Observed Rainfall Time Series Research Articles

Evaluating stochastic rainfall models for hydrological modelling

Stochastic rainfall models are important tools for evaluating hydrological risks such as flooding and drought because of their ability to randomly generate alternative plausible climatic timeseries. The stochastic generation of climatic timeseries is not an end in itself, since they are typically applied to a catchment to determine the performance of water-related infrastructure systems, such as reservoirs or flood-control measures. This methodology typically involves a train of models to determine the end-of-system impact, yet the evaluation of stochastically generated rainfall timeseries is usually a stand-alone procedure focused on metrics directly related to the stochastic generator. This paper demonstrates discrepancies in this approach by evaluating two, daily-timestep, stochastic rainfall models in terms of rainfall metrics and their subsequently generated flow metrics after rainfall-runoff transformation. The two models are a Markov-based model and a latent-variable model, where each model is calibrated and evaluated showing ‘overall good’ performance. Stochastically generated timeseries, alongside observed rainfall timeseries are inputted to a calibrated catchment model (GR4J) to derive daily flow timeseries. Whereas the rainfall metrics typically showed ‘good’ performance, streamflow-based metrics are not necessarily ‘good’. The procedure is repeated for 277 stations from Australia and 106 stations from the United States of America. Depending on the strictness of the flow-based comparison and region analysed, using the Markov-based model 12–26% of sites were classified as ‘poor’ performing, and 1%-9% of sites were classified as ‘poor’ using the latent-variable model. The results demonstrate that catchment-based performance of flow metrics is more holistic since it magnifies features of the rainfall not otherwise visible to rainfall-based evaluation.

Comparison between statistical and dynamical downscaling of rainfall over the Gwadar‐Ormara basin, Pakistan

AbstractThis paper evaluated and compared the performance of a statistical downscaling method and a dynamical downscaling method to simulate the spatial–temporal rainfall distribution. Outputs from RegCM4 Regional Climate Model (RCM) and the CanESM2 Atmosphere–Ocean General Circulation Model (AOGCM) were selected for the data scarce Gwadar‐Ormara basin, Pakistan. The evaluation was based on the climatological average and standard deviation for historic (1971–2000) and future (2041–2070) time periods under Representative Concentration Pathways (RCP) 4.5 and 8.5 scenarios. The performance evaluation showed that statistical downscaling is preferred to simulate and project rainfall patterns in the study area. Additionally, the Statistical DownScaling Model (SDSM) showed low R2 values in calibration and validation of the simulations with respect to observed data for the historic period. Overall, SDSM generated satisfactory results in simulating the monthly rainfall cycle of the entire basin. In this study, RegCM4 showed large rainfall errors and missed one rainfall season in the historic period. This study also explored whether the grid‐based rainfall time series of the Asian Precipitation—Highly Resolved Observational Daily Integration Towards Evaluation (APHRODITE) dataset could be used to enlarge and complement the sample of in situ observed rainfall time series. A spatial correlogram was used for observed and APHRODITE rainfall data to assess the consistency between the two data sources, which resulted in rejecting APHRODITE data. For the future time period (2041–2070) under RCPs 4.5 and 8.5 scenarios, rainfall projections did not show significant difference for both downscaling approaches. This may relate to the driving model (CanESM2 AOGCM) and not necessarily suggests poor performance of downscaling; either statistical or dynamical. Hence, the study recommends evaluating a multi‐model ensemble including other GCMs and RCMs for the same area of study.

Research on Rain Pattern Classification Based on Machine Learning: A Case Study in Pi River Basin

For the purpose of improving the scientific nature, reliability, and accuracy of flood forecasting, it is an effective and practical way to construct a flood forecasting scheme and carry out real-time forecasting with consideration of different rain patterns. The technique for rain pattern classification is of great significance in the above-mentioned technical roadmap. With the rapid development of artificial intelligence technologies such as machine learning, it is possible and necessary to apply these new methods to assist rain classification applications. In this research, multiple machine learning methods were adopted to study the time-history distribution characteristics and conduct rain pattern classification from observed rainfall time series data. Firstly, the hourly rainfall data between 2003 and 2021 of 37 rain gauge stations in the Pi River Basin were collected to classify rain patterns based on the universally acknowledged dynamic time warping (DTW) algorithm, and the classifications were treated as the benchmark result. After that, four other machine learning methods, including the Decision Tree (DT), Long- and Short-Term Memory (LSTM) neural network, Light Gradient Boosting Machine (LightGBM), and Support Vector Machine (SVM), were specifically selected to establish classification models and the model performances were compared. By adjusting the sampling size, the influence of different sizes on the classification was analyzed. Intercomparison results indicated that LightGBM achieved the highest accuracy and the fastest training speed, the accuracy and F1 score were 98.95% and 98.58%, respectively, and the loss function and accuracy converged quickly after only 20 iterations. LSTM and SVM have satisfactory accuracy but relatively low training efficiency, and DT has fast classification speed but relatively low accuracy. With the increase in the sampling size, classification results became stable and more accurate. Besides the higher accuracy, the training efficiency of the four methods was also improved.

Application of the non-stationary peak-over-threshold methods for deriving rainfall extremes from temperature projections

Concerns about climate change are amplifying interest in future rainfall extremes. However, there are big differences between the statistics of rainfall extremes obtained using future rainfall time series produced from various climate models. Such large uncertainties create a lot of confusion in establishing climate change adaptation measures. Looking at future rainfall extremes at a particular site yields increasing trends in some climate models and decreasing trends in others. The spatial patterns of rate of change in rainfall extremes also vary widely, depending on the climate model. As a result, they often do not gain the public’s trust. We believe that this difficulty in obtaining credibility does not come from a lack of theory or technique, but from an approach that persuades the public of uncertain future rainfall extremes. In this study, we employed a novel approach to integrate a co-variate of the not-stationary Peak-Over-Threshold (POT) – Generalized Pareto distribution (GPD) model identified at each site with its future projection information for obtaining future rainfall extreme ensembles. Rainfall extremes are obtained from the observed rainfall time series using the POT method, and the scale parameter among GPD parameters are applied as a function of surface air temperature (SAT) or dew-point temperature (DPT). At this time, the threshold of the POT series is set to match the results of frequency analysis of the annual maximum series and the POT series for each site as much as possible. The behavior of future rainfall extremes is analyzed by inputting the future SAT or DAT produced from various climate models into the non-stationary frequency model using the co-variate. As a result of comparing the rainfall extremes obtained using the future rainfall time series directly with the future rainfall extremes obtained indirectly using the proposed method, it was found that the proposed approach projected future design rainfall depths with much less variation between climate models. The spatial pattern of rate of change was also consistent regardless of climate model. The proposed method is expected to contribute to the public’s confidence in future rainfall extremes under climate change scenarios and to be of practical help in formulating reasonable climate change adaptation policies.

A Data-Driven Surrogate Modelling Approach for Acceleration of Short-Term Simulations of a Dynamic Urban Drainage Simulator

In this study, applicability of a data-driven Gaussian Process Emulator (GPE) technique to develop a dynamic surrogate model for a computationally expensive urban drainage simulator is investigated. Considering rainfall time series as the main driving force is a challenge in this regard due to the high dimensionality problem. However, this problem can be less relevant when the focus is only on short-term simulations. The novelty of this research is the consideration of short-term rainfall time series as training parameters for the GPE. Rainfall intensity at each time step is counted as a separate parameter. A method to generate synthetic rainfall events for GPE training purposes is introduced as well. Here, an emulator is developed to predict the upcoming daily time series of the total wastewater volume in a storage tank and the corresponding Combined Sewer Overflow (CSO) volume. Nash-Sutcliffe Efficiency (NSE) and Volumetric Efficiency (VE) are calculated as emulation error indicators. For the case study herein, the emulator is able to speed up the simulations up to 380 times with a low accuracy cost for prediction of the total storage tank volume (medians of NSE = 0.96 and VE = 0.87). CSO events occurrence is detected in 82% of the cases, although with some considerable accuracy cost (medians of NSE = 0.76 and VE = 0.5). Applicability of the emulator for consecutive short-term simulations, based on real observed rainfall time series is also validated with a high accuracy (NSE = 0.97, VE = 0.89).

Uncertainty of Rainfall Products: Impact on Modelling Household Nutrition from Rain-Fed Agriculture in Southern Africa

Good quality data on precipitation are a prerequisite for applications like short-term weather forecasts, medium-term humanitarian assistance, and long-term climate modelling. In Sub-Saharan Africa, however, the meteorological station networks are frequently insufficient, as in the Cuvelai-Basin in Namibia and Angola. This paper analyses six rainfall products (ARC2.0, CHIRPS2.0, CRU-TS3.23, GPCCv7, PERSIANN-CDR, and TAMSAT) with respect to their performance in a crop model (APSIM) to obtain nutritional scores of a household’s requirements for dietary energy and further macronutrients. All products were calibrated to an observed time series using Quantile Mapping. The crop model output was compared against official yield data. The results show that the products (i) reproduce well the Basin’s spatial patterns, and (ii) temporally agree to station records (r = 0.84). However, differences exist in absolute annual rainfall (range: 154 mm), rainfall intensities, dry spell duration, rainy day counts, and the rainy season onset. Though calibration aligns key characteristics, the remaining differences lead to varying crop model results. While the model well reproduces official yield data using the observed rainfall time series (r = 0.52), the products’ results are heterogeneous (e.g., CHIRPS: r = 0.18). Overall, 97% of a household’s dietary energy demand is met. The study emphasizes the importance of considering the differences among multiple rainfall products when ground measurements are scarce.

A comparison of the discrete cosine and wavelet transforms for hydrologic model input data reduction

Abstract. The treatment of input data uncertainty in hydrologic models is of crucial importance in the analysis, diagnosis and detection of model structural errors. Data reduction techniques decrease the dimensionality of input data, thus allowing modern parameter estimation algorithms to more efficiently estimate errors associated with input uncertainty and model structure. The discrete cosine transform (DCT) and discrete wavelet transform (DWT) are used to reduce the dimensionality of observed rainfall time series for the 438 catchments in the Model Parameter Estimation Experiment (MOPEX) data set. The rainfall time signals are then reconstructed and compared to the observed hyetographs using standard simulation performance summary metrics and descriptive statistics. The results convincingly demonstrate that the DWT is superior to the DCT in preserving and characterizing the observed rainfall data records. It is recommended that the DWT be used for model input data reduction in hydrology in preference over the DCT.

Rainfall Trends, Drought Frequency and La Niña in Tuvalu: A Small Equatorial Island State in the Pacific Ocean

Droughts, as complex climatic hazards, can threaten livelihoods, economies, and ecosystems in low-lying island states. In extreme cases, drought may cripple national development in these countries, and produce long-term impacts that hinder national efforts to achieve the United Nations’ sustainable development goals. This study addresses rainfall trends, the frequency of droughts, La Nina influences and the relationship between rainfall and Sea Surface Temperature (SST) in the small Pacific country of Tuvalu. The study follows this order of approach: (1) examine observed rainfall time series for four meteorological stations across Tuvalu; (2) decompose observed rainfall time series and develop detrended rainfall time series; (3) evaluate and identify rainfall trends, including drought frequency; (4) define drought in Tuvalu using box plots; (5) evaluate the seasonal cycle of rainfall; (6) identify La Nina years and (7) test the correlation between SST, an indicator of La Nina events, and rainfall. The findings of this study revealed that (1) de-trended rainfall time series show declining trends in all four rainfall stations over the period 1953-2012; (2) the frequency of drought ranges from three to fourteen years with a mean of nine years; (3) the occurrence of drought appears to follow the La Nina years; (4) boxplots provide an effective option for defining drought and, finally, (5) there is empirical support for a moderate to strong correlation between the de-trended values of SST and rainfall in the area of study.

포아송 클러스터 가상강우생성 웹 어플리케이션 개발 및 검증 - 우리나라에 대해서

본 연구에서는 포아송 클러스터 강우생성모형의 하나인 MBLRP 모형의 매개변수지도를 우리나라에 대하여 제작하고 이에 기반을 둔 가상강우생성 웹 어플리케이션을 개발 및 검증하였다. 이를 위하여 우리나라의 62개 ASOS 지상 강우 관측소에서 관측된 강우자료를 기반으로 서로 다른 수문모의의 목적(홍수량 모의, 장기 유출량 모의, 일반 모의)에 따른 MBLRP 모형의 매개변수지도를 산정한 후, 이를 Ordinary Kriging 기법을 통해 공간 보간하여 우리나라에 대한 매개변수지도를 제작하였으며, 이에 기반을 두고 가상강우 시계열을 생성하는 웹 어플리케이션을 개발하였다. 검증을 위하여 웹어플리케이션을 사용하여 가상강우를 생성한 후 평균, 분산, 자기상관계수, 무강우 확률, 극한강우량 및 다양한 유역에 대한 극한홍수량과 유출량을 계산하고 이를 관측 강우에 근거하여 산출된 값과 비교하였다. 비교 결과 가상 강우의 각종 통계값은 관측강우에 근거한 값과 매우 유사하게 나타났으나, 극한강우와 극한홍수는 관측치에 근거한 값과 비교하여 16%-40% 정도 과소산정되는 경향을 보였다. 이러한 결과는 교정계수로 활용할 수 있도록 등고선도의 형태로 제공되었다. 본 연구에서 개발한 웹 어플리케이션은 모형의 매개변수 산정부터 가상 강우 시계열 생성까지 일련의 과정을 포함하고 있어 강우자료를 필요로 하는 다양한 수문 분석에 활발히 활용될 것으로 기대된다.

Assessing the impact of global changes on the surface water resources of southwestern Nigeria

Understanding the relative impact of land use, land cover (LULC) and climate change (CC) on basin runoff is necessary in assessing basin water stress, for which long-term observed rainfall time series and LULC spatial data are required. However, there are challenges with the availability of spatio-temporal data, particularly the limited range of available historical hydro-meteorological measurements. The study used long-term (1961–2007) rainfall data to drive the Pitman monthly rainfall–runoff model to assess changes to the water resources of three basins in Nigeria—Asa, Ogun and Owena. Three CGCMs—CSIRO Mark3.5, MIROC3.2-medres and UKMO-HadCM3—dynamically downscaled to a 60 km by 60 km grid using the Conformal-Cubic Atmospheric Model (C-CAM) are used to simulate impacts of future climate changes on water resources. These three models were found suitable for simulating rainfall–runoff based on the insignificant differences of the modelled mean with mean of observed rainfall and temperature for pre-2010 data compared to other downscaled C-CAM models (GFDL-CM2.0, GFDL-CM2.1 and ECHAM5/MPI-Ocean model). The model results show increases in the runoff coefficient with decreases in forest cover between 1981 and 2007, with average runoff coefficients of 5.3%, 12.0% and 6.4% for Asa, Ogun and Owena basins respectively. Based on annual reduction in rainfall trend projected by CSIRO, MIROC and UKMO, the future scenarios revealed a low runoff coefficient for the three basins—Asa (CSIRO 6.0%, MIROC 6.0% and UKMO 5.9%), Ogun (CSIRO14.6%, MIROC 14.6% and UKMO 14.4%) and Owena (CSIRO 8.5%, MIROC 8.7% and UKMO 8.9%). In all scenarios, Asa basin has a lower runoff coefficient when compared to Ogun and Owena basins, indicating that future water stress in Asa basin would be much greater.Editor Z.W. Kundzewicz; Guest editor D. Hughes

Forecasting quantitative rainfall over India using multi-model ensemble technique

A new approach to ensemble forecasting of rainfall over India based on daily outputs of four operational numerical weather prediction (NWP) models in the medium-range timescale (up to 5 days) is proposed in this study. Four global models, namely ECMWF, JMA, GFS and UKMO available on real-time basis at India Meteorological Department, New Delhi, are used simultaneously with adequate weights to obtain a multi-model ensemble (MME) technique. In this technique, weights for each NWP model at each grid point are assigned on the basis of unbiased mean absolute error between the bias-corrected forecast and observed rainfall time series of 366 daily data of 3 consecutive southwest monsoon periods (JJAS) of 2008, 2009 and 2010. Apart from MME, a simple ensemble mean (ENSM) forecast is also generated and experimented. The prediction skill of MME is examined against observed and corresponding outputs of each constituent model during monsoon 2011. The inter-comparison reveals that MME is able to provide more realistic forecast of rainfall over Indian monsoon region by taking the strength of each constituent model. It has been further found that the weighted MME technique has higher skill in predicting daily rainfall compared to ENSM and individual member models. RMSE is found to be lowest in MME forecasts both in magnitude and area coverage. This indicates that fluctuations of day-to-day errors are relatively less in the MME forecast. The inter-comparison of domain-averaged skill scores for different rainfall thresholds further clearly demonstrates that the MME algorithm improves slightly above the ENSM and member models.

극한수문사상의 모의를 위한 포아송 클러스터 강우생성모형의 적용성 평가

본 연구는 우리나라의 극한강우와 극한홍수를 모의하기 위한 MBLRP 포아송 클러스터 강우생성모형의 적용성을 평가하였다. 국내 61개의 기상청 지상기상관측시스템의 강우량 관측지점에 대하여 고립입자 군집화 최적화(ISPSO) 기법을 적용하여 모형의 매개변수를 추정하고, 추정된 매개변수를 바탕으로 각 강우관측지점에서 100년치의 가상 강우시계열을 생성하였다. 생성된 강우시계열을 이용하여 확률강우량 및 확률홍수량을 산정하고 이 값들을 관측치에 근거하여 산정된 값들과 비교하였다. 비교 결과, 모형에 의한 확률강우량은 관측치보다 평균적으로 20~42% 작았으며, 강우의 재현기간이 증가할수록 과소산정되는 정도가 증가하였다. 확률홍수량의 경우, 모형에 의한 값이 관측치에 근거한 값보다 31%에서 50% 작았으며, 이 과소산정량은 홍수의 재현기간의 증가 및 유역의 불투수도의 증가와 함께 증가하였다. This study evaluated the applicability of the Modified Bartlett-Lewis Rectangular Pulse (MBLRP) rainfall generation model for modeling extreme rainfalls and floods in Korean Peninsula. Firstly, using the ISPSO (Isolated Species Particle Swarm Optimization) method, the parameters of the MBLRP model were estimated at the 61 ASOS (Automatic Surface Observation System) rain gauges located across Korean Peninsula. Then, the synthetic rainfall time series with the length of 100 years were generated using the MBLRP model for each of the rain gauges. Finally, design rainfalls and design floods with various recurrence intervals were estimated based on the generated synthetic rainfall time series, which were compared to the values based on the observed rainfall time series. The results of the comparison indicate that the design rainfalls based on the synthetic rainfall time series were smaller than the ones based on the observation by 20% to 42%. The amount of underestimation increased with the increase of return period. In case of the design floods, the degree of underestimation was 31% to 50%, which increases along with the return period of flood and the curve number of basin.

포아송 클러스터 강우생성 모형의 홍수 모의 적용성 평가

본 연구는 우리나라 전역에 대하여 제작된 Modified Bartlett-Lewis Rectangular Pulse (MBLRP) 강우생성 모형의 모수 지도의 적용성을 홍수 재현의 관점에서 평가하였다. MBLRP 모형을 통해 생성된 가상 강우시계열을 사용하여 산정된 확률강우량은 관측치를 사용하여 산정된 확률강우량 보다 약5%에서 40%정도 작았고, 확률강우량의 재현기간이 클수록 과소산정의 정도가 크게 나타났다. 가상의 도시 유역에 MBLRP 모형을 적용하여 산정한 확률홍수량은 관측치를 사용하여 산정한 확률홍수량 보다 약20%에서 45%정도 작게 나타났고, 확률홍수량의 재현기간이 클수록, 그리고 유역의 불투수성이 작을수록 과소산정의 정도가 크게 나타났다. The applicability of the parameter map of the Modified Bartlett-Lewis Rectangular Pulse (MBLRP) model for the Korean Peninsula was assessed from the perspective of flood prediction. The design rainfalls estimated from the MBLRP model were smaller than those from observed values by 5% to 40%, and the degree of underestimation of design rainfall increases with the increase of the recurrence interval of the design rainfall. The design floods at a virtual watershed estimated using the simulated rainfall time series based on MBLRP model were also smaller than those derived from the observed rainfall time series by 20% to 45%. The degree of underestimation of design flood increases with the increase of the recurrence interval of the design flood.

Stochastic control of Indian megadroughts and megafloods

A multi-millennial run of the CSIRO Mark2 coupled climatic model has been used to investigate megadroughts and megafloods during the Indian summer monsoon (June–September). These extreme events were defined as having rainfall anomalies at least two standard deviations from normal. More than ten megafloods and more than twenty megadroughts, so-defined, were found to occur in a 5,000-year period of the simulation. The simulation replicated most of the major features of the observed summer monsoon, but a comparison of observed and simulated probability density functions suggests that the limited observed rainfall time series to date does not adequately sample the possible range of Indian monsoonal rainfall. An investigation of causal mechanisms of Indian rainfall variability reproduced the observed negative correlation with ENSO events, but it was found that neither extreme ENSO events or extremes of a range of other climatic phenomena coincided with the simulated, extreme megadroughts and megafloods. This disconnect between these events is succinctly illustrated with examples related to ENSO events in particular. Autoregressive and FFT analysis of observed and simulated Indian summer monsoon rainfall time series revealed them to consist of white noise. Since these time series therefore consist of random outcomes, it is apparent that these Indian megadroughts and megafloods are the consequence of stochastic influences. Thus, it is concluded that the interannual variability of Indian summer monsoonal rainfall cannot be predicted in general, nor can megadroughts and megafloods in particular.

최근의 강우유출특성이 반영된 장기유출 모의를 위한 장기강우 사상의 모의기법 개발

연간 유출량 산정과 같은 장기간 분석에서는 연속적인 강우자료를 이용하여 장기 유출이 모의되어야 한다. 그리고 장기 유출 모의에 대한 신뢰성을 확보하기 위해서는 충분한 자료계열이 이용되어야 한다. 국내의 경우 장기간의 관측 강우자료들이 존재하여 통계적 분석을 위한 신뢰성을 확보할 수 있다. 그러나 최근 도시화와 기후변화 등으로 강우의 특성이 변화하고 있으므로 수문학적 분석에 있어서 이에 대한 고려가 이루어져야 할 것이다. 이에 있어서 관측된 장기간의 강우자료를 그대로 사용할 경우 최근의 강우 특성 변화를 고려하지 못하는 문제점이 있으며, 반면 최근의 단기간 강우자료를 이용할 경우 통계적 분석의 신뢰성을 확보하기 어렵다. 따라서 본 연구에서는 통계적 분석을 통하여 최근의 강우 특성이 변화하는 변동 기준년을 선정하였으며, 기준년 이후의 단기간 강우자료에 대하여 Neyman-Scott 모형을 이용하여 장기간의 강우자료를 발생시켰다. 분석 결과 강우의 특성이 변화되는 변동 기준년은 1990년으로 결정되었다. 이것은 최근의 강우특성을 반영하는 한편, 통계적 신뢰성을 확보하기 위한 것으로 본 연구에서는 서울지방의 48개년(1961~2008년)의 관측 강우자료를 이용하였다. 강우특성의 변화에 대한 분석 결과 변동 기준년을 1990년으로 설정하였으며, 1990년 이후 19개년(1990~2008년)의 단기강우자료를 이용하여 100년의 장기 강우 모의를 하였다. 또한 단기 실측강우와 모의 강우간 비교 분석을 통하여 발생 강우자료의 적정성을 검증하였다. To perform a long-term simulation which can be used for the estimation of annual runoff or other analyses, a long-term rainfall-runoff simulation relies on a continuous daily- or monthly-rainfall data. For this purpose, sufficient observed rainfall time series data must be used to satisfy the reliability of runoff analysis. In Korea, many rainfall stations have enough observed rainfall data for the reliable statistical analysis. However, as the characteristics of rainfall change due to urbanization and climate change, using all the rainfall data including older ones may average out their effects. Therefore, in this study, the year of the rainfall characteristic change was determined by the statistical analysis, and the long-term rainfall data was then generated by the Neyman-Scott model using the more recent rainfall data after the year of the rainfall characteristic change. For the observed rainfall data of 48 years(1961~2008), the Year 1990 was determined as the year of the rainfall characteristic change. Based on this finding, the 100- year daily-rainfall time series were generated by the Neyman-Scott model using the rainfall data observed from 1990 to 2008. Finally, the simulated daily-rainfall time series were verified for the statistical reliability by comparing with the more recent observed data.

A multisite daily rainfall generator driven by bivariate copula‐based mixed distributions

This work describes a simple and parsimonious multisite Markov model deduced from bivariate copula‐based mixed distributions useful for modeling and generating daily rainfall series. The structure of the model (involving only joint probabilities of wet/dry condition, a copula, the distribution of positive rainfall values, and a spatial cross‐correlation matrix) allows preserving spatial and temporal intermittency and several other properties of hydrologic interest (e.g., wet spell length, daily rainfall amount, rainfall accumulated on wet spells, first steps of the autocorrelation function, and spatial Kendall's correlation coefficient). The model does not require marginal transformations of the observed values, and non‐Gaussian temporal structures of dependence can be introduced by copulas. The spatial dependence is accounted for by simulating temporally independent but spatially correlated standard uniform random sequences. Application to observed rainfall time series and Monte Carlo simulations are carried out to assess the model performances. The approach appears to be a viable way to simulate daily rainfall sequences in a fairly easy way.

Applying climate model precipitation scenarios for urban hydrological assessment: A case study in Kalmar City, Sweden

There is growing interest in the impact of climate change on urban hydrological processes. Such assessment may be based on the precipitation output from climate models. To date, the model resolution in both time and space has been too low for proper assessment, but at least in time the resolution of available model output is approaching urban scales. In this paper, 30-min precipitation from a model grid box covering Kalmar City, Sweden, is compared with high-resolution (tipping-bucket) observations from a gauge in Kalmar. The model is found to overestimate the frequency of low rainfall intensities, and therefore the total volume, but reasonably well reproduce the highest intensities. Adapting climate model data to urban drainage applications can be done in several ways but a popular way is the so-called Delta Change (DC) method. In this method, relative changes in rainfall characteristics estimated from climate model output are transferred to an observed rainfall time series, generally by multiplicative factors. In this paper, a version of the method is proposed in which these DC factors (DCFs) are related to the rainfall intensity level. This is achieved by calculating changes in the probability distribution of rainfall intensities and modelling the DCFs as a function of percentile. Applying this method in Kalmar indicated that in summer and autumn, high intensities will increase by 20–60% by year 2100, whereas low intensities remain stable or decrease. In winter and spring, generally all intensity levels increase similarly. The results were transferred to the observed time series by varying the volume of the tipping bucket to reflect the estimated intensity changes on a 30-min time scale. In an evaluation of the transformed data at a higher 5-min resolution, effects on the intensity distribution as well as single precipitation events were demonstrated. In particular, qualitatively different changes in peak intensity and total volume are attainable, which is required in light of expected future changes of the precipitation process and a step forward as compared with simpler DC approaches. Using the DC transformed data as input in urban drainage simulations for a catchment in Kalmar indicated an increase of the number of surface floods by 20–45% during this century.

Modelling of monsoon rainfall for a mesoscale catchment in North-West India II: stochastic rainfall simulations

Abstract. Within this study we present a robust method for generating precipitation time series for the Anas catchment in North Western India. The method employs a multivariate stochastic simulation model that is driven by a time series of objectively classified circulation patterns (CPs). In a companion study (Zehe et al., 2006) it was already shown that CPs classified from the 500 or 700 Hpa levels are suitable to explain space-time variability of precipitation in that area. The model is calibrated using observed rainfall time series for the period 1985–1992 for two different CP time series, one from the 500 Hpa level and the over from the 700 Hpa level, and 200 realizations of daily rainfall are simulated for the period 85–94. Simulations using the CPs from the 500 Hpa level as input yield a good match of the observed averages and standard deviations of daily rainfall. They show furthermore good performance at the monthly scale. When used with the 700 Hpa level CPs as inputs the model clearly underestimates the standard deviation and performs much worse at the monthly scale, especially in the validation period 93–94. The presented results give evidence that CPs from the 500 Hpa, level in combination with a multivariate stochastic model, make up a suitable tool for reducing the sparsity of precipitation data in developing regions with sparse hydro-meteorological data sets.

Teleconnections between global sea-surface temperatures and the interannual variability of observed and model simulated rainfall over southern Africa

Sea-surface temperatures (SSTs) for the thirty-year period 1961–1990 are prescribed as boundary forcing for a series of atmospheric general circulation model (AGCM) experiments. The results of five separate multidecadal AGCM runs, each forced with the same SSTs, but different initial conditions, have been used to form an ensemble. The interannual variability of AGCM simulated rainfall over South Africa and Namibia (southern Africa) are compared with observations. Empirical orthogonal function (EOF) analyses revealed a strong correlation between the dominant observed austral summer season (October–March) and mid-summer season (December and January) rainfall patterns over southern Africa and the corresponding model results. It is shown that the AGCM simulated austral summer season rainfall variability in the dominant amplitude time series (first principle component or PC1 time series) compare well with SST fluctuations over the equatorial Pacific and tropical western Indian Oceans. Although the associated dominant observed rainfall time series accounts for a larger fraction of the total variability (relative to the AGCM), it also compares well with equatorial Pacific and tropical western Indian Ocean SST fluctuations. To a certain degree these results accentuates the model's ability to capture the major summer seasonal rainfall variability as a response of global SST forcing, which might make the AGCM suitable for future use in seasonal rainfall forecasting research. Similar associations could not be found for the austral winter season (May–August).

A nonparametric approach for daily rainfall simulation

A nonparametric model for daily rainfall simulation is presented. Nearest neighbour methods are used to conditionally simulate rainfall spells and amounts. A “local” subset of the observed record is used to formulate the conditional densities needed for simulation. This provides an effective yet simple way to model local and seasonal features in the observed rainfall time series. The model is applied in two stages. First dry and wet spell lengths are conditionally simulated. Next rainfall amounts for each day of the wet spell are simulated assuming an order one Markov dependence structure. Higher order dependence is modelled by considering the number of days from start of the spell as an additional variable. Rainfall distributional characteristics are observed to have distinctly different characteristics depending on the length of the wet spell. A procedure is developed to reproduce such differences in the simulations. The model is applied to 123 years of daily rainfall from Sydney, Australia.