MONTHLY WEATHER REVIEW Editor, James E. Caskey, Jr.
CLOSED OCTOBER 6, 1948
AUGUST 1948 ISSUED NOVEMBER 16,1948 VOL. 76, No. 8
W. B. No. 1630
AN OBJECTIVE METHOD FOR FORECASTING PRECIPITATION AMOUNTS FROM
WINTER COASTAL STORMS FOR BOSTON
SAMUEL PENN
[Weather Bureau Airport Station, East Boston, Mass.]
Manuscript submitred February 24, 1948
INTRODUCTION
The problem of precipitation forecasting in New Eng- land has been emphasized by the needs of the many varied industries of that region for accurate forecasts when rain or snow is in prospect. Some are especially interested in the type of precipitcttion, others in amourts. Among tbose which become extremely dependent upon estimates of the amount of future preci itation in directing their operations are the power and Eght companies, transpor- tation interests, the U. S. Engineers, and others. Because of this need for forecasting service, the newly established Weather Bureau forecasting research unit a t Boston initi- ated the project described in this paper; the problem of forecasting the type of precipitation was not included in the project, since it is a separate one and fully as complex as that of forecasting amounts. In this study an attempt was made to combine the tech- niques of several previous studies and apply them to the particular problem of forecasting for Boston the precipi- tation amounts to be expected from winter coastal storms. Earlier investigations by Rodgers [l] and by Miller [2 ],
which were concerned with the typing and the recognition of pressure patterns which lead to Atlantic coastal de- velopments included no attempt to evaluate quantitatively the resultant precipitation. Brier [3], however, demon- strated in his study of the T. V. A. Basin that objective techniques could be successfully employed in making quantitative forecasts of precipitation. This study, patterned loosely after Briers investigation,
was made with a threefold objective:
1. To develop a practical method for computing the
precipitation amounts from coastal storms, using data available a t the time of the forecast.
2. To show the relative values of the factors con- tributing to the computation of precipitation amounts. 3. To test the reliability of specific factors now fav- ored by some of the Boston forecasters in deter- mining precipitation amounts.
Briefly, the method employed to gain this objective con- sisted of choosing several indices in the synoptic field, both at the surface and at upper levels, which were con- current with the first a pearance of a storm in the coastal
amounts of precipitation recorded.
area. These were re P ated graphically to subsequent
Si-8
Data used in the study were for the months of Novem- ber, December, January, February, and March for the five winters of 194243, 194344, 194445, 1945-46, and
194647. For nn independent check study, data of No- vember 1942, January 1943, December 1944, February
1946, and March 1947, were set aside. These data were selected so that each month would be represented by data from a different year. In all, 96 storms were studied to develop the computation charts and 21 storms to test the results. Although the investigation of precipitation data was restricted to precipitation amounts resulting from coastal storms, it was found that the greater and most important portion of winter precipibation for southern and central New England was covered. Examination showed that 80 percent of the total winter precipitation and nearly all amounts in excess of 0.35 inch resulted from coastal storms. In addition, and somewhat contradictory to the belief that coastal storms are accompanied by heavy amounts of precipitation, actual observa.tion (see Figure 1)
showed that in 25 percent of the cases included in the 5-
p a r study the resultant rainfall was less than % inch; in only 25 percent of the cases did the amounts equal 1
inch or more.
AMOUNTS (INCHES)
Ficnar 1.-Frequency distrlbution of observed amounts of precipitation In the Boston area resulting from mastal storms which oceurred during the Wear period of investi- gation.
149
150 MONTHLY WEATHER REVIEW
71 I
Fionsr 2.-Map showing stations in the Boston area wed to obtain representative obsemed precipitation amounh for conatel storms.
It should be pointed out that since not all of the factors afFecting precipitation could be evaluated, the computa- tions in this aper yield only an approximate, but never- theless usefuf solution to the forecasting problem. Al- though encouraging results can be obtained by exclusive use of the suggested techniques, forecasts are often com- plicated by interactlons, accelerations, and developments on the weather map which require considerable subjective consideration. Therefore, the sim le, objective technique
of forecasting per se, but rather an auxiliary tool for the forecaster which will allow him to evaluate pro erly sev-
results in forecasts, however, can be obtained by not losing sight of the unevaluated factors.
presented here should not be consi B ered a complete method
era1 of the important meteorological variab P es. Best
DEFINITION OF TERMS
As a preliminary step to examining the data to be used, it was necessar to decide upon the limitations of the
planations of the factors involved in assigning these
s ecific meanings to the basic terms used throughout
Forecast area.-The area selected for this study included the Boston Airport and four cooperative stations within
10 miles of Boston (Figure 2). Precipitation amounts
officially reported for these five stations for each coastal storm were averaged to obtain the areal precipitation for each storm. "his areal amount was computed for all storms which occurred in the 5-year period and was used
as the Boston precipitation in the study. For this period
it was found that precipitation amounts varied little over the area. The correlation coacient, for example, be-
study. The fo 8 owing resulting definitions include ex-
t Fu 's presentation.
FlOURE 3.-Map with isopleths &wing relative dlstribution
Atlantic Seaboard m a (shaded portion). of storms within the
tween the recorded amounts a t Boston and at Chestnut Hill (a cooperative station about 5 miles west) was com- puted at 0.97.
Precipitation amounts.-These amounts are storm totals
rather than fixed-period amounts, since the totals are more $cant and useful and they also simplify the study. recipitation amounts greater than 1.49 inches were
classed in one group and assigned the value of 1.50 inches, the value which was used for verification purposes.
Coastul stom.-A coastal storm was defined as the pres- ence at the surface level along the Atlantic Seaboard (shaded area of Figure 3) of e.ither (a) a definite wave formation in the front, (b) a c.yclonic wind field, or (c) a
closed low. In addition, it was required that there be a center of 3-hourly pressure falls associated with the wave or storm. The study was not limited to storms which originated in the prescribed coastal area but included those which might have moved into the Atlantic Seaboard
from any direction. However, of the 125 storms included in the basic and test data, 115 were true secondaries, or new developments within the prescribed area.
In order to determine the favored locations of coastal developments, the area along the Atlantic Seaboard was anal zed with regard to the number of storms found in
tude in dimension. The value, then of an isop eth at any point in Figure 3 indicates the number of storms whose ori in or point of entry into the coastal area was located
WitL a section centered at that point and bounded by meridians and parallels 2 degrees apart. Figure 3 shows that there is an area of maxirprn occurrence between Hatteras and Charleston and a m o r secondary maximum near Long Island. '
Y
over 9 apping sections 2 degrees latitude by 2 de ees longi-
AUGUET 1948 MONTHLY WEATHER REVIEW 151
FIOUBE 4.--700-mb. chart showiog a resure pattern with a closed low southwest of Boston which would not influence t i e circulation over Boston. (Arrows and dashed line indicate past 12-hour movement of the low center.)
FiaoRrK.-~mb.chartshowing the pressure patternexisting 12homlaterthan that in Figure 4. (Arrows and dashed lines indicate past two 12-hour movements of the low center.)
METHOD OF INVESTIGATION
SELECTION OF VARIABLES
In selecting the meteorological variables to be related to observed precipitation amounts, the results of previous research and the experience of other forecasters formed a partial basis for consideration. In one investigation,
for instance, Petterssen [4] concluded that coastal storms seem to develop in the lower levels of the atmosphere, where air mass contrasts are greatest and wind fields are most favorable. This conclusion directed attention to the requirement for selecting variables in the lower atmosphere which expressed a measure of the potential strength of developing storms, and those in the upper levels which pointed to the contribution made by the primary storm or trough to the coastal development. Primarily, however, the independent variables were selected on the basis of a stud of many individual storms,
optic surface map and the latest available upper-air c arts precedin it. To find variables, both at the surface
and a t upper evels, which appeared to be particularly sigdicant to the problem of forecasting amounts of precipitation, i t was necessary to look for those which expressed (a) some indication of the precipitation amounts which occurred near the center of the storm, or (b) some indication of the path of the storm with relation to the forecast area. The latter consideration is, of course, important to the amount of precipitation to be forecast, since it is obvious that the passa e of an intense storm far
amount of precipitation at that station. Finally, the selected independent variables were divided into two groups: (1) the primary variables, which were applied to all storms; (2) the secondary variables, which were applied selectively according to the surface pressure pattern over the eastern portion of the storm map. Primary uariu6Zes.-The primary variables were labeled
and defined as follows:
using data in each case o t tained from the 6-hourly
si? B
to the east of Boston, for examp 7 e, will give only a small
XI The 850-mb. wind direction immediately over the surface storm. This is a partial measure of the influx of warm, ,moist air to be expected. In the absence of actual wind observations, this variable was estimated, using pibal data from nearby stations and the geostrophic wind.
X, The 700-mb. contour direction immediately over the surface storm. This variable indicates to some extent (a) comer ence due to the latitude
(c) direction of movement of the surface storm.
a& The latitude of the surface storm. The largest amounts of precipitation were found to accompany these storms which develop farthest to the south, other factors being equal.
X, The minimum latitude reached by following the 700-mb. contour upwind through Boston no farther than 95O W. long., which indicates to some extent the amplitude of the 700-mb. trough. Where this contour did not o south of Boston
was defined as the latitude where the contour crossed the 95th meridian.
Ita determination is not objective when a closed low is found to the southwest of Boston, and the contour through Boston, instead of extending southwestward to the low, reaches weatward or even northwestward.
Given this situation, the forecaster must decide on the basis of his experience whether Boston will remain in the westerly flow or will come under the influence of the low pressure to the southwest; furthermore, this decision, an all-important one, must be made by the forecaster whether or not he embodies objective techniques in his forecast.
For the purpose of this study, however, the value
effect; (b) orientation o 9 the 700-mb. trough; and
between Boston and 95' W. 5 ong., the variable
153 MONTHLY WEATHER REVIEW Au~uer 198
Ronna 8 .4 0 000-Ioat map ahowlng a pressure pattern with a closed low southwest of Boston which presages a change in thn clrrmlatlon over Boston. (Arrows and dashed
llnea on loft show past two 12-hour movements of low center.)
X' for the 15 cases involving a closed low sout,h- west of Boston (as, for example, those shown in Figures 4 and 6) was determined by looking ahead at subsequent maps, although the forecast prooedure would usually be objective and straight- forward. In Figure 4 the arrows and dashed line indicate the previous 12-hour movement of the low, which was rapid and eastward; the easterly circulation of the trough extends only to 38' N. lat. Simple
extrapolation of the low pressure movement indicated that it would continue eastward without disturbing the westerly flow over Boston. This
was veri6ed by a look at the 700-millibar inap 12 hours later (Figure 5). The value for X4 in
this example was 47'. Figure 6, on the other hand, is an example of an upper-air chart which does presage a change in the circulation over Boston. Here the low (the past two 12-hour movements shown by
arrows and dashed lines) is seen to be moving very slowly eastward, and the easterly circulation extends to about 45' N. lat. The value of 32'
was assigned to X,, since the 700-mb. isobar
moving up to Boston was expected to become art of the 700-mb. isobar to the southwest.
h ure 7, which shows the pressure pnttern 12 hours later, verified this.
Swo+ va&bZa.-The secondary variables selected were sea level pressure distribution patterns found on storm maps.
Type 1 (a) There is present on the surface map a center of high pressure north or northwest of Hew England, with a wedge extending southwd. into New York, Vermont, or
New' Hampshire;
They were labeled and defined as follows:
'
Fiousr showing the pmssure pattern existing 12 hours later than that in Figure 6.
(b) the past 12-hour movement of the wedge near 45' N. lat., has been 250 miles or less;
(c) the sea level pressure at Caribou, Maine, is at least 15 mb. higher than the pressure a t Gander, Newfoundland;
(d) there is a second high-pressure center within 5 de.grees of latitude south of
Bermuda.
The pressure pattern of Type 1 (exemplified by Figure 8) shows the orientation of the two hghs with a col or trough near 32' to 3 9 O N. lat., a favored path for coastal storms. The
specific Caribou-Gander pressure difference indicates the presence of the force necessary to propel the storm eastward between the two
highs. The greater this difference, the sooner the storm can be expected to recurve, and Type 1 maps are associated with storms whch recurve to the east while still south of Long Island. They give southern New England less precipitation than would be forecast using only the primary variables.
2 When the surface map did not fulfill the conditions of Type 1, it was examined for Type 2 criteria. In this type (Figure 9) a center of high pressure must be north of 41' N. lat., and to the north or northeast of the coastal storm. When the high center is east of north with relation to the storm, a
westward extension of the ridge must be north of the storm. This pressure pattern
AUGUST 1948 MONTHLY WEATHER REVIEW 153
FIGURE 8.-SurIace map showing Type 1 pressure distribution, associated with storms that recurve to the east while south of Long Island.
is necessarily accompanied by slow mope- ment of the storm, due to blocking action of the high. Therefore, Type 2 indicates a longer period of precipitation than would be forecast using only the primary variables.
It is interesting to note that only six storms of the 5-year study resulted in precipitation amounts greater than 2 inches, and all six were associated with maps classified as Type 2.
Type 3 All maps not meeting the requirements of Types 1 or 2 were generally classified as Type 3. In this type (Figure 10) the wave was found on the west side of the At'lantic high cell, with no wedge in the apparent path of the storm. Isobars from the wave northward were oriented in a south-north
or southwest-northeast direction. Such a pressure distribution favors rapid movement of the storm and therefore lesser amounts of precipitation than would be forecast using only the primary variables.
There are occasionally situations for which it is difficult to distinguish between Type 2 and Type 3 pressure pat- terns or in which Type 2 is changing to Type 3. In those cases the objective forecast is based only on the primary variables.
CLASSIFICATION O F MAPS WITH RELATION TO PRECIPITATION
OCCURRENCE
Before relating the selected variables to observed pre- cipitation amounts, i t was necessary to stratify the synoptic surface maps used in the investigation according to whether or not they indicated that precipitation could be expected to occm a t Boston. A procedure similar to
that used by Brier in his T. V. A. study was employed. Whenever a storm was found in the prescribed coastal area on any surface map, the contour passing through
PICUBE 9.-Surface map showing Type 2 prellsure dlstribution, associated with more slowly moving storms.
Boston and the one passing through Block Island were each taken from the corresponding 700-mb. chart and traced on the map. When the coctouric channel thus delineated on the surface map intersected, east of the 90th meridian, an area of precipitation associated with a low pressure center or a front, the map was placed in Group A; when the contouric channel did not cross such
a precipitation area, the map was placed in Group B.
FIGURE lO.-Surface map showing Type 3 pressure distribution, associated with laster- moving storms.
154 MONTHLY WEATHER REVIEW AUQU~V~ 1948
Upon exmination i t was found that precipitation occurred subsequently at Boston for every Group A case (Table l), whereas only 6 Group B cases resulted in pre- cipitation, while 24 had none. Obviously, no additional
TABLE l.-Preliminary stratification of storm maps into those showing oeeuwence and nonoccurrence of precipitation
subdivision of Group A cases was necessary, but Group B cases needed further stratification. This was accomplished by plotting graphically the minimum latitude reached by the 700-mb. contour through Boston, variable X,, a ainst recorded amounts of precipitation. Figure 11
tion when Zr, was 38 or less, whereas only one case was followed by precipitation when X, was greater than 38,
and then the amount was only 0.07 inch. Therefore, those cases in which Zr, was 38 or less were relabeled Group B1, and together with Group A cases were used in applying the selected primary and secondary variables to determine amounts of precipitation to be expected. Those cases having an & value greater than 38 were relabeled Group Be, and a forecast of no precipitation was assigned to them. Since application of the criterion described above de- pended upon precipitation areas as far west as the Missis- sippi River, it suggested that a close relationship exists between primary and secondary storms. Previously, other investigators, including Brunt [5] and Austin [6],
have pointed to a close relationship existing between the deepening of the wave and its accompanying cloudiness and precipitation. Petterssen, Austin, et al. [7] and others [8, 91 have also investigated many aspects of sec- ondary cyclones on the Atlantic Coast. Experience too has supported this implied relationship, since it has shown that the two belts of precipitation associated with the primary and secondary storms, respectively, often merge into one, which appears to be moved along by the upper- level flow associated with both. The heaviest precipita- tion usually has been found to accompany the developing secondary, a fact also indicated by the data of this study. However, although this implied relationship should be noted in passing, it is beyond the scope of this paper to attempt an explanation of the physical and dynamical relationship between the primary storm and its secondary.
s E ows that all but two cases were followed by precipita-
X4 . MINIYUY LATITUDE O f 700 YB. CONTOUR THRW6H BOSTON
FIGURE 11 .-Stratiflcatbn of B map cases (see Tahle 1) into BI and BI cases hy applica- tion of variable Xd.
CONSTRUCTION OF COMPUTATION CHARTS
Application of the variables to recorded precipitation amounts for the storms connected with the A and B, map classifications was accomplished in the manner shown in the schematic diagram of Figure 12. The general pro- cedure was to work with the variables in pairs. For example, the terms XI and X a were used to derive the function Yl; terms X3 and X, were used to derive the function Y2. In turn, these functions, Y, and Ya were combined to obtain the function 2, which was then modi- fied, when necessary, by applying the appropriate second- ary variable. The final result was the computed precipi- tation amount, C.
A --y I t (%.%)=x } f(r:,v,) =Z S r v # TYPE e I } c
-
0, / &)f*cSA)=v. b P E 3
OROUPB
\- Sa (FORECASTS OF NO PRECIPITATION')^ c = 0
FIGURE 12.-Schematic working Ian showing the stem in making an objective forecast Irom the preliminary clawiRcat&n of the map to the flnal computation or precipitation forecast value c.
The specific procedure in determining the dependence of precipitation amounts upon the several variables involved three steps. First, for each case the value of XI was plotted as the abscissa and the corresponding value of Xa as the ordinate on a scattergram, and (the point was labeled with the observed precipitation amount (Figure
13). Secondly, the scattergram was then marked off into cells of several observations each, with the mean of each cell entered in large figures within its limits. Thirdly, isopleths of precipitation amounts were drawn to these mean figures, keeping the lines as smooth as possible. From the isopleths in Figure 13 it is evident that Xl (the 850-mb. wind direction above the storm) and X2 (the 700-mb. contour direction over the storm) exert about equal effects upon the precipitation amounts. Using X3 and X, in place of the former variables, Figure 14 was constructed in the same manner. Since the isopleths in most portions of the chart tend to approach the horizontal, it can be assumed that the influence of Xt (the latitude of the surface storm) generally is not as
effective as X, (the minimum latitude of the 700-mb. contour through Boston). Figure 15 shows the derivation of the function Z, deter- mined by plotting functions Y, and Y2 against each other, and indicating on the chart the corresponding amounts of observed precipitation. Isopleths of amounts were drawn, using the technique applied to the two previous charts. The function, 2, thus derived from computation based
on the four primary variables, was then modified by application of the appropriate secondary variable. Figure
16 was constructed with reference to modification neces- sary in Type 1 cases (see Figure 8). In this diagram the computed amounts of precipitation (2 values) were plotted against the observed amounts, with the corre- sponding values of the Caribou-Gander sea level pressure differences indicated. Two isopleths were drawn by inspection, one for 15 mb., and one for 20 mb. The 20-
mb. curve was used for all values 20 mb. or greater; pressure differences below 15 mb. did not, by definition, fall into the Type 1 classihation. Since the ordinate of this diagram expresses the final corrected values (as well as observed amounts), the chart is entered by following the line for the computed Z value upward until it inter- sects the proper pressure-difference curve. The ordinate
AUGVST 1948 MONTHLY WEATHER REVIEW 155
.n
XI m WINO DIRECTION AT --M a OW% W F M E WYE
FIGURE 13.-Chart showing derivation of PI. a function of primary variables XI and XI.
value at this point of intersection represents the h a 1 com- puted precipitation amount (C) to be forecast. The slope of each of these pressure curves is less than one, indicating that too much precipitation would be forecast using
only the primary parameters, unmodified by application of the secondary variables. This eff ectprecipitation amounts less than the average for coastal storms-would be expected from a Type 1 pressure field.
I
.I*
1.55
I
x, m LATITUDE OF SURFACE WAVE (*I
PIWEE ll.-Chart showing derivation of YI, afunctlonof primary variables XI and X4.
.i5 \
Y1= fl (X I X,)
FIousr I5.-Chart showing derivation of Z, a functlon of derlved values of YI and Ya.
/
7. COMPUTED ANOUNTS OF PRECIPITATION
FIGWEE lR.-Chart showing isopletha indicating necessary modification of Z values (computed amount8 ,of pwApitatlon) to obtain C values (observed or corrected amounts) for forecastmg Type 1 cases.
156 MONTHLY WEATHER REVIEW
I w.
I *o-
I
c i a o
z
Z l t O
I.*Ol
I..*
1.40.
/
. .
*/
e
TYPE 2
I I I I I I I I 1 3 1 1 1 .1 ,
0 .IO .80 .SO r(0 .80 .a0 1 0 A0 .W 1.00 LIO LW LIO LIO 1.W
2 * COUPUTEO AMOUNTS OF PRECIPITATION
FIGnRr 17.-Chart showing regression curve indicatln necessary modiflcation of Z values (computed amounts 01 precipitation) to obtain 8 values (observed or corrected amounts) [or Iorecastlng Type 2 cases.
In Figure 17, the computed amounts (Z) for all Type 2
cases (see Figure 9) were plotted against the observed amounts of precipitation, and a resultant regression curve was fitted by inspection to the individual points. The average slope of this curve is greater than one, indicating that insufficient precipitation would be forecast if only primary variables were used. This result is consistent with forecasting experience in Type 2 cases, where the blocking high cell in the path of the storm results in pro- longed and therefore larger amounts of precipitation than are otherwise indicated. Figure 18, for Type 3 cases (see Figure lo), WRS also constructed by plotting the computed amoiints against the observed amounts of precipitation, the regression curve being obtained by using group averages. Its slope is less than one, a result in agreement with the observed rwults of fast-moving storms, which ordinarily give less precipitation than would be computed from application of the primary variables alone. Finally, the observed amounts were plotted against the computed forecast amounts (C) for all cases (Figure 19),
aad the regression curve was obtained by using group averages. The resulting correlation coeficient was 0.84,
with a standard error of estimate of 0.15 inch. It was noted that a correlation coeficient of 0.73 between the above computed amounts and the observed amounts a t New Haven suggested that these charts could be applied with almost equal efficacy to most of southern New England.
.
AUGUET 1948
ATJQUf3T 1Qa MONTHLY WEATHER REVIEW 157
Class 0 0-Trace _________.________.________ 1 .01-.I9 __________________._...- __..
ORBERVED 2 .20- .49 ________.___.___._.........~
PRECIPITATION 3 .s .9 9 .____._.._____._........._..
(Inches) 4 1.OC-1.49 ._._._.___._._.___._.....-. 6 1.50ormore _..._._..._......._.~...
Total csses _________.____________
While the use of the preceding charts will yield a com- putation based on mean values, it is sometimes more desirable to base a computation on the mode. The fre- quency distribution of precipitation amounts is usually skew (Figure l), so t'hat the mean does not correspond to the mode. The following method was used to develop a chart to indicate the probabilit,y that the precipit A t ' ion amount will fall within a specified ran e. Observed
five, with the following limits: 0-trace; 0.01-0.19 inch;
0.20-0.49 inch; 0.50-0.99 inch; 1.00-1.49 inches; and 1.50
inches and greater amounts. Similarly, computed values of C were divided arbitrarily into groups, numbered one to eight, with the following limits: 0.01-0.20 inch; 0.21-
0.40 inch; 0.41-0.60 inch; 0.61-0.80 inch; 0.81-1.00 inch;
1.01-1.20 inches; 1.21-1.40 inches; 1.41 and greater amounts. Table 2 shows for each graded value of C the number of times that observed precipitation amounts fell into each of the five classes. In Table 3, which presents the same data in terms of cumulative frequencies and percents, frequency values shown for each graded value of C represent the number of times that observed pre- cipitation fell into the corresponding precipitation class
or a lower one; percentage values similarly indicate the probability of occurrence, based on the comparison of observed and computed amounts for these 73 cases. From Table 3, Figure 20 was prepared, using the graded values of forecast amount C and the cumulative percents of frequency as coordinates to plot the class numbers
precipitation amounts were divided into c F asses zero to
0 2 0 0 0 0 0 0 2 2 7 2 0 0 1 0 0 12 4 I n 5 1 1 0 0 0 21 3 5 2 3 5 1 1 20 0
.__._... ___._... ___..___ 6 2 2 1 1 12 6 6 ____.... -....... -.. .... _......_ _. . .. ........ ___-_._.
6 22 12 9 G 8 2 8 73
FINAL COMPUTE0 VALUE .C. (INCHES)
FIGURE 3.-Prohsbility chart lor determining prrcipitation class Irom C vnl~ie, based on Table 3.
which re.present the corresponding or lower amounts of observed precipitation. Distribution of these numbers on the diagram determined the slope of the curves which were drawn to divide the classes. Use of Figure 20 as a probability graph in the forecasting procedure is demon- strated in the nest section of this paper.
TABLE %.-Table showing the freqriency of occurrence of each of six classes of precipiiation as a function of the graded values of computed fore- cast value C
Total
I
GRADED VALLIES OF C (Inches)
.01-. 20 .?I-. 40 .41-. 60 .61-. 80 .81-1.00 1.01-1.20 1.21-1.40 1.41 up cases
I
TABLE 3.-Table showing the cumulative frequencies and percentages of occurrence of six precipitation clnsses as a function of the graded value# of computed forecast value C'
Cumula-
.01-. m .21-. 40 .41-. 60 .61-. 80 . SI-1.00 1 1~1-1.2U 1.21-1.40 1.41 and tire totals
j
GRADED VALKlEb OF C (Inch<,-)
more
Clssa 0 &Trace - ___. ____ __ - - -. . . - ~.
1 or l e s .OC- .I9 ..._____..__________-.-.
2 or less .oO- .49.. __ __ __ -. - __ .. - ___ __ .. .
3 or less . oO- .!% .______._._.__.__.....-.
4 or less .W1.49 _______._..._....._.-.-.
6 or less .Wl. 50 sud more _____________.
ORSERVED
(Inches)
PRECIPITATION
0
2
6
6
6
6
0%
32%
100%
100%
10070
100%
0
2
7
12
12
12
0%
17%
5%
100%
Ion%
Ino%
0
0
1
3
9
9
0%
0%
11%
3%
10070
100%
0 0%
0
0% 1
17% 4
67% 6
100% 6
100%
0
0% 0
0% 0
0% 1
50% 2
1 W o 2
100%
0
0% 0
0% 0
0% 1
12% 2 2% 8
100%
2
14
35
63
67
73
158 MONTHLY WEATHER REVIEW Auousr 1848
FIGURE Zl.-Surface map u s d in example of objective forecast. Shaded area indicates FIOUBP Z?.-7Wmb. chart used in example or objective forecast, with location Of SUrfaca
pressure wave indicated. where precipitation was occurring.
EXAMPLE OF AN OBJECTIVE FORECAST
By using these constructed charts, at the time the storm first appears in the prescribed coastal area, the forecaster can compute the precipitation to be expected from a
coastal storm. The routine of the computation for the objective forecast can be demonstrated by reference to the synoptic situation of January 19, 1947, at 1330 E. S. T. Figures 21, 22, and 23, show, respectively, the surface map, 700-mb. chart, and 850-mb. chart for this date.
1. Since precipitation is occurring upstream within the 700-mb. contouric channel, this case belongs in Group A.
2. Primary variables determined from these charts have the following values:
XI= 170=850-mb. wind direction above wave
X2=2400=700-mb. contour direction above wave a t 33' N., 77-1/2' W. (Figure 23)
(Figure 22)
X3=33'=latitude of surface storm (Figure 21) X 4 =3 6 .5 ' =m ~u m latitude (east of 95' W. long.) of 700-mb.' contour line through Boston (Figure 22)
3. The pressure pattern, similar to that shown in Figure 9, indicates a Type 2 classification with reference to the secondary variables.
4. The derived functions and values determined from these parameters follows:
Y1=l.10 (from Figure 13, using X1 and X,) Ya=0.60 (from Figure 14, using Xt and X,) Z=0.90 (from Figure 15, using Y, and YJ C=1.19 (from Figure 17)
The computed precipitation amount of 1.19 inches for the forecast compares favorably with the
observed amount for this storm, which was 1.05 inches.
5. Figure 20 is used to obtain an indication of the most likely class in which the precipitation will occur; from this chart the following is noted, when C = 1.19 inches:
(a) There is a zero chance that the amount of precipitation will be 0.19 inch or less.
(b) There are 6 chances in 100 that the amount will be 0.49 inch or less.
(c) There is a 30-percent chance that the amount will be 0.99 inch or less; and 24
(30 minus 6) chances in 100 that the amount will be greater than 0.49 inch and less than 1.00 inch.
(d) There are 99 chances in 100 that the amount will be 1.49 inches or less; and there are 69 (99 minus 30) chances in 100 that the ob- served amount will be greater than 0.99 inch and less than 1.50 inches.
(e) There is only one chance (100 minus 99) in 100 that the observed amount will be greater than 1.49 inches.
The highest probability, when C=1.19 inches, is for the precipitation amount to occur in Class IV (1 .OO-1.49 inches). The amount actually observed, 1.05 inches, is in this group.
AW~JBT 1948 MONTHLY WEATHER REVIEW 159
Rowr 23.435l-mb. chart uaed in example of objective foncnst, with location of surface pressure wave indicated.
TEST OF METHOD ON INDEPENDENT DATA
The 24 storms included in the test data contained 16
cases in the Group A map classification or in Group B1 (all followed by precipitation at Boston), and 8 cases in Group B2. Seven of the latter resulted in no precipita- tion at Boston, and one (February 24, 1946) was followed by 0.02 inch.
16 i3
84
t:
$2
0
maN
MAGNITUDE O f ERROR IN FINAL COYPUTEO VALUE 'C. (kchas)
FIGUR~ 24-Distribution of errors in computed forecast value. C, for 24 cases of mast81 storms used as test data.
Data for all variables of these 24 test cases and resulting computed forecast amounts are shown in Table 4. The correlation between the observed and forecast amounts (last two columns) was 0.85, and the standard error of estimate was 0.29 inch. Figure 24, the distribution of errors in the 24 tests forecasts, shows that when only the
16 cases involving precipitation were considered, the correlation between computed forecast amounts and observed amounts was 0.71, and the standard error of estimate was 0.36 inch. The signiticance of the secondary variables is indicated by the fact that the correlation of
0.71 is reduced to 0.58 when these variables are not used. Table 5 is a contingency table based on the probabilit
values of the 24 test cases. This tabulation reveals 14
cases having no class error; 8 involving 1 class error; only
2 cases erring by 2 classes; and none with greater errors.
curves of Figure 20, as applied to the computed ( B )
TABLE 4.-Tabulation of computations made for forecasting 24 test cases, and corresponding observed precipitation amounts
Date
A BO Ba _________ A 170 A 260
BI _________ A 280
A 230
A 190 A 180 A m A 230
Ba - ____ - __ -
XI
Variables
.30 38 39.5 .35 1. 10 33 32 1.40
.30 39 39 .35
Computed amounts
(C)
0.93
.oo .oo .oo .oo
.49
.oo .86 .05
.oo .25 .07
1.10 1. 50 .2Q .67
.oo
.2Q
1.50
.20
.oo .87 1. 60 1.37
Observed amounts
1. 50 T .oo .oo .oo
.Ea .oo 1.08 .05
.m .a6
.as
.38 1.10 .30 .70
.oo
.&a 1.60
.u .w .89 1.49 . a
Pressure difference between Caribou, Maine, and Oander, Newfoundland, taken fmm mufaca map.
160 MONTHLY WEATHER REVIEW AUGUBT 1948
,.e+ TESTS OF OTHER VARIABLES
MEAN VALUES
p .I+
aog ma so0 no0 1000 nw moo is00 i a o
numm mius OOCD .in AT TOO I#. cxiws WSST OF WAVE
FIOURE ?,&--Charts showing correlation of mean valws of ohserved precipitation amounts with values of th- number or miles that cold air advection at iW-mb. lrvel extends west or surface preswre wave.
*MEAN VALUES
10 I 8 Lo
hmnATuna suo(cni AT ma IL 1%. PSI .oo mLEsi
FIGURE 213-Chart showing correlation of values or temperature cradicnt nt i00-mb. level with mean vslucs of observed amounts of precipitation.
WAN VALUES
I 4
FIGUBE 2i.-Chart showing correlation of mean values of ohserved relative humidlty at 850 mb. with mean values of observed prrcipitation amounts.
In the course of the selection of significant meteoro- logical variables to be related to precipitation amounts, several of those which experienced forecasters have be- lieved to be of value in making precipitation forecasts were tested. Use of a simple graphical method for relating these upper-air factors to observed amounts of precipita- tion demonstrated that for this type of forecasting they were, on the whole, insignificant. Charts were constructed for such variables as (a) cold-air aclvection at 700-mb., (b) the 700-mb. temperature gradient, and (c) the moisture a t 850 mb. In each case the variable to be tested was first plotted on a graph as the abscissa, and the corre- sponding precipitation amounts were plotted as the ordi- nate. Then the variable was divided into several sections or classes, and the mean amount of precipitation was de- termined for each. The curve which was finally drawn from these mean values was taken to indicate the degree
of dependence of the precipitation amounts upon the vari- able being tested. Because this method of testing was elementary, the results cannot be considered conclusive; the joint relationships provide a field for further research.
COLD AIR ADVECTION AT 700 MB.
The influx of colder air from the west a t the 700-mb. level has been suspected by forecasters of being the ex- plosive necessary to set off wave developments. The sub- sequent advection of colder air to a position over the warm coastal waters has been assumed to have two major effects: (a) of increasing the potential enexgy of the area; (b) of increasing the vertical instability of the air (that is, the steepening of the temperature lapse rate). Since both effects might probably lead to increased precipitation, a test of the effect of this variable on precipitation amounts was made, following the graphical method outlined above. Figure 25 is the graph resulting from plotting the observed precipitation against the number of miles the cold air ad- vection at 700 nib. extended west of the surface wave, as determined from the orientation of isotherms and contours. Contrary to the belief prevalent among forecasters, this diagram indicates little relationship between the proximity of cold air advection a t 700 mb. and subsequent precipita- tion amounts a t Boston.
TABLE 5.-Contingency table based on the probability curves of Figure 20, for the 24 test case8
.50-.93 1.00-1.49 1.50 or more Total cases
I
COMPUTSD PR6CIPITATION (Inchrs)
&Trace .01-.19 .20-.49
I
0-Trace. ............................... 7 ....................................................... .01-.19 ................................... 1 1 ............................................ .~. 49 1 2 ........... 1 ........... .50-.99 2 3 1 ........... 1.00-1.49 1 ........... 2 1.5&or more 1 ........... 1
OBSERVED
PRECIPITATION
(Inches)
~~ ~ ~~~ ~~
Total cases.-. ........................ 2 4 5 2
AUQU~T 1948 MONTHLY WEATHER REVIEW 161
In 61 cases for which completely analyzed upper-air charts were available, the cold air advection was further tested by extracting from the 700-mb. chart for each case the subsequent 12-hour temperature change over the orig- inal position of the storm. The following results pointcd to no generally significant effect.
(a) 27 cases showed a falling temperature change. (b) 34 cases showed rising temperature or no change.
THE 700-MB. TEMPERATURE GRADIENT
The 700-mb. temperature gradient, expressed in degrees centigrade per 500 miles, was determined by getting the temperature difference between a point near the storm and one 500 miles back into the cold air. The curve shown in
Figure 26 indicates little apparent relationship between the temperature gradient as determined here and subse- quent precipitation amounts recorded in the Boston area
for 43 cases.
MOISTURE AT 850 MB.
The amount of moisture near the 5,000-foot level has also been suggested as a useful factor in determining future precipitation amounts. In this test the mean relative
humidity, used as a measure of the nioisture content, was determined along a path from a position directly over the storm to a point 300 miles upwind, unless the path inter- sected the trough in a shorter distance; in that event, the mean relative humidity was determined only as far as the trough. The plotted curve of Figure 27, based on 61 cases, shows that the relative humidity measured in this way has little relationship to the precipitation amounts.
Substitution of mixing ratio for the relative humidity gave similar negative results.
ADDITIONAL VARIABLES
Several other variables tested were: (a) the distance between the forecast area and the path of the storm, measured along a line normal to the storm path; (b) the deepening of the storm between the time of beginning of the forecast period and the time the storm passes the fore- cast point; (c) the length of the precipitation period. These three variables were found to be significantly re- lated to the precipitation amounts. Unfortunately, these
variables, which themselves must be forecast, are usually
as difficult to determine as is the precipitation amount.
CONCLUSIONS
The results of this study clearly demonstrate t.hat objective techniques can be utilized advantageously in forecasting precipitation amounts for winter coastal storms. Parameters XI (the 850-mb. wind direction above
the storm), Xs (the 700-mb. contour direction over the storm), Xs (the latitude of the surface storm), and X I (the minimum latitude of the 700-mb. contour through Boston) are all significant factors that can be easily de-
termined and effectively used for objective f0recast.s. However, it is also evident that the introduction of the secondary variables entails some loss in simplicity and objectivity of method, upon which so much emphasis has been laid, although elimination of the secondary variables
is not justifiable in the light of forecast results. For instance, the correlation coefficients between the observed and computed amounts of precipitation for those cases used to develop the study, including no-rain cases, were 0.74 when the primary variables alone were used, but 0.84
when the secondary variables also were applied. Corre- sponding correlation coefficients for the test data were 0.85 when all variables were used, but only 0.78 when primary variables alone were employed. The fised periods and the precipitation classes of the conventional, official forecasts issued by the Boston Fore- cast Center prevented comparison of those forecasts with the storm total forecasts obtained by the objective method. However, the correlation of 0.85 for the test cases might be compared with the 0.69 correlation Brier obtained in his application of objective techniques for the T. V. A. Basin forecasts. The seemingly insignificant relationship between the precipitation amounts and some of the upper-air factors
must be interpreted with caution. The results, which apply only to this study, do not necessarily lend themselves to generalization. There are, of course, other factors influencing quantita- tive precipitation which have not been utilized in this
study. Some, such as the processes of vertical motion and divergence, still await some effective means of measurement.
REFERENCES
1. L. T. Rodgers, New England Coastal Storms, Weather
Bureau Airport Station, Boston, Mass. (Unpub- lished.) 2. J. E. Miller, Cyclogenesis in the Atlantic Coastal Re- gion of the United States, Journal of Meteorology,
3. G. W. Brier, A Study of Quantitative Precipitation Forecasting in the T. V. A. Basin, U. S. Meather Bureau Research Paper No. 26, Washington, D. C., 1946. 4. S. Petterssen, Weather Analysis and Forecasting, McGraw-Hill Book Company, Inc., New York, 1940, p. 324.
5 . D. Brunt, Physical and Dynamical Meteorology, Uni- versity Press, Cambridge, Mass., 1939, p. 355. 6. J. M. Austin, Cloudiness and Precipitation in Rela- tion to Frontal Lifting and Horizontal Convergence, Papers in Physical Oceanography and Meteorology, Vol. IX, No. 3, Cambridge and Woods Hole, Mass.,
V O ~. 3, NO. 2, 1946, pp. 31-44.
- August  1943, p. 46. 7. S. Petterssen. J. M. Austin. M. Whitcomb. 0. R. Wulf, et a1,Cyclogenesis over Southeastern United States and the Atlantic Coast (Abstract of a
Symposium a t the Washington Meeting, April 30, 1941), Bulletin, American Meteorological Society, vol. 22, No. 6, June 1941, pp. 269-280.
8. H. G. Dorsey, Jr., Local Forecasting of Heavy Winter Precipitation a t Blue Hill (1-11) ,) BuZlet,in, Ameri-. can Meteorological Society, vol. 19, No. 7, September .-
1938, pp. 281-297. 9. E. H. Bowie and R. H. Weightman, Types of Storms of the United States and their Average Movements. Monthly Weather Review Suppleme5 No. 1, Wash- ington, D. C., 1914.
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