Meteorol. Atmos. Phys. 50, 21-30 (1992)
Meteorolog E
and Atmospheric
Physics
9 Springer-Verlag 1992
Printed in Austria
551.509.324
Norwegian Meteorological Institute, Oslo, Norway
Initialization of Cloud Water in a Numerical Weather
Prediction Model
J. E. Kristjfinsson 1
With 9 Figures
Received May 6, 1992
Revised June 30, 1992
Summary
1. Introduction
In recent years many studies have shown the importance of
treating condensation processes in a consistent manner in
numerical weather prediction models. Among emerging
improvements is the explicit treatment of cloud water, and
in some cases precipitating water. An unresolved problem
then is how to initialize the cloud water, especially since this
quantity is not treated in the most commonly used analysis
schemes.
In this study, a method for initializing the cloud water in
a numerical weather prediction (NWP) model will be presented
and tested. The implications for the model's spin-up are
investigated. Information from an earlier run ("first guess
fields") is used, together with satellite data. If necessary,
humidity enhancement is performed where clouds are indicated by those sources. The results indicate that initialization
of the cloud water field by itself does not have a large effect
on the spin-up of precipitation and clouds. A much larger
effect is obtained when the humidity field is enhanced. The
spin-up time for precipitation is then reduced from 12 to 6
hours, while for cloud cover it is reduced to only 1-2 hours.
The method is computationally very efficient, and is particularly useful over data-sparse areas, such as the oceans.
An investigation of the different terms in the cloud water
tendency equation is done and the results interpreted in terms
of spin-up of cloud parameters. These tests confirm that the
cloud water field only accounts for a small part of the spin-up
effect. These also show that the production of cloud water
per time step increases throughout the simulation.
Cloudiness and precipitation are important output
parameters in numerical weather prediction (NWP)
models, both for their own sake and because they
strongly affect other parameters, e.g., surface
temperature. In order to improve the treatment of
condensation and clouds in N W P models, Sundqvist (1978) introduced cloud water content as a
prognostic variable. In this way, an improved
consistency between latent heat release and sources
and sinks of humidity and cloud water is obtained.
Recently, a few model groups have introduced
related cloud treatments, e.g., Zhang et al. (1988),
Raymond and Olson (1991), Zhao et al. (1991),
Sundqvist et al. (1989).
The present study is based on the last paper. At
every point in the three-dimensional grid, a tendency
equation for cloud water is solved at each time
step, accounting for condensation, evaporation and
precipitation. Also the cloud water is advected by
the wind. The "missing link" in this treatment is
the cloud water content at the start of integration
since cloud water content is not incorporated into
the analysis/assimilation system of the applied
model. (In the case of a limited area model (LAM),
boundary values of cloud water are also missing.)
Indeed, the same applies to nearly all N W P models
that are currently being used. The simplest procedure is simply to start with zero cloud water
1 Present affiliation: Los Alamos National Laboratory,
EES-5, NM 87545, U.S.A.
22
J.E. Kristjfinsson
at all points and let the model gradually build up
cloud mass. The main disadvantage with this procedure is the occurrence of a "spin-up time" of
several hours, during which the model presumably
will have unrealistically small amounts of cloud
coverage and precipitation.
The spin-up problem is a more general problem
that arises because of deficiencies in observations,
analysis techniques and initialization procedures.
Sparse and inaccurate humidity observations cause
the humidity analyses to be inaccurate, in particular
over the sea. Analysis techniques such as optimal
interpolation (0I) tend to smooth the fields too
much. Finally, initialization techniques, such as
normal-mode initialization give initial fields with
too weak divergent circulations. All these effects
put together result in a period of a few hours, at
the start of integration, during which precipitation
will be underestimated. Through non-linear coupling with surface temperature, surface evaporation,
etc., this may also affect the results at later stages
in the prediction, i.e., beyond the spin-up time.
An attempt to reduce the spin-up time was
made by Turpeinen et al. (1990), who from satellite
data over the sea extracted temperature tendencies
corresponding to latent heating within the observed
clouds. At the same time the humidity field was
enhanced. As a result, simulations of precipitation
were improved and the spin-up time reduced. This
was based on earlier work by, e.g., Perkey (1976)
and Danard (1985) who also demonstrated the
potential improvement in cyclone simulation
resulting from humidity enhancement. In this
study, a combination of cloud water data from
"first guess" and from satellite will be combined to
yield an initial cloud water field. This field will also
be used as a basis for humidity enhancement. The
effects on spin-up of clouds and precipitation will
be investigated.
Next section describes the model features. The
proposed method is explained in section 3, while
section 4 gives the main results. In section 5, the
results are interpreted in terms of the cloud water
budget. Finally, a summary follows in section 6.
sophisticated condensation scheme explained by
Sundqvist et al. (1989). A brief outline of the
scheme is given below. The horizontal grid distance
is 50 km. In the vertical there are 18 sigma-levels
and a "lid" at 100 hPa. Analyses are used both as
initial and boundary data. For two of the cases
(AUG-case and SEP-case) analysis data have
been interpolated from 150 km analysis, while the
other (JUL-case) is based on a 50 km analysis. The
analysis scheme of the model, described by Gr0nSs
and Midtb0 (1986) is based on successive corrections, but can be shown to converge to 0I. The
model uses a dynamical initialization scheme,
which yields an efficient damping of the gravity
modes (Bratseth, 1982). Only two vertical modes
are treated by this scheme.
The basic equations of the "Sundqvist scheme"
are the following:
gt
-A,,+Q-P-Ec
~=Aq-
Q + E r + Ec
~ T = A r + --L (Q - Er -ec).
~t
Cp
(1)
(2)
(3)
Here, and in the following, T denotes temperature,
q specific humidity, m cloud water mixing ratio,
Q condensation rate, P rate of release of precipitation, Er evaporation of cloud water, Er evaporation from precipitation. L is latent heat of condensation while c, is the specific heat capacity at
constant pressure. The A-terms denote effects of
advection, diffusion and radiation. In the case of
cloud water vertical advection is omitted, since it
is assumed that the fall speed of the cloud droplets
is balanced by the updraft wind speed. Furthermore, turbulent difussion of cloud water and
droplet evaporation due to solar heating are
ignored so that:
A,, = v.Vm
(4)
where vis the horizontal wind vector. The advection
of cloud water is treated by the upstream scheme,
assuring that negative values cannot occur.
2. Model Description
The N W P model used in this study is a modified
version of the Norwegian operational model,
described by Nordeng and Rasmussen (1992). The
modification consists of the introduction of a
3. Methodology
As mentioned in the Introduction, cloud water
content is not given by the analysis schemes of
most models. A possible way of obtaining an
Initialization of Cloud Water in a Numerical Weather Prediction Model
initial field is to use the "first guess" directly as
initial field. This may, however, be inconsistent
with the humidity field. Better cloud information
is obtained if satellite data are available. Unfortunately, there are no available satellite data
that can give a vertical distribution of cloud water
content. However, there are two types of satellite
information on the vertical integral of this quantity.
They are microwave data as given by the Special
Sensor Microwave Imager (SSM/I), and a combination of information from infrared and nearinfrared channels obtained by the Advanced Very
High Resolution Radiometer (AVHRR). Both
data types were described and compared by
Raustein et al. (1991). Here it is proposed to
combine the satellite information with the model's
cloud parameterization scheme, since this would
seem to be a good way of obtaining consistent
cloud and moisture fields. F o r this purpose, the
AVHRR-data, interpolated by a navigation method
onto model gridpoints and then averaged, were
used.
The m e t h o d proposed here can be described by
the following 4 steps, assuming that a satellite
measurement of vertically integrated cloud water
content is available, otherwise steps (i)-(iii) are
dropped.
(i) F r o m the "first guess" 3-dimensional cloud
water field, m'j, k, compute the vertical integral at
all points; (mlg)i,j (Here and subsequently, indices
i, j refer to horizontal grid positions while index k
refers to vertical level):
( m f o ) i , j = ~m*~,k'(Ps - Pt) dak + e
,)
9
(5)
Here p~ and Pt are respectively, surface pressure
and pressure at the "lid", g is gravity, and e is a
small number (10- lo) included to avoid singularity
in (6).
(ii) Defining the satellite estimate as (m~)i,j,
obtain a "corrected" cloud water field as:
m** = m* . (ms)id .
i,j,k
i,j,k ( m f g ) i , j
(6)
(iii) The result is limited such that:
mij,k = m i n ( 2 . 1 0 - 3, mij,k)"
(7)
(iv) Perform humidity enhancement in the following manner: The specific humidity in those
points that contain cloud water is raised, so that
23
the conditions for cloud formation in the condensation scheme of the model are satisfied. At
present, the humidity is enhanced to 95% in those
cases, but this figure may be modified (see section 5).
The humidity is not allowed to increase by more
than a factor 2 through this procedure. The
following relation is hence used:
mi,j, k >
10-6, q < 0.95*qs = > qi,j,k
= min(0.95, qs, 2.0. q)
(8)
where qs is the saturated mixing ratio at the actual
temperature and pressure.
An obvious weakness with this simple formulation is that if the first guess and satellite cloud
water fields are entirely out of phase, the product
in (6) will be zero. Provided that the first guess is
reasonably accurate, this should not be a big
problem. Otherwise, it might be necessary to add
a small n u m b e r to m'j, k in (6), so that mi,j, k can
never become zero as long as (ms)i,j is different
from zero. The vertical distribution could then be
obtained, e.g., from satellite information on cloud
top height and cloud thickness.
The above equations contain several empirical
constants. In (7), the value 2"10 -3 as an upper
b o u n d on cloud water is empirical and may need
to be modified. Equation (8) contains 3 empirical
constants that may need tuning, as will be discussed
in section 5. Finally, it should be noted that the
computational cost of the m e t h o d is negligible.
4. Results
So far, three cases have been run. We shall mainly
concentrate on one case here, namely 15 August
1989 (AUG-case). For this case an AVHRRanalysis, based on the m e t h o d of Raustein et al.
(1991) is available at 12 G M T . We will use this
analysis to initialize the cloud water field in the
model, as explained below. Figure 1 shows the
synoptic situation at the start of the integrations
with an extensive cyclone over the N o r t h Atlantic.
Associated with it there is frontal precipitation
along the occluded front that bends from Iceland
into southern Scandinavia, Figs. 1 and 2, and
convective precipitation in the unstable air mass
behind the front, e.g., over and west of the British
Isles. The model's integration area normally covers
120 x 100 points, but has in this case been reduced
to a smaller area of 60 x 50 points, since the
satellite data only cover about half of that area.
24
J.E. Kristjfinsson
200
150
100
50
0
Fig. 1. First-guess sea-level pressure (isolines, mb) and vertically integrated cloud water content (shading, intervals:
0.05, 0.20, 0.50,1.0,1.5 kg m - 2) at 12 UTC 15 August 1989
\
r
~
""
~
iiiii i : Y
.........
0
I
I
I
I
I
6
12
18
24
30
HUM
-E~ CLW
--+-- CTRL
--O- F U L L
---X-- ENH
--A-
OLD
:i:i
ii:::i
Fig. 2. Vertically integrated cloud water content (intervals
as in Fig. 1) from AVHRR-data at 12 UTC 15 August 1989.
Note that the analysis only applies to the subarea marked
by solid lines. Also shown are surface fronts based on
synoptic data
Some results will also be shown for another
case, an explosive cyclone that hit Scandinavia
on 5-6 September 1985 (SEP-case). This case has
been studied extensively by Sundqvist et al. (1989)
and Lynch and Huang (1992). Here, as well as in
the JUL-case, no satellite information was available,
so the cloud water was initialized using only "first
guess" cloud water from an earlier run.
Six different runs will be compared: 1) Control
run, starting without cloud water and with
analyzed humidity (CTRL); 2) Cloud water initial-
Fig. 3. Area-averaged precipitation rates (units of 10-3 ram/h)
from experiments CTRL, CLW, HUM, ENH, FULL, OLD;
-see text; 15 August 1989 case
ization from "first guess" only (CLW); 3) As in
control, but with humidity enhancement based on
"first guess" only (HUM); 4) Combination of 2 and
3 (ENH); 5) As in 4, but with cloud water from a
combination of satellite data and "first guess" run,
as explained by Eqs. (5)-(8) (FULL); 6) Cloud
water and humidity fields taken directly from "first
guess" (OLD).
Assuming that the area-averaged precipitation
rate is fairly constant in this mature cyclone, we see
from Fig. 3 that runs 1) through 5) all underestimate precipitation during the first few hours
of the simulations. Cloud water initialization
alone (CLW) only increases precipitation by 20%
during the first hour, and after this the effect
almost vanishes. A similar result is valid for cloud
cover and cloud water content, Figs. 4-5. Tests
not shown reveal that a larger effect on precipitation is found if the first guess is out of phase with
the observations, since the condensation scheme
will dump out as precipitation all cloud water that
does not coincide with condensation. This is understood from the equation describing precipitation
release:
" c~
ex (
m
2
Initialization of C l o u d W a t e r in a Numerical W e a t h e r Prediction M o d e l
40
30 -
~
'
20 - / ...........................................................................................................
0
i
6
i
12
4
18
i
24
.L_
30
HUM
~
CTRL
~
ENH
CLW
~
FULL
~
OLD
Fig. 4. AsFig. 3, b u t ~ r c l o u d c o v e r ( % , m a x i m u m o v e r l a p )
140:
becomes efficient. As Eq. (9) shows precipitation
increases monotonically with increasing cloud
water content.
The reason why the effect of CLW vanishes after
approximately 3 hours is obvious, namely that
unless the humidity is enhanced, the inserted cloud
water will simply evaporate or fall out as precipitation. Berge and Kristj~nsson (1992) estimated
the lifetime of cloud water in this model to be of
the order 1-2 hours, agreeing well with this
argument.
Humidity enhancement, (HUM and ENH)
reduces the spin-up time considerably, particularly
for cloud cover, Fig. 4. Defining the spin-up time
as the time it takes for precipitation and cloud
cover to reach a "semi-steady" state, we find a
reduction from about 12 hours to 6 hours for
precipitation and cloud water content, while the
corresponding figures for cloud cover are 6 hours
and 2 hours, respectively. Note also that the total
precipitation remains higher in ENH than in
CTRL throughout the whole 24 hour forecast.
Including the satellite data; FULL; improves the
positioning of the precipitation. This is seen at
65 ~N, 0 ~E in Figs. 6a, b, where the front has been
shifted northwards, in accordance with Figs. 1 and
2. The effect of humidity enhancement on the
model fields is demonstrated in Fig. 7, which
shows the enhancement of the 700 hPa equivalent
potential temperature as well as analyzed frontal
positions. The enhancement is greatest in the
frontal zone over southern Scandinavia and in a
developing trough in the North Sea, which caused
heavy rainshowers and thunderstorms along the
Norwegian west coast around 00 UTC 16 August.
The OLD run has no spin-up, but instead
displays a large degree of overshooting (Fig. 3),
which is persumably caused by it being incompatible with the other model fields, that have been
modified against observations and subjected to
initialization. The OLD run gives up to 50 mm
in 6 h over parts of Scandinavia (Fig. 6c), which is
not supported by observations of precipitation
(Fig. 6d; 12 h precip.). The observations also seem
to indicate that FULL (Fig. 6b) yields more realistic
precipitation during the first 6 hours than CTRL
(Fig. 6a), especially over Scotland and England.
Turning to the SEP-case, the initial state has a
developing wave over the British Isles and the
North Sea (see Sundqvist et al. (1989) for details).
The geographical distribution of the differences
,0011
.Ii.i .ii.....................................
40 I .............................................................................................................................
20
...........................................................................................................
0
0
I
i
~
i
t
6
12
18
24
30
HUM
-4~ CLW
~
CTRL
--,g-- ENH
"-0- FULL
--A- OLD
Fig. 5. As Fig. 3, b u t for vertically integrated cloud water
c o n t e n t (10 -3 k g m -2)
Here c o is an inverse time scale for conversion of
cloud water to precipitation, b is the cloud cover
and mr is a "threshold value" which the cloud
water content must exceed before precipitation
25
26
J.E. Kristj~nsson
,
.
c
.
.
.
.
.
.
.
.
/
.
d
Fig. 6. Accumulated precipitation between 12 and 18 UTC 15 August (a) CTRL, (b) FULL, (c) OLD. Isolines are: 0.5, 1.0,
2.0, 4.0, 6.0, 10.0, 15.0, 20.0, 25.0, 30.0, 40.0, 50.0 mm. (d) Observed (subjective analysis) precipitation between 06 and 18 UTC
15 August for the intervals 0.5, 5.0, 10.0, 20.0, 30.0mm
between CTRL and ENH indicate that the humidity
field becomes most enhanced along the warm
front over the North Sea (not shown). This has an
effect not only on initial precipitation but also on
the dynamics through production of potential
vorticity by latent heat release. To see the magnitude
of this effect, Fig. 8 displays the surface pressure at
+ 2 4 hours in runs with and without the ENH
formalism for the SEP-case. The cyclone is
deepened by just over 1 hPa, giving an improved
position and central pressure as compared to
observations (cf. Sundqvist et al., 1989). In the
AUG-case, the cyclone had a much broader
structure and therefore there was a general deepening of 0.5-1.0 hPa over a large area. Comparison
with observations (not shown) indicates an
improved pressure pattern over Scandinavia, while
over Scotland the pressure is 1 - 2 h P a too tow.
This may be due to other effects, such as incorrect
cyclone position in the analysis, but may also
indicate an exaggerated effect of the humidity
enhancement in the convective region, cf. discussion
in section 5.
In the JUL-case, the reduction of spin-up in the
ENH-run was somewhat smaller than for the
other cases (not shown). This is probably because
Initialization of Cloud Water in a Numerical Weather Prediction Model
27
the first-guess in this case was more similar to the
analysis, since the analysis was done at 5 0 k m
resolution (see section 2). It remains to be investigated how this result would be affected by using
satellite data, as in the AUG-case.
5. Discussion
Fig. 7. Differences in equivalent potential temperature (2 K
intervals) at 700 hPa between runs FULL and CTRL at
+ 6h in AUG-case. Also shown are surface fronts based on
synoptic data at the same time
\
~U ~ I~ I S L ~ ~ 9 8
~ ~ J ~ . ~
~ ~ . ~
.... /
a
In this section possible improvements of the
proposed m e t h o d will be discussed. This will be
followed by some considerations of the different
terms in the cloud water tendency equation with
respect to the above results.
Returning to the question of empirical constants
in Eqs. (5)-(8), it may be desirable to modify the
95% figure in convective areas. This is because
convective condensation may occur at relative
humidities m u c h lower than stratiform condensation, due to the larger subgrid-scale variation in
those cases. For instance, the cloudy points in the
first guess field can be "masked", according to
whether they exhibit stratiform condensation or
convective condensation. The humidity enhancement would then only be performed on those
points that belong to the "stratiform category".
The other constants, especially the 2.0 in Eq. (8),
also need further testing.
A possible extension of the m e t h o d is to derive
temperature tendencies from the cloud water
data and use these as a forcing term during the
initialization (diabatic initialization). This was
tested but turned out to have a small effect on the
simulations presented here. The reason is probably
that the heating has a relatively shallow structure,
at the same time as the initialization scheme of
Bratseth (1982) only takes into account the first
two vertical modes. Therefore, the heating will
have very little impact in the initialization, and
since the heating would have occurred during the
first time-steps of integration anyway, very little
has been gained.
We shall look back at the tendency equation for
cloud water, (1), which after integration (using
centered time differencing, r denoting time-step)
becomes:
m~+ I = m ~ - 1 + 2 A t ' ( A ~
b
Fig. 8. Sea-level pressure (hPa) at +24 h in SEP-case. (a)
CTRL, (b) ENH
+ Q~ -
P~ -
E~).
(10)
Physically, the five terms on the right hand side
represent respectively, existing cloud water mass
(m~- 1); transport of cloud water by advection (Am);
source by condensation (Q); sink by precipitation
release (P); sink by evaporation of cloud mass (Ec).
28
J.E. Kristjfinsson
To understand better the role of the different
terms a few test runs have been made: We can
dump out all the cloud water at every time-step
by setting the "threshold value" mr (see Eq. (9)) to
0 and the inverse time scale c o t o 1/Atphys, where
A tphysis the length of the physics time-step (900 s).
Thus all excessive cloud water will fall out through
the term P, and me§ 1 will always be close to zero.
We call this experiment D U M P . Another experiment was made where the threshold value was
unchanged, while instead the term m~-1 was
omitted from the equation, meaning that only
cloud water produced at the time-step in question
was stored. We shall refer to this experiment as
NOSTORE. Finally, a run where the advection of
cloud water, A,, was omitted, has been run and
termed NOADV. A comparison of precipitation
between CTRL, NOSTORE, NOADV and D U M P
is shown in Fig. 9a. Apart from the first 2 hours
we see that the advection and microphysics have
a fairly small effect on the precipitation. The
NOSTORE-curve can be seen as a measure of the
production of cloud water per time-step. This is
seen to increase steadily during the first 6 hours
and continues to increase later, although there
are some oscillations also. After 30 hours, the
N O S T O R E run gives 6 0 ~ of the precipitation in
CONTROL. Apparently the humidity field has
now become so "sharp" that the cloud water
production per time step, given by Q~, can account
for more than half of the production of precipitation. Conversely, during the initial stages, the
production per time step was small, due to the
smoother humidity and divergence fields. This
again highlights the importance of the humidity
and wind fields, as compared to the cloud water
field, in controlling the spin-up. To some extent,
of course, the exact values in Fig. 9a depend on
the choice of "tuning" constants (c o and mr) in the
microphysics, but those are tuned so as to give
realistic amounts of cloud water, and it takes a
fairly drastic change in their values to change the
qualitative conclusion of this argument.
The NOSTORE- and DUMP-experiments have
been repeated with a different condensation scheme
that also includes cloud water content as a
prognostic variable, albeit with no advection. The
result was almost exactly the same as in Fig. 9a.
The small effect of the advection of cloud water
should be seen in relation to the discussion on the
lifetime of cloud water in the previous section.
140
120
100
80
60
40
20
....................................
0
0
I
I
I
t
I
6
12
18
24
30
CONTROL
--Y--
~ NOADV
-~- REM6H
DUMP
NOSTORE
',~ /
120 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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..........
ooj .......................................
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40
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0
0
]
i
i
i
i
i
5
10
15
20
25
30
30h simulation
I 6h runs
35
b
Fig. 9. (a) Precipitation rates from experiments CTRL,
DUMP, NOSTORE, NOADV and REM6H. (b) Cloud
water content in 10 .3 k g m -2 in AUG-case for respectively
30 h simulation and 6 h runs
The fact that D U M P gives 50~ more precipitation than C O N T R O L during the first 2 hours
means that the spin-up is partly related to the use
of cloud water as a prognostic variable, since
dumping it out is equivalent to an omission of that
option. However, the enhancement is less than
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Initialization of Cloud Water in a Numerical Weather Prediction Model
what was obtained by enhancing the humidity
field; Fig. 3.
In another run, the NOSTORE option was
applied every 6 hours, rather than every time-step,
REM6H. As we see, it only takes the model about
2 hours to reach again the precipitation rates that
it had before the "dumping". This must be caused
by the humidity and divergent wind fields being
in better balance with the model physics than they
were at time-step zero. Again this suggests that the
spin-up problem has rather little to do with the
cloud water field being zero at the analysis time.
Figure 9b was created by restarting the model
from analyses every 6 hours and shows the evolution
of the cloud water content, as compared to a 30 h
control run. A characteristic ladder-like pattern is
obtained, displaying the "harmful" effect of the
analysis and initialization procedures. According
to this figure the spin-up time for cloud water in
this model is somewhat greater than 6 hours.
It should be mentioned that we have looked at
the effect of vertical resolution by rerunning the
AUG-case with 10 instead of 18 vertical levels.
Small differences were found from the results
presented here.
Although the spin-up effect has been reduced
by the method proposed in this study, it has clearly
not been removed. The main reason is probably
the suppression of divergent motions caused by
the initialization of the mass and wind fields. If the
analysis scheme did a perfect job in adjusting
model fields to observations initialization should
not be necessary and spin-up should not occur.
One technique that seems to hold promise in that
respect is 3-D variational analysis, e.g., Parrish
and Derber (1992). Another promising technique
is diabatic digital filtering, described by Huang
and Lynch (1992). They show that the initial precipitation rates and cloud water content can be
somewhat enhanced when all the fields, including
the cloud water field are obtained in this way.
More testing is needed, before it can be established
to what extent the method can remove the spin-up
effect. The disadvantage with this method is the
computational cost, since the model has to be run
backwards and forward for several hours around
the initial state.
29
how to initialize this quantity. In this paper a
method has been proposed, based on satellite
information on cloud distribution and density and
"first guess" fields of humidity and cloud water
from the model. In the proposed procedure, cloud
information is used as a basis for enhancing the
humidity field. This is based on the assumption
that insufficient humidity observations together
with effects of analysis and initialization schemes
lead to considerable lack of detail in the humidity
fields. The effect of the method on the model's
"spin-up time" has been investigated. The spin-up
was found to be more related to the initial
humidity distribution than to the lack of initial
cloud water. It seems that a significant reduction
in spin-up time can be accomplished with the
proposed method. The method would appear to
be particularly applicable in areas where observational data are sparse. The computational cost of
the method is negligible.
Investigations of the magnitude of the different
terms in the cloud water tendency equation explain
some of the above results. While the initial spin-up
time for cloud water is of the order 6-9 hours, it
only takes the model about 2 hours to recover
when all the cloud water is artificially removed at
a later stage in the simulation. The interpretation
is that the cloud water itself explains about 2 hours
of the 6:-9 hour spin-up time, the remainder being
due to inaccurate humidity fields and lack of
divergent motions in the initial fields.
Further testing is needed to obtain optimal
values of empirical constants in the proposed
scheme. In particular, the method needs to be tried
(and improved) in cases where the "first guess"
fields are significantly out of phase with the
satellite data. It seems likely that the method needs
to be modified in convective areas.
Acknowledgments
The author wishes to thank Professor Hilding Sundqvist for
helpful comments on the manuscript. Elmer Raustein kindly
provided the AVHRR-analysis used in this study. Anstein
Foss is thanked for programming assistance and Mary-Ann
Olson for improving the figures.
References
6. Summary and Conclusions
The treatment of cloud water as a prognostic
variable in N W P models raises questions about
Berge, E., Kristjfinsson, J. E., 1992: Numerical weather simulations with different formulations for the advection of
humidity and cloud water. Mon. Wea. Rev., 120, 1583-1602.
30
J.E. Kristjfi.nsson: Initialization of Cloud Water in a Numerical Weather Prediction Model
Bratseth, A., 1982: A simple and efficient approach to the
initialization of weather prediction models. Tellus, 34,
352-357.
Danard, M., 1985: On the use of satellite estimates of
precipitation in initial analyses for numerical weather
prediction. Atmos. Ocean, 23, 23-42.
Huang, X.-Y., Lynch, P., 1992: Diabatic digital filtering
initialization: An application to the HIRLAM model.
Mon. Wea. Rev. (accepted).
Lynch, P., Huang, X.-Y., 1992: Initialization of the HIRLAM
model using a digital filter. Mon. Wea. Rev., 120, 1019-1034.
Nordeng, T. E., Rasmussen, E., 1992: A most beautiful polar
low. A case study of a polar low development in the Bear
Island region. Tellus, 44A, 81-99.
Parrish, D. F., Derber, J. C., 1992: The National Meteorological Center's spectral statistical interpolation analysis
system. Mon. Wea. Rev., 120 (in press).
Perkey, D. J., 1976: A description and preliminary results
from a fine-mesh model for forecasting quantitative precipitation. Mon. Wea. Rev., 104, 1513-1526.
Raustein, E., Sundqvist, H., Katsaros, K. B., 1991: Quantitative comparison between simulated cloudiness and
clouds objectively derived from satellite data. Tellus,
43A, 306-320.
Raymond, W.H., Olson, W.S., 1991: Initialization and
assimilation of cloud and rainwater in a regional model.
AMS 9th Conference on Numerical Weather Prediction.
Preprints, 430-433.
Sundqvist, H., 1978: A parameterization scheme for nonconvective condensation including prediction of cloud
water content. Quart. J. Roy. Meteor. Soc., 104, 677-690.
Sundqvist, H., Berge, E., Kristjfinsson, J. E., 1989: Condensation and cloud parameterization studies with a mesoscale
numerical weather prediction model. Mon. Wea. Rev., 117,
1641-1657.
Turpeinen, O. M., Garand, L., Benoit, R., Roch, M., 1990:
Diabatic initialization of the Canadian regional finiteelement (RFE) model using satellite data. Part I: Methodology and application to a winter storm. Mort. Wea.
Rev., 118, 1381-1395.
Zhang, D.-L., Hsie, E.-Y., Moncrieff, M.W., 1988: A comparison of explicit and implicit predictions of convective
and stratiform precipitating weather systems with a mesoE-scale numerical model. Quart. J. Roy. Meteor. Soc., 114,
31-60.
Zhao, Q., Carr, F. H., Lesins, G. B., 1991: Improvement of
precipitation forecasts by including cloud water and cloud
ice into NMC's eta model. AMS 9th Conference on
Numerical Weather Prediction. Preprints, 50-53.
Author's address: J6n Egill Kristjfinsson, Geoanalysis
Group (EES-5), MS K401, Los Alamos National Laboratory,
Los Alamos, NM 87545, U.S.A.