Title Page

Contents

요약 15

CHAPTER 1. Introduction 17

1.1. Background and Motivation 17

1.2. Dissertation overview 21

CHAPTER 2. Polarimetric radar capability in attenuation correction 24

2.1. Polarimetric radar variables 24

2.1.1. Radar reflectivity factors at the horizontal and vertical polarizations (ZHH and ZVV)(이미지참조) 25

2.1.2. Differential reflectivity (ZDR)(이미지참조) 28

2.1.3. Co-polarization correlation coefficient (ρhv)(이미지참조) 30

2.1.4. Differential phase (ΦDP) and Specific differential phase (KDP)(이미지참조) 31

2.1.5. Specific and differential specific attenuation (AH, V, DP)(이미지참조) 34

2.2. Review of polarimetric techniques for attenuation correction 35

2.2.1. Conventional attenuation correction 36

2.2.2. Attenuation correction by using optimal coefficients 39

CHAPTER 3. Modified Hot-Spot method for attenuation correction 45

3.1. Attenuation and differential attenuation in hot-spot 45

3.1.1. Characteristics of attenuation and differential attenuation in hot-spot 46

3.1.2. The importance of attenuation correction in hot-spot 52

3.2. Hot-spot method for attenuation correction 53

3.2.1. Concept of the Hot-spot method 53

3.2.2. Derivation of the Hot-spot method algorithm 56

3.3. Modified Hot-spot method 69

3.3.1. Concept of the modified Hot-spot method 69

3.3.2. Design of the modified Hot-spot method algorithm 72

CHAPTER 4. Attenuation correction in heavy rain 75

4.1. Attenuation correction in heavy rain in Oklahoma 76

4.1.1. Description of the storm and dataset 76

4.1.2. Results of attenuation correction 86

4.2. Attenuation correction for the Chicago storm 106

4.2.1. Description of the storm and dataset 106

4.2.2. Results of attenuation correction 114

CHAPTER 5. Validation of the attenuation correction methods 122

5.1. Comparison with S band radar measurements 122

5.2. Rainfall measurement relations 128

CHAPTER 6. Summary and future work 139

6.1. Summary 139

6.2. Future work 142

Appendix - Nomenclature 144

References 148

Table 2.1. Typical ZDR values of raindrops of various sizes and shapes(이미지참조) 29

Table 3.1. Details of the modified Hot-spot method design 74

Table 4.1. System characteristics of OU PRIME radar 81

Table 4.2. System characteristics of KOUN radar 82

Table 4.3. System characteristics of Valpo radar 110

Table 4.4. System characteristics of KLOT radar 111

Table 5.1. Quantitative measures of 1-hour rain total radar estimates at C and S bands radars 138

Fig. 2.1. The incident waves which are horizontally and vertically polarized on an oblate raindrop. 27

Fig. 2.2. (a) Schematic diagram of lagging of the horizontal (dashed line) and vertical (solid line) polarized waves through the rain medium as time passed (T1~T3). (b) Schematic diagram of the propagation phase delay between the horizontal (dashed line) and vertical (solid line) polarized waves.The cumulative value of which along the radial... 33

Fig. 3.1. The dependencies of AH and KDP on raindrop equivolume diameter at C-band (T ＝ 20℃). Raindrop shapes are assumed as in Brandes et al. (2002).(이미지참조) 47

Fig. 3.2. Scatterplot of ZDR vs Z in pure rain at C-band; Z and ZDR are computed from 25920 DSDs measured in central Oklahoma. Raindrop temperature is 20℃. The shape-size dependence of raindrops is assumed to be as in Brandes et al. (2002). The gray line indicates the dependence of median ZDR on Z for 25 〈Z 〈45 dBZ.(이미지참조) 49

Fig. 3.3 Scatterplots of AH (top) and ADP (bottom) vs KDP in pure rain at C-band for (a), (c) all ZDR and (b), (d) ZDR 〈3 dB. Radar variables are computed from 25920 DSDs measured in Oklahoma. 50

Fig. 3.4. Scatterplot of the ratio ADP/KDP vs ZDR in pure rain at C-band. Radar variables are computed from 25920 DSDs measured in Oklahoma.(이미지참조) 51

Fig. 3.5. Conceptual plot illustrating the hot spot between ranges r₁ and r₂ in the radial profiles of (a) Z and (b) ΦDP.(이미지참조) 55

Fig. 3.6. Scatterplots of α0 vs β0 simulated from disdrometer data in Oklahoma for T = 10℃and 20℃ for ZDR varying between 0.5 and 3.0 dB. Dashed line depicts the dependence α0 = 3.33β0 from Vulpiani et al. (2008).(이미지참조) 59

Fig. 3.7. Retrieved radial profiles of specific attenuation AH for α0=0.06 dB per degree,different values of △α in a hot spot, and different locations of a hot spot along the propagation path. The true value of △α in a hot spot is equal to 0.04 dB per degree. Here, L/R is the ratio of the left and right sides of Eq.(3.9). The retrieved profile of AH...(이미지참조) 64

Fig. 3.8. Detailed procedure of polarimetric attenuation correction by using Hot-spot method 68

Fig. 3.9. Procedure of the modified Hot-spot method. In the step for classifying HS radials, corrected Z is preliminarily corrected using Bringi et al. (2001) self-consistent method is utilized. The background correction factors for Z and ZDR correction are utilized with the optimal values αopt and βopt .(이미지참조) 71

Fig. 4.1. (a) Isotachs, streamlines and divergence at 300 mb, (b) geopotential heights, temperature, and wind vectors at 500 mb, (c) geopotential heights, temperature, dew point temperature, and wind vectors at 850 mb, and (d) composite image of surface weather map, satellite infra-red image, and radar reflectivity at 00 UTC 10 March 2009. 77

Fig. 4.2. (a) Isotachs, streamlines and divergence at 300 mb, (b) geopotential heights, temperature, and wind vectors at 500 mb, (c) geopotential heights, temperature, dew point temperature, and wind vectors at 850 mb, and (d) composite image of surface weather map, satellite infra-red image, and radar reflectivity at 12 UTC 14 June 2010. 78

Fig. 4.3. Relative location of OU PRIME and KOUN dual polarization radars. 80

Fig. 4.4. Relative location of Oklahoma Mesonet and Oklahoma City Micronet rain gage stations within 120 km in X and Y directions from OU PRIME C-band radar center (OU PRIME and KOUN dual polarization radars are denoted with square and star, respectively). 85

Fig. 4.5. Fields of measured (a) Z, (b) ZDR, (c) ΦDP, and (d) ρhv measured by OU PRIMEC-band dual polarization radar at 0427 UTC 10 March 2009. Here, the elevation＝1.37° . The areas of visible negative values of ZDR caused by differential attenuation at C-band are marked as "A' and "B" in the ZDR panel. In all panels, a line...(이미지참조) 87

Fig. 4.6. Fields of measured (a) Z, (b) ZDR, (c) ΦDP, and (d) ρhv measured by KOUN Sbanddual polarization radar at 0425 UTC 10 March 2009. Here, the elevation =1.45° . 88

Fig. 4.7. Composite RHI plot of (top) Z, (middle top) ZDR, (middle bottom) ΦDP, and(bottom) ρhv at (left) C and (right) S bands for the storm at 0427 UTC 10 March 2009.Here, azimuth C-band = 351.5° and azimuth S-band = 352° . The azimuthal direction of the vertical cross section is shown in Fig. 4.5.(이미지참조) 89

Fig. 4.8. Composite plot of (a) Z measured by KOUN (S-band) at 0425 UTC, (b) Z measured by OU PRIME (C-band), Z corrected by (c) simple linear method, (d) self-consistent method, (e) Hot-spot method, and (f) modified Hot-spot method, respectively at 0427 UTC 10 March 2009. 93

Fig. 4.9. Composite plot of (a) ZDR measured by KOUN (S-band) at 0425 UTC, (b) ZDR measured by OU PRIME (C-band), ZDR corrected by (c) simple linear method, (d) self-consistent method, (e) Hot-spot method, and (f) modified Hot-spot method, respectively at 0427 UTC 10 March 2009.(이미지참조) 94

Fig. 4.10. Scatterplots of Z and ZDR for (a) measured by KOUN (S-band), (b) measured by OU PRIME (C-band), corrected by (c) simple linear method, (d) self-consistent method, (e) Hot-spot method, and (f) modified Hot-spot method, respectively at 0427 UTC 10 March 2009. Black solid line denotes the median values of ZDR.(이미지참조) 95

Fig. 4.11. Scatterplots of β versus α in the hot spots in the case at 0427 UTC 10 March 2009. Black asterisks denotes values in Hot-spot method, red diamonds in self-consistent method, and blue diamonds in modified Hot-spot method in hot spot areas. 96

Fig. 4.12. Fields of measured (a) Z, (b) ZDR, (c) ΦDP, and (d) phv measured by OU PRIMEC-band dual polarization radar at 1202 UTC 14 June 2010. Here, the elevation＝1.37° .The sector of visible negative values of ZDR caused by differential attenuation at C-bandis marked as,,A' in the ZDR panel.(이미지참조) 98

Fig. 4.13. Fields of measured (a) Z, (b) ZDR, (c) ΦDP, and (d) ρhv measured by KOUN Sbanddual polarization radar at 1202 UTC 14 June 2010. Here, the elevation =1.49° . 99

Fig. 4.14. Composite plot of (a) Z measured by KOUN (S-band), (b) Z measured by OU PRIME (C-band), Z corrected by (c) simple linear method, (d) self-consistent method, (e) Hot-spot method, and (f) modified Hot-spot method, respectively at 1202 UTC 14 June 2010. 102

Fig. 4.15. Composite plot of (a) ZDR measured by KOUN (S-band), (b) ZDR measured by OU PRIME (C-band), ZDR corrected by (c) simple linear method, (d) self-consistent method, (e) Hot-spot method, and (f) modified Hot-spot method, respectively at 1202 UTC 14 June 2010.(이미지참조) 103

Fig. 4.16. Scatterplots of Z and ZDR for (a) measured by KOUN (S-band), (b) measured by OU PRIME (C-band), corrected by (c) simple linear method, (d) self-consistent method, (e) Hot-spot method, and (f) modified Hot-spot method, respectively at 1202 UTC 14 June 2010. Black solid line denotes the median values of ZDR.(이미지참조) 104

Fig. 4.17. Scatterplots of β versus α in the hot spots in the case at 1202 UTC 14 June 2010. Black asterisks denotes values in Hot-spot method, red diamonds in self-consistent method, and blue diamonds in modified Hot-spot method in hot spot areas. 105

Fig. 4.18. (a) Isotachs, streamlines and divergence at 300 mb, (b) geopotential heights, temperature, and wind vectors at 500 mb, (c) geopotential heights, temperature, dew point temperature, and wind vectors at 850 mb, and (d) composite image of surface weather map, satellite infra-red image, and radar reflectivity at 00 UTC 5 August 2008. 107

Fig. 4.19. Relative location of Valpo dual polarization radar and KLOT single polarization radar. 109

Fig. 4.20. Radial profiles of differential phase (a) measured by the Valpo radar, (b) after downward phase shift, and (c) after editing, unfolding, and smoothing at 0149 UTC on 5 August 2008. 113

Fig. 4.21. Fields of measured (a) Z, (b) ZDR, (c) ФDP, and (d) ρhv measured by Valpo Cbanddual polarization radar at 0149 UTC 5 August 2008. Here, the elevation＝0.99° .The areas of visible negative values of ZDR caused by differential attenuation at C-bandare marked as,,A' and,,B' in the ZDR panel.(이미지참조) 115

Fig. 4.22. Composite plot of (a) Z measured by KLOT (S-band), (b) Z measured by Valpo radar (C-band), Z corrected by (c) simple linear method, (d) self-consistent method, (e) Hot-spot method, and (f) modified Hot-spot method, respectively at 0149 UTC 5 August 2008. 118

Fig. 4.23. Composite plot of (a) ZDR measured by Valpo radar (C-band), ZDR corrected by (b) simple linear method, (c) self-consistent method, (d) Hot-spot method, and (e) modified Hot-spot method, respectively at 0149 UTC 5 August 2008.(이미지참조) 119

Fig. 4.24. Scatterplots of Z and ZDR for (a) measured by Valpo radar (C-band), corrected by (b) simple linear method, (c) self-consistent method, (d) Hot-spot method, and (e) modified Hot-spot method, respectively at 0149 UTC 5 August 2008. Black solid line denotes the median values of ZDR.(이미지참조) 120

Fig. 4.25. Scatterplots of β versus α in the hot spots in the case at 0149 UTC 5 August 2008. Black asterisks denotes values in Hot-spot method, red diamonds in self-consistent method, and blue diamonds in modified Hot-spot method in hot spot areas. 121

Fig. 5.1. Scatterplots of the differences Z(S-band)-Z(C-band) vs ZDR(S-band)-ZDR(C-band) (a) before attenuation correction and after (b) simple linear, (c) Hot-spot, (d) self-consistent, and (e) modified Hot-spot methods for attenuation correction at 0427 UTC 10 March 2009. (f) The measured ZDR at C-band (OU PRIME). Black square denotes the...(이미지참조) 124

Fig. 5.2. Scatterplots of the differences Z(S-band)-Z(C-band) vs ZDR(S-band)-ZDR(C-band) (a) before attenuation correction and after (b) simple linear, (c) Hot-spot, (d) self-consistent, and (e) modified Hot-spot methods for attenuation correction at 1202 UTC 14 June 2010. (f) The measured ZDR at C-band (OU PRIME). Black square denotes the...(이미지참조) 125

Fig. 5.3. Scatterplots of the Z(S-band) vs Z(C-band) (a) before attenuation correction and after (b) simple linear, (c) Hot-spot, (d) self-consistent, and (e) modified Hot-spot methods for attenuation correction at 0149 UTC 5 August 2008. (f) The measured ZDR at C-band (Valpo). Black square denotes the selected area for the scatterplots.(이미지참조) 127

Fig. 5.4. Fields of rain rates obtained using R(Z) based on (a) Z measured by KOUN (S-band), (b) Z measured by OU PRIME (C-band), Z corrected by (c) simple linear method, (d) self-consistent method, (e) Hot-spot method, and (f) modified Hot-spot method, respectively at 0427 UTC 10 March 2009. 132

Fig. 5.5. Fields of rain rates obtained using R(Z) based on (a) Z measured by KOUN (S-band), (b) Z measured by OU PRIME (C-band), Z corrected by (c) simple linear method, (d) self-consistent method, (e) Hot-spot method, and (f) modified Hot-spot method, respectively at 1202 UTC 14 June 2010. 133

Fig. 5.6. Fields of rain rates obtained using R(Z) based on (a) Z measured by KLOT (S-band), (b) Z measured by Valpo radar (C-band), Z corrected by (c) simple linear method, (d) self-consistent method, (e) Hot-spot method, and (f) modified Hot-spot method, respectively at 0149 UTC 5 August 2008. 134

Fig. 5.7. Scatterplots of 1-hour rain totals measured by gages versus rain rates obtained using R(Z) based on (a) Z measured by KOUN (S-band), (b) Z measured by OU PRIME (C-band), Z corrected by (c) simple linear method, (d) self-consistent method, (e) Hot-spot method, and (f) modified Hot-spot method, respectively at 1202 UTC 14 June 2010. 135

Fig. 5.8. Scatterplots of 1-hour rain totals measured by gages versus rain rates obtained using (a) R(KDP), R(Z) based on (b) measured Z, Z corrected by (c) simple linear method, (d) self-consistent method, (e) Hot-spot method, and (f) modified Hot-spot method, respectively at OU PRIME (C-band) at 1202 UTC 14 June 2010.(이미지참조) 136

Fig. 5.9. Scatterplots of 1-hour rain totals measured by gages versus rain rates obtained using (a) R(KDP) at OU PRIME(C-band), (b) R(KDP) at KOUN (S-band), and (c) R(Z) based on Z corrected by the modified Hot-spot method, respectively at OU PRIME (C-band) at 1202 UTC 14 June 2010.(이미지참조) 137

다양한 편파 인자들을 이용한 정량 강수추정 및 강수 시스템의 정성적 분석을 위한 이중편파레이더의 중요성이 점차 증대되는 만큼 자료의 품질관리가 매우 중요시되고 있으며, 특히, 단파장 레이더에서 쉽게 발생할 수 있는 반사도와 차등반사도의 감쇠에 대한 보정기술 개발이 요구된다.

편파레이더 인자 중 차등위상(differential phase; ΦDP)은 레이더 보정, 지형 반사장애 및 감쇠 등에 영향을 받지 않으므로 이를 이용한 반사도와 차등반사도의 감쇠보정이 가능하다. 거리에 따른 반사도와 차등반사도의 감쇠비는 AH＝αKDP 와 ADP＝βKDP로 비차등위상 (specific differential phase; KDP)과 비례하는 산단한 선형식으로 표현할 수 있다. 이전 연구들에서는 계수 α와 β 값들을 기후학적 경험 값으로 레이더 전체 자료에 적용해 왔으나, α와 β가 온도 및 강수 시스템의 입자분포(drop size distribution; DSD)와 매우 밀접한 관련이 있으므로 보다 세분된 계수 값 분포를 구하는 것이 필요하다. 본 연구에서는 특히, C-band 레이더가 가지는 공진효과에 의한 반사도와 차등반사도의 급격한 감쇠에 영향을 주는 큰 강수 입자를 포함하는 강한 강수세포(hot spot)를 선행적으로 추정하고 이 영역의 차등위상 증량(ΔΦDP)을 이용하여 계수 α와 β의 변화를 고려하는 감쇠보정 방법(Hot-spot method)과 이 방법에 사용되는 배경 계수 값 α0와 β0를 Bringi et al. (2001)이 제안한 방법을 이용해 최적 값을 도출하여 적용하는 개선된 Hot-spot 방법을 제안하였다.

제안된 방법들은 기존 연구들이 소개한 선형 보정법(Bringi et al. 1990) 과 최적계수 도출법(Bringi et al. 2001)과 함께 각각 미국 오클라호마주와 인디애나주에 있는 C-band 이중편파레이더를 이용하여 오클라호마주에서 발생한 두 개의 강한 강수 사례와 시카고 도심 지역에서 발생한 하나의 강수 사례에 적용하여 성능을 비교하였다. 본 연구에서 새롭게 제안된 감쇠보정 기법들은 기존의 기법이 가지고 있는 감쇠 보정계수를 일정 상수값으로 가정하는 단점을 보완하고 큰 강수입자를 많이 포함하고 있는 강한 강수 세포 내에서의 감쇠 보정계수 증가를 객관적인 접근을 통해 도출함으로써 보다 정확하고 신뢰성 있는 감쇠보정 효과를 얻을 수 있었다. 보정된 자료를 각 C-band 이중편파레이더 인근에 있는 감쇠 영향이 적은 S-band 이중편파레이더 자료와 비교 검증한 결과, (시카고 사례는 S-band 단일 편파레이더 사용), 새롭게 제안된 기법들이 가장 좋은 결과를 보였다. 또한, 보정된 반사도 값을 Z-R 관계식을 이용해 강우량 값으로 변환하여 이를 지상의 우량계 자료와의 비교 검증을 한 결과, 개선된 Hot-spot 방법에서 도출된 값이 지상 우량계 값과 가장 작은 오차를 보이며 좋은 결과를 보였다.

감쇠현상이 큰 C-band 이중편파레이더를 이용하여 큰 감쇠를 보였던 대류형 강수시스템의 감쇠보정을 정확히 산출함으로써 이중편파레이더 자료의 품질을 크게 향상시켰으며, 아울러 C-band 레이더가 가지고 있는 전자기파의 공진효과에 대한 이해와 이중편파 인자들의 자기상관 특성 이해에도 본 연구가 좋은 참고자료로 사용될 수 있을 것으로 생각된다.