The GLOBAL global warming signal



Global warming involves warming of the whole globe (the clue is in the name), but it does not necessarily affect every part of the globe at the same rate.

Different parts of the globe can experience very different changes under greenhouse warming. As a result, if you want to measure global warming, you have to measure the whole globe, not just a part of it. But of the three main in situ temperature records (GISTEMP, NCDC and HadCRUT), only GISTEMP is near-global in coverage over recent decades, and only by means of allowing each weather station to cover a larger region of the map. The incomplete coverage of the Hadley and NCDC datasets may be seen in Figure 1, along with three global temperature reconstructions.

Figure 1: Coverage maps for various temperature seriesFigure 1: Coverage maps for various temperature series. Colors represent mean change in temperature between the periods 1996-2000 and 2006-2010, from +2C (dark red) to -2C (dark blue). Note that the cylindrical projection exaggerates the polar regions of the map.

In this article I will attempt to redress the balance by presenting 16 new versions of the temperature record (10 of which I consider to be realistic), each of which has global or near-global coverage. Thirteen of these are created by creating a composite of a non-global series (HadCRUT3/4, NCDC or BEST) with a global series (GISTEMP, UAH or the NCEP/NCAR reanalysis). The remaining three series are derived by extrapolating the HadCRUT3/4 and NCDC data.

As with my previous article, these results have not been subject to peer review and should be treated as tentative. However the diversity of methods and consistency of the results are strongly suggestive.

Summary of results

I will start by summarizing the results, and then describe the methods and data in detail.

Since the main impact of incomplete coverage is seen in recent temperature trends, we will start by looking at these. The trend over the 15 year period 1996-2010 is shown in Figure 2 for each of the 16 new temperature series (colored bars), compared to the official versions (white bars with coverage percentages superposed). Some of the temperature series have known problems, however two clusters of likely trends have been identified; I have named these the GISS cluster (due to similarity with GISTEMP) and the Had4 cluster (for series based on HadCRUT4).

Figure 1: Global temperature trends 1996-2010 Figure 2: Global temperature trends 1996-2010

The global temperature records from these two clusters are shown in Figure 3, along with GISTEMP, NCDC and HadCRUT3 using a 60 month moving average. Use the buttons below the graph to select between 30- and 60- year views. The records are also available as a .CSV file which may be read into any spreadsheet program.

Figure 2: Comparison of official and global temperature series
Figure 3: Comparison of temperature series 1950-2010 1980-2010

The 15 year trend (1996-2010) for the GISS cluster of 6 temperature series is 0.147°C/decade (this is the value for NCDCext,  chosen because it is unaffected by the HadSST2 1998 discontinuity). However there has been a tendency towards more frequent La Nina conditions over the period, which has impacted this trend. Foster and Rahmstorf (2011) estimate this influence at -0.026°C/decade, so the underlying warming trend is 0.173°C/decade. This is comparable to the 0.17°C/decade long term trend found by Foster and Rahmstorf. (They also estimate a net cooling effect due to the solar and volcanic influences, however these terms are less well determined and so I have omitted them.)

The 15 year trend (1996-2010) for the Had4 cluster of 3 temperature series, each of which includes the new HadSST3 bias corrections, is 0.179°C/decade (for HAD4ext). Including the El Nino term, the underlying warming trend is 0.205°C/decade.

The two representative trends quoted above are conservative estimates and include a known cool bias due to smoothing - the other trends variously include known cool and warm biases. There is additional evidence for each of these biases, but they have not yet been quantified.

The problem

I have presented 3 articles on the subject of coverage bias - HadCRUT3: Cool or uncool?, GISTEMP: Cool or uncool? and HadCRUT4: Analysis and critique. The most important issues are as follows:

How can this problem be addressed? Two approaches are explored here. We could use a globally complete dataset, such as the  GISTEMP extrapolated data, the UAH satellite data, or the NCEP/NCAR reanalysis data to fill in the missing regions of the map. Alternatively, we could simply extrapolate the Hadley or NCDC data to fill in the missing regions of the map. We will consider each of these approaches in turn.

Coverage completion using two datasets

In HadCRUT4: Analysis and critique I showed how the GISTEMP or UAH map data could be used to estimate the coverage bias in the Hadley datasets. The basic method was to work out how much the GISTEMP (or UAH) temperature estimate for any month would be biased if its coverage were reduced to match the corresponding month from the Hadley dataset (with one caveat - the map series need to be adjusted to have the same baseline period).

But if we know how big the bias is, we can correct for it by subtracting the bias term from the biased data, and thus create an unbiased temperature series. To do this we need two temperature series:

Map series are required for both datasets. The maps from the time series are used to determine a coverage mask for each month, and a (biased) global temperature estimate. The maps from the coverage series are used to determine the coverage bias. Temperatures for the coverage map are calculated with and without the mask - the difference between them is an estimate of the coverage bias.

There is an alternative (mathematically equivalent) way of looking at this method. We are taking the map from the coverage series, and adding a constant to every cell so that the mean of the map matches the mean of the times series map over cells where they both have coverage. The average over the whole of the adjusted coverage map then provides the unbiased temperature estimate.

It should be clear that we can add or subtract a constant to every cell in a map for the coverage series - and thus adjust the global temperature for that series up or down for any month - without affecting the result. Thus temporal instability or bias in the coverage series does not affect the results. The only factor which affects the results is the difference in mean temperature between the masked region and the whole map.

I have performed this calculation using 4 time series and 3 coverage series. The time series are as follows:

The coverage series are as follows:

These datasets allow the construction of 12 composite series. These have been named using a composite of the name of the time series followed by the name of the coverage series, i.e. HAD3giss, HAD4giss, NCDCgiss, BESTgiss, HAD3uah, HAD4uah, NCDCuah, BESTuah, HAD3ncep, HAD4ncep, NCDCncep, BESTncep.

One additional issue arises with the BEST time series data. Since the BEST data is based on land stations and covers land areas only, to make a realistic assessment of bias, the common coverage region of the coverage series map must be defined in the same way. In the GISTEMP land-ocean data and in the UAH and NCEP data, coastal cells contain a hybrid of land and ocean temperatures, which prevent the calculation of an uncontaminated land-only series. This leads to an undercorrection, and so an overestimate of the resulting trends. To address this issue I constructed one additional composite series - BESTgiss2 - in which the common coverage temperature for GISTEMP was constructed from the GISTEMP land-only data (i.e. the dTs 1200km dataset).

Extrapolating a single dataset

The simplest approach to improving the coverage of a temperature series is to fill in any map cell for which no observations are available with the temperature from the nearest cell for which an observation is available. Omitting the cell completely is mathematically equivalent to setting it to the mean value for the whole map. The reasoning for using a nearby value is that this is likely to be a better estimate of the temperature than the value of the more distant cells which comprise the bulk of the map. Like GISTEMP I have imposed a maximum distance limit of 1200km, which is enough to provide near complete coverage for most of the last 60 years.

GISTEMP uses a related but more sophisticated approach of allowing each station to influence an area of radius 1200km around the station, with a weight that decreases with distance. This is a form of kernel smoothing.

These methods are not without their own biases. If the missing region represents an extreme of temperature anomaly, then the global average from the incomplete data will be biased, as shown in Figure 4. Kernel smoothing introduces two effects - firstly it flattens out both high and low extremes (which doesn't introduce a bias in the global average), and secondly it extrapolates from well populated regions into sparsely populated regions (which does). As a result, GISTEMP and GISTEMP-based temperature series (see below) may be expected to have a cool bias.

Figure 4: Bias due to nearest neighbor or kernel smoothing Figure 4: Bias due to nearest neighbor or kernel smoothing

Can this cool bias be confirmed from the data? GISTEMP provide two datasets based on land temperate stations only: dTs 1200km and dTs 250km, which differ in the area of influence of a given station. The 250km radius dataset should show less smoothing bias over the region where both datasets have coverage. Temperature series were therefore calculated for both series over the region where they share coverage, and the trends on the period 1996-2010 compared, with the following results:

GISTEMP dTs 250km: 0.312°C/decade
GISTEMP dTs 1200km: 0.284°C/decade

Note that this bias only applies to temperatures estimated from land stations, but does not account for regions where there is no coverage and thus no bias estimate is available. Therefore at this stage the total impact of this bias is unknown.

The extrapolation approach allowed the construction of 3 additional series, named using the name of the time series and the suffix 'ext', i.e. HAD3ext, HAD4ext, NCDCext. Extrapolation cannot be applied to the BEST data due to the lack of maps and the small starting coverage.


The trends in °C/decade on the 15 year period 1996-2010 (with the previously noted caveat for the BEST data) are given in the following table for all 16 new temperature series. Values I consider likely to be unreliable are given in italics.


The following details are noteworthy:

The outlier temperature series (i.e. the ones I suspect are unreliable) are shown in Figure 5. BESTuah highlights the problem of undercorrection when using UAH for infilling - the BEST land-only series overestimates recent warming, and UAH does sufficiently correct for this. The NCEP corrected series also show higher rates of warming over recent decades - this could reflect the fact that they avoid the smoothing bias of the other series, but my working hypothesis is that there is an unindentified problem in using the reanalysis data in this way.

Figure 4: Outlier temperature seriesFigure 5: Outlier temperature series

The remaining series, BESTgiss2, is shown in Figure 6. This provides an indication of what a future BEST land-ocean temperature series might look like (assuming that the HadSST3 bias corrections are not included). This series shows more pronounced warming since 2002 than GISTEMP.

Figure 5: BESTgiss2 land-ocean seriesFigure 6: The BESTgiss2 temperature series


Coverage bias signficantly impacts recent temperature trends. The methods used here to estimate and correct for that bias are rudimentary, but present a coherent picture of continued warming. It is striking that three different approaches, when applied to either the HadCRUT3 or NCDC data, yield a record which is very similar to GISTEMP. The same approaches applied to the HadCRUT4 data lead to a greater warming trend owing to the inclusion of the HadSST3 bias corrections.

Taking into account the effect of the El Nino cycle on recent trends, the warming rate of the largest cluster of datasets is consistent with longer term trends. If the HadSST3 adjustments are also correct, the underlying warming rate probably exceeds 0.2°C/decade. There are still known cool biases in each of these time series.

We have not taken any account the impact of a possible increase in aerosol cooling. This raises the worrying possibility that the underlying warming rate has been accelerating, and has been masked by aerosol emissions and the biases in the temperature series. Further developements on SST adjustments and aerosol impacts will hopefully clarify the situation.

Posted by Kevin C on Wednesday, 4 July, 2012

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