Quantitative Precipitation Estimate (QPE) by Classification of Cloud Types and Variability of Raindrop Size Distribution

Abstract

기상레이더를 이용한 정량적 강수 추정(Quantitative Precipitation Estimate: QPE)은 기기오차, 관측오차, 강수 시스템의 특성, 강수입자의 변동성 등과 같은 다양한 요인에 의해 영향을 받는다. 본 연구에서는 강수입자의 변동성을 줄이기 위해 강수입자 직경분포의 특성을 알아보았고, 강수입자를 시뮬레이션 할 수 있는 최적의 감마 추정식을 구하였으며, 강수시스템의 특성을 고려하기 위하여 층·적운 구분 알고리즘을 개발하여 강수 유형별 Z-R 관계식을 산출하였으며, 레이더의 calibration에 의한 오차를 최소화하기 위한 레이더 반사도 자료보정 기법을 disdrometer를 이용하여 개발하였다. 이러한 과정을 종합적으로 알고리즘화 시킴으로서 정량적 강수 추정의 정확도를 향상시키고자 하였다. 레이더가 산출하는 반사도와 강우강도는 강수입자 직경분포 (DSD: Drop Size Distribution)의 함수이므로 이론적 수농도 분포를 구하기 위하여 감마 함수를 적용하여 moment 접근 방법으로 감마 변수들(N_(0), μ, Λ)을 구하였다. 본 연구에서는 모멘트 M012, M234, M246, M346, M456, 그리고 M-P를 각각 적용하여 최적의 estimator를 구하는 분석을 실시하였다. 중간크기에서의 moment를 사용하였을 때 전체적으로 오차가 작게 나타났으며, M456을 이용하여 수농도 분포를 추정하였을 때 FSE 값이 가장 낮게 나타났으며 관측값과 가장 유사한 결과를 가졌다. 강수입자 직경분포의 변동성에 의한 강수량 추정에서의 오차를 줄이기 위하여 sequential intensity filtering technique (SIFT) 방법을 적용하여 강수시스템의 특성과 강수유형을 구별한 후 강수량 추정에서의 정확성을 높일 수 있는 좋은 도구로서 사용이 가능하게 하였다. 강수입자 직경분포의 변동성으로 인해 강우강도가 강한 영역에서 median volume diameter가 낮게 나타나는 사례가 많았으며, 이는 Ulbrich (1983), Tokay and Short (1995)가 제시한 'N_(0) jump'의 결과와 잘 일치하였다. 따라서 강우강도가 높은 영역에서 median volume diameter 값을 이용한 층·적운과 대류형 강수 구별의 가능성을 제시하였다. 강수시스템의 유형 구분을 위해 CAPPI 자료로 레이더 반사도의 연직 분포(Vertical Profile of Reflectivity: VPR)를 구하였으며, 이들로부터 밝은띠 피크(BBP), 밝은띠 두께(BBT), 그리고 밝은띠 영역(BBR)을 탐지하여 여러 변수들의 경계조건(threshold)을 지정하여 알고리즘화 함으로써 층운형과 대류형을 구분하였다. 레이더를 이용한 강수량 추정에 레이더 반사도 보정을 위하여 Sorting and Moving Average (SMA) 방법을 적용하여 반사도를 보정하였다. 정량적인 강수량 추정의 정확성을 알아보기 위하여 Z = 200 R^(1.6)을 사용하여 강수량을 추정한 것과 반사도 보정식을 사용하여 레이더 반사도를 보정한 후 강수 유형별로 산출된 각각의 Z-R 관계식에 적용하여 강수량을 추정 비교하였다. 보정된 반사도를 새롭게 산출된 Z-R 관계식에 대입하였을 때 89.03%로 추정하는 것으로 나타났으며, 강수 유형별 강수량 추정 결과, 층상형에서는 보정된 레이더 반사도를 적용하여 부산레이더에서 93.6%, 고산레이더에서는 71.8%까지 강수량을 추정함으로써 강수량 추정 오차를 크게 줄이는 결과를 가져왔다. 대류형에서는 대류형에서 구한 Z-R 관계식에 보정된 레이더 반사도를 적용하여 부산레이더에서는 80.41%, 고산레이더에서는 62.64%까지 강수량을 추정하게 되었다. 따라서, 본 연구에서는 레이더와 강수입자 직경분포를 이용하여 정량적인 강수량 추정의 정확도를 향상 시키는 새로운 알고리즘을 개발함으로서, 악기상 감시 및 단시간 강수예측에 적용시 강수량 추정의 정확도 향상에 큰 기여가 될 것으로 판단된다.

The purposes of this study were to improve the accuracy of quantitative precipitation estimation (QPE) using weather radar. The characteristics of DSDs, best fitted DSD model, and the application of the various gamma functions based on moment scheme were examined. Rainfall estimation error due to the variability of drop size distribution was investigated. To reduce the variability of DSD, Sequential Intensity Filtering Technique was used and to find out the optimal Z-R relationships with respect to the cloud types stratiform and convective, were classified using VPR threshold algorithm. The calibration of radar reflectivity was also applied to improve for quantitative rainfall estimate. To obtain the DSD theoretically, the gamma distribution was used to DSDs model and moments approach were calculated the N_(0)(mm^(-1-m)m^(-3), Λ(mm^(-1)), μ and (shape parameter). The DSDs parameters of gamma distribution are retrieved and various moments of observed DSD have been used to estimate DSDs parameters. The appropriate combinations of DSDs moments were used to estimate DSD gamma parameters. In order to find out the optimal DSD estimator, five moment estimators (M012, M234, M246, M346, and M456) were analyzed and M-P estimator was compared with other moment estimators. The fractional standard error (FSE) was used to compare statistical errors between the retrieved rainfall rate-reflectivity and observed rainfall rate-reflectivity. When the estimated and observed results were compared, the estimators of M234, M246, M346, and M456 were similar to observed results, while there were large errors on M012 moment and MP moment. The middle moment estimators are better than the estimators with low or high moments in this study and M456 which is larger moment estimator gave the lowest values of FSE on rainfall rate and reflectivity. The results suggest that M456 estimator needs to be further investigated in future studies for the best DSD estimation. Each number concentration distributions of small (below about 1.5 mm diameter), medium (1.5 mm ∼ 4 mm), and large drops (above 4 mm diameter) were observed according to characteristics of precipitation system and the intensity of rainfall rate, respectively. The number concentration at small drops gave a dominant effect to the rainfall rate as compared with medium or big drops, whereas number concentration at medium or big drops gave a dominant effect to the reflectivity. Therefore, the variability of DSD is a major error in rainfall estimation. In general, the median volume diameter is increased along with increasing rainfall rate, however, an opposite pattern was observed in this study. The median volume diameter was lower at the range of the higher rainfall rate and the distribution of number concentration was high at small drops. The median volume diameter decrease is agreed with the classification index (N_(0) jump) of cloud types by Ulbrich (1983) and Tokay and Short (1995). Consequently, the decrease of median volume diameter with the range of higher rainfall rate can be used to classify the cloud types as index. For the purpose of recognizing the decrease of median volume diameter (above 10 mm/hr), cloud types, vertical profile of reflectivity (VPR) by radar and number concentration by POSS were investigated to classify and compare with time series distribution. The number density at small drops is higher than others when the convective cell passes over observation site. In addition, there are the increase of intercept parameter and the decrease of median volume diameter, obviously. In these results, the increase of intercept parameter and the decrease of median volume diameter are the specific phenomena of convective cell which passes over observation site. Consequently, the decrease of median volume diameter using DSDs is able to use as the classification index of cloud types when the convective cell passes through. The rainfall estimation has errors due to the DSDs variability when the Z-R relationship is calculated using raw data. In order to reduce the rainfall estimation errors depending on DSDs variability, sequential intensity filtering technique (SIFT) by Lee and Zawadzki (2005) was applied and tested. The scatter of rainfall rate and reflectivity calculated by raw data was widely revealed due to the variability of DSDs and the correlation coefficient was recorded below 0.9. After applying the SIFT, the correlation coefficient between rainfall rate and reflectivity was appeared above 0.95. Therefore, on the estimation of DSDs, SIFT application provided better Z-R relationship which had an appreciable reduction of the scatter around a best-fit line. Vertical profile of reflectivity (VPR) which is calculated by radar CAPPI data was used to identify stratiform cloud by detecting bright band. The VPR parameters (BBP, BBT, and BBR) were identified and applied to classify the cloud types and prediction system using a threshold value for detection of the bright band. The maximum reflectivity near the melting levels was taken as an indication of a bright band. The height of maximum reflectivity (bright band peak: BBP), bright band thickness (BBT), and bright band range (BBR) are determined to classify the cloud types in the vertical profile of reflectivity. The height of maximum reflectivity (BBP) and bright band thickness were detected in VPR. Bright band was determined when BBP is located between 2 km and 6 km (bright band in mid latitude generally exists between 2 km and 6 km) and its thickness is within 2 km. The top of bright band was designed as a decreasing 4 dB above maximum reflectivity height and the height of bright band bottom was regarded as a decreasing 2 dB below (Burrows, 2001). Vertical lapse rate of reflectivity was defined as the ratio of the reflectivity at the BBP to the reflectivity at 3 km above the BBP. It turns out that stratiform precipitation can be defined when the lapse rate is greater than 3.5 dB per kilometer (3.5 dB/km). There are regarded as convective cases that VPR does not fall in the previous threshold conditions, when the value of maximum reflectivity is greater than 40 dBZ and the thickness of bright band (BBT) has wider than 2 km. In addition, vertical lapse rates from maximum reflectivity for convective type were smaller than 3.5 dB per kilometer (3.5 dB/km). To estimate the quantitative precipitation of Busan radar and Gosan radar, rainfall rate and cumulative rainfall amount were calculated using Z = 200R^(1.6), total Z-R relationships, and classified Z-R relationships. Most of results using uncorrected reflectivity are underestimated for both radars, since the radar reflectivity would be contaminated by radar calibration. Therefore, to estimate rainfall rate and amount more accurately, radar reflectivity ZR has to correct to corrected reflectivity (ZC). The sorting and moving average (SMA) method is applied to correct the reflectivity of radar and POSS. After appling to SMA method, the correction of reflectivity was performed to find the optimal relationship using polynomial least square fitting. The rainfall estimation using the corrected reflectivity had better results of reducing the errors. In addition, to reduce the errors due to DSDs variability, SIFT method was applied. The Z-R relationships with cloud type were calculated using classification algorithm. To investigate the accuracy of rainfall estimation more detail, the rainfall estimation with cloud types were examined. The classification of cloud types were performed using VPR threshold algorithm and D_(0) decrease. In the stratiform type (convective type), when the corrected reflectivity were substituted to Z = 200R^(1.6) (calculated Z-R relationship at convective type), the accuracy of rainfall estimation were improved. The values of statistical errors (RMSE and bias) were also corresponding to the previous results. As a result of the algorithm which was developed as shown in Fig. 7.1, there was reduced errors from underestimation or overestimation in the rainfall estimation and improved the accuracy of quantitative precipitation estimation. This new developed QPE algorithm will be contributed not only to extend the quantitative utilization of radar rainfall but also to improve the accuracy of severe weather forecasting related to nowcasting.