APPRAISAL OP RESULTS 23 



7.2 Accuracy of AiV Maps 



As a check on the method used to calculate the 



AiV values from which the maps in appendix B 

 were derived, the AiV values from the weather 

 summary data were obtained for all 90 of the 

 stations which were a lso contained in the mean 

 iV-profile sample ; the AiV values for the months 

 of February, May, August, and November were 

 then compared with the corresponding values 

 from the actual mean iV-profiles. However, the 

 period of record involved in the mean iV-profile 

 study was not, in general, even partially coin- 

 cident with the 1960-64 period used for the AiV 

 study. Thus it was expected that the variance, 

 "d 2 , of the differences between the weather sum- 

 mary AiV values (from which the maps given in 

 appendix B were obtained) and the aA7 values 

 from the mean .V-profiles would have two com- 

 ponents, 



« D - = " R 2 + « E 2 , (8) 



where °r 2 is the variance of the real difference 

 in the two 5-year mean values of AiV (because 

 they are obtained from different time periods) , 

 and "e- is the variance of the differences which 

 are caused by the interpolation errors inherent 

 in the method used to obtain the AiV from the 

 weather summary data. Since the real differ- 

 ences (represented by "r) would be expected to 

 have a near-zero mean for a worldwide data 

 sa mple , a regression analysis of the two types 

 of AiV values should reveal any bias which had 

 been p rod uced by the interpolation method used 

 in the AiV study. Figure 8 shows the results of 

 such a comparison, with AiV from the mean 

 iV-profiles as the dependent variable, and AiV 

 from the weather summary data as the inde- 

 pendent variable. There is no statistically sig- 

 nificant bias shown, since the regression line is 

 almost identical with the "perfect agreement" 

 line (zero intercept and slope of unity). 



An evaluation of the relative sizes of °" R and °e 

 was made by calculating the rms difference be- 

 tween the two types of AiV values for a restrict- 

 ed sample containing only those stations where 

 the mandatory pressure level used to calculate 

 the A/V values from the weather summary data 

 was within ± 100 m of 1 km above the surface; 

 the rms difference thus calculated was 3.9 N- 

 units. Since any interpolation errors would be 

 expected to be quite small for this restricted 

 sample, it was concluded that the 3.9 iV-unit 

 rms represented essentially the value of ° R as 

 given in (8). 



The value of » D as given in figure 8 is 5.2 

 iV-units; thus by (8) the value of <r E is probably 

 on the order of 3.5 iV-units. This should be a 

 good approximati on to that part of the overall 

 rms error in the AiV maps which is assignable 



to the interpolation method used on the weather 

 summary data. 



The overall accuracy of the AiV maps given in 

 figures B-2 through B-13 depends on several 

 factors : the accuracy of the interpolation meth- 

 od, the variability of the 5-year mean period as 

 compared with a standard WMO 30-year mean 

 period, and the heterogeneous nature of the 

 local observation times included in the data 

 sample. The weather summary data were most- 

 ly derived from observations taken at 0000 

 GMT, although many stations in different parts 

 of the world supplied data taken at 1100 or 1200 

 GMT, while others supplied data averaged at 

 two, or in a few cases four, times per day. In 

 this study no attempt was made to correct for 

 diurnal variations imposed by the fixed observa- 

 tion times of the various stations ; hence diurnal 

 variability must be added to the sources of pos- 

 sible error in the maps. It is reasonable to 

 assume that the actual (unknown) standard 

 error of the maps is not independent of the true 

 value of monthly mean AiV desired, but that it 

 is more likely a certain percentage of the true 

 value. Since the overall correlation between the 

 contoured and true values is probably quite 

 high, it is plausible to estimate the standard 

 error of the maps as a percentage of the con- 

 toured values. On figure 8 it is found that an 

 allowance of ± 10 percent from the perfect- 

 agreement line (in the vertical) will exclude 

 only 23 percent of the 360 data points (40 above 

 the limits, and 44 below the limits) ; for a nor- 

 mal distribution, 32.5 percent of the points 

 should be excluded by the standard error limits. 

 Therefore, allowing for some added error from 

 diurnal variability, it seems reasonable to esti- 

 mate the overall standard error of the maps of 

 AiV as approximately 10 percent of the con- 

 toured values. 



This is equivalent to assuming an error model, 



= «V + "E 2 + 



(9) 



where the terms have the same meaning as 

 those in (7) and (8), with V = ° R 2 (possibly 

 as low as V& "k 2 ) m (8), and where a t 2 is the 

 variance assignable to diurnal variations in AiV. 

 The value of " t should be on the order of 2 to 4 

 iV-units, which is an estimate based on inspec- 

 tion of the CCIR maps [CCIR, 1965]. 



There is doubtless some bias error in the AiV 

 maps ; the discussion given for bias errors in 

 the N (z) maps is mostly applicable to the AiV 

 maps. Here the bias due to the radiosonde is 

 relatively larger, because of the differencing 

 used to obtain aN values. This mean bias error 

 may be as high as 1 percent of the AiV values, 

 but data adequate for checking on this possi- 

 bility are not available. 



