Calculating global temperature

I’m happy to present this essay created from both sides of the aisle, courtesy of the two gentlemen below. Be sure to see the conclusion. I present their essay below with only a few small edits for spelling, format, and readability. Plus an image, a snapshot of global temperatures.  – Anthony

By Zeke Hausfather and Steven Mosher

There are a variety of questions that people have about the calculation of a global temperature index. Questions that range from the selection of data and the adjustments made to data, to the actual calculation of the average. For some there is even a question about whether the measure makes any sense or not. It’s not possible to address all these questions in one short piece, but some of them can be addressed and reasonably settled. In particular we are in a position to answer the question about potential biases in the selection of data and biases in how that data is averaged.

To move the discussion onto the important matters of adjustments to data or, for example, UHI issues in the source data it is important to move forward on some answerable questions. Namely, do the methods for averaging data, the methods of the GISS, CRU and NCDC bias the result? There are a variety of methods for averaging spatial data, do the methods selected and implemented by the big three bias the result?

There has been a trend of late among climate bloggers on both sides of the divide to develop their own global temperature reconstructions. These have ranged from simple land reconstructions using GHCN data

(either v2.mean unadjusted data or v2.mean_adj data) to full land/ocean reconstructions and experiments with alternative datasets (GSOD , WDSSC , ISH ).

Bloggers and researchers who have developed reconstructions so far this year include:

Roy Spencer

Jeff Id

Steven Mosher

Zeke Hausfather

Tamino

Chad

Nick Stokes

Residual Analysis

And, just recently, the Muir Russell report

What is interesting is that the results from all these reconstructions are quite similar, despite differences in methodologies and source data. All are also quite comparable to the “big three” published global land temperature indices: NCDC , GISTemp , and CRUTEM .

[Fig 1]

The task of calculating global land temperatures is actually relatively simple, and the differences between reconstructions can be distilled down to a small number of choices:

1. Choose a land temperature series.

Ones analyzed so far include GHCN (raw and adjusted), WMSSC , GISS Step 0, ISH , GSOD , and USHCN (raw, time-of-observation adjusted, and F52 fully adjusted). Most reconstructions to date have chosen to focus on raw datasets, and all give similar results.

[Fig 2]

It’s worth noting that most of these datasets have some overlap. GHCN and WMSSC both include many (but not all) of the same stations. GISS Step 0 includes all GHCN stations in addition to USHCN stations and a selection of stations from Antartica. ISH and GSOD have quite a bit of overlap, and include hourly/daily data from a number of GHCN stations (though they have many, many more station records than GHCN in the last 30 years).

2. Choosing a station combination method and a normalization method.

GHCN in particular contains a number of duplicate records (dups) and multiple station records (imods) associated with a single wmo_id. Records can be combined at a single location and/or grid cell and converted into anomalies through the Reference Station Method (RSM), the Common Anomalies Method (CAM), and First Differences Method (FDM), or the Least Squares Method (LSM) developed by Tamino and Roman M . Depending on the method chosen, you may be able to use more stations with short records, or end up discarding station records that do not have coverage in a chosen baseline period. Different reconstructions have mainly made use of CAM (Zeke, Mosher, NCDC) or LSM (Chad, Jeff Id/Roman M, Nick Stokes, Tamino). The choice between the two does not appear to have a significant effect on results, though more work could be done using the same model and varying only the combination method.

[Fig 3]

3. Choosing an anomaly period.

The choice of the anomaly period is particularly important for reconstructions using CAM, as it will determine the amount of usable records. The anomaly period can also result in odd behavior of anomalies if it is too short, but in general the choice makes little difference to the results. In the figure that follows Mosher shows the difference between picking an anomaly period like CRU does, 1961-1990, and picking an anomaly period that maximizes the number monthly reports in a 30 year period.  The period that maximizes the number of monthly reports over a 30 year period turns out to be 1952-1983.  1953-82 (Mosher). No other 30 year period in GHCN has more station reports. This refinement, however, has no appreciable impact.

[Fig 4]

4. Gridding methods.

Most global reconstructions use 5×5 grid cells to ensure good spatial coverage of the globe. GISTemp uses a rather different method of equal-size grid cells. However, the choice between the two methods does not seem to make a large difference, as GISTemp’s land record can be reasonably well-replicated using 5×5 grid cells. Smaller resolution grid cells can improve regional anomalies, but will often result in spatial bias in the results, as there will be large missing areas during periods when or in locations when station coverage is limited. For the most part, the choice is not that important, unless you choose extremely large or small gridcells. In the figure that follows Mosher shows that selecting a smaller grid does not impact the global average or the trend over time. In his implementation there is no averaging or extrapolation over missing grid cells. All the stations within a grid cell are averaged and then the entire globe is averaged. Missing cells are not imputed with any values.

[Fig 5]

5. Using a land mask.

Some reconstructions (Chad, Mosh, Zeke, NCDC) use a land mask to weight each grid cell by its respective land area. The land mask determines how much of a given cell ( say 5×5) is actually land. A cell on a coast, thus, could have only a portion of land in it. The land mask corrects for this. The percent of land in a cell is constructed from a 1 km by 1 km dataset. The net effect of land masking is to increase the trend, especially in the last decade. This factor is the main reason why recent reconstructions by Jeff Id/Roman M and Nick Stokes are a bit lower than those by Chad, Mosh, and Zeke.

[Fig 6]

6. Zonal weighting.

Some reconstructions (GISTemp, CRUTEM) do not simply calculate the land anomaly as the size-weighted average of all grid cells covered. Rather, they calculate anomalies for different regions of the globe (each hemisphere for CRUTEM, 90°N to 23.6°N, 23.6°N to 23.6°S and 23.6°S to 90°S for GISTemp) and create a global land temp as the weighted average of each zone (weightings 0.3, 0.4 and 0.3, respectively for GISTemp, 0.68 × NH + 0.32 × SH for CRUTEM). In both cases, this zonal weighting results in a lower land temp record, as it gives a larger weight to the slower warming Southern Hemisphere.

[Fig 7]

These steps will get you a reasonably good global land record. For more technical details, look at any of the many http://noconsensus.wordpress.com/2010/03/25/thermal-hammer-part-deux/different  http://residualanalysis.blogspot.com/2010/03/ghcn-processor-11.html models  http://rankexploits.com/musings/2010/a-simple-model-for-spatially-weighted-temp-analysis/ that have been publicly  http://drop.io/treesfortheforest released http://moyhu.blogspot.com/2010/04/v14-with-maps-conjugate-gradients.html

].

7. Adding in ocean temperatures.

The major decisions involved in turning a land reconstruction into a land/ocean reconstruction are choosing a SST series (HadSST2, HadISST/Reynolds, and ERSST have been explored  http://rankexploits.com/musings/2010/replication/ so far), gridding and anomalizing the series chosen, and creating a combined land-ocean temp record as a weighted combination of the two. This is generally done by: global temp = 0.708 × ocean temp + 0.292 × land temp.

[Fig 8]

8. Interpolation.

Most reconstructions only cover 5×5 grid cells with one or more station for any given month. This means that any areas without station coverage for any given month are implicitly assumed to have the global mean temperature. This is arguably problematic, as high-latitude regions tend to have the poorest coverage and are generally warming faster than the global average.

GISTemp takes a somewhat different approach, assigning a temperature anomaly to all missing grid boxes located within 1200 km of one or more stations that do have defined temperature anomalies. They rationalize this based on the fact that “temperature anomaly patterns tend to be large scale, especially at middle and high latitudes.” Because GISTemp excludes SST readings from areas with sea ice cover, this leads to the extrapolation of land anomalies to ocean areas, particularly in the Arctic. The net effects of interpolation on the resulting GISTemp record is small but not insignificant, particularly in recent years. Indeed, the effect of interpolation is the main reason why GISTemp shows somewhat different trends from HadCRUT and NCDC over the past decade.

[Fig 9]

9. Conclusion

As noted above there are many questions about the calculation of a global temperature index. However, some of those questions can be fairly answered and have been fairly answered by a variety of experienced citizen researchers from all sides of the debate. The approaches used by GISS and CRU and NCDC do not bias the result in any way that would erase the warming we have seen since 1880. To be sure there are minor differences that depend upon the exact choices one makes, choices of ocean data sets, land data sets, rules for including stations, rules for gridding, area weighting approaches, but all of these differences are minor when compared to the warming we see.

That suggests a turn in the discussion to the matters which have not been as thoroughly investigated by independent citizen researchers on all sides:

A turn to the question of data adjustments and a turn to the question of metadata accuracy and finally a turn to the question about UHI. Now, however, the community on all sides of the debate has a set of tools to address these questions.