Multiple-Doppler Radar Data Assimilation using GSI with Cloud
Analysis and Objected-based Precipitation Forecast Verification for
Tropical Storm Erin (2007) through its Inland Reintensification Phase
Kefeng Zhu1,2,3, Yi Yang2,3, Ming Xue2,3 , Shouting Gao1, Steven Weygandt3, Ming Hu3 and Stan
Benjamin3
Laboratory of Cloud-Precipitation Physics and Severe Storms (LACS), Institute of Atmospheric
Physics, Chinese Academy of Sciences, Beijing, China1
Center for Analysis and Prediction of Storms2 and School of Meteorology3
University of Oklahoma, Norman Oklahoma
Global System Division, Earth System Research Laboratory, NOAA4
January, 2010
Submitted to Weather and Forecasting
Corresponding author address:
Dr. Ming Xue
Center for Analysis and Prediction of Storms
University of Oklahoma
120 David L. Boren Blvd, Norman OK 73072
mxue@ou.edu
Abstract
Tropical storm Erin (2007) unexpectedly reintensified in western Oklahoma from
0000UTC to 1500UTC 19 August 2007. When Erin moved across the Oklahoma, the
evolution and dissipation was well captured by the radar situated in the Oklahoma State.
And the data collected by these Doppler Radars provided a good database to examine the
performance of multiply Radar observation in the high resolution data assimilation
system.
In this paper, the impact of different part of radar data on the short range
precipitation forecast is studied. The radar radial winds were assimilated through three
dimensional variation packages in the Grid-point Statistical Interpolation (GSI) system.
And three-dimensional radar mosaic reflectivity is analyzed by the implemented cloud
analysis package embedded in the GSI system. The assimilation of radar radial winds
improve the rain band structure prediction while the assimilation of reflectivity is found
to be associated with the heavy rain center location in the first few hours forecast. With
both radar radial winds and reflectivity assimilated, the experiment has the best extreme
centre location of six hour accumulated rainfall. In order to better understand the
assimilation system, two key parameters were also examined: the configuration of
horizontal de-correlation scale factor and the cloud analysis option. The former is key
parameter for acquiring reasonable error structure space distribution and the latter is
semi-empirical microphysical approach for retrieving the hydrometeors fields from the
radar reflectivity.
In additional, the neighborhood and object-based verification method within the
Model Evaluation Tools (MET) are employed for the verifying and identifying. Through
the comparison of neighborhood verification scores with and without radar radial winds
assimilation, it is found that experiment with radial winds data significantly upgrades the
forecast skill. The object-based verification method is introduced to better describe the
bending structure difference among the forecasts. The total interest calculated from the
resolved and matched objects is used for determining the similarity between the forecast
and observation. Meanwhile, the object-based storm moving path which represents the
mobile centriod of rain cluster is computed. The verification results suggest the
assimilation of both radar radial winds and reflectivity have the best performance not
only in the rain band structure prediction but also the location of the heavy rain cluster.
1. Introduction
The insufficient information of Single-Doppler Radar in the three dimensional wind
fields is always an issue in the directly assimilation of radar radial winds. MultipleDoppler Radar observation to some extent can relieve such problem in the cross section
region. The overland restrengthening and dissipating of tropical storm Erin (Arndt et al.
2009) happened to occur over a region equipped with dense observation, and more
important, within the observation range of four Doppler Radar located in the Oklahoma
state. This provides a good opportunity to study the performance of Multiple-Doppler
Radar of both radar radial winds and reflectivity in the high resolution data assimilation
system.
The use of semi-empirical microphysical methods to retrieve hydrometeors field
from the radar reflectivity is a common way in the reflectivity data assimilation. The GSI
convective cloud analysis package was implemented from the ARPS (Advanced Regional
Prediction System) cloud analysis (Xue et al. 2000; Xue et al. 2001; Xue et al. 2003).
More details of ARPS cloud analysis can be found in the Jian Zhang dissertation(Zhang
1999). And the latest improvement of in-cloud temperature adjustment and the way of
retrieving hydrometeors fields from radar reflectivity were described in the MingHu’s
paper (Hu et al. 2006a). Encouraging results with radar radial winds assimilated by the
ARPS 3DVAR and the radar reflectivity through cloud analysis procedure have been
achieved. In MingHu’s study, with both type of radar data assimilated, the forecasted
lower level vorticity centers associated with tornadoes were largely improved (Hu et al.
2006b). Recently, the ARPS 3DVAR with the cloud analysis package was applied to
predict hurricane IKE (Zhao and Xue 2009). It was found the radar radial winds
improved the track forecast while the reflectivity improved the intensity forecast. Similar
results could be found in this study.
Although the experiments using the ARPS 3DVAR with cloud analysis has been
proved to be successful, the experiment using GSI with the implemented cloud analysis
package with both type of radar data assimilated in the high resolution system are
relatively new. Initial tests with radar reflectivity data and surface observation assimilated
employing the GSI with and without cloud analysis procedure in the 9km resolution have
been made(Hu and Xue 2007). More experiments to examine the capability of GSI with
full package cloud analysis package in the prediction of serve weather event with both
radar reflectivity and radar radial winds assimilated are still needed.
In addition, the Model Evaluation Tools (MET) (Brown et al. 2009) developed by the
National Center for Atmospheres Research (NCAR) Development Testbed Center (DTC)
will be used for the verification purpose of Erin. The narrower band in the west-to-east
and relatively longer in the south-to-north feature of Erin’s rain band makes the
traditional forecast-observation verification method unreasonable especially when the
forecasted system was mis-displayed half degree away from the observation and
surrounded by the fake rain produced by the unresolved model properties. The
neighborhood (Ebert 2008) verification method which verifying the grid within a range
can reduce such displacement error a little bit but cannot distinguish the structure
difference between the forecast and the observation. The object–based (Davis et al.
2006a; Davis et al. 2006b)verification methods, however, determine the difference
between forecast and observation based on the resolved and matched objects properties.
It is a prospective way to study the impact of different part radar data especially when the
forecast result comes out with big outline differences.
In this paper, the pre-process of radar velocity data and the experiments design will
be briefly introduced in section 2. In section 3, the compassion between different
horizontal correlation scale factors for the radar radial winds and different microphysics
approach for retrieving the hydrometeors fields from the reflectivity data will be
discussed. A detailed comparison among various experiments and its verification for
quantity precipitation will be presented in section 4, and the results are further discussed
and summarized in section 5.
2. Radar radial winds data preprocess and experiment design
a. Radar radial winds preprocess
Four Doppler radars KFDR, KTLX, KVNX and KINX along the Erin moving path
which situated in the Oklahoma states were collected (see Fig.1). These data were first
preprocessed by an automatic data quality control package 88D2ARPS of the ARPS
model but with the input interface modified to the WRF background and output interface
to the GSI (rename to 88D2GSI below). This data quality control module includes
velocity dealiasing, ground clutter contamination and shielding removal, etc(Eilts and
Smith 1990). In case the 88D2GSI failed to clean the data, manual interactive software
SOLO developed by the National Center of Atmosphere Research (NCAR) was used to
remove the rest cluster or unfolded velocity. The data after QC were then read in by the
88D2GSI and super-obed to the model grid using the least square method:
A  a0  a1 x  a2 x 2  a3 y  a4 y 2  a5 xy  a6 z
(1)
Where A is the analyzed variable, ai are the polynomial coefficients and x, y and z are
the distance of radar observed points to the model grid in the horizontal and vertical
coordinate respectively.
b. Brief introduction of Erin and design of experiments
Erin began as Atlantic Tropical Depression Five (2007). Throughout its existence
over open water, its sustained winds never exceeded 18 m s-1, and its lowest reported
central pressure was 1003 hPa. But during the day immediately following Erin’s landfall,
it unexpectedly and dramatically reintensified from 0000 UTC through 1500 UTC 19
August 2007 over western Oklahoma which is approximately 500 miles inland from the
Gulf of Mexico (see Fig. 1 (a)). It reached its peak intensity between 0600 UTC and 1200
UTC. Fig. 1 (b) shows the lowest sea level pressure measured by the Oklahoma mesonet
site and Fig. 1 (c) shows the mean value of sea level pressure of all mesonet observation.
The minimum value of sea level pressure recorded by these mesonet sites was near 999
hPa at 0725 UTC while the lowest average value was near 1009 hPa between 0800 UTC
to 1100 UTC. During 0900 and 1300 UTC, an eye-like feature can be clearly indentified
in WSR-88D radar imagery. However, this episode was short-lived and the eye-like
feature dissipated around 1300 UTC. After 1800 UTC, Erin degenerated into a remnant
low pressure area as the circulation dissipated over northeastern Oklahoma.
All the experiments were initialized with the NAM background from the 0000 UTC
19 Aug 2007 and ended at 1800 UTC 19 Aug 2007. The experiments with data
assimilation were started from 0000 UTC with radar data assimilated every 10 minutes
for 2 hours long. The model domain is 881x881x41 grids with horizontal space resolution
3km. The Noah land-surface model was employed and the cumulus parameterization was
turned off in WRF (Weather Research and Forecast) forecast. The model microphysical
scheme was depended on the cloud analysis option applied in the GSI.
Tabel. 1 lists the experiments for testing the configuration in GSI and also the
experiments for examining the impact of different parts of radar data on the short range
precipitation forecast. Experiment start from the 0000 UTC without the data assimilation
was named as ‘CTR00’. Experiment with both radar radial winds and radar reflectivity
data assimilated is named as ‘CTRRAD’. ‘CTRRAD10’ means the horizontal decorrelation scale used in GSI was 10 times larger than the ‘CTRRAD’.
And the
‘CTRFER’ denotes the Ferrier microphysical scheme is chosen for retrieving the
hydrometeors fields from the radar reflectivity in the cloud analysis procedure in GSI.
Experiment with only superobed radar radial winds assimilated by three dimensional
variation (3DVAR) package of GSI is named as ‘VEL’. And ‘REF’ represents
experiments with only radar reflectivity data assimilated. This kind of three dimensional
mosaic reflectivity data was produced by the National Serve Storm Laboratory (NSSL).
3. Configuration test
In this section, two key parameters: horizontal de-correlation scale factor for
determining the radar radial winds error space distribution in the 3DVAR procedure and
the cloud analysis option for retrieving the hydrometeors like rain, snow and hail from
reflectivity were examined. Comparison between different groups of horizontal decorrelation scale factors has been made. The analyzed fields were remapped to radar
coordinate through the radar emulator and verified against the radar observation in the
same elevation angle. Three different cloud analysis approaches available in the current
GSI were introduced. Detail quantity analysis was described below.
a. The configuration for radar radial winds
The background error covariance and its correlation scale are two of the main factors
in obtaining reasonable analyzed fields. In GSI, the initial values of the background error
covariance and its correlation scale were given by the statistic results of North American
Mesoscale Model (NAM). Both can be rescaled through the parameters in the GSI.
Traditional observation like the surface or the sounding observation may represent the
prosperities of synoptic scale weather system while the radar data observation may reveal
cloud scale characteristic for the local convective system. The former should have the
influence radius over several hundred kilometers and the latter may only affect the nearby
grids. For this study, the sensitive of radar radial winds to the horizontal de-correlation
scale factor was illustrated.
In GSI, the statistical background error covariance and its correlation scale are the
function of latitude and height. The one adopted by the experiments in this paper was
ranged from have 2.5 oS to 89.5 oN with horizontal space resolution of 1 deg and 60
levels for vertical. The observation innovation together with the background error
covariance structure was spread through the recursive filter. GSI employs four-degree
recursive filter three times in horizontal with influence radius increased for each loop and
single time in vertical. Fig. 2 (a), (c) and (e) show the analysis results of three groups
horizontal de-correlation scale factors (named ‘hzscl’ below) for a single-point xcomponent wind analysis. 5m/s observation increment was introduced at 700 hPa level
over the Erin’s track center of 0600 UTC. When hzscl=0.006, 0.012, 0.024, the actual
influence radius plotted in the Fig. 2 (a) was approximate 4 grids.
When these
parameters enlarge for ten times, the influence radius was extended to 20 grids or so (see
Fig. 2 (c)). The adoption of the same configuration as the current RR setting for the
traditional observation hzscl=0.373, 0.746, 1.5 is obviously too large for the assimilation
of radar radial winds (see Fig. 2 (e)).
Fig. 2 (b), (d) and (f) depict the single-time analysis of four Doppler Radars radial
winds using the hzscl as (a), (c) and (e) respectively at 0600 UTC 19 Aug 2007. With
influence radius no more than 4 grids, the smallest group parameters of hzscl was able to
keep some small scale information like convergence of the wind fields (see the red line in
Fig. 2 (b)). The maximum wind vector speed for this analysis is 39.5 m/s. Usage of larger
value of hzscl, spread the increment within a far range, over-smooth the cloud scale
information. The analyzed wind fields come out much smoother with large circulation.
The analyzed maximum wind vector speed is 33.9 m/s and 27.6 m/s for the middle and
largest parameters. The maximum value decreased significantly when the horizontal decorrelation scale factor increased. Notice the increments outline for a single-point test is
not a standard circle. That was due to the map projection of the model domain. The
recursive filter in GSI uses the large-circle distance of earth as the cut of radius of decorrelation scale.
To better distinguish the difference between the observation and assimilation results,
the simulated radar radial winds at elevation angle of 0.38o through the radar emulator
was plotted in Fig. 3. The center point location is as the KTLX. With several maximum
centers scattered in the positive speed region, the observation looks much noise (Fig. 3
(a)) when compared to the NAM background (Fig. 3 (b)). The latter appears smooth with
a single extreme value center. The observed minimum and maximum radial winds speed
was -31.5m/s and 32.5m/s. Obviously, with minimum -23.4m/s and maximum 25.8m/s
the NAM background underestimates the radial winds. The assimilation of radar radial
winds with smallest configuration as Fig. 2 (a) increase the absolute value, the analyzed
minimum and maximum radial speed is -27.82 m/s and 27.80m/s respectively. And
meantime, the simulated radial winds profile looks more similar with the observation
especially in the boundary area. The assimilation employing the middle parameters of
hzscl as Fig. 2 (c) filters out the center of maximum radial winds in the positive speed
area. While the configuration used for traditional data was used, the general pattern
surrounding the center of KTLX was changed a lot.
RMSE against the observation was calculated to better determine the value of hzscl.
And RMSE against the NAM was computed to see the impact of different configurations.
RMSEobs 
RMSEnam 
n
 (x  o )
i 1
i
2
i
/n
n
 ( x  xb )
i 1
i
i
2
/n
Where the xi represents the simulated radar radial winds, xbi denotes the simulated results
using NAM background as environment for the radar emulator and oi is the observed
radar radial winds. The RMSEobs for the NAM background ground is 3.9589m/s and
3.6388m/s after assimilation of radar radial winds using the smallest hzscl. When the
same setting as the traditional data was adopted, RMSEobs is 5.4021m/s. The RMSEnam is
1.7403m/s, 2.2987m/s and 2.8445m/s for the hzscl of Fig. 2 (a), (c) and (e) respectively.
The bigger value of hzscl means farther influence radius and the increment of local wind
vectors will be spread to more surrounding grids through the recursive filter. Therefore,
the RMSEnam is largest when biggest value of hzscl was employed. Since the radar radial
winds represent the small scale weather system, it may not be reasonable for larger value
of hzscl. In this paper, we chose hzscl=0.006, 0.012, 0.024 as the default value for radial
winds. The comparison of forecast results with different hzscl will be present in the next
section.
b. The different microphysical analysis approaches for retrieving hydrometeors from
reflectivity in GSI
Before retrieving hydrometeors from the reflectivity, precipitation types were first
classified on the basis of the grid reflectivity (GREF below) and wet-bulb temperature
(Tw below). In GSI, it is categorized into six types: ‘No rain’ if GREF is below 0 dbz;
‘rain’ if Tw >=1.3 oC; if 0.0 oC <Tw <1.3 oC, it takes the value of nearest up-level
precipitation type; if Tw is below 0.0 oC , it defined as ‘snow’ or ‘freezing rain’ or ‘sleet’
depending on the nearest up-level precipitation type; the precipitation type is further
updated to ‘hail’ when GREF is larger than 50 dbz.
After that, the mixing ratio of hydrometeors material ‘rain’, ‘snow’ and ‘hail’ are
calculated from the different reflectivity factor equations depending on the precipitation
type and environment temperature. Tabel. 3 lists three available options: Thompson
(Thompson et al. 2004), Ferrier (Ferrier 1994; Ferrier et al. 1995) and KRY (Kessler
1969; Rogers and Yau 1989) for retrieving the hydrometeors field in the current GSI
cloud analysis package.
The KRY method was empirical warm-rain theory While
Thompson and Ferrier were semi-empirical microphysical scheme. The calculation in the
KRY option is simple: if the precipitation type classified as rain or freezing rain, the
mixing ratio of rain water will be retrieved from the formula Z r listed in KRY column in
Table.3; if the precipitation type classified as snow, the mixing ratio of snow will be
retrieved from the formula Z s listed in the KRY column in Tabel. 3; if the precipitation
type classified as sleet or hail, the mixing ratio of hail will be retrieved from the formula
Z h listed in KRY column in Tabel. 3.
On the other hands, the calculation for the Ferrier option is much more complicated.
Not only the precipitation type but also the grid temperature is considered. If the
precipitation type is rain or freezing rain, it retrieves the rain water mixing ratio using
equation Ferrier’s Z r in the Tabel. 3. If the precipitation type is snow, when the grid
temperature (T below) is below 0 oC, it retrieved the snow mixing ratio (calculated from
dry snow formula) using equation Ferrier’s Z s in the Tabel. 3; when T is between 0 oC
and 5.0 oC, it divided the reflectivity into the contribution of snow and rain, and then the
mixing ratio of snow (calculated from wet snow formula) and rain will be calculated from
the corresponding equations; when T is above 5.0 oC, only rain water mixing ratio are
retrieved. If the precipitation type is sleet, when T is below 0 oC, it retrieved the hail
mixing ratio using equation Ferrier’s Z h in the Table.3; when T is between 0 oC and 10.0
o
C, it divided the reflectivity into the contribution of hail and rain, and then the mixing
ratio of hail and rain will be computed from the corresponding equations; when T is
above 10.0 oC, only rain water mixing ratio are retrieved. When the precipitation is
unknown, the procedure was treated as the precipitation type of snow. Both the KRY and
Ferrier methods are calculated in the region of grid reflectivity above 0dbz. The rests of
the domain are set to the missing value. The calculation in Thompson is similar to Ferrier
but using different reflectivity factor equation to retrieve the hydrometeors. And the
threshold used for Thompson is 10dbz, that is to say the calculation is limited in the
region of grid reflectivity above 10 dbz.
Fig. 4 plots retrieved hydrometeors material based on the different reflectivity factor
equations. For fair comparison, the minimum reflectivity value was given as 10dbz for
the rain, snow and 50dbz for hail. And if Thompson scheme was employed, the mixing
ratio of snow is also a function of temperature when below zero point. The snow mixing
ratio retrieved from dry snow increased as temperature decrease. We set -5 oC for this
comparison. The curve indicates the retrieved mixing ratio of hydrometeors fields from
Thompson scheme have the largest value of all. The retrieved mixing ratio of rain, hail
and wet snow from KRY is larger than from Ferrier. But Ferrier has larger retrieved
mixing ratio of snow value than KRY. When grid reflectivity is 10dbz, the retrieved
value of rain water mixing ratio is 0.076 g/kg, 0.010 g/kg and 0.011 g/kg for the
Thompson, Ferrier and KRY respectively. When grid reflectivity is 50dbz, the retrieved
value of rain water mixing ratio is 2.85 g/kg, 1.92g/kg and 2.11g/kg for each option; and
is 4.48g/kg, 4.11g/kg and 1.20 g/kg if calculated from dry snow equation and is 3.47g/kg,
0.13 g/kg and 1.20 g/kg if calculated from the wet snow equation. The retrieved value of
hail mixing ratio is 1.59 g/kg, 0.26 g/kg and 1.20 g/kg for each option. And when the grid
reflectivity is 75 dbz, the retrieved value of hail mixing ratio is 16.87 g/kg, 8.17 g/kg and
16.4 g/kg. In the following section, the forecast result using the retrieved formula of
Thompson or Ferrier will be presented.
4. Results/verification
In this study, the NCEP 4-km gridded Stage IV precipitation data are used as
observation. The forecasted hourly rainfall with part of radar data and with full radar data
assimilation is verified against the Stage IV data. The performance of multiple Doppler
radar data on the short range precipitation forecast is presented. And the forecast results
employing different configuration mentioned in the above section are briefly described.
Two verification methods in the MET software are applied and discussed.
a. The forecasted results
Erin was an asymmetric with its main precipitation dropped in the southeast part of
the system. At 0950 UTC, radar reflectivity observations displayed the first appearance of
an eye like feature (not show here). At 1200 UTC, this eye like features can still be
clearly identified in the radar map (see first row of Fig. 5). After that, the eye expanded in
size and began to dissipate. Experiment ‘CTR00’ started from 0000 UTC without data
assimilation fails to forecast the eye like features (see second row of Fig. 5). The forecast
reflectivity region slanted to the Oklahoma south boundary when compared with the
observation. At 1800 UTC, the forecasted reflectivity was situated in the west boundary
of the observation which indicates the forecasted storm was moving a little bit slow. At
0600 UTC and 0900 UTC, the angle of forecasted reflectivity y-axes was rotated to the
south-to-north after the radar radial winds assimilated (see third row of Fig. 5). Although
the ‘VEL’ unable to predict the eye like features, the bending structure at 1200 UTC was
well depicted. The simulated storm was heading east faster than the one without data
assimilation (see the third row of Fig.5 at 1500 UTC). When only reflectivity assimilated,
an eye like feature could be identified at 1200 UTC (see the fourth row of Fig. 5).
However, the simulated eye is larger than radar observed. Without the help of radial
winds, the forecasted reflectivity of ‘REF’ was unable to form the continuous spiral
structure but with many isolated storm scattered in and around the main precipitation
object. The shape at 0600 UTC is mostly similar to the observation with several tails
extended from the main body. But the forecasted object is larger in size when compared
to the observation. With both type of radar data assimilated, the experiments ‘CTRRAD’
successfully captured the eye like feature of the storm (see the fifth row of Fig. 5). The
forecasted reflectivity spiral characteristic is much more continuous and compact than the
‘REF’. And forecasted reflectivity outline at 1500 UTC was significantly improved. At
1800 UTC, the forecasted storm of ‘CTRRAD’ is closest to the observation among all the
experiments tested in this study.
As stated earlier, the forecasted result of experiments ‘CTRRAD10’ and ‘CTRFER’
were presented. The former uses almost the same configuration as ‘CTRRAD’ but with
horizontal de-correlation scale factor enlarged for 10 times during the 3DVAR procedure
of GSI. As ‘CTRRAD’, the later employs the Ferrier instead of Thompson option to
retrieve the hydrometers fields from reflectivity during the cloud analysis procedure of
GSI. And the microphysical scheme adopted in the WRF integration was changed to the
Ferrier scheme. The analyzed results in the above section shows using the parameters of
Fig. 2 (c) may over-smooth small scale information within the radial winds and further
reduce the radial winds impact on the forecast. Since the analyzed quantity of mixing
ratio of rain, snow and hail is much smaller than the Thompson option, the forecasted
storm intensity was expected to be weaker than the experiment ‘CTRRAD’. At 1200
UTC, the simulated results for both experiments have no eye like features. On the
contrary, with the larger horizontal de-correlation scale, the impact of radar radial wind
seems a little bit delay. At 1800 UTC, ‘CTRRAD10’ displayed an eye like circulation.
Fig. 6 (a) shows the predicted minimum mean sea leave pressure for all the
experiments except the ‘CTRRAD10’. The NHC best track data were chosen as the
observation. The plot starting point is 0600 UTC which is 4 hours forecast for the
experiments with radar data assimilation and 6 hours forecast for the experiment without
data assimilation. The Erin’s best track data for the minimum mean sea level pressure
was obtained from the mesonet observation: ‘…An Oklahoma Mesonet site located seven
miles west of Watonga (about 50 n mi northwest of Oklahoma City), reported sustained
winds (5-minute average) of 47 kt near 0725 UTC, with sustained winds of gale force
occurring there much of the time between 0600 and 0800 UTC. Also, at 0725 UTC, this
station measured a surface pressure estimated to be equivalent to 999 mb at sea level, so
the minimum central pressure was likely lower than that observation and is set to 995 mb
at 0600 UTC in the best track…. ‘.At 0600UTC, the WATO site was located north-toeast of the Erin’s tropical storm center. Since the best track was given at 6 hours interval,
the mean sea level pressure for this assumption was reasonable. Fig. 1 (b) and (c) draw
the minimum mean sea level pressure and average value of mean sea level pressure for
all the Oklahoma mesonet sites respectively. The time frequency is 5 minutes. As
described in the NHC tropical storm Erin’s report, the lowest mean sea level pressure
measured by the mesonet site during the reintensification process was ~999mb at
0725UTC. However, the minimum average value of mean sea level pressure was found
between 0900 UTC to 1200 UTC which indicates the storm reaches its peak intensity
among 0900 UTC to 1200 UTC. The average value of mean sea level pressure is 1010.4
hPa at 0600 UTC and is 1009.8 at 1200 UTC. Therefore, the center pressure tendency of
Erin should drop from 0600 UTC to 1200 UTC and reach its peak intensity between 0900
UTC to 1200 UTC. This deduction could be further illustrated by the radar reflectivity
observation. As mentioned above, the radar observation first displayed eye like feature at
0950 UTC. At 1200 UTC, this eye like feature could still be clearly identified through the
radar map.
Among all the experiments, the ‘CTRRAD’ with radial winds assimilated and with
reflectivity analyzed through Thompson option and using Thompson microphysical
scheme during the WRF integration have gotten the peak intensity. ‘CTRFER’ which
employed Ferrier methods for retrieving the hydrometeor fields and uses Ferrier
microphysical scheme in the model forecast is obviously weaker than ‘CTRRAD’.
Experiment ‘CTR00’ started from 0000 UTC without any data assimilation
underestimated the intensity. Assimilation of radar radial winds strengthened the intensity
of the storm a little bit but did not reach the intensity as the observation. The assimilation
of reflectivity significantly decreases the mean sea level pressure with the average
reduction of 9hPa when compared to the ‘CTR00’. The contribution of radar radial winds
to the intensity is smaller with 0.5 hPa on average. And when both data assimilated, the
mean sea level pressure was dropped about 12hPa on average. Based on the analyzed
results in the above paragraph, the observed mean sea level pressure will be probably
lower at 1200 UTC than 0600 UTC. Therefore, the forecasted intensity error at 1200
UTC should be no more than 5 hPa.
The forecasted tracks and track errors together with best track data were depicted in
the Fig. 6 (b). The best track was plotted every 6 hours from the 0000UTC to 1800 UTC
with dashed line between 0000 UTC to 0600 UTC. All the forecasts were plotted with 3
hours interval but start from 0600 UTC. The predicted storm moving speed was slower
than the observation. At 0600 UTC, four hours (six for the ‘CTR00’) forecasted track
errors is 107.6km, 136.9km, 87.7km, 112.9km and 89.2611km for experiments ‘CTR00’,
‘REF’, ‘VEL’, ‘CTRRAD’ and ‘CTRFER’ respectively. The track of experiment
‘CTR00’ without any data assimilation was far too north when compared with the
observation. The assimilation of radial winds drives the system closer to the observation.
The track errors were reduced ~20km at 0600 UTC. The assimilation of radar reflectivity
data only, however, over-drives the system to the Oklahoma south boundary. The track
error of ‘REF’ was 49.2km larger than ‘VEL’. With the help of radial winds, the
predicted storm center was moved upwards and the track error of ‘CTRRAD’ was
corrected for about 34km. The power for dragging the system to the southeast may due
to southeast location of precipitation region in the Erin. The assimilation of reflectivity
not only introduced the hydrometeors fields which help to reduce the spin up time for the
precipitation, but also brought plenty moisture in that area.
The assimilation of radar data accelerates the storm moving speed. During 0600
UTC to 1200 UTC, the observed storm center was moved to northeast for about 99.5km
while the experiments ‘CTR00’, ‘REF’, ‘VEL’, ‘CTRRAD’ and ‘CTRFER’ are 73.4km,
130.5km, 123.5km, 152.6km and 99.3km respectively. Among all the experiments, the
experiment ‘CTRRAD’ was moving fastest. At 1200 UTC, the ‘CTRRAD’ predicted
storm center was very closer to the observation with only about 38.3km. This was
minimum track error among all the experiments during the forecast. After that, the
predicted storm moved across the observation path and continued to head northeast. The
16 hours track errors for the ‘CTRRAD’ was 65.9km.
b. Applied the neighborhood method to the precipitation verification
Precipitation verification is helpful for identifying the impact of different kinds of
observation on the short range forecast. Traditional point-to-point based verification may
get lower value when the predicted system have position deflection. The neighborhood
verification method which computes matched point within a range can reduce the
displacement errors in a measure. The formulas of verification scores used in this study
are listed below.
PODY 
n10
n
n11
n
n11
 11 , FAR 
 10 , CSI 
n11  n01 n.1
n11  n10  n01
n11  n10 n1.
Where the counts n11, n10, n01, and n00 denotes “Hits”, “False alarms”, “Misses”, and
“Correct rejections” respectively. Details of how to calculate the counts using the
neighborhood method of each point can be found in (Ebert 2008) .
Fig. 7 (a)-(f) show the six hour accumulated rainfall from 0600 UTC to 1200 UTC
and (g)-(h) plot the corresponding verification scores. The forecasted six hours
accumulated extreme value center of ‘CTR00’ is southerly to the observation. The
assimilation of reflectivity data, with the help of retrieved hydrometeor fields rain, snow
and hail, correct the maximum rainfall center. However, it introduces fake rain cluster
surrounding the heavy rain center. This leads to higher FAR (false alarm rate, a perfect
forecast would have value 0) value of ‘REF’ when compared with the ‘CTR00’. The
assimilation of radial winds data, on the other hands, help the system to be well organized
and further improve the structure. The outline of precipitation area is mostly similar to
the observation. When lower threshold 5mm was adopted, the ‘VEL’ with improvement
in the structure forecast and with clean forecast, got the highest CSI (Critical Success
Index, also named as Threat Score, a perfect forecast would have value 1) score. But
without the reflectivity data, the predicted heavy rain center is like the ‘CTR00’. This
caused the CSI drops relatively when higher threshold was employed. The experiment
‘CTRRAD’ with both type radar data assimilated is able to depict the heavy rain center
successfully. However, similar to the experiment ‘REF’, the ‘CTRRAD’ have higher
FAR value and lower CSI score when compared with the experiments with reflectivity
data excluded. When higher threshold 50mm was used, the PODY (Probability of
Detection Yes, a perfect forecast would have value 1) drops rapidly for all the
experiments except for the ‘CTRARD’. Although the false alarm rate is obviously higher
than ‘VEL’, the computed CSI score is approaching the ‘VEL’. Experiment ‘CTRFER’
which uses the Ferrier option to retrieve hydrometer fields and employs the Ferrier
microphysical scheme in the model forecast performs slightly better than ‘CTR00’ when
higher threshold was applied. In all, when lower threshold was used, the experiments
with reflectivity assimilated, got relatively lower scores. Experiment without any data
assimilation, performs better than the form. Experiment with radial winds assimilated,
perform best in this test. When higher threshold was employed, experiments ‘CTRRAD’
with better heavy rain center location forecast and less false alarm rates, is ranked second
among all the experiments. The ‘VEL’ performs best based on the CSI scores.
Erin’s asymmetric characteristic is reflected by the observed rain structure. A small
eye like feature can be spot in the six hour accumulated rainfall map between 1200 UTC
to 1800 UTC (see the arrow point in the Fig. 8 (a)). The precipitation region is located
southeast part of Erin. Among all the experiments, although the predicted eye is wider in
size and located southeast to the observation, ‘CTRRAD’ is the only one experiment
simulated the eye like feature. In addition, ‘CTRRAD’ successfully predicted two
extreme value centers with slightly angle errors. When lower threshold was adopted,
similar to the verification results between 0600 to 1200 UTC, the ‘VEL’ which have
lowest FAR value, got the highest CSI scores.
Unlike the big difference between
‘CTR00’ and ‘CTRRAD’ in Fig. 7, the CSI scores are closer for these two experiments.
The evidence of radial winds improve the precipitation structure forecast could also be
found during this period. The ‘VEL’ successfully predicted the two heavy rain centers but
with narrow band in the east-west direction which may due to the slow movement of the
simulated precipitation system (see the track analyzed results above). Without the help of
radial winds, the predicted system of ‘REF’ is loose and one of the extreme centers even
entered the TEXAS which is southern of Oklahoma. When high threshold was employed,
the ‘CTRRAD’ got the highest CSI score. The ‘VEL’ perform slightly better than
‘CTRFER’.
We further look into the hourly verification scores of CSI to see the performance of
different experiments and also the sensitivity of CSI score to the neighborhood width.
The threshold used in the hourly verification is lower than the six hour accumulated
rainfall. As expected, when lower threshold 1.25mm employed, the CSI score curve line
of experiment ‘VEL’ is above all other experiments except the last two hours forecast.
This may due to the rapid dissipation of the predicted system in ‘VEL’.
The
improvement of radial winds to the forecast is significantly when compared without any
data assimilation. Experiments ‘REF’ and ‘CTRRAD’ with reflectivity data assimilated
have the same behaviors in the first few hours forecast. However, with the increase of
display errors and the fade of impact from reflectivity, the CSI scores of ‘REF’ decreased
while the verification scores of ‘CTRRAD’ is stable and even goes up slightly. Although
the experiment ‘CTR00’ almost failed to predict the structure of Erin, with relatively
clean forecast, is perform better than ‘CTRRAD’ in most of the time.
The increase of neighborhood width is helpful if the forecast system is mis-displaced
within the range of influence radius or if the forecasted system matches the observation
with extension in boundary. For the lower threshold 1.25mm, the increase of
neighborhood width up to 25 grid points in this set of tests increase the CSI value for all
the experiments. Between 0600UTC to 0900 UTC, the increment of experiments with
reflectivity assimilated is larger than without reflectivity data. This may indicated the
forecast system is larger than the observation. The extension of neighborhood width
reduces the size error in some aspects. Among all the experiments, the CTRRAD is most
sensitivity to the neighborhood width with the average increment 0.0672 in CSI value.
The rest are 0.0274, 0.0434, 0.0499 and 0.0622 for ‘CTR00’, ‘REF’, ‘VEL’ and
‘CTRFER’ respectively. The ‘CTR00’ with largest displacement error, are not sensitivity
to the neighborhood width. When higher threshold 15mm was employed, the CSI value
drops rapidly. On the contrary, the increase of neighborhood width decreases the CSI
value in most of the time. In the test, we take ‘conv_thresh=0.5’, which means the
computational of ‘Yes’ of each point requires at least half of 25x25 surrounding grid
points larger than 15mm. With higher threshold, the isolated object is small in size. When
the system have no more than half of 25x25 grid points in space, there are no ‘Hits’ point.
The CSI would have the value of 0. And this explain why when the neighborhood width
extended, the CSI value are 0 after 1500 UTC for all the cases. Therefore, in order to get
reasonable scores using the neighborhood verification method, the neighborhood width
needs to be specified properly. Not only the distances, but also the area of the forecast
and observed system for a given threshold should be considered.
c. Applied the Objected-based method to the precipitation verification
The neighborhood verification method is meaningful when the forecasts are similar to
each other but with deviation in intensity or position. However, it cannot distinguish the
shape difference between different forecasts. The CSI scores calculated from the
neighborhood method shows the ‘CTR00’ is better than ‘CTRRAD’ in most of the time
even when larger threshold was applied. The main reason for that is higher false alarm
rate for the ‘CTRRAD’. Clearly, the ‘CTRRAD’ have better structure forecast through a
side-to-side comparison between the observed and forecasted reflectivity (see Fig. 5).
Well predicted eye like features are essential for a successful forecast in this tropical
storm Erin case. To better describe the outline of the forecasts and distinguish the
structure difference among the experiments, the object-based verification approach was
introduced. The total interest calculated from varies resolved and matched object
properties were used to illustrate the similarity between forecast and observation.
The approach for resolving the rain system objects are described more detail in
(Davis et al. 2006a; Davis et al. 2006b). Simple introduction are presented here. There
are general two steps: convolution and thresholding. The raw data were first convoluted
using a simple filter function followed by the thresholding process. After the objects were
identified, the original rainfall values were restored to the isolated objects. Fig. 10 shows
an example of the MODE resolved objects of experiment ‘CTRRAD’ and Stage IV
precipitation valid at 1100 UTC. There are total 9 isolated objects for the forecast and 1
for the observation. Blue color in the forecast column means the object does not match
any objects in the observation column. And the red color is the matched objects. Two
objects in the forecast column were merged together and the convex hull enclose the
objects was plotted. The forecast have similar outline as the observation with a slight
position deflection (see the column of the forecast with observation outline and
observation with forecast outline). But the forecast yields more fake rain region than the
observation.
Fig. 11 plots some properties of MODE resolved objects. The raw data threshold is
taken as 10mm and the convolution threshold is 15mm. Therefore, the light rain area is
not considered in this paragraph. The curvature adopted here is the radius of curvature of
the object defined in terms of third order moments. The observation has larger value of
curvature than the forecast. Since the observed system have bending rain band, the closer
indicates the better of curved structure forecast. Among all the experiments, the
computed curvature of ‘CTRRAD’ is closest to the observation which illustrate the
‘CTRRAD’ have best rain band structure forecast. During 0600 UTC to 1500 UTC, as
seen from the Fig. 5, almost all the experiments except ‘CTRFER’ have overestimated
the precipitation area. These features are enlarged especially when the reflectivity data
are assimilated. After 1500 UTC, the ‘VEL’ due to the dissipation of the forecast system,
the resolved objects is smaller than the observation. The 90th percentiles intensity is
defined as 9% of the object values are above that while 90% are below. This could
represent the intensity of the extreme rainfall center in this case. The ‘CTR00’ and ‘VEL’
have larger 90th percentiles value than the observation while the curves of ‘REF’ and
‘CTRRAD’ lie slightly below. The ‘CTRFER’ underestimates the intensity of the storm.
This could also help to explain the extreme heavy rain center in Fig. 7 and Fig. 8. The
‘CTR00’ and ‘VEL’ have wider dark red area than the observation while the colors for
the rest experiments are lighter.
The intensity and track prediction plays an important role in the tropical storm
forecast. The location of the precipitation area is another key aspect for a successful
forecast especially for the inland flooding case. The connection among centroids of the
resolved and matched objects by the MODE tools could be served as the storm moving
path for this particular purpose. The total interest T ( ) depicted in the Fig. 12 are
calculated from the formula below, more details see the MET’s manual (DTC 2009).
 w C ( ) I ( )
T ( ) 
 w C ( )
i
i
i
i
i
i
i
i
Where  is the vector of vary object attributes (1 ,  2 , 3 ,...,  n ) . Ci is the confidence
map range from 0~1 and is a function of the entire attribute vector (1 ,  2 , 3 ,...,  n ) .
wi is the weight assigned to each attribute.
At 0600 UTC, the center of precipitation area for each experiment was located
southeast to the observation (see Fig. 12 (a)). It differs with the track in Fig. 6 (b). When
the predicted central of Erin is northeast to the observation for the ‘VEL’ and ‘CTR00’,
the precipitation region for these two experiments are located in the southwest-south part
of the system. These lead to the forecasted precipitation centers south to observation. For
the lower threshold, ‘CTRRAD’ starts with larger displacements error 85.7km and ends
with 66.7km. And it reaches the minimum displacement errors 35.3km at 1500 UTC
when the predicted move across the observed path. This error was only 5km bigger than
the lowest position error which is also obtained at that time. The ‘VEL’ with relative
clean forecast, have the lowest distance error 48.9km on average. As the analyzed results
of neighborhood, the total interest curve for ‘VEL’ lies over all other experiments for
most of the time (see Fig. 12 (b)). The performance of ‘CTRRAD’ and ‘REF’ is similar
to each other at the first beginning. As the impact from the reflectivity faded, the
‘CTRRAD’ performs better than ‘REF’. The ‘REF’ due to the largest displacement error,
has lowest interest value on average.
Heavy rain location is extremely important for the inland flooding prediction. To
satisfy that purpose, we upgraded the raw data threshold from 0mmm to 10mm. The
upgrade of threshold significantly reduced the distance error for the ‘CTRRAD’ which
indicates the accurate prediction of heavy rain center. The average displacement error is
no more than 50km with lowest distance error measured 22.7km at 1500 UTC. It can be
seen from the Fig. 12 (c) that the curve line of ‘CTRRAD’ is below all of other
experiments. For the ‘VEL’ and ‘CTR00’, however, the increase of threshold enlarges the
displacement error. The change for the centriod ‘REF’ is obvious with distance errors
from matched observation reduced over 10km on average. Fig. 12 (d) depicts the total
interest of all the experiments against NCEP stage IV. The ‘CTRRAD’ gets the highest
interest value which indicates the forecast system has best similarity as the observation.
Before 1500 UTC, experiment ‘VEL’ is slightly below the ‘CTRRAD’. The rapid growth
of displacement error between 1500 UTC to 1800 UTC causes the total interest value
declined rapidly. The ‘CTRFER’ is ranked third on average. For most of the time, ‘REF’
lies above ‘CTR00’.
5. Summary
In this paper, the inland reintensification tropical storm Erin was chosen to examine
the performance of multiple-Doppler radar in the GSI data assimilation system. Data
from four Doppler radar located within the Oklahoma state were first qualified and then
superobed to the model resolution. All the experiments with radar data assimilation were
initialized from 0000 UTC Aug 19 2007 using NAM as background. The assimilation
cycle were lasted of two hours long with intermittent assimilation interval of 10 minutes.
Two key parameters: the horizontal de-correlation scale factor for radial wind and the
option for retrieving the hydrometeor field of mixing ratio of rain, snow and hail from the
reflectivity data were tested and analyzed. The analyzed result for the radial winds
suggest influence radius with approximate 3~4 grids are much better than with more than
20 grids or larger. Instead of yielding large increment near the observation point, the
larger horizontal de-correlation scale factor spreads the innovations to wider area and
over-smoothes the small scale information. The smaller horizontal de-correlation scale
factor, however, helps to reserve the storm scale information. This conclusion was further
proved by the forecast results. With 3~4 grids influence radius, the experiment
‘CTRRAD’ was able to depict the eye like features while the experiment ‘CTRRAD10’
with 10 times than the smaller configuration failed to predicted this key characteristic.
The comparison between different retrieve method demonstrate the Thompson have
largest amount of retrieved fields of rain, snow and hail. The KRY option retrieved rain
and hail are larger than the Ferrier method. The retrieved snow from Ferrier is higher than
KRY only when the observed reflectivity is over 40dbz. The Thompson and Ferrier
option were further examined through intermittent data assimilation. The Thompson
approach performs much better than Ferrier in this tropical storm case.
We also examine the impact of different part of radar data for the short range
precipitation forecast. With local wind circulation information included by the multiple
radars, the assimilation of radar radial wind enhances the convergence and divergence in
the storm developing area and further improves the model storm scale circulation to a
certain extent. This feature could be reflected by the side-to-side comparison of
forecasted 3km height reflectivity between the experiments with and without radar radial
winds assimilation. With the radar radial winds assimilated, the experiment ‘VEL’ was
able to delineate the bending structure much better than the ‘CTR00’. On the other hand,
the assimilation of reflectivity, since it introduced the rain, snow and hail field to the
model environment, reduces the spin up time for the precipitation formation process and
further improves the heavy rain center forecast. The six hour accumulated rainfall from
0600 UTC to 1200 UTC (4 to 10 hours forecast) suggests that the assimilation of
reflectivity data corrects the heavy rain center to the north. The assimilation of both radar
radial wind and reflectivity has best performance. Not only does it have the lowest track
errors on average, but also does it successfully predict the eye like features. In addition,
the six hour accumulated rainfall from 0600 UTC to 1200 UTC demonstrates the
‘CTRRAD’ have the best location of heavy rain region. Ignoring the phase error, the
predicted outline of six hour accumulated rainfall of ‘CTRRAD’ is most similar among
all the experiments when compared with the observation during the 1200 UTC to 1800
UTC. The ‘CTRRAD’ is the only experiment that delineates the eye like feature during
that time period.
The NCEP Stage IV data was used as the observation. And the neighborhood
verification method together with the object-oriented approach within the MET was used
to verify the impact of different part of radar data in the short range quantitative
precipitation forecast. The verification score of CSI computed from the neighborhood
method shows the assimilation of radar radial wind (VEL) significantly improves the
forecast skill. The assimilation of reflectivity data, however, performs worse than the
‘CTR00’. That result could be acceptable to a certain degree since the assimilation of
reflectivity data only introduced too much fake rain outside the main precipitation body.
Although the assimilation of both type of radar data (CTRRAD) shows the best structure
and lowest track errors and so on, the CSI score for the lower threshold shows the
‘CTRRAD’ perform slightly better than the ‘REF’ but worse than the ‘CTR00’. During
0600 UTC to 1200 UTC, when higher threshold were adopted, the CSI scores of six hour
accumulated rainfall for the ‘CTRRAD’ are higher than the ‘CTR00’ as expected but
lower than ‘VEL’. The CSI scores for the same threshold suggest the ‘CTRRAD’ are
slightly better than ‘VEL’ between 1200 UTC to 1800 UTC. The hourly verification CSI
scores suggest the ‘CTR00’ have better forecast skills than the ‘CTRRAD’ even when the
higher threshold was applied. The neighborhood verification method which verifying
each point within a range can reduce the impact of displacement error to the verification
scores a bit. Since it does not consider the shape difference between two verifying objects,
it shows the experiment with clean system but with worse structure are better than the
experiment with better structure forecast.
To better understanding the verification method and describing good or bad forecast
among experiments with obvious structure difference, the object-based verification
approach was employed in this study. Several object properties including the curvature,
area and 90th percentiles intensity were calculated from the resolved objects.
The
curvature suggests the ‘CTRRAD’ were successful in the rain band bending structure
forecast. The intensity helps to explain the extreme heavy rain center of experiments
‘VEL’ and ‘CTR00’. The storm moving path depicted from the centriod of the resolved
objects could be used as the track for the storm precipitation area. This could be useful
especially for the identification of heavy rain center of the inland flooding case. The
storm moving path indicates the ‘CTRRAD’ have the best precipitation location forecast
for the heavy rain area. The average distance error is no more than 50km and the lowest
value is 22.7km. The total interest computed from the different attributes of the resolved
and matched objects can represent the similarity between the forecast and observation.
The total interest calculated in this case suggests that the ‘CTRRAD’ is obviously better
than ‘VEL’ and ‘CTR00’. The ‘CTRRAD’ have the best structure forecast based on this
investigation.
Acknowledgments. This work was primarily supported by DOT-FAA grant
NA17RJ1227 through NOAA. M. Xue was also supported by NSF grants…..
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List of figures
Fig. 1 (a) Best track of Erin when moving across the Oklahoma state, Oklahoma mesonet
sites distribution and four Doppler Radars location in Oklahoma. (b) The minimum sea
level pressure and (c) the average sea level pressure of all the mesonet sites.
Fig. 2 (a) single-point experiment with the observation of x-component increment of 5
m/s introduced at 700 hPa. (horizontal de-correlation scale) hzscl=0.006,0.012,0.024. (c)
and (e) the same as (a) but with hzscl=0.06,0.12,0.24 and hzscl= 0.373,0.746,1.5
respectively. Real time four Doppler Radars data analysis at 06 UTC 19 Aug, 2007 (b), (d)
and (f) using the same hzscl as (a), (c), (e) respectively.
Fig. 3 (a) Observed radar velocity at elevation 0.38o (b) NAM background emulated to
the radar coordinate (c) the analyzed wind fields using the configuration of Fig.2 (a) and
emulated to the radar coordinate as (b). (d) and (e) the same as (c) but using the
configuration of Fig. 2 (c) and (e) respectively.
Fig. 4 different reflectivity factor equations based on Thompson (red), Ferrier (blue) and
KRY (green) microphysical schemes for retrieving mixing ratio of (a) rain (g/kg), (b) hail
(g/kg)and (c) dry snow (g/kg) (d) wet snow (g/kg). Note: the temperature used for the
equation of dry snow in this plot is -5 oC.
Fig. 5 3km-height NSSL radar mosaic reflectivity (first row) from 0600 UTC to 1800
UTC with 3 hours interval (the same below), forecasted reflectivity without data
assimilation (second row), with radar radial winds assimilated (third row), with radar
reflectivity assimilated (fourth row), with both radar radial and reflectivity data
assimilated (fifth row), with both types data assimilated but using the horizontal decorrelation of Fig. 2 (c) (sixth row), with both types data assimilated but using the Ferrier
option to retrieve the hydrometeor fields (last row).
Fig. 6 (a) National Hurricane Center (NHC) observed and model predicted minimum
mean sea level pressure of Erin. Notice the mean sea level observation at 1200 UTC are
doubted, details will be explained in the paper. (b) NHC best track data and predicted
tracks of Erin. The inner small box in the up-right corner of (b) plots the track errors (km).
The best track was plotted at 6 hours interval with the starting point at 0000 UTC and the
predicted track was plotted every 3 hours started from 0600 UTC. Both were ended at
1800 UTC Aug 2007.
Fig. 7 six hour accumulated rainfall between 0600 UTC to 1200 UTC for (a) NCEP Stage
IV 4km grid precipitation data (b)CTR00 (c) REF (d) VEL (e) CTRARD (f) CTRFER. (g)
FAR, PODY, CSI scores against NCEP Stage IV precipitation data with threshold 5mm
(h) with 50mm
Fig. 8 The same as Fig.7 except (h) uses threshold 25mm. And the time period is from
1200 UTC to 1800 UTC.
Fig. 9 Hourly CSI scores against the NCEP Stage IV precipitation. (a) Threshold >=
1.25mm and with 5x5 grid points surrounding each point; (c) Threshold >= 1.25mm and
25x25 grid points; (e) (c) minus (a); (b) Threshold >= 15mm and 5x5 grid points; (d)
Threshold >= 15mm and 25x25 grid points. The convolution threshold is 0.5 for the
neighborhood method.
Fig. 9 Hourly CSI scores against the NCEP Stage IV precipitation. (a) Threshold >=
1.25mm and with 5x5 grid points surrounding each point; (c) Threshold >= 1.25mm and
25x25 grid points; (e) (c) minus (a); (b) Threshold >= 15mm and 5x5 grid points; (d)
Threshold >= 15mm and 25x25 grid points. The convolution threshold is 0.5 for the
neighborhood method.
Fig. 11 MODE resolved objects prosperities (a) curvature (b) rain area and (c) 90
percentiles intensity of forecast and observation. Raw threshold is taken as 0mm and the
convolution threshold is 5mm.
Fig. 12 (a) The storm moving path based on the resolved objects and the small box in the
upright corner is the distance between two matched objects. (b) The interest between the
combined objects of forecast and observation. Raw threshold is taken as 0mm and the
convolution threshold is 5mm. (c) and (d) as (a) and (b) but use 10mm and 15mm
respectively.
List of tables
Tabel. 1 lists of all the experiments
Tabel. 2 statistic results of emulated radial wind verse observed radial wind
Tabel. 3 lists of reflectivity factor equations based on the different microphysical
schemes.
a
b
c
Fig. 1 (a) Best track of Erin when moving across the Oklahoma state, Oklahoma mesonet
sites distribution and four Doppler Radars location in Oklahoma. (b) The minimum sea
level pressure and (c) the average sea level pressure of all the mesonet sites.
a
b
c
d
e
f
Fig. 2 (a) single-point experiment with the observation of x-component increment of 5
m/s introduced at 700 hPa. (horizontal de-correlation scale) hzscl=0.006,0.012,0.024. (c)
and (e) the same as (a) but with hzscl=0.06,0.12,0.24 and hzscl= 0.373,0.746,1.5
respectively. Real time four Doppler Radars data analysis at 06 UTC 19 Aug, 2007 (b), (d)
and (f) using the same hzscl as (a), (c), (e) respectively.
a
b
c
d
e
Fig. 3 (a) Observed radar velocity at elevation 0.38o (b) NAM background emulated to
the radar coordinate (c) the analyzed wind fields using the configuration of Fig.2 (a) and
emulated to the radar coordinate as (b). (d) and (e) the same as (c) but using the
configuration of Fig. 2 (c) and (e) respectively.
a
c
b
d
Fig. 4 different reflectivity factor equations based on Thompson (red), Ferrier (blue) and
KRY (green) microphysical schemes for retrieving mixing ratio of (a) rain (g/kg), (b) hail
(g/kg)and (c) dry snow (g/kg) (d) wet snow (g/kg). Note: the temperature used for the
equation of dry snow in this plot is -5 oC.
Fig. 5 3km-height NSSL radar mosaic reflectivity (first row) from 0600 UTC to 1800
UTC with 3 hours interval (the same below), forecasted reflectivity without data
assimilation (second row), with radar radial winds assimilated (third row), with radar
reflectivity assimilated (fourth row), with both radar radial and reflectivity data
assimilated (fifth row), with both types data assimilated but using the horizontal decorrelation of Fig. 2 (c) (sixth row), with both types data assimilated but using the Ferrier
option to retrieve the hydrometeor fields (last row).
a
?
b
Fig. 6 (a) National Hurricane Center (NHC) observed and model predicted minimum
mean sea level pressure of Erin. Notice the mean sea level observation at 1200 UTC are
doubted, details will be explained in the paper. (b) NHC best track data and predicted
tracks of Erin. The inner small box in the up-right corner of (b) plots the track errors (km).
The best track was plotted at 6 hours interval with the starting point at 0000 UTC and the
predicted track was plotted every 3 hours started from 0600 UTC. Both were ended at
1800 UTC Aug 2007.
a
b
c
d
e
f
g
h
Fig. 7 six hour accumulated rainfall between 0600 UTC to 1200 UTC for (a) NCEP Stage
IV 4km grid precipitation data (b)CTR00 (c) REF (d) VEL (e) CTRARD (f) CTRFER. (g)
FAR, PODY, CSI scores against NCEP Stage IV precipitation data with threshold 5mm
(h) with 50mm
a
b
c
d
e
f
g
h
Fig. 8 The same as Fig.7 except (h) uses threshold 25mm. And the time period is from
1200 UTC to 1800 UTC.
a
b
c
d
e
Fig. 9 Hourly CSI scores against the NCEP Stage IV precipitation. (a) Threshold >=
1.25mm and with 5x5 grid points surrounding each point; (c) Threshold >= 1.25mm and
25x25 grid points; (e) (c) minus (a); (b) Threshold >= 15mm and 5x5 grid points; (d)
Threshold >= 15mm and 25x25 grid points. The convolution threshold is 0.5 for the
neighborhood method.
Fig. 10 Example of MODE isolated objects of CTRRAD and Stage IV within the MET
software valid at 1100 UTC Aug 2007.
a
b
c
Fig. 11 MODE resolved objects prosperities (a) curvature (b) rain area and (c) 90
percentiles intensity of forecast and observation. Raw threshold is taken as 0mm and the
convolution threshold is 5mm.
a
b
c
d
Fig. 12 (a) The storm moving path based on the resolved objects and the small box in the
upright corner is the distance between two matched objects. (b) The interest between the
combined objects of forecast and observation. Raw threshold is taken as 0mm and the
convolution threshold is 5mm. (c) and (d) as (a) and (b) but use 10mm and 15mm
respectively.
Tabel. 1 lists of all the experiments
name
Observation
CTR00
CTRRAD
CTRRAD10
CTRFER
VEL
REF
No
VEL+REF
VEL+REF
VEL+REF
VEL
REF
Microphysical
scheme
Thompson
Thompson
Thompson
Ferrier
Thompson
Thompson
Horizontal decorrelation scale
0.006,0.012,0.024
0.06,0.12,0.24
0.006,0.012,0.024
0.006,0.012,0.024
Tabel. 2 statistic results of emulated radial wind verse observed radial wind
background
nam
namgsi
namgsi10
namgsi60
hzscl
rmse
3.9589
0.006,0.012,0.024 3.6388
0.06,0.12,0.24
3.7411
0.373,0.746,0.15 5.4021
rmsenam
0.0
1.7403
2.2987
2.8445
Absolute bias
2.9374
2.7596
2.8590
4.0147
R
0.9759
0.9786
0.9752
0.9491
Tabel. 3 lists of reflectivity factor equations based on the different microphysical
schemes.
Thompson scheme
Zr 
Zs 
Zh 
Ferrier scheme
1018  720
(  qr )1.75
 1.75  NOr 0.75 r1.75
1018  720  0.224 s 0.25
(  qs )1.75
 1.75  NOs 0.75 r 2

2.4423
1018  720  0.224
(  qh ) 2.4423
1.57 0.75/ 0.52 r 2 h 0.4423
Zr 
KRY scheme
Z r  a(  1000  qr )b
1018  720
1.75
  qr 
1.75
0.75
1.75 
  NOr   r
 1018  720  K 2   s 0.25
1.75
ice

   qs  ,tc  0 oC
2
  1.75  K water  NOs 0.75  i 2
Zs  

1018  720
1.75
  qs  ,0 oC  tc  5 oC
 1.75
0.75
1.75 
   NOs   s


1018  720
Z h   1.75
0.75
1.75 
   NOh  h 
0.95
   qh 
1.6625
Z s  c(  1000  qs ) d
Z h  c(  1000  qh )d
where
where
0.0002  qr
1 9
1
(10  2 107 )  tanh(
)  (109  2 107 )
2
0.0001
2
o

 min  2.0E8, 2.0E6  exp  0.12  t c   , t c  0 C
NOs  

o

2.0E6, t c  0 C
NOr  8.0E+06,NOs  3.0E+06,NOh  4.0E+04
a  17300.0; b  1.75
K ice  0.176, K
c  38000.0; d  2.2
NOr 


2
Where
2
water
 0.93
r  1000,  s  100, i  917, h  913
 r  1000,  s  100,  h  400
Note: the units of mixing ratio of rain qr , snow qs and hail qh is kg/kg