Temperature averages of continuously reporting stations from the GISS dataset

Guest post by Michael Palmer, University of Waterloo, Canada

Abstract
The GISS dataset includes more than 600 stations within the U.S. that have been
in operation continuously throughout the 20th century. This brief report looks at
the average temperatures reported by those stations. The unadjusted data of both
rural and non-rural stations show a virtually flat trend across the century.

The Goddard Institute for Space Studies provides a surface temperature data set that
covers the entire globe, but for long periods of time contains mostly U.S. stations. For
each station, monthly temperature averages are tabulated, in both raw and adjusted
versions.

One problem with the calculation of long term averages from such data is the occurrence of discontinuities; most station records contain one or more gaps of one or more months. Such gaps could be due to anything from the clerk in charge being a quarter drunkard to instrument failure and replacement or relocation. At least in some examples, such discontinuities have given rise to “adjustments” that introduced spurious trends into the time series where none existed before.

1 Method: Calculation of yearly average temperatures

In this report, I used a very simple procedure to calculate yearly averages from raw
GISS monthly averages that deals with gaps without making any assumptions or adjustments.

Suppose we have 4 stations, A, B, C and D. Each station covers 4 time points, without
gaps:

In this case, we can obviously calculate the average temperatures as:

A more roundabout, but equivalent scheme for the calculation of T1 would be:

With a complete time series, this scheme offers no advantage over the first one. However, it can be applied quite naturally in the case of missing data points. Suppose now we have an incomplete data series, such as:

…where a dash denotes a missing data point. In this case, we can estimate the average temperatures as follows:

The upshot of this is that missing monthly Δtemperature values are simply dropped and replaced by the average (Δtemperature) from the other stations.

One advantage that may not be immediately obvious is that this scheme also removes
systematic errors due to change of instrument or instrument siting that may have occurred concomitantly with a data gap.

Suppose, for example, that data point B1 went missing because the instrument in station B broke down and was replaced, and that the calibration of the new instrument was offset by 1 degree relative to the old one. Since B2 is never compared to B0, this offset will not affect the calculation of the average temperature. Of course, spurious jumps not associated with gaps in the time series will not be eliminated.

In all following graphs, the temperature anomaly was calculated from unadjusted
GISS monthly averages according to the scheme just described. The code is written in
Python and is available upon request.

2 Temperature trends for all stations in GISS

The temperature trends for rural and non-rural US stations in GISS are shown in Figure
1.

This figure resembles other renderings of the same raw dataset. The most notable
feature in this graph is not in the temperature but in the station count. Both to the
left of 1900 and to the right of 2000 there is a steep drop in the number of available
stations. While this seems quite understandable before 1900, the even steeper drop
after 2000 seems peculiar.

If we simply lop off these two time periods, we obtain the trends shown in Figure
2.

The upward slope of the average temperature is reduced; this reduction is more
pronounced with non-rural stations, and the remaining difference between rural and
non-rural stations is negligible.

3 Continuously reporting stations

There are several examples of long-running temperature records that fail to show any
substantial long-term warming signal; examples are the Central England Temperature record and the one from Hohenpeissenberg, Bavaria. It therefore seemed of interest to look for long-running US stations in the GISS dataset. Here, I selected for stations that had continuously reported at least one monthly average value (but usually many more) for each year between 1900 and 2000. This criterion yielded 335 rural stations and 278 non-rural ones.

The temperature trends of these stations are shown in Figure 3.

While the sequence and the amplitudes of upward and downward peaks are closely similar to those seen in Figure 2, the trends for both rural and non-rural stations are virtually zero. Therefore, the average temperature anomaly reported by long-running stations in the GISS dataset does not show any evidence of long-term warming.

Figure 3 also shows the average monthly data point coverage, which is above 90%
for all but the first few years. The less than 10% of all raw data points that are missing
are unlikely to have a major impact on the calculated temperature trend.

4 Discussion

The number of US stations in the GISS dataset is high and reasonably stable during the 20th century. In the 21st century, the number of stations has dropped precipitously. In particular, rural stations have almost entirely been weeded out, to the point that the GISS dataset no longer seems to offer a valid basis for comparison of the present to the past. If we confine the calculation of average temperatures to the 20th century, there remains an upward trend of approximately 0.35 degrees.

Interestingly, this trend is virtually the same with rural and non-rural stations.

The slight upward temperature trend observed in the average temperature of all
stations disappears entirely if the input data is restricted to long-running stations only, that is those stations that have reported monthly averages for at least one month in every year from 1900 to 2000. This discrepancy remains to be explained.

While the long-running stations represent a minority of all stations, they would
seem most likely to have been looked after with consistent quality. The fact that their
average temperature trend runs lower than the overall average and shows no net warming in the 20th century should therefore not be dismissed out of hand.

Disclaimer
I am not a climate scientist and claim no expertise relevant to this subject other than
basic arithmetics. In case I have overlooked equivalent previous work, this is due to my ignorance of the field, is not deliberate and will be amended upon request.