KDP estimation - Revision history

Jcdehart: /* References */

2021-02-24T22:48:22Z

References

Jcdehart: /* Self-consistency */

2021-02-23T23:45:20Z

Self-consistency

Jcdehart: /* Algorithm */

2021-02-23T23:45:11Z

Algorithm

Jcdehart: /* Algorithm */

2021-02-23T23:45:00Z

Algorithm

Jcdehart: /* Background and Objectives */

2021-02-23T23:44:52Z

Background and Objectives

Jcdehart at 23:44, 23 February 2021

2021-02-23T23:44:15Z

Jcdehart: /* Background and Objectives */

2021-01-26T23:49:25Z

Background and Objectives

Jcdehart at 23:48, 26 January 2021

2021-01-26T23:48:08Z

Jcdehart: /* Background and Objectives */

2021-01-26T23:47:23Z

Background and Objectives

Jcdehart: /* Background and Objectives */

2021-01-26T23:43:22Z

Background and Objectives

@@ Line 40: / Line 40: @@
 === '''References''' ===
 Hubbert, J. and V.N. Bringi, 1995: An Iterative Filtering Technique for the Analysis of Copolar Differential Phase and Dual-Frequency Radar Measurements. J. Atmos. Oceanic Technol., 12, 643–648. [https://journals.ametsoc.org/doi/pdf/10.1175/1520-0426%281995%29012%3C0643%3AAIFTFT%3E2.0.CO%3B2 Link]
 Stepanian, P. M., K. G. Horton, V. M. Melnikov, D. S. Zrnić, and S. A. Gauthreaux Jr., 2016: Dual-polarization radar products for biological applications. Ecosphere, 7, e01539. [https://doi.org/10.1002/ecs2.1539 Link]

@@ Line 36: / Line 36: @@
 === '''Self-consistency''' ===
-One drawback of this method is that it can over-smooth the PHIDP profile and broaden regions of higher <math>K_{DP}</math> to radar gates that are beyond the precipitation causing the phase shift. The self-consistency method attempts to identify regions where high <math>K_{DP}</math> is likely. The algorithm can estimate <math>K_{DP}</math> from Z and ZDR (this estimated <math>K_{DP}</math> will be incorrect and differ from observations). The synthetic <math>K_{DP}</math> is then compared to the measured <math>\phi_{DP}</math> change and is then scaled to match the observed values.
+One drawback of this method is that it can over-smooth the <math>\phi_{DP}</math> profile and broaden regions of higher <math>K_{DP}</math> to radar gates that are beyond the precipitation causing the phase shift. The self-consistency method attempts to identify regions where high <math>K_{DP}</math> is likely. The algorithm can estimate <math>K_{DP}</math> from Z and ZDR (this estimated <math>K_{DP}</math> will be incorrect and differ from observations). The synthetic <math>K_{DP}</math> is then compared to the measured <math>\phi_{DP}</math> change and is then scaled to match the observed values.
 === '''References''' ===
 Hubbert, J. and V.N. Bringi, 1995: An Iterative Filtering Technique for the Analysis of Copolar Differential Phase and Dual-Frequency Radar Measurements. J. Atmos. Oceanic Technol., 12, 643–648. [https://journals.ametsoc.org/doi/pdf/10.1175/1520-0426%281995%29012%3C0643%3AAIFTFT%3E2.0.CO%3B2 Link]
 Stepanian, P. M., K. G. Horton, V. M. Melnikov, D. S. Zrnić, and S. A. Gauthreaux Jr., 2016: Dual-polarization radar products for biological applications. Ecosphere, 7, e01539. [https://doi.org/10.1002/ecs2.1539 Link]

@@ Line 21: / Line 21: @@
 === '''Algorithm''' ===
-(1) unfold PHIDP.
+(1) unfold <math>\phi_{DP}</math>.
 (2) apply a finite impulse response (FIR) filter to unfolded <math>\phi_{DP}</math>, a specified number of times, to create 'smoothed <math>\phi_{DP}</math>'. This step is similar to Hubbert and Bringi (1995), but uses fewer iterations.
@@ Line 29: / Line 29: @@
 (4) apply FIR filter to 'conditioned <math>\phi_{DP}</math>' a number of times, to provide further smoothing.
-(5) Compute <math>K_{DP}</math> as the (slope of conditioned PHIDP in range) / 2.0.
+(5) Compute <math>K_{DP}</math> as the (slope of conditioned <math>\phi_{DP}</math> in range) / 2.0.
 ==== '''Notes''' ====

@@ Line 23: / Line 23: @@
 (1) unfold PHIDP.
-(2) apply a finite impulse response (FIR) filter to unfolded PHIDP, a specified number of times, to create 'smoothed <math>\phi_{DP}</math>'. This step is similar to Hubbert and Bringi (1995), but uses fewer iterations.
+(2) apply a finite impulse response (FIR) filter to unfolded <math>\phi_{DP}</math>, a specified number of times, to create 'smoothed <math>\phi_{DP}</math>'. This step is similar to Hubbert and Bringi (1995), but uses fewer iterations.
 (3) for increasing range, identify peaks in 'smoothed <math>\phi_{DP}</math>' which are followed by a minimum. Remove these peaks, by trimming them down to the minimum that follows. We call the result the 'conditioned <math>\phi_{DP}</math>'. This step removes the local increases in <math>\phi_{DP}</math> due to backscatter differential phase.

← Older revision		Revision as of 23:44, 23 February 2021
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	=== '''Background and Objectives''' ===		=== '''Background and Objectives''' ===
−	As a radar beam propagates through a precipitating medium, the electromagnetic wave slows down resulting in a phase shift. In radar volumes where the hydrometeors are not spherical, the phase shifts of the horizontal and vertical pulses are different. <math>\phi_{DP}</math> measures the difference between these phase shifts. However, <math>\phi_{DP}</math> accumulates along the beam, which makes the field difficult to interpret. Calculating the range derivative of ~~PHIDP~~ produces the <math>K_{DP}</math> field, which highlights areas of strong changes in <math>\phi_{DP}</math>.	+	As a radar beam propagates through a precipitating medium, the electromagnetic wave slows down resulting in a phase shift. In radar volumes where the hydrometeors are not spherical, the phase shifts of the horizontal and vertical pulses are different. <math>\phi_{DP}</math> measures the difference between these phase shifts. However, <math>\phi_{DP}</math> accumulates along the beam, which makes the field difficult to interpret. Calculating the range derivative of <math>\phi_{DP}</math> produces the <math>K_{DP}</math> field, which highlights areas of strong changes in <math>\phi_{DP}</math>.

@@ Line 1: / Line 1: @@
-LROSE procedure to estimate KDP from PHIDP
+LROSE procedure to estimate <math>K_{DP}</math> from <math>\phi_{DP}</math>
 === '''Overview''' ===
-KDP is estimated from the range derivative of PHIDP, which accumulates along a radar beam as it passes through a precipitating medium. Regions of higher KDP correspond to regions of increased raindrop size and concentration. PHIDP must be pre-processed so that KDP is useful.
+<math>K_{DP}</math> is estimated from the range derivative of <math>\phi_{DP}</math>, which accumulates along a radar beam as it passes through a precipitating medium. Regions of higher <math>K_{DP}</math> correspond to regions of increased raindrop size and concentration. <math>\phi_{DP}</math> must be pre-processed so that <math>K_{DP}</math> is useful.
-The LROSE method for estimating KDP is based on an updated version of the technique developed by [http://wiki.lrose.net/index.php/KDP_estimation#References Hubbert and Bringi (1995)].
+The LROSE method for estimating <math>K_{DP}</math> is based on an updated version of the technique developed by [http://wiki.lrose.net/index.php/KDP_estimation#References Hubbert and Bringi (1995)].
 === '''Background and Objectives''' ===
-As a radar beam propagates through a precipitating medium, the electromagnetic wave slows down resulting in a phase shift. In radar volumes where the hydrometeors are not spherical, the phase shifts of the horizontal and vertical pulses are different. PHIDP measures the difference between these phase shifts. However, PHIDP accumulates along the beam, which makes the field difficult to interpret. Calculating the range derivative of PHIDP produces the KDP field, which highlights areas of strong changes in PHIDP.
+As a radar beam propagates through a precipitating medium, the electromagnetic wave slows down resulting in a phase shift. In radar volumes where the hydrometeors are not spherical, the phase shifts of the horizontal and vertical pulses are different. <math>\phi_{DP}</math> measures the difference between these phase shifts. However, <math>\phi_{DP}</math> accumulates along the beam, which makes the field difficult to interpret. Calculating the range derivative of PHIDP produces the <math>K_{DP}</math> field, which highlights areas of strong changes in <math>\phi_{DP}</math>.
-In order to ensure the KDP field is useful, pre-processing of the PHIDP field is necessary. First, PHIDP is a noisy field. We want the KDP algorithm to identify regions of substantial change in PHIDP. Second, although phase shifts in Rayleigh-scattering regimes are dominated by changes in the wave propagation speed, Mie-scattering regimes induce a additional phase shift component related to backscatter differential phase (or phase shift on backscatter). That is, where nonspherical hydrometeors are large compared to the radar wavelength, constructive and destructive interference in the backscattered signal due to resonance can produce local phase shifts that aren't directly related to the liquid water content slowing down the radar beam. Refer to Figure 3 of [http://wiki.lrose.net/index.php/KDP_estimation#References Stepanian et al. (2016)] for a good visualization of Mie-scattering effects. Before KDP is calculated, these two issues need to be accounted for.
+In order to ensure the KDP field is useful, pre-processing of the <math>\phi_{DP}</math> field is necessary. First, <math>\phi_{DP}</math> is a noisy field. We want the <math>K_{DP}</math> algorithm to identify regions of substantial change in <math>\phi_{DP}</math>. Second, although phase shifts in Rayleigh-scattering regimes are dominated by changes in the wave propagation speed, Mie-scattering regimes induce a additional phase shift component related to backscatter differential phase (or phase shift on backscatter). That is, where nonspherical hydrometeors are large compared to the radar wavelength, constructive and destructive interference in the backscattered signal due to resonance can produce local phase shifts that aren't directly related to the liquid water content slowing down the radar beam. Refer to Figure 3 of [http://wiki.lrose.net/index.php/KDP_estimation#References Stepanian et al. (2016)] for a good visualization of Mie-scattering effects. Before <math>K_{DP}</math> is calculated, these two issues need to be accounted for.
-'''The primary objectives of the LROSE KDP computation are:  '''
+'''The primary objectives of the LROSE <math>K_{DP}</math> computation are:  '''
-* smooth the PHIDP profile
+* smooth the <math>\phi_{DP}</math> profile
-* remove local increases in PHIDP caused by backscatter differential phase
+* remove local increases in <math>\phi_{DP}</math> caused by backscatter differential phase
 === '''Algorithm''' ===
@@ Line 23: / Line 23: @@
 (1) unfold PHIDP.
-(2) apply a finite impulse response (FIR) filter to unfolded PHIDP, a specified number of times, to create 'smoothed PHIDP'. This step is similar to Hubbert and Bringi (1995), but uses fewer iterations.
+(2) apply a finite impulse response (FIR) filter to unfolded PHIDP, a specified number of times, to create 'smoothed <math>\phi_{DP}</math>'. This step is similar to Hubbert and Bringi (1995), but uses fewer iterations.
-(3) for increasing range, identify peaks in 'smoothed PHIDP' which are followed by a minimum. Remove these peaks, by trimming them down to the minimum that follows. We call the result the 'conditioned PHIDP'. This step removes the local increases in PHIDP due to backscatter differential phase.
+(3) for increasing range, identify peaks in 'smoothed <math>\phi_{DP}</math>' which are followed by a minimum. Remove these peaks, by trimming them down to the minimum that follows. We call the result the 'conditioned <math>\phi_{DP}</math>'. This step removes the local increases in <math>\phi_{DP}</math> due to backscatter differential phase.
-(4) apply FIR filter to 'conditioned PHIDP' a number of times, to provide further smoothing.
+(4) apply FIR filter to 'conditioned <math>\phi_{DP}</math>' a number of times, to provide further smoothing.
-(5) Compute KDP as the (slope of conditioned PHIDP in range) / 2.0.
+(5) Compute <math>K_{DP}</math> as the (slope of conditioned PHIDP in range) / 2.0.
 ==== '''Notes''' ====
-For these steps, the user can modify the FIR length and the number of iterations in steps 2 and 4. The number of gates used to calculate KDP are reflectivity-dependent, where the number of gates decreases from 8 to 4 to 2 where reflectivities surpass thresholds of 20 and 35 dBZ.
+For these steps, the user can modify the FIR length and the number of iterations in steps 2 and 4. The number of gates used to calculate <math>K_{DP}</math> are reflectivity-dependent, where the number of gates decreases from 8 to 4 to 2 where reflectivities surpass thresholds of 20 and 35 dBZ.
 === '''Self-consistency''' ===
-One drawback of this method is that it can over-smooth the PHIDP profile and broaden regions of higher KDP to radar gates that are beyond the precipitation causing the phase shift. The self-consistency method attempts to identify regions where high KDP is likely. The algorithm can estimate KDP from Z and ZDR (this estimated KDP will be incorrect and differ from observations). The synthetic KDP is then compared to the measured PHIDP change and is then scaled to match the observed values.
+One drawback of this method is that it can over-smooth the PHIDP profile and broaden regions of higher <math>K_{DP}</math> to radar gates that are beyond the precipitation causing the phase shift. The self-consistency method attempts to identify regions where high <math>K_{DP}</math> is likely. The algorithm can estimate <math>K_{DP}</math> from Z and ZDR (this estimated <math>K_{DP}</math> will be incorrect and differ from observations). The synthetic <math>K_{DP}</math> is then compared to the measured <math>\phi_{DP}</math> change and is then scaled to match the observed values.
 === '''References''' ===
 Hubbert, J. and V.N. Bringi, 1995: An Iterative Filtering Technique for the Analysis of Copolar Differential Phase and Dual-Frequency Radar Measurements. J. Atmos. Oceanic Technol., 12, 643–648. [https://journals.ametsoc.org/doi/pdf/10.1175/1520-0426%281995%29012%3C0643%3AAIFTFT%3E2.0.CO%3B2 Link]
 Stepanian, P. M., K. G. Horton, V. M. Melnikov, D. S. Zrnić, and S. A. Gauthreaux Jr., 2016: Dual-polarization radar products for biological applications. Ecosphere, 7, e01539. [https://doi.org/10.1002/ecs2.1539 Link]

← Older revision		Revision as of 23:49, 26 January 2021
Line 12:		Line 12:


−	In order to ensure the KDP field is useful, pre-processing of the PHIDP field is necessary. First, PHIDP is a noisy field. We want ~~to ensure~~ the KDP algorithm ~~identifies~~ regions of substantial change in PHIDP. Second, although phase shifts in Rayleigh-scattering regimes are dominated by changes in the wave propagation speed, Mie-scattering regimes ~~will~~ induce a additional phase shift component related to backscatter differential phase (or phase shift on backscatter). That is, where nonspherical hydrometeors are large compared to the radar wavelength, constructive and destructive interference in the backscattered signal due to resonance can produce local phase shifts that aren't directly related to the liquid water content slowing down the radar beam. Figure 3 of [http://wiki.lrose.net/index.php/KDP_estimation#References Stepanian et al. (2016)] ~~offers~~ a good visualization of Mie-scattering effects. Before KDP is calculated, these two issues need to be accounted for.	+	In order to ensure the KDP field is useful, pre-processing of the PHIDP field is necessary. First, PHIDP is a noisy field. We want the KDP algorithm to identify regions of substantial change in PHIDP. Second, although phase shifts in Rayleigh-scattering regimes are dominated by changes in the wave propagation speed, Mie-scattering regimes induce a additional phase shift component related to backscatter differential phase (or phase shift on backscatter). That is, where nonspherical hydrometeors are large compared to the radar wavelength, constructive and destructive interference in the backscattered signal due to resonance can produce local phase shifts that aren't directly related to the liquid water content slowing down the radar beam. Refer to Figure 3 of [http://wiki.lrose.net/index.php/KDP_estimation#References Stepanian et al. (2016)] for a good visualization of Mie-scattering effects. Before KDP is calculated, these two issues need to be accounted for.

← Older revision		Revision as of 23:47, 26 January 2021
Line 12:		Line 12:


−	In order to ensure the KDP field is useful, pre-processing of the PHIDP field is necessary. First, PHIDP is a noisy field. We want to ensure the KDP algorithm identifies regions of substantial change in PHIDP. Second, although phase shifts in Rayleigh-scattering regimes are dominated by changes in the wave propagation speed, Mie-scattering regimes will induce a additional phase shift component related to backscatter differential phase (or phase shift on backscatter). That is, where nonspherical hydrometeors are large compared to the radar wavelength, constructive and destructive interference in the backscattered signal due to resonance can produce local phase shifts that aren't directly related to the liquid water content slowing down the radar beam. Before KDP is calculated, these two issues need to be accounted for.	+	In order to ensure the KDP field is useful, pre-processing of the PHIDP field is necessary. First, PHIDP is a noisy field. We want to ensure the KDP algorithm identifies regions of substantial change in PHIDP. Second, although phase shifts in Rayleigh-scattering regimes are dominated by changes in the wave propagation speed, Mie-scattering regimes will induce a additional phase shift component related to backscatter differential phase (or phase shift on backscatter). That is, where nonspherical hydrometeors are large compared to the radar wavelength, constructive and destructive interference in the backscattered signal due to resonance can produce local phase shifts that aren't directly related to the liquid water content slowing down the radar beam. Figure 3 of [Stepanian et al. (2016)] offers a good visualization of Mie-scattering effects. Before KDP is calculated, these two issues need to be accounted for.