Preliminary
Report on
TRMM[1]LBA
Rainfall Estimation Using the SPOL Radar
L. D. Carey[2], R. Cifelli, W. A.
Petersen, and S. A. Rutledge
Department of Atmospheric
Science
Colorado State University
Fort Collins, CO 80523
1.
Introduction
By measuring the returned power and phase at both
horizontal and vertical polarizations, polarimetric radars provide information
on the drop size distribution, shape, orientation, and thermodynamic phase of
hydrometeors. As a result, polarization
radar techniques afford a more accurate estimate of rainfall than conventional
reflectivitybased radar methods (Zrnic and Ryzhkov, 1999). The presence of the NCAR SPOL radar (10.7
cm, polarimetric) during the LBA (Large Scale BiosphereAtmosphere) field
campaign in Rondonia, Brazil provides the TRMM (Tropical Rainfall Measuring
Mission) validation community with an unprecedented opportunity to accurately
estimate rainfall over a large domain (O 10,000 km^{2}) in a
tropical continental locale.
This report summarizes preliminary progress toward
the estimation of rainfall with the SPOL radar during the LBA field
campaign. In Sec. 2, we highlight key
elements of our data processing and rainfall analysis methodology. In Sec. 3, we describe the available Version
1 (V1) SPOL rainfall products. We then
present a simple comparison between V1 SPOL radar and gauge rainfall
accumulations. In Sec. 4, we summarize
some key scientific results to date.
Finally, we discuss our Version 2 (V2) strategy for improving the SPOL
rainfall estimate and plans for scientific applications of this data. The SPOL radar V1 rainfall products and a
more comprehensive description of our TRMMLBA research can be found at http://radarmet.atmos.colostate.edu/trmm_lba/.
2.
Methodology
a. Data
Processing
The raw SPOL data suffers from the presence of
clearair echo, ground clutter, anomalous propagation, secondtrip echoes,
partial beam blocking, precipitation attenuation, calibration biases, and
gaseous attenuation. Many of these
deleterious effects can be readily seen in the lowlevel PPI summaries provided
by NCAR ATD at http://www.atd.ucar.edu/rsf/TRMMLBA/trmm_intro.htm. Polarization radar data allow novel
approaches to the mitigation of all these problems except the last. For gaseous attenuation, we apply a simple
range correction using an assumed correction coefficient.
As shown by Ryzhkov and Zrnic (1998), thresholds in
the correlation coefficient (r_{hv}) and the variance of the
differential phase (f_{dp}) can be used to remove the
majority of nonmeteorological, clearair returns, ground clutter, secondtrip
echoes, and anomalous propagation.
Based on statistical analyses of the data, we characterized any echo
with r_{hv} > 0.8 and s(F_{dp}) < 12° as hydrometeors. All other echoes were removed.
Additional clear air echo was identified and removed by searching for
anticorrelated pairs of very large Z_{dr} and small Z_{h}. If Z_{h} < 35 dBZ and Z_{dr}
> Z_{drca}(Z_{h}), then the range gate was identified as
clear air and removed where Z_{dr} “clear air” is defined as:
_{}
We then filtered the measured differential phase and
estimated the specific differential phase (K_{dp}) according to the
procedures outlined in Hubbert and Bringi (1995).
Frequent vertical pointing scans during LBA
demonstrated that there was little or no absolute bias (Z_{drbias}<
0.1 dB) in the differential reflectivity (Z_{dr}). For more information, reference the analyses
and discussion by Mr. Bob Rilling (NCARATD) at the following web site, http://www.atd.ucar.edu/rsf/TRMMLBA/quicklook/qa/trmm_zdr_bias.html. As detailed by Scarchilli et al. (1996),
internal consistency between observations of the horizontal reflectivity (Z_{h}),
the differential reflectivity (Z_{dr}), and the specific differential
phase (K_{dp}) can be used to estimate a calibration offset in Z_{h}
if the relative bias in Z_{dr} is known. In this method, K_{dp} is estimated from measurements of
Z_{h} and Z_{dr} as determined by a theoretical
relationship. This estimated K_{dp}
is then compared to the measured K_{dp}. The offset in Z_{h} is varied until the match between
estimated and observed K_{dp} is optimized. Utilizing this procedure, we determined that Z_{h} was
biased by about 0.8 dB (biased 0.8 dB low, see Fig. 1). Dr. Steve Bolen of CSU/EE and Mr. Scott
Ellis and Dr. J. Vivekanandan of NCAR (personal communication, 2000) obtained
similar bias results in the range of –0.3 to –0.75 dB. Since there is some uncertainty in this
methodology (e.g., assumed drop shape) and since the absolute bias was small
(Z_{hbias}< 1 dB, we chose not to apply an engineering bias
correction to the Z_{h} data.
Fig. 1. The differential propagation phase is estimated from the horizontal and differential reflectivity and then plotted against the observed differential propagation phase. The red +’s are prior to any bias correction and the green X’s are after a –0.8 dB correction is applied to the horizontal reflectivity.
a.
b.
Fig. 2. Trend of the (a) horizontal reflectivity and (b) differential reflectivity with the differential propagation phase. The slope of the line in a (b) is the negative of the correction coefficient for horizontal (differential) attenuation. See Carey et al. (2000) for a detailed explanation of the propagation correction procedure. For these plots, we isolated points from 80 hours of data that satisfied 2 £ K_{dp} £ 3° km^{1}.
To correct for propagation effects caused by
precipitation at Sband, we used the procedure outlined by Bringi et al.
(1990), Ryzhkov and Zrnic (1995a), and Carey et al. (2000). As seen in Figs. 2a,b, horizontal
(differential) attenuation correction coefficients can be obtained by analyzing
the trend of Z_{h} (Z_{dr}) with f_{dp}. We obtained the correction coefficients a=0.0145 and b = 0.0042
and applied them according to Carey et al. (2000).
a.
b.
Fig. 3. Plot of the (a) horizontal reflectivity and (b) differential reflectivity as a function of azimuth. The red (blue) points are from the 1^{st} (2^{nd}) tilt of a series of lowlevel PPI’s over 80 hours during twelve different case days for which 1 £ K_{dp} £ 2° km^{1}.
We also identified areas adversely affected by
partial (and occasionally complete) blocking by analyzing the azimuthal trend
of Z_{h} and Z_{dr} that satisfied 1 £ K_{dp} £ 2° km^{1}. Independent of blocking effects, this
threshold in K_{dp} should result in a fixed range of Z_{h} and
Z_{dr} values (as determined by drop size distribution characteristics
and measurement error). As seen in
Figs. 3ab, blocking effects are readily apparent in these plots.
Note the severe
partial (and occasional complete) blocking effects evident in Figs. 3ab from
about 250° to 315° in azimuth (i.e., from WSW to NW).
To avoid biasing V1 rainfall estimates, the differential reflectivity
was masked out of regions with significant blocking and the horizontal
reflectivity was corrected by adding a fixed dB offset as a function of range
(see Fig. 4) if the correction exceeded 1 dB.
If the inferred correction to Z_{h} exceeded 35 dB, then no
correction was applied and Z_{h} in those rays were set to the bad data
flag.
Fig. 4. This plot represents the DZ_{h} correction (dB) for partial blocking as a function of azimuth for the first (red) and second (green) tilts. For V1 processing, the correction was added if it exceeded 1 dB and was less than 35 dB. If DZ_{h} correction > 35 dB, the horizontal reflectivity was not corrected but was set to the bad data flag. If DZ_{h} correction < 1 dB, no correction was made.
The above steps
were accomplished in Universal Format (UF) using FORTRAN code written by Dr.
Lawrence D. Carey and Mr. Paul Hein of CSU Radar Meteorology. The resulting processed data set was output
in UF out to a range of 100 km from the SPOL radar and up to a height of 3.5
km AGL in order to minimize beam spreading and contamination by melting
hydrometeors. For rainfall maps, we
utilized processed UF data from full 360° surveillance scans only, which typically
consisted of only 2 lowlevel tilts at elevation angles of about 0.7° and 1.1°. The
surveillance scans were available approximately every ten minutes. Using the
REORDER software package, these scans were interpolated to a 100 km ´ 100 km horizontal Cartesian grid, centered
on the SPOL radar at a height of 1 km AGL.
The horizontal grid resolution is 2 km x 2 km. Radii of influence for the interpolation process were 1.0 km in
the horizontal and 1.0 km in the vertical.
Although rain maps are available approximately every ten minutes for the
entire operational period of the SPOL radar (10 Jan 99 – 28 Feb 99), around
the clock SPOL radar operations (24 hours per day, 7 days per week) began on
16 January 1999. After this time, the
SPOL radar ran nearly continuously, with only short interruptions until 28 February
1999, 2213 UTC. During 24/7 operations,
there were approximately 3 hours of unplanned and 8 hours of planned down
time. The planned SPOL down times were
always accomplished during convectively quiescent periods.
b. Rainfall
Estimation
Our first efforts were aimed at making a quick
estimate of areal mean rain rates over the SPOL domain. We applied the new polarimetric radar
technique introduced by Ryzhkov et al. (2000) to estimate areal rainfall. The method utilizes values of the
differential propagation phase, f_{dp}, on the areal contour of
the region of interest. In our study, a
series of concentric rings in the SPOL domain out to 120 km were utilized in
the areal integrals found in Ryzhkov et al. (2000). This approach minimized the error associated with assuming a mean
constant rain rate in the integrated range.
These data were used to analyze the time series of rainfall, the diurnal
cycle of rainfall, and the distribution of areal rain rates by meteorological
regime (See Sec. 3).
Reliable point estimates of rain rates for each
radar volume were calculated using an optimization technique with the
parameters Z_{H}, Z_{DR}, and K_{DP} (Jameson, 1991;
Chandrasekar et al. 1993; Carey and Rutledge 1998; Petersen et al. 1999; Carey
and Rutledge, 2000). The rain rate
relation for each grid point is chosen based on thresholds in the above three
polarimetric variables that minimize the rain rate standard error as described
in Fig. 5. In essence, we are
optimizing the rain rate relation for the given microphysical situation and
radar measurement error in the above three variables at each grid point. The rain rate relations for each
polarimetric radar rain rate estimator are shown in Table 1.
Table 1.
Polarimetric radar rain rate estimators^{*}

1. R(K_{dp},
Z_{dr}) = _{} mm h^{1} 
2. R(Z_{h},
Z_{dr}) = _{} mm h^{1} 
3. R(K_{dp})
= _{} mm h^{1} 
4. R(Z_{h})
= _{} mm h^{1} 
* Units: K_{dp}, ° km^{1}; Z_{dr}, dB; and Z_{h}, mm^{6} m^{3}. Equations (1) – (3) were taken from Bringi and Chandrasekar (2000). Equation (4) was derived from TRMMLBA disdrometer data by Dr. Ali Tokay (personal communication, 2000)
Figure 5. Decision tree algorithm used to determine which polarimetric estimator is used to calculate rain rate for a specific grid point using the polarization radar optimization technique. The rain rate estimator equations are shown in Table 1.
3. Version 1
(V1) TRMMLBA SPOL Rainfall Maps
a. Available
products
Areal rain rate estimates were computed over the
TRMMLBA domain using the differential phase method of Ryzhkov et al.
(2000). This effort was completed
during May 2000. Since all surveillance
scans were utilized, the temporal sample is typically every ten minutes or
better. Selected scientific results on
the diurnal cycle and the dependency of areal rainfall statistics on
meteorological regime (i.e., easterly versus westerly lowlevel flow) are
presented in Sec. 4 of this report. A
nearly continuous record of areal rain rate is available from 16 Jan 99 to 28
Feb 99. For those TRMM scientists
interested in these data, please contact the CSU Radar Meteorology Group for a
copy of the ASCII files containing areal rain rates for each Julian day.
Version 1 (V1) SPOL rain maps for the LBA field
campaign were completed during September 2000.
Instantaneous rain map images (GIF format) such as in Fig. 6 are now
available to the public at http://radarmet.atmos.colostate.edu/trmm_lba/rainlba.html
. These rain rate maps were created at
a temporal frequency of about once every ten minutes during the operational
period of the SPOL radar (see Sec. 2 for more details). Daily and monthly rain accumulation map
images, as in Figs. 7 and 8 respectively, will be made available at the same
web site soon. In addition, TRMM
scientists can request rain accumulation maps for any arbitrary time period
lasting over 20 minutes during the LBA field campaign (e.g., specific case study
time interval, weekly, 5day, 30day) by contacting the CSU Radar Meteorology
Group.
Fig. 6. Example of a SPOL V1 instantaneous rain rate (mm h^{1})
map from the 26 January 1999 (2127 UTC) easterly regime MCS case. Instantaneous
rain maps from TRMMLBA
are now available at the CSU Radar
Meteorology web site.
Fig. 7. Example of a SPOL V1 daily rain accumulation (mm) map from 15 Feb 99 (UTC), which was characterized by widespread and occasionally heavy nocturnal rain.
Fig. 8. Example of a SPOL V1 monthly rain accumulation (mm) map for February 1999 (UTC) over the TRMMLBA domain.
Fig. 9. Diagram of the rain gauge network deployed in Rondonia, Brazil for the TRMMLBA field experiment.
b.
Comparison with TRMMLBA rain gauges
In order to evaluate and validate the V1 SPOL radar
rainfall estimates, we performed a simple comparison between the gridded SPOL
radar estimate of rain accumulation and the readings from 33 tipping rain
gauges available within 100 km of the radar for the entire month of February
1999. The 33 rain gauges were located
at the TOGA radar and rain gauge networks # 1, 2, and 3 (Fig. 9). Several of the gauges in network #3 and all
of the gauges in Network #4 were excluded from the comparison because they are
outside of the 100 km radius from SPOL.
Because of known issues in comparing radar and gauge
estimates of rainfall, we utilized three different (yet all simple) techniques
for comparing the gridded (2 km x 2 km) radar data to the gauge accumulations. First, we simply picked the grid point
within a characteristic grid scale length (_{}) of
each rain gauge that most closely matched the corresponding gauge rain total
(optimal method). Second, we utilized
the median SPOL rain estimate with 2.8 km of each gauge (median method). Third, we chose the SPOL rain estimate
physically closest to each gauge (closest method).
Results of the SPOLtogauge rain total comparison
are summarized in Tables 2 and 3. The
SPOL radar rainfall estimate was biased low in the range of 4.8%  11.1%. The standard error of the SPOL rain total
estimate ranged from 14.4% to 20.6%.
These ranges of standard error and bias for polarimetric radartogauge
comparisons are typical (e.g., Ryzhkov and Zrnic, 1995b; Ryzhkov and Zrnic,
1996; Ryzhkov et al., 1997; Bolen et al., 1998; May et al., 1999; Carey et al.,
2000).
Table 2. TRMMLBA: SPOL versus gauge rainfall statistics for February 1999
Statistic 
Gauges 
SPOL Optimal 
SPOL Median 
SPOL Closest 
Count 
33 
33 
33 
33 
Mean 
215.1 mm 
204.8 mm 
192.1 mm 
191.3 mm 
Standard
Deviation 
44.2 mm 
25.5 mm 
26.8 mm 
35.8 mm 
Median 
224.6 mm 
208.3 mm 
198.8 mm 
197.6 mm 
Minimum 
100.1 mm 
143.2 mm 
140.2 mm 
128.0 mm 
Maximum 
360.5 mm 
233.9 mm 
225.2 mm 
228.2 mm 
Table 3. Performance
of the SPOL rainfall estimate relative to rain gauges for February 1999
Method 
NORMALIZED BIAS 
NORMALIZED STANDARD ERROR 
SPOL Optimal 
4.8% 
14.4% 
SPOL Median 
10.7% 
17.9% 
SPOL Closest 
11.1% 
20.6% 
A scatter plot of individual radartogauge
comparison points is depicted in Fig. 10.
Note that there are two outliers out of the 33 gauges that do not
compare well to the SPOL estimate. In
one instance, the gauge total is nearly 100 mm lower than the SPOL
estimate. In the other case, the gauge
accumulation is more than 100 mm greater than the SPOL estimate. Interestingly, these two gauges were within
2 km of each other. The mean gauge
total for these two outliers (230.3 mm) compares very favorably to the mean of
the SPOL rain totals in the two grid points closest to the two gauges (225.8
mm). After averaging in this manner,
the cumulative SPOL rain estimate for these two gauges is within 2%.
Fig. 10. A scatter plot of the optimal SPOL radar versus gauge total rain accumulations for February 1999.
4. Selected
Preliminary Scientific Results
While quality controlling the SPOL data and
creating the V1 SPOL rain maps, we have utilized the areal rain rate estimates
made from SPOL differential propagation phase (f_{dp}) in our scientific
research. With these data, we have
investigated the LBA time series of rainfall (Fig. 11), the characteristics of
areal rain rate by meteorological regime (Table 4 and Fig. 12), and the diurnal
cycle of rainfall by regime (Fig. 13).
When comparing the magnitude of areal rain rates
calculated with the SPOL phasebased technique to other data sources, it is
important to note that the areal rain rates are unconditional over the
radar domain due to the very nature of the method. In other words, the mean areal rain rate includes nonraining
areas over the radar domain.
Fig. 11. Time series of SPOL (unconditional) areal rain rate (mm h^{1}) during the TRMMLBA experiment as determined by the differential phase method. The red impulses depict the unfiltered time series. The green line represents the 3day filtered time series.
At the simplest level, the time series of areal rain
rate in Fig. 11 demonstrates how ubiquitous rainfall is in Amazonia (see also
fractional rain durations in Table 4).
It is also apparent that rainfall is highly diurnally modulated. Yet there are some hints of nocturnal
rainfall, which appears to be occasionally very intense. During the easterly lowlevel wind regime,
rainfall tends to be narrowly peaked in the diurnal (e.g., JD 21 – 27 and 41 –
51). During the westerly wind regime,
the areal rainfall is often more broadly peaked in the diurnal (e.g., 16 – 18,
52 – 60). Apparently, there are also
exceptions to this general rule. The
3day filtered areal rain rate shows several broad peaks and brief minima. Interestingly, the amplitude and period of
the 3day cycle increases as the experiment progresses. Periods of increasing 3day filtered areal
rain rate include JD 2023, 3738, 4145, and 5157. During January (February), the broad maxima and narrow minima are
separated by about 5 (10) days.
Detailed spectral analyses of the rain rate time series are under way.
Fig. 12. Frequency histogram of the SPOL (unconditional) areal rain rate (mm day^{1}) that is partitioned by meteorological regime.
As seen in the frequency histogram (Fig. 12) and
statistical summary (Table 4) of SPOL areal rain rate, the biggest differences
between the easterly and westerly regime occur in the extremes of the
distribution. The easterly regime has a
larger fraction (52%) of the distribution at very low rain rates (» 1 mm day^{1}) than the westerly
regime (37%). The distribution of the
easterly regime areal rain rate also possesses a long tail into large values
while the westerly regime does not. As
a result, the 25^{th} percentile, median, 75^{th} percentile
and mean areal rain rate are larger for the westerly than the easterly
regime. On the other hand, the 95^{th}
percentile and maximum areal rain rate are higher in the easterly regime
compared to the westerly regime. Also
due to the behavior in the tails, the standard deviation of the areal rain rate
is larger in the easterly regime. The
fractional duration is noticeably higher at lowtomoderate areal rain rates (0
 10 mm day^{1}) in the westerly regime. Conversely, the fractional duration of heavy areal rain (50 mm
day^{1}) is significantly larger in the easterly regime. Even though the SPOL radar undersampled the
westerly regime, the measured mean areal rain depth is still larger in the
westerly regime.
Fig. 13 clearly demonstrates the highly peaked
diurnal nature of convection over Amazonia.
Daily solar insolation is clearly a primary control over rainfall with a
rapid increase in convective development and associated rainfall from late
morning (11 am) to early afternoon (1 pm).
However, nocturnal systems did occur on occasion. A secondary peak in the areal rainfall is
present at about 1 am with local minima in rainfall at 10 am and 10 pm. The amplitude of the diurnal cycle is larger
in the easterly regime. The nocturnal
maximum is largely absent in the westerly regime. Also, the daytime peak is two hours later in the easterly regime
(3pm) compared to the westerly regime (1pm with a hint of secondary maxima at 4
and 8 pm).
Table 4.
Fig. 13. SPOL (unconditional) areal rain rate (mm day^{1}) versus time (local hour). The plot depicts the composite diurnal cycle of (unconditional) areal rain rate over the SPOL TRMMLBA domain during the entire experiment (all), during easterly lowlevel winds regime (easterly), and during westerly lowlevel wind regime (westerly).
5. Plans for
Version 2 (V2) SPOL Rainfall Maps and Associated Science
a. Version 2
Improvements
Although we consider the performance (5% to 11%
negative bias and 14% to 21% standard error relative to the gauges) of the V1
SPOL monthly rain maps to be exemplary and consistent with prior polarimetric
radar studies, there are still opportunities for improvement. Here is a bulleted list of our intended
improvements for the Version 2 rain map effort, which should be complete before
January 2001.
b. Future
Science Plans
Once the V2 SPOL radar rainmaps are complete, we
intend to research a host of scientific questions associated with
TRMMLBA. Here are some issues that we
plan to explore in collaboration with other TRMM scientists:
Acknowledgements.
This
research is supported by grants (NAG54754 and NAG59642) from the NASA
Tropical Rainfall Measuring Mission (TRMM).
We would like to thank Professors Chandrasekar and Bringi of CSUEE for
sharing a preliminary draft of their upcoming textbook, Polarimetric Doppler
Weather Radar Principles and Applications.
We gratefully acknowledge helpful conversations regarding polarimetric
radar techniques with Drs. Chandrasekar, Bringi, Ryzhkov (NSSL), Zrnic (NSSL),
Vivekanandan (NCAR ATD), and Mr. Scott Ellis (NCAR ATD). We thank Mr. Bob Rilling of NCAR ATD for
providing timely NCAR SPOL radar data and support and the entire NCAR SPOL
staff for delivering a quality LBA SPOL data set. We acknowledge Drs. Brad Fisher and Jianxin Wang of the TRMM
Satellite Validation Office for making their 30day rain gauge totals available
for our use. We also acknowledge Dr.
Ali Tokay (TRMM Satellite Validation Office) for providing a ZR relationship
based on the TRMMLBA disdrometer data.
We thank Ms. Brenda Dolan (CSU) for her dedicated and diligent data
processing assistance during the course of this research. Finally, we acknowledge Mr. Paul Hein (CSU)
for his able computer software and hardware assistance.
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