EFFECT OF RADAR RANGE ON RADAR RAINFALL
ESTIMATION
SUDARAT COMPLIEW
Doctoral Student, Department of Irrigation Engineering, Faculty of Engineering at
Kamphaengsaen, Kasetsart University, Nakhon Pathom,Thailand
Email: scompliew_4@hotmail.com
BANCHA KWUANYUEN
Assistant Professor, Department of Irrigation Engineering, Faculty of Engineering at
Kamphaengsaen, Kasetsart University, Nakhon Pathom,Thailand
The accuracy and resolution of rainfall data records is an important factor on the
hydrological modelling. The weather radar provides real time spatially continuous
measurements covering a large area at short time intervals. It is highly effective in
estimating average rainfall over a river basin which is important for flood forecasting.
However, considerable uncertainty remains in the procedures used to estimate the rainfall
from weather radar observations. This uncertainty may be caused by the variability of
raindrop size distribution, the variation of reflectivity with height and with range, and the
temporal and spatial resolutions adopted for sampling the radar reflectivity. This paper
accounts for the effect of radar beam geometry as a function of distance. Due to the
conical shape of the radar beam, the observed rainfall volume is increased with range
from the radar which leads to bias and increasing the standard errors of the measured
reflectivity. In this study, a simple scaling transformation was proposed to remove the
bias caused by the radar beam spreading. Data collected during March 2001 to December
2002 of rainfall reflectivity record from the Royal Rainmaking Research center at Pimai,
Nakhon Ratchasima Province and surface rainfall from automatic rain gauge were used to
illustrate the efficiency and applicability of the reflectivity scaling transformation. The
result shown that the transformed reflectivity become relative free from range dependent
bias, so the reflectivity led to more accurate rainfall estimation than the result from
conventional radar rainfall algorithms.
INTRODUCTION
The application of meteorological radar to check rainfall measurement and hydrological
forecasting is more popular nowadays. Radar has obvious advantages for rainfall
estimation in hydrology ie. spatial and temporal resolution over an extensive spatial
domain with the ability to forecast the future rainfall. Generally, radar rainfall estimation
involves the using of a parametric relation which based on the measurements of radar
reflectivity and rainfall from the rain gauge. However, such relations are often uncertain
and their use in practical scenarios leads to significant bias on the rainfall estimation.
Numerous factors are responsible for this uncertainty, including relating of reflectivity
2
measurements that reflect above ground rainfall, to values of measured rainfall on ground
level, using of point measurements of ground rainfall as a surrogate of pixel averaged
values, the variation of reflectivity with height and with range, the temporal and spatial
resolutions adopted for sampling the radar reflectivity and radar hardware miscalibration
and noise. For such uncertainties, a probabilistic approach such as the Probability
Matching Method (PMM), [1] has been used to eliminate the need for specifying a formal
relationship between reflectivity and rainfall. The rational of this method is that rainfall
and reflectivity values for a specified exceedence probability can be considered to be
equal to each other which is assumed that the cumulative distribution function (CDF) is
invariant with range.
A conical shape of the radar beam causes the volume of radar bin to increase as the
square of the distance to the radar. Therefore, the small intense features that are present in
a rain field will be averaged out by the measurement process which leads to an
underestimation of the probability of high intensity echoes at far range. Assume that the
cumulative distribution function (CDF) of reflectivity is independent of range results in
an uncertain representation of the reflectivity, which lead to uncertainty in the radar
rainfall estimation. It is necessary that the measured reflectivity is transformed to a
variable that can be considered free from range dependent bias before use in estimating
radar rainfall. This paper presents two related concepts that attempt to associate some of
the problems that identified above: firstly, to formulate and evaluate a reflectivity scale
transformation function that assume reflectivity to be a simple scaling variable; secondly,
to apply the scale transformation function into two radar rainfall estimation methods and
evaluate the effectiveness of using the transformed reflectivity in estimating radar
rainfall.
MATERIALS AND METHODS
Materials
The radar reflectivity and rainfall data
Hourly radar reflectivity obtained from rain events which occurred in the Northeast
region of Thailand during March 2001 to December 2002 for long rainfall - reflectivity
record from the Royal Rainmaking Research center at Pimai, Nakhon Ratchasima
Province which correspond to 1.5 km of CAPPI radar products and surface rainfall from
automatic rain gauge. The Royal Rainmaking Research center at Pimai, Nakhon
Ratchasima Province operates a S-band polarmetric radar that transmits radiation with a
wavelength of 10.7 cm and produces a beam width of 1.2 degrees, maximum range is 480
km, as illustrated in Table 1. This study assumes that there is no bias caused by the bright
band effect and different observation altitude in 1.5 km. CAPPI data that lie within 200
km from the radar, the reflectivity values are less than 10 dBZ and greater than 55 dBZ
were exclude from the analysis. Rainfall data were obtained from 50 automatic tipping
bucket rainfall stations located in 200 km of S-band polarmetric. Figure 1 and Table 2
represent a rain gauge network which can be divided into Chi and Mun basins.
3
Table 1. The characteristic of radar of Royal rainmaking at Pimai, Nakhon
Ratchasima Province
Detail of radar
- Type of radar
Characteristic
Doppler weather surveillance Radar
model DWSR-8500 S , S band
10.7
1.2
0.8
1 degree x 1 degree x 1 km
850
480
Operation A : 0.8, 1.7, 2.5
Operation B : 3.4, 4.2, 5.1, 6, 7.4, 9.2,
11.6, 14.8, 18.4, 22
- Wave length : cm
- Beam width : degree
- Pulse length : microsecond
- Resolution of record data
- Maximum transmission power : Kw
- Maximum Range : km
- Sequence of elevation angles
Table 2. Details of automatic rain gauge network
Range of radar
Automatic rain gauge in
(km)
Mun basin (stations)
Chi basin (stations)
0-50
8
50-100
22
9
100-150
4
6
150-200
1
101.5
ed
ut
iat
L
102
102.5
103
103.5
104
Total
(stations)
8
31
10
1
104.5
16.5
16.5
16
16
15.5
15.5
15
15
50
km.
100
km.
14.5
14
101.5
102
150
km.
102.5
14.5
14
103
103.5
Longitude
Figure 1. Rain gauge network
104
104.5
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This paper tries to show that the cumulative distribution function (CDF) of measured
radar reflectivity is a function of range, the amount of rainfall from rain gauge and the
reflectivity data for each 25 and 50 km range interval as illustrated in Figure 2.
Methods
The objective of the paper is to remove the bias caused by the radar beam spreading. A
simple scaling transformation method is proposed [2] and have been applied to the
measured reflectivity. A scale transformation function can be derived assuming that the
measured reflectivity at different ranges are connected through generalized scaling
relation. So in this study the proposed transformation function was derived based on the
simple scaling theory of rainfall. The hourly of reflectivity that lie in 200 km range from
the radar were used in estimating a scaling exponent which estimated the scaling of
moments of measured reflectivity and a CDF must be selected, which then to be fitted to
data. Distributions of Log-normal two parameters (LN Type II), extreme value (EV Type
I) and generalized extreme value (GEV) were selected to test to data. The extreme value
is (EV Type I) appropriate to data, so the extreme value was selected to plot a CDF.
RESULTS AND DISCUSSIONS
The measured reflectivity which can be considered as a random variable characterized by
the CDF and the hourly reflectivity data lying in 200 km range from the radar were used
to estimate a scaling exponent .The cumulative distribution function (CDF) of measured
radar reflectivity of the 25 and 50-km range were selected as a reference. The study
assume that simple scaling holds for the measured reflectivity and assumption has been
verified by estimating the scaling of moments of measured reflectivity at different
moment orders (q).
q (moment order)
0.00
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06
-0.07
-0.08
-0.09
-0.10
-0.11
-0.12
-0.13
-0.14
-0.15
-0.16
1
2
3
4
5
6
0.00
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06
-0.07
-0.08
-0.09
-0.10
-0.11
-0.12
-0.13
-0.14
-0.15
-0.16
Equation:
Y = -0.0275 * X + -0.0135
Number of data points used = 5
Regression sum of squares = 0.0075625
Residual sum of squares = 0.0001075
Coef of determination, R-squared = 0.985984
Residual mean square, sigma-hat-sq'd = 3.58334E-005
0
1
2
3
q (moment order)
4
5
6
Figure 2. Scaling exponent for hourly measured reflectivity
Scaling exponent of different moment orders K(q)
Scaling exponent of different moment orders K(q)
0
5
Figure 2 shows that the relation of dependence on q and scaling of moments is rather
linear and scaling exponent is 0.0275. Therefore the proposed scale transformation
function can be defined as :
Z transformed (dBZ) = {d/25} 0.0270 Z measured (dBZ)
(1)
Z transformed (dBZ) = {d/50} 0.0275 Z measured (dBZ)
(2)
Where d
= The observation range of the measured reflectivity in km units
Z measured = The measured reflectivity at ange d in dBZ units
The proposed scale transformation function was used to transform the measured
reflectivity at different range interval to have the same cumulative distribution function
(CDF) as measured reflectivity at the 50-km range interval. The cumulative distribution
function (CDF) of transformed reflectivity of each range interval was estimated as shown
in Figure 3. The cumulative distribution function (CDF) of measured radar reflectivity of
the different range intervals to be close to 50 km, this is a confirmation of the scaling
hypothesis of the measured reflectivity. The mean of transformed reflectivity can be
compared with the mean of rain gage as shown in Figure 4.
Figure 3. (a) The CDF of Reflectivity and rainfall from automatic rain gauge
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Figure 3. (b) The CDF of Reflectivity and rainfall from automatic rain gauge
Mean reflectivity (dBz)
50
10
8
40
6
30
4
20
2
10
Mean gauge rainfall
(mm/h)
Mean reflectivity (dBZ)
Transformed reflectivity
Mean gauge rainfall (mm/h)
0
0-50
50-100
100-150
150-200
Range from radar (km)
Figure 4. Comparison of mean measured reflectivity and mean ran gauge rainfall
Two events of rainfall in the Northeast region of Thailand were obtained and four
rainfall calibration methods were studied to evaluate the effectiveness of using the
transformed reflectivity on rainfall estimation. These methods were parametric Z-R
relationship [3]; parametric Z-R relationship with transformed reflectivity; PMM; and
PMM with transformed reflectivity. For parametric Z-R relationship; Z = 294 R1.33 was
investigated and the result was shown in Table 3. The result indicated that the use of
transformed reflectivity could reduce the relative dispersion coefficient which calculated
from the ratio of the standard deviation of rain gauge rainfall and radar rainfall which
accumulated and averaged ratio over each storm about 4 and 2 percentages for calibration
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and cross validation, respectively. It means that the slopes of the G/R ratios as a function
of range are significantly flatter, if the transformed reflectivity values have been obtained
in both the conventional radar rainfall estimation methods. Even if the transformed
reflectivity values can be considered to be independent of range in the application for
radar rainfall estimation. The result of performance test indicated that the R 2 results of the
calibration and cross-validation of two events from the parametric method are significant.
This indicated that the stability of parameters due to the widespread rainfall. Besides, the
R2 results indicated that increasing accuracy of radar rainfall is insignificant if the
transformed reflectivity can be considered as independent of range. This uncertainty in
radar rainfall may occur from the other factor as shown in Table 4.
Table 3. Gage - radar comparisons of the calibration and cross validation
Events
Number of
gages
(Calibration
/Cross
validation)
Duration
of
Storm
(hr )
Mean
of Rain
Gauges
Rainfall
( mm )
14-15 May
15/22
35
4.5/4.3
2000
10-14 August
15/22
72
6.5/6.0
2001
Remark : Calibration methods
1: parametric Z-R relationship from [3]
2: parametric Z-R relationship with transformed
3: PMM
4: PMM with transformed reflectivity
G/R: The relative dispersion coefficient
G/R (%)
based on calibration
methods
1
2
3
4
31/29 27/25 30/28 26/24
30/28 28/26 31/29 27/25
reflectivity
Table 4. Performance of model
R2
Events
Parametric
Parametric
+ Scaling
14-15 May 2000
0.650/0.635
0.750/0.673
10-14 August 2001
0.576/0.534
0.645/0.613
Remark: 0.650/0.635 = calibration / cross-validation
PMM
0.634/0.621
0.557/0.532
PMM
+ Scaling
0.663/0.641
0.614/0.578
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CONCLUSION
The result concluded that the values of radar reflectivity which transformed from a
simple scaling method can reduce the relative dispersion of the gage-radar ratios at the
location of raingauge. This is a confirmation in reducing the errors due to observation
range problems. Besides, the improvement of the accuracy of the radar rainfall were
estimated in the term of R2 is significant, it indicated that the effectiveness of applying
the transformed radar reflectivity. Although the attenuation effect and the error of
selecting point raingauge of radar grid size still have not been accounted in this study, the
transformed reflectivity values can be used and lead to more accuracy in radar rainfall
estimation.
ACKNOWLEDGEMENT
The first author gratefully acknowledges Mahasarakham University for funding the PhD
studies at Kasetsart University and funding from Graduate school. The authors also
deeply sincere thanks to the authorities of the Royal rainmaking and Meteorological
Department for their kind advice and support data.
REFERENCES
[1] Rosenfeld, D., Wolf, D.B. and Atlas, D., “General probability - match relations
between radar reflectivity and rain rate”, J. Appl. Met.32, (1993), pp 50-72.
[2] Menabde, M., Seed,A. and Pegram,G., “A simple scaling model for extreme
rainfall”, Water Resour.Res.35(1), (1999), pp 335-339 .
[3] Compliew, S. and Kwanyuan, B., “Relation between measured radar reflectivity and
surface rainfall in Northeast of Thailand”, Proceeding of Agricultural Engineering,
(2002), pp 335-339.