Estimates Precipitation by Radars
V. Chandrasekar, Colorado State University R. Meneghini, NASA Goddard Space Flight Center I. Zawadzki, McGill University Presented at the 2003 Radar Meteorology Conf
Quantitative Precipitation Estimation
Radar have come along way in contributing to quantitative precipitation estimation. One of the major advance is we are starting to get a much clearer picture of the error structure of QPE. This talk will be restricted to few selected issues to focus the discussions in this otherwise large subject matter.
We will start with the structure of errors and in particular, will focus on errors due to beam broadening and height of measurements
Ground clutter of the McGill radar on a 0.5 elevation PPI
Laurentians shadows
Tall building
Adirondacks 120 km
The curvature of the earth and the topography forces the measurements to be taken well above ground over a good part of the area
Computation of the errors due to the range effect
Data at short range are projected outward to the lowest non-contaminated measurement height
The effects taken into account are: beam smoothing, post detection integration and height of measurement
For a benign stratiform case with a relatively weak bright band
1-hour accumulation map
Comparison of the values at the measurement height to actual values at ground as obtained by projecting non-contaminated measurements at the 20-40 km range to the lowest non-contaminated position of the measurement over the entire radar coverage (one hour of data) :
Bias due to the on the average change in reflectivity with height
Residual RMS error of one of measurements after bias removal
BIAS
Measurement in snow
From Gyu Won Lee (PhD thesis)
Contamination by the BB
The residual RMS error in R assumes a perfect Z-R relationship
Effect of area averaging
Error structure in height-range coordinates.
BIAS [expressed as factors in R] Residual RMS error [in %]
3x3 km2
13x13 km2
From Gyu Won Lee (PhD thesis)
AREAL RAINFALL ESTIMATE
Introduction
The concept of using path integrated measurements to Areal Rainfall is discussed in RaghavanandChandrasekar(1994)JAM Ryzhkovetal(2000)JAM Bringietal(2001)J.Tech.
The areal rainfall is defined as
AR = ( x, y ) dxdy R
R(x,y) is the rain rate field Converting this to polar coordinates
AR =
r2 r1
2
1
R (r , )rdrd
This can be reduced to(with assumptions)
r2 c 2 AR = [{r2 dp (r2 , ) r1 dp (r1 , )} dp (r , )dr ]d r1 2 1
In the previous formula for a given beam
(constant) AR depends on its boundary values at r and r as well as area under the
1 2
range profile. 1 2, As azimuth angle changes from to an
areal sweep of over rain occurs naturally performing spatial integration.
dp dp
dp
Advantage No need to estimate K which is
a difficult estimator basins
Good for estimating precipitation over small
How well does this work?
Illustrates the dense gage network near Darwin, and the boundaries of the polar area used for estimating the area rainfall
Time series of mean areal rain rate (R ) from using the AR estimator and from the gage network (R ) versus time for the storm event of 18 February 1999. The radar sampling interval is 10 min. Standard error bars on R
csu g
csu
reflect both the parameterization error as well as the
The storm total rain accumulation from radar versus gage network accumulation for 12 storm events. The normalized error is 14.1% and the normalized bias is 5.6 % for the AR estimator.
Similar studies have been done with data
from Florida and Brazil and obtained similar results
POLARIMETRICALLY TUNED Z-R RELATIONS
Concept
N ( D ) = nc f D ( D ) m 3mm 1
Using the normalization of DSD as described in Tested et al(2001), the Z-R relation can be expressed as b Z R N =a N , b 1.5 w w Using Polarimetric radar measurements, we can estimate parameters of a DSD (N ,D ) (Gorgucci et al., 2001, JAS; Bringi et al., 2002, J. Tech.) Subsequently the following Z-R relation can be derived 1b b
w o
Z = aN w
R
The following example shows application of
such a Z-R relation over time over a profiler and gage network
Global estimates of rainfall global rate
rainfall requires a satellite-based instrument PR alone does not define space-based weather radar GPM dual-wavelength radar (w/ bore-sighted radiom) CloudSat (94 GHz cloud radar) near-nadir Doppler radar (polarimetry, adaptive scan) conical-scanning geostationary common features of PR and ground-based radars restricted viewing of rain near surface dependence on Z-R relations (at least in part) sensitivity to radar calibration errors
Global estimates of rainfall rate
differences of PR with ground-based radars attenuation correction required near-nadir viewing geometry poor temporal resolution/ but w/ global coverage polarimetric/ Doppler methods not available common features among spaceborne radars (LEO) poor temporal resolution restricted swath use of frequencies at X-band or higher
Rain Estimation Methods from Space
single wavelength Hitschfeld-Bordan (initial-value)/ iterative Hitschfeld-Bordan with constraints -, C-adjustment final value hybrid mirror-image/ stereo-radar dual-wavelength (w/ or w/o radiometers) difference of differences Hitschfeld-Bordan with constraints integral eqs. for DSD parameters constraints surface reference method radiometer
Rain Estimation Methods from Space
statistical (over large space-time regions) probability matching fractional-area methods log-normal based retrievals
Calibration & Validation
Calibration of PR is stable and accurate active radar calibrator (CRL) comparisons with TOPEX comparisons with WSR-88D dBZ above BB Attenuation correction must be checked compare on instant. & statistical basis dBZ above melting layer (cal check) near surface (attenuation correction check) So too rain rate and rain classification accuracy compare near-surf rain rates (instant. & statistically) compare rain classification (convective/ stratiform)
0
Summary
the TRMM PR has demonstrated the utility of space radar improved global rain estimation more frequent monitoring of severe storms/ typhoons provides rain classification/ improved latent heating est. increasing use in modeling, data assimilation
Future Prospects
Global Precipitation Missions goals better temporal resolution (3 hr revisit time) use of dual-wavelength radar for DSD estimation (rain & snow), more accurate RR, improved rain classification, phase state detection Research is needed, however: better/ more uniform validation methodologies dual-wavelength...