Bridging Between CAD & GIS: 6 Ways to Automate Your Data Integration
De5.1 report
1. Algorithms for QPE, 3D mosaic and hydrometeor
classification
Deliverable De5.1
L. Liu1 , H. Wang1 , Y. Xiao1 , Z. Hu1
1
Chinese Academy of Meteorological Sciences, CAS, P.R. China
Dissemintation level: Programme Participants
Lead beneficiary ID: CAMS
2.
3. ISSN/ISBN:
c 2010
Edited by the CEOP-AEGIS Project Office
LSIIT/TRIO, University of Strasbourg
BP10413, F-67412 ILLKIRCH Cedex, France
Phone: +33 368 854 528; Fax: +33 368 854 531
e-mail: management@ceop-aegis.org
No part of this publication may be reproduced or published in any form
or by any means, or stored in a database or retrieval system, without the
written permission of the CEOP-AEGIS Project Office.
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Table of content
1.! Introduction ................................................................................................................................................... 2!
1.1.! Identification .......................................................................................................................................... 2!
1.2.! Overview ................................................................................................................................................ 2!
2.! 2. Algorithm Description I (QPE and 3D mosaic)........................................................................................ 2!
2.1.! Introduction ............................................................................................................................................ 2!
2.2.! Targets to be observed ........................................................................................................................... 2!
2.3.! Observation radar system....................................................................................................................... 2!
2.4.! Coverage of radar network..................................................................................................................... 4!
2.5.! QC of radar data ..................................................................................................................................... 5!
2.6.! Remap of raw data ................................................................................................................................. 8!
2.7.! Mosaic .................................................................................................................................................. 10!
2.8.! Qualitative Precipitation estimation (QPE).......................................................................................... 11!
3.! Algorithm Prototyping ................................................................................................................................ 13!
3.1.! Mountain blockage and radar coverage ............................................................................................... 13!
3.2.! Radar data Quality................................................................................................................................ 14!
3.3.! Remap of reflectivity............................................................................................................................ 15!
4.! Validation Plan............................................................................................................................................ 15!
4.1.! Introduction .......................................................................................................................................... 15!
4.2.! Approach .............................................................................................................................................. 16!
4.3.! Validation Sites .................................................................................................................................... 16!
5.! Ancillary Data ............................................................................................................................................. 16!
6.! 6. Algorithm Description II (Hydrometeor classification).......................................................................... 16!
6.1.! Introduction .......................................................................................................................................... 16!
6.2.! Targets to be observed ......................................................................................................................... 16!
6.3.! Input and output ................................................................................................................................... 17!
6.4.! Inference............................................................................................................................................... 20!
6.5.! Aggregation.......................................................................................................................................... 20!
7.! Algorithm Prototyping ................................................................................................................................ 20!
8.! Validation Plan............................................................................................................................................ 21!
8.1.! Introduction .......................................................................................................................................... 21!
8.2.! Approach .............................................................................................................................................. 22!
8.3.! Validation Sites .................................................................................................................................... 22!
9.! Ancillary Data ............................................................................................................................................. 22!
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1.1. Identification
The Algorithm for Qualitative Precipitation Estimation (QPE), 3 Dimensional (3D)
mosaic. Algorithm for hydrometeor type classification with polarimetric radar.
1.2. Overview
In this report, the radar scan strategies and the associated beam geometry in Tibetan
and Qinghai Province is first introduced. The following section (2 to 5) provides the radar
coverage in mountain regions, radar data quality, transformation of radar data from
spherical coordinate to Cartesian grid, mosaic of reflectivity.
The fuzzy logic method for classification of hydrometeor type based on polarimetric
radar measurements is described in sections 6 to 9.
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2.1. Introduction
The Algorithm for Quantitative Precipitation Estimation (QPE), 3 Dimensional (3D)
mosaic include: (1) radar data quality control; (2) transformation of radar data from
spherical coordinate to Cartesian grid; (3) mosaic of reflectivity; (4) Z-R relationship and
precipitation estimation.
2.2. Targets to be observed
The Algorithm is used to construct 3D reflectivity and precipitation estimation products
with high temporal and spatial resolutions.
2.3. Observation radar system
In Tibetan Plateau, there are four C band Doppler radars, located in Lasa, Naqu, Rikeze
and Linzhi, respectively. There are also 2 C band Doppler radars in Qinghai Province,
located in Xining and. There radars do continuously 24h observation one day in summer
with volume scan 6 minute. The C band Doppler radar works on 5.5 cm wavelength with
beam width of 1.0°, and gate width of 250m. There radars performed volume scan with 14
or 9 elevation angles once every 5 min which are similar with WSR-88D (Fig.2.1 ).
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19.5 16.7 14 12 10 8.7 7.5 6.2 5.25 4.3 3.35
2.4
1.45
0.5
19.5 14.6 9.9 6.0 4.3 3.35
2.4
1.45
0.5
Fig.2.1 The volume scans of VCP11 top and VCP21 bottom)
The radar data analyses should provide end users with high-resolution radar reflectivity
data fields that are comparable to the raw data with the advantage of a Cartesian coordinate
system (longitude, latitude, altitude (above mean sea level (MSL) ). A Cartesian coordinate
system provides a common framework in which other observational datasets, such as
precipitation data, can be merged and cross-correlated.
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2.4. Coverage of radar network
The mountain blockages to radar network were analyze with ground surface altitude data,
and the radar data for precipitation cases were used in examining the mountain blockage for
radar beams. The beam blockage by mountain was calculated using an algorithm that used
high resolution DEM digital elevation model data, radar beam pattern (Gaussian beam
approximation), and radar beam propagation path (assuming radar beams propagate under
standard atmospheric refraction conditions).
Assuming the ground target position is defined , the radar position is
. The distance along the earth surface, azimuth and elevation of ground
target with radar are calculated by:
2.1
2.2
2.3
Where is earth radius is equivalent radius is linear distance from
radar to ground target, which is got by:
2.4
The altitude of ground target is got with DEM data.
According to the calculation results, we can get the hybrid scan for each scan. The hybrid
scan mean that for each radar beam and gate, it defines as the lowest elevation angle with no
mountain blockage for echo azimuth, using hybrid scan data for each radar, we can define
the radar coverage and reflectivity for QPE.
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2.5. QC of radar data
The fuzzy logical based algorithm is used to detect the anomalous propagation ground
clutter. Briefly, a fuzzy logic classifier uses various derived fields (formally known as
"features") as input, scales them to a common reference frame by use of a "membership
function," and then computes a weighted sum of the resultant "interest" fields. After
application of a threshold, the final output product of the detection algorithm is obtained and
contains the locations of the AP ground clutter. The general schematic of AP clutter
detection algorithms is shown in Fig. 2.2. The reflectivity, radial velocity and spectrum
width in polar coordinate are input into the “feature generator” for calculation of the
features. The features used in the software includes: texture of the reflectivity (TdBZ), the
vertical difference of the reflectivity (GDBZ) between two elevation angles, the median
radial velocity (MVE) and spectrum width (MSW), the standard deviation of radial velocity
(SDEV), Percent of all of possible differences, that exceed the minimum difference
threshold (SPIN) and mean sign of reflectivity change along range (SIGN). The TDBZ,
SDEV and RGDZ are defined as:
(2.5)
(2.6)
where the Ngates and Nbeams are range and azimuth interval to defined a regional area. For
features derived from reflectivity, Ngates=5 and Nbeams=5, for radial velocity and
spectrum width, the Ngates=9 and Nbeams=5.
(2.7)
where Rangewet defined in Fig.2 (H) is range weighting function.
(2.8)
where the ALL_counts is toll number of radar data in specified area . SPINchang_counts
and All_counts is calculated as:
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(2.9)
The value of Zthresh=2dBZ for WSR-88D is suitable to separate the AP clutter from
precipitation echo (Sterner and Smith, 2002).
(2.10)
where: (2.11)
The MDVE and MDSW are calculated by median filtering along the range for 7 gates.
Three features from reflectivity, two features from velocity, one from spectrum width and
one from vertical structure of reflectivity are used in the software to detect AP clutter. The
seven features calculated gate by gate are input to the memberships to calculate the interests,
respectively. Fig.2.3 shows the memberships for the seven features. The echo with low
radial velocity and spectrum width, high horizontal and vertical spatial gradient, has high
likelihood to be AP clutter. The difference between this algorithm described in this paper
and method proposed by Kessinge are that the median velocity and spectrum are used in this
model, instead of mean velocity and spectrum, considering the velocity folding and noise of
the data.
All of memberships are given a equal weight when calculating the interest field of AP
clutter, and 0.5 is the threshold to detect the AP clutter.
Fig. 2.2 The general schematics of AP clutter detection algorithms.
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a b
c d
e f
Fig 2.3 The membership functions of MDVE a SDVE b SW c TDBZ d
GDBZ e SPIN f for ground clutter detection.
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2.6. Remap of raw data
The transformation of radar data from a spherical coordinate to a Cartesian grid
provides a more direct approach of combining multiple radars onto a common grid. This
provides the ability to integrate the full-resolution base-level data from multiple radars onto
a common 3D framework. The 3D mosaic grid can benefit forecasters, meteorologists, and
researchers with a wide variety of products and displays, including flexible horizontal or
vertical cross sections in addition to regional rainfall maps. High-resolution reflectivity
analyses can also serve as an important source in data assimilations for convective-scale
numerical weather modeling over large domains and for merging conventional datasets with
the radar data.
Four interpolation approaches were investigated to remap raw radar reflectivity fields
onto a 3D Cartesian grid with high resolution.
(1)Nearest-neighbor mapping
The nearest neighbor mapping (NNM) uses the value of the closest radar bin to grid cell,
where distance is evaluated using the location of the centers of the radar bins.
(2)nearest neighbor on range-azimuth planes combined with a linear interpolation in
vertical direction NVI
The Fig. 2.4 shows the schedule of the approach. For each grid ( )in small
elevation angles (<20°), Find two observations of radar raw data points
( , ) on the two adjacent tilts below and above the grid cell, respectively,
and at the same range and azimuth as the grid cell.
2.12
Here are the interpolation weights given to the he reflectivity observations below
and above the grid cell, respectively. The weights are determined by :
2.13
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2.14
where !i, !o1, and !o2 represent elevation angles of the grid cell and the radar bins below and
above, respectively.
3 Linear interpolation in vertical direction plus a horizontal interpolation VHI
Fig.5 shows the VHI approach. For the grid cell , the four reflectivity
observations are ,the analysis
formula for the vertical and horizontal interpolation (VHI) scheme is
2.15
Here are nterpolation weights given to the he reflectivity observations
2.16
2.17
(4) Dual linear interpolation
As shown in Fig.
are 8 reflectivity
observations near the grid cell , the analysis values is :
(2.18)
2.19
2.20
In this study, the third approach is used to remap the raw radar data to 3D grid data.
Figure 2.5 dual linear interpolation
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2.7. Mosaic
In addition to remapping single radar reflectivity fields, one must consider a multiple
radar scenario where more than one radar collects reflectivity data for the same point in
space. The 4DDG provides a methodology that takes advantage of multiple observations
while handling those observations that do not agree with each other.
Some grid cells are sampled by more than one radar bin. The mosaic approach is to
calculated a final reflectivity value for grid cells oversampled by radar bins. Three
approaches of combining multiple-radar reflectivity fields were investigated. They are
maximum reflectivity, Nearest-neighbor reflectivity and distance weighted means.
Results have shown the distance- exponential-weighted mean scheme provided a spatially
consistent reflectivity mosaics while retaining the magnitude of the observations from the
close radar. Mosaics could mitigate various problems that caused by the geometry of radar
beam such as data voids with the cone of silence above the radar and in regions below the
lowest beam.
(1) Nearest-neighbor mosaic approach
In this approach, the analysis value from the closest radar is assigned to the grid cell.
The nearest-neighbor method does not impose any smoothing when creating a mosaic from
multiple radars. However, discontinuities may appear at the equidistant lines between radars
in the mosaicked field.
2 Maximum reflectivity
This mosaicking method simply uses the maximum reflectivity value among the
multiple observations that cover the same grid cell. This method does not involve smoothing
and it retains the highest reflectivity intensities in the data fields.
3) Distance weighted means
The mosaic method considered is a weighted mean, whereby the weight is based on the
distance between an individual grid cell and the radar location. Two weighting functions
were tested; both monotonically decrease with range, that is exponential weighting function
and Cressman weight function are used in this study. These distance weighted means take
advantage of multiple observations while handling those observations that do not agree with
each other. The shape of an exponential weighting function is easily adjustable to achieve a
rapid decrease with range while retaining a positive weight value. Thus, an exponentially
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decaying function is especially useful for radar analysis and is employed in the algorithm.
The two functions are expressed as following:
2.21
Here r is the distance of the observation from its respective radar and R is an adaptable
length scale (i.e., 100 km).
2.22
Where is effective radius (i.e. 300 km) and r is the distance of the observation from its
respective radar.
The shape of an exponential weighting function is easily adjustable to achieve a rapid
decrease with range while retaining a positive weight value. Thus, an exponentially
decaying function is especially useful for radar analysis and is employed in the algorithm.
2.8. Qualitative Precipitation estimation (QPE)
The QPE Algorithm in this study is based on 3D mosaic. It composed of five main
scientific processing components and one external support functions. The five scientific
subalgorithms are identified as follows: 1) preprocessing 2) rain rate estimation, 3)
accumulation , 4) adjustment , and 5) products ). The two support functions, precipitation
detection and rain gauge data acquisition.
(1) Rain gauge data acquisition
The external support function within the QPE is called the rain gauge data acquisition
function. It receives the rain gauge reports. In order to deal with all of kinds of rain gauge
data, the precipitation rate is transfer into unit structures, which include the position of
raingauge, beginning and end of time, precipitation amount.
(2) Reflectivity preprocessing
The CAPPI of 3D mosaic reflectivity between 2-5 km (MSL) is chosen to calculate the
precipitation. The altitude of CAPPI depend on the domain for QPE, the blockage of radar
beam, the precipitation system (deeply or shallow developed ) . The horizontal and vertical
resolution of 3D grid data are 2km and 0.5km, respectively. Because the blockage of radar
beam in Tibetan is very serious, the compositive reflectivity will be used.
This quality control step removes reflectivity data that are abnormally large in
magnitude but small in area, such as those associated with nonmeteorological targets
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(airplanes, anomalous propagation returns, or residual ground clutter). Two reflectivity
thresholds are used here. Isolated sample bins are defined as grids with reflectivities that
exceed a certain threshold (an adaptable parameter currently set at 15 dBZ) and for which no
more than one of the eight surrounding neighbors is also above that same threshold. Isolated
bins are replaced with a valid reflectivity.
A second maximum reflectivity threshold parameter (currently set at 65 dBZ) is used to
quality control the extremely large point outlier reflectivity bins typically associated with
residual ground clutter or anomalous propagation that have not previously been removed by
AP detection . If a grid has a reflectivity that exceeds this threshold, it is replaced with either
an average of surrounding values if none of them are above the same threshold, or otherwise
it is assigned a very small value (7 dBZ; an adaptable parameter). This step will not remove
all occurrences of residual clutter or anomalous propagation, and hence additional quality
control steps are necessary.
(3) Rain rate conversion from reflectivity
It converts reflectivity factor data from the CAPPI of reflectivity in 3D mosaic into rain
rates using a standard Z–R power law relationship derived from the empirical relationship
between the two variables. The current default equation is
Z = 300R1.4 2.23
where Z has units of mm6 m"3 and R in mm h"1. The Z–R parameter settings are designed to
be adjustable at each site.
In this work, we design method to form Z-R relationship every volume scan. The rain rate
and respective reflectivity are matched to fitting the Z-R relationship under the assumption
of Z–R power law relationship.
The reflectivity stronger than 55dBZ are considered as hail cores of thunderstorms, it is
necessary to cap them at a maximum value expected to be associated with rain only. The
“hail cap” threshold, an adaptable parameter representing the maximum expected
instantaneous, rain rate, has typical values ranging from about 75 mm h"1 (3 in. h"1) to about
150 mm h"1 (6 in. h"1) except in highly unusual events.
(4) Gauge–radar adjustment
A temporally fixed Z–R relationship, as is the current design of the PPS, will not be
appropriate for all rainfall events. Because it is not currently feasible to manually adjust the
Z–R parameters in real time due to the lack of proven, robust, and objective criteria valid
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over a broad range of rainfall types, it is useful to make automated adjustments to the
rainfall estimates by comparing them with real-time rain gauge data on an hourly time step.
Real-time rain gauge data can be used to adjust the radar rainfall estimates in the algorithm.
Optimal interpolation (OI) analysis is used in this QPE.
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3.1. Mountain blockage and radar coverage
The mountain blockages for radars in Tibetan and Qinghai are calculated. Figure 3.1
shows the example of blockage of radar. The heavy rainfall case is used to examine the
coverage of the radar (Fig. 3. 2)
Fig. 3.1 the blockage of Xining radar
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Fi.g 3.2 the CAPPI of reflectivity at 3.0km
3.2. Radar data Quality
The ground clutter and radio noise distinguish with the radar QC algorithm are shown in
Fig. 3.3 and 3.4
Fig. 3.3 The raw data and after QC data at 11:43, July 15, 2008 in Henan Province
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Fig. 3.4 The raw data and after QC data at 14:46, July 15, 2008 in Jiangsu Province
3.3. Remap of reflectivity
(a) (b)
Fig. 3.5 the CAPPI of reflectivity in Xining
Fig. 3.5 shows the CAPPI of reflectivity at 3km.
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4.1. Introduction
In mountain areas, radar observations are often contaminated by echoes from ground
clutter, high-speed moving vehicles and by point-wise ground clutter under either normal
propagation (NP) or anomalous propagation (AP) conditions. Many factors can introduced
the bias of reflectivity measurement, such as transmitter power, noise figure variations.
Transformation of radar data from spherical coordinate to Cartesian grid can also produce
horizontal and vertical structures variations of reflectivity. The reflectivity bias between
different radars can affect the 3-D mosaic.
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4.2. Approach
In order to validate the algorithm, the ground data, raw data display are compared with
the products from the algorithm. The experts can distinguish the ground clutter and radio
noise pixels of radar each, this data is used to examine the radar data QC.
4.3. Validation Sites
Chinese Academy of Meteor. Sciences.
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The raw radar data from Qinghai Province and Tibetan;
Raingauge data rom Qinghai Province and Tibetan;
Processing radar data and provide 3D reflectivity data to WP5. Grid Reflectivity in
Qinghai from 18 July 2008 -21 July 2008 were product with spatial and temporal
resolution (0.01°#0.01°#0.5km#5min), the radar data in Tibetan from 18 June 2008 to19
June 2008, 18 July 2008 to 20 July 2008 were provide.
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6.1. Introduction
There are several methods that can be potentially used for hydrometeor identification,
such as classification using differential reflectivity (ZDR) classification using linear
depolarization ratio (LDR), classification using specific differential propagation phase (KDP)
and coefficient ($HV), classic statistical decision theory, neural networks, and fuzzy logic.
Fuzzy logic is used in this study for classification because it has many inherent advantages
over other methods. Many polarimetric radar measurements lie in a limited measurement
space for each hydrometeor type. The fuzzy logic system possesses the ability to reach
distinct decisions based on overlapping and “noise contaminated” data. The fuzzy logic
method for classification of hydrometeor type based on polarimetric radar is developed by
Chinese Academy of Meteorological Sciences.
6.2. Targets to be observed
Algorithm for hydrological classification with polarimetric radar can generate the
hydrological classification products (rain, snow, crystal, hail and graupel) from polarimetric
radar raw data. A fuzzy logic method for classification of hydrometeor type based on
polarimetric radar measurements is described in this report.
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First, the four radar measurements and altitude are fuzzified by using membership
functions. There are 10 membership functions for each of the input variables in the system.
After fuzzification, then the membership functions are aggregated from each hydrometeor
type. The last step is defuzzification, which can convert aggregation result to a single
hydrometeor type. The following provides detailed description of the steps used in the
classification process.
6.3. Input and output
Four radar measurements, namely, horizontal reflectivity (ZH), differential reflectivity
(ZDR), differential propagation phase shift (KDP) and correlation coefficient ["HV] have been
used as input variables to the fuzzy logical hydrometeors classification.
ZH for horizontally and vertically polarized waves are proportional to the hydrometeor’s
cross section integrated over a volume. ZDR can be related to the axis ratio and size of
hydrometeors. The differential phase KDP is the difference between propagation constants
for horizontally and vertically polarized waves .In the region filled with horizontally
oriented hydrometeors such as rain or ice crystals, a horizontally polarized wave has larger
phase shifts (per unit length) and propagates more slowly than a vertically polarized wave
does; the opposite holds for vertically oriented hydrometeors. In theory, KDP allows
discrimination between statistically isotropic and anisotropic hydrometeors; isotropic
hydrometeors produce similar phase shifts for horizontally and vertically polarized waves.
The degree of decorrelation as measured using the correlation coefficient at zero lag $HV
between horizontally and vertically polarized echoes results. Decorrelation physically
occurs if the horizontal and vertical backscatter fields do not vary similarly. $HV decreases
with increasing diversity of hydrometeor orientations and shapes. When particles are wet or
when they are large and irregular in shape. Moreover, $HV is lower when there are mixtures
of hydrometeor types rather than when just one type is present.
The output of the neuro-fuzzy system is one of the many possible hydrometeor types:
1) drizzle, 2) rain, 3) dry and low density snow, 4) dry and high-density crystals, 5) wet and
melting snow, 6) dry graupel, 7) wet graupel, 8) small hail, 9) large hail, and 10) a mixture
of rain and hail.
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Table 6.1 Output of the Algorithm
for hydrological classification
Hydrometer type Classify output Hydrometer type Classify
output
DRizzle(DR) 1 Dry Graupel(DG) 6
RAin(RA) 2 Wet Graupel 7
(WG)
Dry Snow(DS) 3 Small Hail(SH) 8
Dry Cristal(DC) 4 Large Hail(LH) 9
Wet Snow (WS) 5 Hail Rain(HR) 10
The function of the “fuzzification” is to convert the crisp inputs (or precise
measurements) to the fuzzy sets ( 0-1 ) with a corresponding membership degree. A specific
crisp input can be to different fuzzy sets but with different membership degrees (or truth
value). The most important component in fuzzification is the membership function, which is
used to describe the relationship of the crisp input and the fuzzy sets in the input domain.
The definition of membership function is as follows: T(x) is called membership function of
fuzzy set A (for a fuzzy variable x), whose value is the degree to which x is a member of
fuzzy set A.
(6.1)
We can define the functions MBFi-j for each polarization variables i and hydrometeor
types. Fig. 6.1 shows the member function for polarization variables and hydrometeor
classifications.
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6.4. Inference
In a fuzzy logic system, rules are used to describe linguistically the complex relationship
between the input and output fuzzy variables in the form of IF–THEN statements. Typically,
the rule is composed of several antecedents in the IF statement and one or several
consequents in the THEN statement. The process of deducing the “strength” of these
consequents from the strength of the antecedents is called rule inference. The most
commonly used inference methods are correlation minimum, correlation product, and MIN–
MAX. The total contributions of polarization variables to the hydrometeor type are defined
as:
(6.2)
Here Ai is coefficient weight for ith polarization variables. AZH=AZDR=1 AKDP=0.8
A$HV=0.5.
6.5. Aggregation
We can use the inference methods to derive the strength of each rule, then the
aggregation method can be used to determine an overall fuzzy region. Two commonly used
aggregation methods are additive aggregation and MAX Aggregation, which mean that the
maximum values of RSj is the hydrometeor type.
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The Koun radar in USA for hail storm is used to examine the algorithm. Figure 7.1 shows
the radar measurement. Figure 7. 2 shows the hydrometric classification results.
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(a) (b)
(c) (d)
Figure 7.1 Four PPI image at 0.5 of the Oklahoma City tornado on 10 May2003 1903 UTC.Radar is
located at the central point of half circle. (a) ZH (dBZ) (b)ZDR(dB) (c) DP(deg Km-1) (d) HV
(a) (b)
Figure 7.2 Two kinds of hydrometeor type classification results at 19:03 UTC by different inference rules: (a)
PSi-j multiply (b) PSi-j plus
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8.1. Introduction
Knowing what precipitation type is reaching the ground is a fundamental prerequisite for
accurate determination of amount. Thus, for quantitative precipitation estimation (QPE),
first a correct classification needs to be made so that appropriate semiempirical relations can
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be chosen to estimate the corresponding rates and/or accumulations. Because of sensitivity
to hydrometeor concentration, shape, orientation, dielectric constant, and size, polarimetric
variables have emerged as leading discriminators of precipitation type. The situ observation
with aircraft is simpler means to develop and evaluate the algorithm, we also rely on spatial
continuity, height above ground, and comparison with conceptual models to qualify the
algorithm's performance.
8.2. Approach
The radar observation will be compared with model output, the results are analyze to
examine the algorithm performance.
8.3. Validation Sites
Chinese Academy of Meteor. Sciences.
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The raw radar data from C band polarimetric radar;
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28. Acknowledgments
The work described in this publication has been supported by the European
Commission (Call FP7-ENV-2007-1 Grant nr. 212921) as part of the CEOP-
AEGIS project (http://www.ceop-aegis.org) coordinated by the University
of Strasbourg, France.