Stochastic multi-site generation of daily rainfall occurrence in south Florida

This paper presents a stochastic model to generate daily rainfall occurrences at multiple gauging stations in south Florida. The model developed in this study is a space–time model that takes into account the spatial as well as temporal dependences of daily rainfall occurrence based on a chain-dependent process. In the model, a Markovian method was used to represent the temporal dependence of daily rainfall occurrence and a direct acyclic graph (DAG) method was introduced to encode the spatial dependence of daily rainfall occurrences among gauging stations. The DAG method provides an optimal sequence of generation by maximizing the spatial dependence index of daily rainfall occurrences over the region. The proposed space–time model shows more promising performance in generating rainfall occurrences in time and space than the conventional Markov type model. The space–time model well represents the temporal as well as the spatial dependence of daily rainfall occurrences, which can reduce the complexity in the generation of daily rainfall amounts.     

Pulse generation models for daily intermittent streamflows / Modèles de génération d’impulsions pour des débits journaliers intermittents

Abstract

Abstract Generating pulses and then converting them into flow are two main steps of daily streamflow generation. Three pulse generation models have been proposed on the basis of Markov chains for the purpose of generating daily intermittent streamflow time series in this study. The first one is based on two two-state Markov chains, whereas the second uses a three-state Markov chain. The third model uses harmonic analysis and fits Fourier series to the three-state Markov chain. Results for a daily intermittent streamflow data series show a good performance of the proposed models.     

Use of daily precipitation uncertainties in streamflow simulation and forecast

Among other sources of uncertainties in hydrologic modeling, input uncertainty due to a sparse station network was tested. The authors tested impact of uncertainty in daily precipitation on streamflow forecasts. In order to test the impact, a distributed hydrologic model (PRMS, Precipitation Runoff Modeling System) was used in two hydrologically different basins (Animas basin at Durango, Colorado and Alapaha basin at Statenville, Georgia) to generate ensemble streamflows. The uncertainty in model inputs was characterized using ensembles of daily precipitation, which were designed to preserve spatial and temporal correlations in the precipitation observations. Generated ensemble flows in the two test basins clearly showed fundamental differences in the impact of input uncertainty. The flow ensemble showed wider range in Alapaha basin than the Animas basin. The wider range of streamflow ensembles in Alapaha basin was caused by both greater spatial variance in precipitation and shorter time lags between rainfall and runoff in this rainfall dominated basin. This ensemble streamflow generation framework was also applied to demonstrate example forecasts that could improve traditional ESP (Ensemble Streamflow Prediction) method.     

Estimating minimum streamflow from measurements at ungauged sites in regions with streamflow‐gauging networks

Estimation of low flows in rivers continues to be a vexing problem despite advances in statistical and process‐based hydrological models. We develop a method to estimate minimum streamflow at seasonal to annual timescales from measured streamflow based on regional similarity in the deviations of daily streamflow from minimum streamflow for a period of interest. The method is applied to 1,019 gauged sites in the Western United States for June to December 2015. The gauges were clustered into six regions with distinct timing and magnitude of low flows. A gamma distribution was fit each day to the deviations in specific discharge (daily streamflow divided by drainage area) from minimum specific discharge for gauges in each region. The Kolmogorov–Smirnov test identified days when the gamma distribution was adequate to represent the distribution of deviations in a region. The performance of the gamma distribution was evaluated at gauges by comparing daily estimates of minimum streamflow with estimates from area‐based regression relations for minimum streamflow. Each region had at least 8 days during the period when streamflow measurements would provide better estimates than the regional regression equation, but the number of such days varied by region depending on aridity and homogeneity of streamflow within the region. Synoptic streamflow measurements at ungauged sites have value for estimating minimum streamflow and improving the spatial resolution of hydrological model in regions with streamflow‐gauging networks.     

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.     

Simulation of streamflow with statistically downscaled daily rainfall using a hybrid of wavelet and GAMLSS models

ABSTRACT

A rainfall–streamflow model is proposed, in which a downscaled rainfall series and its wavelet-based decomposed sub-series at optimum lags were used as covariates in GAMLSS (Generalized Additive Model in Location, Scale and Shape). GAMLSS is applied in climate change impact assessment using CMIP5 general climate model to simulate daily streamflow in three sub-catchments of the Onkaparinga catchment, South Australia. The Spearman correlation and Nash-Sutcliffe efficiency between the observed and median simulated streamflow values were high and comparable for both the calibration and validation periods for each sub-catchment. We show that the GAMLSS has the capability to capture non-stationarity in the rainfall–streamflow process. It was also observed that the use of wavelet-based decomposed rainfall sub-series with optimum lags as covariates in the GAMLSS model captures the underlying physics of the rainfall–streamflow process. The development and application of an empirical rainfall–streamflow model that can be used to assess the impact of catchment-scale climate change on streamflow is demonstrated.     

IMAGE: a multivariate multi-site stochastic weather generator for European weather and climate

Capturing the spatial and temporal correlation of multiple variables in a weather generator is challenging. A new massively multi-site, multivariate daily stochastic weather generator called IMAGE is presented here. It models temperature and precipitation variables as latent Gaussian variables with temporal behaviour governed by an auto-regressive model whose residuals and parameters are correlated through resampling of principle component time series of empirical orthogonal function modes. A case study using European climate data demonstrates the model’s ability to reproduce extreme events of temperature and precipitation. The ability to capture the spatial and temporal extent of extremes using a modified Climate Extremes Index is demonstrated. Importantly, the model generates events covering not observed temporal and spatial scales giving new insights for risk management purposes.     

Comparison of daily and sub-daily SWAT models for daily streamflow simulation in the Upper Huai River Basin of China

Despite the significant role of precipitation in the hydrological cycle, few studies have been conducted to evaluate the impacts of the temporal resolution of rainfall inputs on the performance of SWAT (soil and water assessment tool) models in large-sized river basins. In this study, both daily and hourly rainfall observations at 28 rainfall stations were used as inputs to SWAT for daily streamflow simulation in the Upper Huai River Basin. Study results have demonstrated that the SWAT model with hourly rainfall inputs performed better than the model with daily rainfall inputs in daily streamflow simulation, primarily due to its better capability of simulating peak flows during the flood season. The sub-daily SWAT model estimated that 58 % of streamflow was contributed by baseflow compared to 34 % estimated by the daily model. Using the future daily and 3-h precipitation projections under the RCP (Representative Concentration Pathways) 4.5 scenario as inputs, the sub-daily SWAT model predicted a larger amount of monthly maximum daily flow during the wet years than the daily model. The differences between the daily and sub-daily SWAT model simulation results indicated that temporal rainfall resolution could have much impact on the simulation of hydrological process, streamflow, and consequently pollutant transport by SWAT models. There is an imperative need for more studies to examine the effects of temporal rainfall resolution on the simulation of hydrological and water pollutant transport processes by SWAT in river basins of different environmental conditions.     

Extreme value theory for precipitation: sensitivity analysis for climate change

Extreme value theory for the maximum of a time series of daily precipitation amount is described. A chain-dependent process is assumed as a stochastic model for daily precipitation, with the intensity distribution being the gamma. To examine how the effective return period for extreme high precipitation amounts would change as the parameters of the chain-dependent process change (i.e., probability of a wet day, shape and scale parameters of the gamma distribution), a sensitivity analysis is performed. This sensitivity analysis is guided by some results from statistical downscaling that relate patterns in large-scale atmospheric circulation to local precipitation, providing a physically plausible range of changes in the parameters. For the particular location considered in the example, the effective return period is most sensitive to the scale parameter of the intensity distribution.     

Spatial interpolation schemes of daily precipitation for hydrologic modeling

Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs.     

Daily flow time series patching or extension: a spatial interpolation approach based on flow duration curves

Abstract

An algorithm is described that was initially developed as a simple method for patching and extending observed time series of daily streamflow. It is based on the use of 1-day flow duration curves for each month of the year and on the assumption that flows occurring simultaneously at sites in reasonably close proximity to each other correspond to similar percentage points on their respective duration curves. The algorithm has been incorporated into a model that allows flows at a destination site to be estimated from flows occurring at several source sites. The model has been applied to six groups of catchments within southern Africa and the resulting streamflow simulations compare favourably with those obtained using a semi-distributed, physically-based, daily time step rainfall-runoff model. The current limitations of the approach and its future potential value are discussed.     

Derivation of streamflow statistics based on a filtered point process

This work presents the derivation of general streamflow cumulants from daily rainfall time series. The general streamflow cumulants can be used to compute basic streamflow statistics such as mean, variance, coefficient of skewness, and correlation coefficient. Streamflow is considered as a filtered point process where the input is a daily rainfall time series assumed to be a marked point process. The marks of the process are the daily rainfall amounts which are assumed independent and identically distributed. The number of rainfall occurrences is a counting process represented by either the binomial, the Poisson, or the negative binomial probability distribution depending on its ratio of mean to variance. The first three cumulants and the covariance function of J-day averaged streamflows are deduced based on the characteristic function of a filtered point process. These cumulants are functions of the stochastic properties of the daily rainfall process and the basin-response function representing the causal relationship between rainfall and runoff.     

Conceptually-based shot noise modeling of streamflows at short time interval

A conceptual-stochastic approach to short time runoff data modelling is proposed, according to the aim of reproducing the hydrological aspects of the streamflow process and of preserving as much as possible the dynamics of the process itself. This latter task implies preservation of streamflow characteristics at higher scales of aggregation and, within a conceptual framework, involves compatibility with models proposed for the runoff process at those scales. At a daily time scale the watershed response to the effective rainfall is considered as deriving from the response of three linear reservoirs, respectively representing contributions to streamflows of large deep aquifers, with over-year response lag, of aquifers which run dry by the end of the dry season and of subsurface runoff. The surface runoff component is regarded as an uncorrelated point process. Considering the occurrences of effective rainfall events as generated by an independent Poisson process, the output of the linear system represents a conceptually-based multiple shot noise process. Model identification and parameter estimation are supported by information related to the aggregated runoff process, in agreement to the conceptual framework proposed, and this allows parameter parsimony, efficient estimation and effectiveness of the streamflow reproduction. Good performances emerged from the model application and testing made with reference to some daily runoff series from Italian basins.     

Conceptually-based shot noise modeling of streamflows at short time interval

A conceptual-stochastic approach to short time runoff data modelling is proposed, according to the aim of reproducing the hydrological aspects of the streamflow process and of preserving as much as possible the dynamics of the process itself. This latter task implies preservation of streamflow characteristics at higher scales of aggregation and, within a conceptual framework, involves compatibility with models proposed for the runoff process at those scales. At a daily time scale the watershed response to the effective rainfall is considered as deriving from the response of three linear reservoirs, respectively representing contributions to streamflows of large deep aquifers, with over-year response lag, of aquifers which run dry by the end of the dry season and of subsurface runoff. The surface runoff component is regarded as an uncorrelated point process. Considering the occurrences of effective rainfall events as generated by an independent Poisson process, the output of the linear system represents a conceptually-based multiple shot noise process. Model identification and parameter estimation are supported by information related to the aggregated runoff process, in agreement to the conceptual framework proposed, and this allows parameter parsimony, efficient estimation and effectiveness of the streamflow reproduction. Good performances emerged from the model application and testing made with reference to some daily runoff series from Italian basins.     

MÉLANGES MAURICE PARDÉ

Abstract

Existing models for generating synthetic daily streamflow data are unsuitable for reproducing the predominant features of daily flows, the rising and recession of flood flows, the peaks of the floods, the volume of the waves and the range. In this paper, a model is presented which is able to reproduce the important features of daily flows. In the model the measured record of daily data is assumed to be the output of a linear system. The input of the system consists of pulses, occurring on certain days. The pulses are convoluted with the system function in order to produce the output. The form of the system function depends on the magnitude of the output. First, the days on which pulses occur, the magnitude of pulses, and the form of the system function as a function of the system output, are determined. Subsequently, a model was developed for the generation of the pulses. The model consists of a combination of two processes. Using a Markov chain model, the sequence of dry and wet days (days with and without pulses) is generated. Thereafter, a pulse of certain magnitude is assigned to each wet day. A modified first-order autoregressive process is used to produce these correlated pulses. The random components of the pulses are taken from a transformed exponential distribution. The periodicity of the flows within the year is reproduced by using different model parameters for each month of the year. The model yields good results for small and medium size basins, especially as far as peak flows, the volume of the waves, and the range are concerned. A sequence of daily flows from at least 20 years is required for input data.     

洞庭湖近30a水位时空演变特征及驱动因素分析

洞庭湖地处北亚热带季风湿润气候区,水情时空变化尤为明显.为了探明洞庭湖水位时空演变特征,以洞庭湖6个水位站(城陵矶、鹿角、营田、杨柳潭、南咀、小河咀)、出入湖流量("三口"总入湖流量、"四水"总入湖流量、城陵矶出湖流量)和长江干流流量(宜昌、螺山)等1985-2014年逐日数据为基础,通过构建泰森多边形计算湖泊水位,运用Morlet小波分析、层次聚类分析和地统计理论研究湖泊水位的周期性变化规律及空间分布格局和自相关性.研究结果表明:洞庭湖水位变化具有典型的季节性,且年际变化具有28和22 a的多时间尺度特征;水位空间分布格局呈现出小河咀、南咀、杨柳潭(Group 1)以及城陵矶、鹿角、营田(Group 2)两种聚类,且在不同水文季节的空间自相关性依次表现为丰水期退水期涨水期枯水期.通过建立两类水位在不同水文季节与径流量的多元逐步回归模型揭示了洞庭湖水位时空演变的驱动因素,其中Group 1水位演变主要受长江干流水文情势的影响,Group 2水位演变由出入湖径流量和长江干流径流量共同作用,并随着不同水文季节江湖关系的改变以及湖泊自身水力联系的变化而变化.研究结果对于科学认识洞庭湖水位的时空演变规律以及湖泊生态系统保护和水资源的规划、管理与调控具有重要意义.     

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.     

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.     

Temporal change of spatial heterogeneity and its effect on regional trend of annual precipitation heterogeneity indices

A statistical test on climate and hydrological series from different spatial resolution could obtain different regional trend due to spatial heterogeneity and its temporal variability. In this study, annual series of the precipitation heterogeneity indices of concentration index (CI) and the number of wet days (NW) along with annual total amount of precipitation were calculated based on at‐site daily precipitation series during 1962–2011 in the headwater basin of the Huaihe River, China. The regional trends of the indices were first detected based on at‐site series by using the aligned and intrablock methods, and field significance tests that consider spatial heterogeneity over sites. The detected trends were then compared with the trends of the regional index series derived from daily areal average precipitation (DAAP), which averages at‐site differences and thus neglects spatial heterogeneity. It was found that the at‐site‐based regional test shows increasing trends of CI and NW in the basin, which follows the test on individual sites that most of sites were characterized by increasing CI and NW. However, the DAAP‐derived regional series of CI and NW were tested to show a decreasing trend. The disparity of the regional trend test on at‐site‐based regional series and the DAAP‐derived regional series arises from a temporal change of the spatial heterogeneity, which was quantified by the generalized additive models for location, scale, and shape. This study highlights that compared with averaging indices, averaging at‐site daily precipitation could lead to an error in the regional trend inference on annual precipitation heterogeneity indices. More attention should be paid to temporal variability in spatial heterogeneity when data at large scales are used for regional trend detection on hydro‐meteorological events associated with intra‐annual heterogeneity.     

Modelling streamflow trends for a watershed with limited data: case of the Litani basin,Lebanon

Abstract

Streamflow variability in the Upper and Lower Litani basin, Lebanon was modelled as there is a lack of long-term measured runoff data. To simulate runoff and streamflow, daily rainfall was derived using a stochastic rainfall generation model and monthly rainfall data. Two distinct synthetic rainfall models were developed based on a two-part probabilistic distribution approach. The rainfall occurrence was described by a Markov chain process, while the rainfall distribution on wet days was represented by two different distributions (i.e. gamma and mixed exponential distributions). Both distributions yielded similar results. The rainfall data were then processed using water balance and routing models to generate daily and monthly streamflow. Compared with measured data, the model results were generally reasonable (mean errors ranging from 0.1 to 0.8?m³/s at select locations). Finally, the simulated monthly streamflow data were used to investigate discharge trends in the Litani basin during the 20th century using the Mann-Kendall and Sen slope nonparametric trend detection methods. A significant drying trend of the basin was detected, reaching a streamflow reduction of 0.8 and 0.7 m³/s per decade in January for the Upper and Lower basin, respectively.

Editor D. Koutsoyiannis; Associate editor Sheng Yue

Citation Ramadan, H.H., Beighley, R.E., and Ramamurthy, A.S., 2012. Modelling streamflow trends for a watershed with limited data: case of the Litani basin, Lebanon. Hydrological Sciences Journal, 57 (8), 1516–1529.