HYDROMETEOROLOGY IN THE UNITED STATES 
relationships to develop optimum distributions of mois- 
ture, temperature, and wind. 
Vertical Motion. The precipitable-water depth is the 
amount of moisture available for precipitation in an air 
column. By itself, however, it does not provide sufficient 
information for computations of precipitation imtensi- 
ties. Lifting of a saturated column produces a cooling 
according to the pseudoadiabatic lapse rate, and there- 
fore a decreasing water-vapor content. Thus, if the 
lift-speed of the column is known in detail, the rate of 
decrease of W—and hence the rate of condensation— 
ean be computed. If the cloud-particle content of the 
air column remains fixed, the condensation rate becomes 
the precipitation intensity. For saturated air with con- 
stant cloud-particle content, precipitation itensities 
can be determined by means of a diagram prepared by 
Fulks [6], which shows the condensation rate, per unit 
vertical lift, in 100-m layers of air for various values of 
pressure and temperature. The equation for intensity of 
precipitation J, under the same assumptions, 1s 
T= | Vepe! ae, (3) 
Zo 0z 
where V, is upward velocity and p is air density. An 
integrated form of this equation has been discussed by 
Showalter [19]: 
I = V.,po(%o — %1)/7 inches per hour, (4) 
where Vz, is the vertical velocity at the bottom of the 
air column in which the rain is produced, po is the 
density at the bottom, and 2 and a are the mixing 
ratios at the bottom and top, respectively, of the 
column. 
Use of equation (3) requires detailed knowledge of 
both q and V,. The volumetric distribution of humidity 
can be estimated from available aerological soundings 
or, indirectly, from surface observations in cases of 
heavy rain. Only under very special conditions, how- 
ever, can the space distribution of vertical velocity be 
estimated with an accuracy sufficient for hydrometeor- 
ology, and direct measurements of this factor are almost 
completely lacking. Miller [14] has discussed a number 
of ways of expressing vertical velocities in terms of 
quantities more amenable to measurement. Combina- 
tions of such expressions with equation (38) can produce 
various rainfall-intensity equations. 
Equations of Continuity. Basic to all theoretically 
derived rainfall relations used in hydrometeorology is 
the equation of moisture continuity. This relation states 
that the average depth F of rainfall through duration D 
and over area A is equal to the moisture flowing into 
the space above A, minus that flowing out, plus the 
moisture above A at time ¢ = 0, minus the moisture 
att = D. The moisture gq, to be exact, should be defined 
as the total number of grams of water in the air per 
gram of air, whether it be in the form of water vapor, 
cloud droplets, rain, or snow. Lacking sufficient data as 
to atmospheric content of liquid- or solid-water par- 
ticles, hydrometeorologists have assumed that con- 
sideration of the water-vapor content, alone, leads to 
conclusions that are satisfactorily accurate. The as- 
1037 
sumption may involve important errors in the case of 
short-duration, small-area rainfall, the errors probably 
diminishing, however, with an increase of duration 
and/or area. 
The equation of continuity for moisture may be 
written 
ja = Wa) LEU poor ds de dt 
= [i¢ aps Gs Ge Oh te ([ [ waaa) (6) 
= Cee gp dz a) | 
where V; and V2 are the horizontal inflow and outflow 
components, respectively, of the wind normal to a 
horizontal linear element ds of the vertical wall of the 
cylinder extending upward from the boundary of area A. 
The quantities V, g, and p must all be forecast if the 
equation is to be used for the quantitative prediction 
of precipitation. For purposes of estimating maximum 
possible precipitation, the most critical combination and 
values of the ndependent variables must be determined. 
For the horizontal wind, unlike the vertical velocity, 
measurements are available. Indeed, successful attempts 
have been made to compute rainfall by direct applica- 
tion of equation (5), although qg has had to be considered 
as a measure of water vapor only, and time and space 
interpolations of wind between pilot-balloon observa- 
tions have been necessary. Unfortunately, while several 
meteorological projects have been undertaken, incor- 
porating dense rain-gage networks and dense coverage 
of upper-air observations, a near-maximum rainstorm 
has never occurred when they were in simultaneous 
operation. As a consequence, investigations of major 
rainstorms have required approximations of equation 
(5), with substitutions of available measurements. Fur- 
thermore, the choice of elements to be used has neces- 
sarily been restricted to those with considerable abun- 
dance and length of record in order that methods and 
results could be comparable. 
In some approaches to the problem, the continuity 
equation for air is used: 
v= [fp evsas ae a - [ [fp eveasae a 
+([[edas) - ([/[ eda). 
in which the variables are the same as those appearing 
in equation (5). When simplifying assumptions are 
made, the use of equation (6) can bring about elimina- 
tion of one of the more-difficult-to-measure variables of 
equation (5). 
Storage Equation. Relationships (5) and (6) are quite 
general. When applied to certain simple flow models, 
they may be transformed into a rainfall equation which 
has demonstrated its ability to produce results com- 
parable with observed rainfall amounts. In one such 
flow model—a two-dimensional one—the wind blows 
(6) 
