7. Appraisal of Results 



7.1. Accuracy of N(z) Maps 



The general accuracy of the 5 - year mean 

 values used in the N (z) study was checked by 

 computing the standard deviation of the year- 

 to-year monthly means and dividing by the 

 square root of 5. This should be a good estimate 

 of the rms (standard) error of the 5-year mean 

 values as compared to the true long-term mean 

 (assuming there are no trends in the data) . 

 Table 1 shows the estimated standard error of 

 the 5-year mean N s values for 40 stations, ar- 

 ranged by climatic classification. The percent- 

 age errors should be similar for the N(z) pa- 

 rameters (with the possible exception of scale 

 heights) at various altitudes. The combined 

 (rms) standard error of 5-year mean N s for the 

 40 stations for February and August was 2.37 

 A-units, or about 0.7 percent of the mean A r s . 

 It is significant that even the standard 30-year 

 period recommended (e.g., by the WMO) for 

 standard climatological normals would have a 

 nominal standard error of about ±1.0 A r -unit 

 (2.37 divided by \/6), or about 0.3 percent of 

 mean A s values. 7 The 30-year means would thus 



Table 1. Standard errors of 5-year mean values of monthly 

 mean Ns for J,0 stations. 



*For stations in the Southern Hemisphere, months were 

 reversed (February was combined with August for northern 

 stations, etc.). 



1 Thirty-year means are used because there are long-term trends 

 in most climatological series ; thus a standard period is desirable for 

 comparison between stations. 



have an advantage of only about 50 percent in 

 rms error, as opposed to the 5-year means 

 actually used. 



The overall accuracy of the three-part expo- 

 nential model was checked in two ways. First, a 

 che ck w as made of the accuracy of recovering 

 the AiV values using the three-part exponential. 

 Here the value of AA was calculated, using the 

 wet- and dry-term tropospheric exponentials, 

 and th e va lue obtained was compared with the 

 actual aA t from the mean A-profile. Figure 7 

 shows the results of such a comparison for 95 

 of the 112 stations in the original sample for 

 which coincident data of s eve ral types were 

 available. The true value of aA t from the mean 

 A 7 -profile is the dependent variable, and the 

 value recovered from the wet and dry expo- 

 nentials is the independent variable. The rms 

 error in recovering aA was 9.2 A-units ; how- 

 ever, if those stations (points shown as crosses 

 on fig. 7) which are in areas where the three- 

 part exponential model is of questionable valid- 

 ity (as shown in fig. A-30) are eliminated from 

 the sample, the rms error is reduced to 6.4 

 xV-units. The regression line shown in figure 7 

 is for this reduced sample. The deviation of the 

 regression line from the 45° line (labeled "per- 

 fect agreement" in fig. 7 : zero intercept and 

 unity slope) is significant at the 5-percent level ; 

 thus it would appear that this is not the best 

 usage for t he three-part exponential model. Use 

 of the aA maps in appendix B is recommended 

 rather than the A (z) maps, for this purpose. 



The second check was to use the N(z) maps 

 to recover the values of N (z) for some of the 

 actual station locations, at different heights 

 above the surface, and compare these with the 

 actual values of mean A (z) . This would be a 

 check not only on the three-part exponential 

 model but also upon the contouring process. 

 Table 2 shows the results of such an error an- 

 alysis. 



Thirty-two of the original 112 stations were 

 selected on an areal basis, and the correspond- 

 ing three-part exponential model was construct- 

 ed for each of these stations, for all 4 months, 

 using the maps in appendix A. These exponen- 

 tial models were then used to calculate A (z) for 

 three heights (3, 8, 16 km) for each month, and 

 the results were compared with the actual mean 

 A-profiles. The mean and maximum values of 

 the absolute errors thus derived are shown in 

 table 2. Stations and seasons in this sample 



20 



