A STUDY OF THE EFFECTIVE MOISTURE-STEERING LEVEL IN A CLOUD
AND
PRECIPITATION PREDICTION MODEL
INST. TEC 4
s
"T $
BR
by
-
Harold E. Headlee
B.S., United States Military Academy
(1951)
SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
January 1965
Signature of Author. .
S
..
..
. .
.
..
...
.
.
Dqpatmept of Meteorology, January1965
Certified by
O
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.
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ThesisySupervisor
Accepted by. . . .
...
. .
. . . . . .
Chairman, Dep/±tmenfal Committee on Graduate Students
A STUDY OF THE EFFECTIVE MOISTURE-STEERING LEVEL IN A CLOUD
AND
PRECIPITATION PREDICTION MODEL
by
Harold E. Headlee
Submitted to the Department of Meteorology on
January 18, 1965 in partial fulfillment of the
requirement for the Degree of Master of Science
ABSTRACT
In the Younkin, LaRue, and Sanders objective method for
predicting clouds and precipitation, the effective moisture
steering level is an important part.
It was shown that the optimum selection of this level
is dependent on both seasonal and geographical effects.
In the actual model used for forecasting, the optimum
level is at 833 mb. This differs from what the theoretical
level would be in most cases.
Testing this optimum level versus its theoretical counterpart, it was shown that even under a severe test of both orography and frontal conditions, the model's effective moisturesteering flow compared favorably with its theoretical counterpart.
Thesis Supervisor:
Title:
Frederick Sanders
Associate Professor of Meteorology
iii
ACKNOWLEDGEMENT
The author is indebted to Professor Frederick Sanders
for his advice and encouragement throughout the course of
this study.
Acknowledgement is made to Mr. Martin Hurwitz and Mr.
Howard Fairman for computer programming assistance, to Mr.
Jon Plotkin and Mins Ann Corrigan for plottin
the n@ecessary
data, and to Mrs. August Shumbera for typing the thesis.
iv
TABLE OF CONTENTS
I
II
I II
IV
V
VI
VII
INTRODUCTION
SEASONAL EFFECTS ON THE EFFECTIVE MOISTURE-STEERING
LEVEL
4
DISCUSSION AND RESULTS
14
CONCLUSIONS
18
THE EFFECTS OF OROGRAPHY AND A FRONTAL ZONE ON THE
EFFECTIVE "MOISTURE STEERING LEVEL" OF THE WORKING
MODEL"
19
DISCUSSION AND RESULTS
27
CONCLUSION
BIBLIOGRAPHY.
34
APPENDIX
35
LIST OF FIGURES
o, I
and c&
for Nashville (72327)
1.
Profiles of
2.
Profiles of
3.
Mean seasonal profiles for
4.
0000 GMT 1 April 1964 855-mb map
5.
1200 GMT 1 April 1964 833-mb map
6.
0000 GMT 2 April 1964 833-mb map
7.
0000 GMT 3 April 1964 833-mb map
8.
1200 GMT 3 April 1964 833-mb map
9.
0000 GMT 4 April 1964 833-mb map
and o4Q for April,
o-,
and
1961
o4
I.
INTRODUCTION
In the past fifteen years numerical weather prediction
has developed from a theoretical idea into an almost exact
science.
The local forecaster of today has more aids than
ever before in making his weather forecasts.
In addition, -
more and more of his forecasts are being made by the numerical
weather prediction unit of the United States Weather Bureau.
This can be attributed to the improved products of the
machine forecasts.
But, at present, the area of forecasting
clouds and precipitation has lagged behind the general overall
improvement of other forecast elements involved in weather
prediction.
Admittedly, the forecasting of clouds and precipitation
is very difficult when all of the different physical processes
involved are considered.
Generally in the past subjective
type forecasts have been made for clouds and precipitation.
In recent years, many objective methods (1) have been tried
but have failed to perform the required tasks.
These methods
have either failed to show improved skill over subjective type
forecasts or by the complex nature of their prediction equations
are not readily adaptable to computer techniques.
With this in mind Younkin, LaRue, and Sanders (1965)
have recently developed an objective method which they hope will
(1) Several of these methods are listed in the references
for the reader's convenience.
definitely fulfill the requirements of an improved forecasting
tool as well as be appropriate for use by the numerical weather
prediction unit.
well.
In a few test cases it has performed very
Another very important feature of this method is its
simplicity, so that it can be used for single-station forecasts
by the forecaster with the present data available at any local
weather station.
In the theoretical development of this ipethod YLS (2)
has featured an effective "moisture-steering level" which is
a major part of the model.
Based on modeling techniques and
using a vertically integrated moisture concept, this level represents the flow of the moisture field.
The concept of
using a vertically integrated moisture transport is not new.
Earlier work in this field has been done by Benton and Estoque
(1954).
Further developments in water vapor transport were
carried on by Starr et.al. (1955) in investigation on the
general circulation problem.
These reports were primarily
concerned with water balance over large areas.
YLS uses a
slightly different technique in representing the advection of
moisture by an effective steering flow.
The purpose of this thesis is to investigate three aspects
of the effective moisture-steering level of the YLS model for
predicting clouds and precipation.
The first of these will
involve the derivation of this level which was made on a
(2) For the remainder of this paper, any reference to
Younkin, LaRue and Sanders will be as (YLS).
climatological basis.
The "constants" involved and the resulting
steering level will be investigated for seasonal effects.
The second and third aspects will concern the "working
model".
In this "working model" an average level has been
assumed for ease of computations.
To test this model, it was
decided to check the effects of orography and a fairly intense
frontal zone on the effective moisture-steering level.
4.
II.
SEASONAL EFFECTS ON THE EFFECTIVE "MOISTURE STEERING LEVEL"
Any method for predicting clouds and precipitation depends
on the ability to predict the amount of moisture above a given
point at a given time.
In the theoretical development of the
YLS model, it is stated that with knowledge of the initial
moisture field, it is possible to predict the local changes in
time, thus predicting the field at any given, time.
The complete derivation of the model will not be presented
here.
For a complete derivation the reader is referred to the
future publication by YLS.
A synopsis of the main points is as follows:
where q is the specific humidity, ?7 is the pressure at the
surface of the earth, and W is the mass of water vapor in
a column of unit horizontal cross section extending through
the entire atmosphere.
It was also decided since it was important in dealing
with lower boundary conditions and the influence of terrain
effects to use 6s-,-(Phillips 1957) as a vertical coordinate.
Equation (1) becomes:
(la)
W
0,
Using the assumption that q is a conservative quantity,
we regard the quantity q as a "virtual" specific humidity q
and W' as the "virtual" precipitable water.
This follows the
convention of the Staff Members of Tokoyo University (1955).
After formulating the quantities in the 4r-system and
using the principle of conservation of mass, the following was
derived:
(2)
--
jV'-(y.
'
vt)
do.j + I
f4-Y
Vr)a-
The problem was then to evaluate the right hand side of
the above equation.
Sanders, with some misgivings, but noting the success of
analogous assumptions in other meteorological prognoses, assumed
that the integrals could be evaluated by modeling the vertical
variations of q,gandV-..
Thus,
Then ()
(3)
f(4
x,,)
=
oC)
is a quantity which denotes an average through-
out the entire depth of the atmosphere.
The subscripts 1 and 0
represents the surface of earth and the top of the atmosphere.
With this representation it can be seen that the following
constraints are made on the modeling paremeters:
o4
,
= 1
=0
Making the required substitutions, and developing a relationship for dL , Sanders equations evolved into this prediction
equation:
equation:
.
.,
1_1~
(6)
-l
W-o
-
V f
+
6Clevel
The subscript a designates the
where
V=
k
In evaluating K 1 , K 2 , K3, Sanders used the monthly mean
sounding data for Lake Charles (72240), Ely (72486), Portland
(72606), Green Bay (72645) and Spokane (72785) from
Climatological
aa for April 1962.
To evaluate the seasonal effects, it was decided to use
the same stations with an additional station of Nashville
(72327).
Besides offering more data, Nashville was added to
see if there might be a latitudinal effect on the values of
K1 , K 2 , and K 3 .
Data from January, April, July and October
were used for both 1961 and 1962.
In this way it was hoped
that the corresponding periods would provide additional information on the possible year to year variations, if any.
The procedures used were the same as Sanders.
The
soundings were plotted versus Cras a vertical coordinate.
The value.-of q was assumed to drop discontinuously to zero at
6d- =.5.
If humidity data were missing, the relative humidity
was assumed to be 30 percent.
the /e- component of the wind.
Values of q
were taken from
If the direction of the-wind was
within ten degrees of due west or east, then the wind speed was
taken as shown.
The following relationships were used in plotting the
different soundings:
21)
_
i=
-a,
where i designates the level, u 1 is the value at d'al, and
the bar is the average for the entire depth of the atmosphere.
It was also assumed that u = o at d"= o or at the top of the
atmosphere.
The mean level(s) d" will be those levels where
= 1.
In making the assumption concerning the moisture being.
discontinuous at d'
= .5 is not an unusual assumption when we
observe the results of climatological data.
Very few stations
report moisture above 500 mb in the monthly mean soundings.
Starr et.al. (1955) assumed no moisture transport above 500 mb
when working with a pressure coordinate system.
If we assumed
q to be linear from its value at 6' = .5 and decreases to 0 at
S= 0, it would increase our value of q by approximately 10%.
This assumption would give an
of the
o
profile within the same limits
profile and would increase 7B in our computations.
The
net result would be to raise our effective "moisture steering
level" by approximately 30 to 50 mb.
If we were to assume that
q would decrease linearly from its last slope and hence decrease
to 0 faster, then this increase would be smaller.
From an
observational point of view, the values of q at upper levels
in the atmosphere are certainly small when compared to values
8.
in the lower atmosphere and would only net a small increase in
raising our moisture steering level.
YLS also mention that in the climatological data the
moisture advection near the ground will be underestimated
because the mean wind near the surface is undoubtedly decreased
by terrain and frictional effects.
Also, at present, there is
a bias in the humidity measurements in the data.
In the mean
humidity data only those observations reporting humidity are
averaged.
Therefore the values at upper levels more so than
lower would be biased toward the moist side.
Taking both
features into consideration would probably lower the effective
"moisture steering level".
In any case, the previously mentioned features are opposed
and may tend to cancel out.
The effect of moisture above 6= .5
can be taken into consideration but the effects of terrain and
friction near the surface can be only estimated.
The results of calculating for o,
Table 1 for Nashville (72327) only.
,
and W@ are shown in
Results for the other
stations were calculated in a similar manner.
The procedure
was to plot both moisture and wind versus O'and then selecting
the values at intervals of
-=
.05.
computed using the trapzoidal rule.
All averages were then
In solving for values of
SK
3 , area integration was also done by the trapzoidal rule.
The results for 7,
, and P
q, ul, u, K1 , K 2 , K3,
are shown in Table 2.
are included here.
*C, Q ,
o,
,
YLS results for April 1962
and dQ profiles are shown in
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11.
Figures la - c, 2a - c, and 3a - c.
shown here.
Only certain profiles are
The first figure is for only one station (72327)
and reflects the variation in time.
The second figure shows
the variation among the selected stations for one time period
(April 1961).
The third figure shows the mean profile of the
selected stations for January, July, October and April.
Since YLS profiles for April 1962 were not available only
April 1961 and Nashville 1962 is included for the April mean
soundings.
The other profiles are made up of two values at
each station for the months mentioned.
When comparing the
mean profiles between years, only a very small variation was
observed and therefore we could expect only a small year to
year variation in our results for the mean profiles.
Before we enter into the discussion of the results from
a seasonal aspect, it might help us to ascertain the effect
of assuming a linear variation of oand Q between 6= 1.0 and
*5. From observation it can be seen that the mean profiles
•
do show a tendency to be linear.
If we assume that our profiles
are linear we can arrive at the following:
Given:
<°
(7)
[
E-
-YX
then
(9 )
OU
-
e/n 2.
) at (
q(,-.
aqd
and integrating,
(io)
(10)
=fe
)
os +
-p( ) -J
3L+
4 ol(0,S)(osjno#c
((A(
s
. to S)
a' a,*'
12.
At C* , the "effective moisture steering" level,
~)
=
therefore,
(11)
L'-
s (o.s)
.2
( (r)
J
-
oli
=
,(os)
, o/)
4 (o$)
4("44s
solving for U we find
(12)
6'
(0o -) +
Under this linear
/ condition and our,previous constraint
condition,
oL
between the values of
4 -
oZ(/)
+ aCOS)
equation for
(13)
.
'
k/.)
, we can state a relationship
and
.(o.s)
, i.e., 2 -
3
'
or
Substituting this relationship into our
we get either of the following:
;4 z
(14)
- /
fo
0
__
-
-
The second relationship might be the better one to use in
calculating
4- because it is independent of low-level inversion
effects on
o-
soundings.
(1.0) which was apparent in several of the
It is understood that this would only give an
estimate of the
,- level in evaluating our "effective
moisture steering level".
Using this as an estimate, it can be shown that with od
(1.0) having a range from approximately 3.0 to 5.0 that 4r would
have limits from .79 to .87.
In Table 2, 4' is also shown for
the stations concerned excluding YLS April 1962 data.
the estimated value based on equation (13).
(14) then it can be shown that
.833, and since
o(
0d
67
is
If we were to use
would always be less than
(0.5) is usually very small the
c-level
13.
would be near .833.
The significance of this will be shown in
the "working model".
The assumption of linear profiles for
a
and
also
provides a mathematical estimate of the value of K 3 .
If we were
to find the equation for the beat fit of our near linear profiles,
we could then solve for 06
for a variety of
0profiles.
In
observing the mean profiles for the various months Figure 3a-C,
it can be seen that the
than the o4 profiles.
9
profiles are much more consistent
Therefore, using the following linear
relations
=
(15)
<()
(16)
<L-) =
(17)
=
oe)
406-/
- 1-2k
f-
= 3o
where
o()
where
o'o)
6 10
where
e'oC
=
and
(18)
4C' )
=
.5- 2.
.-
=
.co
and in this relationship
(19)
I'q4d-='
=
hence
(20)
-
"
where
we can solve for the various constants in SANDERS prediction
equation.
In the above it was found that c
would vary from
approximately .41 to .52 and K 3 would vary approximately from
2.9 to 2.4.
When we compare the results (Table 2) of the individual
soundings which are not usually linear, it was found that in
most cases these were the limits of the desired K
constant.
14.
III.
DISCUSSION AND RESULTS
In computing the values of the desired coefficients
of K 1 , K 2 , and K 3 , and the value of
d;Z
which denotes
the effective "moisture steering level" the following
observations were noted:
(1)
Large variations in the at ,
, and *@ profiles
are evidenced by Figures la-C and 2a-C which would be expected from observational evidence.
(2)
The strong appeal for working in a
6-coordinate system
was evident when comparing the values of
Z
and P
among .
the various stations.
(3)
The weakness of our q computation in making our mean
value calculations is made evident by the values of K 1 and
K 2 at Lake Charles for July 1961 and 1962.
S
which is the equation for any cd
represents the wind speed at that level.
if A
As stated before,
level, where
s
It can be seen that
approachese,, then our value approaches infinity.
This feature was even more evident in the second part of this
thesis where for one sounding when
O was computed by a
computer program its value was nearly 100 times the usual
value for
c
.
Since the values of K 1 and K 2 for Lake
Charles were so large in absolute magnitude when compared to
the other stations, the
@ values were omitted when computing
the mean sounding for July (Fig. 3-b).
To avoid extra weighted
factors such as this, the mean values of K 1 , K 2 , K 3,
0
and 0
15.
(Table 4) were computed from the mean ol and mean
seasonal data (Table 3).
(4)
The mean
profiles (Fig. 3a) showed a striking variation
between January and the other three selected time periods.
the
If
c~ values for Green Bay for January 1962 and the surface
inversion effect at Ely were omitted then the mean curve would
adjust more closely to the other three curves but would still
show a variation.
(5)
The feature of linearity of the profiles evidenced by
the mathematical estimate of 4W by knowing the value of oc at
Sthe surface only.
This was shown when comparing the value of
d0 to the actual values of 4' (Table 2).
(6) Geographical differences were noted when we compared the
average OW values for each station (Table 5).
The largest
values were at Lake Charles and Nashville and the smallest
at Green Bay and Portland.
Tale 3
Mean
-
JAN
-..
9...
00..
3.59
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..
T-
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.
__ .00
9
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1R
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-1_'
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.15
_
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.72
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1i
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.07
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1.8.
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17.
TABLE 4
CALCULATIONS BASED ON MEAN VALUES FROM TABLE 3
JAN.
APRIL
.64
JULY
.55
OCT.
.58
67
K3
K2
K,
.36
.42
2.62
.59
.819
2.99
.59
.820
2.75
.61
.855
2.78
.59
.83
CALCULATION BASED ON AVERAGE VALUE FROM TABLE 2
K
K2
JAN.
2.66
.595
.81
APRIL
.62
.38
2.96
.590
.82
JULY
.54
.46
2.19
.59
.86
OCT.
.59
.41
2.71
.585
.84
TABLE 5
AVERAGE
ELY
.841
GREENBAY
.811
NASHVILLE
.834
LAKE CHARLES
.870
PORTLAND
.810
SPOKANE
.828
18.
IV.
CONCLUSIONS
Although only a limited amount of data was examined
it can be definitely stated that the optimum values of K1 ,
K2 , K
dm
and
are influenced by seasonal and
o
geographical effects.
Since this thesis is primarily interested in the level
of effective moisture steering it can be seep from the
results of the data that this steering level is lowest in
summer and highest in winter.
One may conclude that there is also a latitudinal and
geographical effect on the values of the mean 4
(Table 5)
as evidenced by Lake Charles (72240), Nashville (72327),
Green Bay (72645) and Portland (72606).
point was the data on Spokane (72785).
Another interesting
In January and October,
generally considered the rainy period for the station, the
d-level was lower than during the other two seasons.
Therefore one might conclude source regions might influence
the values of
%
.
If more stations were included, the
answer to possible latitudinal or source regions of moisture
would probably be ascertained.
No conclusion was made on why the mean January data
should vary as much as it did from the mean values of the
other months.
19.
V.
THE EFFECTS OF OROGRAIHY iND A FRONTAL ZONE ON THE EFFECTIVE
"MOISTURE STEERING LEVEL" OF THE "WORKING MODEL"
YLS, having evaluated the optimum values of K 1 , K2 , K3 ,
d
and 04 could now use these values in the prediction
equation for the moisture.
From the prediction equation,
stated previously where
(6)
- _._,2.
V__.'
_V
v
0,+)Cwr
it was desired to develop an operation model for forecasting.
Since, at present, all observed and forecast parameters
are in a constant-pressure system, the operational model had
to be made compatible with this system.
The portion of the
conversion which is being investigated for this thesis is
the first term or the moisture advection term.
Rewriting
the prediction equation derived in the theoretical develop-
ment YLS now shows:
(6a)
-
--
W-.v W
4
/o ow
The last term involving
neglected here.
+
W7
oomb
_7 of the theoretical equation was
In this conversion
=AkY* +14Y
where V
and V5 are the values of the wind at 1000 and 500 mb.
YLS
used the values of K1 = 2/3 and K2 = 1/3, therefore if we
assume a linear wind profile V will be the wind at 833 mb
or if the surface pressure is 1000 mb, cf will equal .833.
The significance of.this value was mentioned previously in
this paper.
20.
The complete details of the YLS derivation of the working model will not be shown here.
Taking equation (6a) and
using a terminology involving "saturation thickness" h s
,
"saturation deficit" ho, and adjusted values of same when the
surface pressure is other than 1000 mb, the following result
is obtained:
where
.V_
JW -t
fWJ.d
I
Ai)J=
1OWPO~~
Kit
h
S,A5
44
With further modeling assumption regarding
and other math-
ematical developments regarding certain constants, the final
working equation becomes:
where
P/
=
/
-t- !V
= saturation deficit
-P
P-A
= term dependent on land elevation
h
= thickness from 1000 mb to 500 mb
The term which is under investigation here is the
term.
In this section of the thesis the value
V.
V*
of the
"working model" is to be compared to the theoretical value
of
V
.
In
the 'orking
model":
V#
3
°*
In test cases a major failure of the model has been in
the Rocky Mountain area.
Also, evident from the equation is
the large dependence on the advection of the thickness term
which would be greater in a frontal zone.
Therefore, V
in
21.
a frontal zone should be very accurate since the thickness
gradient is at its maximum.
To test the model in these two areas, it would be well
to compare the
<V of the "working model" to that of
V
of the theoretical development.
In the first case, a synoptic situation was chosen where
a low-pressure system from the Pacific moved into the Rocky
Mountain area and maintained a closed surfacp center of circulation as it proceeded eastward across the mountains.
The
situation of O000OGMT 1 April 1964 to OOOOGT 2 April 1964 was
selected.
The soundings for 19 selected upper-air stations-
were plotted for the three time periods OOOOGMT 1 April,
1200GMT 1 April, and O000OGMT 2 April.
The procedure for solving for oz and
Q
and hence the
other values which are calculated for the
0
level or levels
was slightly different than the procedure in the previous
climatological case.
In the case of moisture, (4-), the values for missing
or motorboating data was not taken as 30 percent relative
humidity.
The values were based on temperature and varied from
12 percent for warmer temperatures to about 20 percent for
colder temperatures.
Calculating the
in procedures.
as a
values also required slight changes
Instead of taking the direction of the wind
--component, the direction component of the advecting
wind of the "working model" was used.
In some cases, another
22.
Q
direction was used and this did alter the
sounding.
P
level for the
This did not prove to be significant from an overall
point of view.
Since the wind soundings were plotted at intervals in
feot, subjective oonversions were made to the pressure levels.
Also, significant wind changes in velocity or direction were
taken into account and plotted on the sounding.
The data was piaced into digitized for% and a computer
program was used to calculate the values of
S,
to P
eC0
.
.
and q
This value of
'w
" ,
,
, 0 ,
was then converted back
Returning to the sounding the value of the wind was
obtained from the P*--level and hence is the advection wind
of the theoretical method.
The values ofo 06,
, and P
,
and the winds at that level are shown in Table (6).
In computing
V
for the working model, the winds were
obtained geostrophically from the graphical addition of the
1000 mb pattern plus one-third the thickness pattern between
1000 mb and 500 mb for the time periods indicated.
The
resulting pressure field is given in Figure 4, 5, and 6 for the
respective time periods.
The values of the wind for the selected stations were
then obtained from a geostrophic scale and were plotted
accordingly.
model".
These winds represent
Y
of the "working
The value of these winds at the selected stations
are also listed in (Table 6).
In selecting a situation involving a strong frontal zone
23.
Table (
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25.
and to eliminate terrain effects as much as possible, a synoptic situation was selected for the area in the eastern half
of the United States.
The situation previously considered
continued to develop as it moved across the United States.
Hence, the period of O000GMT 3 April 1964 to O000GMT 4 April
1964 gave the required data.
The procedures for solving for V of the theoretical
method and V of the "working model" were the same as in the
orographic case.
These values are listed in Table 7.
In
this second case, only 10 stations were selected since this
gave the best coverage of the area of the front in
periods indicated.
the time.
The pressure pattern of the "working
model" from which our geostrophic wind at Ve was obtained are
shown in Figures 7, 8, and 9.
26.
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27.
VI.
DISCUSSION OF THE RESULTS
In making our comparison of the "working model" wind
to that of the theoretical method wind it must be remembered
that in computing the geostrophic wind that a certain amount
of human error was involved in the graphical addition of the
required pressure patterns.
Also we know that the
V
winds
in the theoretical method are observed winds and are not
geostrophic.
Allowing for this error difference the following
classifications were made for comparing
model" to that of
V
V
of the "working
of the theoretical method.
Here E
indicates difference between the geostrophic wind of the model
and the observed wind of the theory.
o
E
c
<
2
4
The following results were obtained for the orographic case:
Table 8
Error Classification
0
1
2
3
4
April 1 O0000GMT
8
7
2
1
1
April 1 1200GMT
6
6
2
4
1
April 2 0000GMT
3
3
1
3
8
28.
From the values in Table 8 it can be seen that the model
gave very good results for the beginning and middle time
periods.
In the last time period the results were very poor.
From knowledge of the pressure patterns from surface to 500 mb,
it could be expected if the next time period was compared, the
model would again show fairly good results.
This observation
is made with the knowledge that the 700-mb and 500-mb winds
would show a northwesterly flow thus closer agreeing to reduced
1000-mb pressure pattern for that mountain area.
It appears
that the model has been affected adversely by cold air advection.
Here one could expect the model's wind shift to the northwest
be premature to the change in the actual observed winds.
The effect of the jet over the southern area stations
was apparent in that the model underestimated the wind speeds
for stations 274, 374, 290, 270 in the 1 April 1200GMT time
period.
Diverting from our comparison of the V4 winds, the values
of o' ,
, and therefore
FP
show a much larger variation
from station to station and from time period to time period
than what we observed in the monthly mean sounding evaluations.
This, of course, would be expected.
in computing 9
S
Also, as mentioned earlier,
it was apparent from some of the results that
and hence ag
can have very great magnitudes.
768 and 785 for last time period illustrate this with
values of
-21.411 and
-54.004 respectively.
Stations
oC0
In computing
the d level in the monthly mean soundings, we found only one
29.
V-level in the lower levels.
station with five
(-levels
In these cases there was one
below
6"= .5 and in many cases
more than one.
In the investigation of the frontal zone case the
following results were obtained using the same criteria when
evaluating the difference between the V winds in the mountains.
Table 9
Error Classification
0
1
2
3
4
3 April OOOOGMT
7
1
1
0
1
3 April 1200GMT
4
3
0
2
1
4 April 0000GMT
5
1
1
1
2
The model results were very good in this case.
The major
error differences in every case but one occurred near cols in
the model's steering flow.
The direction of the model's wind
vector was exceptionally good in almost every case.
The im-
portance of an accurate geostrophic pattern was apparent here.
The shift of the winds in comparing the time periods were
very reliable when compared to the theoretical results.
When one compares the variation of
1Z ,
0
,
and the
other parameters considered in the theoretical development,
again we can see quite a variation in the daily values.
The
one feature here is that in the values in the latter case,
there are far fewer d
levels than were observed in the mountains.
In most of the stations considered here, only one
6
level
~
30.
was found in the lower levels.
This is indicative of a strong,
well defined wind shear and should be expected in or near the
frontal zone.
31.
VII.
CONCLUSIONS
In comparing the values of
to that of the
V of the "working model"
of the theoretical method certain con-
olusions may be made.
Wh en the model w
subjecedt
o the
test of orography it was found to be satisfactory, when the
1000-mb flow and the 500-mb flow are nearly in the same
direction.
If these flows are in different directions, the
result is less accurate and large errors may result in the
advection of moisture.
The ficticious flow at 1000-mb is a definite factor inthe error.
The immediate thought here is that in the model
we are weighting the 1000-mb flow too strongly in mountains.
The amount of required change involving K 1 and K 2 of the
"working model" in the mountain areas should be subject to
investigation.
It would be reasonable to assume that the
constants which determine the
imately .6 and .4 respectively.
level.
* value should be approxVo would then be at the 800 mb
If K1 and K 2 were equal to 1/2, then the V* level
would be at 750 mb.
To check these values it would require a
separate computation for the mountain area from the remaining portion of the country.
Since the YLS model is being
converted to a computer solution in the numerical weather
prediction center, it would not be too difficult for trajectories
in the mountain areas to be computed at different levels than
those away from the area.
32.
In fact, at present, the Weather Bureau is planning to
computerize the entire upper-air sounding twice daily, and
with a computer program similar to the one used in this
paper it would be possible to solve for
station.
V
,V
at each
Then using these winds trajectories the initial
could be computed from actual soundings.
It is real-
ized that this would give a more accurate trajectory in the
first few hours only.
After this time, in making our fore-
cast, the model is dependent on the prognosis of the 1000-mb
surface and the 500-mb surface.
In any case, when subject to
maQhine computationa, the values of K
and K2 may be more
-
variable than those used by YLS.
When YLS derived the working model, a portion of that
derivation included an orographic term which was (IVo
and was made equal to
Y
for ease of computation.
4.59)
Again
since the model is going to be used by the numerical weather
prediction, a separate value could be computed which would be
more accurate than assuming the term to be equal to Y
.
Examination of the results in a frontal zone, one can
conclude that the effective "moisture steering flow" of the
model does not need to be altered in this area.
The only
conclusion that could be made here is that care should be
taken in computing the geostrophic
Vo
pattern as col areas
will be a possible source of error in computing the required
trajectories.
For a summary conclusion, it is evident that both the
33.
"working model" and the theoretical method involving the
development of an effective "moisture steering level" are
compatible.
The fact that the "working model" winds for the
advection of moisture is very close to the theoretical method
winds is definite support for the concept of horizontal
advection of moisture being of great importance in forecasting
clouds and precipitation.
The fact that the effective moisture steering flow of the
"working model" has greater errors in the mountains is not
surprising.
for@
I
This could be ascertained when the ao
Y4luQ
diff@r go widely when 1i4gh
iJigtyggiQ
and there@tgtg
are considered.
In any case the idea of an effective "moisture steering
flow" for moisture advection has stood the test and any errors
in the prediction model will be more likely to occur in the
other terms.
34.
BIBLIOGRAPHY
Benton, G.L. and M.A. Estoque, 1954:
American Continent.
J. Meteor.,
Collins, G.O. and Kuhn P.M.,
forecasting, Part 3.
Estoque, M.A.., 1957:
Water vapor transfer over the North
1954:
11, 462-477.
A generalized study of precipitation
Mon. Wea. Rev.,
82, 173-182.
An approach to quantitative precipitation forecasting.
J. Meteor. 13, 50-54.
Phillips, N.A., 1957:
A coordinate system having some special advantages
for numerical forecasting. J. Meteor. 14, 184-185.
Smagorinsky, J. and Collins G.O., 1955:
On the numerical prediction of
precipitation, Mon. Wea. Rev., 83, 53-57.
Smebye, S.J.,
1958:
J. Meteor.,
Computation of precipitation from large scale motion,
15, 547-560.
Staff Members Tokyo University, 1955:
itation with the numerical method.
Starr, V.P. and White R.M.,
1955:
poleward flux of water vapor.
Starr, V.P. and Peixoto, J.,
the northern hemisphere.
1960:
The quantitative forecast of precipJ. Meteor. Soc. Japan,33, 204-216.
Direct Measurement of the hemispheric
J. Mar. Res. 14, 217-225.
On the zonal flux of water vapor in
Geofisica Pura e App. 39, 174-185.
Younkin, R.J., LaRue, J.A. and Sanders F.,
1965:
The objective prediction
of clouds and precipitation using vertically integrated moisture and
adiabatic vertical motions.
J. App. Meteor.,
in press.
35.
APPENDIX
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