On another branch of this web site, extrapolation from temperature forecasts at climate divisions to forecasts for station temperature is provided using simple linear regression equations. Those equations are derived from an analysis of the basic statistics of the temperature observations for the climate division and those for the station (i.e., their means, their year-to-year variabilities, and the correlation between them). Here, those basic statistics are provided for additional understanding, and also so that users can derive different translation formulae if desired. The following blocks of information are provided for each of 2114 cooperative stations and large urban stations: (1) monthly mean station temperature history for 1951-1997, and (2) 3-month period statistics of the station versus the four most highly correlated climate divisions. The second block is given for each of the 12 overlapping 3-month seasons of the year. That block consists of several sub-blocks: (a) correlations between the stations and the climate divisions, (b) history of the mean temperature for the given 3-month season over 1983-97 for the station and for the corresponding climate divisions (and the temperature difference between the station and the climate divisions), (c) multi-year biases, or mean differences, between the station and the climate division, (d) multi-year ratio of year-to-year variations (standard deviations) of the station in comparison to the climate divisions, and (e) resulting regression equations, as given in another branch of this web site. More specific detail about each of the above sub-blocks is now given.
Following the line giving station identification, the four climate divisions having the highest correlation with the station for the given 3-month season are identified by climate division number (1 to 102). The 1951-97 period is used to compute the correlation. Farther to the right, the correlations themselves are shown. For example, in the line "4 3 7 5 0.957 0.928 0.893 0.892", climate division 4 has a 0.957 correlation with the station, division 3 has a 0.928 correlation, etc. Next, the seasonal mean temperature of the station, and the same four most highly correlated climate divisions, are displayed for each year from 1983 to 1997. Below the temperatures for the four climate divisions, the differences between the temperature at the station and that at each climate division are shown. The notation "S- 4" means the station temperature minus the temperature at climate division number 4. Next appears a block of data showing statistics of the bias, or mean difference, between the temperature at the station and the temperature at each of the four related climate divisions. Let us describe the information by example. Suppose the following data, shown for the station at Block Island, Rhode Island for the DJF (Dec-Jan-Feb) season, appears:
BIAS=== 47yr by decade, 1950s to 90s Early means dif Recent means dif Bchange
DJF CD 5197 5160 6170 7180 8190 9197 S5165 C5165 S-C S8397 C8397 S-C rec-old
4 5.90 5.50 5.58 5.89 6.41 6.20 33.13 27.53 5.60 34.67 28.31 6.35 0.75
First, in the third line we see that it is climate division 4 that is being compared to the station. (The three additional lines, not shown here, do likewise for the three next most highly correlated climate divisions.) The middle line of the example gives abbreviated periods. For example, "5197" means 1951 through 1997. The number underneath this heading (5.90) is the mean difference between the temperature at Block Island and that at climate division 4, for the DJF season, over the 1951-97 period. The next 5 columns give this difference for five shorter subperiods, namely 1951-60, 1961-70, etc. This enables a user to check the consistency of the bias over time. Farther to the right are found the mean temperatures at the station ("S") for the "old" 1951-65 period, then the same for climate division (denoted by "C") 4, and then for the difference. Still farther to the right, the same analysis is applied to the more recent 1983-97 period. The final column gives the change in the bias from the 1951-65 period to the 1983-97 period.
Beneath the BIAS block is the SDEV block. This gives a similar analysis, except for the year-to-year variability, or standard deviation. Rather than using differences as was done for the bias comparisons, ratios are used. Consider the following example, also taken from Block Island, Rhode Island for the DJF season.
SDEV=== 47yr sdevs (S=station) Early sdevs Recent sdevs Rchange
DJF CD S5197 C5197 (C=CD) S5165 C5165 S/C S8397 C8397 S/C rec/old
4 2.53 2.51 2.52 2.73 0.92 2.00 2.14 0.94 1.02
As in the case of the bias statistics, statistics for climate division 4 are shown in this example, with additional lines given for the three next most highly correlated climate divisions (not shown in this example). The results shown in this example are just with respect to climate division 4. Because standard deviations are subject to much greater sampling variation than means, comparisons for sub-periods such as 1951-60 are not computed for standard deviations. Thus, the bottom line shows the year-to-year standard deviation of Block Island for the entire 47-year period (1951-97), which is 2.53 degrees, followed by that for climate division 4, which is 2.51 degrees. In this case the two are nearly identical. Farther to the right, the same comparison is shown for the early part of the period (1951-65), and the ratio of the standard deviations ("S/C"). That is, 2.52/2.73 equals 0.92. This implies that the climate division has more year-to-year variability than the station of Block Island. This stands to reason, since Block Island is closely surrounded by water that acts as a moderating influence on the temperature, insulating Block Island from the extremes that would affect the interior stations of the climate division more. Farther to the right, the same analysis is applied to the more recent period of 1983-97.
Finally, the ratio of the recent standard deviation to the early standard deviation is given, i.e., 0.94/0.92 = 1.02. It should be stressed that unless this ratio is substantially different from 1.00, its deviation from 1.00 might well be due to sampling factors. In this example, the 10.02 ratio is likely to be due to sampling alone. One way to increase the credibility of a standard deviation ratio would be to make certain that it remains consistent for the majority of the additional climate divisions shown, and also for neighboring 3-month periods. Both of these extensions are ways to increase the effective sample size for the comparison.
