How dependent are GISTEMP trends on the gridding radius used?

A guest post by Nic Lewis


Global surface temperature (GMST) changes and trends derived from the standard GISTEMP[1] record over its full 1880-2016 length exceed those per the HadCRUT4.5 and NOAA4.0.1 records, by 4% and 7% respectively.  Part of these differences will be due to use of different land and (in the case of HadCRUT4.5) ocean sea-surface temperature (SST) data, and part to methodological differences.

GISTEMP and NOAA4.0.1 both use data from the ERSSTv4 infilled SST dataset, while HadCRUT4.5 uses data from the non-infilled HadSST3 dataset. Over the full 1880-2016 GISTEMP record, the global-mean trends in the two SST datasets were almost the same: 0.56 °C/century for ERSSTv4 and  0.57 °C /century for HadSST3. And although HadCRUT4v5 depends (via its use of the CRUTEM4 record) on a different set of land station records from GISTEMP and NOAA4.0.1 (both of which use GHCNv3.3 data), there is a great commonality in the underlying set of stations used.

Accordingly, it seems likely that differences in methodology may largely account for the slightly faster 1880-2016 warming in GISTEMP. Although the excess warming in GISTEMP is not large, I was curious to find out in more detail about the methods it uses and their effects. The primary paper describing the original (land station only based) GISTEMP methodology is Hansen et al. 1987.[2] Ocean temperature data was added in 1996.[3] Hansen et al. 2010[4] provides an update and sets out changes in the methods.

Steve has written a number of good posts about GISTEMP in the past, locatable using the Search box. Some are not relevant to the current version of GISTEMP, but Steve’s post showing how to read GISTEMP binary SBBX files in R (using a function written by contributor Nicholas) is still applicable, as is a later post covering related other R functions that he had written. All the function scripts are available here.

How GISTEMP is constructed

Rather than using a regularly spaces grid, GISTEMP divides the Earth’s surface into 8 latitude zones, separated at 0°, 23.58°, 44.43° and 64.16° (from now on rounded to the nearest degree).  Moving from pole to pole, the zones have area weights of 10%, 20%, 30%, 40%, 40%, 30%, 20% and 10%, and are divided longitudinally into respectively 4, 8, 12 16, 16, 12, 8 and 4 equal sized boxes. This partitioning results in 80 equal area boxes. Each box is then divided into 100 subboxes, with equal  longitudinal extent, but graduated latitudinal extent so that they all have equal areas. Figure 1, reproduced from Hansen et al. 1987, shows the box layout. Box numbers are shown in their lower right-hand corners; the dates and other numbers have been superseded.

Figure 1. 80 equal area box regions used by GISTEMP. From Hansen et al. 1987, Fig.2.

Where the distance from a land meteorological station to a subbox centre is less than a gridding radius (limit of influence), normally set at 1200 km, its temperature anomalies[5] are allowed to influence those of that subbox.[6] Figure 3, reproduced from Hansen et al. 1987, illustrates the areas thereby influenced in 1930 by the set of stations originally used. Almost all land outside Antarctica was by then within 1200 km of a meteorological station. Coverage was slightly poorer in 1900.

The 1200 km limit of influence was set to equal that at which the average correlation of annual temperature changes between pairs of stations falls to 0.5 at mid and high latitudes, or 0.33 at low latitudes.  It is implicitly assumed that correlation of annual changes is indicative of similarity of trends, which may not be entirely accurate. Hansen et al. 1987 found no directional dependence of annual correlations, but while temperature trends have no general longitudinal dependence they do vary systematically by latitude.

Figure 2. Distribution of land stations and their 1200 km radii of influence in 1930. From Hansen et al. 1987, Fig.1.

Subboxes in ice free ocean areas use SST data – and are therefore not subject to influence by land stations within the 1200 km limit – whenever it is available, provided that at least 240 months SST data exist and that at no time was there a land station within 100 km of the subbox centre.[7] Although ERSSTv4 SST data is complete in ocean areas, Hansen et al. 2010 stated that SST data is only used in regions that are ice free all year. The effective ocean area is on this basis reduced by 10%, to 64% of the global surface area, from its actual fraction of 71%. Although the Hansen et al. 2010 statement seems to be inaccurate,[8] in most calendar months SST data appears to be used only over a fairly small fraction of the ocean north of 60°N and south of 60°S.

Figure 3, reproduced from Hansen et al. 2010, shows the ice-free ocean area. The added lines showing the extent of the GISTEMP polar latitude zones. Their position indicates that temperature anomalies in those zones are dominated by land station data. The use of land station data to infill temperatures over sea ice hundreds of kilometres away appears to provide a preferable measure of surface air temperature to the use of equally distant SST data (or to setting the temperature in sea ice cells to seawater  freezing point), provided the intervening sea ice cover is almost complete. Where, however, a significant proportion of the ocean surface in or near the grid cell concerned is open water, as in areas of broken sea ice, it is not clear that using land temperatures is appropriate.

Figure 3. Ice-free ocean area in which GISTEMP uses SST data. From Hansen et al. 2010 Fig. A3, with
lines (red) added showing boundaries of the northern and southern polar boxes latitude zones.

Records for each box are built up by combining records from each constituent subbox with data, equal-weighted, after first converting them to anomalies.[9] Records for each latitude zone are then built up from each constituent box, weighted according to the number of its subboxes with data.

A peculiarity of the GISTEMP method for combining land and ocean data is that their relative weight in each latitude zone, and hence the global, temperature anomaly time series changes over the record, as the availability of land station data varies. It also depends on the limit set for a land station’s influence. With a 1200 km limit variation in the relative land and ocean weights should be small after 1900 save in the southern polar latitude zone, but with a smaller limit the variation would be larger and the land weight might increase significantly over time. Prior to 1900 the land weighting may have been materially too low in the two tropical latitude zones, at least, even with a 1200 km limit.[10]

The GISTEMP global record was originally created by combining latitude zone temperature anomalies weighted in the same way. But in 2010 an important change was made. In subsequent versions of GISTEMP, latitude zone anomalies have been weighted by each zone’s area, even if it only has defined temperature changes over part of its area.

The relevance of the 1200 km limit of influence

Hansen et al. 1987 stated that using alternatives to the 1200 km limit on a station’s influence had no significant effect on global temperature changes. Hansen et al. 2010 stated more specifically that the global mean temperature anomaly was insensitive to the limit chosen for the range from 250 to 2000 km, and that the GISS Web page provides results for 250 km as well as 1200 km. In support of this insensitivity, it gave the 1900–2009 linear trend based change in global mean temperature as 0.70°C with a 1200 km limit and 0.67°C with a 250 km limit.

I was surprised that the GMST trend was not more affected by the limit on a station’s influence, and decided to examine the sensitivity for the current GISTEMP version. Unfortunately, GISS appears no longer to provide global mean LOTI data using a 250 km limit on their Web pages. However, very commendably, GISS makes available computer code to generate GISTEMP.[11] The code has recently been rewritten in the modern language Python and, although I am unfamiliar with that language, the code and procedure for running it are well documented and I found it simple to run and to modify parameters it uses.[12]

I checked my results, with the gridding radius set at the standard 1200 km, against those from output on the GISTEMP web pages.[13] The global trends were within 0.01°C/century of each other over 1880-2016, 1900-2009 and 1979-2016. The linear trend based change in GMST over 1900-2009 I obtained was 0.89°C, a remarkable 27% higher than that given in Hansen et al. 2010.

Global mean comparisons

Figure 4 shows a plot of global temperature computed for GISTEMP using 1200 km (green) and 250 km (red) limits on land stations’ influence, and also on an intermediate 500 km limit (blue). It is relevant to show the NOAAv4 global time series (orange) for comparison, as like GISTEMP it is based on ERSSTv4 ocean and GHCNv3.3 land data.[14] Unlike the post-2010 version of GISTEMP, NOAAv4  area weights  the temperature anomalies of all cells with data.[15] To provide a fairer comparison with GISTEMP, I have computed a NOAAv4 global time series (black) giving, as for post-2010 GISTEMP, a full area weight to each of the eight GISTEMP zonal latitude bands irrespective of how many of the cells in it have data.[16]


Figure 4. Global temperature anomalies (°C) for GISTEMP at different  limits of influence, and for
NOAAv4.0.1 area weighted by grid cells with data (standard) or by 5° latitude bands with data

Although all the global time series follow each other closely over most of the record, there are clear differences in the first half century or so and over the last few decades. In the late 1800s, and to a modest extent during most of the 1915-1935 period, the GISTEMP 1200 km line tends to lie below the other lines, although the NOAA lines fall some way below it for several years in the 1890s. Contrariwise, in the late 1800s the GISTEMP 250 km line generally lies above the other lines, with the GISTEMP 500 km line next.  Over the last few decades, the GISTEMP 1200 km line is generally the highest,  followed by the GISSTEMP 500 km line. These tendencies are reflected in the linear trends for the different global time series over various periods, given in Table 1.

Dataset / trend period 1880-2016 1880-1950 1950-2016 1979-2016
GISTEMP 1200 km 0.72 0.37 1.42 1.72
GISTEMP 500 km 0.66 0.28 1.38 1.64
GISTEMP 250 km 0.62 0.22 1.30 1.52
NOAAv4 standard 0.68 0.37 1.35 1.62
NOAAv4 zone weighted 0.65 0.34 1.29 1.60

Table 1. Linear trends in GMST (°C/century) by dataset and period

The GISTEMP GMST trend I obtain over the full 1880-2016 record is 0.72°C/century when using a 1200 km gridding radius. When this limit of influence is reduced to 250 km, the trend becomes 0.62°C/century. So, using a 1200 km limit rather than 250 km now leads to a 16% higher full record trend, rather than the 4½% higher trend as reported in Hansen et al. 2010. Slightly over half the difference appears to relate to the early decades of the record. The average GMST anomaly over 1880-1900 was approaching 0.1°C warmer when a 250 km rather than 1200 km limit of influence was used. However, a substantial part of it arises over recent decades, when global land station coverage is much more complete. Over 1979-2016 the GMST trend is 1.72°C/century with a 1200 km limit of influence, but only 1.52°C/century with a 250 km limit. So, the claim in Hansen et al. 2010, the latest paper documenting GISTEMP, that the global mean temperature anomaly – and by implication the trend in GMST – is insensitive to the limit on a station’s influence over the range 250 km to greater than 1200 km is simply not true in relation to the current version of GISTEMP.

Examining temperature anomaly time series for the latitude zones where varying the limits of influence has the greatest effect provides some insight into the sources of the trend differences. It turns out that the largest contributions to differences in the 1880-2016 GMST trend come from the polar zones.

Southern polar zone comparisons

Figure 5 shows time series for the 90S-64S GISTEMP latitude zone at different limits of influence.

Figure 5. 90S-64S latitude zone temperature anomalies (°C) at different  limits of influence (km)

The 90S-64S latitude zone time series at 1200 km influence limit is remarkable. The wild swings between 1903 and 1943, not exhibited to any extent when a limit is set at 250 km or 500 km, turn out to be caused by a single meteorological station, Base Orcadas, located in the South Orkney islands, some way outside this latitude band. The South Orkney Islands have a climate of transition to polar cold weather, not participating in the polar regime; weather conditions can vary markedly from year to year.[17] Despite it being at 60.7°S, the centres of 18 subboxes in the 90S-64S zone are within 1200 km of Base Orcadas. Although a station’s weight in a subbox declines linearly with distance of the subbox centre from the station, reaching zero at its limit of influence, in the absence of other data for the subbox the station’s influence does not diminish until the limit is reached.[18] As there were no other data for the 18 subboxes involved, their temperature anomalies were set equal to those of Base Orcadas. And because there were very few observations in this latitude zone until after WW2 – a smattering of ship SST readings in the ice-free ocean area during summer months – the Base Orcadas data dominated the southern polar zone temperature anomaly for the 1200 km limit time series over 1903-1943; its weight only fell below 33% in 1955.[19]

After working this out, I found that the influence of Base Orcadas on GISTEMP’s 90S-64S zone had been pointed out back in 2009.[20] However, at that time the effect on GISTEMP’s global time series was completely negligible, as until 2010 the weight given to each latitude zone in determining the GMST anomaly was proportional to the area in it for which there was data, which for the 90S-64S zone was only a small fraction of its total area prior to 1955. However, in 2010 GISTEMP switched to weighting each latitude zone by its full area irrespective of how many of its subboxes had data.

Are changes in temperature at Base Orcadas representative of those for the 90S-64S zone, which is dominated by continental Antarctica and the ocean adjacent to it? I very much doubt it. For a start, the correlations of annual temperature changes at Base Orcadas with those at stations in the interior of Antarctica (with records starting circa 1957) are low.

With Base Orcadas dominating them, temperature anomalies for the 90S-64S zone during the first decade or so after 1903 and during the 1930s were generally strongly negative. By contrast, those from data restricted by a 500 km or 250 km limit of influence were only weakly negative, which mirrors much more closely the behaviour of anomalies in the adjacent 64S-44S zone, where data was much less sparse. In my view, the standard GISTEMP methodology is unsuitable for application in the southern polar zone prior to the mid 1950s. While the influence of Base Orcadas on GMST trends is only minor, it is not completely negligible even over the entire record. If pre-1955 Base Orcadas data is removed, the GISTEMP 1880-2016 GMST trend, with a 1200 km limit of influence, falls by 0.01°C/century – over a quarter of the excess of the GISTEMP trend over that for the standard version of NOAAv4.

One other unusual feature of GISTEMP in this latitude zone is that it uses a reconstructed record for Byrd station in Antarctica, the only location in the interior of West Antarctica with a useful pre-1981 record. The reconstruction stitches together, without any offset, the records of two stations having somewhat different locations, construction and instrumentation, and whose records are separated by some years. This procedure, which produces a fast warming record for Byrd, is not in accordance with normal practice for temperature datasets. The reconstructed Byrd record is not used by in HadCRUT4v5 nor to my knowledge in any other dataset apart from the Cowtan & Way infilled version of HadCRUT4. However, its contribution to the GISTEMP global temperature trend is very small.[21]

Linear trends for the different 90S-64S time series over various periods are given in Table 2.

Dataset / trend period 1880-2016 1880-1950 1950-2016 1979-2016
GISTEMP 1200 km 0.60 -1.54 1.25 0.71
Ditto ex Orcadas pre 1955 0.27 -1.30 1.32 0.70
GISTEMP 500 km 0.23 -1.10 1.06 0.56
GISTEMP 250 km 0.10 -0.75 0.72 0.94
NOAAv4 zone weighted 0.08 -0.66 0.35 -0.86

Table 2. Linear trends in 90S-64S anomalies (°C/century) by datasets and period

The GISTEMP 1200 km limit southern polar temperature trend over the satellite period, 1979-2016, during which Base Orcadas had limited influence, exceeded that using a 500 km limit.[22] A comparison with ERAinterim, arguably the best reanalysis dataset, suggests that the standard GISTEMP 1200 km limit version produced an excessive trend in southern polar latitudes since 1979.[23]

Northern polar zone comparisons

I now turn to GISTEMP’s northern polar zone. Figure 6 shows  time series for the 64N-90N GISTEMP latitude zone.  Here, there are noticeable differences between the various datasets in both early and late decades in the record. These differences are larger than for the southern polar zone, if one ignores the impact of Base Orcadas, despite data being less sparse in the northern than the southern polar zone, especially early in the record.

Figure 6. 64N-90N latitude zone temperature anomalies (°C) at different  limits of influence (km)

The lower temperature anomalies up to 1900, relative to those over the stable period from 1903 to 1916, when using the 1200 km limit of influence are questionable. The NOAAv4 dataset weighted in the same way as GISTEMP shows a considerably smaller increase, as (to a lesser extent) do the 250 km and 500 km limit GISTEMP versions.  The Cowtan & Way infilled version of HadCRUT4.5 warms only a third as much as the standard 1200 km GISTEMP version in this latitude zone between these two periods.

Linear trends for the different 64N-90N time series over various periods are given in Table 3.

Dataset / trend period 1880-2016 1880-1950 1950-2016 1979-2016
GISTEMP 1200 km 1.77 2.85 3.16 5.74
GISTEMP 500 km 1.60 2.61 3.02 5.44
GISTEMP 250 km 1.42 2.32 2.75 4.96
NOAAv4 zone weighted 1.11 1.68 2.39 4.34

Table 3. Linear trends in 64N-90N anomalies (°C/century) by datasets and period

The large divergence between all GISTEMP variants and NOAAv4 in the 64N-90N latitude zone almost certainly relates to the treatment of sea ice. In a non-infilled record like HadCRUT4, cells with sea ice have no data; their temperature anomaly is effectively treated as always equalling the mean for the region over which anomalies are averaged. In HadCRUT4 this is entire hemispheres, although it would be possible instead to average over latitude zones, as in GISTEMP.[24] In NOAAv4, the spatially complete ERSSTv4 ocean data is used in cells with sea ice. The temperature for such cells is set to -1.8°C, near the freezing point of seawater. In GISTEMP, as the ERSST SST data is flagged as missing in subboxes with sea ice, their temperature anomalies are set equal to those of any land stations with data within the 1200 km (or 500 or 250 km) limit of influence, on a distance-weighted basis where more than one such land station exists. The Cowtan & Way infilled version of HadCRUT4 effectively does much the same through its use of kriging.[25]

Insofar as temperatures over sea ice do reflect those of land temperatures within the radius of influence used, the NOAAv4 method can be expected to understate surface air temperature changes for cells with sea ice; this is also so (to a lesser extent) for the HadCRUT4 method.

It is unclear why the 1200 km GISTEMP version has warmed faster than the 250 km and 500 km versions in 64N-90N in recent decades. Possibly it reflects a higher weighting being given to the highest latitude land stations, and an even lower weighting being given to the very small ice free ocean area included in the zone. Comparisons with the ERA reanalysis dataset suggest that the GISTEMP 1200 km limit version produced realistic trends in arctic temperatures from 1979 until the late 2000s, with a slight underestimation of warming since then.23


The answer to the question originally posed, “How dependent are GISTEMP trends on the gridding radius used?”, is that they are much more dependent than claimed, with use of a 250 km, rather than the standard 1200 km, limit producing materially lower GMST trends over all periods investigated. That does not mean use of a 250 km limit produces a more accurate record. In my view, a 1200 km limit is in general preferable to a 250 km limit, although use of some intermediate value between 500 km and 1200 km might be best.  In any event, a 1200 km limit is clearly unsuitable for use in the southern polar zone prior to the middle of the 20th century, since doing so results in unrepresentative temperatures at Base Orcadas – some way outside that zone – dominating  temperature changes for the entire 90S-64S zone.

In principle, GISTEMP as currently constructed has several features that arguably make it more suitable for  comparisons with global climate model simulations of surface air temperature than HadCRUT4 or NOAAv4, the most prominent other global temperature datasets.[26] GISTEMP:

  • gives a full area weight to all latitude zones (unlike HadCRUT4)
  • uses nearby land temperatures rather than SST to estimate temperatures where there is sea ice
  • uses ocean temperature data that were until recently tied, on decadal and longer timescales, to marine air temperature rather than SST records.[27]

However, against this GISTEMP has a few problematic features that seriously detract from its suitability as a global temperature dataset. GISTEMP:

  • fails to ensure ice-free ocean temperature anomalies are weighted by the area they represent
  • uses a simplistic infilling method that sets cell anomalies equal to the weighted average of those for land stations up to 1200 km  away, with no kriging-like reversion towards the mean with distance.

By contrast, the Cowtan & Way infilled version of HadCRUTv4.5 does not suffer from either of these shortcomings, while matching GISTEMP as regards all but one of its positive attributes identified for making comparisons with climate model surface air temperature data. And while HadCRUTv4.5, and hence Cowtan & Way, use HadSST3 for ocean temperatures  rather than the marine air temperature data linked ERSSTv4 dataset, over 1880-2016 the two datasets have essentially identical global trends.[28]  Although simulations by the vast majority of global climate models show that ocean surface (2 m) air temperature warms marginally faster than SST, it is not clear that their behaviour in this respect correctly reflects reality. Such models do not properly represent the surface boundary layer, within which steep temperature gradients exist; their uppermost ocean layer is typically 10 m deep. The fact that HadSST3 has warmed as fast as ERSSTv4 (and HadNMAT2) suggests that ocean surface air temperature may not actually warm any faster than SST.

If one is after a globally complete dataset for comparison with global climate model  simulations, the Cowtan & Way infilled version of HadCRUT4 therefore looks a better choice than GISTEMP.  Interestingly, it is only prior to 1890 and during the last decade that the Cowtan & Way GMST estimate systematically differs from the unfilled HadCRUT4v5 one; the two datasets’ 1890-2006 trends differ by under 1%. IMO, no infilling technique will be that successful prior to 1890 – there isn’t enough data to go on, and data accuracy is also an issue. It is much more plausible that HadCRUT4v5 understates warming since the early years of the 21st century, a period when the Arctic – where there are limited in-situ temperature measurements – warmed very fast. However, over the fifteen years to 2016 the HadCRUT4v5 and Cowtan & Way GMST trends, of 0.138°C /century and 0.160°C /century respectively, are equally close to the 0.149°C /century ERAinterim trend; the GISTEMP and NOAAv4.0.1 trends are both above 0.17°C /century.

Nic Lewis


[1]   GISTEMP LOTI, combined land and ocean data: see

[2]   Hansen, J.E., and S. Lebedeff, 1987: Global trends of measured surface air temperature. J. Geophys. Res., 92, 13345-13372, doi:10.1029/JD092iD11p13345.

[3]   Hansen, J., R. Ruedy, M. Sato, and R. Reynolds, 1996: Global surface air temperature in 1995: Return to pre-Pinatubo level. Geophys. Res. Lett., 23, 1665-1668, doi:10.1029/96GL01040

[4]   Hansen, J., R. Ruedy, M. Sato, and K. Lo, 2010: Global surface temperature change. Rev. Geophys., 48, RG4004, doi:10.1029/2010RG000345

[5]   Changes from the mean for the corresponding month over a reference period.

[6]   Stations without, for at least one month, data for a total of 20 or more years are dropped.

[7]   Hansen et al. 1996 states that “A coastal [sub]box uses a meteorological station if one is located within 100 km of the box centre.” But in fact, if there was at any time a station within 100 km GISTEMP throughout the record uses data from all land stations within 1200 km.

[8]   It is unclear whether the GISTEMP code accurately implements this condition. The GISS-pre-processed ERSSTv4 data it uses appears to have had subbox SST data removed throughout the  record but by individual month rather than for all year. I presume data was removed for all calendar months in which the subbox concerned contained sea ice in any year of the record. If SST data remain for at least two calendar months then the 240 months minimum data requirement will be met and SST data used for those calendar months. The presence of sea ice appears to be deduced from the subbox SST being cooler than –1.77°C. It is not evident that the ice-free condition was applied before 2010, but it was irrelevant when GISTEMP started using ocean SST data since then used dataset only covered 45°S–59°N.

[9]   Curiously, monthly means over 1961-1990 are subtracted to compute subbox temperature anomalies, while an anomaly reference period of 1951-1980 is used when combining subboxes into boxes.

[10] Judging from the January 1886 land coverage for HadCRUT4 shown in Figure 5 of Morice CP, Kennedy JJ, Rayner NA, Jones PD, 2012. Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: The HadCRUT4 dataset. J. Geophys. Res. 117: D08101..

[11] The data files it uses are GISS supplied, with sea-ice affected areas of ERSSTv4 data already masked out and the reconstructed Byrd record substituted for the original.

[12] The GISTEMP code is available via I used frozen data files from the provided input.tar.gz file, both for speed of processing and to ensure consistent results from different runs. The data files were dated 18 January 2017; slightly different results may be obtained if downloaded current data is used instead, as some pre 2017 values may have been revised. I ran the code on a 64 bit Windows 7 computer with the Anaconda36 implementation of Python, which includes required library modules, installed.

[13] File, downloaded 4May17. I also checked the trends produced by the Python code against those I calculated from a global time series produced by weighting each month the anomalies for individual boxes making up each latitude zone by the number of subboxes with data to give zonal anomalies and then combining these latitude zone anomalies, area-weighted. They were almost the same globally.

[14] NOAAv4 anomalies, which are relative to the 1971-2000 mean, have been restated relative to the 1951-1980 mean used by GISTEMP.

[15] In NOAA’s case, 5° latitude by 5° longitude grid cells, not equal area subboxes. However, cell anomalies are area weighted when combined to give zonal anomalies, so the difference should in principle be unimportant.

[16] To simplify the calculations, I reduced the monthly grid cell series to annual mean anomalies before rather than after combining them into zonal latitude bands and then a global time series. NOAA grid cells falling into two GISTEMP zonal latitude bands had their area weight split appropriately. As in GISTEMP, zonal anomalies were derived by combining on an area-weighted basis anomalies for all cells in the zone with data, but each zonal anomaly was given a full weight in computing the global anomaly irrespective of for what proportion of its area cell data existed. Note that a similar comparison is not given for other global temperature datasets since they do not use ERSSTv4 data.

[17] Argentina National Meteorological Service

[18] Since with only one data source the divisor in the calculation of the weighted subbox anomaly is the same as the weight given to that data source.

[19] Between 1945 and the mid-1950s, both 1200 km and 500 km limit 90S-64S zonal anomalies were also influenced by data from Esperanza Base station, located near the tip of the Antarctic peninsula, 1° outside the zone.


[21] The inclusion of the  reconstructed 1957-2016 Byrd record nevertheless increases the 1957-2016 warming trend in GISTEMP’s 90S-64S region by approximately 0.25 °C/century, compared to when using the original Byrd and Byrd AWS records.

[22] Use of a 250 km limit gave the highest trend over the 1979-2016 period, due to it producing lower temperature anomalies in the 1980s and 1990s.

[23] Simmons, AJ et al., 2017. A reassessment of temperature variations and trends from global reanalyses and monthly surface climatological datasets. Q. J. R. Meteorol. Soc. 143: 101–119, DOI:10.1002/qj.2949. The comparison is for the a 30 degree latitude band around the pole.

[24] I did this in 2014 using 10° latitude zones; the effect on HadCRUT4 GMST trends was very small (zero over 1850-2013), indicating that sparse polar coverage in HadCRUT4 has not of itself led to any significant bias in GMST estimation.

[25] Although as the distance away from any station falls the anomaly for a cell with sea ice will gradually tend towards the global mean land anomaly.

[26] A potential understatement of warming arising from use of temperature anomalies when sea ice cover reduces has however been pointed out (Cowtan, K., et al., 2015: Robust comparison of climate models with observations using blended land air and ocean sea surface temperatures, Geophys. Res. Lett., 42, 6526–6534). This occurs even when sea ice anomaly temperatures are land-based, as the change to SST in temperature anomaly terms is generally less than the change in absolute temperature. However, bias arising from using temperature anomalies when sea ice cover is reducing is likely to be substantially smaller than suggested by the climate model simulations carried out by Cowtan et al., since the reduction in Antarctic sea ice extent simulated by climate models during the period over which they find a bias developing has not occurred in the real world.

[27] In ERSSTv4 ship sea surface temp (SST) measurements, on decadal and longer timescales, are adjusted to match movements in night-time marine air temperature data (per the HadNMAT2 dataset).

[28] As they do over the ice-free 60S-60N latitude zone, which is more relevant to their use by GISTEMP and Cowtan & Way.


  1. Zeke Hausfather
    Posted May 18, 2017 at 3:28 PM | Permalink | Reply

    The Berkeley Earth land/ocean dataset is also quite similar to the Cowtan and Way one, but has a bit better spatial resolution over land where it kriges individual stations rather than precomputed HadCRUT grid cells:

    • Posted May 18, 2017 at 4:56 PM | Permalink | Reply

      Thanks, Zeke; kriging based on individual stations makes sense, but I wouldn’t have thought it would make much difference on a global or zonal basis.
      I believe BEST also homogenises land station data differently from HadCRUT4, and hence from Cowtan and Way.

    • Zeke Hausfather
      Posted May 18, 2017 at 7:09 PM | Permalink | Reply

      It does, though the homogenization makes relatively little difference over land globally, at least since 1950 or so (though some regions like the U.S. and Africa are more strongly affected). HadCRUT4 also uses homogenized land data, but obtains it from national MET offices rather than via a consistant automated process.

      Here are Berkeley and C&W anomalies over time:

  2. Posted May 18, 2017 at 5:18 PM | Permalink | Reply

    They have models to figure out how CO2 affects temperature which in turn is a modelled value and that model may be tuned to match the predictions that CO2 will affect temperature.

    “Models All The Way Down” (TM) IPCC.

  3. Jeff Norman
    Posted May 18, 2017 at 7:54 PM | Permalink | Reply

    Thank you Nic. I remember John Daly puzzling over this a couple of decades ago.

  4. Gerald Browning
    Posted May 18, 2017 at 9:24 PM | Permalink | Reply


    The paucity of data is evident in your plots, especially in the Southern hemisphere. If one wanted to compute
    an approximation of the mean temperature (integral of T over the sphere above integral of the sphere), one would need a very fine equally spaced grid to do so accurately (I believe if T is smooth the actual accuracy could be computed using a standard local numerical error analysis). In any case the error using the current available observational data would probably be on the order of 100%, i.e., completely untrustworthy. Thus I find the arguments about global temperature trends nonsensical. And comparing those temperatures with global climate models that are based on the wrong reduced system of equations is pathetic. I am not saying there isn’t some global warming, just that the climate scientists science is not science.


    • Pat Frank
      Posted May 19, 2017 at 10:20 AM | Permalink | Reply

      Plus, Jerry, they ignore instrumental resolution. It’s apparently a little known fact that climate thermometers are infinitely accurate.

      • Steven Mosher
        Posted May 21, 2017 at 12:28 PM | Permalink | Reply

        The spatial estimate or prediction will always represent more precision than the observations. The prediction represents what you would have measured with a perfect sensor.
        It’s not an average of the observations. It’s a prediction. Very different animal than yo u are used to.
        And we actually test the prediction.

        • Ed Snack
          Posted May 21, 2017 at 2:56 PM | Permalink

          Citation please, not that Mosher ever, ever, exaggerates, but…

      • Pat Frank
        Posted May 22, 2017 at 10:47 AM | Permalink | Reply

        Instrumental resolution is not a precision problem. It’s a problem of the instrument itself unable to detect the difference between two external magnitudes.

        The undetected difference is data lost forever. It remains an error in the record, forever.

        Every single instrument will contribute its resolution error. It enters the record as an irreducible uncertainty in the measurement. No amount of averaging will ever remove it.

        Instrumental resolution is the lowest possible limit of accuracy. It is entirely ignored in the published air temperature record; set aside.

    • Posted May 20, 2017 at 10:14 AM | Permalink | Reply

      Actually Gerry, this is a good point. In areas where the stations are sparse, its equivalent to having a very large grid for the integration and errors in the integral could be large.

      • Posted May 20, 2017 at 2:24 PM | Permalink | Reply

        ” errors in the integral could be large”
        That’s just guessing. People actually work it out. It’s treated as coverage uncertainty in Sec 5.3 of Morice et al, 2012. It is a substantial part of the overall error quoted. I discussed in here, with tests here and here. It’s not nothing, but not huge.

      • Posted May 20, 2017 at 2:26 PM | Permalink | Reply

        ” errors in the integral could be large”
        That’s just guessing. People actually work it out. It’s treated as coverage uncertainty in Sec 5.3 of Morice et al, 2012. It is a substantial part of the overall error quoted. I discussed in here, with tests here. It’s not nothing, but not huge.

        • Posted May 23, 2017 at 4:12 PM | Permalink

          Nick, I’ve now approved both your comments that were stuck in moderation; sorry for the delay. However, they seem to be near duplicates?

          If you have a problem with comments containing links getting stuck again, please post a comment asking for them to be released from moderation.

        • Posted May 23, 2017 at 6:06 PM | Permalink

          “a short paragraph giving the essence of the argument that the mathematical error estimate is not applicable”
          It comes back to my initial statement – you don’t have a derivative. I’m pretty sure that you and Jerry are thinking about integrating things determined by PDE. That tells you about derivatives – pressure gradient implies acceleration etc. But here we don’t have that. We just have a sampled field variable.

          Numerical integration here basically makes an interpolation function based on the samples, and integrates that. So the question is, how good is the interpolation. The JB formulae would say, fit a polynomial based on the derivatives, and the error is attributable to neglected higher order terms. Here we can’t do that. The basis for saying interpolation is possible is correlation. That is why Nic’s post talks about 250km, 1200km etc. Correlation doesn’t have to work at all times (eg fronts) – it just has to work well enough on average for integration.

          Jerry refers to his spherical harmonics example. I think that is instructive – I use SH integration extensively, and find it gives similar (good) results to triangle mesh. I posted here

          a study of residuals, with a WebGL globe picture, especially of SH (following posts also are on integration accuracy). The number of SH is limited, because the scalar product is not an exact integral (unobtainable) but a product on the observation points, and so orthogonality fails. When the high-order SH start to have wavelengths on the order of gaps in the data, the failure is total (ill-conditioning) and you have to stop. When you do, the residuals are still large, and if you use a random model for them, you will deduce a large error.

          But the residuals I show are clearly not random. They actually look very like a combination of the higher order SH’s that couldn’t be used. And the point is that, though the amplitude is large, those SH have zero (exact) integrals. The large residuals have been pushed by the fitting process into a space that makes almost no contribution to the integral.

        • Posted May 23, 2017 at 6:09 PM | Permalink

          Thanks for releasing. The sameness is becauseI was exploring for the limit on links – I though three might work where four didn’t.

      • Steven Mosher
        Posted May 21, 2017 at 12:29 PM | Permalink | Reply

        Except they are not. You can test this. That would end rank speculation.

      • Posted May 21, 2017 at 7:26 PM | Permalink | Reply

        Steven, It’s a mathematical point. The error in the integral is proportional to the maximum grid spacing times the first derivative of the function. At least that’s the rigorous bound. We have seen things like this in Antarctica where there have been papers that made these errors as I’m sure you know.

        • @whut
          Posted May 21, 2017 at 10:32 PM | Permalink

          That’s wrong Young.

        • Posted May 22, 2017 at 2:44 AM | Permalink

          It is wrong. The key difference is that the integrand has only a finite number of known values (and no derivative). Any gridding will yield either very large grid cells, mixing inhomogeneous values, or smaller cells where some have no data points. It is the problem of dealing with those missing cells that creates most of the coverage uncertainty. GISS’ two-level system is a way of trying to get around this, but can only go so far.

          There has been much work to estimate coverage uncertainty. Morice et al 2012 is much quoted.

        • Gerald Browning
          Posted May 22, 2017 at 3:56 PM | Permalink


          I suggest you read a numerical analysis text on the approximation of an integral using a discrete number of points.
          Or read my counter example in the text below. The mean is defined by the integral of the function over the surface of the sphere divided by the area of the surface, not a sum of a few points divided by the number of points. Numerical analysis tells us that the the numerical approximation of an integral for a smooth function requires a fine grid to be accurate. The more points the more accuracy. Note that temperature across a front is almost a discontinuity.
          And that means you would need a huge number of grid points to compute the mean accurately.


        • Posted May 22, 2017 at 5:20 PM | Permalink

          “And that means you would need a huge number of grid points to compute the mean accurately.”
          But what is huge? No quantification here. I have investigated this extensively at my blog Moyhu. I can’t give links here, because that causes the comment to go into moderation – two of my comments have now been there for 3 days. But on April 5 2017 (see archive) there is just one of several studies (others linked) which show that the number of grid points is ample to establish an integrated monthly global mean reliably. And of course there are studies in the literature – I mentioned above Morice et al 2012, but it goes back to early Hansen.

        • Posted May 22, 2017 at 8:37 PM | Permalink

          Nick, Can you explain what the mathematical basis of your claim is? Forward error analysis might be nice. I think Gerry’s point is that in regions like the Southern hemisphere, where data is sparse, the normal mathematical analysis would yield a quite large error. The exact size depends on how smooth the function is.

          An analogy you know well is aeronautical test data. Even a very large number of pressure measurements at discrete points give a very inaccurate estimate of global forces and moments, which are always measured by smart engineers separately.

        • Posted May 22, 2017 at 9:20 PM | Permalink

          “The exact size depends on how smooth the function is.”
          The exact size is important, but all we have here is hand waving. It isn’t like PDE solving, where you basically create the integration data. It isn’t even really like pressure testing, which I don’t think you would try to interpret without some mathematical model based on the physics of flow. You have just a number of isolated anomalies, and you have to have some basis for interpolating (and integrating the result) to get a global average. That basis is usually correlation.

          I’ve referred to one method of estimating error (coverage uncertainty) which is subset selection. I spoke of a a post where I did this systematically for one month integration.
          Other methods are used. Morice et al used model results restricted to the measuring points. You can’t use methods that depend on an estimate of derivative – that is more uncertain than the integral. But you have to find some quantification.

        • Posted May 23, 2017 at 10:46 AM | Permalink

          Thanks for the response Nick, but could just give me a short paragraph giving the essence of the argument that the mathematical error estimate is not applicable? I usually avoid this area as it seems very complicated and not very interesting, but Jerry does seem to me to have a valid point that is pretty obvious and rigorous in its origins.

        • Posted May 23, 2017 at 6:10 PM | Permalink

          I misplaced my response on the sub-thread above.

        • Gerald Browning
          Posted May 24, 2017 at 12:34 AM | Permalink


          Try your interpolation scheme or other gimmick on my counterexample and tell me what the mean is. Any interpolation method also relies on the smoothness of the function being interpolated and that smoothness is used by standard numerical analysis to determine the error. What is the numerical error in your interpolation method? The only person doing hand waving is you.


        • Posted May 24, 2017 at 2:45 AM | Permalink

          “The only person doing hand waving is you.”
          You have given no numbers relevant to the integration of temperatures on Earth. I have, and I have been putting this into practice on my blog, calculating the average from raw data every month for over six years now. I post this each month in advance of the others, and it agrees very well with what they get, by other means. And I have extensively analysed and tested the errors.

          In terms of your “examples”, yes, one observation of a sinusoid in a period will give an unreliable mean. One hundred, randomly placed, on the other hand, will do very well. And I have dealt with your spherical harmonics example above, with link.

  5. Posted May 18, 2017 at 9:32 PM | Permalink | Reply

    Nic –
    “If pre-1955 Base Orcadas data is removed, the GISTEMP 1880-2016 GMST trend, with a 1200 km limit of influence, falls by 0.01°C/century.” This does not seem consistent with the values of Table 2, which gives 90S-64S trend for 1880-2016 (1200 km) is 0.60 °C/century; sans Orcadas, 0.27 °C/century.

    • Posted May 19, 2017 at 3:26 AM | Permalink | Reply

      HaroldW – Table 2 is for the 90S-94S zone, which has an area and hence weight of is only 5% in the global mean. 5% of (0.60 – 0.27) is 0.0165 °C/century. That is still slightly higher than the GMST trend change of 0.01 °C/century (0.009 to 3 decimal places). The difference doesn’t seem due to the minor influence Orcadas on the 64S-44S. It might be because the GISTEMP code only outputs zonal and global temperature anomalies to 2 d.p., or to the data being converted from monthly to annula values before trends were calculated.

      • Posted May 19, 2017 at 1:49 PM | Permalink | Reply

        Thanks Nic. I misread the text, didn’t realize that it referred to global anomalies with and without Orcadas.

  6. Posted May 19, 2017 at 12:19 AM | Permalink | Reply

    Welcome back Climate Audit!
    Thanks for the work!

  7. Posted May 19, 2017 at 12:22 AM | Permalink | Reply

    Question at Zeke, have you guys published your homogenization algorithm?

    • Zeke Hausfather
      Posted May 19, 2017 at 8:55 AM | Permalink | Reply

      Back in 2013. Its available here:

    • Steven Mosher
      Posted May 21, 2017 at 12:32 PM | Permalink | Reply

      Published and tested in double blind studies. Nevertheless..folks continue to speculate. Speculation. Arm Chair science. Never touch the data just speculative thoughts.

      • Gerald Browning
        Posted May 22, 2017 at 12:23 AM | Permalink | Reply


        I suggest you try this simple test. Generate a spherical harmonic function
        using Spherepack with a reasonably realistic temperature in physical space (my guess is that any non constant function with several harmonics will be sufficient). Then use the locations of the observations to generate the mean temperature for the function and compute the error. What is the relative size of the error ?


        • Gerald Browning
          Posted May 22, 2017 at 3:33 PM | Permalink


          I assume you know what a counter example means. Assume you have a two pi periodic function that has a single observation at pi/2. The value there is 5. What is the mean of the function? Any answer you guess is wrong. And that is because the observations are not dense enough to correctly determine the mean. If there were sufficient obs to compute the necessary integral of the function accurately, then the mean could be computed. So much for the double blind (climate scientist) test.


        • Olof R
          Posted May 24, 2017 at 2:22 AM | Permalink

          Gerald Browning,
          Why generate climate data? There is plenty of synthetic data from models, reanalyses, or real data with global coverage that one can play with.
          Like this example: Throw away 99.83 percent of the spatial information, and see if you can reconstruct the whole..

          Do you still have doubts about sparse sampling? Do you believe that global warming in the long run can hide between those 18 dots?

  8. Anonymous
    Posted May 20, 2017 at 10:20 PM | Permalink | Reply

    Interested in the topic, but the writing style makes it extremely hard to process.

    This entire phrase is the subject of the first sentence: “Global surface temperature (GMST) changes and trends derived from the standard GISTEMP[1] record over its full 1880-2016 length”. An 18 word nominative phrase. You have to wander through that entire tortured set of words to figure out that this is just the subject and then a verb comes.

    While the topic is technical, that does not mean the writing should be obscure.

    • Jeff Norman
      Posted May 22, 2017 at 11:28 AM | Permalink | Reply

      May I suggest you compose a better sentence that conveys the same information? I am interested in what you would say instead.

      • Anonymous
        Posted May 23, 2017 at 9:14 PM | Permalink | Reply

        “According to the GISTEMP record, the Earth has warmed faster in recent years than according to X record or Y record.”

        That is a more reader-friendly topic sentence. You don’t have to overload the first sentence with every caveat and qualifier. After all, several sentences will follow.

        Also, it is a bad idea to have such a long meandering phrase as a subject. The reader has to read far too long to see where the actual verb is in the sentence in relation to the subject (actually has to read forever to see that that whole phrase is acting as an 18 word noun). Has to parse 18 words and scratch skull to see that there is not an action taking place within that monstrosity.

        Again, the topic is interesting. I would love to learn why the different temperature records differ. But the topic is poorly explained. Having to deal with that 31 word monstrosity of a first sentence to open an essay will just turn many people off. And it doesn’t have to be that way.

  9. Gerald Browning
    Posted May 22, 2017 at 4:06 PM | Permalink | Reply

    It has just been shown that an insufficient number of observations can lead to a mean that is completely wrong.
    Thus the time series are not trustworthy to any extent and the arguments based on those series are nonsense.
    Mathematical analysis cannot be refuted, though I am sure that climate “scientists” will try.


  10. Gerald Browning
    Posted May 22, 2017 at 4:13 PM | Permalink | Reply

    David and Pat,

    Does my counterexample prove the point we are trying to make. It is amazing how poorly educated some of the climate “scientists” seem to be.


  11. Gerald Browning
    Posted May 22, 2017 at 4:20 PM | Permalink | Reply

    Davi and Pat,

    The next piece of enlightenment is to have them understand that the climate and forecast models are based on the wrong set of equations. There is only one well posed reduced system of equations for a hyperbolic system with multiple time scales and for the atmospheric equations of motion that is not the hydrostatic equations. Minor problem. 🙂


    • Posted May 22, 2017 at 11:14 PM | Permalink | Reply

      I know Jerry, but the standard method is to add unspecified dissipation to make the scheme stable and then claim that somehow that dissipation doesn’t impact accuracy. It’s not very satisfying.

      • Gerald Browning
        Posted May 24, 2017 at 12:18 AM | Permalink | Reply


        In fact we did compare the accuracy of the spectral method when the typical dissipation used in climate models is added. (I had to insist that the accuracy comparison of the three methods be added for this case.) And as you can see in the included BHS manuscript the accuracy of the spectral method was reduced by two orders of magnitude.

        So adding unrealistically large dissipation substantially degrades the accuracy of the numerical method, i.e., the dissipation is a poorer approximation of the differential equations (and a better approximation of the heat equation 🙂


  12. Olof R
    Posted May 24, 2017 at 4:19 AM | Permalink | Reply

    This post is interesting, but I believe that the issue with 250 km,1200 km (or other ) influence radius is even more important in the met station only index, Gistemp dTs.
    Almost all attention is on the blended surface indices nowadays, but I have reason to believe that Gistemp dTs is much closer to the true global 2m SAT compared to Gistemp loti or other blended indices.

    Since you have the Gistemp code up and running, you could tweak Gistemp dTs to 2000 km influence, or more, to achieve complete global coverage.

    Right now dTs has the trend 0.218 C/decade for 1970-2016, whereas the CMIP5 multimodel mean is 0.211 C/dec. Gistemp loti is only 0.182 C/ decade.
    It looks like Gistemp dTs trend will converge to about 0.215-0.216 C/decade when the globe is completely infilled.

    The ultimate test of the global SAT representation by Gistemp dTs would be to mask model data in space and time to mimic that of dTs, then run this data with the dTs code, and see how much it differs from the complete global model dataset.

    I am not the man to do such a complex analysis, so I have done it in a simpler way. I have made a simple dTs-emulating global index, by subsampling 100 evenly distributed dTs gridcells (more or less the RATPAC method), and also made an exact model equivalent of this:

    The conclusion is that dTs exaggerates the global SAT by less than 0.01 C/decade (best guess 0.006), which is a much nearer estimate than Gistemp loti.

Post a Comment

Required fields are marked *


%d bloggers like this: