MONTHLY WEATHER REVIEW
VOLUME 97, NUMBER 1
JANUARY 1969
UDC 551.509.33: 551.509.313(215-17)
EXPERIMENTALEXTENDEDPREDICTIONSWITH A NINE-LEVELHEMISPHERICMODEL
K. MIYAKODA, J. SMAGORINSKY, R. F. STRICKLER, and G. D. HEMBREE
Geophysical Fluid DynamicsLaboratory, ESSA, Princeton, N.J.
ABSTRACT
Two-week predictions were made for two winter cases by applying the Geophysical Fluid Dynamics Laboratory
high-resolution, nine-level, hemispheric, moist general circulation model. Three versions of the model are discussed:
Experiment 1 includes the orography but not the radiative transfer or the turbulent exchange of heat and moisture
with the lower boundary; Experiment 2 accounts for all of these effects as well as land-sea contrast; Experiment 3
allows, in addition, the difference in thermal properties between the land-ice and sea-ice surfaces, as well as an 80%
relative humidity condensation criterion reduced from the 100% criterion in Experiments 1 and 2.
The computed results are compared with observed data in terms of the evolution of individual cyclonic and
anticyclonic patterns, the zonal mean structure of temperature, wind, and humidity, the precipitation over the
United States, and the hemispheric energetics.
The forecast near sea level was considerably improved in Experiments 2 and 3 over Experiment 1. The experiment
succeeded in forecasting the birth of second and third generation extratropical cyclones and their behavior thereafter.
The hemispheric sum of precipitation was increased five times in Experiment 2 over that in Experiment 1, and even
more in Experiment 3, the greatest contribution occurring in the Tropics. Two winter cases were considered. The
correlation coefficients between the observed and the forecast patterns for the change of 500-mb geopotential height
from the initial time remained above 0.5 for 13 days in one case and for 9 days in the other.
There are, however, several defects in the model. The forecast temperature was too low. I n t h e flow pattern
the intensities of the Highs and Lows weakened appreciably after 6 or 8 days, reflecting the fact that the forecast
of eddy kinetic energy was less than the observed. On the other hand, the intensity of the tropospheric westerlies
was too great.
CONTENTS
1
2
3
5
5
1 0
15
15
19
22
28
29
32
32
33
E3
75
I. INTRODUCTION
This is an extension of the work of Smagorinsky,
Strickler, et al. (1965) that was presented at the Moscow-
Symposium on Dynamics of Large Scale Processes in the
Atmosphere. That paper discussed a set of 4-day predic-
tions made with a general circulation model. In the
present study, refined versions of that model have been
applied to an extended prediction period of 2 weeks.
The period of 2 weekswas chosen for several reasons.
A period of 4 days is not long enough to study the bias in
the mathematical prediction model, if there is any, because
the solution at the 4th day obtained by a model is still
undergoing initial adjustment. Second, it may be desirable
to c,over the period of a zonal index cycle that has a charac-
teristic time scale of 11 to 14 days. Third, there has
recently been a great deal of discussion about the predic-
tability of cyclone-scale systems through the hydro-
thermodynamical method. According to the recommenda-
1
tions of the Panel on International Meteorological Co-
operation to the Committee on Atmospheric Sciences,
National Academy of Sciences, U.S.A. (1966), the limit
of deterministic predictability for the atmosphere is about
two weeks in the winter and somewhat longer in the
summer. We, of course, agree with the concept that it
would be impossible to make determinate forecasts for
arbitrarily long time intervals, because of the continuous
character of the turbulent spectrum and the limitations
of any observational net. It might, however, be unduly
pessimistic to speculate that, within 5 days or IO days or
2 weeks, the forecast result on the synoptic scale is utterly
different from the observed. One purpose of the present
study is, therefore, to challenge this idea. Our attitude
might seem naive to those who accept the short limit of
predictability. We believe that it is still worthwhile t o
attack this problem from a standpoint different from
previous works, even if the limit mav eventually prove
t o be 2 weeks.
In order to make a %week prediction, it is quite
probable that radiant energy must be considered to main-
tain large-scale atmospheric features. On the other hand,
past experience (for example, Bushby and Hinds, 1955)
tells us that the effect of the land-sea contrast is also very
important even for 1- or %day predictions (together with
the orographic effects). These effects have been included
in our prediction model.
Other processes were also included in the hope of
improving the prediction model. The present study con-
tains three major experiments. Why these experiments
were designed and what results were achieved will be
described in the main part of this paper. Many of the
details are given in the Appendixes.
2. THE PREDICTION MODEL
The basic equations used in this study were described
in the papers by Smagorinsky, Manabe, and Holloway
(1965) and Manabe, Smagorinsky, and Strickler (1965).
The general characteristics of the model are: nine vertical
levels (see table 1); primitive equations; hemispheric;
N=40 horizontal resolution (there are 40 gridpoints
between the Pole and the Equator, so the grid size is
approximately 320 km at the Pole, 270 km at midlatitude,
and 160 km at the Equator); moist model including the
orography (fig. 1).
All the equations governing the atmospheric state and motion
are defined on the stereographic projection map at nine vertical
levels using Phillips r-coordinates. The lateral boundary is
roughly at the Equator and is an insulated, free-slip wall. The
surface pressure is variable with time and space. The internal
viscosity is Smagorinskys nonlinear version (with.effective Karman
constant k=0.4). The surface friction is such that the drag co-
efficient is everywhere constant. The horizontal gradient of geo-
potential height is computed on constant pressure surfaces. (See
Smagorinsky, Strickler, et al., 1965). The differential equations
are then approximated by the Arakawa-Lilly kinetic energy
conserving finite difference method. The entirc Northern Hcm-
isphere is covercd by 5,025 gridpoints per levcl.
Tcmperature is determined by thc usual thermal equation, and
in addition the lapse rate is instantaneously adjusted to thc dry
adiabatic ratc in any layer in which i t is cxcccded.
2 MONTHLY WEATHER REVIEW V0.l. 97, No. 1
The hydrologic processes are incorporated. Water vapor is
transferred three dimensionally by existing winds. Then the process
of small-scale convection, Le., subgrid-scale convection, is simulated
by a moist adiabatic temperature adjustment. The temperature
is instantaneously adjusted to the moist adiabatic lapse rate when-
ever supersaturation occurs and at the same time the lapse rate
exceeds the moist adiabatic lapse rate. On the other hand, large-
scale condensation is assumcd to take place if supersaturation
occurs and the lapse rate is submoist adiabatic. The heat released
by these condensation processes is fed back into the corrcsponding
layer.
Shortwave and longwave radiation is calculated by Manabe and
Stricklers (1964) scheme. Cloud coverage is taken from Telegadas
and London (1954) and London (1957). These data are climatological
monthly means (see tables in Appendix I) which are functions of
latitude and height. The gases which act as absorbers of radiant
energy, including water vapor, are climatological monthly means
and are also functions of latitude and height (see table in Appendix I).
The sea-surface temperature used in this study is the January
normal (fig. 2), which is assumed constant with time during the
entire prediction period. The turbulent transfer of momentum, heat,
and moisture in the boundary layer is taken into account. The
land-surface temperature is determined through the heat balance
at the surface, where the soil is assumed to have no heat capacity.
The albedo of the sea is taken from Budyko (1956). The albedo of
land is assumed t o be a function of latitude only, taken from
Kung, Bryson, and Lenschow (1964) and Posey and Clapp (1964)
(see Appendix I ). The availability of soil moisture on land (see
Saltzman, 1967, for the definition), which is used for determining
evapotranspiration, is assumed 0.5 everywhere over land, and 1.0
over sea. The snowline is fixed with time, and, when computing the
heat budget at the ground, the surface temperature north of this
snowline is not allowed t o exceed 0C (the excess heat is assumed
to melt some of the snow).
It should be noted that the following effects were not taken into
account: the diurnal or seasonal variations of insolation, the time
and space change of albedo due to the deposit of new snow, the
response with the oceans, and the time and longitudinal variation
of cloud cover.
In the present study, experiments were made with three
versions of the model:
Experiment 1 has no radiative transfer and no turbulent
exchange of heat and moisture with the earths surface.
This result was reported previously by Smagorinsky,
Strickler, et al. (1965).
Experiment 2 includes the effects of radiative transfer
and turbulent exchange with the surface and also accounts
for land-sea contrast.
Experiment 3 contains, in addition to these features, the
difference in thermal properties between the land-ice and
sea-ice surfaces, and the condensation criterion is 80%
instead of 100% as in Experiments 1 and 2.
TABLE I.-Standard heights and pressures of the nine-level model
p : pressure, p*: surface pressure
PIP.
_
.008916
,074074
. 188615
,336077
,500000
,811385
,663923
.925926
,991084
Standard height (km)
I?. w
8.30
5. 50
3.30
1. 70
)Troposphere
:: :,}Boundary layer
January 1969 K. Miyakoda, J. Srnagorinsky, R. F. Strickler, and G. D. Hembree 3
FIGURE 1.-The orography. The lighter solid contours are elevations in 2,000-ft intervals and are marked by italics in thousands of feet.
Extrema are indicated by stars.
The reasons for doing these particular experiments will
be discussed later.
Concerning the speed of the present prediction model,
10 hr of computing time are required for each day of the
prediction with the UNIVAC 1108 computer. An addi-
tional 1 hr for each day is nsed in checking and computing
diagnostic integrals.
3. INITIALCONDITIONS
The forecasts were made for two initial data cases. One
was for tjhe 2-week period which began 1200 GJIT, Jan. 9,
1964, and the other was for the period which began 1200
GMT, Jan. 4, 1966. Note that the 1964 case was also used
by Smagorinsky, Strickler, et al. (1965). The 1964 case
includes Experiments 1, 2, and 3 (also referred to as
53F, 53G2> and 535) for the three versions of the model
mentioned in section 2. The 1966 case was used in the
Experiment 3 version (also referred to as 61J). Analyzed
aerological data n-ere supplied by the National Meteoro-
logical Center (NMC) at Suitland, Md.
Height analyses for 11 mandatory pressure surfaces from 1000
mb to 10 mb and tcmperature analyses for 10 levels, from 8.50 mb
4 MONTHLY WEATHERREVIEW Vol. 97, No. 1
. .. -. .
FIGURE 2.-Sea-surface temperature, the January normal in OK, and the sea-ice area, stippled (after U.S. Navy Hydrographic Office, 1944).
The real geography is given by thin lines, and the model gcography is by thick lines.
to 10 mb, were made. The moisture data for the 850-, 700-, and quasi-circular 5,025-point grid with the grid distance of 320 km
500-mb levels were specially analyzed for these experiments by a t t h e Pole.
January 1969 K. Miyakoda, J. Stnagorinsky, R. F. Strickler, and G. D. Hembree
The initialization of the data was made by conven-
tional techniques. The horizontal wind velocity was
obtained by solving the so-called balance equation and
the vertical velocity was by the w-equation.
In the following sections, for the sake of simplicity, the
specific illustrations will be mostly for the 1964 case, but
the results of the 1966 case are also reflected in the
discussion.
4. EXPERIMENTS 1 AND P
Figure 3 shows an important result of Experiment 1. It
is the error in temperature, i.e., the forecast hemispheric
mean temperature by Experiment 1 minus the observed
as a function of height. It is noted that the computed
temperature in midtroposphere during the forecast be-
comes higher than the observed, whereas in the lowest
troposphere it becomes lower than the observed. The
reason may be that heat was released by condensation,
and there was no compensating effect such as radiative
cooling, or interchange of heat with the surface. The
dynamics of the atmosphere normally tends to stabilize
the temperature distribution, especially in the lowest
levels.
In expectation of removing this error, additional
physical effects were included in the more sophisticated
model used in Experiment 2. Before discussing the tem-
perature in Experiment 2 we should first examine the
time evolution of precipitation and evaporation for
Experiments 1 and 2 in order to determine the difference
in latent heat release. Figure 4 shows that:
1) The precipitation in Experiment 2 is five times
greater than in Experiment 1.
2 ) The precipitation starts from small values, inweases
fairly rapidly, and levels off after about 4 days.
3) The rate of evaporation is large at the very be-
ginning.
4) The rate of precipitation becomes balanced with
that of evaporation as computation goes on.
To understand 1) better, it may be useful to look at
the latitudinal distribution of precipitation (fig. 5).
These are 24-hr rates obtained by taking the zonal and
time average for Experiment 1 (0-4 days), Experiment
2 (3-14 days) and Experiment 3 (3-11 days), where the
number of days in parentheses is the averaging period.
As was seen in figure 4, the precipitation in Experiment 1
is already near its maximum level after the first day,
so the averaging was started with the first day. One of
the most noteworthy features of Experiment 1 in figure 5
is that the distribution has no maximum at the Equator,
whereas those of Experiments 2 and 3 have sharp peaks
at the Equator.
This shows that much of the precipitation in Experi-
ment 2 occurs in the Tropics, though. even at middle
latitudes the rate of precipitation in Experiment 2 is
twice as large as that in Experiment 1. This is due to
both the supply of water vapor from the surface and the
radiative exchanges, which are allowed in Experiment 2
but not in Experiment 1. The radiative process over
land is important because together with the high sea-
l !
A Y
z .J
1 DAY -
2 DAY --- 3 DAY ----A
4 DAY ---
-3 -2 -1 0
T COMP - T OBS.-(C)
5
FIGURE 3.-Temperature error, i.e., the computed minus the
observed temperatures, which are hemispherically averaged, in
Experiment 1 is shown for 1, 2, 3, and 4 days. The ordinate is the
vertical level.
surface temperatures in the Tropics it contributes to the
destabilization of the atmospheric stratification. The
two maxima in the precipitation distribution werealso
characteristic of thc general circulation study (Manabe
et al., 1965), in which the tropical peak was even sharper.
This may be shown more clearly by figure.6, where the
latitudinal distribution of the 24-hr precipitation rate
is displayed for the lst, 3d, and 5th days for Experiment
2. The precipitation starts first in the middle latitudes]
and then it develops in the Tropics. This point is related
to 2) above. Our initial data have no disturbances in the
tropical area, so that it takes time for tropical precipita-
tion to develop.
Figure 7 illustrates the time evolution of the rates of precipita-
tion at the two maxima, Le., at 3N and 39N lat. It appears to
take about 4 days for the tropical precipitation to reach its equi-
librium although some increase is noticed after that time.
A more detailed analysis reveals that the condensation
in the Tropics started over land. The disturbances ap-
parently developed first near the tropical mountains in
the initially calm Tropics, though this effect was diminished
later.
As for 3) above, the larger initial rate of evaporation
results from a defect in the initialization technique. The
surface wind was computed by the balance equation
excluding surface friction, so that the wind intensity was
too large initially, and accordingly evaporation was
intensified.
6
~~
MONTHLY WEATHERREVIEW Vol. 97, No. 1
.09 EXP.3
r'
.06 ,_"""/
EXP.2
-
'"'ti
.03 1 - PREClPllATlON -I
.0 2 2
EVAPORATION
EXP.1
.Ol
o I 2 3 4 3 6 7 a v 1 0 1 1 1 2 1 3 1 1
DAY
FIGURE 4.-Time evolution of the 6-hr rates of precipitation (solid
lines) and evaporation (dashed lines) hemispherically averaged
for Experiments 1, 2, and 3.
CM
53 F - 10-4DAYS] -
53 62 - 16-13DAYS] "-
53 I - (4-10DAYS] --
.5
c
:I
.2
.I
0
-LATITUDE
FIGURE 5.-Latitudinal distribution of the 24-hr rate of precipitation
for Experiments 1, 2, and 3.
Next, let us look at other characteristics of the precipita-
tion forecast. Figure 8 is the land and sea distribution of
precipitation for the period of 3-14 days. The dots in the
figure are the estimated precipitation for minter by
Moller (1951). It may be seen that in the middle latitudes
the precipitation over the seais greater than over land in
both results. I n the Tropics, the precipitation is much
greater over land than over sea, although this tendency is
not observed in Moller's result. Note that the condensa-
tion over the sea at high latitudes is extremely high.
An.al,ysis revealed that this result is due to the extreme
-
LATITUDE
FIGURE 6.-Time variation of the latitudinal distribution of the
24-hr rate of precipitation in Experiment 2. The curves are for
1, 3, and 5 days.
CM
0 .1 1
t /
+ DAY
FIGURE 7.-Six-hour rates of precipitation at the two latitudes of
maxima, 3 O and 3g0N, in Experiment 2. The abscissa is time
in days.
coldness over the land and sea ice in the lower part of the '
model atmosphere in contrast to the relatively warm
temperature of the very small area of open sea at high
latitudes. We will return to this point later.
Let us next consider the heat fluxes from the surface.
Figure 9 is the latitudinal distribution of the turbulent
fluxes of latent and sensible heat over land and sea. The
winter data from Budyko (1963) over sea are also shown.
It is seen that the heat fluxes over sea at high latitudes
are extremely large. As mentioned earlier, this is partly
caused by the erroneous coldness over land. The effect
is amplified bedause of the small area of open sea at high
latitude in January.
January 1969 K. Miyakoda, J. Stnagorinsky, R. F. Strickler, and G. D. Hembree 7
CM
1.6
1 .4
1.2
1 .c
0.E
0.c
0.4
0.;
O .(
LATITUDE (DEG. 1
FIGURE 8.-Latitudinal distribution of the 24-hr rates of precipi-
tation over land and sea in Experiment 2. The dots are estimated
data for winter by Moller (1951). The small solid circle is forsea,
and the triangle is for land.
Now to return to the discussion of the temperature
error. Figure 10 is the vertical profile of hemispheric mean
temperature error in Experiment 2. Contrary to the case
of Experiment 1, the computed temperature is appreci-
ably lower than the observed. Even at the 13th day, the
cooling tendency in Experiment 2 continues.
This characteristic has already been noticed by Manabe
et al. (1965). In that experiment] the computed tempera-
ture at the 500-mb level was 5C less than the observed.
However, the two results are not exactly comparable,
because the general circulation study treated the annual
mean, whereas we are now dealing with a particular
January.
To examine this degeneracy in greater detail, a height-
latitude diagram of the temperature error of Experiment 2
at the 1 lth day is given in figure 11. We see that the
cooling is especially pronounced at high latitudes near the
surface and also at middle latitudes in the middle tropo-
sphere and stratosphere. The local temperature deficit at
high latitudes sometimes amounted to as much as 50C.
Because of this discrepancy, one may suspect some type
of error in the radiationd computation. The net transfers of
radiant energy at the surface and at the top of the atmos-
phere have been computed and verified against those of
London (1957) (see fig. 43 in Appendix 11). The agreement
is good. However, in our experiments we used the same
cloud coverage as was used by London. It is also noted
that the albedo of land at that latitude is irrelevant in
327-215 0 - 69 - 2
lyimin
.6
.5
.4
.3
2
1
0
-LATITUDL
-
FIGURE 9.-Latitudinal distribution of turbulent heat flux at the
lower boundary in Experiment 2, averaged for 14 days. SEN.
(SEA) and SEN. (LAND) are the sensible heat fluxes over sea
and land, respectively. LAT (SEA) and LAT (LAND) are the
latent heat fluxes over sea and land. Budykos (1963) winter
values of moisture and heat fluxes over the sea are shown by
small solid circles and triangles, respectively.
the present computation, since there is no insolation in the
polar night.
It is thought that the excessive cooling at high latitudes
may be explained] at least in part, by two effects. One is
that the difference in the thermal properties of land ice and
of sea ice has to be considered. Another point is that a
fictitious land breeze effect might be accelerating the
cooling tendency.
We shall return to the former in the next section, but
will now discuss the land-breeze effect. When the land-
sea contrast is accounted for in the model, a strong
temperature gradient develops along the coast. Under this
situation, erroneous cold spots are created if the wind
blows from land to sea. Figure 12 illustrates this, though
it is for Experiment 3. The temperature at level 9 some-
times becomes very lowl say -50C. Note that these
temperature errors are not produced if the wind direction
is from sea to land.
Our interpretation of this result is that a strong temperature
gradient will produce a land breeze, but the present grid cannot
properly resolve such small-scslc developments (about 100 km)
and a considerable truncation error is created.
In connection with the temperature discrepancy a t
middle latitudes which was mentioned above, one may
consider the possibility that an increase in the amount of
condensation may contribute toward eliminating the
temperature deficit.
As a matter of fact, the humidity computed in Experi-
ment 2 appeared too large in comparison with the ob-
8 MONTHLY WEATHER REVIEW Vol. 97, No. 1
I
-5 -h -3 -2 -1 6 T COMP - T OBS, ( "C )
-
!
i
w
e 2
3
4
5
6
7'
8
9
30
25
20
- 3 Z 15 c3
2
10
5
0
FIGURE 10.-Temperature error, i.e.,/the computed minus the ob-
served hemispherically averaged temperatures, in Experiment 2 is
shown for I, 4, 7, 10, and 13 days.
served humidity. I n figure 13 are shown the forecast
time variation of the latitudinal distribution of hu-
midity at 850 mb in Experiment 2 and the observed
variation. This may indicate that when the 100% con-
densation criterion is used, the water vapor storage is
overestimated. This tendency was also noted by Manabe
et al. (1965). In that report the humidity is found to be
even higher than in the present study (see also figs. 72-88
in Appendix 111).
5. EXPERIMENT 3
I n Experiment 3, the condensation criterion was set
to 80% instead of 100%. The argument for a reduced
criterion was made by Smagorinsky (1960). The hu-
midity that we are concerned with is, so to speak, the
gross humidity, which is a space-averaged quantity.
Namely, with a finite grid size the upper limit of the
relative humidity-need not be 100~o. If the grid size were
reduced to zero, the criterion should converge to LOO%.
Presumably, the limit should also depend upon the height
and the latitude of the place a t which the condensation
occurs. Since little was known about the spatial distribu-
tion of the limit, 80% was employed at all latitudes and
at all heights in the present study.
C- LATITUDE
FIGURE 11.-Meridional section of the zonally averaged tempera-
ture error in Experiment 2 for the 11th day in units of "C. The
areas where the difference is more negative than -2C are stip-
pled, and those where the difference is larger than 2C are shaded.
The ordinate is the vertical level.
This criterion was already tested in the previous experi-
ment (Smagorinsky, Strickler, et al., 1965). It was then
concluded that only a slight increase in precipitation was
obtained in the area north of 45"N, but the precipitation
over the area south of 45"N was nearly doubled compared
to that for the 100% criterion. But the forecast period in
that experiment was only 12 hr.
This time we extended the period to 2 weeks. This
would, we hoped, provide us with a greater insight on
this problem. One could expect that the allowed water
vapor storage would be reduced by the lowered condensa-
tion criterion. Simultaneously, the rate of evaporation
would be increased, the condensation would be increased,
and accordingly more heat should be released.
Another degree of freedom added in Experiment 3 is the
distinction in the thermal properties of surface land ice
and sea ice. Recognition must be given the fact that there
is a great deal of heat conduction through solid ice over-
lying a sea surface, as well as through breaks in the ice.
According to Sverdrup et al. (1942), quoting the result of
the ['Maud" expedition 1918-25, the temperature at the
surface of the ice (covered by snow) for the Northern
Hemisphere varies as shown in table 2.
I n the present experiment, therefore, we assumed that
the surface temperature of the sea ice is -28.OOC. The
availability of moisture over sea ice was arbitrarily as-
sumed to be 0.5 (the same as over land).
January 1969 K. Miyakoda, J . Srnagorinsky, R.
A and V,, 3 days 531 T9,*g.w
l3 He [%I 531 3 Days
FIGURE 12.-An example of the fictitious land breeze effect along
the coast of the North American Continent at thc 3d day in
Experiment 3. (A) temperature at d e v e l 9 is shown by contours
in K at an interval of 5K. The wind velocity at level 9 is also
illustrated by arrows. The cold spots in question are seen on
both the East and the West Coast. It is noted that the extremely
cold area over the sea ice in Experiment 2 is not found in this
result of Experiment 3. (B) relative humidity in percent at level 9
is shown by contours. The moisture saturation area, where the
relative humidity is SOY0, is shaded. The coastlines are indicated
by small segments of slanting lines. The erroneous cold spots in
the upper figure correspond to the area where the humidity is
extremely low in this figure.
Let us first look at the time variation of humidity a t the
850-mb level in Experiment 3 (fig. 14). This figure can be
compared with the observed humidity in figure 13. It is
evident that the humidity in Experiment 3 is much
F. Strickler, and G. D. Hembree 9
-/A m
-
FIGURE la.-Latitude-time diagram of the zonally averaged
relative humidity in percent a t t h e 850-mb level. (A) the observed,
and (B) the computed humidity in Experiment 2. The area where
humidity is higher than 70% is shaded, and that where it is less
than 55% is stippled.
closer to the observed than it was in Experiment 2, as far
as the 850-mb level is concerned.
Next we turn to the temperature prediction. The
vertical profile of the hemispherically averaged tempera-
ture error in Experiment 3 is shown in figure 15. I n com-
paring it with the result of Experiment 2 (fig. lo), we see
that the temperatures at levels 1, 2, and 3 are not very
different, but those a t levels 4 through 9 have been clearly
improved, especially after the first 4 days. It is noted that
the temperature deficit is already large in the first 4 days.
This is probably due to the deficiency in the amount of
condensation at the beginning of the forecast. However,
the final temperature deficit, after a s d c i e n t period of
time, may not be influenced by this initial handicap.
Figure 16 is the height-latitude diagram of the tem-
perature error at the 11th day in Experiment 3, which
corresponds to figure 11 for Experiment 2. First of all, the
temperature at the lowest level a t high latitude is closer
to the observed temperature than that of Experiment 2,
but still deficient. The middle troposphere in the sub-
tropics and in the middle latitudes is slightly warmer than
in Experiment 2. This is due to the increased release of
heat by condensation.
Yet the computed temperature is still lower than the
observed. The largest underestimation occurs at level 3
near the Tropics (not shown here). Factors which might
contribute to this deficiency are the lack of a seasonal
march of temperature due to the fixed zenith angle of the
10 MONTHLY WEATHER REVIEW Vol. 97, No. 1
TABLE 2.-Annual variation of the surface temperature of sea ice,
after Suerdrup et al. (1942) in O C
Jan. June May Apr. Mar. Feb .
-28.0
July
-1.5 -7.4 -21.6 -29.1 -30.9
Dee.
-29.9 -23.0 -12.3 -4.7 -0.0 -0.0
Nov. Oct. Sept. Aug.
I I I I 1 I I 1 I I I I I 1 0 1 2 3 d 5 6 7 8 P m l I
DAY-*
FIGURE 14.-Latitude-time diagram of the computed relative
humidity in percent in Experiment 3 at the 850-mb level. This is
compared with figure 13.
sun, and also the assumption that the heat capacity of the
land is zero. The cold stratospheric temperature might be
due to an abrupt drop in the vertical gradient in the
mixing ratio of water vapor that is used for the radiation
computations in the stratosphere (see Appendix 1). This
discrepancy in stratospheric temperatures will be dis-
cussed again later.
Next let us look back at the latitudhal distribution of
precipitation in figure 5. I t may be seen that at the
Equator the precipitation in Experiment 3 is almost the
same in amount as in Experiment 2, and in the middle
latitude it is greater than in Experiment 2 . The sub-
tropical minimum is shifted northward, i.e., 21N in
Experiment 3 from 15N in Experiment 2. Furthermore,
the amount of precipitation at the minimum point is
appreciably higher. In other words, the heat released by
condensation in Experiment 3 is more evenly distributed
with latitude than in Experiment 2 . This is an important
characteristic of Experiment 3. As will be mentioned later,
this feature is relevant t o the atmospheric circulation,
especially in the Tropics and also to some extent in the
middle latitudes.
Figure 17 distinguishes between the precipitation over
the land and sea in Experiment 3; it should be compared
with figure 8 for Experiment 2 . One can see that the
increase of precipitation in Experiment 3 over that in
Experiment 2 is conspicuous over the sea. Comparing the
-5 -4 -3 -2 -1 0 1
T COMP - 1 OBS. ( T I -
FIGURE 15.-Hemispherically averaged temperature error for
Experiment 3 a t 1, 4, 7, 10, and 13 days. The ordinate is the
vertical level.
computed precipitation with Mollers data (1951) , the
precipitation over the sea in Experiment 3 is much higher.
But this may not necessarily imply that the precipitation
in Experiment 3 is overestimated.
The turbulent flux of heat and moisture at the surface
is displayed in figure 18, which can be compared with
figure 9 for Experiment 2. It is noticed that the evapora-
tion over the ocean is increased greatly in Experiment 3
and that the sensible heat flux over the sea is decreased
significantly in Experiment 3 (see the hemispheric evapora-
tion in figure 67 of Appendix 11).
The elimination in Experiment 3 of the large precipita-
tion and the large sensible and latent heat fluxes at high
latitudes over the sea is partly due to the increased tem-
peratures of the sea ice effect. However, the areas con-
sidered are not identical in that the area covered by sea
ice was included with the land points in Experiment 2
but counted as sea in Experiment 3.
6. SYNOPTIC PATTERNS
THEOBSERVED 1000-MB GEQPQTENTlAL FIELD
In short-range forecasts, i.e., 1 or 2 days, the movement
of cyclones and the tendency for deepening or filling are
the major problems. On the other hand, in a %meek
forecast, the life histories of cyclones are also important
features of the prediction. The model should be capable
of simulating all of these variations.
Before going into a discussion of the prediction results,
it is perhaps useful to describe the actual evolution of the
individual cyclone and anticyclone patterns of the 1964
case.
January 1969 K. Miyakoda, J. Srnagorinsky, R. F. Strickler, and G. D. Hernbree 11
9 CM
FIGURE 16.Meridional section of zonally averaged temperature
error for Experiment 3 at the 11th day in units of C. See figure 11
for the details.
811
926 LATITUDE ( DEG. ) 991
FIGURE 17.-Latitudinal distribution of the 24-hr rates of precipi-
tation over land and sea in Experiment 3. See figure 8 for further
explanation.
Figure 79 in Appendix I1 is the daily series of 1000-mb
patterns of geopotential height for 15 days from the 9th
through the 23d of January 1964. Incidentally this example
was described by Sawyer (1965) in detail. As he mentioned,
the most characteristic feature of this case is the blocking
anticyclone whichmas located over the British Isles and
persisted virtually intact from December 1963 through
Fehruary 1964.
There were three major cyclones over the entire
Korthern Hemisphere. For the sake of convenience, we
shall name these cyclones A , B, and C. A was located over
the Pacific Ocean, and it moved gradually for 10 days
from near Japan to the Rocky Mountains in North
America. B stayed at almost t,he same place over the
Atlantic Ocean off the west coast of Europe; it was
blocked by the anticyclone. C was persistently located
over northwestern Siberia.
It is interesting and important that near Formosa in
Asia and over the Gulf of Mexico or sometimes near the
northern Rocky Mountains, new cyclones were formed
every few days. They developed rapidly within a couple
of days, moved northeastward, and then merged into the
preexisting major cyclones. It is likely that these cyclones
are generated only when upper level vortices pass over the
points in question. (Namias (1954) mentioned cases in
which the genesis is related to the basic long-period mid-
tropospheric wave patterns.) The areas of cyclone de-
velopment correspond roughly to the so-called west Paci$c,
the Atlantic, and the middle Pacijic polar frontal zones.
Let us call the newly formed cyclones A  , A , B, B, etc. for
the two regions, Le., east of the Asian continent and over the
United States, respectively. For example, A is the second genera-
tion cyclone formed over Formosa. The following is the record of
new cyclones for the 2 weeks. The number in parentheses indicates
the day of cyclogenesis or merging. For example, the fact that
A is merged into A is expressed by A+A.
Genesis: A (3 ), A (S), B (0), B (3), B (S), BV (lo),
BV (13). BIV and BV were formed near the northern Rockies.
Merging: A+A (6), A became major cyclone (l l ), B+B (31,
B+B (B), B became major cyclone (11), BIV+B (14).
THE PREDICTED 1000-MB GEOPOTENTIAL FIELD
The series of the daily predicted patterns of 1000-mb
geopotential height in Experiment 3 are shown in figure
49.
As seen, the blocking anticyclone continued to stay
over or near Europe during the entire 2 weeks. This agrees
well with the observed. Concerning the forecast of the
formation and merging of cyclones, it can be safely said
that the formation of the third generation cyclone B on
the 3d day was successfully computed, and also that the
merging of B into the major cyclone B on the 6th day
was well predicted. In detail the results are as follows:
Genesis: A (3), A (8), B (3) are successful, and BIV (10) is
also good. But B (8) and BV (13) are unsuccessful. Note that
B appeared in the prediction on the 10th day, so there was a
2-day discrepancy.
Merging: A became major cyclone (11) and B became the
major cyclone (11). B+B (3) and B+B (6) are successful, but
A+A (6) is not good.
42 MONTHLY Vol. 97, No. 1
I 1 .3 t J
.2
I
c LATITUDE
-. 1 5%
FIGURE 18.-Latitudinal distribution of turbulent heat flux a t t h e
lower boundary in Experiment 3, averaged for 10 days. See
figure 9 for further explanation.
It is quite significant that even after 14 days it is possi-
ble to find a one-to-one correspondence between the cy-
clones of the observed and the computed patterns.
Perhaps the largest defect in the present forecasts is
that the amplitude between the cyclones and anticyclones
diminishes progressively and considerably with time.
Another shortcoming in the present forecast is the wiggling
(roughness) in the pattern of geopotential height which becomes
more pronounced as the computation continues. The general circu-
lation experiments show greater wiggling with "moist" models than
with "dry" models, and it also increases when the horizontal grid
resolution is increased from N=20 to N = 40. It is probable that
the scheme for small-scale convection is partly responsible f o r i t
(Sy6no and Yamasaki, 1966).
As seen in figure 49, the first great error in the present forecast.
occurred with the lack of development of cyclone A on the 2d and
3d days along the middle PacSc polar frontal zone. Associated
with this, the merging of A' into A on the 6th day was not well
computed. The reason for the failure is not clear. One may suspect
that an error in the sea surface temperature pattern was responsible,
but we have recently made a recomputation of the same case in
which a more realistic sea surface temperature was used, and the
development of A was not appreciably different. It is our present
opinion that this error may be due to inadequacies in the init,ial
data, though tangible evidence is lacklng.
It is worthy of note that cyclone A, which had almost faded out,
redeveloped on the 7th day when it came close to the west coast of
the United States. This is a good example of how continentality
might act to enhance the determinism of the atmosphere. This will
be shown and discussed further in connection with the trough ridge
diagram.
THE500-MBGEOPOTENTIALFIELD
The 500-mb geopotential forecast isin general better
than the lower level forecast in any verification measure.
Figure 19 shows, as an example, the 500-mb forecast for
the 11th day. The rest of the results for 500 mb are given
in figure 50 of Appendix 11.
We see that identification of the individual troughs and
ridges can easily be made between the preclicted and the
observed patterns. One difference between the forecast
and observed patterns is that the predicted pattern is
smoother in the middle scale. For instance, on some days
there was an observed cutoff cyclone which did not appear
in the forecast.
THE50-MBGEOPOTENTIALFIELD
The details of the forecast of the lower stratospheric
geopotential height will be discussed in a separate paper.
One important feature is the progressive decrease in tem-
perature of the middle latitudes at about the 50-mb level.
It causes the region of polar-night westerlies to be ex-
tended southward and to be connected with the tropo-
spheric westerlies (see Appendix 11).
COMPARISON OF THEGEOPOTENTIALHEIGHTPATTERNS
OF EXPERIMENTS 1, 9, AND 3
Next, let us compare the geopotential fields of the three
experiments. There are important differences between
Experiments 1 and 2, which can be attributed to the
inclusion of land-sea contrast in Experiment 2. It is now
well known that, due to the supply of the heat from the
ocean, cyclone development (fig. 20) is intensified off the
east coast of continents especially in winter. There has
been a great deal of study of the effects of heat from the
ocean. It is not appropriate to enumerate these papers
here, but from the standpoint of numerical prediction
models, some of the papers that discuss this point are:
Bushby and Hinds (1955), Reed (1958), Spar (1960),
Petterssen, Bradbury, and Pedersen (1962), and Japan
Meteorological Agency (1965).
In our case also, the 1000-mb height patterns of Experi-
ments 1 and 2 reveal a sizable difference at the 4th day.
A cyclone over the Atlantic Ocean is predicted more
accurately in Experiment 2 than in Experiment 1.
The difference between Experiment 2 and Experiment
3 can be illustrated by comparing figure 21 which gives
the 1000-mb geopotential height for the 11th day. As was
demonstrated earlier, the difference between the two
experiments in the supply of heat from condensation is
quite large, and, as a consequence, the amplitude of
cyclones and anticyclones is larger in Experiment 3 than
in Experiment 2, and the amplitude in Experiment 3 is
slightly closer to that of the observed.
It is very interesting that the birth of cyclone B"' on
the 8th day, which was not computed at all in Experiment
2, was successfully simulated in Experiment 3, but this
cyclone was not very deep and the date of genesis was 2
days late, compared with reality.
I t should be mentioned that these differences are not
as large as one might suppose. One of the lessons we
learned is that the midtroposphere does not seem to be
particularly sensitive over periods of the order of a week
to the usual external effects, such as the sea-ice effect,
a 20% reduction in condensation criterion, or the sea-
surface temperature anomaly, at least as far 85 this
model is concerned.
January 1969 K. Miyakoda, J. Srnagorinsky, R. F. Strickler, and G. D. Hernbree 13
This is a very important point in estimating the pre-
dictability of the atmosphere. Probably, a substantial
difference between Experiment 2 and Experiment 3 will
appear after the 2-week period.
THE TROUGH AND RIDGE DIAGRAM
To get a comprehensive view of the movement and the
variation of intensity of the atmospheric waves, it is
useful to look at a trough and ridge diagram (Hovmoller,
1949), which is a longitude-time chart of geopotential
height taken along a certain latitude circle.
Figures 22 and 23 are the diagrams for the 500-mb and
1000-mb geopotential heights, respectively, for the zone
between 35" and 45"N at intervals of 24 hr for the observed
and the prediction in Experiment 3 over the 2-week
period. Each value is obtained by averaging over 5" of
long. and 10" of lat.
It has been noted by Hovmoller (1949) and Graham
(1955) that the patterns in this type of diagram consist
generally of two modes. One is the basic flow,which is
characterized by the longitudinally quasi-stationary waves
and is represented by the first three harmonics of a
Fourier expansion series. The other is the superposed
perturbation, which is characterized by the eastward-
moving waves that progress at a speed of about 9" long,
per day or less. Notice that the moving waves penetrate
into the stationary ridges, and always redevelop on the
other side.
The wave motion in the smaller scale is complex.
Almost two decades ago Charney and Eliassen (1949)
made the first attempt at dynamical treatment of dis-
persive waves and demonstrated the prediction of 500-mb
geopotential values 24 hr ahead. The behavior of these
complex waves was computed with.remarkable success.
Now let us turn to the results in the present study,
i.e., see figures 22 and 23 (also figs. 87 and 88 in Appendix
I11 for the 1966 case).
In the following, we discuss the results for 500 mb:
1) The agreement between the prediction and the
observed is very good. The behavior of the longwaves
(for instance, the ridge over the middle Pacific Ocean a t
153"W on the initial day which moved slightly toward the
west after the 7th day) was accurately predicted. The
wave trains of medium scale (for instance, the waves over
the Atlantic Oc.ean between 0" and 60"W around the 11th
day) were also well simulated.
2) The "excessive westward propagation of the long-
waves" discussed by Wolff (1958) and Cressrnan (1958)
is not found in this prediction.
3) The speed of the moving troughs (for instance, 147'E
on the initial day) in the computation is rather good. Even
after 14 days, the error in location of the predicted trough
was 10" to 15" long. Why is the wave speed predicted well
FIGURE 19.-The 500-mb geopotential height patterns for the 11th day. (A) the observed, and (B) the forecast in Experiment 3. The
contour interval is 60 m. The belts of the geopotential height between 5220 and 5280 m and between 5460 and 5520 m are stippled
to bring-out the patterns. The trough lines are shown by dashed lines.
14 MONTHLYWEATHERREVIEW
1000 MB
Vol. 97, No. 1
~~ ~~
~~ ~
January 1969 K. Miyakoda, J . Smagorinsky, R. F. Strickler, and G. D. Hembree 1 5
FIGURE 21,"The predicted 1000-mb geopotential height pattern for the 11th day for Experiment 2 (A) and Experiment 3 (B).
despite the fact that the zonal wind of the computation
was appreciably stronger than it should be? One possibility
is that, since the space truncation error causes a reduction
in phase speed, its effect in this casewasoffset by the
excessive advection. Anot,her possibility is tha.t t'he zonal
wind a t the steering level, probably level 5, did not deviate
very much from the observed wind after all (see fig. 21).
However, the 10"difference may cause the phase of
synoptic-scale disturbances to be completely opposite,
whic.h is serious from a practical viewpoint.
4) I t is interesting to note that, even if some trough
(for instance, 63"E on the 4th day) or ridge (for instance,
128"lV7 on the 6th day) in the c,omputation did not agree
with the observation a t a n early stage of t,he prediction,
sometimes agreement is improved a t a later time. This
may be partly because we are looking a t only the geo-
potential height at a certain latitude on a certain level.
The disturbance might have just deviated from this
latitude or level temporarily and returned later. However,
we tend toward the notion that the geographically fixed
heat sources and continentality are instrumental in the
subsequent improvement in the computed state.
5 ) However, there is an obvious defect in the predicted
pattern that is common to both the 1964 and 1966 cases.
The quasi-stationary modes, or longwaves, are more
dominant, while the eastward-moving components, the
relatively shorter waves, are t'oo small in amplitude.
7. VERIFICATION
To evaluate the prediction skill, we have c,omputed
standard deviations of error in geopotential heights and
correlation coefficients with respect to the time changes in
height. These measures are the same 8s those defined in
the report of WMO's working group on numerical weather
prediction (1965).
The standard deviation of error is the root-mean-square
error of the forecast height with mean error removed.
This quantity is usually compared with persistence; which
refers to a hypothetical forecast of no change of the geo-
potential height from the initial time. The correlation
c,oefficient is taken between the observed and the computed
time change of the height from the initial time.
Let us denote zoos as the observed height and zIcsl as
the forecast, height. Definitions of the various quantities
are as follows:
Deviation of z:
X =Z f C S ,-Z O b S ,
M e a n of deviation:
X= C X J n ,
where the summation is made for gridpoints north of
20"N and n is the number of gridpoints.
327-215 0 - 69 - 3
16 MONTHLY WEATHERREVIEW Vol. 97, No. 1
FIG URE 22.-Trough-and-ridge diagrams of the 500-mb level for the 1964 case. (A) the observed, and ( 3) the prediction of Experiment 3.
The contours are for the 500-mb geopotential height in a zonal belt between 35" and 45"N. The units are decameters. The interval is
50 m. The ordinate is time in days, and the abscissa is longitude. The ridge areas with geopotential greater than 5600 m are hatched,
and the trough areas with values lower than 5400 m are stippled.
January 1969 K. Miyakoda, J. Srnagorinsky, R. F. Strickler, and G. D. Hembree 17
FIG
EUROPE HIMALAYAS PACIFIC ATLANTIC
3 13 22 32 42 5 2 63 12 82 92 102 113 122 133 142 152 162 112 112 162 112 142 133 122 113 102 92 82 7 2 6 3 52 42 32 2 2 13 3
E W W
URE 23.-Trough-and-ridge diagrams of the 1000-mb level for the 1964 case. (A) the observed, and (B) the prediction of Experiment 3.
The contours are for the 1000-mb gcopotential height in a zonal belt between 35" and 45"N. The units are meters. The contour interval
is 50 m. The ordinate is time in days, and the abscissa is longitude. The anticyclone areas with geopotential values higher than 200 m
are hatched, and the cyclone areas with values loyer than 100 m are stippled.
18 MONTHLY WEATHER REVIEW Vol. 97, No. 1
Standard dewiution:
Denoting z (t ) the geopotential height for the day t and
z (0 ) that for the initial day, we have
Time change of the observed height:
y ,(t )=z ,b s (t )-Z o b s (O ),
Time change of the forecast height:
Persistence: yz(t)=z,cst(t)-zo~s(O),
Correlation coescient:
If the entire Northern Hemisphere is taken instead of
an area north of 20"N as the verification domain, the
standard deviation will be decreased because of the small
variability of the geopotential in the Tropics, and the
correlation coe$cient will be lower compared with that
for the domain north of 20"N because of the inclusion
of the uncorrelated region.
Figure 24 shows how the standard deviations for 1000-,
500-, and 50-mb geopotential heights vary with time. In
the same figure, the values for persistence are also plotted,
which is a measure of the natural variability of the geo-
potential height. The standard deviation between Experi-
ments 2 and 3 is shown for comparison.
Now, looking at these figures together with those for
the 1966 case in Appendix 111, we note that the standard
deviation at 500 and 50 mb for Experiments 2 and 3 are
smaller than the persistence until about 7 days, while the
standard deviation at 1000 mb is as large as that of the
persistence even at the 4th day. Literally interpreted, this
could mean that the forecast of 1000-mb geopotential
height is completely unacceptable at the 4th day.
But it is readily seen by visual inspection of the synoptic
maps that the 1000-mb forecast at the 4th day is still
similar to the observed. Presumably the standard devia-
tion of error is a very severe measure. A judgment of
prediction skill based on this quantity requires some cau-
tion. As a matter of fact, even the induced inertia-gravita-
tional component, which appears sometimes as wiggling
superposed on the basic geopotential field, increases the
value of the standard deviation.
I n this respect, the correlation coefficient seems to be
less sensitive. Figure 25 gives the correlation coefficients
for Experiments 1, 2 , and 3.
We note that the values of correlation coefficient grad-
ually decrease with time (except for the 1000-mb level
in the 1966 case, which was lower at 8 days, see fig. 90).
At the 14th day, the values are 0.4, 0.5, and 0.8 at the
1000-, 500-, and 50-mb levels. In both cases, the 10OO-mb
correlation coefficient is lowest. It is generally high for the
500-mb level. The coefficient for the 50-mb level in the
1964 case is perisistently high, but it is lower in the 1966
case. In the latter case, a breakdown of the polar night
vortex occurred during the forecast period, making the
prediction more difficult. From the standpoint of the corre-
lation coefficient, the results of Experiments 2 and 3 are
quite similar even at the 11th day.
I t is remarked, however, that the forecast changes
corresponding to a return to normal may yield values
significantly greater than zero for this type of correlation
coefficient. Other kinds of verification scores are suggested
and will be computed in the near future. It seems that no
single verification score is universally accepted.
8. PWECIPITATBQN FORECAST FOR THE UNUTED STATES
We now turn to the results of the precipitation forecast
for middle latitudes. For a detailed verification we took
the United States and the southern part of Canada, where
high density data were easily accessible. Data of approxi-
mately 3,000 rain-gage stations were used.
The observed amounts of precipitation at these stations
were averaged over the unit domain surrounding each
gridpoint. ,411 the results of the time evolution of forecast
c.ondensation for Experiment 3 of the 1964 case and the
observed rainfall are contained in figure 53 of Appendix 11.
Figure 26 shows an example of the condensation pat-
terns. It is the %day accumulation of the observed rainfall
and the predicted condensation for Experiments 1, 2, and
3 for the 3d and 4th days.
In this figure, we note the following points:
1) The computed condensation in each experiment is
diffused over a wider area than in the observed pattern.
This tendency is more conspicuous for Experiment) 3 than
for the other experiments. The computed quantity is
condensation, and it does not really correspond to pre-
cipitation. For instance, ev~poration from falling droplets
mas ignored.
2 ) Earlier dynamical prediction studies of precipitation
have usually concluded that the computed amounts were
appreciably less than the observed amounts. This is not
true of the present experiments, especially those in
Experiments 2 and 3 for the middle latitudes. The reasons
are that the primitive equations are used with a high
resolution grid, the moist convection is accounted for,
the feedback of heat released by condensation into tche
atmosphere is allowed, the effects of evaporation from the
surface and radiation are included, and in Experiment 3,
the condensation criterion is reduced t o 80%.
3) I n t h e observed rainfall patterns the area in the
Northwest is limited to a small area near the coast. The
computed area, however, spreads farther inland. It was
concluded by Smagorinsky, Strickler, et al. (1965) that
the mountain effect in the model is distorted by smoothing.
Another factor may be that the surface drag coefficient
~~
January 1969 K. Miyakoda, J. Srnagorinsky, R. F. Strickler, and G. D. Hernbree 19
-DAYS
220
1
PERSISTENCE 7
tF
EXP.3
-
DAYS
m
2w-
I80 -
1M -
140 -
120 -
IW -
-
DAYS
FIGURE 24.-Standard deviation of error in geopotential height
between the observed and the predicted for the domain north of
20"N in units of meters. (A) the 1000-mb level, (B) 500-mb, and
(C) 50-mb. The errors for Experiment 1, Experiment 2, Experi-
ment 3, and a persistence forecast are shown as marked. The
difference between Experiments 2 and 3 is also shown. The abscissa
is time in days.
over land is too small and accordingly the air in the lower
atmosphere tends to move inland too easily compared
with reality (see the wind intensity at level 9 in fig. 12).
4) The patterns of the computed condensation in the
middle latitudes do not differ much from one experiment
t o another during the 2-week forecast. Therefore, it is
difficult to choose one experiment as superior in terms of
the precipitation prediction.
Verification scores for the occurrence of precipitation
greater than 0.10 in. were computed for both cases by
D. L. Gilman, Extended Forecast Division, NMC, and
were reported by Namias (1968) in his Harry Wexler
Memorial Lecture. The scores were computed for 100
stations in the United States.
Figure 27 shows the average for the two cases. It
appears that the skill was positive until about the 9th day.
A random forecast should give an expected skill score of
zero. Refer to Namias (1968) for further details and for
the individual scores.
The scores were obtained by the usual skill score form-
ula,
c-x s=- T-X
where S= skill score; C= number of stations with correct
forecast, occurrence, or nonoccurrence; where 0.10 in. is
the criterion for the forecast of occurrence (the 0.10-in.
criterion was adopted arbitrarily and tentatively for the
study); X=number of stations at which correct forecast
is expected by chance; T=total number of stations.
In computing X, a special weighting was used to allow
for the variable likelihood of precipitation at the stations
considered. Derivation of this formula will be given in a
forthcoming paper by Gilman (1968).
9. HEMISPHERICANDZONALMEANS
Figures 28 and 29 show the kinetic energy integrated
over the whole hemisphere, i.e.,
~m ~~p ~(r z +2 ' P )d z dy dz,
and the internal plus potential energy, Le.,
~mJJ(Pc"T+PL7z)dx (iY dz,
where the r~otation is conventional. As is seen, the kinetic
energy level is highest in Experiment 3, and that in
Experiment 2 is second highest. This is because the heat
released by c,ondensation is largest in Experiment 3 , and
it contributed t o the increase of kinetic energy. The
kinetic energy in Experiment 1 decreases very rapidly
with time due t o the lack of condensation in the Tropics,
which, in turn, comes from the omission of radiation.
The computed kinetic energies do not coincideclosely
20 MONTHLY WEATHER REVIEW Vol. 97, No. 1
0 a ,,,,l ,,,,,,, I
0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4
with the observed. Inertia-gravitational oscillations are
observed in all three cases, and their variations with time
are very similar in each case. The amplitude is large at
the beginning of the forecast, probably due to imperfec-
tion in the initialization. They gradually fade with time,
though the wiggling increases.
A comparison of the potential plus internal energy
curves (fig.29) reflects the temperature forecast. In
Experiments 2 and 3, the potential plus internal energies
are lower than the actual, since the computed atmosphere
was too cold.
One important statistic in the atmospheric circulation
is the eddy kinetic energy. In the general circulation study
(Manabe et al., 1965), it was concluded that the eddy
kinetic energy is appreciably smaller than the observed
mean values. At that t'ime, however, the generd circulation
model excluded orography and continentality. It was
3QlUEz
DAY
- t h o u g h t t h a t b y accounting for these effects one might
correct the deficiency. In the present study, both effects
EN! 2 \IS. 3 have been included. Furthermore, the effective viscosity
is smaller because of the smaller grid size.
first to the zonal kinetic energy. Figure 30 is the time
variation of the vertical distribution of the hemispherically
1.0- = - - = - - /
- Y:.. Before looking a t t h e e d d y k i n e t i c energy, let us turn y.
.8 - 'tt:. Q:.. EXP 3 -
EXE' FTk<G9.$h?,q. ...*e x ....... - A- x ...... -/ averaged zonal kinetic energy in Experiment 2, i.e.,
.6 - ..#....."' +.:.q;,
... w EXP, 2
\..x b
- ".".:.:.%, :, K - (G+i2) 1
L- 2
.4 -
-
kinetic energy appears to grow gradually in the tropo-
where the bar is the zonal average. The computed zonal
.2 - sphere, and it exceeds the observed values considerably
- at levels 3 and 4. This point will be discussed later.
0 B I I 1 1 1 1 1 1 1 I 1 1 1 1 Figure 31 is the eddy kinetic energy in Experiment 2, i.e.,
0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4
50 NIB 2
1
DAY
-
EXE 2 \IS. 3
1.0 -1
i
EXE 2
EXF! 1 EXP 3
FIGURE 25.-Correlation coefficient between the observed and the
forecast pattern of the change in geopotential height from the
initial time for the domain north of 20"N. (A) the 1000-mb level,
(B) 500-mb, and (C) 50-mb. The comparisons between Experi-
ments 2 and 3 are also shown.
where u'=u"U, and v'=v--2). The computed eddy kinetic
energy decreases as the computation goes on, and it is
much smaller than the observed value in the troposphere.
So, despite the inclusion of the mountains and the land-sea
contrast, a reasonable intensity of eddy kinetic energy
has not evolved in this model. This feature may also be
easily noticed in the synoptic patterns of geopotential
height, as was shown earlier.
This characteristic may be measured in another form,
i.e., the ratio of the zonal to the eddy kinetic energies,
KJK, at' level 3 (fig. 32). The observed value of the ratio
in the 1964 case ranges between 1.0 and 1.5, whichis
probably larger than in a normal year. On the other hand,
the computed v$lue is definitely larger than the observed,
and it increases with time. In A4snabe et al. (1965), this
ratio W:LS 3.5 at level 3. 111 connection with this problem,
the following should be mentioned. The 'hloist" model
produces muchless eddy kinetic energy than the '(dry"
modeldoes in the middle latitudes. This is probably be-
cause the role of water vapor in general, except in the
Tropics, is to moderate the large-scale thermal contrast
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree 21
OBSERVED, DAYS. 3d and 4th
Y ."
I 3d and 4th. DAY FORECAST. EXP. 2 I
3d and 4th, DAY FORECAST. EXP. 1
Y .Y O
3d and 4th, DAY FORECAST. EXP. 3
u ."
FIGURE 26.-Comparison of the observed precipitation and the predicted precipitation for the United States and a part of Canada. The
examples are 2-day accumulations of precipitation for the 3d and 4th days in inches. The contours are at 0.1, 0.3, and 1.0 in. (A) the
observed, (B) Experiment 1, (C) Experiment 2, and (D) Experiment 3.
(as shown by computation of the latitudinal temperature
gradient in the moist model and the dry model (Manabe
et al., 1965)).
It is likely that the deficiency in eddy kinetic energy
might be due to the effective Karman constant governing
the internal viscosity that we have employed. We made
some exploratory experiments on this problem. A tentat'ive
conc,lusion is that a reduced Karman constant does im-
prove the result, though it does not completely solve the
problem.
Let us now turn to the zonal averages of the zonal wind
and the 850-mb and 50-mb temperatures. It is perhaps
useful to compare the three experiments. First, figure 33
shows the observed and the computed zonal wind at level
6, p/p,=O.664, and the zonal index.
In the general circulation study (Nlanabe et al., 1965),
an important defect was that the center of the computed
westerlies was located at latitudes as low as 25"N in t,he
moist model (us compared to 37"N in the dry model).
This was a point of concern in the present study. Figure 33,
however, indicat,es no such tendency for the jet axis to be
shifted to the south during this 2-week period. The 1966
case (Experiment 61J) was extended for 3 weeks and the
conclusion is the same. Conceivably, the inclusion of
mountains and land-sea contrast is mainly responsible for
t'he improvement. (Ahlabe, 1965, has mentioned that if
the horizontal resolution is below N=20 the grid size has
u large influence on the position of the jet stream.)
The agreement between the observed zonal wind and that for
Experiments 2 and 3 is not particularly good. The axis of westerlies
at 33'N a t t h e beginning moves northward to about 4joN on the
7th day, and then is displaced southward. The north branch of
westerlies at 69"N is present until the 3d day and then disappears.
The weakest westerlies a t 51N moves northward and then be-
come easterlies a t 6, 7, and 8 days. These features were correctly
22 MONTHLY WEATHER REVIEW
60
PREOlCTlOW
"'1
.l"
c;., LU r A
u ~--"\-l /-/"\
oav
FIGURE 27.-Skill score for each day for the precipitation forecast
for the United States and part of Canada. The average is shown for
the 1964 and 1966 cases. (Solid line) forecast and (dashed line) per-
sistence (after D. L. Gilman, 1968).
2.41 I , ,
computed but the splitting of the westerlies into two branches on
the 11th day was not successfully forecast. The same defect is
noticed in the 1966 case (see fig. 69 in Appendix 111).
Figure 34 is the time evolution of the zonally averaged
temperature at 850 mb. I t may be seen that the tem-
perature in Experiment 2 is lower than the observed at
high latitudes, but that the deficiencyis not as great in
Experiment 3. This improvement was achieved, as was
mentioned earlier, by including the effect of sea ice, and
possibly by the 80% condensation criterion.
Figure 35 is the zonally averaged temperature at 50
mb. It is very clear that the well-known warmer region
in the middle latitudes around 51"N gradually disappears
as the computation proceeds. Associated with it, the zonal
wind in the lower stratosphere weakened, and furthermore
the region of westerlies extended southward. Also, the
stratospheric westerlies tend to connect with the tropo-
spheric westerlies. Because of these defects, the strato-
sphere in the present forecast looks different from the
actual as the integration goes on.
18. STATUSTICAB QUANT8TBES
When characterizing the atmospheric structure and
motion on a hemispheric and climatological scale, certain
I , I 1 I
I KlUFTlf! FMFPCY !
191' I I 1 1 I I I 1
I 1 I
0 3 4 5 6 7 8 9 10 11 12 13 14
DAYS -
FIGURE 28.-Time variation of kinetic energy integrated over the whole hemisphere for Experiments 1, 2, and 3 in units of loz7 ergs. The
observed values are shown by small circles.
I ! - 6.40 - tXP 1
0 - p -.V-.j-.-.-
"--"--"-------"--"-- """_______"_____"""""""~
3
L -
> ............................. """_"___________"""""""""""""" E
U P 2 2
/ E - - - 6.30- 0 OBSERVED c
n. - -
EXPl 5%
EXP.2 5362
EXP.3 531 "". - 6 25
I I I I I I I I I 1 1 I I
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
DAYS -
FIGURE 29.-Time variation of the internal plus potential energy integrated over the whole hemisphere for Experiments 1, 2, and 3 in units
of 1 0 3 0 ergs. The observed values are shown by small open circles.
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree
KZON IN 107CM2/SEC2, 5362
23
0 1 2 3 4 5 6 1
8 9 10 11 12 13 14
DAYS -
FIGURE 30.-The vertical distribution of the zonal kinetic energy in Experiment 2, which is hemispherically averaged, in units of lo7 crnZ/secz.
The solid and dashed curves are the computed and observed results, respectively.
KEDD IN io7 CM~/SEC~, 5362
0 1 2 3 4 5 6 1 I
DAYS -
FIGURE 31.-The vertical distribution of the eddy kinetic energy in Experiment 2, which is hemispherically averaged, in units of lo7 crn2/sec2.
The solid and dashed curves are the computed and obesrved results, respectively.
statistical quantities are often used in general circulation
studies. These quantities are computed by taking time
averages for a certain span of time and also by taking
zonal averages around the hemisphere. They are com-
puted for the basic meteorological variables, wind, tem-
perature, a2d humidity, and also for derived quantities
such as the angular momentum and the kinetic and
potential energies.
In the work by Smagorinsky, Manabe, and Holloway
(1965) and Manabe et al. (1965), these statistical quantities
327-215 0 - 69 - 4
mere computed for each simulation and were compared
with independently computed results for the real atmos-
phere, i.e., the climatology. These comparisons were
essential in interpreting t'he results. Although the present
experiments are not general circulation studies, these
st'atistic,al quantities were computed for the prediction
results (averaged from 3 to 14 days) as well as for the
observed data (averaged from 0 to 14 days). This permits
one to detect systematic degeneracies in the long-term
behavior of the forecast.
24 MONTHLYWEATHERREVIEW Vol. 97, No. 1
3.4
! 1
o.81
0.6
0.4
I I I I I I I I I I I ~~
0 I 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4
DAY -
FIGURE 32.-Time variation of the ratio of zonal t o eddy kinetic
energy a t level 3 for Experiments 1, 2, and 3.
To make this possible each of the observed 14 days has
been subjected to initialization processing. The three-
dimensional wind velocity was obtained by solving the
so-called balance equation and the w-equation
(nonadiabatic) using the observed geopotential height
and temperature for the 2-week period. The analysis was
valid only north of 2ON.
As usual, the zonal mean quantities are expressed with
the bar, i.e.,
where X is an arbitrary quantity and X is longitude.
Eddy quantities are expressed as primes, i.e., X=x--X.
In the following meridional sections, the ordinate is the
vertical coordinate at equal geometrical heights in units
of kilometers, and the abscissa is latitude at 6 intervals.
The tropopause is shown by the dashed curve. In January
the arctic tropopause is indefinite. The tropical tropopause
in these charts is too high compared to climatological
values which are normally at about the 100-mb level.
It is because of the low resolution in the vertical in these
charts (see the temperature distribution in fig. 54). The
two columns at the right-hand side of the diagram show
m-
n-
75-
m-
Q-
- T 51 51:
i D b -
Y
2 3 31-
3-
n-
21
E-
V-
-
i
);A, I I I I I I I 1 I I 1 1 1 I
0 1 2 1 4 5 6 1 8 V 1 0 1 1 U I 3 I 4 DAY +
N I I I I I 1 1 I I I l l I
81
81 -
a-
-
m-
Q-
! 1:: b -
9 - 2
J I l -
-
n-
21 -
E-
P -
3t
Y
the horizontal average of the quantity for the -
FIGURE 33.-The zonal average of zonal wind at level 6 in units of meters per second. The ordinate is latitude, and the abscissa is time.
(A) the observed, (B) Experiment 1, (C) Experiment 2, and (D) Experiment 3. The westerlies are indicated by plus, and the easterlies
by minus. The maxima of the westerlies are connected by the thick dashed lines.
January 1969 K. Miyakoda, J . Smagorinsky, R. F. Strickler, and G. D. Hembree
NI I I l l I
25
280 280- I
' I C , 1 1 1 1 1 1 I I 1 1 1 1 1 I l l I I 1 I 1
0 I 2 J 4 5 6 7 B 9 1 0 1 1 1 2 1 1 1 4
DAY -
0 1 2 1 0 5 6 7 8 1 1 0 1 1
DAY-
FIGURE 34.-The zonal average of temperature st the 850-mb level in units of "K. The ordinate is latitude, and the abscissa is time.
(A) the observed, (B) Experiment 1, (C) Experiment 2, and (D) Experiment 3. The area where temperature is higher than 285'K is
hatched, and that where it is lower than 250'K is stippled.
whole Northern Hemisphere and (right) the horizontal
average for the area north of 20'N. For observed charts
only the second column is included.
THE ZONAL WIND
In the observed data there are two marked centers of
westerlies, i.e., the tropopause jet and the polar-night jet
in midstratosphere. (See fig. 36.) In Experiments 2 and 3,
these two areas of westerlies tend to join and the latitudi-
nal splitting of the tropospheric westerlies disappears
(see also fig. 71 in Appendix 111). The tendency for the
westerlies to join is closely related to the erroneous cooling
of the midlatitude zone in the lower stratosphere, and it
is also related to the southward extension of the strato-
spheric westerlies. Indications from other studies (Manabe
and Hunt, 1968) suggest that it is mainly due to vertical
truncation error and that. higher vertical resolution is
needed to remedy it.
The computed tropospheric westerlies are stronger than
those for the observed data. The partitioning of kinetic
energy into zonal and eddy parts may be affected by the
internal viscosity and surface friction.
The computed lower level tropical easterlies appear
to be rather shallow (Manabe and Smagorinsky, 1967).
It is interest'ing to note that Mintz (1965) obtained a
reasonable intensity of westerlies in both winter and
summer hemispheres in his global general circulation
study, even though the calculations were at two levels
and vertical extrapolations were made for the westerlies.
He suggested that "when a smooth wall is placed at the
Equator, no mean easterly wind is generated at any level
over the Equator." Our model has a smooth wall at the
Equator, but the easterlies are present. It has been
speculated that the shallowness of the layer of easterlies
in the Tropics might be due to inadequate diffusion of
momentum in the Ekman boundary layer.
EDDYKINETICENERGY
This quantity is defined by
where p is the density. (See fig. 37.)
The computed eddy kinetic energy is much smaller
than the observed, as has been ment'ioned in section 9.
However, both the observed and the computed data have
two midlatitude maxima of eddy kinetic energy in the
vertical distribution. One is at level 4 and the other at
26 MONTHLY WEATHER REVIEW Vol. 97, No. 1
FIGURE 35.-The zonal average of temperature at the 50-mb level in units of OK. The ordinate is latitude, and the abscissa is time. (A)
the observed, (B) Experiment 1, (C) Experiment 2, and (D) Experiment 3. The area where temperature is higher than 217.FjOK is
hatched, and that where it is lower than 212.5OK is stippled.
level 8 or 9. The vertical spacing of the centers is con-
sistent with the vertical flux o f geopotential, which is
given by m, where
z being the geopotential height (fig. 57 in Appendix 11).
This quantity is known to play a role in the vertical
propagation of eddy kinetic energy. The source of eddy
kinetic energy (-cola') is located at level 6 or 7 as in
figure 40. The flux largely redistributes the eddy
kinetic energy upward above level 4.5 or 5.5, and down-
ward t o the lower levels.
In the 1964 and the 1966 cases, the observed eddy kinetic
energy has two maxima; one is a t 45"N and the other
a t 75"N. On the other hand, Experiments 2 and 3 for
the 1964 case have two maxima, but they are not widely
separated. In the experiment for the 1966 case, there is
only one maximum, which is at 39"N.
VERTICALVELOCITY
-
I t may be rather surprising that the distribution of
vertical velocity computed from the w-equation and from
the prediction computation are not very different from
each other, except in the Tropics, of course. (See fig. 38.)
However, as is to be expected, the vertical velocities
calculated by the w-equation (which excludes heating) are
weaker than those taken from the prediction computa-
tion, which is based on the time dependent primitive
equation.
Comparing the vertical velocities between Experiments
2 and 3, i t is seen that the intensity of the tropical Madley
circulation is weaker in Experiment 3 than in Experiment
2. This is consistent with the fact that condensation in the
Tropics is relatively large in Experiment 2 compared with
that in the middle latitudes. On the other hand, the
intensity of the middle latitude Perrel circulation in the
troposphere is stronger in Experiment 3 than in
Experiment 2.
MERlDlONAL CIRCULATION
The meridional circulation was constructed using
and determined by first applying the w-equation to the
observed data and then computing it by the model in
Experiment 3. (See fig. 39.) The vectors were drawn
exactly, and the streamline analyses were done subjec-
tively. These ciroulations were computed for the domain
of the Northern Hemisphere below an altitude of about
30 km. A distortion of circulation pattern may be included
due to the restriction of the domain.
I n the troposphere, me see the typical three-cell circula-
tion. The tropical cell extends into the lower stratosphere,
where it expands polewards.
~~
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree
I
2
3
4
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30-
25 -
20 -
164 2
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5 4
E
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166 4
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13.1 19.6
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18.1 22.4
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15.4 19.2
10.0 13.2 5
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UH. nom" YEA" 0, I b N
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2
3
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LI
L \ // lo=
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87 81 75 69 63 57 51 45 39 33 27 21 I5 9 3
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3.7
YL 3.6
FIGURE 36.-Meridional section of zonal wind in units of FIGURE 37.-Meridional section of the eddy kinetic energy p (3 2
meters per second. The regions of westerlies (W) where wind +7 2 )/2 in units of lo2 ergs/cm3. The regions where the intensity
intensity is larger than 30 m/sec are stippled, and the easterlies is larger than lo3 ergs/cm3 are crosshatched. The maxima are
(E) are hatched. Extreme values are plotted. (A) the observed plotted. (A) the observed (time averaged for the period 0 t o 14
(time averaged for the period 0 t o 14 days), (B) Experiment 2, days), (B) Experiment 2, and (C) Experiment 3 (the latter two
and (C) Experiment 3 (the latter two are averaged for the are averaged for 3 to 14 days).
period 3 to 14 days).
28 MONTHLY WEATHER REVIEW Vol. 97, No. 1
In the lower stratosphere in January, there is a two-cell
circulation with a strong downward current a t about
45"N to 63bN. This type of stratospheric circulation
predominated during January for the years 1957, 1958,
1963, 1964, and 1966.
CONVERSION OF EDDY POTENTIAL TO EDDY KINETIC ENERGY
The rate of conversion is defined by -p ~' d , where
a-p" is the specific volume. (See fig. 40.) If this quantity
is positive? it means that eddy available potential energy
is converted into eddy kinetic energy (see Qort, 1964, for a
general discussion).
The distribution of this quantity in the predicted result
-
corresponds fairly well with its observed distribution as
determined from the solution of the w-equation. However,
the intensity of the rate of conversion is much greater in
the prediction.
I n both the 1964 and the 1966 cases (fig. 76), there are
four large positive regions. Two are located in the middle
latitudes? i.e., about 39"N to 45"N and 57"N to 75"N a t
level 7 (prediction) or level 6 (w-equation). The third is
in the lower stratosphere at level 1 at about 63"N. The
fourth is just under the tropical tropopause at level 4.
This last one was first found by Manabe and Smagorinsky
(1967), though it is still not completely confirmed.
The region in the Tropics is of special interest, because
it may be one of the source regions of eddy kinetic energy
for the development of easterly waves. It should be said,
however, that the location and intensity of the region as
well as the shallowness of the tropical easterlies are yet to 2o
be confirmed by other models.
I1 and 111.
Other statistical quantities are also given in Appendixes
?I5
3
r
s
11. BREClPBTABlONFORECAST
FOR THE NORTHERNHEMISPHERE
=l o
It is almost impossible at present to collect worldwide
observations of precipitation, expecially over the oceans.
Televised cloud pickures of recent meteorological satellites
could provide the basis for estimating the distribution of
the global weather. However, for these present cases,
33 27 21 15 9 3
daily- satellite coverage of the whole globe was not
available.
Figure 41 is the climatological cloudiness for January.
The data were taken from TIROS satellite analysis by
Clapp (1964) and Sadler (1968). Since the satellite pictures
did not cover the polar region, Landsberg's (1945)cloud
data based on surface observations were also used. Figure
41 was constructed by using Sadler's result between 0"
and 25"N, Clapp's between 25" and 55", and Landsberg's
between 55" and 9Q"N.
The northern hemispheric precipitation predicted in
Experiment 3 of the 1964 case and averaged for the
period 3 t o 14 days (fig. 42) (the 1966 case is in fig. 91
of Appendix 111) is compared with the total cloudiness
(fig. 41).
FIGURE 38.--Meridional section of the vertical velocity W =d z /d t
in units of 10-1 cmisec. The direction of velocity is indicated by
arrows. The regions where the upward velocity is larger than
0.2 cm/sec are hatched, and the regions where the downward
velocity is larger than 0.2 cm/sec are stippled. (A) computed by
applying the w-equation t o t h e d a t a for each of the 14 days and
then averaged, (B) Experiment 2, and (C) Experiment 3 . The
latter two are averaged for 3 to 14 days.
"
It is noted by comparison that 1) in the middle and
high latitudes the agreement is fairly good, but 2) the
computed precipitation over western Russia appears too
small, and 3) the tropical precipitation in the prediction
departs very definitely from the speculated reality through
the observed cloudiness.
~~~~~ ~~
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree
I 2 m./Wc=Y
D
- UTlNOf
FIGURE 39.--Meridional circulation. The arrows plotted at the
gridpoints are drawn according to the scales shown in the lowest
right corner. The centers of the tropopause jet and polar-night
jet are indicated by shading and by (W). (A) obtained by solving
the w-equation (see fig. 38) and (B) Experiment 3 (time averaged
for 3 to 14 days).
The tropical discrepancy is especially pronounced over
equatorial Africa and the middle Pacific Ocean. In these
areas, there were few clouds in reality, whereas there was
a large amount of precipitation in the prediction. In view
of this serious error, it would be interesting to know how
much damage was done to the middle latitude flow fore-
cast.
12. CONCLUSIONS
The 2-week prediction of synoptic-scale weather sys-
tems in January by hydrodynamical methods appears
promising. Of course, we cannot make a definitive state-
M
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2.0 1.4
3.2 4.0
3.9 5.8
1:I 9:a
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YIAW 4 1O.N
-
FIGURE 40.-Meridional section of the conversion of eddy available
potential energy to eddy kinetic energy, "pw" in units of
ergs ~m -~ sec-l. The regions where the intensity of -p m is
greater than 2X10-3 ergs see-* are crosshatched. Negative
regions are .hatched. (A) obtained by solving the w-equation and
using the observed temperature, (B) Experiment 2, and (C)
Experiment 3; the latter two are averaged for 3 to 14 days.
30 MONTHLY WEATHERREVIEW Vol. 97, No. 1
FIG -URE 4L"Mean total cloudiness for January. The data are taken from Landsberg (1945), Clapp (1964), and Sadler (1968), and gi
in percent of cover. The areas where cloudiness is higher than 707' are hatched, and those where cloudiness is less than 40y0
stippled.
ven
are
ment because of the small sample size. I n the present the deterioration was not as rapid as one might have
study, the trough and ridge diagrams show a correspond- thought.
ence between forecast and observed, and the correlation The 1000-mb forecasts were inferior to the 500-mb
coefficientsof the heightchange of the 500-mb surface forecasts, but the fact that the 500-mb predictions were
from the initial time between the observed and the fore- good is encouraging. Further improvements can be ex-
cast were 0.5 in the 1964 case and 0.4 in the 1966 case pected in the foreseeable future through more adequate
a t the 14th day. The coefficients decreased with time, but observations, more effective assimilation of the data, a
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree 31
FIGURE 42.-Twenty-four hour rate of precipitation for Experiment 3 averaged for the period 3 to 14 days, units in ,cm.
more realistic and sophisticated model, and reduced 2) The forecast beyond 3 days for the lower levels was
truncation error. greatly improved by allowing heat exchange ,with the
In particular, ocean surface.
1) It was possible to account for the formation and 3) Because of the indusion of radiative effects and
evolution of second- and third-generation extratropical moisture supply, the hemispheric precipitation is increased
cyclones. by a factor of 5, the main increase occurring in the Tropics.
327-215 0 - 69 - 5
32 MONTHLY WEATHER REVIEW Vol. 97, No. 1
4) The computed amount of condensation is comparable
to the actual rainfall intensity, but the computed con-
densation covers a wider area than the real rainfall area.
It is quite often not zero in areas where there is no rain
reported.
5) The 80% condensation criterion leads to a consider-
able improvement in the forecast of water vapor especially
at the 850-mb level, and it contributes to an increase in
precipitation. With a reduction of the condensation
criterion from 100% to SO%, the condensation remains
almost the same at the Equator, whereas it increases
farther north in the Tropics and in the middle latitudes.
6 ) The tropical Hadley circulation is more intense with
a 100% criterion, while the middle latitude Ferrel circu-
lation is more intense with 80%.
7) A distinction between the thermal properties of sea-
ice and land-ice surfaces is necessary for the prediction of
reasonable temperatures in the lower levels at high
latitudes.
8) In all of the present experiments, the computed
temperature is lower than the actual temperature.
9) When oneallows for land-sea thermal contrast, a
strong land breeze is created in winter. A large truncation
error results because the horizontal resolution of the grid
is too coarse.
10) The zonal kinetic energy in the forecast is system-
atically larger than observed, especially at the tropospheric
jet level.
11) On the other hand, the eddy kinetic energy in the
forecast is smaller than the observed in the troposphere.
This is reflected in the pattern of geopotential height. The
difference in height between cyclones and anticyclones in
the forecast becomes considerably smaller than in the
observed pattern in the troposphere as the forecast
progresses. Likewise, in considering only the large-scale
flow of the stratosphere, the computed flow pattern tends
to become zonally symmetric.
12) The eddy kinetic energy in the troposphere and the
intensity of the conversion of eddy potential energy into
eddy kinetic energy is systematically larger with an 80%
condensation criterion than with a 100% criterion.
13) In the latitude-time chart of zonal wind, the
northern branch of the jet maximum disappears as the
prediction proceeds.
14) In this hemispheric model, the tropical precipitation
seems to deviate from reality especially in equatorial
Africa and in the middle Pacific Ocean.
ACKNOWLEDGMENTS
The authors are indebted t o several staff members for propram-
ming and technical assistance and wish to thank especially Mr.
Irving I. Shulman, Mr. Merlin L. Neff, Mr. Terry L. Mauk, Mr.
Lemuel W. Reed, Jr., Mr. Howard H. Englebrecht, Mr. Edward C.
Harrigan, Jr., Mrs. Ernestine J. Campbell, and Miss Vivian Camp-
bell. Gratitude is also expressed for important suggestions by
Dr. Kirk Bryan, Mr. Reginald H. Clarke, Dr. Donald L. Gilman,
Mr. Roderick D. Graham, Mr. Barrie G. Hunt, Dr. Ernest C. Kung,
Dr. Yoshio Kurihara, Dr. Syukuro Manabe, Mr. Jerome Namias,
and Dr. Eugene M. Rasmusson. For programming assistance we
wish to extend grateful acknowledgment also to Mr. J. Leith
Ilolloway, Jr., Mr. Philip L. Baker, Mrs. Catherine J. I-Iiland,
Mrs. Willette M. Carlton, and Mr. Jerry M. Kennedy. In addition
we wish to thank Mr. Philip F. Clapp, Dr. Takio Murakami, Mr. I
James Oconnor, Dr. Abraham H. Oort, Mr. Peter Rowntree, and
Dr. Gareth P. Williams for reviewing the paper, Mr. Otha Fuller, Jr.,
for supplying special analyses, and Mrs. Joyce A. Simpson for
typing assistance.
APPENDIX O.-TABLES OF QUANTITIES USED FOR THE RADIATIONCOMPUTATION
TABLE 3.-Cloud distribution in January (after Telegadas and London, 195.4)
Latitude
10
0
20
30
40
50
60
80
70
90
ITeight (km)
-___
9.4
9.9
10.2
10.0
8.9
7.6
7.0
6. 8
6.8
6.8
High
Level
4
4
3
4
4
4
4
4
5
5
Amount
"
.213
.159
.136
.157
.186
,197
,2 0 3
,157
,116
,085
leight (km)
4.2
4.2
4.2
4.0
3.8
3. 7
3.6
3.5
3.4
3.4
Middle
Level
.___-
6
6
6
6
6
6
6
6
6
6
Amount
. om
,060
,055
,069
,095
,122
,121
,099
,083
.073
Top height
3.0
2.9
2. 7
2.5
2.3
2.2
2.0
1.9
1.8
1. 7
"
Low
Top level Rase height
6
6
1. 6
1. 7
6 1. 7
1. 7
1.3
1. 5
1.2
1.1
0.9
1.0
Base level
"
7
7
7
7
7
7
8
8
8
8
.~
Amount
.-
,343
,261
.231
,291
.384
,441
,438
,375
,304
,250
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree
TABLE 4.-Mizing ratio of water uaporin January (10-3 gmlgm
I
Latitude
3
-~-
0
10
.034
.032
20 .022
30
40
.o n
50
,0070
60
.0054
70
.m4
80
.0040
90
.MI36
.0034
4 5
"
.59
.78 .19
1.30 .34
1.80 .52
2.30
,062 .011
.OM .016
.13 .024
. 19 .036 '
.31 .064
.50 .12
Level (k)
6
4.00
5.40
2.80
2.00
1.40
.85
.50
.34
.22
.14
._
-
7
-
10.00
5.60
7.60
.3. 80
2.60
1.60
.84
.48
.28
.17
8
-
14.00
12.00
8.80
6.20
3.60
2.00
1.00
.53
.30
.18
9
"
18.00
12.00
16.00
7.50
4.20
2.20
1.20
.55
.30
.18
TABLE 6.-Surface albedo for January
Latitude
-
10
0
20
30
40
50
60
80
70
90
r (k=1)=0.023X10-8 gm/gm. r (k=2) =O.O028XlO-~ gmlgm for all latitudes.
TABLE 5.-Ozone in January (1 0 -5 em STP)
Latitude
10
0
20
40
30
50
60
70
so
90
Land
,072
.lo5
.180
.167
.244
.410
.443
.662
.785
.800
Sea
,060
.060
.070
.090
.160
. 110
.200
.240
.250
.250
1 2
"
17327
17470
5158
17454
5833
16766 8829
14964
14090
11599
14378
13127
12377
15540
11860
15297
11769
14548
14436
6784
3 4
"~ "
660
413 731
347 647
347
564
922
1394
1425
1665
1800
1786
1149
3165
4859
6057
6693
6988
6934
Level
5 6
" "
203
201
120
127
252
376
151
271
495 341
486 319
463 296
388
487
265
483
287
285
7 8
" _"
94
98
46
56
125 71
207
280
111
160
248 142
216 123
196 109
207 112
206 111
9
14
21
27
39
53
60
46
40
40
39
APPENDIX11.-SUPPLEMENTINGTABLE AND FIGURES FOR EXPERIMENTS I, 2, AND 3 (1964 CASE)
TABLE 7.-Hemispheric averages. Time averages are for the 3- to 14- day period f o r Experiment 8 and the 3- to 10-
day period for Experiment 3.
I Precipitation I Convective precipitation
Mean over land Mean over sea Mean over land Mean over sea cm/cm2/day cm/cmz/day c m l c m z l d a y c m /c m 2 /d a y
Exp. 2 ____________ j 0.2032 1 0.3060 I 0.0970 I 0.1613
Exp. 3 _______.____ 0.2232 0,0982
~
0.2329 0.4416
I I
"
cm/cmZ/day over oceans.
Budyko's (1963) estimate of annual mean precipitation is 72 cm/cm~/yr=0.1972 cm/cmz/day over continents and 112 cm/cm2/yr=0.3068
34 MONTHLY WEATHERREVIEW
RADIATIONATTHETOP AND BOTTOM OF THEATMOSPHERE
lylmin -LATITUDE
.3 - -
.2 - -
\ SEA \
-
B
90 80 70 60 50 40 30 20 IO 0
-LATITUDE
FIGURE 43.-The computed radiation averaged for 14 days in Experiment 2 for the 1964 case. (SR) is the net downward solar radiation,
and (LR) the net upward longwave radiation. The quantities over land (solid lines) and over sea (dashed lines) are shown. The dotted
curves (small solid circles and triangles) are SR and LR for winter by London (1957), with no distinction between land and sea. Figure
(A) is at the top of the atmosphere, and (B) is at the earth's surface.
VERTICALTEMPERATUREPROFILE
-
1.11
FIGURE 44.-The vertical distribution of zonally averaged temperature a t 75", 39", and 3"N. The results for Experiments 2 and 3 are shown
at the three latitudes, and those for the observed are at 75" and 39". The thin lines are the moist and dry adiabatic lines.
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree
HEMISPHERICALLYORZONALLYAVERAGEDPRECIPITATIONANDEVAPORATION
CM
.? I I I I I I I I I I I I I I J
3 5
I 4
o i 1 ;1 I d 1 6 +*, 1
D A Y "-+
FIGURE 47.-The same as figure 46 but for Experiment 3 (80%
condensation criterion). -LATITUDE
FIGURE 45.-Latitudinal distribution of the 24-hr rates of precipita-
tion and evaporation for Experiment 3. These are zonally and
time averaged for the period 4 to 10 days. Triangles are estimates
of precipitation for winter by Moller (1951).
X I O ~~C M ~
I EVAP. - SEA
,"A"*--"C-+"C -&--&-+--A
I I I I I I I I 1 I I I I I I 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
"t DAY
FIGURE 46.-The time variation of the 6-hr rates of precipitation and evaporation in Experiment 2. Both quantities are the total volumes
over land and sea for the whole hemisphere. Note that the precipitation was maximum a t 2.5 days over land.
36 MONTHLY WEATHERREVIEW Vol. 97, No. 1
LATITUDE IDEG.)
FIGURE 48.-Latitudinal distribution of convective and nonconoectiue precipitation in Experiment 2 averaged for the period 3-13 days
As mentioned in section 2, the amount of condensation of water vapor was calculated in the following way. Within one time step,
and at each gridpoint, the moist adiabatic temperature adjustment is first made, and next the large-scale condensation is computed
(see detail in Manabe et al., 1965). In constructing this figure, the part of the condensation obtained in the first process is called con-
vective type precipitation, and that in the second is the nonconvective type. Although this classification is artificial, it gives an
approximate idea of the intensity of these quantities. The convective precipitation takes place mostly in the Tropics, whereas the
nonconvective precipitation dominates in middle latitudes.
FIGURE 49.-The observed (0 day and left columns) and Experiment 3 (right columns) 1000-mb geopotential height patterns for the period
0 t o 14 days commencing a t 1200 GMT, Jan. 9,.1964. The contour interval is 60 m. The anticyclone areas with the geopotential value
greater than 240 m are hatched, and the cyclone areas with the geopotential value less than 0 m are stippled. The mountains are
blank areas enclosed by small segmented lines. The number in the lower right corner is the day of the forecast. Blocking anticylcones
and newly formed cyclones are indicated by the respective letters and arrows. The letters A , B, C, etc. are used for identification.
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree 37
FIGURE 49.-Continued
38 MONTHLY WEATHERREVIEW Vol. 97, No. 1
FIGURE 49.-Continued
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree 39
FIGURE 49.-Continued
327-215 0 - 69 - 6
40
~~
MONTHLY WEATHERREVIEW
FIGURE 49.-Continued
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree 41
FIGURE 49.-Continued
42 MONTHLYWEATHERREVIEW Vol. 97, No. 1
FIGURE 49.-Continued
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree 43
FIGURE 49.-Concluded
44 MONTHLY WEATHER REVIEW Vol. 97, No. 1
FIGURE 50.-The observed (0 day and left columns) and Experiment 3 (right columns) 500-mb geopotential height for every other day
for 2 weeks commencing Jan. 9, 1964, in units of decameters. The contour interval is 60 m. The number in the lower right corner is
the day of the forecast.
January 1969
_______~ ~
K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree 45
FIGURE 50.-Continued
46 MONTHLYWEATHERREVIEW Vol. 97, No. 1
FIGURE 50.-Continued
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree 41
FIGURE 50.-Continued
48 MONTHLY WEATHER REVIEW
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree 49
FIGURE 51.-The observed (left columns) and Experiment 3 (right
columns) 50-mb geopotential height for 2 weeks commencing
Jan. 9, 1964, in units of decameters. The contour interval is 60 m.
50 Vol. 97, No. 1
FIQURE 51.-Continued
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree 51
FIQURE 51.-Continued
52 MONTHLY WEATHER REVIEW
FIGURE 51.-Concluded
January 1969 K. Miyakoda, J. Srnagorinsky, R. F. Strickler, and G. D. Hembree
TIMEVARlATlON OF THELATITUDINALDISTRIBUTION OF 1000-MB GEOPOTENTIALHEIGHT
X lo4 CM t 1000
2.0 1 0.4p,,,
O m 4 E 1 .8 1 0.0
OAY S lot1 1
0 -6 E U """
- O M .
EXP. 2
0.2 1.1......111.111"
EXP. 3
-
87 81 75 69 63 57 51 45 39 3327 21 15 9 3
-
LATITUDE
53
FIGURE 52,"Latitudinal distribution of 1000-mb geopotential height for the observed (solid lines), Experiment 2 and Experiment 3 for
the 1964 case. Zonal averages and 2-day averages were taken. The computed results deviated largely from the observation especially
at high latitudes.
MONTHLY WEATHER REVIEW Vol. 97, No. 1
PRECIPITATIONOVERTHEUNITEDSTATES
-Q
:$
1st and 2d, DAY'FORECAST.EXP. 3 n ..P-
FIGURE 53.-Two-day accumulations of precipitation over the United States and part of Canada. The units are. inches. The contours are
a t 0.1, 0.3, and 1.0 in. The dots are the gridpoints used for computation. Left columns, the observed, and right columns, Experiment
3, for the 1964.case.
January 1969 K. Miyakoda, J. Srnagorinsky, R. F. Strickler, and G. D. Hembree
I OBSERVED. DAYS. 9th and 10th I
r
1
u \ 'J 13 TH AND 14 TH DAY. OBSERVED
I 7th and 8th. DAY FORECAST. EXP. 3
I
.__
i
!
55
FIGURE 53.-Concluded
56 MONTHLYWEATHERREVIEW
[g"
vol. 97, No. 1
January 1969
f-
? m I
K. Miyakoda, J. Smcgorinsky, R. F. Strickler, and G. D. Hembree
J I
-4 \"-N
57
58
s
L
MONTHLYWEATHERREVIEW Vol. 97, No. 1
/
-"
/-
k
January 1969
m ?
K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree
l l A P 1
f
- ,+ -b +**
60 MONTHLY WEATHERREVIEW V O l . 97, No. 1
- N
r- N
0 0
01 m
6
m 10
m r.
Y L
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree
62
-.
MONTHLYWEATHERREVI W Vol. 97, No. 1
~~~
January 1969
w
2 v
K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree 63
64
c
N
MONTHLY WEATHERREVIEW V O l . 97, No. 1
5: VI N 0 LD VI 0
0
(WXI l H D l P H
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree
66
"! s
MONTHLY WEATHER REVIEW Vol. 97, No. 1
P
?
January 1969
8 0
K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree 67
N
N
9
W
9
68
8 d
tm
? - I
I I I ,
c m
* 4 4 * x"9P
V O l . 97, No. 1
0
2
.z
z r:
0 r. m
69
70 MONTHLYW,EATHERREVIEW
1
W
0 3
I
.X
I:
r.2
&
c 2 4
January 1969 K. Miyakoda, J. Smagorinsky, R. F. Strickler, and G. D. Hembree
1.5
20-
;I5- 2.5
3 : "4
"10- 3.5
4.5
5 - 5.5
6.5
7.5
0 -
-0.36
-1.M
-2.23
-2.43
-1.31
YllH d 2 b N
N.H. NORTH
FIGURE 84.-Vertical flux of water vapor by eddies
(7)'~' in
units of lo-' gm em-2 sec-I. (A) from the wequation, valid between
850 and 500 mb, and (B) the prediction. See figure 64.
30
25
20
= 10
5
0
1.5
20 -
i 15-
5
L A
2.5
3 : "i
'10- 3.5
4.5
5.5
6.5
7.5
8.5
5 -
.......,,,,,,,,
87 01 75 69 63 57 51 45 39 33 27 21 15 P 3
o.mca am-
0.007 0.m
Or06 0.04
0.35 0.25
1.19 0.79
2.58 1.57
4.90 2.96
7.76 4.90
N.8. "011" "E l " d 2 b "
87 81 75 69 63 57 51 45 39 33 27 21 15 9 :
L l l l l U D l
,...
-
71
- .17
- .60
-4Jn
-2.66
6 2
.I 6
YIll d IO." N.H. NORTH
-.31 -.4I
-.66 -8 8
-6.96 -9.66
-3.35 -3.54
-.55 1.01
-.17 -.44
-a1 -4 5
::as 2%
Y l l Y o( 10.N *.". NO","
FIGURE 86.--Conversion from zonal kinetic t o eddy kinetic energy
(k,.kB) in units of ergs ~r n -~ sec-I. (A) observed data and
from the wequation, and (B) the prediction. See figure 65.
L I I l l U D l
-
FIGURE 85.-Mixing ratio of water vapor r in units of gr/kg.
(A) the observed, and (B) the prediction.
72 MONTHLY WEATHERREVIEW
TROUGH AND RIDGE DIAGRAMS
Z 500 CASE 61 OBSERVED 35ON-45"N
VOI. 97, No. 1
-1 I
0' 20' 40' $0" 80" 160' 120' 140" 160" 180" 160" 140" 120" 100" 80" 60" 40" 20" 0"
E LONGITUDE + W
E LONGITUDE =? W
FIGURE 87.-Trough-and-ridge diagrams for 35"-45" lat. at 500 mb in the 1966 case. (A) the observed, and (B) the prediction. See figure 22.
January 1969 K. Miyakoda, J. Srnagorinsky, R. F. Strickler, and G. D. Hernbree 73
FIGURE 88.-Trough-and-ridge diagrams for 35"-45" lat. n t 1000 mb in the 1966 case. (A) the observed, and (B) the prediction. See figure 23.
74 MONTHLY WEATHERREVIEW
VERIFICATBONSTATISTICS
t
1 1 1 1 1 1 1 1 1 1 l l 1 0 I 2 I 4 5 6 7 8 9 1 0 1 1 1 2 1 3 I I
b -
1
O*YS--"..
FIGURE 89.-Stsndard deviation of the difference between the
observed and predicted geopotential heights for the 1966 case.
(A ) 1000 mb, (B) 500 mb, and (C) 50 mb. See section 7 and
figure 24 for further details.
1000 MB b
Vol. 97, No. 1
.2 -
-
0 C 1 I I I I I I 1 I 1 I I I I 0 1 2 3 4 5 6 7 8 9 10 1 1 1 2 1 3 14
DAY
- FIGURE 90.-Correlation cocfficient for the observed and predicted
patterns of time change of the geopotcntinl heights for the 1966
case. (A) 1000 mb, (B) 500 mb, and (C) 50 mb. See section 7 and
figure 25 for further details.
January 1969 K. Miyakoda, J. Smagorinsky, R.
HEMISPHERICMAPS OF PRECIPITATIONANDEVAPORATION
FIQURE 91.-Twenty-four-hour rate of precipitation averaged for
the period 3 t o 14 days. The details are the same as given for
figure 42.
FIGURE 92.-Twenty-four-hour rate of evaporation avcraged for the
period 3 to 14 days. The details are t,he same as given for figure 67.
Compare this with figure 66.
F. Strickler, and G. D. Hembree 75
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[Received May 16, 1968; revised July 22, 19681
CORRECTIONNOTICE
Vol. 96, No. 5, May 1968, pp. 271-272: equations (18), (19), and (20)
should read
Also on p. 272 add the following paragraph just above GROUND
TEMPERATURE.
The values of K,, K,, and K, obtained from the formulation of Estoque
[3] when 0 _< Ri 5 0.2 and the formulations explained above in respect of
the other ranges of Ri are assigned to the level z=h. A linear fall of this
value to Xoth at N=2050 m is assumed.