(A) framework for correcting radar-based rainfall and uncertainty quantification to improve urban flood forecasts = 도시 홍수 예측 개선은 위한 레이더 강우 보정 및 불확실성 정량화 기법

국문 초록 (Abstract)

도시홍수는 전 세계 도시에서 발생하는 가장 심각한 수재해 요소 중 하나이다. 도시화 등 환경변화에 의한 수문학적, 수문기상학적 변동으로 불확실성은 증대되었으며, 이로 인해 도시홍수는 과거에 비해 더욱 예측이 어렵고 복잡해지고 있다. 따라서, 도시홍수 예측은 홍수 피해저감을 위한 수자원 관련 전문가들의 의사결정 지원에 있어 필수적이다. 특히, 강수예측은 도시지역의 홍수예측, 물 관리, 수문 모델링 연구에 있어 중요한 요소이다. 강수예측 자료로 레이더 기반 시스템이 활용되고 있으나, 레이더 기반 시스템 및 강우예측 모델과 관련된 불확실성 때문에 강우예측 정확도는 여전히 제한적이다. 특히, 집중호우와 같이 강우량이 많은 사상에서 강우량 예측의 정확도 확보는 더욱 어려운 특징이 있다.
기상자료와 도시 수문모델의 결합은 도시유역의 흐름과 침수현상을 예측하는 가장 대표적인 방법으로, 여러 연구에서 많이 활용되어 왔다. 특히, 레이더 기반 예측 시스템의 산출물은 도시수문모형의 입력으로 사용되며, 홍수예측의 정확도는 레이더 자료의 정확도에 따라 좌우된다. 강우예측 방법 중 하나인 라그랑지안 외삽 알고리즘은 강수의 성장과 소멸, 이동을 예측 모의하는 기법으로 많이 활용되고 있으나, 강한 호우사상에서 강수량 예측의 부정확성 문제가 제기되어 왔다. 반면, MAPLE의 정량적 추정강수의 불확실성은 평균 강우장의 시스템적 오류(예: 레이더 반사도-강수강도(Z-R) 관계식), 거리에 의한 오차, 랜덤 오차, 레이더 간 보정오차 등의 요인에 의해 발생한다. 더욱이, 강한 호우 사상에서의 예측자료의 신뢰도는 더욱 낮을 수 있다. 홍수예측을 위해서는 강우-유출해석이 필수적이며, 연구에서는 도시 소유역의 강우-유출해석을 위한 1D/2D 결합모델을 개발하였다. 모델은 1D 관망모델과 2D 범람모델로 구성되며, 1D 모형의 구성요소는 Storm Water Management Model (SWMM) 버전 4.4h의 두 가지 모듈을 기반으로 한다.
최근 수십 년 동안 많은 연구자들은 레이더 기반 외삽 시스템의 정확성도 한계를 개선하여 강우예측의 품질을 개선하기 위해 노력해왔다. 선행연구에서는 단기 외삽을 통해 산출된 강우장과 장기수치예보(NWP) 모델로부터 산출된 강우장에 가중치를 적용하여 강우를 예측하는 혼합기법이 활발히 적용되고 있다. 또 다른 방법은 현황시스템의 모의성능 향상시키기 위한 앙상블 예측기법이 활용되고 있다. 앙상블 기법의 장점은 확률론적 예측을 통해 강수량의 불확실성을 추정할 수 있다는 것이다. 일반적으로 두 방법은 레이더 기반 단기 예측강우의 정확성을 개선하기 위해 다양한 정량적 강수 예측자료를 결합해야 한다는 특징이 있다.
한편, 강수예측의 정확도 확보를 위한 또 다른 이슈는 호우 사상에서 다른 강수예측자료들과의 결합 없이 레이더 기반 강우예측 정보의 신속하게 생산하는 것이다. 이에 대한 방안은 인공지능(AI)이나 머신러닝(ML) 알고리즘, 회귀 기반 경험 모델 데이터 기반 모델을 활용하는 것이다. 본 연구에서는 한반도를 대상으로 라그랑지안 외삽(MAPLE) 시스템에 의해 생산된 강우현황 자료를 수집하였다. 본 연구에서는 호우사상의 관측강우량과 레이더 기반 시스템의 예측강우량에 데이터 기반 모델인 multiple linear regression (MLR), multivariate adaptive regression splines (MARS), multilayer perceptron (MLP), basic recurrent neural network (Basic RNN), and long short-term memory (LSTM) 기법을 적용하여 각 기법 간의 성능비교를 수행하였다. 다음으로, 레이더 기반 시스템의 3시간 예측 면적평균수량(MAP) 보정을 위한 LSTM 기법의 성능을 검토하고, LSTM 기법으로 보정된 예측 MAP를 1D/2D 결합모형에 적용하여 호우사상에서의 도시홍수예측 성능을 평가하였다. 모형의 정량적인 평가를 위해 평균제곱근오차(RMSE), 예측편차 (FB), 상관계수(R), 누적강우량의 절대오차를 산정하였고, 정성적 평가지표로는 Critical Success Index (CSI), and Probability of Detection (POD)를 활용하였다. 평가결과, 모든 데이터 기반 모델은 강우예측의 성능을 개선할 수 있는 것으로 나타났다. LSTM 기법은 Basic RNN, MLP, MARS, MLR에 비해 모의 성능이 우수하였으며, 특히 호우사상에서 모의 성능이 우수하였다. MAP 예측값 보정에 있어서도 LSTM 모델은 MLR 및 MLP에 비해 CSI 점수가 우수하여 예측값 보정성능이 뛰어난 것으로 나타났으며, 홍수예측의 정확도도 개선되는 것을 확인하였다.
또한, 예측 강수량 및 이와 관련한 수문학적 해석에 있어 불확실성 분석은 수자원 관리에 있어 중요하다. 본 연구에서는 MAPLE MAP 및 LSTM 보정 MAP 예측자료로부터 모의된 수위예측의 불확실성을 정량화하기 위해 adaptive Bayesian Markov Chain Monete Carlo (MCMC) 접근법을 제안하였다. 5개 집중호우 사상에서 2가지 종류의 예측 MAP를 1D/2D 모델에 결합하여 강남 지역의 관측소에서 수집한 수위 데이터와 비교하여 모의성능을 비교하였다. 매개변수 추정을 위해 제안된 Bayesian 접근법은 delayed rejection and adaptive metropolis (DRAM) 알고리즘과 popular Metropolis-Hastings (MH) 알고리즘을 활용하였다. 정량적 추정강수량(QPE), 면적평균강수량(MAP), 결합 1D/2D 모델에 이르는 각 단계에서 입력자료의 불확실성 기여도를 분석하였다. 평가결과, MAPLE 예측 MAP의 불확실성 기여도가 가장 높은 비율을 차지하였다. MAPLE 예측 MAP 에 대한 정량적 강수추정(QPE)에 대한 불확실성 기여도는 가장 낮았으나, LSTM 으로 보정된 MAP, 1D/2D 결합 모델 등 두 출처의 기여도는 QPE에 비해 상대적으로 큰 것으로 분석되었다. 도시 홍수 관리를 위한 각 단계별 및 입력자료의 불확실성 분석에 있어 DRAM 알고리즘을 사용한 MCMC 접근법이 불확실성 기여도를 정량적으로 분석하는데 더 효과적일 수 있음을 보여준다.

다국어 초록 (Multilingual Abstract)

Urban flooding is one of the most serious risks in cities around the world. Urban flooding becomes less predictable and more complicated than in the past, with major uncertainties due to hydrological and hydrometeorological variations driven by overall environmental change. Therefore, urban flood forecasting is required to support water-related managers in mitigating damage. In fact, precipitation forecasts have been a primary driver of flood forecasting, water management, and hydrologic modeling studies in the urban area. Nevertheless, the accuracy of forecasts remains limited due to the uncertainties associated with rainfall prediction models, such as radar-based systems. The predictions of the systems are often inaccurate for heavy rainfall events. These limitations may lead to the ineffective alleviation of urban flood damage.
The coupling of meteorological and urban hydrological models is the most popular method for predicting streamflow and inundation phenomena in urban catchments. This approach has received considerable attention from scientists. In these studies, radar-based forecasting systems outputs were used to drive hydrological urban models. The accuracy of flood prediction strongly depends on radar-based forecasting systems performance. However, due to the intrinsic drawbacks of the Lagrangian extrapolation algorithm, including those related to the growth and decay of precipitation, and changes in the movement of rain fields, the system issues poor forecasts for severe rainfall events. Additionally, sources of uncertainty can exist in MAPLE input data (quantitative precipitation estimate (QPE) data), such as mean-field systematic errors (e.g., the radar reflectivity-rainfall intensity (Z-R) relationship), range-dependent systematic errors, random errors, and radar-to-radar calibration differences, which can affect the accuracy of forecasts. The rainfall forecasts in the heavy rain events may have low reliability with solely a few tens of minutes of forecast time in acceptable accuracy.
In present study, a coupled 1D/2D model was developed with a simple model structure for a small urban catchment. In the model, there are two main modules including a 1D conduit network model and a 2D overland flow model. The 1D component is based on two modules of the Storm Water Management Model (SWMM) version 4.4h.
In recent decades, many researchers have attempted to address the limitations of the accuracy of radar-based extrapolation systems and improve the quality of their forecasts. Two main approaches have been used in these previous studies. Firstly, the blending techniques are popular applied, in which the forecasted results are acquired by weighting rainfall fields of both short-term extrapolation and a forecast of long-term numerical weather prediction (NWP) model. Secondly, the methods of ensemble forecasting are also utilized popularly for enhancing the performance of the nowcasting system. The advantage of the ensemble techniques is that they result in probabilistic forecasts which try to estimate the forecasts with the uncertainty of precipitation. In general, above reviewed methods normally require to combine multiple sources of QPF data to improve the accuracy of radar-based short-term forecasts.
It is raised the question of how to quickly reproduce rainfall forecasts of radar-based forecasting system in the heavy rain events without combining with other sources of QPF data. Consequently, data-driven models can be possible solutions, such as artificial intelligence (AI) or machine learning (ML) algorithms, and regression-based empirical models. In this study, the data collected from McGill Algorithm for Precipitation nowcasting by Lagrangian Extrapolation (MAPLE) system, which was applied in the Korea Peninsula. Present study was conducted to compare the performance of the data-driven models, namely multiple linear regression (MLR), multivariate adaptive regression splines (MARS), multilayer perceptron (MLP), basic recurrent neural network (Basic RNN), and long short-term memory (LSTM) in term of correcting the rainfall forecasts of radar-based system at rain gauges (point scale) in the heavy rainfall events. Next, the performance of LSTM was investigated in correcting 3-hour mean areal precipitation (MAP) forecasts of radar-based system, then applied the LSTM-corrected MAP forecasts to the coupled 1D/2D to evaluate the capability in improving urban flood predictions in the heavy rainfall events. Regarding comparative study, the evaluation of the models using the quantitative criteria such as Root Mean Square Error (RMSE), Forecast Bias (FB), correlation coefficient (R), and absolute difference of accumulated rainfall, and qualitative indicators including Critical Success Index (CSI), and Probability of Detection (POD). All the data-driven models presented the capability in improving the rainfall forecasts to a certain extent. However, with the gating structures in neurons, LSTM outperformed Basic RNN, MLP, MARS, and MLR, especially capturing high rainfall values. Similarly, in the context of correcting MAP forecasts, the LSTM model showed the superior correction capability with higher CSI scores at high thresholds compared to MLR and MLP. Corresponding to the improvement in the MAP forecasts, the flooding predictions also reflect remarkable increases in accuracy based on the analyses of R, RMSE, Relative Error of Peak Depth (REPD), and relevant urban flood terms.
Uncertainty assessment of the different sources including predicted precipitation inputs and related-components is an important issue in hydrological practice and water resources management. In present study, an approach using the adaptive Bayesian Markov Chain Monte Carlo (MCMC) was proposed for uncertainty quantification of water level predictions forced by MAPLE MAP and LSTM-corrected MAP forecasts. The water level data collected from two stations named 22-0002 and 22-0006 in Gangnam catchment by the coupled 1D/2D model from the two types of MAP forecasts in the five heavy rainfall events. The proposed Bayesian approach using delayed rejection and adaptive metropolis (DRAM) algorithm was compared with the popular Metropolis-Hastings (MH) algorithm for parameter estimation. The uncertainty contributions of the stage and sources in the related process were analyzed such as quantitative precipitation estimation (QPE) input, MAP input and the coupled urban hydrological model. The approach results showed the uncertainty contribution of MAPLE MAP forecast source accounts for the highest proportion in the three-hour forecast period. The contribution of QPE input for MAPLE MAP forecasts is the smallest component, while that of two sources, namely LSTM-corrected MAP source, and MAP and coupling model, is relatively larger than QPE input. This work shows that the adaptive Bayesian MCMC approach using the DRAM algorithm may be more effective in quantitative analysis of uncertainty contribution of stages and sources for urban flood management.
The success of the proposed framework proves that the viability of the methodologies suggested in this study. Notably, the LSTM model still reproduces slightly underestimation of heavy rainfall values and peak water levels in certain events. Further study would be investigate the approach to overcome the limitation for improving the effectiveness of the framework.

목차 (Table of Contents)

• Abstract i
• Table of contents vi
• List of figures xi
• List of tables xvii
• Chapter 1 . Introduction 1
• 1.1 Problem statement 1
• 1.1.1 Motivation in urban flood forecasting 1
• 1.1.2 Motivation in the method for urban flood forecast 1
• 1.1.3 Limitations of radar-based forecasting system, and existing uncertainties 2
• 1.2 Background information 4
• 1.2.1 Post-processed methods for radar-based forecasting system 4
• 1.2.2 Capability of machine learning method in post-processing for radar rainfall forecasts 5
• 1.2.3 Evaluation of the coupled 1D/2D urban hydrological models 7
• 1.2.4 Uncertainty quantification by Bayesian MCMC 8
• 1.3 Objectives of the research 10
• 1.4 The structure of dissertation 11
• Publications from dissertation 13
• Chapter 2 . Methodology, study area and data 14
• 2.1 Brief descriptions of methods used 14
• 2.1.1 Coupled 1D/2D urban inundation model 14
• 2.1.2 Data-driven models 14
• 2.1.3 Bayesian Markov Chain Monte Carlo 15
• 2.1.4 Criteria of forecast errors evaluation and uncertainty quantification 15
• 2.3 The brief presentation of methodology 15
• 2.3 Study areas 18
• 2.4 Brief description of data used in this study 18
• 2.4.1 Observation data and quality control 18
• 2.4.2 Radar forecasting data 19
• Chapter 3 . Use recurrent neural networks to improve rainfall forecasts from radar-based systems in an urban catchment 20
• 3.1 Abstract 20
• 3.2 Introduction 21
• 3.3 Study area and data processing 25
• 3.3.1 Study area 25
• 3.3.1 Rainfall observation and forecasted data of MAPLE system 27
• 3.4 Methodology 30
• 3.4.1 MARS 30
• 3.4.2 MLP 31
• 3.4.3 Basic RNN and its problem in long-term dependencies 32
• 3.4.4 LSTM network 34
• 3.4.5 Training datasets and model implementation 36
• 3.4.6 Model performance parameters 37
• 3.5 Results and discussions 38
• 3.5.1 Training of ANN models 38
• 3.5.2 Performance of data-driven models 39
• 3.5.3 Comparison with new collected data 55
• 3.6 Conclusions 60
• Chapter 4 . Correcting mean areal precipitation forecasts to improve urban flooding predictions by using long short-term memory network 63
• 4.1 Abstract 63
• 4.2 Introduction 64
• 4.3 Study area and data processing 68
• 4.3.1 Study area 68
• 4.3.2 Rainfall observations and forecasting data from the MAPLE system 71
• 4.3.3 Training datasets 74
• 4.3.4 Sewer network and topographical data 74
• 4.4 Methodology 75
• 4.4.1 LSTM network 75
• 4.4.2 Coupled 1D/2D urban inundation model 76
• 4.5 Results and discussion 78
• 4.5.1 Coupled 1D/2D model calibration and verification 78
• 4.5.2 Correcting MAP forecasts 86
• 4.5.3 Urban flooding prediction with corrected MAPs 93
• 4.6 Conclusions 103
• Chapter 5 . Uncertainty quantification of water level predictions from radar-based mean areal precipitation forecasts using adaptive Markov Chain Monte Carlo algorithm 105
• 5.1 Abstract 105
• 5.2 Introduction 106
• 5.3 Study area and data processing 110
• 5.3.1 Study area 110
• 5.3.2 Data collection 111
• 5.4 Methodology 113
• 5.4.1 MCMC methods and Metropolis–Hastings algorithm 113
• 5.4.2 Combining delayed rejection and adaptive metropolis (DRAM) 114
• 5.4.3 Uncertainty quantification indicators 116
• 5.4.4 Steps of proposed method 118
• 5.5 Results and discussion 120
• 5.5.1 Implementation of proposed method 120
• 5.5.2 Comparison between DRAM and MH algorithm 125
• 5.5.3 Comparison between the uncertainty of MAPLE MAP and LSTM-corrected MAP forecasts 127
• 5.5.4 Uncertainty contribution of QPE input 134
• 5.5.5 Discussion on the uncertainty contribution of the coupled model and MAP inputs 137
• 5.6 Conclusions 140
• Chapter 6 . Summary, conclusions and future works 142
• 6.1 Summary and conclusions 142
• 6.1.1 Conclusions regarding the rainfall correction using LSTM model 144
• 6.1.2 Conclusions regarding adaptive Bayesian MCMC method on uncertainty quantification 145
• 6.2 Limitations and future works 146
• References 148
• Appendix A Inverse distance weight method 162
• Appendix B Multiple linear regression method 163
• Appendix C Multivariate adaptive regression splines 164
• List of abbreviations 166
• Acknowledgments 174