Design and evaluation of a specific differential phase estimation algorithm for dual-polarization radar using scale-adaptive local polynomial fitting

Nagumo, Nobuhiro; Yamauchi, Hiroshi

doi:10.5194/egusphere-2026-1290

Preprints

https://doi.org/10.5194/egusphere-2026-1290

Preprints

22 Jun 2026

| 22 Jun 2026

Design and evaluation of a specific differential phase estimation algorithm for dual-polarization radar using scale-adaptive local polynomial fitting

Nobuhiro Nagumo and Hiroshi Yamauchi

Abstract. We propose a method for estimating the specific differential phase (K_DP) with high spatial resolution from the received differential phase (Ψ_DP) observed by dual-polarization radar and then evaluate the performance of the estimated K_DP. Because Ψ_DP contains noise, its range derivative, K_DP, is prone to significant errors. The proposed method performs scale-adaptive local polynomial fitting, wherein the fitting window is dynamically adjusted based on the magnitude of the K_DP. This adjustment enables high resolution in regions with large K_DP and noise suppression in regions with small K_DP through optimal setting of parameters. The method was applied to Ψ_DP data from both idealized synthetic experiments and actual radar observations. Compared to existing algorithms, the method improved noise suppression in low-K_DP regions while enhancing accuracy in regions exhibiting fine-scale K_DP variation. The good agreement of the results with Ψ_DP in terms of the cumulative phase shift demonstrated a balance between fine-scale accuracy and robustness.

Received: 09 Mar 2026 – Discussion started: 22 Jun 2026

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Nobuhiro Nagumo and Hiroshi Yamauchi

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-1290', Anonymous Referee #1, 17 Jul 2026

Find attached the minor comments about the manuscript

Citation: https://doi.org/10.5194/egusphere-2026-1290-RC1
- AC1: 'Reply on RC1', Nobuhiro Nagumo, 27 Jul 2026
  
  General Comments (Correspondence between text and Figure 1 / Section 2.3)
  
  → To clarify the correspondence between the text and Figure 1, we have added explicit cross-references at the following locations:
  
  * After the description of Figure 1 in Section 2.1 (specifically, after Equation (4)).
  
  * After Equations (5) and (6) in Section 2.2.
  
  Furthermore, regarding Section 2.3, we added a cross-reference at the beginning of the section to clarify its connection to the figure. Additionally, we newly included Figure 1b to visually illustrate and explain Equations (7) and (8).
  Minor Comments
  
  • Some Equations are in italic and some other are not.
  
  → Unified the font styles (such as italic variables and roman subscripts/abbreviations) throughout the manuscript to ensure consistency.
  • Lines 192 and 196 refer to Figure 4, not Figure 3.
  
  → Revised as suggested.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1290-AC1
RC2:
'Comment on egusphere-2026-1290', Anonymous Referee #2, 18 Jul 2026

This manuscript presents a scale-adaptive local polynomial fitting algorithm for estimating the specific differential phase (KDP) from dual-polarization radar observations. The method provides a useful improvement to KDP estimation techniques. However, several aspects of the manuscript require further clarification and improvement.
Line 15, The good agreement between calculated and observed Ψdp...
Line 22, KDP represents the range derivative of the differential phase, and this definition should be revised.
Line 49, achieves a spatial resolution of 250 m
Line 80, where Δr
Line 126, as follows.
Line 135, Section 2 provides a clear description of the algorithm, noting that a threshold N is used to distinguish between signal and noise. However, the process of determining N by sensitivity analysis is not presented. How can the choice of N be justified as reasonable? The dose parameter N related to a and b?
Line 143, an azimuthal range resolution of 250 m ?
Line 175, Idealized experiments involving parameters a and b demonstrate the effectiveness of the adjustment window in improving Kdp estimation. Dose hese parameters require adjustment for different radar systems and precipitation types?
Line 185，distributions cantered, recommand changed into centered
Figure 8, Line 256 0145 UTC, Line 265 0114 UTC. Which time is correct?
Reference formatting， Please check the formatting of the reference list. The references of Marshall and Palmer (1948) and Reimel and Kumjian (2021) appear to be merged without proper line separation.

Citation: https://doi.org/10.5194/egusphere-2026-1290-RC2
- AC2: 'Reply on RC2', Nobuhiro Nagumo, 27 Jul 2026
  
  Line 15, The good agreement between calculated and observed Ψdp...
  
  → Revised as suggested.
  Line 22, KDP represents the range derivative of the differential phase, and this definition should be revised.
  
  → Revised as suggested.
  Line 49, achieves a spatial resolution of 250 m
  
  → Revised as suggested.
  Line 80, where Δr
  
  → Revised as suggested.
  Line 126, as follows.
  
  → Revised as suggested.
  Line 135, Section 2 provides a clear description of the algorithm, noting that a threshold N is used to distinguish between signal and noise. However, the process of determining N by sensitivity analysis is not presented. How can the choice of N be justified as reasonable? The dose parameter N related to a and b?
  
  → Added a note after Equation (8) in Section 2.3 stating that the choice of N is based on RMSE from observational data.
  Line 143, an azimuthal range resolution of 250 m ?
  
  → Revised as suggested.
  Line 175, Idealized experiments involving parameters a and b demonstrate the effectiveness of the adjustment window in improving Kdp estimation. Dose hese parameters require adjustment for different radar systems and precipitation types?
  
  → Revised as suggested.
  Line 185, distributions cantered, recommand changed into centered
  
  → Changed to "centered" as suggested.
  Figure 8, Line 256 0145 UTC, Line 265 0114 UTC. Which time is correct?
  
  → Revised to 0145 UTC to unify the timestamp.
  Reference formatting, Please check the formatting of the reference list. The references of Marshall and Palmer (1948) and Reimel and Kumjian (2021) appear to be merged without proper line separation.
  
  → Revised as suggested.
  
  Citation: https://doi.org/10.5194/egusphere-2026-1290-AC2

Nobuhiro Nagumo and Hiroshi Yamauchi

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Short summary

Dual-polarization radars are vital for rainfall observation. A key parameter, specific differential phase, provides detailed rain intensity but faces a trade-off between noise reduction and spatial resolution. We developed a real-time method that dynamically maintains high resolution in heavy rain while suppressing errors in light rain. Our approach captures fine-scale structures more reliably than previous techniques, avoiding over-smoothed artifacts to provide authentic weather maps.


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