convenience” because $latex S(0)$ is undefined otherwise, for $latex \nu > 0$.]
To insure convergence of integrals, we will require that $latex S(f) = 0$ for $latex f \ge f_s/2$, where we can take $latex f_s$ to be the “sampling rate” that we are measuring our signal at. [In signal-processing jargon, we are digitizing our signal at a rate $latex f_s$ after passing it through a brick-wall low-pass antialiasing filter.]
Since the distribution is band-limited, we can replace the continuous $latex x(t)$ with a finite sequence
$latex x_1,x_2,. . .,N$,
where $latex N = f_s T$.
Using Parseval’s Theorem, we can then write:
$latex {1\over N} \sum_1^N x^2(t) dt = \int_0^\infty S(f) df$.
If you want, this serves as to define the normalization of $latex S(t)$. But notice that, because the mean of $latex x(t)$ is zero, the left hand side is just the variance of the noise squared.
In keeping with our desire to not evaluate $latex 1/f^\nu$ at 0, we’ll impose a lower frequency cut off at $latex 1/T$. We then have:
$latex \sigma_x^2 = \int_{1/T}^{f_s/2} {1\over f^\nu} df$
With a little work, this can be rewritten as:
$latex \sigma_x^2 = T^{(\nu-1)} \int_{1/N}^{1/2} {1\over z^\nu} dz$ where $latex z = f T$.
The important thing to note with this expression is that (for $latex \nu > 1$) the variance $latex \sigma_x^2$ scales as $latex T^{(\nu-1)}$. For $latex \nu=1$, we get explicitly $latex \sigma_x^2 = \log (f_s T/2)$. Only for $latex \nu = 0$ do we get a value of $latex \sigma_x^2 $ to be independent of $latex T$.
For this type of noise (other than $latex \nu = 0$), we can see that correlated noise is the same thing as a variance that depends on the observation interval.
Processes associated with “real world” measured signals are band-limited at both the low-frequency end as well at the high end (that is usually enforced by the anti-aliasing filter). Typically you’ll see a figure like this:
Typical source spectra
So the trick to getting $latex \sigma_x$ to be constant is to measure for a long enough an interval that we resolve the source region. This will show up, for example, as a variance that approaches a constant value with increasing $latex T$.
For smaller values of $latex T$, the variance will increase with increasing $latex T$. The effect of the low-frequency $latex 1/f$ spectrum will be to add an offset, which we subtract off, as described above.
The reason for the “double-peak” is kind of cool, as $latex \nu \rightarrow \infty$, the $latex 1/T$ cut-off acts as a high-pass filter, and you essentially end up (in the spectral domain) with something that approaches a line spectrum…
The Fourier transform of this is sinusoidal-like (over periods of $latex T$), and the PSD of a sinusoid with noise gives a double-peaked histogram.
Hope that makes sense. It’s obviously a fairly dense explanation, and I apologize in advance for any typos.
Another thing I could have pointed out was for $latex \nu = 0$, the limit for $latex T\rightarrow 0$ is $latex \sigma_x^2 = f_s/2$.
… and yes we could have chosen a different normalization so that $latex \sigma_x$ is dimensionless. Just add an $latex N_0 = f_s^\nu$ normalization to $latex S(f)$ in that case… (and your variations of $latex \sigma_x^2$ will be with respect to $latex N$ instead of $latex T$). This sort of mathematical nicety isn’t so necessary here, because I was normalizing my results with respect to $latex \sigma_x$ before histogramming them in the notes I left at ScienceOfDoom.
I suppose it would be helpful to plot out a family of curves for how $latex \sigma_x^2$ varies with $latex T$ (or $latex N$) for different values of $latex \nu$. Exercise for the reader?
Also I noticed one typo already. Parseval’s Theorem should read as:
$latex {1\over N} \sum_1^N x_n^2 = \int_0^\infty S(f) df$.
If I’ve done my math right, adding this normalization, we have the general form:
$latex \sigma_x^2 = \frac{2^{\nu -1}-N^{\nu -1}}{1-\nu }$
with the special case
$latex \sigma_x^2 = \log(N/2)$
when $latex \nu\rightarrow 1$.
[You can verify that the first expression reduced to the second if you take the limit as $latex \nu \rightarrow 1$.]
[Second typo above, the normalization factor should be $latex N_0 = f_s^{(\nu-1)}$.]
steven mosher (Comment #79871)
OK I will generate the steric only for past and a few future warming scenarios (say, 0C, 0.1C, 0.2C, and 0.3C per decade). But I am first going to switch over to the updated Church and White data (which continues to show acceleration, but less acceleration than the earlier Church and White data, mainly due to less of a dip in the middle part of the record, near 1930). I am also going to look at the impact of the estimated reservoir accumulations and the estimated ground water depletion… just eye-balling them looks to me like they may torque the post 1970 trend up and down way more than credible changes in the melt rate would suggest. We will see, but these non-climate contributions look like they may be less reliable/credible than the tide gauge data.
Carrick,
Do you have lecture notes on that? 😉
SteveF, unfortunately no.
The closest thing I have is a couple of papers that use these type of results.
One of the things I’ve learned from doing “real world” statistical analysis of data is that many of the results taught in introductory courses, like CLT, are approximations at the level of the spherical chicken.
(The problems with how many statisticians try and frame problems is they aren’t couched in terms of how the data were collected or eventually used, and data handling needs to to be part of the analysis method.)
Thanks Carrick, that clarifies things (some of the math was a little heavy but I pulled through) haven’t been able to respond so far as I am travelling, but I do appreciate the work you did. Thanks! 🙂
You’re welcome Andrew. For my own curiosity, I’m still interested in why “blue” noise ($latex \nu < 0$) gives a leptokurtic distribution. The variance explanation doesn't help there, since the variance goes to a constant in that case for large $latex N$.
Always something more to think about!
Tilo: Lindzen has a model? That’s funny, You have no idea what you are talking about.