Area Weighted Antarctic – Offset Reconstructions
Posted by Jeff Id on August 31, 2009
Ok, I know you guys are tired of area weighted reconstructions but for those who say publish, the detail of this is important. What I’ve been attempting to do is verify that the anomaly based area weighted reconstruction is of good quality. As we discussed before, even two thermometers of the same exact measurements value can have different anomalies when the timeframe is different. As an example, assume we have an noiseless linear upslope in temp for 20 years. Thermometer 1 measures for all 20 years and thermometer 2 measures for only 10 but both record the exact same number. When anomalized the mean of each record is zero, the thermometer 2 anomaly will have a lower value than thermometer 1 and the average will have a sudden step when the second thermometer is introduced.
These steps can be corrected by looking at the beginning of the new record and making sure it is offset to match the longer term record. This method implicitly makes the assumption that both records are the same even though we’re not sure what the heck thermometer two would have measured had it had existed for the same time as thermometer 1. Confounding the issue is the fact that we’re looking at tenths or hundredths of a degree C in noisy data that can vary by 10C anomaly per month.
To calculate reasonable offsets for shorter length surface stations, an algorithm was created that starts from the earliest 1957 ground station records and works its way forward. When a new station is introduced, it finds the absolute closest already offset station and computes an offset for the new station in the hopes that we can remove the step. Unfortunately, the noise level of the data makes the whole process less simple than we might imagine. First, the no offset anomaly data looks like this.
The trend for this data is 0.052 Deg C/Decade. This or a version of this, is the most important super simple version reconstruction as it is verifying the validity of the complex algorithms both in spatial distribution and magnitude. The regression modes used do not have the ability to offset station data to create trends. The question then becomes, how much of a problem is that, because we want to make sure we’re doing good work and not just adding on to an improved hockey stick paper or something.
After creating the algorithm for calculating the step in the data, the mean of the overlapping data of both stations was used to calculate the offset. I found that final trend was sensitive to the amount of overlap use to compute the offset. By overlap, I mean the number of months of data points available at both stations.
If we use all of the overlap data to compute the offset, the result is almost the exact same thing as the no – offset data. This makes sense as the ground stations which have long histories control the trend and make sure the short record stations have mean values corresponding to the long station trends. Consider what happens when thermometer 2 were centered (mean) perfectly on the graph of thermometer 1. Even if 2 had a steep trend in comparison, the net trend wouldn’t change much. On checking the amount of overlap I found that most stations had very long records of overlapping data with the next closest station, therefore the full record length is not ideal for determining a true trend as differences would be suppressed.
Figure 2 is the full record overlapped data. The trend for this was – 0.057 C/Decade which is very similar to the 0.052 for the anomaly only data. This is a good confirmation of the reasonableness of the method. You can see there is very little difference between Figure 2 and 1.
So the question becomes, what is a reasonable level of overlap, too much gives no difference, too little and we get ridiculous results. It seemed impossible from poking in different numbers and getting different trends over and over. However, after a few dozen attempts, I decided to plot the trend vs months of overlap in reconstructions. Each reconstruction takes 30 seconds or so so when I ran about 100 of them it was a clear case of computer abuse but the graph is interesting.
So this graph that the number of overlapping months used to compute the offset has an effect on trend. Fortunately the trend starts from as low as zero and even negative overall trends and launches as more months are added to a plateau of around 0.7C/Decade. After enough months are added it drops back down to the no-offset average of around 0.5C/Decade. The plateau saves our butt, it appears that the true trend according to the thermometer data is actually about 0.065 Degrees C/Decade and is reasonably independant of months average for a fairly wide range. The result, however, is exciting in that it makes very little difference if these offsets are accounted for or not. Figure 4 is a plot of the Antarctic area weighted trend with a 60 month maximum overlap as chosen according to the Figure 3 graph.
The temperature slope distribution is shown in Figure 5.
The trend from this version is 0.067 +/- 0.0848 C/Decade.
So what does it mean Jeff, right?
Well, the change in trend from reasonable accounting of station offsets results in a warming trend of very slightly higher than the far simpler no-offset anomaly averaging used previously. Considering that Hu had the continental confidence interval at +/- 0.10 C/Decade the difference of 0.015 C/Decade is hardly worth mentioning. However, the various reconstructions take the basic form of Ax=b. The x value is a multiplier matrix which converts the surface stations into the missing data. This matrix is complex in time for RegEM which actually helps fit temp data to principal components in RegEM (an unnatural calculation as noted by RomanM a long time ago). You’ll notice there is no method in the equation for compensating for offsets in anomaly (i.e. Ax +c = b). Therefore, if I’m understanding everything correctly, different forms of expectation maximization and regression, when correctly applied, should converge to a value similar to the no-offset solution trend of 0.052 and contain spatial distributions more similar to Figure 1 than Figure 5.
For reference, Figure 6 is the Regularized least squares version of the reconstruction. There have been many but this one does the best job visually of localizing individual stations. I need to do a post explaining why it’s superior to RegEM for this reconstruction but that will be for a later project.