METEOROLOGY — FORECASTING 251 
can be approximated as indicated in Figure 15 by 
assuming that standard conditions prevail above the 
duct and that the M deficit (AM) is the difference 
between the actual M value at the sea surface and 
the M value that would exist at the sea surface if the 
standard conditions were extended down to the surface. 
The method is not applicable to conditions over 
land. 
In the case of air with a purely sea trajectory, it 
turns out that the procedure is closely valid if, in 
place of the air temperature and humidity measure- 
ments made over land, these measurements are taken 
in the air at a slight elevation above the sea surface, 
for example, at bridge level on a large ship. 
In practical application results will be most reliable 
when the assumptions listed under “General Proce- 
dure” are satisfied. However, this docs not mean 
that the method is useless under other circumstances. 
Figure 19, which is the crux of the method, is largely 
empirical and is based on relationships: which have 
been observed to hold under various meteorological 
conditions. Consequently, reasonably accurate results 
are not limited to only a few idealized situations. 
it should be mentioned also that use of the method 
in a literal manner can be improved upon if the cal- 
culated results are modified by the judgment of 
someone trained or experienced in meteorology. Com- 
plicating factors such as variations in the initial sta- 
bility conditions, variability of the sea surface tem- 
perature, effects of convergence, divergence, and sub- 
sidence, and presence of fronts can best be taken into 
account by one familiar with their effects. 
QUALITATIVE PREDICTION OF RapaR RANGES 
The method described above gives a means of esti- 
mating surface duct formation, whereas what is needed 
is a knowledge of the effect of the duct on radio propa- 
gation. It is impossible to make a blanket statement 
giving the exact range that will be obtained with any 
particular duct width, since the range depends on the 
power of the radio or radar set (also on the character 
of the target, in the case of radar), as well as on the 
factors listed on pages 245-248. However, some numer- 
ical estimates of trapping effects can be made. 
Dependence on Duct Width, Frequency, and Eleva- 
tion of Site. An approximate expression relating the 
maximum wavelength that can be trapped by surface 
ducts is given by 
Amax = 0.076d\/AM — 0.086d, 
in which Amax is the maximum wavelength in centi- 
meters, d is the duct width in feet, and AM is the M 
deficit in M units. Table 2 is developed from this 
formula and indicates, for given values of AM and d, 
the wavelength above which trapping will not occur. 
A rough generalization can be made by stating that, 
when the wavelength of the radiation is around 3 cm, 
duct widths of 20 ft or more will be sufficient to cause 
simple surface trapping, and, when the wavelength is 
around 10 cm, duct widths of at least 40 or 50 ft will 
be sufficient, provided in each case that the transmitter 
is located within the duct. Thus, for a particular radar 
frequency and location, an estimation of duct width 
becomes a critical factor in anticipating whether an 
appreciable amount of trapping will occur and con- 
sequently whether radar ranges will be appreciably 
larger than under standard conditions. 
TABLE 2. Values of the maximum wavelength (in em) 
for which waves can be trapped in a surface duct for 
given values of M deficit (AM) and duct width (d). 
AM (M units) 
d(ft) 2 5 10 15 20 25 
10 0.97 1.63 2.36 2.90] 3.36 3.78 
20 1.72 | 3.14 462 5.75 6.67 7.49 
30 2.19 | 4.52 6.80 8.50 9.93 11.1 
40 2.28 | 5.74 8.88 | 11.2 13.1 14.7 
50 1.69 | 6.80 10.9 138 162 18.3 
60 ee 7.65 128 163 19.2 21.8 
70 ie 8.35 145 188 22.2 25.2 
80 ee 8.82 162 212 25.2 28.6 
Dependence on Extraneous Factors. Meteorological 
conditions other than ducts often have important 
effects on propagation. Surface fog frequently causes 
substandard conditions. Rain and clouds may attenu- 
ate the propagated energy and effectively decrease 
the range. Heavy rain and sometimes cumulo nimbus 
clouds cause radar echoes. 
OprraTIonaL Usr AND LIMITATIONS 
The restrictions surrounding the possible utilization 
of this prediction technique have been covered earlier 
in this section, where it is indicated in what respects 
applicability is limited. Subject to these limitations, 
the method can be employed to advantage. Short-term 
predictions (a day or so ahead) of duct formation and 
radar range can aid in estimating the coverage of a 
particular radar set. Information of this nature should 
lead to the more efficient use of radar facilities. 
Computed Climatological Information 
on Surface Ducts 
Punrrost or THis INrFoRMATION 
Inasmuch as the present report is designed to aid 
radar and meteorological officers in the Pacific theater 
of war, it has been thought expedient to include 
climatological information on that area which gives 
an indication of the occurrence of surface ducts. For 
this purpose, computations have been carried out, 
using the methodology given on pages 249-150, to 
yield the following : 
1. Estimation of the per cent of time surface ducts 
of certain widths are likely to occur at various times 
of the year and at various places in the western Pacific 
theater. 
2. Estimation of the variation in duct width with 
