Radar rainfall estimation technique when attenuation is negligible

• US 7,158,071 B2
• Filed: 07/11/2002
• Issued: 01/02/2007
• Est. Priority Date: 07/11/2001
• Status: Expired due to Term

• Current Assignee: Novimet SA
• Original Assignee: Centre National De La Recherche Scientifique
• Inventors: Testud, Jacques, Le Bouar, Erwan
• Primary Examiner(s): Sotomayor; John B.
• Application Number:
  US10/483,188
• Publication Number:
  US 20040201515A1
• Time in Patent Office: 1,636 Days
• Field of Search: 342/26.R, 342/26.A, 342/26.B, 342/26.C, 342/26.D, 342/188, 342/460
• US Class Current: 342/25.00R
• CPC Class Codes: G01S 13/95 for meteorological use
• CPC Class Codes: G01S 7/025 involving the transmission of linearly polarised waves
• CPC Class Codes: Y02A 90/10 Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

A method of using a bipolar radar to estimate a precipitation rate for rain that generates negligible attenuation. The method includes using the bipolar radar to measure the differential phase Φ_DP and the apparent reflectivity Z_e on at least one of horizontal polarization H and vertical polarization V over a given interval [r₀, r₁] of path radii relative to the radar. An estimate of the value N_o* representative of the dimensional distribution of rain drops is made on the basis of the differential phase difference in the range r₀ to r₁ and on the basis of an integral of a function of the apparent reflectivity Z_e along the interval [r₀, r₁]. A value is deduced for the precipitation rate at a point from N₀* and the apparent reflectivity at the point.

Claims

1. A method of using a bipolar radar to estimate a precipitation rate for rain that generates negligible attenuation, the method comprising the following steps:

using said bipolar radar to measure the differential phase Φ

_DP and the apparent reflectivity z_e on at least one of horizontal polarization H and vertical polarization V over a given interval [r₀, r₁] of path radii relative to said radar;

making an estimate of the value N₀* representative of the dimensional distribution of rain drops on the basis of the differential phase difference in the range r₀ to r₁ and on the basis of an integral of a function of the apparent reflectivity Z_e along the interval [r₀, r₁]; and

deducing a value for the precipitation rate at a point from N₀* and the apparent reflectivity at said point.

2. The method according to claim 1, wherein N₀* is deduced directly from the differential phase difference between r₀ and r₁ and from the integral of the apparent reflectivity Z_e raised to a selected exponent.

3. The method according to claim 1, wherein the selected exponent is an exponent b satisfying:

$\frac{K_{\mathrm{DP}}}{N_O^{*}}={a<br><br>\left[\frac{Z_e}{N_0^{*}}\right]}^b$

where K_DP is the rate of variation in the differential phase along the radius, a and b being specified by the type of precipitation under consideration and by temperature.

4. The method according to claim 3, wherein the type of precipitation is a corresponding type selected from rain type and ice crystal type.

5. The method according to claim 1, wherein the apparent reflectivity function which is integrated depends on N₀*, and further comprising the step of calculating said function in a plurality of iterations using a value for N₀* as determined at a preceding iteration.

6. The method according to claim 5, wherein N₀* is calculated from the following relationship:

${\mathrm{\Phi <br><br>}}_{\mathrm{DP}}<br><br>\left(r_2\right)-{\mathrm{\Phi <br><br>}}_{\mathrm{DP}}<br><br>\left(r_1\right)=N_0^{*}<br><br>{\int <br><br>}_{\mathrm{r1}}^{\mathrm{r2}}<br><br>F<br><br>\left(\frac{Z_e}{N_0^{*}}\right)<br><br><br><br>d<br><br>s$

where Φ

_DP is the differential phase and where F is a function satisfying the following relationship;

$\frac{K_{\mathrm{DP}}}{N_0^{*}}=F<br><br>\left(\frac{Z_e}{N_0^{*}}\right)$

where K_DP is the rate of variation in differential phase along the radius.

7. The method according to claim 5 wherein, for the first iteration, the value used for N₀* is given by:

$N_O^{*}={\left[\frac{{\mathrm{\Phi <br><br>}}_{\mathrm{DP}}<br><br>\left(r_2\right)-{\mathrm{\Phi <br><br>}}_{\mathrm{DP}}<br><br>\left(r_1\right)}{a<br><br>{\int <br><br>}_{\mathrm{r1}}^{\mathrm{r2}}<br><br>Z_e^b<br><br><br><br>d<br><br>s}\right]}^{\frac{1}{1-b}}$

8. The method according to claim 1 wherein the rainfall rate R is determined from N₀* and from the apparent reflectivity Z_e by the relationship:

R=c└

N₀*┘

<sup>1−

d</sup>Z_e^d

9. An apparatus for estimating a precipitation rate, comprising a bipolar radar and a processor, said radar configured to measure differential phase and reflectivity on at least one of horizontal polarization H and vertical polarization V, said processor configured to use said bipolar radar to measure the differential phase Φ

_DP and the apparent reflectivity Z_e on at least one of horizontal polarization H and vertical polarization V over a given interval [r₀, r₁] of path radii relative to said radar;

make an estimate of the value N₀* representative of the dimensional distribution of rain drops on the basis of the differential phase difference in the range r₀ to r₁ and on the basis of an integral of a function of the apparent reflectivity Z_e along the interval [r₀, r₁]; and

deduce a value for the precipitation rate at a point from N₀* and the apparent reflectivity at said point.