1. The anomaly was 0.460 C, down from 0.495 C in January. ( Note that the January temperature was revise from 0.470 to 0.495.)
2. According to my tally, this was the 7th warmest February 4 in the HadCRUT NH&SH record. February anomalies are circled in the graph above; as you can see most of those warm Februaries occurred this century.
3. If computed using data since Jan 2001, both the simple trend based on time only and the trend computed using a multiple regression involving both MEI and time remain negative. The nominal trend of 0.2C/decade remains outside the ±95% confidence intervals for the MEI corrected trend; these confidence intervals computed based the assumption that the residuals for the observations are ARMA(1,1).

Take this graph for example. It shows the U.S. CONUS (e.g. lower 48) trends from USHCN stations in 2.5 x 3.5 lat/lon grids with both less than 10 population density and greater than 100 population density stations (via 2010 GWPv3 data). It compares the raw trend from the low pop density stations to the adjusted trend of all stations in the same gridcells, and finds dramatically different results. The raw data from low pop density stations shows a trend of 0.093 C per decade, while the adjusted data from all stations shows a trend of 0.238 C per decade, some 2.5 times larger. Does this provide clear evidence of “a substantial spurious warming component”? Well, not necessarily. For that strong a conclusion, a more detailed and thorough examination of the data is required.

Before we dive into a more detailed examination, lets quickly review the methods we are using to spatially weight and anomolize station data.

• This analysis uses a spatial gridding model outlined in this post: http://rankexploits.com/musings/2010/a-simple-model-for-spatially-weighted-temp-analysis/
• As always, the latest source code can be found here: http://drop.io/0yhqyon/asset/temp-analysis-v0-10-zip
• Data used to produce all the graphs in this article is available in a spreadsheet here: http://drop.io/0yhqyon/asset/us-uhi-xls
• Click on any of the graphs to embiggen

I use 2.5 x 3.5 lat/lon gridcells and a 1961-1990 baseline for anomaly calculation because these are the standards used by NCDC in analyzing USHCN data. Based on the feedback from prior articles, I decided to de-emphasize the use of spaghetti graphs because they tend to obscure small (or even moderate) differences in datasets when the data is noisy. Instead, I’ll primarily be showing comparisons of trends in datasets over two different periods (1900 – 2009 and 1960 – 2009) to show long-term and “modern warming period” trends respectively.

I’ll be looking at three different proxies for urbanity:

• Population density, via GWPv3 2010 spatial data
• Urbanity, via GRUMP urban boundry data (using both population density and remote sensing data of settlement extent to define urban borders)
• Satellite nightlight brightness, using DMSP-OLS v4 data

All of these are taken from external sources and are not obtained from any station metadata provided by NCDC. They are indexed to station lat/lon coordinates through work by Ron Broberg over at The Whiteboard.

To better understand the data used in this analysis, its worth discussing USHCN for a bit and the various raw and adjusted datasets that it provides.

The U.S. Historical Climatological Network (USHCN)

The USHCN provides a number of substantive improvements over the GHCN data I used in the prior global UHI analysis. For one, the station metadata is considerably better (specifically, the lat/lon coordinates are generally accurate, which is essential for the approach I’m taking). USHCN stations also are much denser than GHCN stations, which makes a pair-wise comparison approach effective without resulting in the loss of the majority of gridcells. Finally, USHCN stations tend to have long, continuous records and there is little station “dropout” in recent years.

The map below (from Menne et al 2009) shows all USHCN stations and COOP stations not included in USHCN in the United States. The spatial coverage of the network is quite good, though there is some local clustering that we can account for by spatially gridding the stations in our analysis.

USHCN provides three different sets of data (raw, TOB, and F52) for three different temperature readings (mean, max, and min). Raw data is the rawest of the raw; a simple monthly average mean, max, and min from each station with very basic quality control checks. TOB data is the raw data corrected for bias introduced by changes in observation times over time for a portion of the USHCN stations without hourly temperature data (e.g. primarily those in the COOP network). F52 is the final adjusted dataset that takes the TOB data as a starting point and uses an algorithm to detect step changes and other inhomogeneities in individual station data by comparing the record of each station to that of other nearby stations. The F52 data also has missing datapoints infilled from nearby stations.

Time of observation (TOB) adjustments occur primarily in stations without hourly temperature data available. These stations will tend to measure temperatures only a few times a day, and the time they measure the temperature will have a strong effect on the max and min temps recorded. If the time of observation changes over time, it can introduce a bias into the raw temperature data. Because stations record the time of observation associated with each reading, researchers can measure how the TOB changes over time. The Figure below (also from Menne et al 2009) shows the general TOB for each station by year. Immediately obvious is a dramatic shift from PM TOB to AM TOB over the past 60 years; a change which Menne et al 2009, Karl et al. 1986, Vose et al 2003, Pielke et al 2007, and numerous other papers all conclude introduces a spurious cooling bias into the temperature record.

Adjustments to correct the TOB effects have the net impact of slightly lowering temps at the start of the century and significantly increasing temps near the end of the century. The net effects of TOB adjustments to USHCNv2 are shown in the figure below (yet again from Menne et al 2009). The effects of TOB adjustments are effectively identical in the old USHCNv1 and the new USHCNv2.

USHCNv2 introduced a new method for detecting and correcting inhomogeneities in station data that replaces the numerous independent adjustments used for station moves, UHI effects, and changes in measurement instruments (e.g. the shift to MMTS) in USHCNv1. The USHCNv2 inhomogeneity detection works by looking at multiple pair-wise comparisons of stations in a region to identify spurious step-changes or unusual changes in trends and correcting them to be in line with records from nearby stations. It also uses the documented station history to identify and correct for known changes in station location and instrument type. The net effects of non-TOB adjustments (e.g. F52 minus TOB) is shown in the figure below (again from Menne et al 2009). The pronounced increase in maximum temperature due to adjustments in the last 30 years is primarily associated with the switch from old LiG (liquid-in-glass) thermometers to new MMTS systems.

To examine all the difference approaches to detecting UHI, we can use the three urbanity proxies identified earlier (pop density, urban boundaries, and satellite nightlights) to compare the trends in temperature constructed from stations in the same gridcells with different urbanity characteristics. Specifically, we will look at three pair-wise comparisons within 2.5 x 3.5 lat/lon gridcells:

• Stations with less than 10 pop density and greater than 100 pop density
• Stations within urban boundaries and outside urban boundaries (rural)
• Stations with bright nightlight readings (40 to 63 brightness index) and dark nightlight readings (0 to 20 brightness index)

In all cases, the number of gridcells available for use in temperature reconstructions will be smaller than the total number of CONUS gridcells, because not all gridcells have stations of both types for a given proxy. The figure below shows the total number of 2.5 x 3.5 CONUS gridcells, and the number available for each pairwise comparison by urbanity proxy. The population density proxy is the most restrictive, allowing us to use only 30 percent of CONUS gridcells. The urban boundary proxy allows the use of 80 percent of gridcells, while the satellite nightlight proxy allows the use of 72 percent of gridcells.

Lets examine each proxy in turn, and see what they tell us about the potential effect of changes in urban form on the temperature trend. It is worth noting that all three proxies represent a snapshot in time, and cannot perfectly account for changes in urban form over time. However, if the low population density / rural / dark stations represent the measurements least susceptible to UHI effects, the difference between the temperature trends reconstructed from just those stations and that from all stations in the gridcells used can give us an estimate of the relative effect of UHI, assuming that locations rarely become less dense / more rural / darker over time.

I’ve also chosen to focus on trends in mean temperatures rather than max or min due to time constraints, though expanding the analysis to include max/min temps would provide additional information about potential UHI effects.

Population Density

The population density data used in this analysis comes from the GWPv3 2010 estimates, a database maintained by Columbia University. The dataset provides 2.5 arc-minute resolution, and is mapped to USHCN stations using the station lat/lon provided in the metadata file. 1214 stations are successfully located using the 2.5 arc-minute data, while 2 additional stations are located via 15 arc-minute data and a final 2 by 60 arc-minute data. The figure below shows the 2010 population distribution for the CONUS.

Having assigned a population density figure to each USHCN station, we can look at the distribution of stations by population density as shown below:

The majority of stations have fewer than 25 people per square kilometer, with the plurality having less than 10 per square kilometer. Relatively few USHCN stations have a population density greater than 100, and even fewer have a density over 400. The two population brackets used in this analysis, under 10 and over 100, provides a large pool of stations in the former category and a relatively small pool in the latter category.

If we further restrict our analysis to gridcells with both under 10 and over 100 pop density stations, we get the figure below, showing around 150 stations with under 10 density and around 80 stations with over 100 density in 36 2.5 x 3.5 gridcells.

We can use these stations to find the trend for the periods 1900-2009 and 1960-2009 for the three datasets (raw, TOB, and F52), along with their 5^th to 95^th percentile ranges. Note that the trend confidence intervals shown here are slightly smaller than the true confidence intervals, as they do not correct for autocorrelation present in the underlying data.

The difference between the trends of low and high-density stations is quite large in the raw data. However, TOB adjustments appear to mostly eliminate the difference in trends. This may be due to the fact that stations in areas of lower population density regions are more likely to be COOP stations without hourly temperature readings, and thus more subject to spurious cooling biases due to changes in TOB.

We can take a closer look at the relative effect of each adjustment on the trend:

Here we can see TOB adjustments have a large effect of the trend on low density stations, increasing the trend by close to 100 percent over both periods. The TOB adjustments have a negligible effect on high density stations for the 1900-2009 period and a minor effect for the 1960-2009 period. Inhomogeneity adjustments have a similar effect on both classes of stations for the 1900-2009 period and a slightly larger effect on low density stations in recent years.

To estimate the magnitude of the UHI effect on the overall trend for the gridcells in question, we can compare the trends in low density stations to those of all stations. This comparison is shown in two formats: the percent effects, which allows for a comparison across both time periods (calculated via all station trend / low density trend minus 1), and the absolute effects on the trends (calculated via all station trend minus low density trend, in degrees C per year).

In both cases, the UHI effect is much more pronounced in the raw data, is modest in the TOB data, and is negligible or even slightly negative in the inhomogeneity-adjusted data.

Urban Boundaries

Urban boundary data is taken from the GRUMP dataset, also from Columbia University. As Ron Broberg explains, “The [GRUMP] data set consists of a merging of two sources of information: population and settlement extents. Population data is derived from a variety of sources, primarily national census. Settlement extent is derived from the Defense Meteorological Satellite Program (DMSP) Operational Linescan System (OLS) for a seven month period in 1994/1995, from an ESRI Digital Chart of the World (DCW), and Tactical Pilotage Charts (TPC).” A chart of CONUS GRUMP urban boundaries is shown below:

There are 97 gridcells with both urban and non-urban (rural) GRUMP stations that we can use in our pair-wise comparison. The total number of stations in those gridcells, as well as the number of urban and rural stations, are shown below. Unlike the population density case examined previously, all stations in the gridcells are classified as either urban or rural.

Lets take a look at the trends for both periods for raw, TOB, and inhomogeneity-adjusted data:

And the relative effects of each round of adjustments on rural and urban stations:

Again, we see that TOB adjustments are considerably larger (nearly 2x) for rural stations than for urban stations, though the difference here is smaller than that observed in the population density analysis. This makes sense, since the population density proxy was looking at a more extreme division. We also se that inhomogeneity adjustments are similar for both datasets over the 1900-2009 period, but considerably larger for rural stations than urban stations over the 1960-2009 period.

Turning to the estimate of UHI (comparing the trend in rural stations to all stations in the gridcells), we find that the effect of urban form on temperature trend is diminished after each subsequent round of adjustments, with the small exception of the absolute effect of inhomogeneity adjustments in the 1900-2009 period.

In general, the effect of urban form estimated via the urban boundaries proxy is smaller than that found via the population density proxy, except in the final inhomogeneity-adjusted data where it is notably larger.

Satellite Nightlights

By measuring the visible light at night from space via satellites, we can create an assessment of the relative urbanity of a specific area. This analysis uses raw DMSP-OLS v4 nightlight data from 2008 kindly processed by Ron Broberg to assign a brightness rating ranging from 0 to 62 to each station. Its worth noting that DMSP-OLS data is also one of the inputs used by the GRUMP urban boundary designations, so these proxies are not completely independent. Below is an image showing satellite nightlight brightness for the CONUS.

NOAA used an older version of DMSP-OLS data to classify each USHCN and GHCN station as Dark, Dim, or Bright. Unfortunately, the scale used in that classification is different than the 0 to 63 scale provided by the current satellite data. After examining the distribution of stations by brightness, I somewhat arbitrarily labeled stations with a nightlight brightness of 0 to 20 as “Dark” and 40 to 63 as “Bright”. This leaves us with slightly under a third of stations that are neither dark nor bright, and provides a proxy that is less restrictive than the population density division but more restrictive than the binary urban/rural GRUMP proxy. It also gives us 87 gridcells with both dark and bright stations for pair-wise comparisons, with the number of stations available for each class for each year shown below:

If we calculate the trends for dark, bright, and all stations over both periods for raw, TOB, and inhomogeneity-adjusted data we see that it looks fairly similar to the figure for urban boundaries.

A closer look at the relative effects of each adjustment shows that the TOB adjustments for dark stations are much larger than those we observed for rural stations, especially for the 1900-2009 period. The inhomogeneity adjustments are comparable for 1900-2009, but are quite small for bright stations post-1960.

Looking at the estimated effects of urban form on the temperature trend (e.g. all station trend vs. dark stations only), we see a very large urban form effect present in the raw data for the 1900-2009 period, much of which disappears after TOB adjustments are applied.

Conclusions

By examining the effects of three different urbanity proxies on trends in raw, TOBs, and inhomogeneity-adjusted USHCN data for the periods of 1900 to 2009 and 1960 to 2009 we can get a good picture of all the different ways to evaluate the effects of urban form on temperature trends in the United States. Some of the results we obtained were expected, others somewhat less so.

Among expected results are that UHI effects seem to be larger (as a percent change of the trend) over the full century than over the past 50 years, at least in the urbanity and nightlight proxies. This holds across all three datasets, even the adjusted one, perhaps indicating the presence of a small-to-modest UHI signal robust to potential biases introduced by both TOBs and inhomogeneity issues. We also find that TOBs adjustments have a much larger effect on low pop density / rural / dark stations than their counterparts, something we would expect if these stations were more likely to be COOP stations without hourly temperature data available. What was slightly less expected is that inhomogeneity adjustments appear to have a much greater effect on low density / rural / dark stations in recent years (1960-2009) than their high density / urban / bright counterparts. It may be that this is due to MMTS-related inhomogeneities, since rural stations are perhaps less likely to experience a switch to MMTS.

So where does this leave us? It turns out that the size of the UHI effect you can claim from U.S. data depends largely on whether or not you accept the need for TOB and inhomogeneity adjustments. If you reject all adjustments, UHI appears rather significant (increasing the U.S. temp trend between 25 and 90 percent depending on the period and proxy used). If you accept all adjustments, UHI turns out to be fairly small (changing the trend by between -5 and 14 percent). If you just look at TOB adjustments but ignore inhomogeneity, you end up with modest UHI effects (increasing the trend between 10 and 25 percent). However, the analysis shown in the initial graph, comparing a non-urban raw dataset to the adjusted data from all stations gives a misleading impression, since the adjustments (both TOB and inhomogeneity) have a strong correlation with urban form.

Update

MikeC asked about micro-site effects, which aren’t necessarily perfectly correlated with changes in urban form. Since we do have data on the CRN rankings of some stations via the Surface Stations project, we can use CRN as a proxy for micro-site effects, with CRN12 assumed to have few micro-site biases and CRN345 assumed to have large microsite biases.

Because there are relatively few CRN-rated stations available to me (especially in the CRN12 bin), I can’t do a pair-wise comparison using the same grid cells, so there may be spatial coverage biases in these results. YMMV.

The full list of CRN12 and CRN345 stations in the < 10 and > 100 pop density brackets, along with their reconstructed anomalies and trends, are available here: http://drop.io/0yhqyon/asset/ushcn-crn-xls

And the results, using raw data:

CRN12 stations seem to have a higher trend than CRN345 stations, consistent with our earlier analysis and replication of Menne et al 2010. This may be due to the fact that CRN345 stations are more likely to have undertaken a switch to MMTS sensors (and had a spurious max temp cooling bias introduced), so I’d be careful about concluding too much regarding micro-site effects from this chart. That said, it at least suggests that micro-scale effects aren’t enormous.

Above is a graph showing how the trend of 0.2 C/decade fits into ±95% uncertainty intervals computed for NOAA observation. The uncertainty intervals are estimated assuming the residuals to the linear fit have an ARMA(1,1) structure, and part of the ‘weather noise’ is explained by the MEI index. (I have documented the methodology for estimating uncertainty intervals using ARMA(1,1) only partially at the blog. The method of estimating the uncertainty intervals uses a “number of effective data points” method that is asymptotically correct as we acquire an infinite number of samples. In my applications, the coefficients required to estimate the effective number of data points are based on the first three lagged correlations in the correlogram for the residuals and monte-carlo tests indicate my method returns uncertainty intervals that are slightly too large.)

The graph shown is one of the “default” graphs in the spreadsheet I update when new monthly temperature anomalies are published. I alternate showing new data along with trends 1980 or 2001, with no particular pattern. Sometimes I show a graph with both trends. If I noticed that the 2001 graph flipped form “rejecting” 0.2 C/decade (as it has been for many months) to “accepting”, I would consider that news and show highlight that graph. Similarly, if 1980 flipped from “accepting” to “rejecting”, I’d highlight that one. Otherwise, it’s a toss up; earlier this month I happened to pick the 1980 graph when presenting GISSTemp for this month.

As long as I’m showing the 2001 graph, I’ll discuss what this communicates. When the analysis using the assumptions discussed briefly above is performed, a trend equal to exactly 0.2 C/decade falls outside the ±95% confidence intervals for the trend consistent with the NOAA/NCDC data observations. This means that based on the assumptions of this analysis, if we select a confidence level of 95%, we should treat the assumption that the trend is 0.2 C/decade as false.

In contrast, because, for the purpose of analysis, we’d assumed the trend of 0.2 C/decade projections is true, if that trend fell inside the uncertainty intervals, we’d continue to assume it was true.

Note that currently, if we create equivalent graphs for GISSTemp or Hadley, the analysis based on HadCRUT returns the result similar to NOAA shown above; while the analysis using GISSTemp results in a ‘fail to reject’ conclusion.

In either event, before we’d performed the analysis, we would know that we would ultimately accept a chance of making the wrong decision, with errors falling in two possible classes:

1. False positive error. (i.e. ‘Type I’ or α error.) Contingent on our statistical model being correct, (i.e. the residuals are ARMA(1,1), etc.), the chance of decreeing 0.2 C/decade false when it is, in fact, true would be α=(1-95%)=5%. The way these tests are constructed, false positive error remains constant at the chosen level of α no matter how much data we collect. I’ve set up my test to give false positives at a rate of 5%.
2. False negative error. (i.e. ‘Type II’ or β error.) Once gain, contingent on our statistical model being correct, we have some chance of failing to reject the null hypothesis. In this case, that is saying the trend of 0.2C/decade is correct when it is incorrect. The rate of β error can never truly be known because it is a function of the the magnitude of the actual trend– which cannot be known. However, in the limit of zero data, this rate is 95% and declines as we obtain more data. So, this type of error– accepting the null hypothesis, is the error we generally worry about when we have very little data.

Other sources of making the wrong diagnosis is using an incorrect statistical model. This is not directly related to using a short time period. There is, however, an indirect effect because lack of data can make it difficult to perform fiduciary tests to determine whether or statistical model is correct. For example, in the current case, if we have insufficient information, but had assumed the residuals are AR(1) as opposed to ARMA(1,1), white or any other statistical model, tests to show our assumptions are incorrect will have little power.

In any case: What the result illustrated in the graph above indicates is that, assuming the statistical model is true, and assuming 2001 is a good start year, we should reject the assumption that the trend of 0.2C/decade falls inside the range consistent with data.

Have I shown results of other tests starting in 2001 recently?

Since I’m not entirely sure why Nathan seemed to suggest I stopped doing something starting specifically in January, 2001, I think it’s worth showing that I have been recently presented results of analysis using data that begin specifically in 2001

That’s easy enough to show Nathan that I am in habit of including what results of statistical tests if we begin in Jan 2001 along with results starting in other years. For example, in January of this year, I posted various graphs comparing the multi-model mean projections computed from 22 models used by the IPCC to create projections published in the AR4 to observations. That method used in that post permitted me to include the uncertainty arising from both the ‘weather noise’ and spread in biases for that collection of 22 models. The results for Hadley and GISTemp were posted here and here respectively.

Both graphs contain results of analysis initiated in decadal years since 1950, supplemented with the year 2001.

Some new readers might wonder why I always include 2001 in particular. I always include 2001 because the emissions scenarios or SRES used to drive climate models was first released in Nov. 2000 (a noted here). So 2001 is, in some sense, the first year presenting a pure comparison of observations to projections driven by the SRES. (On can argue whether purity matters, but I think it’s worth noting the distinction between testing hindcasts and forecasts.)

I’m aware this post may prompt Nathan to clarify what precisely he thinks I stopped doing. One thing I do not believe I have stopped doing is comparing observations to IPCC projections with the analysis using data beginning in January 2001 and reporting whether the statistical test guides us to deem the projections ‘true’ or ‘false’. Quite often, if we chose a confidence level of 95%, the result of a statistical analysis guides us to conclude a trend that we can connect to information reported in the IPCC AR4 is found to be is false. (For example, the trend of 0.2C/century is diagnosed as false above.) Occasionally, we the analysis does not guide us to conclude a trend is not false. By convention, if that trend was the null hypothesis, we continue to treat it as true– because, by convention, we treat a null hypothesis as true even if when we have absolutely no data.

It seems to me that I show graphs and presents result of analyses using data starting in Jan. 2001 rather consistently and plan to continue to do so. I will, of course, also continue to show what happens if we apply the same analysis using longer time spans, or what happens if we change the assumptions in our statistical model and also sometimes publish blog posts that don’t happen to include a graph or a trend computed starting in 2001.

Update

I goofed up and showed a NOAA graph but discussed GISSTemp. I’ll update by adding the GISSTemp, which may well show trends inside the ±95% uncertainty intervals as that’s what we get when I look at the full model with the spread as see if you click the link discussing that more detailed analysis.

Figure 2: GISSTemp since 2001.

Figure 1: GISTemp Feb. 2010

This is a hot start for the year. Factoids about the GISSTemp data:

1. This is the second highest Feb. anomaly in the record; Feb. 1998 hit 0.80C.
2. At 0.705C, the year is is tied for second highest average based on both Jan. and Feb. The Jan+Feb average for 2007 was 0.745C.

With El Nino still alive and kicking, this year is in the running to break some GISTemp records. Maybe next month.

Figure 1: Temperature anomalies for the lower troposphere. Projections for surface provided for reference.

Comparison of the RSS and UAH observations indicates the observed least squares trend applied to observations during the observational record continues to lag the least squares trend based on the multi-model mean anomaly for the surface. Of course, it would be more appropriate to compare to projections for the lower troposphere, but for monthly blog posts I’m using trends from simulations that are available at “The Climate Explorer”. The most recent individual monthly observations are warmer than the value corresponding to the multi-model mean temperature anomaly. We must all wait to see whether the current El Nino will provide a sufficient number or warm months to close the gap in the trend.

The current reported anomalies are compared to those from last month and February 1998 below:

February 2010 exhibited a warm lower troposphere, but records for observed February values set in 1998 remains unbroken. Now, we await GISS and Hadley to see what they show for February!

The Toy Thermometers

As in yesterday’s post, applied the Hansen and Lebedeff (1987) method to compute the ‘temperature’ in a sub-box. (For details download the pdf and read yesterday’s post.) The sub-box will be assumed be instrumented with 5 pairs of thermometers. The pairs will consist of one thermometer that has been placed in a ’slow warming’ location, warming at 0.01 C/year and one placed in a ‘fast warming’ location warming at 0.03 C/year. The crack team of scientists will be monitoring both sets of thermometers from years 1-28; afterwards they will monitor only the “slow warming” thermometers. Meanwhile, the monks across the street will continue to monitor the “fast warming” thermometer, permitting us to compare computed ‘temperatures’ based on the all 10 thermometers and compare them to the set examined by the crack team of scientists.

Raw Data

This is synthetically generated data from all thermometers during the full period. Notice one group definitely warms fater than the other. (Notice I also set the ‘noise’ to a low value; I did t his on purpse to highlight the things that can go wrong. )

Figure 1: Raw data for 'toy' problem with fast warming and slow warming thermometers.

If you examine that graph it is clear that if the scientists only used the ’slow trend’ thermometers — shown in red (because scientists expect warmer regions to warm more slowly) they would report that the sub-box was warming at the slow rate.

If scientists only used the ‘fast trend’ (shown in blue because cliamte scientists believe cold regions will warm more slowly) thermometers, they would report the box was warming at the faster rate.

Even someone with the IQ of a vegetable would realize that if you want to know the rate at which temperature changes in the sub box, you want these thermometers distributed evenly; failing that, if all 5 “fast trend” thermometer were in one tight region, and the 5 slow warming spread out, you want to weight the various thermometers to avoid over sampling the “fast trend.” Climate scientists actually try to do that by using area weighting and gridding. But for now, we’ll just focus on the sub-box and what happens to it’s computed temperature.

Result after incorporating all available thermometers

Yesterday, I wanted to show people how data from each thermometer was incorporated, so I showed intermediate computed results for the first two thermometers and when the 6th thermometer was incorporated. Today, I’ll simply show the final graph comparing the ’sub-box’ temperature computed using the all thermometers during all 60 months– that is the graphs the monks monitoring all thermometers would create, and also the ‘temperature’ computed using only those available to the crack-team of scientists.

Notice that with this toy data, the result with stations dropped is different from the result if we had access to temperature made available only to the monks. After month 28, when the “fast warming” thermometer were dropped, we see:

1. The trend computed over all 60 data points declines using all thermometers (orange) is higher than the trend computed using all thermometers prior to year 28 but only the slow wearming thermometers after year 28.
2. Both the ‘temperatures’ and the trend in the temperature a based on the series with drop outs shows a step change at year 28.

Some of you who don’t like anomaly methods will think this result shows that raw temperature methods are better. That conclusion is incorrect. We would see the same discontinuity in trends and similar discontinuities in anomalies if we used computed the temperature in the sub-grid using ‘raw’ temperatures. That’s because the problem here is not related to the choice of data processing method; it is related to biased sampling relative to the question we wish to ask.

So, what does this problem show? It shows that if the trends vary in the sub-box, we do need to take care to distribute thermometers such that we properly register the variation in trends. That is to say, if mountains tops– though cold– are warming more rapidly than the warmer valleys below, dropping all the “cold” mountain top thermometers will cause a bias. However, those who think droppping these “cold” thermometers the bias the computed trend toward more warming would be mistaken. The bias would be be to make the computed trend toward less warming and the reason would be because the warm valleys were warming less rapidly.

Now, what of climate and GISTemp? Computation in cells of for GISTemp use the method described here. During the “march of the thermometers” many of the thermometers near the cold polar regions were dropped. Climate scientists expect that these regions are warming at a faster rate than the tropics. This means that if climate scientists theories about polar amplification are right, dropping northerly thermometers would tend to introduce in a cold bias in the computed trend.

That said, while my toy example shows dramatic effect, it’s unlikely we’d expect a large cold effect due to ‘the march of the thermometers’. For the most part, the we expect variation in long term trends to strong spatial correlation. That is, we don’t expect the trend in El Salvador to differ dramatically from Guatemala City; instead we expect the long term trend in Greenland to differ from both those Central American cities. So, Eeven though the number of thermometers in cold locations was lost, the area used to compute the temperature for the surface of the earth, protects somewhat against the loss of thermometers in polar regions introducing an large bias in the computed trend for the earth’s surface trend. As long the loss of thermometers doesn’t result in a method failing to account for areas with fast warming, the first order effect on the computed trend for the earth will tend to be to add noise, not bias.

In the end, the proof is in the pudding. We can ask. “Did the cold bias materialize?” It seems not– of if it did materialize, it appears small. The exact same analyses by Zeke, Tamino,, CCC, The Whiteboard etc. all suggest that any biases that might have been introduced by “the march of the thermometers” were quite small. So, while this post shows a potential issue that can arise when applying GISTemps method of computing surface temperatures, the situation where that potential actually creates a real bias does not appear to have occurred.

The article will provide a novel examination of UHI impacts on global temperature trends from the Global Historical Climatological Network (GHCN) using three different proxies for urbanity: subjective classifications of stations as urban or rural in the station metadata, classifications of stations as “dark” or “bright” based on nighttime satellite observations, and the year 2000 population density at the station location via the Gridded Population of the World Version 3 database. All of these represent a single snapshot in time, and don’t show changes in urban characteristics over time. However, if we make the reasonably conservative assumption that areas rarely de-urbanize, the vast majority of UHI effects over the past few decades should appear in those stations classified as urban/bright/high density if these classifications are reasonably accurate.

Before we dive into data analysis, a few bits of housecleaning:

- As always, the latest source code for the spatial gridding model (version 0.8) can be found here: http://drop.io/0yhqyon
- The raw model outputs used to generate all these graphs can be found in an excel file here: http://drop.io/0yhqyon/asset/uhi-xls
- The model has been updated to use the standard NCDC baseline of 1961-1990 instead of the prior 1960-1970 baseline. The net effects of this change on global temp trends should be negligible.

Detecting the UHI signal

Lets start by simply estimating the global temperature using a number of different sets of stations. I’ll divide these into “urban” and “rural” proxies based on their expected effect on the resulting temperature vis-a-vis a run using all stations:

Urban proxies:

• Urban designation
• Bright nightlights
• Airport location
• Population density > 100 people per square kilometer
• Population density > 500 people per square kilometer
• Population density > 1000 people per square kilometer

Rural proxies:

• Rural designation
• Dark nightlights
• Population density < 1 person per square kilometer
• Population density < 2 people per square kilometer
• Population density < 10 people per square kilometer

Note that these are by no means mutually exclusive. We would expect, for example, most stations with a population density of < 1 person to fit into all five of the rural proxies.

You can see the number of stations (wmo_id imods) of each type by year in the figure below:

For population density data (which was kindly provided by Ron Broberg over at the Whiteboard), its worth looking quickly at the breakdown of stations by population density. Here is the cumulative percent of stations (1 = 100%) by population density for < 100 pop density (people per square km):

And < 1000 pop density:

Here we see that over 60% of stations have a population density under 100 people per square km, and almost 90% of stations have under 1000 people per square km.

Now, we tell the model to simply estimate a global temperature using each of these different UHI proxies, to produce this lovely spaghetti graph:

What immediately stands out is that, no matter which set of stations we use, the result isn’t immensely different. Apologies to those convinced that UHI would account for the bulk of modern warming, but that doesn’t seem to be the case at least based on the proxies we have available here.

What you will notice as odd if you look carefully at the graph is that the single highest trending set of stations appears to be those with < 1 pop density! This clearly is not correct, and is due to the different spatial coverage by each proxy. Because there aren’t as many grid cells with stations < 1 pop density as, say, those with dark or urban stations, they end up having a different trend simply by virtue of their location. If we really want to dive deeply into the impact of each of these factors, we need to develop a more advanced model.

Pair-wise comparisons of UHI factors

I added a module to my spatial gridding model that would identify all grid cells with at least x stations of each of a given set of classifications. For example, it can give me all grid cells that contain at least one urban and rural station, or all grid cells that have both low pop density and high pop density stations. This lets me compare trends generated using exactly the same spatial coverage.

I’ll be examining a number of pair-wise comparisons of 5×5 grid cells containing at least one of both sets:

• Urban and rural stations
• Dark and bright nightlight stations
• < 10 and > 100 pop density stations
• < 2 and > 500 pop density stations

However, restricting the cells like this can dramatically reduce the number of grid cells available for use in generating the temperature record. Particularly in the < 2 and > 500 pop density stations case, we end up with very few viable grid cells to use, and this can potentially introduce bias due to the selection of odd characteristics of the cell (e.g. cells that have both very rural and very urban areas with stations might also have other exogenous factors). To mitigate the most extreme case, we also try a 10×10 grid cell model for < 2 and > 500 pop density stations (which gives us twice as many grid cells to work with, each with 4x the area of 5×5 cells):

So lets dive right in and take a look at temperatures from stations categorized as urban and rural in the metadata, using only grid cells containing both:

Here we see that rural stations are noticeably cooler than urban stations. Indeed, for this set of grid cells, the trend in urban stations over the period covered (0.199 C per decade) is 22% greater than the trend in rural stations (0.164 C per decade).

Next comes dark and bright stations based on satellite nightlight designation:

The trends here are quite similar to urban/rural; 0.198 C per decade for Bright, 21% greater than the 0.164 C trend for Dark.

Now we move on to examining population density, starting with < 10 pop density vs. > 100 pop density:

The trend here is 0.209 C per decade for the > 100 pop density stations and 0.182 C per decade for < 10 pop density stations, with the former being 15% larger than the latter.

Finally, we look at two cases for < 2 vs. > 500 pop density stations; 5×5 grids with very sparse coverage, and 10×10 grids with about 7 times more area covered:

For the 5×5 grids, we get 0.253 C per decade for > 500 density stations, which is 35% larger than the 0.188 C trend for < 2 density stations. The difference isn’t quite as dramatic for the 10×10 grids, with the 0.231 C trend for > 500 density only 16% larger than the 0.198 C trend for < 2 density.

We can compare the percent differences in the trends side-by-side:

Now, a word of warning here: just because urban stations appear to be warming 22% faster than rural stations does not mean that 22% of observed warming is due to UHI, because the majority of stations are not urban (indeed, rural outnumber them nearly two to one). Additionally, these graphs don’t really tell us how a rural station compares to a dark station in its effects, for example. Identifying how much each UHI factor influences the overall observed warming is a bit trickier, and that’s what we will examine next.

Multi-factor comparisons

One way to compare the relative effect of each UHI proxy is to look at a small sub-set of grid cells that contain all the proxies we want to examine. For example, we can find between 40 and 100 grid cells for any given year that contain rural, urban, dark, bright, < 10 pop, and > 100 pop stations. When we construct a temperature record from each set, we get:

And we can break down the relative difference in the slope of the subset compared to all stations:

For these grid cells, we see that the urban/rural designation has the most impact, followed by population density and nightlights.

However, these results can be sensitive to the grid cells used. If we look at 10×10 grid cells instead of 5×5 grid cells (which, incidentally, lets us add in < 2 density and > 500 density stations), we get a somewhat different spaghetti graph:

And the effect comparison:

We can look at similar graphs for the max and min temps. Unfortunately, only about half the stations in GHCN provide max and min readings, so we are limited to 10×10 grid cells even for the easy comparisons.

Here are max temps:

and min temps:

Similar to what we saw in the U.S., min temps show considerably more warming than max temps. If we look at the relative breakdown of each proxy, we see that in all cases UHI factors appear to have a greater impact on the min temp than the max temp:

Now, this method of comparing the temperature from all stations to the temperature record constructed using each factor isn’t ideal (though it makes for pretty comparison spaghetti charge), because of the small number of grid cells available where all factors hold.

As an alternative, we can do separate pair-wise comparisons of records generated from all grid cells containing a certain proxy (say, Dark nightlights) using both Dark stations and all stations. The difference in the trend between dark stations and all stations gives us a good idea of the relative effect of the dark proxy while allowing us to keep a large sample size of stations and grid cells. If we do this for each proxy, we get the following:

Oddly enough, < 10 density seems to have a slightly larger effect than < 2 and < 1 density, though this may be due to the rather small sample size of the latter two.

To help put the size of these UHI estimates into perspective, I included the difference between the v2.mean temp using all stations and the land temp records provided by GISSTemp (using their own UHI-correction method) and NCDC (using v2.mean_adj data).

Next Steps

Because the GPW population density data provides information for 1990, 1995, 2000, and 2005, it should be possible to compare direct and measurable changes in population density with station readings. Ron Broberg over at the Whiteboard was instrumental in helping me obtain year 2000 GPW population density estimates for each GHCN and USHCN stations, and hopefully will be interested in collaborating on a project to measure the effects of density changes on temperature trends.

As always, click on images to embiggen.

If anyone has suggestions on other subsets of stations that might capture UHI effects, I’d be happy to take a look.

Update

Per Carrot Eater’s request, here are the 1960-present trends from land stations via GISSTemp, NCDC, and my model’s output for all GHCN v2.mean stations:

• GISSTemp – 0.169 C per decade
• NCDC – 0.221 C per decade
• v2.mean – 0.201 C per decade

“The bulk of the GHCN analysis I have done is exactly this kind of “characterize the data” process. And it finds bias “by altitude”, “by latitude”, “by airport percentage”, and a few others. Those biases do not go away from the data just because someone has a way of fixing it that is not used in GIStemp.”

He is correct that if biases are introduced into a data set for some reason, showing those biases are handled correctly by some method other than GISTemp doesn’t prove GISTemp handles them correctly. Since Chiefio’s beef is specifically with GISTemp, I’m going to examine how GISTemp implements the anomaly method. Specifically, I will be discussing steps 2 and 5 in the Clear Climate Codes version of the program. (For more information on the steps, refer to The Whiteboard.) Step 3 implements gridding and setting to a baseline for ’sub-boxes’; step 5 repeats this to create temperature anomalies for “boxes” . Of course both steps rely on GISTemp doing steps 2 and step 4 being sound (i.e. urban adjustment and merging ocean data); I have not checked those.

My major conclusion will be: In isolation, steps 3 and 5, the “gridding” and “rebaselining” parts of the code appear to be “robust” to “the march of the thermometers” problem. To show this, I am going to explain what they do using a “toy” problem.

Gridding

When discussing this, I will assume that the reader is familiar with the “toy planet” idea from Friday’s post; the purpose of these “toy planet” discussions is to help people focus on the general idea of what GISTemp does, and understand whether an issue could possibly be a problem under any circumstances at all. I also assume the reader is somewhat familiar with Hansen and Lebedeff pdf. In particular, they understand that Hansen and Lebedeff’s method involves dividing the earths’ surface into 80 number of equal area boxes illustrated below:

Figure 1: GISTemp divides the earth's surface into 80 equal area 'boxes'.

Each of the 80 boxes show above is further subdivided into 100 equal area sub-boxes; so there are 8,000 sub-boxes. Each sub-box contains some number of stations, which I will refer to as “thermometers”. Taking the output from GISTemps steps 1 and 2, GISTemp does this:

1. Step 3: Compute the ‘temperature’ in a sub-box from all thermometers in that box. Turn this into a temperature anomaly. (Oddly, for the purpose of entering step 5, this could be skipped.)
2. Step 4: Do something with ocean data. (I’m going to ignore this today.)
3. Step 5: Compute the ‘temperature’ in a box based on temperature anomalies in the 100 sub-boxes.

I’ve used the scare-quotes around ‘temperature’ judiciously. The reason is that the ‘temperature’ exiting an intermediate processing stage in steps 3 and steps 5 are one a somewhat odd impossible to describe baseline. This does not prevent them from being set to an appropriate one in the final operations of steps 3 and steps 5, but it can lead to some confusion if anyone tries to compare these ‘temperatures’ to raw data.

Step 3: Computing the temperature anomaly for a sub-box.

Theory
Section 3. of H&L (pdf) discusses the method of computing the temperature series for exactly one sub-box. The process uses equations 1-3 below, with the average

Figures 2a and 2b: Equations from Hansen and Lebedeff 1987.

with the quantities “T_bar” defined as in HL figure 5 below:

Figure 3: Definition of Tbar.

Application to Toy Model
Recall in Friday’s “Toy Model”, I had a “planet” with 5 pairs of thermometers distributed on 5 continents. The two thermometers in a pair were “near” each other, with one in a cold place, one in a warm place on that continent– I suggested one might be on the top of a mountain; on in a valley. Let’s tweak the idea and think of the 5 pairs thermometers being a “sub-box” with each of the pairs spread around the sub box. Once again, the warm and cold thermometers in a pair are ‘near’ each other. For example: maybe a ‘warm’ one is mounted over an asphalt covered parking lot at Benedictine University while the “cool” one is in a grassy covered field at St. Procopius Abby, just across the street as seen below:

Assume that the crack team of scientists has been monitored these thermometers once each January for 28 years and then for reasons of economy got rid of all the ‘cold’ thermometers, retaining the warm ones; they then continued to monitor only the “warm” thermometers. Meanwhile, the patient Monks at the monastery continued to record temperature at their “cool” thermometer, so it will be available for our analysis with toy data. Now, while I think we can all agree that there could be quality issues with the thermometer over the asphalt parking lot– but the question we are asking today is this:

If the trend at all 10 thermometers was similar, and we use GISTemp to compute a temperature anomaly, would the loss of thermometers in month 29 result in any sudden warm bias in the computed anomaly for this grid?

Let’s step through. Suppose I have numbered the thermometers such that ‘1′ has the longest record and ‘10′ has the shortest records; don’t worry about ties. Now, suppose all the raw data looks like this:

Figure 6: Raw Data From Toy Model.

Note that I made the temperature at “warm 1″ really, really warm. It’s warmer than all the other thermometers. Note in year zero, it’s temperature is near “3″ in whatever units I apply in this toy world. I made this very warm for a reason. Maybe thermometer is in a really, really big, very very heat absorbing parking lot. Also, I generated all this data synthetically and I know all 10 series share an underlying trend of -0.02 C/year.

Given the temperatures from 10 stations above, I could now go through the process of computing the ‘temperature’ using equations 1-3 in Hansen and Lebedeff. The end result of the process is T_1,10(t); that is the quantity on the left hand side of equation 3b but with n=10.

To begin, I need to compute values for n=1. This is a unique operation.

If there at data for thermometer “warm 1″ at time (t), I set T_1,1(t) = T₁(t), where T₁(t) is just the temperatures for “warm thermometer 1″ shown in the figure above. I compute W₁ using equation (2); to do this I need to know the distance between “warm thermometer 1″ and the center of the sub-box, d_i, and the size of my reference distance, D. I’d know d_i based on the latitude and longitude of the thermometer location; in Hansen and Lebedeff this is D=1200 km. After computing W₁, I set W_1,1= W₁ using equation 2. (Basically, the ‘weight’ for the non-existent thermometer ‘zero’ is W₀=0.)

If there is no data at thermometer 1 at time(t), I leave T_1,1(t) blank; (I could actually shove whatever I want in this variable. It will be multiplied by zero later). I then set W_1,1= 0 as in equation (3c).

I know have an array of T_1,1(t), which I can plot. In my toy problem, thermometer one has data for all 60 years and it’s indicated in red below:

Figure 7: T1,1(t) and T1,2(t) computed using equation 3b in Hansen and Lebedeff.

Notice that the initial temperature for ‘thermometer 1″ is near “3″ in whatever the heck temperature scale we are using. (This is a toy model after all.) That’s hotter than any other thermometer.

Next, I need to compute the T_1,2(t), which is the temperature after incorporating in the data from thermometer n=2; in our case, this is “warm 2″. To do this, I

1. 1. Identify times (t) where I have readings from both thermometers 1 and 2. In the next step use compute averages over these specific thermometer readings. ( In this toy example, when incorporating 2nd thermometer (i.e. n=2 ) case, both thermometers provide readings for all 60 years. )
2. 2. Compute the average temperature all thermometer 2. That’s called T_bar₂ in equation (1). Using the same time periods, I compute the average temperature over all computed values for T_1,1(t) I obtained in the previous step. That’s called T_bar_1,1 in equation (1). I subtract to obtain δT₂.
3. 3. Knowing the distance of thermometer 2 from the center of the sub-box, compute W₂ using equation (2).
4. 4. Compute W_1,2(t) using equation 3(a) or 3(c) to for each of the 60 times. In this toy example, I have temperature readings at thermometer 2 at every single time, so I use 3(a) in every case.
5. 5. Compute T_1,2(t) using equation 3(b) or 3(d) for each of the 60 times. In this toy example, I have temperature readings at thermometer 2 at every single time, so I use 3(b) in every case.

At the end of this step, I have incorporated thermometer “2″. This is illustrated with yellow symbols in the figure above.

Interlude
Now, recall that when we looked at raw data, warm thermometer 1 was much warmer than thermometer 2. But, at this stage in the process, the temperatures for thermometer “2″ have been shifted warm. Weird… huh?

This is an intermediate result of the Hansen and Lebedef method. When processing a “sub-box”, as data from each new thermometer, ‘n’ is added to T_1,n-1(t), the temperature from the new thermometer is shifted so that the average of T_n matches the average of T_1,n-1 in the overlap region. This means we are not computing the average temperature of the sub-box. That’s not a problem because no one claims T_1,n(t) is the average temperature in the box. The only thing anyone claims about T_1,n(t) is that it correctly represent changes in temperatures over time.

Back to computation.
In the toy problem I have 10 thermometers, so I need to repeat the process for incorporating temperature 2 with thermometers 3-10. For this toy problem, thermometers 3-5 have data for all 60 years. This means data from these thermometers is incorporated exactly as we incorporated data for thermometer 2. I can keep cranking away without worry about the slightest change until I get to thermometer 6.

Thermometer 6 is the first “cold” thermometer and doesn’t have data after year 28. So, when incorporate data for thermometer n=6, I need to notice this that data only exist at both thermometer during the first 28 years. So, when computing the T_bar₆ and T_bar₅ for step 2, I compute the average over only those 28 years. When I get to step 4, I notice that for early years, I have data at both thermometers, so I use 3(a) and 3(b) in steps 4 and 5. In later years, I use 3(c) and 3(d).

It’s worth comparing T_1,5(t) to T_1,6(t). Note that T_1,5(t) = T_1,6(t) after 28 years, but differ before.

Because this post is motivated by some people’s worries that dropping all the “cold” thermometers in the GCHN record might cause GISTemp temperature to suddenly “jump” when the “cold” thermometers drop out, there are a few things worth noting.

1. Even though thermometer 6 is “cold” relative to the earlier thermometers updating to compute T_1,6 by incorporating the “cold” thermometer into the computed value of T_1,5(t) does not drag the temperature down.

2. There is no “jump” at year 28 in the computed value of T_1,6(t).

Once thermometer 6 is added, we repeat the procedure to incorporate 7-10. The final result is T_1,10(t), illustrated by the blue diamonds below:

Note the following features of the trend at this point:

1. The temperature T_1,10(t) is near the values for “really, really warm thermometer 1″ shown in the figure illustrating “raw” data T₁(t); the process did not seem to produce anything anyone would call an “average” temperature over all 10 thermometers in the grid box. This is because the process isn’t even trying to compute a true average temperature. It just doesn’t care. It wants a temperature that will be set to a baseline in the next step, and then used to compute averages for all stations.

2. T_1,10(t) less noisy that T_1,10(t). Blending to reduce noise is a goal for the process.

3. When computed using all thermometers, T_1,10(t) does have a trend near -0.02 C/century as it should. That is: the method creates a product that captures the correct trend. However, the actual temperatures may be shifted by some constant amount from the real honest to goodness average in the sub-box. We don’t know what that constant is. For the purpose of determining changes in temperatures from year 0 to year 28 we don’t care.

4. When computed using with all cool thermometers dropped at year 28, T_1,10(t) also has a trend near -0.02 C/century as it should. The “march of the thermometers” did not affect this trend.

So, the temperature in the grid box is ok.

Now, suppose we want to turn this into an anomaly based on the average for years 1-20. What do we do? Well, we compute the average temperature of T_1,10(t) based on years 1-20 and then subtract that average from every one of the 60 values of
T_1,baseline(t) = T_1,10(t)- T_average.

This is now an anomaly. The method differs from the one I describe Friday, but it is equally robust to “march of the thermometers.

What about the boxes?

So far, I only described how to compute the temperatures of one sub-box. There are 100 of those in each “box”? How do we compute the temperature for the boxes?

Simple: Use the same process as for computing the temperature of a sub-box, except

1. Treat the “sub-boxes” as “thermometers”.
2. Treat the “boxes” as “sub-boxes”.
3. Simplify eqn (2) in Hansen and Lebedeff with W_n=1 for all n.

Obviously, since the method for computing temperatures of sub-boxes is robust to “march of the thermometers”, the method for computing the temperature of a “box” is robust to “march of the thermometers”. This is true for arbitrary toy data and should be true for real data. The only caveat is that the data for individual stations must be good enough data.

Conclusions: Going forward

I can’t claim to have throroughly tested every pesky thing in step 3 and step 5 of GISSTemp. This is a “toy data” and designed to test precisely one feature: Does a sudden drop out of all ‘cold’ thermometers in and of itself, suddenly inject any bias in the computed temperature trends in GISTemp. Toy data is useful for answering these sorts of questions.

The conclusion stepping through the equations in Hansen and Lebedeff is that if implemented correctly, that the gridding portion of the GISTemp method should be robust to “march of the thermometers”. Specifically, it correct problems that would arise if one did not use an anomaly method when trying to determine whether the earth’s surface is warming overall.

I also examined the Clear Climate Code implementation, and the code text performed the steps I describe above. To the extent that CCC is a faithful re-working of GISTemp, this should mean that gridding in GISTemp should minimize any trend-injection due to a while bunch of cold stations being dropped circa 1980-1990.

For those of you who do believe there are problems with GISTemp, and believe this based on runs posted by The Chiefio, the look for problems in homogenization, infilling or corrections to UHI that are not necessarily specific to any “march of the thermometers”. Then, if possible, describe precisely what feature of data causes GISTemp to “break” and create false trends. Anything that can happen with real data can also happen with properly created synthetic data. So, if you find a feature, we should be able to test that– either by running CCC with synthetic data or by looking at the mathematical descriptions published by Hansen himself.

Right now, it appears that loss of “cold” thermometers by itself cannot inject a warming trend into the data. This demonstration should supplement all the other demonstrations that suggest that when run using real data the mere dropping of warm thermometers does not inject a warming trend into data.

The spreadsheet

AnomalyHansenLedebeff

This makes PEHarvey this month’s top winner: he was who was bang on correct! Congratulations. Spend those quatloos wisely.

I am still able to access the detailed values for version 5.2 here; as usual, I tacked the reading Roy posted for version 5.2 onto the record and plotted temperatures and trends from the inception of the record, since 2000 and since 2001. I’ve also highlighed all Januaries and ran a trace so you can see how many months had temperatures exceeding the most recent one:

Figure 1: UHA TLT with OLD system.

I’m sure you are all wondering what plots using version 5.3 look like. I have no idea. I don’t know the url where those will appear! I suspect Roy will announce that address pretty soon. (Or maybe Anthony Watts beat him to the punch. Anthony’s ear to the ground sometimes seems to know things before anyone else!)

Meanwhile, for those of you wondering if you won any quatloos, the winnings are posted below.

During the discussion of possible bias caused by “the march of the thermometers”, there has also been a lot of discussion of “the anomaly method”, along with people advancing theories about whether or not use of “the anomaly method” guaratees there can be no bias caused by “the marchof the thermometers”. The answer, as in many problem is: Depends on what you mean by “the anomaly method” and how it is implemented. Today, I am going to discuss the anomaly method in its simplest and most ideal form and and explain how, when applied in its ideal form, anomalies can be useful for detecting temperature changes even when we do not know absolute values in temperatures.

To support my explanation, I am going to create a “toy planet”, one which someone has placed thermometers which provide us with time series. The “temperatures” at each thermometer will be generated synthetically. Because the data are synthetic, we will know the trend that would be measured if we could repeat the experiment with an infinite number of thermometers. Then, we will make the someone decides to be more thrifty and reduce the number of thermometers. Using that data, we will estimate the synthetic trend based using the anomaly method. This will be contrasted with using a method based on simple weighting of the thermometers.

The Toy Planet

The “toy” planet will be assumed to be a planet with 5 large continents called each of which consists of mountains and vallies. A crack team of scientists will decide to place two thermometers on each continent with one placed on a mountain and one placed in the valley. These will be called the “cool” and “warm” thermometers respectively.

The scientists will start monitoring temperatures for some unstated reason. During the first 25 years, the scientists continue to support all 10 thermometers, fixing broken ones running QA checks etc. But after a while, someone cuts their budget. Inspecting the data, the scientists decide they don’t need to record the temperatures from all 10 thermometers. To save manpower, they can record the temperature from with 5: one from each continent. Because mountain tops stations are difficult to maintain, they stop recording the mountain top thermometers. (Meanwhile a secret band of conspirators does record those, so we here in toyland can look at those temperatures.)

Then, in year 35, someone advances the theory that the planet is cooling at a rate of 0.2C a year. For the purpose of the toy-problem, this theory will turn out to be correct. (Otherwise, the toy model won’t teach us anything!) Suddenly, the scientists want to figure out if they can detect this based on the data they have.

What to do? We are going to see that if they use the anomaly method the will be able to detect a trend.

Raw temperatures.

Let’s now start to see whether we can detect the temperature trend on this planet. But since this is a toy planet, and the purpose is to explain how anomalies help us do this, I’m going to let the cat out of the bag and tell you that all temperature are generated synthetically, and the trend for the ‘planet’ is -0.2C/year and the raw temperatures from all 10 thermometers for 35 years and the simple weighted average from all 20 thermometers are shown below:

Now, lets focus on the warm and cold thermometers in region 1, including all thermometer readings (whether or not the crack team of scientists recorded them). The temperature in the warm valley, on the cool mountain top and the contentinental average — estimated as the sum over both — are all shown below. Notice all three series exhibit a downward trend. If we fit a straight line, all three series are “noisy” in the sense that the temperatures seem to vary randomly about a straight line. ( Of course, I generated them to do that.)

Note that the trends for each thermometer are shown– as are the trends from all three thermometers.

Temperature Anomalies

Let’s suppose someone suggested that it seemed to him that the trends are all more-or-less similar. He wanted to figure out a way to see if the “noise” at the mountain top and valleys was similar. So, he creates an anomaly as follows: For the “warm” series, compute the average temperature over the first 20 years. Subtract that from all temperature from every warm temperature in the series. Repeat this for the “cool” series, and the average series.

This is plotted below:

(Note: If you compare the trend for the “average” temperature computed using both the anomaly method to the trend based on the “raw” temperature shown in the previous figure, the two don’t match exactly. This is due to a pesky EXCEL feature, which refreshes every time I copy an image! However, if I don’t copy and image and just click back and forth in EXCEL, both trend are always identical because when both series are complete with no dropouts, with respect to computing trends, the anomaly method is no different from the “raw” method. This is true even if, owing to “noise”, the trend from the “warm”, “cold” and average series are not equal to the “known” underlying trend of -0.2C/year. )

Despite the fact that the computed trends will be identical computed using either method, I think you can already see a strength of the anomaly method: Using the “eyeball method”, you can already see that noise is the series is highly correlated. You also begin to detect the fact that the warm and cold thermometers may share a trend. (In this toy problem, they do.) You can also being to imagine that you could make a pretty good guess about temperature at the top of the mountain using the thermometer in the valley. Your guess would be imperfect, but the two are correlated.

For what it’s worth, here ar the temperature anomalies for all 10 thermometers.

Thermometer Drop Out

Now, back to the crack team of scientists. Remember, they didn’t come up with the theory of toy-planet cooling until after they stopped recording temperatures from the mountain top thermometers. Nevertheless, they are interested in testing the theory. What can they do?

Trends based on Raw Temperatures

First, someone could suggest that raw temperatures are the only “thermodynamically meaningful” thing, mumbling words like “enthalpy”. That person might decide that,for this reason, they must, must, must use raw temperatures to do anything and everything. So, they could compute the temperature by simply averaging over all thermometers– never mind that some were at the top of mountains and some at the bottom, and this scientists does not know the readings from the “cool” thermometers after year 25.

The plum colored circle shows what this scientist would compute for the “average temperature” over all thermometers. For the first 25 year, it is equal to the average over the 5 warm-valley thermoeters; for the final 10 years it is equal to temperatuer of the cold thermometers. what this scientist comes up with:

Note that while the average over all 10 thermometers would have shown cooling, averaging over the available thermometers shows warming. This happens when you don’t use the anomaly method. Of course, unless this scientists didn’t look at the mountain and valley temperature separately, this scientist would like notice the problem because he could easily see that both the mountain top and valley thermometer show cooling.

Trends based on Anomalies

So, what if the scientist recognized that he is not doing a thermodynamics problem. He is merely trying to detect whether or not the surface of the earth cooled. He might also want to use the maximum number of measurements available (because that results in less noise). He previously noticed the fact that the anomaly method tended to make all the data collapse around a singal trend. He might decide to do this:

1) Create anomalies for all 10 time series, using the baseline from 1-20.
2) During periods when he has measurements from both warm and cool thermometers, compute the temperature anomaly for each region toy planet by averaging the anomalies from both warm and cool thermometers.
3) When only only 1 thermometer is available, compute the anomaly for the continent using the anomaly from that thermometer.
4) Compute the average for the toy planet by averaging over all 5 continents.

Below, I’ve illustrated the anomalies obtained as if the scientist had access to all 10 thermometers during the entire 35 years, and what he gets if he computed the anomaly with data available to him. (That is: ignoring temperaures from the cold thermometers after year 25.)

Note that by using the anomaly method, the scientists gets much closer to the right answer. The data show cooling; his anomaly shows cooling.

Advantage of Anomaly Method

Examining this problem we can see the major advantage to the anomaly method: When the avearge local temperature varies–as for mountains and vallies– and a database of temperatures over a long time period includes incomplete records, the anomaly method reduces any “warming” or “cooling” bias introduced by adding or subtracting thermometers from warmer or cooler regions.

Does the anomaly method fix everything? No. In this problem, I used synthetic data. When doing this, the synthetic series for every thermometer was generated to give a trend of -0.2 C/century. If I’d made the mountains and valleys warm at different rates, dropping out thermometers would have resulted in bias.

Does this result show that the anomaly method as implemented by GISSTemp, CRU or NOAA cannot have any problems? No. I don’t know precisely how those groups implement the anomaly method. The implementation in GISSTemp is is sufficiently complicated that it needs to be inspected to verify that the method properly. I’m pretty sure Hansen intended for the anomaly concept to be carried forward and applied fully– but I haven’t personally checked this. Moreover, my impression based on Chiefio’s posts is that he thinks something happens during the complicated series of adjustments to prevent the anomalies from being applied fully. So, he would describe the toy problem I show as “a spherical cow”.

Do the results of this analysis mean the only anomalies are “interesting”? No. It means the anomaly method is advantageous when we want to tease out the trend for the earth’s surface temperature from the suboptimal database of temperatures we earthlings are stuck with. In other circumstances, the anomaly method can conceal rather than reveal information. For example, when testing whether or not climate models faithfully reproduce the climate of the earth, the anomaly method can hide problems. For example, if a model matches trends in surface temperature pretty well, but matches the surface temperatures of the earth poorly, a modeler might hide the short comings of his model by highlighting comparisons on an anomaly basis while avoiding comparisons to absolute temperatures. They might, for example, highlight anomaly graphs in summaries for policy makers while relegating comparisons to absolute temperatures to the appendices of longer chapters. An entire community might go so far as to decree that anomalies are the only “interesting” feature, when, in fact, both anomalies and absolute values are “interesting” with each revealing answer to different questions.

Returning to the question that has been perplexing us these past few weeks: Does the march of the thermometers introduce bias into metrics like GISSTemp? As I noted, Chiefio thinks so. It seems unlikely — and more and more unlikely as various people look at data in various ways. That said, I think Carrot Top and Nick Barnes are looking a the clear climate code and tweaking it to run a number of experiments that change the way the code deals with anomalies.

I’m beginning to think a good experiment would be to modify the input to test GISSTemp on synthetic data. I hate to suggest runs and assign the work to the wide world of “someone other than me”. So, I’m almost tempted to figure out how to run Python on my mac and maybe figure out how to change the input files to compute results using “synthetic” data as input to see what happens.

I’ve never run or written Python. It’s going to be warm out this weekend. So, for now: Nah. But, hypothetically, it should be easy enough for a programmer to run CCC or GISSTemp replacing the actual data with appropriately difficult synthetic input and dropping the “cold” thermometers to see if this results in any warm bias. I think that would resolve the question of whether “the march of the thermometers” could even hypothetically result in a warm bias. If a big snow storm hits and people are stuck inside, maybe an eager beaver will do it.

End Notes;

1. EXCEL Spreadsheet: AnomalyNutshell
2. Chiefio’s upcoming post to explain how the march of the thermometers biases GISSTemp. (I think.)

If we are looking at the effect of adjustments and station quality, we should really be looking at maximum and minimum temperature data rather than mean data, because mean data simply averages the max/min temps and a fair bit of information is lost in the process.

Before we dive in to a look at the effects of adjustments (TOB and non-TOB) for all stations and CRN12/CRN345 stations, lets step back and talk a bit about baselines, anomalies, and grid sizes.

One of the downsides of the anomaly approach is that it makes it difficult to compare the magnitude of the difference between anomalies for different series at any discrete point in time. Comparing the trends is easy, but because anomalies are calculated respective to each series, its hard to definitively claim that a particular series was adjusted “down” or “up” relative to another because such statements are highly dependent on the chosen baseline. For example, if a series was not adjusted at all for the first half, and adjusted quite a bit for the second half, a simple comparison of the adjusted and non-adjusted anomalies using a baseline that stretches the whole length of the series would tend to show the adjusted series having lower temps than the non-adjusted series near the beginning and higher near the end, despite the fact that all adjustments really occurred in the second half.

Thankfully, we know from USHCN that most adjustments to the data did occur in the latter part, e.g. via charts like:

(which shows v1 adjustments, but v2 show a similar pattern). To better display the net effect of adjustments over time, I’ve chosen to use a 1900-1940 baseline for all charts that show multiple adjustments to the same series, as that is the period that appears to have the least adjustments in USHCN. For charts that compare two different series I’ll stick with my standard baseline, mostly because there may be secondary effects (e.g. station availability) back that far that make a difference when comparing anomalies generated from differing sets of stations.

When I initially analyzed USHCN data I used the same 5×5 grid as I was using for GHCN. However, upon reading a bit more about the methods NCDC uses in gridding USHCN data I decided emulate their preferred approach of using 2.5×3.5 grid boxes for the U.S. lower 48. Because the U.S. has so many stations, we can afford to lower the spatial resolution a bit without introducing regional biases, and the 2.5×3.5 resolution appears to give us a good tradeoff between resolution and stations per grid box. The net effect of this switch appears to be a slight reduction in the U.S. lower 48 temperature trend vis-a-vis the 5×5 grid boxes:

All U.S. Stations

Lets start our analysis of USHCN max/min temp data by looking at all stations and the sum total of adjustments (TOB and non-TOB).

We see from this that the net adjustments have a much larger effect on max data than min data, have a positive effect on the trends of both, and tend to make the trends of max and min temps much more similar than we see in the raw data. Next lets break down the adjustments a bit and look at max and min one at a time.

For max temp data, the non-TOB adjustments represent the bulk of total adjustments. The net effect of the adjustments is to strongly increase the trend in recent years.

For min temp data, we see quite a different pattern in adjustments. Here TOB adjustments have a slightly larger effect, while non-TOB adjustments are almost negligible. The trend in min temps over the past few decades is much stronger in the min raw data than the max raw data. Lets take a look at how non-TOB adjustments affect the resulting mean temperatures:

From this we can see that the net effect of non-TOB adjustments appears to create a mean trend that is quite similar to the trend in min temps for the U.S.

CRN12 and CRN345 Stations

Now, lets dig in a bit more and look at the same charts for well-sited stations (CRN12) and poorly-sited stations (CRN345) using the designations from SurfaceStations.org utilized in Menne et al.

First we have max temp data for CRN12

And max temp data for CRN345

Before we look at any adjustments, we can see that the trend in raw max data varies dramatically for the two classes of stations. The raw anomaly is only ~0.4 C for the CRN345 stations in the last decade, while it reaches close to 1 C in CRN12 stations! The TOB adjustments are similar for both, though slightly higher for CRN345 than CRN12. The non-TOB adjustments actually slightly decrease the trend in CRN12 stations, while fairly dramatically increasing the trend in CRN345 stations. Taken together, the net effect of the max temp adjustments to CRN345 stations is to make the adjusted CRN345 max temp record quite similar to both the raw and adjusted CRN12 max temp record. Now we turn to min temps, which are a bit more interesting.

Here are min temps for CRN12

And min temps for CRN345

Here the roles are reversed; raw min temps have a much lower trend in CRN12 data than CRN345 data, reaching only slightly below 0.4 C in CRN12 and to almost 0.8 C in CRN345. At first I thought somehow I must have switched up the data, but upon double checking it is indeed correctly plotted. Again, the TOB adjustments are similar in both sets, though again noticeably larger in min CRN345. Its the non-TOB adjustments that reveal a more perplexing picture.

The non-TOB adjustments in min CRN345 reduce the trend slightly, and seem to be quite similar to the non-TOB adjustments we saw in max CRN12.

We see a large positive non-TOB adjustment in CRN12 min data. If we look closer, it appears to mainly be a step-change in the data in the 1940s:

The net effect of all adjustments is, again, to make the CRN12 and CRN345 min temps much more similar, though in the opposite way that we saw for max temps.

Now lets try our hand at replicating the first half of Figure 2 in Menne et al 2010:

First we need to change the baseline to 1979-2000, which is fairly trivial.

Lets look at max temps first,

both Unadjusted Maximum

and Adjusted Maximum.

Now min temps, Unadjusted Minimum

and Adjusted Minimum

All of these charts are almost identical, as far as I can tell, to the results of Menne et al. (albeit with 2009 data added).

Finally, lets look at the trends (in degrees C per decade) over the 1980-2009 period for each:

CRN12 max raw : 0.224
CRN345 max raw: 0.082
CRN12 max adj : 0.243
CRN345 max adj: 0.255
CRN12 min raw : 0.126
CRN345 min raw: 0.177
CRN12 min adj : 0.186
CRN345 min adj: 0.210

This suggests, at least for the subset of stations examined, that either poor siting or a secondary factor (e.g. MMTS vs. CRS sensors) led to spurious cooling of maximum temps in recent decades. It also suggests that adjustment methods tend to make CRN12 and CRN345 records more similar.

Note: Click on charts to embiggen

Raw data for all of these charts can be found here. They are contained in the USHCN minmax and Menne minmax tabs (as well as the USHCN gridsize tab for that chart).

UPDATE (3/5/10)

Matt Menne was kind enough to chat with me this morning about some of the relationships between raw, tob, and adjusted data.

Among other issues, he explained how MMTS sensors report systemically lower max temps than Stevenson Screens (CRS), so the switch from CRS to MMTS sensors over the past few decades introduced a spurious cooling trend in max temps. This is one of the reasons, according to him, that raw/tob temps from CRN345 stations (which are primarily MMTS) and CRN12 stations (which have a much higher percentage of CRS sensors) have differing trends in max temps in recent years.

As far as then 1940s step change in CRN12 min temps goes, he suggested that this was due at least in part to the movement of a number of stations from urban areas/surfaces to more rural areas during the world war 2 period. He mentioned that he had observed such moves in some of the CRN12 stations that he had looked closely at, and recommended that interested observers should undertake a more systemic look at the station history for CRN12 stations at the time to check for station moves during that period.

Its worth noting that if the 1940s step change in CRN12 min temps was indeed associated with station moves and we accept it as correct, the TOB min temp data for CRN12 stations becomes similar to that of CRN345 stations:

Note that the step change was removed by simply adding 0.4 C to all annual temps after 1945 for CRN12 stations.

Dr. Menne also confirmed that TOB adjustments tend to be applied similarly to max and min readings, and that non-volunteer stations (e.g. airports) tended not to require TOB adjustments because of standard reporting times, while co-op stations (which often are more rural) were more likely to have differing thermostat reading times that necessitated TOB adjustments.

That said, the three may have mad such a claims appear to be EM Smith, Joe D’Aleo, and (possibly) Anthony Watts. A document by “D’Aleo (pdf) and an SPPI publication by D’Aleo and Watts, suggest the analysis to support the claims about warming biases in temperature anomaly records arising from the march of the thermometers was done by Chiefio (EM Smith.)

Possibly, the actual argument about bias arising from the march of the thermometers is either more limited or more nuanced than it appears to those of us reading various pdfs, watching tv or sifting through blog posts. For this reason, I am taking Magic Java’s suggestion and inviting Chiefio to clarify his thoughts on this matter. I have extended the invitation as follows:

Hello Chiefio,

Magic Java has requested that I invite you to guest post your response to the analyses by Zeke, Tamino, ClearClimateCode and Roy Spencer, each of which has investigated the effect of the 90’s loss of thermometers on any bias in computed temperature anomalies. I think this is a good idea, and would like to invite you to guest post, if you are interested.

If you do accept, I would actually like to invite you to do two guest posts. In one, I would ask you to answer some very specific questions of my own devising. These may be questions you do not wish to answer– as they will put you on the spot. The other would simply invite you to post your response to the analyses of others. My most specific interest is to see and understand why you think the loss of thermometers has resulted in an actual warm bias in products like CRU, GISSTemp and NOAA’s surface temperature products for large areas of land. That is: I am interested in the effect averaged over areas as large as the US , the full Northern Hemisphere or the Southern Hemisphere.

With this in mind, I extend and invitation and hope you will take it up either at my blog, or at yours.

Thanks,
Lucia Liljegren

With some luck one or two guests posts will clarify Chiefio’s position on this. Afterwards, we may be able to query key people’s positions as well.

Update Feb. 4 Chiefio politely declined the invitation to guest post, citing the need to focus on his own research. He evidently continue to post at his blog, engaging those points he considers important.

As many climate-blog addicts are aware, weather is not climate. While we are all busy arguing whether this years DC snowstorm was caused by climate change, those in DC were probably just thankful for online services like AccuWeather which could give them advance warming about impending snowmaggedon.

Today, I was lucky enough to learn of Accuweather’s new site, which is still in beta.

Visiting, I entered my zip code to learn it’s a sunny 38F in Lisle; temperatures will drop to 24F tonight. More importantly to me, the monthly forecast predicts we’ll hit the 50s late in March. This means I may finally be able to erect my portable green-house and start some of the less tender annuals soon. I’m planning to buy seeds and potting soil this week. I start these in the window, but I do like to have some advance indications of weather conditions plant schedule actually starting the seeds accordingly. (Lucky for me I’m not planning to go to Florida; an Accuweather story also warns “Breaking Weather: Chilly for Spring Breakers”.)

The site also has some useful forecast maps for the lower 48, including forecasts for rain, snow, UV, windchill, heat index and a number of other indicators as well as slick radar and satellite weather displays of current weather equipped with both “zoom” and “play” features.

But enough about the weather! Accuweather now also links to their a global-warming area, which provided links to Brett Anderson’s blog. Guess what? The first comment on the most recent blog was placed by Patrick AKA Cyclonebuster! If you visit, you can have a chat with our old friend.

I’m now trying to put together a time-line of the more major milestones; as much as possible, I’m going to avoid editorializing. The initial milestones will focus on the meme itself. Later events will include spin-offs as people who appear to have dispensed with the notion that dropping thermometers from the record may have introduced bias begin to explore other issues that might have introduced bias. (These include UHI, siting issues, adjustments for TOBS etc.) In invite readers to suggest some items to contribute to the timeline. I’m mostly interested in: Television coverage, more formal glossy documents (SPPI etc.), blog posts containing analyses rather than mere commentary, coverage by players directly involved, (hese seem to be mostly EM Smith and D’Aleo.)

I’m going to throw out what I have, along with dates, and I hope some of my readers can fill me in with posts, dates, major actors and others in the discussion of this meme.

Meme introduced?

Chiefio August 17, 2009. I don’t know if this post introduced the meme, but way back in August, Chiefio muses

We are still left with the fact that we move about 1/4 of the thermometer records from the cold places to the hot places. That not only increases the impact of the hot places, but reduces the impact of the cold places.

For a time, the notion seems to be discussed in comments, forums and blog posts at various places, but it does not hit the mainstream news.

The Meme Goes Formal

KUSI News Story broadcast Jan. 14, 2010, cover D’Aleo article “Climategate: Leaked Emails Inspired Data Analyses Show Claimed Warming Greatly Exaggerated and NOAA not CRU is Ground Zero”(pdf); this very brief document is written by D’Aleo. The videos discussing the theory that loss of thermometers results in a bias in temperatures are here. D’Aleo and Smith (aka Chiefio) are interviewed.

SPPI January 23, 2010. SPPI publishes Surface Temperature Records: Policy Driven Deception? written by D’Aleo and Watts. The station drop out issue is discussed on pages 9-23. EM Smith (Chiefio) is heavily cited as the source for claims and analyses arguing that the changing number of stations biases the surface temperature record. Discussions of other adjustments focusing on Urban Heat Island and station siting issues follow; this portion of the documents heavily cites Anthony Watts surfacestations.org project and WattsUpWithThat.

Zeke Hausfather, January 21, 2010 posts a graph comparing the simple average temperature anomaly from 1,017 thermometers with data available through 2000 to 402 that stopped providing data sometime bewteen 1970 and 2000. He finds no singificant difference between the two traces suggesting that station drop out is not an important source of biase.

Roy Spencer Feb. 20, 2010. Roy Spencer computes trends using data drawn from the NOAA-merged International Surface Hourly (ISH) dataset, a ground based thermometer record. Using area weighting, he compared land based temperature anomalies for the northern hemisphere computed thermometers in operation from 1986-2010 to trends published by CRU. He finds no difference in trend– though the monthly data from the ISH dataset appears noisier.

Chiefio (E.M. Smith), Feb 22, 2010: elaborats on the KUSI – Coleman TV show discussion which covered the story that dropping thermometers from the temperature record results in a warming bias in surface temperature anomoalies reported to the public. The theory is summarized as

My major point has simply been that much of the available data is not used. It is dropped on the floor. You can call it “deleted” or “dropped” or “ignored” or whatever. It is still NOT in the GHCN data set. The pattern of these “droppings” is that high latitude and high altitude stations are dropped, while low altitude and low latitude stations are kept (with an ever increasing percentage at warm heat islands of airports). There is a clear ’survivor bias’ toward warmer stations (and with warming trends, like airports), with warmer winters, more heat islands, and lots of tarmac.

Smith also responds to those who suggest that dropping thermometer will have little effect, noting there are two reasons advanced for likely non-impact of dropping stations:

First, that there is no person actively pruning thermometers. While the “spin” put on my position has tended to say there is active intentional removal of thermometers for malicious effect; I have gone out of my way to point out that I can not know any person’s intent, only the result. [...], I’m more interested in the FACT of the thermometer deletions (or drops) from the record and what that says about data bias; than about whether there has been a sin of omission or of commission. It’s a sin in either case. Was it murder or involuntary thermometer slaughter? In either case “It’s dead Jim”, and it’s wrong.

So, using the rather vivid allusion to murder, it appears Chiefio is suggesting the bias due to dropping thermometers could be unintentional. Some colorful allusions are also used when countering the notion that use of the anomaly process protects against bias when thermometers are dropped from the record:

Second defense, that the “anomaly” process will prevent thermometer drops from having an impact. ( This is usually followed by a theoretical example of comparing a thermometer only to itself and showing that with perfect anomaly processing and an idealized unbroken record, there is no problem.) But the reality is that we don’t compare thermometers only to themselves and the records are horridly broken and with massive “fill in” with fantasy “data”. So we have “fantasy basket A” to “fantasy basket B” that change over time.

Well, thermometer change / drops / deletions DO have an impact. I’ve run a benchmark through the GIStemp code and using exactly the stations GISS dropped (from the USHCN data from 5/2007 to 11/2009 -when they put them back in, after some postings pointing out how to do it and that it was an ‘issue’… – perhaps just a coincidence…) and the anomaly map shows warming from those station being dropped. We can argue about the price of this streetwalker, but what it does is not in dispute.

The reason it fails to stop all survivor bias impact is two fold. One fixable, one less so.

First, it does not do the anomaly comparison “self to self” [ I call that "selfing" after the pollination process ] but rather “Basket A in time A” to “Basket B in time B”. And once the two things being used to create an “anomaly” are different from each other, you have opened the door for a variety of very subtile biases to change the result. This, too, is not in dispute. (Well, it is by some who are a bit slow to catch on, but it is not in dispute by the folks who wrote the code. One of the NASA FOIA emails admit to this problem and bias.)

The second reason is rather subtile, and it is one I’m “in discussions” about publishing; so I’ll not make it public until some decision is reached on that front. ( I may tire of the whole backbiting “peer reviewed publishing” process and just go for “public reviewed self published”. That is my leaning, but folks keep telling me it’s important to be “in the literature”… We’ll see.) Lets just say that it depends on some assumptions everyone makes that are wrong, and looking at what is ignored. It will impart survivor bias into the First Differences Method, and the Reference Station Method. I believe it will impart bias into the Climatology Anomaly Method as well, but the definition of that method might allow for an approach that would dampen the bias (i.e. “perfect” selfing and lifetime), so I have a bit more homework to do before asserting it as fact for all variations. Basically, for any system where the thermometers change over time, it allows for bias to show in the product. And that’s as far as I can go on that point right now. It is this property that, IMHO, lets the benchmark change for GIStemp.

The bottom line is that survivor bias from thermometer change matters, and there has been a heck fo a lot of biased thermometer change.

I’d snip the above for brevity, but I couldn’t figure out how to do so while still convenying Chiefio’s intended point.

Tamino, Feb 23, 2010 presents preliminary GHCN temperature analyses comparing area weighted temperature anomalies for the Norhern Hemisphere based on “cut-off” thermometers series and data from thermometers that remained in the record to the present time. He finds no significant difference between the two traces.

Clear Climate Code, Feb. 26, 2010 compares GISSTemp type calculations of global surface temperature anomalies based on the “full” and “cut-off” thermometer set. They find no major differences between the two traces.

The Blackboard March 1, 2010, Zeke kindly posts his weighed average of thermometers at my blog. He requests feedback and suggestions for improving the analysis. His post also begins to address “spin-off” issues like UHI, TOBS etc.

Chiefio, March 1, 2010. Though many others are finding it difficult to discern any quantifiable effect of loss in stations, on March 1, 2010 Chiefio has posted a discussion of what he calls “The Smith Effect”– that is the step function in temperatures associated with drop outs in thermometers. What is “The Smith Effect” or it’s cause? Chiefio tells us:

I will not be discussing what the theory is behind The Smith Effect. At least, not until I’ve found out if it’s going into a paper for publication, or not. Once that is resolved, I’ll either post the details here (if it’s not going to publication) or post a pointer to the publication (so we all can sit on pins and needles waiting

So, we have to wait sometime before we read Chiefio’s full response.

If I’m not mistaken, those are the main posts that directly adress “the march of the thermometer” meme. But, I do ask readers, Do you have more “march of the thermometer” milestones to add to my timeline? I’d love to read them.

Spin off: Temperature reconstructions.

I’m also seeing some interesting spin off posts. These seem to be starting to the types of issues in the second half of the SPPI document authored by D’Aleo and Watts, and which tended to link to Watts’ blog and web site. That is, they seem to be mentioning UHI, station citing and issues surrounding adjustments. The posts share similarities with “the march of the thermometer” posts in so much as they are creating reconstructions– but they differ in the specific comparisons made.

I’m going to discuss some of the spin-off posts below.

Roy Spencer , February 27th, 2010 examines US air temperatures time series extending back to 1973– a longer record than treated in his previous post. He compares Jones CRUTemp3 temperature analysis which is computed using (Tmin+Tmax)/2 from approved GHCN stations whose number change over time, to a new temperature anomalies series which Roy computes based on a larger groups of ISH thermometers samped at 06, 12, 18, and 00 UTC. Roy series is based on thermometers that operate through out the entire period. When comparing the two series, Jones CRUTemp3 exhibits a brisker warming trend than Roy’s new series; the difference amounts to 20% of all warming from 1973 forward.

I don’t think Roy’s analysis can reveal the cause of the differences in trends. Investigation of CRU code, lists of stations, and underlying raw data might reveal details and permit sensitivity studies to discover precisely what aspect of adjustments or addition and subtraction of individual stations might be the cause of differences in warming trend computed both ways.

The Air Vent I’ve been searching for other discussions. Jeff Id and Roman R appear to be working on creating temperature anomaly time series using “GHCN and Roman’s seasonal offsetting method”. Perhaps when they are satisfied with their method of weighting, they will post results comparing trends with a fuller set of thermometers compared to CRU. Equally likely, they will focus on other factors like UHI, TOBS, and the sorts of factors that have interested many of us for a long time.

For the time being, JeffId did post a trend from 1978-(now?) based on their gridded product. They find the trend in the global temperature anomaly to be 0.186C/decade which they indicate is a drop from some previously computed product. (I don’t know what the GHCN trend is when computed other ways.) Jeff alerts readers their current series is still affected by UHI, siting issues, TOBS and other features.

If any of you can fill me in on additional milestones in “the march of the thermometers” meme and/or find additional discussion of reconstructions, let me know in comments. I’m very interested in figuring out how this all played out at think-tanks (SPPI), tv and blogs!

Say hello to march
Brave daffodils show green tops,
soon yellow flowers.

Anthony discussed daffodils not yet blooming in England. Mine aren’t blooming yet either. I don’t have any idea how early they bloomed in April.

The latest version of the source code is available in the Temp_Analysis zip file here: http://drop.io/0yhqyon

The model goes through a number of different steps to generate a grid-weighted global (or local) anomaly:

1. Import the data files. Currently the model has been used to import GHCN raw, GHCN adjusted, USHCN raw, USHCNv2 TOB, and USHCNv2 adjusted data, but it should be easily adaptable to any set of temperature data.
2. Assign each station to a 5×5 lat/lon grid. This is accomplished by two for-loops that go through each 5-degree increment of latitude or longitude and check to see if each individual station is contained in that increment. If it is, it assigns the midpoint of the range as the station’s lat or lon grid value. Once these loops are complete, it concatenates the lat and lon grid value for each station to a gridbox identifier.
3. Weight each grid box by its area. This uses the equation grid_weight = 4 * _pi^2 * 6378.1^2 * cos(lat*_pi/180) * 5/360 * 5/360 sin((latgrid+2.5)*_pi/180) – sin((latgrid-2.5)*_pi/180) to calcuate the relative size of each grid box based on the midpoint (thanks RomanM!). I got this equation from Gavin for interpreting GISS Model E outputs, though he mentioned that it was an approximation and not perfect. If anyone has a suggestion for a better way to calculate 5×5 lat/lon grid box areas, please let me know.
4. Optionally apply various filters for different analysis. Filters include restricting stations used by latitude, longitude, country code, U.S. state, urbanity (for GHCN data only right now; don’t have a good urban indicator for USHCN data developed yet), station start year, end year, and duration of station record, as well as custom filters to replicate the Menne analysis and Long document.
5. Combine multiple imod records into a single wmo_id record for GHCN data. GHCN has multiple records associated with a single station ID in a number of cases, and this step simply averages all the records available for each station_id. It occurs after the filters are applied, so if you only want to look at rural stations, it won’t combine a rural imod with an urban imod in the rare case that a single wmo_id has both rural and urban records associated with it. In general, the wmo_id / imod differentiation has to do with cases where a station was moved or stopped reporting and was replaced by a nearby station, and mostly applies to locations outside the U.S. This step does nothing at all for USHCN data.
6. Calculate the anomalies for each month at each station relative to the 1960-1970 base period, and discard any stations with < 10 years of temp data per GHCN methodology. This also discards all wmo_ids without a record in the 1960-1970 period. This is the part I’d like to improve, since it reduces the stations available by about 15% in GHCN data. Note that this has no real effect on USHCN data, since virtually all stations reporting currently have data from the 1960-1970 period.
7. Average the anomaly of all stations in each grid cell for each month to obtain the grid cell anomaly.
8. Calculate a grid-weight for each month of each grid cell in each year, where the grid weight is equal to the cell’s grid area divided by the total grid area of all grid cells available for that month.
9. Multiply the each grid cell anomaly by the grid weight for each month of each year and sum up the results across all grid cells to obtain the average by month.
10. Calculate the annual average anomaly via a weighted average of each monthly anomaly by the number of days per month, taking leap years into account.

We can do some initial validation (to make sure things aren’t too screwy) by comparing GHCN raw data to GISSTemp land temperatures. Note that we don’t expect this to be perfect, because GISS adjusts GHCN data (and actually lowers the global temperature vis-a-vis the raw data, as both this analysis and a similar one by Jeff Id show). The Rural/Urban designation here is based on GHCN station metadata; it may not be perfect, and we can try other collections of stations that we identify as rural or good if we want (indeed, we do this with CRN12 stations in the U.S. later on).

We can also compare stations with records post-1992 to those without, to quickly replicate the work that Tamino and the CCC folks did on addressing E.M. Smith’s whole station dropout arguement:

Since no one has looked into it yet, we can consider the case of Northern Canada and see if station dropout there has had any effect on temperatures:

Lets take a look at just the U.S. for a bit, since its where a lot of the criticism of temperature data has been centered.

We can start by looking at Raw and Adjusted GHCN data stations in the U.S. Lower 48:

And break these stations down into Rural vs. Urban (using an 11 year running mean to smooth out some of the noise):

In addition to the 400 or so GHCN stations in the U.S., we also have access to 1200+ stations in USHCN. Lets incorporate those into our model, and look at raw GHCN, adjusted GHCN, raw USHCN, adjusted USHCN, and GISS for the lower 48 U.S.:

Since GISS uses adjusted USHCN as an input (and further tweaks it), we should expect those series to be quite close. Indeed, we find:

USHCN and GHCN use somewhat different adjustments for Lower 48 U.S. stations. Lets compare them:

Now, USHCN doesn’t have a simple Urban/Rural designation in the Metadata. I’m working on trying to figure one out from the station landuse data, but for the time being we can use Anthony and the SurfaceStation.org effort as a first pass (essentially replicating the work of Menne et al 2010). Here are all 71 CRN12 stations compared to the CRN345 stations:

Similar to Menne et al, we find that “good” CRN12 stations have a slightly higher anomaly than the “poor” CRN345 stations using the raw USHCN data. We can also take a look at the adjusted USHCN data. There are two primary adjustments made to USHCN raw data in USHCN v2: time of observation (TOB) adjustments, and urbanization/discontinuity adjustments. Here are CRN12 stations for all three datasets (raw, TOB, and fully adjusted).

The majority of the adjustments that occur are TOB-related, but there are also non-TOB positive adjustments to the “good” stations, which is interesting. Lets compare this to the adjustments made to CRN345 stations:

Here we see that both the TOB adjustments and the additional adjustments are larger for CRN345 stations than for CRN12 stations, which is a good sign. The difference between CRN12 and CRN345 stations in each dataset bears this out:

After each round of adjustments, CRN345 stations become closer to CRN12 stations. However, the net adjustment to both stations are still positive, for both TOB (which is expected) and non-TOB adjustments. Lets looks at the non-TOB adjustments done to CRN12 and CRN345 in more detail:

Anyhow, thats it for now! If you have suggestions to improve the model, or things you are interested in seeing analyzed, let me know. Also, please download the source code (if you run STATA) or work with me to port it over to R (if you don’t) so you can play around with it yourselves.

Also, click on images to embiggen! And thanks Lucia for giving me a chance to do I guest post on my recent work.

Supposedly, if you have previously posted comments, you will not notice anything. If you have not previously posted a comment, the plugin will send an email to the email you list, and you will be required to respond. After that, you will be whitelisted.

I haven’t plowed through the plugin-code to verify that it actually works as advertised when first activated. I’m worried everyone is going to get an email. If a few of you could try commenting, let me know what happens…. (I’m going to put up a few tests too.)

Update

This comment doesn’t seem to moderate comments when people use new emails. I turned it off.

In that thread, Zeke described a simple model to spatially grid and weight temperature data, and has asked for help improving it”

The latest source code is available here:
The folder name is Temp_Analysis v0.3.zip.
It should easily support importing either GHCN or USHCN data now (or, frankly, any temperature data you want).

Zeke posted output for the code in comment Comment#35622:

Oh, and for those interested, here are the raw vs. adjusted data for the U.S. for all the different series:

http://i81.photobucket.com/albums/j237/hausfath/Picture68.png

And comparing USHCN adjusted to GISS:

http://i81.photobucket.com/albums/j237/hausfath/Picture69-2.png

New Thread!