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An Application of the Kain-Fritsch Cumulus Parameterization to a
Tropical Environment With/Without Nudging
Ronald M. Welch1, Aaron Song1, Adriana Beltrán-Przekurat2, Vani Starry Manoharan1,
Charles Cohen3 , Roger A. Pielke Sr.2
1Department of Atmospheric Science, University of Alabama in Huntsville, Huntsville,
Alabama
2Department of Atmospheric and Oceanic Sciences, Cooperative Institute for Research in
Environmental Sciences, University of Colorado, Boulder, Colorado
3University Space Research Association, Huntsville, Alabama
2
ABSTRACT
Nudging is commonly used in regional modeling simulations, constraining the
model prognostic variables by adjustment towards the large-scale field. The Kain-Fritsch
cumulus parameterization in conjunction with the GEMRAMS mesoscale model
simulated rainfall in a tropical environment and compared results with rain gauge
measurements. With “zero” or with weak central nudging, the K-F scheme significantly
overestimates rainfall at most of the Guatemala rain gauge stations used in this study.
However, the K-F scheme performs well for the first 5-10 days of the simulation. After
this initial period, locally active forcing becomes strengthened without constraint,
building higher convectively available potential energy (CAPE) which leads to
overestimated rainfall. With strong central nudging applied, excellent results were
obtained with the rain gauge data, even with the model run for an entire year. However,
the use of non-zero central nudging is not without penalty, especially in masking of
important surface signals from terrain and landscape data. One way to minimize such a
risk may be to increase the vertical resolution near the surface, realizing that this action
must be balanced by the CPU demand which can be high when running long simulations.
Higher near surface resolution practically assures the proper input of land surface data,
allowing a certain degree of central nudging to balance the local forcing.
3
I. Introduction
A regional scale modeling experiment has been carried out to simulate the impact
of ongoing deforestation in Guatemala’s unprotected areas upon the local climate within
the protected areas (Welch et al., 2005). Deforestation activities (such as the “slash and
burn” practice) consists of cutting and burning forests and woodlands to create fields for
agriculture or pasture for livestock Burning removes the vegetation and may release a
pulse of nutrients to fertilize the soil. Ash increases the pH of the soil, a process which
makes certain nutrients (especially phosphorus) more available in the short term. Over
time, however, the consequences of slash-and-burn agriculture to ecosystems are almost
always deleterious when practiced on a large scale. Furthermore, local rainfall may be
affected by deforestation, although in ways that are not fully understood. For instance,
most modeling studies have concluded that widespread deforestation of Amazonia would
lead to decreased rainfall (e.g. Costa et al., 2007; Sampaio et al., 2007). On the other
hand, Negri et al., (2004) and others concluded that during the dry season, when the
effects at the surface are not overwhelmed by synoptic-scale weather disturbances,
shallow cumulus cloudiness, deep convective cloudiness, and rainfall occurrence all are
larger over the deforested and nonforested (savanna) regions than over areas of dense
forest.
As a fundamental basis for climate investigation associated with localized
deforestation, the observed patterns in local rainfall play a crucial role in providing a “test
bed” for carrying out the desired climate modeling. For instance, in the case of modeling
Guatemala rainfall, it is essential that the model be able to distinguish between 1) dry and
wet seasons, 2) terrain-induced and larger scale weather-induced precipitation processes,
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3) complex terrain and flat ground situations, and 4) various landscape conditions
(including vegetation types, with/without landscape changes), as well as for different
precipitation processes in the highlands and lowlands (Nair et al., 2003; Pielke et al.,
2007).
In this study, the focus is limited to the modeling of Guatemala rainfall (and
particularly in the wet season) rather than modeling the deforestation impacts (which will
be reported in an accompanying study). The GEMRAMS atmosphere-vegetation coupled
model (Eastman et al., 2001; Beltrán 2005; Beltrán et al. 2008) is expected to reproduce
precipitation events in the tropical rainforest environment more accurately than a model
with only atmospheric processes. GEMRAMS is a merged model of the Regional
Atmospheric Modeling System (RAMS; Pielke et al., 1992) and the General Energy and
Mass Transfer Model (GEMTM; Chen and Coughenour, 1994). Cumulus
parameterization is accomplished using both the Kain-Fritsch scheme (Kain and Fritsch,
1993; hereafter “K-F”) and, as a reference, another scheme routinely utilized in the
RAMS model (hereafter “Kuo”).
On the regional scale the K-F scheme has been compared with other schemes
(e.g., Wang and Seaman 1997; Cohen 2002; Saleeby and Cotton, 2004) and examined
regarding its “trigger function” and mass flux profiles (Kain and Fritsch 1992, among
others). However, little attention has been paid to the performance of the K-F scheme on
longer time scales within a regional scale model. In the past, there was no such concern
because only global models were used for “climate-scale” evolutions. Accordingly,
regional models were thoroughly checked and tested only for “regional” time and spatial
scales (typically from diurnal to synoptic time scales of several days and over an area
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several hundreds of km on a side). However, with their more complete model physics (as
compared with current global models), the performance of such regional models over
longer time scales is becoming an important issue (Saleeby and Cotton, 2004; Castro et
al., 2005).
With the length of simulation extended, and with the limited-area domain
unchanged, the model likely faces more challenging issues within the traditional space
and time limits than the model was originally designed for. These issues include 1) those
related to landscape (complex terrain, inland water, vegetation-related or soil-related), 2)
model resolvable and parameterized processes, 3) time-dependent boundary conditions
(data assimilation), and 4) convectively-induced compensating processes (which typically
occupy “larger” space than does the cloud itself). Such issues may not even be detected
unless the total model time is long enough.
Within the computational framework selected for this study, the goal is to
examine the issue of rainfall overestimation which may occur when the model time is
extended. Thus far this issue has not been discussed in the literature regarding the use of
the K-F scheme. Selected rain gauge data were used for the year 2003, provided by the
Guatemalan National Institute of Seismology, Volcanology, Meteorology and Hydrology
(INSIVUMEH). Section 2 briefly describes the model configuration and initialization.
Model results are shown in section 3, with a discussion of the model performance for
model simulation times commonly used in regional models, as well as a look at the
problem of overestimation at longer model times. Section 4 provides a summary and a
discussion on the potential role played by the vertical resolution near the surface.
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II. Model
A. Model Configuration
In all the simulations of this study, two nested domains are used. The outer
domain, with a horizontal grid of 40km x 40km and covering an area about 2000km on a
side, is centered at the point of 16.0N and -90.0W in Guatemala. This domain is used
mainly to incorporate as much real-time weather as possible within the chosen regional
scale domain. Real-time weather data are obtained from NCEP reanalysis, FNL global 1
x 1 degree, 6-hourly data, processed through the RAMS standard pre-processing. The
inner domain has a horizontal grid of 10km x 10km and covers an area of 620km x
620km, centered at the same point. Thirty-five vertical levels are used, with the lowest
level 20m from ground, increasing with a ratio 1.15 up to a maximum of 1200m near the
model top at 18.7km. The fine vertical grid limited the model time step to 30 seconds for
the outer and 10 seconds for the inner domain. The simulation times include one year
(starting at Jan. 1), 30-day (March or September) and 7-day or 2.5-day (early September).
The selection of year 2003 is arbitrary. The model physics parameters are initialized
following Beltrán (2005).
B. Vegetation Initialization
The original GEMRAMS model was built based on RAMS v4.3 (LEAF-2; Walko
et al., 2000; Pielke, 2002, in which, for instance, Appendix-D provides a concise
summary of the LEAF-2). The RAMS model has evolved to the latest version v6.0, and
one of the major improvements includes the use of independent satellite observations of
vegetation greenness represented by the Normalized Difference Vegetation Index
7
(NDVI). This enables vegetation parameters (the vegetation fractional cover, leaf area
index, and vegetation type) to be initialized from LEAF-3 (Walko et al. 2000), including
spatial and temporal variability of greenness.
C. Soil Initialization
The model soil parameters are more difficult to be initialized, due to the lack of
satisfactory data in most regions. Reichle et al. (2004) discussed a three-way comparison
regarding soil modeling (in-situ measurement, remote satellite observation, and
numerical modeling) and pointed out that there is as yet no “consensus” among the three.
In the current study, soil moisture is initialized using the NCEP reanalysis data (the FNL
global 1 x 1 degree, 2-layer soil data), in which vertical variation is incorporated into the
model. Horizontally, the data over Guatemala is averaged. Soil temperature is initialized
with “zero-offset” from the NCEP FNL lowest air temperature. Also, soil (3D) texture is
initialized following the same procedure of LAI and vegetation fraction as provided by
RAMS v6.0.
D. Nudging process
Time-dependent boundary condition (a type of Four-Dimensional Data
Assimilation, or “fdda”) datasets were built before making the model runs using the
NCEP/NCAR reanalysis data (the FNL, enhanced with global rawinsonde and surface
data). If “zero” central nudging is considered, that means fdda was applied only through
the lateral boundaries on an “outer ring” of 5 grid points, and with no other nudging
8
anywhere in the domains), A general form of the nudging process as used in this study
is shown in Equation 1 :
−=
∂∂
τφφφ ),,,(),,,(
),,,(tkjitkji
tkji mdlobs
nudt
qtvu ,,,=φ
Equation 1 illustrates how the nudging process was carried out in the model runs
of this study. The process is applied to only the four major prognostic variables
(φ=u,v,T,q) : u- and v-component of velocity, main thermodynamic variable (normally
Theta), and main water substance variable (normally water vapor mixing ratio). The time
parameter (τ) is the relaxation time as used in this study. It is normally a “shorter” time
(say 900 sec., as suggested in RAMS Technical manual) along the lateral boundary to
inject desired large scale time-dependent information (normally on an outer ring of 5 grid
points) and up in the Stratosphere (to damp out vertically propagating gravity waves).
Any nudging between the outer ring and the domain center is the “central nudging”, of
which the effect upon the model runs is discussed in this study. Note, while the spatial
distribution of the nudging can be easily specified, there is no similar user action in
“time” (that is, once defined, the nudging process is held constant throughout the model
run).
9
III. RESULTS
Model verification is carried out using in-situ measurements at individual rain
gauge stations in Guatemala. First, the large-scale dynamic and thermodynamic
evolutions were verified (Fig. 1) with the data from the World Meteorological
Organization (WMO) surface Station 786410 near the Caribbean coast in Belize
(http://www.ncdc.noaa.gov/oa/ climate/climatedata.html#daily) for 2003. With no
interpolation or averaging of any kind, the model dew point annual evolution (with
correlation of 0.833) is slightly better than the temperature annual evolution (correlation
of 0.756). During the period from about April to September, the model slightly
overestimates the temperature, while no such overestimation is seen on the dew point
field. In the following model rainfall verifications, 18 rain gauge stations were available
and were used in this study.
A. Rainfall Verification
Beltrán (2005), in her GEMRAMS modeling over southern South America, found
that the model rainfall was overestimated as compared with observations, and that the
overestimations may be related both to deficiencies with the K-F scheme and
representation of terrain. In her case, the model tends to produce excessive precipitation
along the Andes Mountains. The “adjusted K-F scheme” (Castro et al., 2002) has been
incorporated in the Guatemala simulations discussed in this study. Beltrán (2005)
hypothesized that the overestimation persists throughout the simulation and in some cases
may be related to a “small topographic feature” located in the area. In the current study,
10
similar situations appear to occur, especially if no, or very-weak, central nudging is
applied.
The observed and modeled accumulated rainfall values are shown in Fig. 2a and
2b for the wet season (September, 2003). With no constraint on the model prognostic
variables from any adjustment toward the large-scale field, Fig. 2 shows that the K-F
scheme significantly overestimates rainfall at most of the stations selected in this study.
Vertical velocities tend to more easily develop over regional-scale mountainous areas
than over relatively flat areas, such that the K-F becomes fully “triggered,” resulting in
heavy rainfall. In contrast, the Kuo scheme produces moderate rainfall, in broad
agreement with the rain gauge data.
Nudging within the interior was used in a second simulation. Central nudging
must be used with caution, however, since it may “mask” the surface characteristics in
any landscape modeling, due to adjustments towards the large scale evolution (Weaver et
al., 2002). To demonstrate that central nudging may play a key role, a relatively strong
(Relaxation time= 3 hours; defined in Eq. 1) central nudging was applied with results
shown in Fig. 3a and 3b. Note that the model was otherwise identical to the above case
except with a year-long simulation. Fig. 3 shows that, with the exception of only one
station (#2), K-F develops rainfall estimates in broad agreement with the rain gauge
measurements and significantly better than the Kuo scheme. This year-long simulation
amply illustrates that the K-F scheme performs quite well in the three-way comparison
when a certain time-dependent constraint (central nudging) is used.
Physically, the central nudging appears to have played a role which is counter to
the local forcing. For instance, in convectively favorable conditions during the tropical
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rainy season, highly activated local velocity perturbations become modified through
adjustment towards the large scale field. The large-scale fields were built using 6-hourly
global model data with spatial grid increments of 1o x 1o Lat/Lon, so there are negligible
signals associated with complex terrain in the model domain. The result is that the more
such large-scale evolution is incorporated, the less “small-scale” terrain effects become
activated (and thereby constraining the K-F scheme). The overall model dynamics
become more “steady” for much longer times than that for which the host model and K-F
scheme were both originally designed. Therefore, we conclude that the use of central
nudging must be done in a way to carefully “weigh the needs” between local- and large-
scale forcing.
B. With/Without Nudging
With no central nudging applied, the K-F scheme tends to overestimate rainfall in
this tropical environment. However, Fig. 2 shows that the K-F scheme performs well for
the first few days of the simulation (from about 5 days up to 10 days). To better
understand the impact of stronger/weaker nudging upon precipitation, a pair of 7-day
runs was made.
In addition to the stronger relaxation time of 3 hours used in this study, Beltran
(2005) used one with 24 hours, while Saleeby and Cotton (2004) used a very weak one
with a relaxation time of “2 days”. When applied to the K-F simulations in this study,
Fig. 4 shows that weak central nudging (τ = 2day) produced relatively strong rainfall
especially over the mountainous areas (southwest Guatemala extending to southern
Mexico). Furthermore, weak central nudging appears to have approached the no-nudging
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case (not shown), such that in such regional-scale modeling, the “lower limit” of the
central nudging (intensity) may be tuned to be “2 days” in terms of the relaxation time.
Longer than this relaxation time, central nudging will not produce any recognizable
effect.
On the other hand, a relatively strong central nudging (τ = 3hour) is applied to
generate the results shown in Fig. 5. Differences in the two approaches are: (a)
significantly less rainfall over the mountainous areas, (b) less total rainfall domain wise,
and (c) more larger scale rainfall in Belize (northeast of Guatemala). These results are
expected, but it appears indeed striking (between Fig. 4 and 5) that with the model
otherwise identical and only differing in the intensity of the central nudging, the rainfall
results over the complex terrain areas show such a significant difference.
As mentioned earlier, the use of strong central nudging is NOT without penalty.
There is a risk of suppressing important surface signals from any landscape modeling
(Weaver et al., 2004). Therefore, a decision concerning the intensity of central nudging
to be used should be based upon a number of factors, including using a sufficiently high
vertical resolution near the surface (such as done in this study). Indeed, the present study
is perhaps “biased” toward favoring the use of central nudging due to the use of higher
vertical resolution which would balance out, to some extent, the un-wanted masking
effect brought up by the central nudging (see a simple test in section 4).
C. Domain-Scale Response
As a reference, rainfall amounts were compared with the Kuo and K-F schemes
for also a pair of 30-day runs. The model was otherwise identical. As mentioned
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previously, the Kuo rainfall values are limited in total amount generated, and the Kuo
scheme appears to be rather conservative in producing significant rainfall over complex
terrain areas, independent of whether strong or weak nudging is applied. Therefore, the
Kuo results are used as a reference to illustrate the domain-scale responses of the K-F
approach.
With a weak or zero central nudging, locally active forcing becomes strengthened
without this constraint, building higher convectively available potential energy (CAPE)
which leads to abundant rainfall applying the K-F scheme. As a result, strong net heating
is produced in the upper troposphere through subsidence warming. This upper heating
then enhances the drop of surface pressure hydrostatically as compared with that from the
Kuo approach, as shown in Fig. 6a. That is, with a weak central nudging, a domain-scale
heated-low pressure is created which tends to both increase net inflow/outflow in the
lower/upper troposphere. In time, the domain-scale cyclonic deepening associated with
the K-F (without a proper balance between local and large scale forcing) eventually leads
to an overestimation of rainfall. Such a potential risk exists regardless of the
environmental seasonal variation. Fig. 6a shows results for one month in the dry season
(March) and one month in the wet season (September). In both cases, the net heating
allows the build-up or enhancement of the heated low pressure, which likely drives more
moist inflow in the lower layers to build up larger CAPE, with the result that subsequent
convective development is stronger.
Thus far in this study only the inner domain is used for the discussions. This
domain has an area of only 620km x 620km. It is well known that atmospheric deep
convective activities tend to organize into mesoscale or regional-scale convective systems
14
during the developing stages (Maddox et al., 1976). When such organization occurs, the
area covered by it would easily approach, or even exceed, that of the inner domain of this
study, thereby likely leading to exaggeration of the net heating and the pressure
deepening. Fig. 6b shows from the 7-day runs the differential sea level pressure
(between the two central nudging runs) for the inner (red) and outer (black) domains. For
the small (inner) domain, the domain pressure deepening reaches about -2.2 (mb), while
for the large (outer) domain, values are limited to about -1.2 (mb). Therefore, with the K-
F scheme, in order to more accurately model the entire precipitation processes, the
domain should be at least large enough to incorporate the environmental processes
accompanying the deep convection (namely the subsidence warming) during the entire
convective lifetime.
IV. SUMMARY and DISCUSSION
An application of the K-F scheme was made in this study for the purpose of
gaining an understanding of its general performance when targeting the localized rainfall
events of Guatemala. Overall, the combination of the host model (GEMRAMS) and
either the K-F or the Kuo scheme appears to be able to produce rainfall which is based on
fundamental atmospheric and environmental physics. In terms of the practical procedure,
however, it appears that a certain “tuning” should be applied in consideration of the
specific target environment. A “balance” between local forcing (terrain, landscape, etc.)
and large scale forcing (a “downscale version” of the NCEP global evolution) should be
maintained throughout the total model time.
15
In regional modeling such as that discussed in this study, there is “always”
incorporation of the large scale forcing which comes into the model through the lateral
boundaries. However, such a dose of the large scale forcing may be “too little” in some
cases, especially over areas in which the local forcing is strong (complex terrain, or
strong landscape gradients). When the local forcing is strong, sufficient vertical velocity
perturbations are developed which trigger the K-F, leading to a production of excess
rainfall. At the same time, localized deep convective development leads to deepened
surface pressure, which typically favors “more” surface moisture influx, thus further
destabilizing the local area and leading to further convective development.
The above argument suggests the use of non-zero central nudging (Beltrán, 2005;
Saleeby and Cotton, 2004) as the most appropriate approach to dynamic downscale, as
also recommended in Rockel et al (2008). However, the use of central nudging is not
without penalty. It is well known that incorporating large-scale forcing (with its original
time and space intervals of only 6-hourly and 1 x 1 Lat/Lon) jeopardizes the input of
important surface signals from terrain or landscape data (Weaver et al., 2002). One
(indirect) way to minimize such a risk may be to increase the vertical resolution near the
surface (to compensate for the lost of some surface signals produced by central nudging),
realizing that this action itself must be balanced by the CPU demand when running very
long simulations.
In order to see the role played by the near-surface vertical resolution upon the
upward propagation of surface signals, a simple test was made over the Guatemala terrain
with a pair of short (2.5 day) runs initialized by a general purpose sounding in RAMS.
The two runs are otherwise identical except one with the lowest level only 20m from the
16
ground and the other 100m from the ground. The result was summarized (Fig. 7) using
the (arbitrarily chosen) model water vapor (lowest air level) and soil moisture (top soil
layer). From Fig. 7 it is seen that the time-averaged differences (between the two
moisture values) are under 1.0 (g/kg) over most of domain with the fine vertical grid,
while they are over 2.0 (g/kg) with the coarse vertical grid over a significant portion of
domain. In time, the land-averaged (ocean is ignored in this discussion) differences are
also clearly smaller with the fine vertical grid than that with coarse vertical grid.
Once the near surface resolution is kept high enough to practically assure a proper
upward propagation of land surface data, a certain degree of central nudging can be
incorporated in order to balance the local forcing. In this case, the model prognostic
fields (over the entire horizontal domain) are all under the constraint such that any local
forcing would be suppressed to some extent. As shown previously, a certain central
nudging with relaxation time perhaps somewhere between a few hours and one day
appears to be able to eliminate most of the K-F rainfall overestimation under the situation
encountered in this study, while the overall model result still appears reasonable
compared with the observations.
Acknowledgements
This research was supported by National Aeronautics and Space Administration grant
number NNX07AF14G. Dr. Chris Castro is thanked for kindly sending the modified K-F
scheme used in the RAMS simulations of this study. Dr. Udaysanka Nair is thanked for
his contributions in early stage of this study.
17
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Figure Captions
Figure 1: A model verification using daily surface data from the WMO Station 786410
for Year 2003. (a) The time curves of model (lowest level) temperature (oC) (blue) and
the station temperature (red), with the correlation shown in (c); (b) Same as (a) except
for the dew point temperature (oC) with the correlation shown in (d).
Figure 2a: A three-way comparison of the accumulated rainfall (mm) for September,
2003, among the Guatemala rain gauge data (solid-blue curve; at rain gauge stations #1 to
#9), model rainfall with K-F (solid-red) and model rainfall with the Kuo scheme (dashed-
blue), in both runs no central nudging was used. The X-axis is tick marked with days in
September, and Y-axis with rainfall amount from 0 to 2000 at interval 400 (mm).
Figure 2b: Same as Fig. 2a except at the rain gauge stations #10 to #18.
Figure 3a: A three-way comparison on the accumulated rainfall (mm) over the entire
year of 2003, among the rain gauge data (solid-blue; at rain gauge stations #1 to #9),
model rainfall with K-F (solid-red) and model rainfall with Kuo (dashed-blue), in both
runs a relatively strong central nudging was used (see text). The X-axis is tick-marked
with the 12 months, and Y-axis with rainfall amounts from 0 to 6000 at interval 1000
(mm).
Figure 3b: Same as Fig. 3a except at the rain gauge stations #10 to #18.
22
Figure 4: The horizontal rainfall pattern of the accumulated rainfall (mm) in the 7-day run
in which model was run with K-F together with a weak central nudging. Red-thick
“numbers” indicate the locations of the 18 rain gauge stations, while the topography is
briefly contoured (starting at 500m with increment of 500m) to illustrate that the
mountainous areas are the preferred places of higher rainfall from KF with weak central
nudging (see text).
Figure 5: Same as Fig. 4 except with a stronger central nudging.
Figure 6: (a) The model 3D domain averaged convective heating (oK/Day) from the run
with K-F (red curves) and Kuo (black curves) for the month March (dashed) and
September (solid). (b) The difference of subtracting the domain-averaged sea level
pressure in the run with the weak central nudging from that with the stronger central
nudging, averaged over the inner domain (red) and outer domain(black). The X-axis
indicates days, Y-axis indicates the pressure differences (mb), from -2.4 to 0.4 at interval
0.4 (mb).
Figure 7: (a) The horizontal distribution of the time-averaged differences of subtracting
the top soil moisture (g/kg) from the model lowest air moisture (g/kg) for the run with
fine vertical resolution near the surface; (b) same as (a) except for the run with coarse
vertical grid; (c) The time curves of domain (Land) averaged top soil moisture (black)
and lowest air moisture (red) for the fine vertical-grid run; (d) same as (c) except for the
coarse vertical-grid run.
23
Figure 1
Figure 1: A model verification using daily surface data from the WMO Station 786410 for Year 2003. (a) The time curves of model (lowest level) temperature (oC) (blue) and the station temperature (red), with the correlation shown in (c); (b) Same as (a) except for the dew point temperature (oC) with the correlation shown in (d).
24
Figure 2a
Figure 2a: A three-way comparison of the accumulated rainfall (mm) for September, 2003, among the Guatemala rain gauge data (solid-blue curve; at rain gauge stations #1 to #9), model rainfall with K-F (solid-red) and model rainfall with the Kuo scheme (dashed-blue), in both runs no central nudging was used. The X-axis is tick marked with days in September, and Y-axis with rainfall amount from 0 to 2000 at interval 400 (mm).
25
Figure 2b
Figure 2b: Same as Fig. 2a except at the rain gauge stations #10 to #18.
26
Figure 3a
Figure 3a: A three-way comparison on the accumulated rainfall (mm) over the entire year of 2003, among the rain gauge data (solid-blue; at rain gauge stations #1 to #9),model rainfall with K-F (solid-red) and model rainfall with Kuo (dashed-blue), in both runs a relatively strong central nudging was used (see text). The X-axis is tick-marked with the 12 months, and Y-axis with rainfall amounts from 0 to 6000 at interval 1000 (mm).
27
Figure 3b
Figure 3b: Same as Fig. 3a except at the rain gauge stations #10 to #18.
28
Figure 4
Figure 4: The horizontal rainfall pattern of the accumulated rainfall (mm) in the 7-day run in which model was run with K-F together with a weak central nudging. Red-thick“numbers” indicate the locations of the 18 rain gauge stations, while the topography is briefly contoured (starting at 500m with increment of 500m) to only illustrate that the mountainous areas are the preferred places of higher rainfall from KF with weak central nudging (relaxation=2day).
29
Figure 5
Figure 5: Same as Fig. 4 except with a stronger central nudging (relaxation=3hr).
30
Figure 6
Figure 6 : (a) The model 3D domain averaged convective heating (oK/Day) from the run with K-F (red curves) and Kuo (black curves) for the month March (dashed) and September (solid). The X-axis indicates a 30-day period, and Y-axis indicate the heating(oK/Day); (b) The difference of subtracting the domain-averaged sea level pressure in the run with the weak central nudging from that with the stronger central nudging, averaged over the inner domain (red) and outer domain(black). The X-axis indicates days, Y-axis indicates the pressure differences (mb), from -2.4 to 0.4 at interval 0.4 (mb)
31
Figure 7
Figure 7 : (a) The horizontal distribution of the time-averaged differences of subtracting the top soil moisture (g/kg) from the model lowest air moisture (g/kg) for the run with fine vertical resolution near the surface; (b) same as (a) except for the run with coarse vertical grid; (c) The time curves of domain (Land) averaged top soil moisture (black) and lowest air moisture (red) for the fine vertical-grid run; (d) same as (c) except for the coarse vertical-grid run.
