RadxRate equations - Revision history

Jcdehart at 15:54, 2 February 2021

2021-02-02T15:54:25Z

Jcdehart: /* PID-based estimates */

2021-02-02T15:53:36Z

PID-based estimates

Jcdehart: /* NCAR Hybrid */

2021-02-02T15:53:09Z

NCAR Hybrid

Jcdehart: /* R(Z, ZDR) */

2021-02-02T15:51:24Z

R(Z, ZDR)

Jcdehart: /* R(Z) */

2021-02-01T19:26:22Z

R(Z)

Jcdehart: /* R(Z) */

2021-02-01T19:25:25Z

R(Z)

Jcdehart at 19:24, 1 February 2021

2021-02-01T19:24:20Z

Jcdehart: /* Polarimetric-based estimates */

2021-02-01T19:08:26Z

Polarimetric-based estimates

Jcdehart: /* R(Z) */

2021-02-01T19:07:16Z

R(Z)

Jcdehart: /* R(Z, ZDR) */

2021-02-01T19:06:29Z

R(Z, ZDR)

← Older revision		Revision as of 15:54, 2 February 2021
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	[[File:Bringi_hybrid.gif\|500px]][[File:Rate_rbringi.png\|600px]]		[[File:Bringi_hybrid.gif\|500px]][[File:Rate_rbringi.png\|600px]]
		+

	===== '''References''' =====		===== '''References''' =====

@@ Line 54: / Line 54: @@
 [[File:Ncar_hybrid.png|400px]][[File:Rate_rhybrid_2.png|600px]]
 ====== '''NCAR Weighted-PID''' ======
@@ Line 71: / Line 72: @@
 [[File:Bringi_hybrid.gif|500px]][[File:Rate_rbringi.png|600px]]
 ===== '''References''' =====

@@ Line 51: / Line 51: @@
 ====== '''NCAR Hybrid''' ======
-The NCAR Hybrid method applies some of the aforementioned precipitation rate equations to different PID categories. The method is described in the logical decision tree below ([http://wiki.lrose.net/index.php/RadxRate_equations#References Dixon et al. 2015]) and an example of the NCAR Hybrid method is also shown (right image).
+The NCAR Hybrid method applies some of the aforementioned precipitation rate equations to different PID categories. The method is described in the logical decision tree below ([http://wiki.lrose.net/index.php/RadxRate_equations#References Dixon et al. 2015]) and an example of output using the NCAR Hybrid method is also shown (right image).
 [[File:Ncar_hybrid.png|400px]][[File:Rate_rhybrid_2.png|600px]]
 ====== '''NCAR Weighted-PID''' ======

@@ Line 16: / Line 16: @@
 ====== '''R(Z, ZDR)''' ======
-R(Z) relationships are known to be overly simplistic, as reflectivity depends on both hydrometeor size and concentration and single polarization only captures hydrometeor size in one dimension. Including ZDR helps mitigate the impact big drops have on Z. R(Z, ZDR) relationships take the form:
+R(Z) relationships are known to be overly simplistic, as reflectivity depends on both hydrometeor size and concentration and single polarization only captures hydrometeor size in one dimension. Including ZDR helps mitigate the impact of big drops on Z. R(Z, ZDR) relationships take the form:
 <div style='text-align: center;'><math>R(Z,Z_{DR}) = aZ^bZ_{DR}^c</math></div>

← Older revision		Revision as of 19:26, 1 February 2021
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−	Many variations of this equation exist, depending on the precipitation type (e.g., convective or stratiform, tropical or mid-latitude). An example of the estimated precipitation from northern Taiwan using a tropical version of the equation (<math>R(Z)=0.027366Z^{0.69444}</math>) is shown in the image below. Since this example is from the lowest elevation angle, the echoes within ~150 km should all correspond to rain. ~~Coefficients for~~ R(Z) ~~relationships~~ have been ~~developed~~ for dry snow (<math>R(Z)=0.0365Z^{0.625}</math>), but aren't shown here given the warm environment near Taiwan.	+	Many variations of this equation exist, depending on the precipitation type (e.g., convective or stratiform, tropical or mid-latitude). An example of the estimated precipitation from northern Taiwan using a tropical version of the equation (<math>R(Z)=0.027366Z^{0.69444}</math>) is shown in the image below. Since this example is from the lowest elevation angle, the echoes within ~150 km should all correspond to rain. R(Z) coefficients have been estimated for dry snow (<math>R(Z)=0.0365Z^{0.625}</math>), but aren't shown here given the warm environment near Taiwan.

	[[File:Rate_rzh.png\|600px]]		[[File:Rate_rzh.png\|600px]]

← Older revision		Revision as of 19:25, 1 February 2021
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−	Many variations of this equation exist, depending on the precipitation type (e.g., convective or stratiform, tropical or mid-latitude). An example of the estimated precipitation from northern Taiwan using a tropical version of the equation (<math>R(Z)=0.027366Z^{0.69444}</math>) is shown in the image below. Since this example is from the lowest elevation angle, the echoes within ~150 km should all correspond to rain. Coefficients for R(Z) relationships have been developed for dry snow, but aren't shown here given the warm environment near Taiwan.	+	Many variations of this equation exist, depending on the precipitation type (e.g., convective or stratiform, tropical or mid-latitude). An example of the estimated precipitation from northern Taiwan using a tropical version of the equation (<math>R(Z)=0.027366Z^{0.69444}</math>) is shown in the image below. Since this example is from the lowest elevation angle, the echoes within ~150 km should all correspond to rain. Coefficients for R(Z) relationships have been developed for dry snow (<math>R(Z)=0.0365Z^{0.625}</math>), but aren't shown here given the warm environment near Taiwan.

	[[File:Rate_rzh.png\|600px]]		[[File:Rate_rzh.png\|600px]]

@@ Line 28: / Line 28: @@
 KDP has been used to estimate precipitation due to its relationship to the rain water content that slows down the propagating wave. Benefits of R(KDP) algorithms include insensitivity to radar calibration, attenuation, partial beam blockage, and ground clutter ([http://wiki.lrose.net/index.php/RadxRate_equations#References Zrnić and Ryzhkov 1996]), though [http://wiki.lrose.net/index.php/KDP_estimation care must be taken] in the choice of filters used to calculate KDP and in Mie-scattering regimes. In RadxRate, R(KDP) takes the following form:
-An example of the estimated precipitation using coefficients from [http://wiki.lrose.net/index.php/RadxRate_equations#References Berkowitz et al. (2013)] is shown below. Note that R(KDP) output has more missing data than other algorithms.
+<div style='text-align: center;'><math>R(K_{DP}) = sign(K_{DP})a\left|K_{DP}\right|^b</math></div>
 [[File:Rate_rkdp.png|600px]]
@@ Line 34: / Line 37: @@
 ====== '''R(KDP, ZDR)''' ======
-Like R(Z, ZDR) algorithms, R(KDP, ZDR) algorithms combine the rain water content and particle size information that can be inferred from KDP and ZDR.
+Like R(Z, ZDR) algorithms, R(KDP, ZDR) algorithms combine the rain water content and particle size information that can be inferred from KDP and ZDR. In LROSE, these algorithms take the following form:
-An example of the estimated precipitation using coefficients from [http://wiki.lrose.net/index.php/RadxRate_equations#References Bringi and Chandrasekar (2001)] and [http://wiki.lrose.net/index.php/RadxRate_equations#References Brandes et al. (2002)] is shown below. Note that R(KDP, ZDR) output has more missing data than other algorithms.
+An example of the estimated precipitation using coefficients from [http://wiki.lrose.net/index.php/RadxRate_equations#References Bringi and Chandrasekar (2001)] and [http://wiki.lrose.net/index.php/RadxRate_equations#References Brandes et al. (2002)] is shown below (<math>R(K_{DP},Z_{DR}) = sign(K_{DP})90.8\left|K_{DP}\right|^{0.93}Z_{DR}^{-2.86}</math>). Note that R(KDP, ZDR) output has more missing data than other algorithms.
 [[File:Rate_rkdpzdr.png|600px]]

@@ Line 8: / Line 8: @@
 R(Z) equations are a simple way of estimating precipitation rates from the horizontal reflectivity factor (Z) and take the following form:
-<math>R(Z)=aZ^b</math>
+<div style='text-align: center;'><math>R(Z)=aZ^b</math></div>
@@ Line 18: / Line 18: @@
 R(Z) relationships are known to be overly simplistic, as reflectivity depends on both hydrometeor size and concentration and single polarization only captures hydrometeor size in one dimension. Including ZDR helps mitigate the impact big drops have on Z. R(Z, ZDR) relationships take the form:
-<math>R(Z,Z_{DR}) = aZ^bZ_{DR}^c</math>
+<div style='text-align: center;'><math>R(Z,Z_{DR}) = aZ^bZ_{DR}^c</math></div>
@@ Line 39: / Line 39: @@
 [[File:Rate_rkdpzdr.png|600px]]
 ===== '''PID-based estimates''' =====

← Older revision		Revision as of 19:07, 1 February 2021
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	<math>R(Z)=aZ^b</math>		<math>R(Z)=aZ^b</math>
		+

	Many variations of this equation exist, depending on the precipitation type (e.g., convective or stratiform, tropical or mid-latitude). An example of the estimated precipitation from northern Taiwan using a tropical version of the equation (<math>R(Z)=0.027366Z^{0.69444}</math>) is shown in the image below. Since this example is from the lowest elevation angle, the echoes within ~150 km should all correspond to rain. Coefficients for R(Z) relationships have been developed for dry snow, but aren't shown here given the warm environment near Taiwan.		Many variations of this equation exist, depending on the precipitation type (e.g., convective or stratiform, tropical or mid-latitude). An example of the estimated precipitation from northern Taiwan using a tropical version of the equation (<math>R(Z)=0.027366Z^{0.69444}</math>) is shown in the image below. Since this example is from the lowest elevation angle, the echoes within ~150 km should all correspond to rain. Coefficients for R(Z) relationships have been developed for dry snow, but aren't shown here given the warm environment near Taiwan.