rnWABY 1956 MONTHLY WEATHER REVIEW 53
QUANTITATIVE ANALYSIS AND FORECASTING
OF WINTER RAINFALL PATTERNS
W. W. SWAYNE
Hydrometeorological Sectlon. U. S. Weather Bureau, Washington, D. C.
manuscript received November 29, 195% revised March 9. 19561
ABSTRACT
A method is given for analysis of current rainfall intensity distribution and for preparation of short-period
quantitative rainfall distribution forecasts using practical synoptic techniques. The analysis procedure is justified
by a formulation which gives the condensation rate associated with the horizontal transport of saturated air through
a stationary temperature field. The forecast procedure in addition utilizes (1) short-period extrapolations of the
fields of moisture, motion, and temperature, (2) volumetric inflow of moisture in depth northward across a fixed bound-
ary near the Gulf Coast as an approximation of the total rainfall during the forecast period, or when this is not appli-
cable, the volume indicated by the moisture-depletion formulation, (3) envelopment of the initial and terminal
period boundaries of moisture depletion to define the boundaries of the forecast pattern, (4) position of the maximum
moisture advection to forecast the rainfall center, and (5) isohyetal analogues to fill in details of the pattern, par-
ticularly the orographic details which have not been treated otherwise in the present application. The results of a
systematic test of forecasts using these ideas are also presented.
1. INTRODUCTION
Oneof the basic problems in hydrometeorology is the
quantitative definition of rainfall distribution in terms of
other meteorological parameters. Good correspondence
between observed and computed rainfall patterns has been
obtained by simultaneous treatment of the fields of mo-
tion, moisture, and temperature for each sub-layer of a
multi-layered atmosphere. Thompson and Collins [I]
used the vertical velocities obtained by divergence compu-
tations at 50-mb. intervals to compute the precipitation
rate. Spar [2]alsoused50-mb. intervals to obtain
“integrated moisture transport vectors” for computing
the rainfall rate. An approach suitable for high-speed
numerical computations has been reported by Smagor-
insky and Collins 131 ; it was applied to a 3-level model of
the atmosphere.
Another approach is to relate the rainfall rate directly
‘t o the transport of moisture through a single deep layer.
This has been done analytically for the case of high oro-
graphic barriers in [4],[5] and other reports. Benton
and Estoque [6] in a climatological-hydrologic study of
water-vapor transport in the 1,000- to 400-mb. layer for
the calendar year 1949 show a good relationship between
monthly and seasonal transport patterns and precipitation.
The feasibility of simple dynamic treatment of moisture
in depth for estimating the volume rate of rainfall for
short-time periods was demonstrated by an experiment
conducted in the Hydrometeorological Section in 1954
[’I]. The instantaneous rate of northward mass transport
of water vapor between the surface and 400 mb. across
the Gulf Coast was computed once daily for two winter
months. Assuming the instantaneous transport rate to
persist for 24 hours, the 24-hour moisture transport for
high inflow rates was found to be about equal to the ob-
served 24-hour volume of rainfall measured over the area
downwind from the inflow boundary the next day (fig. 1).
The present study was initiated in an effort to forecast
the pattern and area of occurrence of the rainfall volume
indicated by the Gulfinflow rate. The approach is to
treat the precipitable water and thickness fields through a
single deep layer in the lower troposphere with the motion
indicated by the height contours at the middle of the
layer. I t has been used both for the determination of the
current distribution of the rainfall rate, and for quantita-
tive forecasts of rainfall patterns. Although the method
is more restrictive than [3], for example, it seems especially
useful for short-period forecasts of heavy, general, winter-
type rainfall, and is simple enough for practical day-to-day
use by conventional synoptic methods.
The point of departure in attacking this problem is
given by the fact that warm air advection is very often
observed upwind from and within the areas of general
rainfall occurrence. (See, for example Appleby [SI and
Means [9].) Temperature advection will concern us here,
however, only as it is related to the horizontal advection of
moisture. Our fist purpose is to determine whether the
condensation rate, whichwould seem to be necessarily
associated with the apparent cooling of deep layers of
saturated air in transport through a field of decreasing
temperature, is reflected in the rainfall intensity distribu-
tion.
In section 2 of this paper a formulation relating hori-
54 MONTHLY FEBBUABY 1956
24- HR. MOISTURE TRANSPORT ACROSS 3O'N. (IO'rq.mi.- inches)
FIQIJBE 1.-Transport of moisture across 30' N. between longitudes
of Tallahassee, Fla., and San Antonio, Tex., fromsurface to
400-mb. level (assuming 1500 GMT rate is maintained 24 hours)
plotted against observed precipitation, during 24 hours beginning
at 0630 CST of day moisture-transportmeasurement was made,
measured downwind from the San Antonio-Tallahassee baseline.
zontal moisture transport to the rainfall rate is developed
from simple physical and synoptic ideas. For practical
synoptic application certain simplifying approximations
and assumptions are required. These have not been tested
intensively; instead, their validity as a set has been
evaluated by the preparation of a series of rainfall rate
analyses (section 3) and short-period forecasts (section 4).
2: MOISTURE TRANSPORT RELATED TO RAINFALL
RATE
The distribution of rainfall is basically dependent on the
transport and condensation of moisture. Thus, fcr a
comprehensive treatment of rainfall it is necessary to re-
late moisture, temperature, pressure, and motion, a t all
levels in the atmosphere. A less comprehensive but still
useful treatment is possible under certain simplifying
assumptions.
ASSUMPTlONS
The rainfall rate can be related to moisture transport in
a simple and convenient way with the following assump-
tions :
(1) To circumvent the dficulty of treating moisture
layer by layer, precipitable water through a single deep
layer in the lower troposphere is assumed to be an appro-
priate moisture variable. Moisture in depth (precipitable
water) aa related to rainfall intensity, is discussedex-
tensively by Showalter [lo], 11 11, [12], [13] and in reports of
the Hydrometeorological Section [14], [15]. The selection of
precipitable water as the moisture variable in this study
has the further advantage that the horizontal distribution
of precipitable water may be conveniently expressed in
terms of thickness, the use of which is already well estab-
lished in synoptic practice. The precipitable water is
related to the thickness (mean virtual temperature of a
layer between isobaric surfaces) by conversion to "satura-
tion thickness". This is defined as the thickness between
the specified constant pressure surfaces of a saturated
pseudoadiabatic column having the same precipitable
water value as the observed column. Tables 2 and 6 of
"Tables of Precipitable Water" [16] provide the required
values; table 2 gives the integrated values and increments
of precipitable water for the various pressure intervals and
height intervals, while table 6 gives the pressure-height
values for a saturated atmosphere. Since the formulas
on which the tables are based are simple and well-known
[17, 181, we shall omit the thermodynamic theory and use
the tabular values directly.
The relationship between saturation thickness and pre-
cipitable water for a saturated layer between 1,000 and
700 mb. is shown in table 1.
'1
(2) An area of general, heavy, winter-type rainfall is
assumed to occur within an area overlain by a deep
saturated layer, that is, a layer whose observed thickness
is approximately equal to the saturation thickness.
(3) Thickness lines in saturated areas are assumed to be
fixed over the area for the duration of general rainfall. In
a preliminary experiment, the 12-hour thickness change at
all radiosonde stations where rainfall was continuous be-
tween soundings was tabulated for two winter months. In
these cases it was found that despite strong warm advec-
tion, the average thickness change was about what would
be expected from the standard observational error. Spar
[2] and Locklear [19] also made this assumption for the
computation of the rainfall rate.
(4) The transport of moisture through the deep layer is
proportional to the geostrophic wind at the middle of the
layer. In synoptic practice it is often assumed that the
vector mean value of the horizontal motion at the base plus
that at the top of an isobaric layer gives the mid-layer
motion-the basis of differential analysis methods for in-
terpolating a mid-layer surface contour field. Conversely,
TABLE 1.-Thickness as afunction of precipitable water in a saturated pseudoadiabatic column between 1,000 mb. and 700 mb. (Smoothed values). (Computed from tables 2? and 6 [la].)
Precipitable water (inches) Precipitable water (inches) thickness S a t u r a t i o n - S a t u r a t i o n -
(feet)
BEBUABY 1956 MONTHLY WEATHER REVIEW 55
it may be assumed that the mid-layer motion approximates
the net motion of air through the layer. We are more con-
cerned, however, with the approximation for moisture
transport through a layer. A test was performed with data
-from the Gulf water vapor transport study. The following
ratio was obtained for the northward component of mois-
ture transport between two radiosonde stations: the sum of
the moisture transport for the 1,000- to 700-mb. and the
700- to400-mb. layers, divided by the product of the
average precipitable water 1,000- to 400-mb. and the
transport at 700 mb. The ratio was found to be close to
unity for the higher transport values.
(5) Vertical moisture transport, other than that implied
by the nonmovement of thickness lines in the rain areas
(see assumption 3), is ignored in this formulation. In-
vastigations of the local intensification of the vertical mo-
? tion and associated rainfall by differential temperature
advection, have been reported by Gilman [20], Appleby
[8], and MiUer [21].
(6) For convenience the variation of the Coriolis param-
eter and the effect of changes in spacing of contours of the
mid-layer pressure surface will be neglected. These sim-
plifications will not introduce appreciable error so long
actual computations are made for small increments of
Under the above assumptions a simple expression for the
moisture transport can now be derived and related to the
rainfall rate.
area.
MOISTURE TRANSPORT
Consider the case of asaturatedlayer, stationary temper-
aturefield, and horizontal geostrophic motion. Since, as
table 1 shows, the thickness specifies the precipitable water
value, the instantaneous moisture transport across a
boundary in the saturated area is specified, under our
assumptions, by superimposing the thickness field and the
pressure contours at the middle of the layer. Thus, the
moisture transport M across the segment of a thickness
line Z that is intercepted by two adjacent contours of geo-
potential c$~ and &, with I spacing A n, is given by
(1) M = V, WAn
where W is the precipitable water defined by the satura-
tion thickness 2, and V, is the geostrophic wind speed
Equations (1) and (2) therefore give the following simple
‘expression for the moisture transport:
M” 1 (42-4J1) w “f
The moisture transport as given by equation (3), though
indicating the volume rate of rainfall (e. g., fig, l ), does not
by itself specify the location or size of the area of rainfall
8 7 9 8 0 2 -6 G 2
FIGURE 2.-Grid element of thickness and height contours in a
saturated region. Z1, Wl and Zz, W2 are thickness and precipita-
ble-water values at the inflow and outflow boundaries of the ele
ment, respectively. The geopotential heights, 41 and 42, are the
geopotential height contours bounding the grid element. Since
the region is saturated, Z defines the value of W . The symbols
As and An are the distances between the thickness lines and the
height contours, respectively. Also &>& and ZI>ZZ, conditions
for condensation of moisture by horizontal advection (assuming
no supersaturation).
occurrence. However, equation (3) can be used to obtain
a convenient expression for moisture advection, which un-
der the assumptions of this paper is proportional to rainfall
rate.
RAINFALL RATE
Consider the condensation process for the limiting case
of a saturated layer, stationary temperature field, and
horizontal geostrophic motion. The differencebetween
the moisture transport at suitably selected inflow and
outflow boundaries, that is the moisture advection, is
determined by the temperature advection. Where initially
saturated air columns are moving into regions of lower
temperature, water vapor must be condensed out (assum-
ing no supersaturation); and where they are moving into
warmer regions, the water-vapor capacity of the columns
is increasing, thereby inhibiting the condensation process.
This study is chiefly concerned with moisture depletion,
that is, with moisture advection in saturated air associated
with warm temperature advection.
In general, measurement of the moisture advection is
not a simple computation. (Seee.g., Spar. [2].) For the
special case of saturated air with geostrophic motion, how-
ever, the indicated warm temperature advection pattern
represented by the superposition of the thickness field and
height contours at the middle of the layer gives a ready
56 MONTHLY REVIEW FEBRUARY 1956
means of computing the moisture depletion (moisture
advection) and the associated rainfall, as nowwill be
shown.
Consider a small rectangular area bounded by a pa.ir of
thickness lines and a pair of contours for an isobaric sur-
face at the middle of the deep saturated layer, with the flow
directed in the sense of warm air advection (fig. 2). Since
the region is saturated, Zl defines Wl and 2, defines W2.
Thus, according to equation (3)) the transport of moisture
MI across the boundary 2, into this grid element is given
by
(4) "'7 (k"J w1
1
Similarly, the transport of moisture M2 across the bound-
ary Z2 out of the grid element is given by
Now the moisture depletion rate M, due to condensat,ion
over the area of the grid element is M1-M2, which from
(4) and (5) is given by
1 (6) M c -7 (42-41) (w 1 -R )
The author is indebted to a reviewer for pointing out
that equation (6) follows immediately from Spar's [2]
expression for precipitation intensity as a function of the
"vapor transport vector" when one uses the mean geo-
strophic wind Vo for tbe layer and makes the assumptions
aw that -=0 and -=O, as was done in the present paper. avo at as
The factor We= Wl-W, represents the amount of
water which would be condensed out by cooling a satu-
rated column at the pseudoadiabatic lapse rate through
the thickness interval Z,-Z2. Table 2 gives values of
this factor for cooling through various thickness intervals.
These values can be used to approximate the rate of con-
densation of water vapor within an isobaric layer, required
by' the apparent advection of -saturated columns from
higher to lower thickness values (neglecting vertical
motion).
,. In equation (6)) the factor 1 ($2-$1) is the familiar
geostrophic transport term, giving the area transported f
TABLE 2.-Amount of precipitable water condensed by cooling a satu- rated column throughspecified thickness intervals (prepared from
i I
data in table 1 )
Change in saturation
(inch@) thicknem (feet) water thickness (feet)
Change in Change in saturation precipitable
""""
-~"
0.298 9,300-8,200 """_"""" - .260 9,400-9,300 """""""" ~
8,8004,700 _________________ .127 8,9004,800 _________________ .147 9,000-8,900 _________________ .170 9,100-9,000 """"""""_ .I96 9,200-9,100 ____..___________ .B6
precipitable Change in
(inches) water
0.109 .093 .078 .066 .062 .040 .029
between height contours on a conatant pressure surface
at a given latitude per unit time. This factor has been
calculated using the Smithsonim wind t,ables 1181. With
use of this factor and values of W, from table 2, values of
M, have been calculated from equation (6) for the 1,000-
700-mb. layer. Values of M, are given in table 3.
The average rainfall rate (B) over the area of the grid
element, if all the condensed water falls out, is propor-
tional to the moisture advection and is given by
It can further be shown that
where K=-a p* is absolute humidity, T* the virtual
temperature, Ap the pressure interval between the top and
bottom of an isobaric layer, pw the density of liquid water,
jj the average pressure in the column, and Ra is the gas
constant for dry air. Then the rate of condensation of
moisture is given by
R d
SPWP
This is the relation between the transport, the absolute
humidity, the virtual temperature, and the condensation
rate.
More comprehensive treatment of the moisture con-
tinuity considerations will be found in two recent papers
[2] and [3] in the Monthly Weather Rewiew to which the
reader is referred for discussion of assumptions. In their
paper, Smagorinsky and Collins [3] proceed from the re-
quirement for continuity of the mixing ratio T, given by
TABLE 3,"Hourly rate of condensation per thickness-contour grid
element in the 1,000- to 700-mb. layer for various latitudes and thick-
ness value intervals (in inch-square-miles per grid element, 1 0 6
f t . contour and thickness intervals)
1
Thickness interval (feet)
I T
10,100-10,ooo """"""""""""
lO,~,~"""""""""""" 9,900-9,800""""""""""""- 9,800-8,700 _""""""""""""
9,M)o-9,wo """""""""""""
9,5069,400 """""""""""""
9,300-6,m. ""_"""""""""" 9,"9,100 """""""""""""
9,100-9,ooo """""""""""""
9,ooo-8,900". """""""""""
9,700-9,600-. .......................
8,900-8,800 .......................... 8,800-8,700 .........................
2 010 1: 750 1,620 1,320 1,140 990
860
630 730
440 530
350 270 200
1,700 1,480 1,290 1,120 970 840 720 620 530
440 370 300 230 170
Latitude O N.
-
35
1,480
980 850 730 630 640 460 390 320 260
200 140
-
-
40
-
1, I50 1,320
1, OOo 870
750 650
480 560
350 410
290 230 180 130
-
45
1280
910 790 680
610 590
370 440
310 280
210 160 120
1: 050 1,110 970 840
630 730
650 470
350 410
290
240 190 160 110
.__
E5
1,040 900
680 780
690 510 440 380 320 270 230
180 140 100
-
FEBBnaBn 1956 MONTHLY WEATHER REVIEW 57
where V is the horizontal wind vector, w=dp/dt, and V
is the horizontal vector gradient operator. In a personal
communication these investigators demonstrate that
equation (9) in the text above can be obtained directly
from their work [3] by essentially one approximation.
They state:
. . . it is merely necessary to make the approximation that the
non-conservation of the mixing ratio is given to a sufficiently good
approximation by the horizontal advection of the mixing ratio
[i.e., =V.Vr]. This implies that the local change in the mixing
ratio [&-/at] is for the most part balanced by the vertical advection
O- . We know that especially in moist tongues there is at least
B tendency for compensation in sign. However, from our own work
we know that during the condensation process -9 V-Vr, and w- br br
tend to be of the same magnitude, so one would expect situations
where there is not adequate compensation between - and co -.
dr
[ 3
at bP
ar br
bt bP
3. ANALYSIS OF RAINFALL
ANALYSIS PROCEDURE
Details of the actual operations in analyzing the mo-
tion, thickness, and moisture fields for a specified isobaric
layerwillnowbe explained utiIizing the observed 1,000-
to700-mb. thickness and precipitable-water fields and
the 850-mb. contours. The 850-mb. contours give the
geostrophicfield of motion of the layer, the 1,000- to
700-mb. thickness pattern gives the temperature field,
and the precipitable-water pattern gives the distribution
of moisture in depth.
Thickness and contour lines were spaced at 100-ft.
intervals. A finer grid would have been desirable, but
the average error of observation [22, 231 would not seem
to justify it. The scale is set by the grid interval. Even
in the moisture-depletion areas associated with the heavi-
est winter rains, 100-ft. x 100-ft. grid elements are seldom
smaller than perhaps 15,000 or 20,000 square miles. The
aim is to define the average depth of rainfall by areas as
large as or larger than this. It is not expected that the
grid elements would represent intensity for time periods
much shorter than 3 hours and it has been assumed that
a 6-hour period is not too long.
The analysis steps are:
(1) The temperature advection pattern is obtained by
superimposing the 850-mb. contours on the 1,000-700-mb.
thickness pattern.
(2) A zero-advection line is then drawn on the super-
imposed field to separate the areas of warm- and cold-air
advection.
(3) The isopleths of saturation thickness are drawn by
converting the precipitable-water pattern to saturation
‘thickness, using the conversion given in table 1.
(4) The 1,000- to 700-mb. observed thickness pattern
is superimposed on the saturation thickness pattern.
Those areas where the saturation thickness is within 100
feet of the observed thickness are outlined. This latitude
is required because the humidity observations are known
to be consistently low.
(5) The outline of the saturation area is placed over the
advection pattern. In general, it is expected that the
rainfall near observation time is occurring within the
region enclosed upwind by the saturation line and down-
wind by the zero-advection line. This area is designated
the moisture-depletion area, because the procedural hy-
pothesis is that a necessary and s d c i e n t condition for
water-vapor condensation is the concurrent existence of
saturation and warm air advection through a deep layer.
(6) The hypothetical lower limit to the hourly volume-
rate of rainfall per grid element, as given by equation (6),
is obtained from table 3 for the appropriate thickness
interval and the latitude at the inflow boundary of each
grid element. However, because 6 hours is considered to
be a more representative time period for determining the
rainfall intensity from the grid elements, each hourly value
obtained from table 3 is multiplied by 6 and assigned to
the appropriate grid element. The total 6-hour volume
of rain for the moisture depletion area is obtained by add-
ing the values for the grid elements.
In the application of the above procedure, it is of course
well to keep in mind the limitations imposed by the under-
lying assumptions. The instantaneous rainfall pattern
is visualized as a system of many moving cells, forming
and dissolving in the general flow, the instantaneous in-
tensities heavy over only a small part, and light over a
much larger part, of the rain area.
The analysis, of course, neglects the contribution of
ageostrophic motions and non-advective processes to the
rainfall production. For example, the rainfall volume
associated with gravitational displacement of warm by
cold air at a steep, rapidly moving, cold front is not
assessed. In general winter rains it is thought that this
is small compared to the volume of the advective contri-
bution. However, experienceshows that the thickness-
moisture analysis will generally differentiate the “wet”
and “dry” sections of such a front.
The centers of heavy winter rainfall patterns are very
often located in strongly orographic regions. In the
present application the orographic contribution has not
been treated; however warm moisture advection seems
always to be present at the time of important rainfall
occurrences over such regions.
One or both of two processesmight end the rain a t a given
point during the 6-hour period. If the inflow moisture
decreases, the upwind boundary of the rainfall area must
move toward lower thickness values. (In such a case,
the saturation line could conceivably move downwind out
of the warm-advection area, and the rainfall area would
vanish.) In the secondprocess, layer motion may shift
relative to the thickness lines in such a way that the net
moisture advection vanishes or is directed toward greater
thickness.
ANALYZED SERIES-JANUARY 1954
The procedure described above has beenfollowed in
analyzing the 6-hour rainfall rate centered at the 0300
GMT and 1500 GMT upper-air observations for January
58 MONTHLY WEATHER REVIEW FEBRUABY 1956
FIGURE 3.-(A) 1,000-700-mb. thickness (solid lines) superimposed on 850-mb. con-
tours (dashed), 0300 GMT, January 20, 1954. The observed &hour rainfall pattern
(3 hr. before to 3 hr. after map time) is shaded. (B) Thickness pattern (solid lines)
and saturation-thickness (dashed lines), 0300 GMT, January 20, in the outlined area
of (A). The near saturation area is that in which the saturation thickness lies
within 100 ft. of the real thickness. (C) Thickness lines at 0300 GMT January 20
(solid) and 1500 QMT, January 19 (dashed) in the outlined area of (A).
1954. To make the analyzed series compatible with the
forecast series (described in section 4), the analyses utilize
the 850-mb. contours and the 1,000- to 700-mb. thickness.
Some other constant level surface, and/or thickness
interval might well have been used for indicating the
moisture advection. However, daily forecasts (section 4)
were &n essential part of the procedure in this experiment;
therefore, practical considerations determined the choice
of thickness interval. *
Thermal windswere computed for every point where
wind observations were available, using the approxima-
tion recently adopted by the National Weather Analysis
Center that the thermal wind is the vector difference
between the observed wind at the top of the layer and
the sea level geostrophic wind. These wereused as an
aid in the analysis of the thickness pattern. Due weight
was given to the observed winds in analyzing the 850-mb.
contours.
The National Weather Analysis Center preparea a mid-layer contour chart for the
I,OC@ to mmb. interval; time was not available for preparation of mid-layer contours for
the 1,aOO- to MtDmb. lnterwl in the dslly forecant procedure.
No such guide as the geostrophic spacing is available
in analyzing the moisture pattern; advecting it with the
speed of the mid-layer wind from map to map appears to
be the best way of keeping track of it in the sparse sound-
ing network. This has been done with the analyzed
examples.
The analysis procedure was that described previously,
with the exception that the precipitable-water values
between the surface and 700 mb. were used to construct
the saturation thickness field.
Examples from an analyzed series are shown in figures
3 to 5. Three charts are shown for each date and time
of observation. Chart A is the contour-thickness grid,
with the zero-advection line indicated. The isohyetal
pattern, based on a fairly dense network of recording
gages, is also shown. Chart B shows the saturation-
thickness field superimposed on the real thickness and an
outline of the area over which the saturation thickness lies
within 100 feet of the real thickness. That portion of the
FEBBIJABY 1956 MONTHLY 59
FIGWEE 4.-(A) 1,000-700-mb. thickness (solid lines) superimposed on 850-mb.con-
tours (dashed), 1500 GMT, January 20, 1954. The observed6-hourrainfall pattern
(3 hr. before to 3 hr. after map time) is shaded. (B) Thickness pattern (solid lines)
and saturation-thickness (dashed lines), 1500 GMT, January 20, in the outlined area
of (A). The near saturation area is that in which the saturation thickness lies within
100 ft. of the real thickness. (c) Thickness lines at 1500 GMT (solid) and 0300 QMT
(dashed), January 20, 1954 in the outlined area of (A).
areaof saturation that lies in a warm advection region is
termed the moisture-depletion area. Chart C compares
the position of the thickness lines a t the time of observa-
tion with the position 12 hours earlier. From the figures
it can be seen that the boundaries of the observed 6-hour
rainfall patterns (3 hours preceding and 3 hours following
the upper-air soundings) correspond well with the position
of the moisture-depletion area. Furthermore, the higher
rainfall values appear to be associated with the grids of
smallersize. It will also be noted that in those areas
continuously within the moisture-depletion area between
observations the indicated thickness change is very small.
A day-to-day comparison of the current day moisture-
depletion and rainfall patterns for more than a year sub-
stantiates the usefulness of these techniques; it appears
that the heavier, general, winter-type precipitation pat-
terns are especially well defined by the moisture-depletion
pattern technique.
4. SHORT-PERIOD FORECASTS
An obvious but important inference from the results of
the analysis of moisture depletion areas is this: A forecast
of the moisture and thickness field, and of the contours of
the middle pressure surface, defines a first approximation
of the rainfall-intensity pattern at the time of forecast.
A forecast experiment will be discussed later in this
section, but fist it is necessary to consider the transport
and advection of moisture in unsaturated areas, attention
thus f a r having been limited to saturated layers.
TRANSPORT OF MOISTURE IN UNSATURATELI AREAS
It is clear that the horizontal moisture advection alone
will not result in condensation until saturation is reached,
whatever the rate of moisture transport. Therefore con-
sideration of rate of change of moisture storage as related
to the change in the water-vapor capacity of an un-
60 MONTHLY W E A T H E R R E V I E W FEJ3BUABY 1956
45'
35
950 85'
FIGURE 5.-(A) 1,000-700-mb.thickness (solid lines) superimposedon850-mb.con-
tours(dashed), 0300 GMT, January21,1954. The observed6-hourrainfallpattern
(3 hr. before to 3 hr. after map time) is shaded. (B) Thickness pattern (solid lines)
and saturation-thickness (dashed lines), 0300 GYT, January 21, in the outlined area
of (A). The near saturation area is that in which the saturation thickness lies within
100 ft. of the realthickness. (C) Thicknesslines at 0300 GMT, January21 (solid)
and 1500 GMT, January 20 (dashed) in the outlined area of (A).
" 'T B \ Bj
saturated layer is an important consideration in a rainfall
forecast.
In general, the thickness lines move more slowly than
the saturation thickness field, and this is especially trlle
in warm-advection areas. Craddock 1241 in a study of
advective changes in the 1,000- to 700-mb., and 700- to
500-mb. thickness patterns, states that the effect of advec-
tion in modifying the thermal field appears to be offset by
other processes, the resultant change being a residual with
a correlation of about 0.6 with the advective component.
In a crude preliminary experiment, the precipitable-
water field at 0300 GMT was moved with the streamline
motion at mid-layer to the saturation position, assuming
no later motion of the thickness lines. The placement
of the saturation line found in this way often corresponded
rather well with the position of the upwind boundary of
the 24-hour rainfall pattern beginning 9 hours later. In
any case, a forecast of the position of the upwind bound-
aries of general winter rains requires a quantitative
appraisal of the rate at which the saturation thickness is
overtaking the real thickness pattern; with a good forecast
of the thickness pattern, the time of initiation and the
placement of the upwind rainfall boundary should be
usefullydefined. (This paper is chiefly concerned with
the treatment of moisture in depth, and discussion of
techniques of forecasting development of thickness and
contour patterns is outside its scope.)
With these considerations taken into account, a forecast
procedure will now be developed for use in a short-period
forecast experiment.
FORECAST PROCEDURE
The procedure €or forecasting the rainfall pattern has
two main steps: First, analysis of the current thickness-
contour grid, and second, preparation and analysis of a
forecast of the grid near the end of the rainfall forecast
period. The analysis procedure has already been described
FEBBUABY 1956 MONTHLY 61
(section 3). Upon completion of the analysis of the
initialgrid-element moisture pattern, the volume-rate
of rainfall and the 6-hour average depth were estirhated
for each grid element. The total 0630-1230 GMT, 6-hour
volume was then calculated.
For step two, a primitive method was used for develop-
ing the forecasted thickness-contour grids. The positions
of the 1,000- to 700-mb. thickness lines were extrapolated
12 hours ahead of the 0300 GMT position at the rate of
their previous 24-hour motion. Next, the 1500 GMT
codguration of the 850-mb. contours was estimated by
noting t.he changes during the 12 hours previous to 0300
GMT. The 0300 GMT saturation thickness pattern was
then advected 12 hours ahead with the motion indicated
by the init.ia1 geostrophic streamlines, and the analysis
was carried through as in step one to obtain the 1230-1830
GMT rainfall pattern.
Finally a pattern was drawn whose volume was as
near the sum of the initial and forecast computed volumes
as a quick eye-estimat,ion would permit, with the axis
of heaviest rain drawn between the position of initial
and forecast-period centers and the outside isohyets of
appreciable rainfall (generally the %-inch isohyet) drawn
within and of a shnpe similar to the swath of the successive
positionsof the moisture-depletion areas.
FORECASTEXPERIMENT
To test the forecast procedure and to assess its practical
value, forecasts of rainfall distribution for the 12 hours
beginning0630 GMT were prepared on a daily basis for
theperiod December 28,1954, to March 1, 1955, using
0300 GMT data. Since the primary interest was in fore-
casting distribution of intense general rains, it was arbi-
trarilydecided to prepare forecasts only for the days
when the rate of water-vapor transport across the Gulf
Coastexceeded50,000 square-mile-inches per 12 hours.
The implicit forecast for the other days is “less than 50,000
square-mile-inches, distribution not defined.”
The basic working materials were the 0300 GMT charts
of the National Weather Analysis Center for the 850-mb.
level, and the 1,000- to 700-mb. thickness. (The 1,000-
to 500-mb. thickness was used with the 850-mb. contours
for the first two weeks.) The 0630 GMT Daily Weather
Map and the 1500 GMT constant pressure charts of the
previous day were also available, but little use was made
of any but the 850-mb., 1500 GMT chart.
The strictures of a practical forecast situation were
observed in every respect. The forecast preparation was
begun as soon as the charts were available, and no later
data were used. By the “rules of the game” no corrections
were allowed after the forecast pattern was presented to a
disinterested “referee” although a few obvious mistakes
were discovered later. A rigidly standardized forecast
scheme would have been desirable in many respect?, but
certain changes in emphasis and modifications in’ tech-
niquewere strongly indicated as the experiment pro-
gressed. These are not fundamental and do not in our
opinion invalidate the general inferences to be made
from the set of forecasts as a whole.
The forecast patterns are compared with the observed
patterns for each forecast day in figure 6.
CLIMATOLOGICAL AIDS
Although the larger features of the distribution are
shown by the analysis, the detail is not clearly defined
because the “model scale” defines average depth for sizes
of area as large as or larger than the grid elements. In oui
experience nearly all heavy winter rains occur in rather
simple and definite patterns. An “isohyetal analogue” is
a convenient guide for drawing a forecast pattern. Thid
is an observed pattern with the total volume equal to that
forecast, in the general region of the moisturedepletion
area, of its general outline, for the length of the forecast
period. The analogue integrates two unassessed contribu-
tions-the orographic effect and convergence-in addition
to that implied by our model.
A high water-vapor transport rate across the Gulf
Coast is a good indicator of future rainfall volume if the
moisture-depletion area lies over the Central States no
more than a few hours downwind from the Coast. In
such a case the forecast volume is better indicated by the
idow than by the depletion, since the inflow-rainfall
relationship (see[7]) includes the unassessed contribu-
tions.
Having the volume-forecast, the initial and finalposi-
tions of the grid elements of least size, and moisture-
depletion boundaries, and an adequate file of isohyetal
analogues, the experienced analyst should be able to
develop a useful isohyetal pattern forecast.
In the first group of forecasts (fig. 6, page 62) the
emphasis was on the “climatological aids,’’ particularly
the moisture inflow rate. Precipitable-water valueswere
computed only for stations near the Gulf Coast. Later,
the moisture-depletion computation was used in regions
far downwind from the Gulf Coast where the inflow rate
was not adequately defining the volume of rainfall. It
was, of course, necessary to prepare the saturation thick-
ness field for the entire area in using this method.
5. CONCLUDING REMARKS
The results of the forecast series indicate that the
assumptions and approximations of the model are usefd:;
and they may suggest that the most important of the
processes contributing to general, heavy, winter-type
rainfall is the ascending motion implied by the non-motion
of the thickness contours. Methods for treating the
orographic contribution are of course implicit in the model
formulation, and work is underway on this aspect. Com-
bined with adequate methods for treating the develop
ment, and perhaps other contributions to the vertical
motion, the short period forecasts of rainfall would v e e
likely be improved, and the period of the forecasts coh-
siderably extended. Whatever successwas attained in
62 MONTHLY FEBBUABY 1956
FEBBUABY 1956 MONTHLYWEATHER REVIEW 63
64 MONTHLY WEATHER REVIEW FEBBUABY 1956
FEBBUAEY 1956 MONTHLY WEATHER REVIEW 65
the forecasts must be attributed to carrying out a system-
atic program of operations for treating the moisture in
depth, and the use of such a program is commended to
every meteorologist concerned with the forecasting of
rainfall.
ACKNOWLEDGMENTS
The author is indebted to: Dr. Charles S. Gilman for
fostering the interest in and environment for study of
applications of dynamic concepts to the rainfall problem;
Vance A. Myers for developing the geostrophic transport
concept in application to synoptic climatology of rainfall,
and for many suggestions which kept this work within
manageable limits, and for monitoring the forecast experi-
ment; Dr. Smagorinsky and Mr. Collins for their com-
ments(seep. 57) elucidating the interpretation of the
experimental results; A. E. Brown for his interest and
facility in processing data for the daily forecasts; also
Robert Frazier and James L. Keister for preparation of
rainfall and moisture data.
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