A spatio-temporal climate-based model of early dengue fever warning in southern Taiwan

Dengue Fever (DF) has been identified by the World Health organization (WHO) as one of the most serious vector-borne infectious diseases in tropical and sub-tropical areas. During 2007, in particular, there were over 2,000 DF cases in Taiwan, which was the highest number of cases in the recorded history of Taiwan epidemics. Most DF studies have focused mainly on temporal DF patterns and its close association with climatic covariates, whereas they have understated spatial DF patterns (spatial dependence and clustering) and composite space–time effects. The present study proposes a spatio-temporal DF prediction approach based on stochastic Bayesian Maximum Entropy (BME) analysis. Core and site-specific knowledge bases are considered, including climate and health datasets under conditions of uncertainty, space–time dependence functions, and a Poisson regression model of climatic variables contributing to DF occurrences in southern Taiwan during 2007. The results show that the DF outbreaks in the study area are highly influenced by climatic conditions. Furthermore, the analysis can provide the required “one-week-ahead” outbreak warnings based on spatio-temporal predictions of DF distributions. Therefore, the proposed approach can provide the Taiwan Disease Control Agency with a valuable tool to timely identify, control, and even efficiently prevent DF spreading across space–time.     

Validation and use of rainfall radar data to simulate water flows in the Rio Escondido basin

This paper presents a combined validation method of radar-sensed rainfall, using rain gauge data and hydrologic closure, with an application to the Rio Escondido basin (North-East of Mexico). The space–time scaling behavior of rainfall between rain gauge and radar scales is compared with the intrinsic variability of rainfall, for a statistical validation of space–time variability. For hydrological validation purposes, the CEQUEAU model is used to perform rainfall-runoff routing. It provides a basin-wide water balance, to be compared with the measured water flow at the Villa de Fuentes hydrometric station, for mean-value gauging closure. A good qualitative agreement in terms of hydrograph shape and timing is obtained between the simulated and the observed water flows, and a multiplicative correction factor of an initially proposed Z–R relationship is adopted for the watershed under study, which agrees approximately with other authors’ findings about that relationship. The results are considered particularly useful as a validation-and-correction methodology of radar rainfall estimates for areas sparsely covered by rain gauges.     

Regional frequency analysis of rainfall extremes in Southern Malawi using the index rainfall and L-moments approaches

Rainfall extremes often result in the occurrence of flood events with associated loss of life and infrastructure in Malawi. However, an understanding of the frequency of occurrence of such extreme events either for design or disaster planning purposes is often limited by data availability at the desired temporal and spatial scales. Regionalisation, which involves “trading time for space” by pooling together observations for stations with similar behavior, is an alternative approach for more accurate determination of extreme events even at ungauged areas or sites with short records. In this study, regional frequency analysis of rainfall extremes in Southern Malawi, large parts of which are flood prone, was undertaken. Observed 1-, 3-, 5- and 7-day annual maximum rainfall series for the period 1978–2007 at 23 selected rainfall stations in Southern Malawi were analysed. Cluster analysis using scaled at-site characteristics was used to determine homogeneous rainfall regions. L-moments were applied to derive regional index rainfall quantiles. The procedure also validated the three rainfall regions identified through homogeneity and heterogeneity tests based on Monte Carlo simulations with regional average L-moment ratios fitted to the Kappa distribution. Based on assessments of the accuracy of the derived index rainfall quantiles, it was concluded that the performance of this regional approach was satisfactory when validated for sites not included in the sample data. The study provides an estimate of the regional characteristics of rainfall extremes that can be useful in among others flood mitigation and engineering design.     

Evaluating spatio-temporal representations in daily rainfall sequences from three stochastic multi-site weather generation approaches

Many hydrological and agricultural studies require simulations of weather variables reflecting observed spatial and temporal dependence at multiple point locations. This paper assesses three multi-site daily rainfall generators for their ability to model different spatio-temporal rainfall attributes over the study area. The approaches considered consist of a multi-site modified Markov model (MMM), a reordering method for reconstructing space–time variability, and a nonparametric k-nearest neighbour (KNN) model. Our results indicate that all the approaches reproduce adequately the observed spatio-temporal pattern of the multi-site daily rainfall. However, different techniques used to signify longer time scale observed temporal and spatial dependences in the simulated sequences, reproduce these characteristics with varying successes. While each approach comes with its own advantages and disadvantages, the MMM has an overall advantage in offering a mechanism for modelling varying orders of serial dependence at each point location, while still maintaining the observed spatial dependence with sufficient accuracy. The reordering method is simple and intuitive and produces good results. However, it is primarily driven by the reshuffling of the simulated values across realisations and therefore may not be suited in applications where data length is limited or in situations where the simulation process is governed by exogenous conditioning variables. For example, in downscaling studies where KNN and MMM can be used with confidence.     

Stochastic generation of hourly rainstorm events

Occurrence of rainstorm events can be characterized by the number of events, storm duration, rainfall depth, inter-event time and temporal variation of rainfall within a rainstorm event. This paper presents a Monte-Carlo based stochastic hourly rainfall generation model considering correlated non-normal random rainstorm characteristics, as well as dependence of various rainstorm patterns on rainfall depth, duration, and season. The proposed model was verified by comparing the derived rainfall depth–duration–frequency relations from the simulated rainfall sequences with those from observed annual maximum rainfalls based on the hourly rainfall data at the Hong Kong Observatory over the period of 1884–1990. Through numerical experiments, the proposed model was found to be capable of capturing the essential statistical features of rainstorm characteristics and those of annual extreme rainstorm events according to the available data.     

Estimation and spatial interpolation of rainfall intensity distribution from the effective rate of precipitation

Great emphasis is being placed on the use of rainfall intensity data at short time intervals to accurately model the dynamics of modern cropping systems, runoff, erosion and pollutant transport. However, rainfall data are often readily available at more aggregated level of time scale and measurements of rainfall intensity at higher resolution are available only at limited stations. A distribution approach is a good compromise between fine-scale (e.g. sub-daily) models and coarse-scale (e.g. daily) rainfall data, because the use of rainfall intensity distribution could substantially improve hydrological models. In the distribution approach, the cumulative distribution function of rainfall intensity is employed to represent the effect of the within-day temporal variability of rainfall and a disaggregation model (i.e. a model disaggregates time series into sets of higher solution) is used to estimate distribution parameters from the daily average effective precipitation. Scaling problems in hydrologic applications often occur at both space and time dimensions and temporal scaling effects on hydrologic responses may exhibit great spatial variability. Transferring disaggregation model parameter values from one station to an arbitrary position is prone to error, thus a satisfactory alternative is to employ spatial interpolation between stations. This study investigates the spatial interpolation of the probability-based disaggregation model. Rainfall intensity observations are represented as a two-parameter lognormal distribution and methods are developed to estimate distribution parameters from either high-resolution rainfall data or coarse-scale precipitation information such as effective intensity rates. Model parameters are spatially interpolated by kriging to obtain the rainfall intensity distribution when only daily totals are available. The method was applied to 56 pluviometer stations in Western Australia. Two goodness-of-fit statistics were used to evaluate the skill—daily and quantile coefficient of efficiency between simulations and observations. Simulations based on cross-validation show that kriging performed better than other two spatial interpolation approaches (B-splines and thin-plate splines).     

Space–time clustering of case–control data with residential histories: insights into empirical induction periods, age-specific susceptibility, and calendar year-specific effects

Our research group recently developed Q-statistics for evaluating space–time clustering in case–control studies with residential histories. This technique relies on time-dependent nearest-neighbor relationships to examine clustering at any moment in the life-course of the residential histories of cases relative to that of controls. In addition, in place of the widely used null hypothesis of spatial randomness, each individual’s probability of being a case is based instead on his/her risk factors and covariates. In this paper, we extend this approach to illustrate how alternative temporal orientations (e.g., years prior to diagnosis/recruitment, participant’s age, and calendar year) influence a spatial clustering pattern. These temporal orientations are valuable for shedding light on the duration of time between clustering and subsequent disease development (known as the empirical induction period), and for revealing age-specific susceptibility windows and calendar year-specific effects. An ongoing population-based bladder cancer case–control study is used to demonstrate this approach. Data collection is currently incomplete and therefore no inferences should be drawn; we analyze these data to demonstrate these novel methods. Maps of space–time clustering of bladder cancer cases are presented using different temporal orientations while accounting for covariates and known risk factors. This systematic approach for evaluating space–time clustering has the potential to generate novel hypotheses about environmental risk factors and provides insights into empirical induction periods, age-specific susceptibility, and calendar year-specific effects.     

A two steps disaggregation method for highly seasonal monthly rainfall

 The need for high resolution rainfall data at temporal scales varying from daily to hourly or even minutes is a very important problem in hydrology. For many locations of the world, rainfall data quality is very poor and reliable measurements are only available at a coarse time resolution such as monthly. The purpose of this work is to apply a stochastic disaggregation method of monthly to daily precipitation in two steps: 1. Initialization of the daily rainfall series by using the truncated normal model as a reference distribution. 2.␣Restructuring of the series according to various time series statistics (autocorrelation function, scaling properties, seasonality) by using a Markov chain Monte Carlo based algorithm. The method was applied to a data set from a rainfall network of the central plains of Venezuela, in where rainfall is highly seasonal and data availability at a daily time scale or even higher temporal resolution is very limited. A detailed analysis was carried out to study the seasonal and spatial variability of many properties of the daily rainfall as scaling properties and autocorrelation function in order to incorporate the selected statistics and their annual cycle into an objective function to be minimized in the simulation procedure. Comparisons between the observed and simulated data suggest the adequacy of the technique in providing rainfall sequences with consistent statistical properties at a daily time scale given the monthly totals. The methodology, although highly computationally intensive, needs a moderate number of statistical properties of the daily rainfall. Regionalization of these statistical properties is an important next step for the application of this technique to regions in where daily data is not available.     

Modelling ocean wave climate with a Bayesian hierarchical space–time model and a log-transform of the data

Long-term trends in the ocean wave climate because of global warming are of major concern to many stakeholders within the maritime industries, and there is a need to take severe sea state conditions into account in design of marine structures and in marine operations. Various stochastic models of significant wave height are reported in the literature, but most are based on point measurements without exploiting the flexible framework of Bayesian hierarchical space–time models. This framework allows modelling of complex dependence structures in space and time and incorporation of physical features and prior knowledge, yet remains intuitive and easily interpreted. This paper presents a Bayesian hierarchical space–time model with a log-transform for significant wave height data for an area in the North Atlantic ocean. The different components of the model will be outlined, and the results from applying the model to data of different temporal resolutions will be discussed. Different model alternatives have been tried and long-term trends in the data have been identified for all model alternatives. Overall, these trends are in reasonable agreement and also agree fairly well with previous studies. The log-transform was included in order to account for observed heteroscedasticity in the data, and results are compared to previous results where a similar model was employed without a log-transform. Furthermore, a discussion of possible extensions to the model, e.g. incorporating regression terms with relevant meteorological data, will be presented.     

Bayesian comparison of different rainfall depth–duration–frequency relationships

Depth–duration–frequency curves estimate the rainfall intensity patterns for various return periods and rainfall durations. An empirical model based on the generalized extreme value distribution is presented for hourly maximum rainfall, and improved by the inclusion of daily maximum rainfall, through the extremal indexes of 24 hourly and daily rainfall data. The model is then divided into two sub-models for the short and long rainfall durations. Three likelihood formulations are proposed to model and compare independence or dependence hypotheses between the different durations. Dependence is modelled using the bivariate extreme logistic distribution. The results are calculated in a Bayesian framework with a Markov Chain Monte Carlo algorithm. The application to a data series from Marseille shows an improvement of the hourly estimations thanks to the combination between hourly and daily data in the model. Moreover, results are significantly different with or without dependence hypotheses: the dependence between 24 and 72 h durations is significant, and the quantile estimates are more severe in the dependence case.     

Regional scale rainfall–runoff modeling using VARX–MGARCH approach

Multivariate time series modeling approaches are known as useful tools for describing, simulating, and forecasting hydrologic variables as well as their changes over the time. These approaches also have temporal and cross-sectional spatial dependence in multiple measurements. Although the application of multivariate linear and nonlinear time series approaches such as vector autoregressive with eXogenous variables (VARX) and multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) models are commonly used in financial and economic sciences, these approaches have not been extensively used in hydrology and water resources engineering. This study employed VARX and VARX–MGARCH approaches in modeling mean and conditional heteroscedasticity of daily rainfall and runoff records in the basin of Zarrineh Rood Dam, Iran. Bivariate diagonal VECH (DVECH) model, as a main type of MGARCH, shows how the conditional variance–covariance and conditional correlation structure vary over the time between residuals series of the fitted VARX. For this purpose, five model fits, which consider different combinations of twofold rainfall and runoff, including both upstream and downstream stations, have been investigated in the present study. The VARX model, with different orders, was applied to the daily rainfall–runoff process of the study area in each of these model fits. The Portmanteau test revealed the existence of conditional heteroscedasticity in the twofold residuals of fitted VARX models. Therefore, the VARX–DVECH model is proposed to capture the heteroscedasticity existing in the daily rainfall–runoff process. The bivariate DVECH model indicated both short-run and long-run persistency in the conditional variance–covariance matrix related to the twofold innovations of rainfall–runoff processes. Furthermore, the evaluation criteria for the VARX–DVECH model revealed the improvement of VARX model performance.     

La descente et la montée étendues: the spatially <Emphasis Type="Bold">d</Emphasis>-anisotropic and the spatio-temporal case

There is a great demand for statistical modeling of phenomena that evolve in both space and time, and thus, there is a growing literature on correlation function models for spatio-temporal processes. In particular, various properties of these correlation functions have been studied only for the merely spatial or temporal case, fact that constitutes a strong motivation for our work. The goal of this paper is to inspect some properties, obtained with respect to partial differentiation and integration, of stationary spatio-temporal correlation functions for which anisotropy is obtained through isotropy between components as in Fernández-Casal et al. (Stat Comput 13(2):127–136, 2003). We show that through partial differentiation and integration it is possible to obtain permissible spatio-temporal correlation functions in the space–time domain. Other new results regard specific classes of space–time correlations introduced in recent literature. A curious result arises by differentiating scale mixtures of Euclid’s hat. Work partially funded by grant MTM2004-06231 from the Spanish Ministery of Science and Education.     

Seasonal and spatial variations in the scaling and correlation structure of streamflow data

Seasonal and spatial variability in scaling, correlation and wavelet variance parameter of daily streamflow data were investigated using 56 gauging stations from five basins located in two different climate zones. Multifractal temporal scaling properties were detected using a multiplicative cascade model. The wavelet variance parameter yielded persistence properties of the streamflow time series. Seasonal variations were found to be significant in that winter and spring seasons where large‐scale frontal events are dominant showed higher long‐term correlations and less multifractality than did summer and fall seasons. Coherent spatial variations were apparent. The Neches River basin located in a subtropic humid climate zone exhibited high persistence and long‐term correlation as well as less multifractality as compared with other basins. It is found that larger drainage areas tend to have smaller multifractality and higher persistence structure, and this tendency becomes apparent in regions that receive large amounts of precipitation and decreases towards arid regions. Copyright © 2012 John Wiley & Sons, Ltd.     

Capturing the residence time boundary layer—application to the Scheldt Estuary

At high Peclet number, the residence time exhibits a boundary layer adjacent to incoming open boundaries. In a Eulerian model, not resolving this boundary layer can generate spurious oscillations that can propagate into the area of interest. However, resolving this boundary layer would require an unacceptably high spatial resolution. Therefore, alternative methods are needed in which no grid refinement is required to capture the key aspects of the physics of the residence time boundary layer. An extended finite element method representation and a boundary layer parameterisation are presented and tested herein. It is also explained how to preserve local consistency in reversed time simulations so as to avoid the generation of spurious residence time extrema. Finally, the boundary layer parameterisation is applied to the computation of the residence time in the Scheldt Estuary (Belgium/The Netherlands). This timescale is simulated by means of a depth-integrated, finite element, unstructured mesh model, with a high space–time resolution. It is seen that the residence time temporal variations are mainly affected by the semi-diurnal tides. However, the spring–neap variability also impacts the residence time, particularly in the sandbank and shallow areas. Seasonal variability is also observed, which is induced by the fluctuations over the year of the upstream flows. In general, the residence time is an increasing function of the distance to the mouth of the estuary. However, smaller-scale fluctuations are also present: they are caused by local bathymetric features and their impact on the hydrodynamics.     

Daily precipitation variability in semiarid agricultural regions in Macedonia,Greece

Abstract

The spatio-temporal variability of daily precipitation series was investigated in a semiarid region of central Macedonia in northern Greece, Ten years of daily rainfall records for seven stations in the region constituted the data base. The spatial characteristics were examined by drawing composite correlation diagrams for the cool (October-March) season and the warm (April-September) season, and the results confirmed the regional homogeneity of the data sets. Furthermore, the temporal analysis indicated that the non-rainy days constituted the major portion of days throughout the year at all the stations. Similarly, light rainfall represented the majority of rainy days. Moreover, the annual rainfall variation showed high values in March, April and November with low values occurring in the summer and autumn. A sharp increase of rainfall between the 185th and the 195th day of the year must be taken into account when the harvest is scheduled. Harmonic and Power Spectrum analyses applied to the annual variation of rain depths using 5-day intervals revealed significant periodicities of 26, 122, 365 and 55 days. Finally the analysis of the annual variation of rain occurrences. revealed periodicities of 365 and 122 days.     

Stochastic multi-site generation of daily weather data

Spatial autocorrelation is a correlation between the values of a single variable, considering their geographical locations. This concept has successfully been used for multi-site generation of daily precipitation data (Khalili et al. in J Hydrometeorol 8(3):396–412, 2007). This paper presents an extension of this approach. It aims firstly to obtain an accurate reproduction of the spatial intermittence property in synthetic precipitation amounts, and then to extend the multi-site approach to the generation of daily maximum temperature, minimum temperature and solar radiation data. Monthly spatial exponential functions have been developed for each weather station according to the spatial dependence of the occurrence processes over the watershed, in order to fulfill the spatial intermittence condition in the synthetic time series of precipitation amounts. As was the case for the precipitation processes, the multi-site generation of daily maximum temperature, minimum temperature and solar radiation data is realized using spatially autocorrelated random numbers. These random numbers are incorporated into the weakly stationary generating process, as with the Richardson weather generator, and with no modifications made. Suitable spatial autocorrelations of random numbers allow the reproduction of the observed daily spatial autocorrelations and monthly interstation correlations. The Peribonca River Basin watershed is used to test the performance of the proposed approaches. Results indicate that the spatial exponential functions succeeded in reproducing an accurate spatial intermittence in the synthetic precipitation amounts. The multi-site generation approach was successfully applied for the weather data, which were adequately generated, while maintaining efficient daily spatial autocorrelations and monthly interstation correlations.     

Spatial rainfall model using a pattern classifier for estimating missing daily rainfall data

Missing data in daily rainfall records are very common in water engineering practice. However, they must be replaced by proper estimates to be reliably used in hydrologic models. Presented herein is an effort to develop a new spatial daily rainfall model that is specifically intended to fill in gaps in a daily rainfall dataset. The proposed model is different from a convectional daily rainfall generation scheme in that it takes advantage of concurrent measurements at the nearby sites to increase the accuracy of estimation. The model is based on a two-step approach to handle the occurrence and the amount of daily rainfalls separately. This study tested four neural network classifiers for a rainfall occurrence processor, and two regression techniques for a rainfall amount processor. The test results revealed that a probabilistic neural network approach is preferred for determining the occurrence of daily rainfalls, and a stepwise regression with a log-transformation is recommended for estimating daily rainfall amounts.     

Comparison of artificial neural network models for hydrologic predictions at multiple gauging stations in an agricultural watershed

This paper reports on an evaluation of the use of artificial neural network (ANN) models to forecast daily flows at multiple gauging stations in Eucha Watershed, an agricultural watershed located in north‐west Arkansas and north‐east Oklahoma. Two different neural network models, the multilayer perceptron (MLP) and the radial basis neural network (RBFNN), were developed and their abilities to predict stream flow at four gauging stations were compared. Different scenarios using various combinations of data sets such as rainfall and stream flow at various lags were developed and compared for their ability to make flow predictions at four gauging stations. The input vector selection for both models involved quantification of the statistical properties such as cross‐, auto‐ and partial autocorrelation of the data series that best represented the hydrologic response of the watershed. Measured data with 739 patterns of input–output vector were divided into two sets: 492 patterns for training, and the remaining 247 patterns for testing. The best performance based on the RMSE, R² and CE was achieved by the MLP model with current and antecedent precipitation and antecedent flow as model inputs. The MLP model testing resulted in R² values of 0·86, 0·86, 0·81, and 0·79 at the four gauging stations. Similarly, the testing R² values for the RBFNN model were 0·60, 0·57, 0·58, and 0·56 for the four gauging stations. Both models performed satisfactorily for flow predictions at multiple gauging stations, however, the MLP model outperformed the RBFNN model. The training time was in the range 1–2 min for MLP, and 5–10 s for RBFNN on a Pentium IV processor running at 2·8 GHz with 1 MB of RAM. The difference in model training time occurred because of the clustering methods used in the RBFNN model. The RBFNN uses a fuzzy min‐max network to perform the clustering to construct the neural network which takes considerably less time than the MLP model. Results show that ANN models are useful tools for forecasting the hydrologic response at multiple points of interest in agricultural watersheds. Copyright © 2008 John Wiley & Sons, Ltd.     

Spatial-temporal rainfall modelling for flood risk estimation

Some recent developments in the stochastic modelling of single site and spatial rainfall are summarised. Alternative single site models based on Poisson cluster processes are introduced, fitting methods are discussed, and performance is compared for representative UK hourly data. The representation of sub-hourly rainfall is discussed, and results from a temporal disaggregation scheme are presented. Extension of the Poisson process methods to spatial-temporal rainfall, using radar data, is reported. Current methods assume spatial and temporal stationarity; work in progress seeks to relax these restrictions. Unlike radar data, long sequences of daily raingauge data are commonly available, and the use of generalized linear models (GLMs) (which can represent both temporal and spatial non-stationarity) to represent the spatial structure of daily rainfall based on raingauge data is illustrated for a network in the North of England. For flood simulation, disaggregation of daily rainfall is required. A relatively simple methodology is described, in which a single site Poisson process model provides hourly sequences, conditioned on the observed or GLM-simulated daily data. As a first step, complete spatial dependence is assumed. Results from the River Lee catchment, near London, are promising. A relatively comprehensive set of methodologies is thus provided for hydrological application.