198 RADIO WAVE PROPAGATION EXPERIMENTS 
pressure and temperature changes. This suggests that 
the data were reliable. 
2. The values of K agreed with those of Giblett? 
for wind variations from the surface to 150 ft. 
3. This extrapolation method, that is, the error 
function extrapolation, gives reasonable values after 
a long period of time. A check was made by compar 
ing Taylor’s data off Newfoundland with computed 
values. This check was quite good. 
4. 'Fhe procedure is simple, and consequently the 
weather officer could readily calculate the M curve. 
However, the entire method may be criticized be- 
cause : 
1. In the integration of the diffusion equation K is 
assumed constant while in the application of the in- 
To? 32C Eo" 12,3 MILLIBAR 
Tw222 C Eye 26.5 MILLIBAR 
Ee 707A 
Pe 275 GS a, 
SR 2 |e 
— Hoth te et 
4HR GHR IOHR R 
VAC DNENENG 
(ESSE SSeS 
700 
600 
is 
8 
° 
400 
HEIGHT IN FEET 
310 320 330 340 350 360 370 380 
M 
Ficure 1. Changes in M curves resulting from modifica- 
tion of warm, dry air over cool, moist surface. Zero time 
corresponds to the coast line; 14 hr, 14 hr, etc., refer 
to the time the air has been over water. 
tegrated formula K was found to vary with elevation. 
The values of K which were used in the final analysis 
are therefore “effective values.” 
2. K has been considered to be independent of the 
degree of roughness (probably a justifiable assumption 
over the ocean), the degree of stability, and the wind 
velocity. These factors were neglected solely because 
the scant data did not allow a complete analysis of 
the variation of K. 
These “effective values” should give some indication 
of the true variation of K. They suggest that K varies 
linearly with elevation except for a quite rapid increase 
in about the first 30 ft. Consequently it seems reason- 
able to assume that 
a 2 | oet y=]. 
z oz 
If K = pz-+q then, from the statement that 
K (8u/8z) = constant (eddy stress does not vary with 
height), the velocity variation with elevation is given 
Dy 
u=alog (+6) +C. 
The question now arises: In the laminar layer, is the 
wind variation with height represented by a logarith- 
mic law? 
Previous Investigations 
For many years research workers have studied the 
wind variation near the ground. A few of the conclu- 
sions will now be presented. 
1. In 1932, Sutton® assumed a certain form of the 
coefficient of correlation between the velocities of the 
air particles considered at time ¢ and at an interval 
of time later. This assumption implied that there 
was a power law for the variation of wind with height. 
u Gy n 
= —) | — n= . 
nl Al 2—n 
2. In 1933, Cardington and Giblett? analyzed an 
extensive series of observations at 4 ft and 143 ft. Of 
course with only two points the observations could be 
made to fit either a power law or a logarithmic law. 
If a power law held, then m is a function of the degree 
of stability and wind velocity. If a logarithmic law 
held, then K is a function of these same quantities. 
3. In 1934, Best* analyzed data which was meas- 
ured at seven elevations between 2 cm and 5 m. He 
concluded that the velocity variation was best repre- 
sented by a logarithmic function of the form 
u— log (2 — C) 
where C’ is a constant. 
Furthermore he found that the power law could be 
TaBLE 2. Values of (T’ — T)/(To — Tw) or (e’ — e)/(€o — ey); initially To > Tx, €0 < ey. 
Time in hours 
Elevation ; 
in ft Ye yy 34 1 14% 
0 1.0 1.0 1.0 1.0 1.0 
20 0.23 0.40 0.49 0.55 0.63 
50 0.17 0.34 0.43 0.50 0.58 
100 0.09 0.23 0.33 0.40 0.49 
150 0.04 0.15 0.24 0.31 0.41 
200 0.02 0.10 0.19 0.25 0.35 
250 0.01 0.08 0.15 0.22 0.31 
300 0.01 0.07 0.14 0.20 0.29 
350 0.01 0.05 0.11 0.17 0.26 
400 0.00 0.04 0.09 0.14 0.23 
450 0.00 0.03 0.07 0.12 0.20 
500 0.00 0.03 0.05 0.10 0.17 
550 0.00 0.02 0.04 0.08 0.15 
600 0.00 0.01 0.03 0.07 0.13 
650 0.00 0.01 0.02 0.06 0.11 
700 0.00 0.00 0.01 005 0.10 
All values are negative. 
2 3 4 6 10 15 20 
1.0 1.0 1.0 1.0 1.0 1.0 1.0 
0.67 0.73 0.77 0.81 0.85 0.88 0.89 
0.63 0.69 0.73 0.78 0.83 0.86 0.88 
0.55 0.63 0.67 0.73 0.79 0.83 0.85 
0.48 0.56 0.61 0.67 0.74 0.80 0.82 
0.42 0.51 0.57 0.64 0.71 0.77 0.80 
0.38 0:47 0.54 0.62 0.69 0.75 0.78 
0.36 0.45 0.52 0.60 0.68 0.74 0.77 
0.33 0.43 0.49 0.58 0.67 0.73 0.76 
0.30 0.40 0.46 0.55 0.65 0.70 0.74 
0.27 0.37 0.43 0.53 0.63 0.68 0.72 
0.24 0.34 0.40 0.51 0.61 0.67 0.71 
0.22 0.32 0.38 0.49 0.59 0.65 0.70 
0.20 0.29 0.35 0.46 0.57 0.64 0.69 
0.18 0.27 0.33 0.44 0:55 0.62 0.67 
0.16 0.25 0.31 0.42 0.53 0.61 0.66 
