Hydrologic Time Series Analysis II
Presiding: P Rasmussen, University of Manitoba; S Durrans, University of Alabama
H52A-01 INVITED 10:30h
Hydroclimatic Time Series: Nonlinearity and Low Frequency Variability
Spatial and temporal coherence in hydrologic and climatic time series is now recognized. Some useful ways of modeling such time series are considered. Inferences as to predictive structures in a dynamical systems context are discussed.
H52A-02 INVITED 10:50h
Understanding the Dynamics of Droughts Based on Stochastic Approaches
Drought is an extreme atmospheric and geophysical phenomenon that occurs from time to time in many parts of the world with significant impacts and consequences to society and the environment. The temporal and spatial evolution of such phenomenon is generally complex. Understanding drought dynamics has been a subject of much interest to hydrologists and water resources specialists for many decades. The purpose of this presentation is to examine alternative stochastic approaches for characterizing droughts, ranging from empirical statistical analysis of the historical data, statistical analysis of generated data, and mathematical closed form solutions. Particularly, we will focus on recurrence properties related to drought duration, magnitude, and intensity, as well as drought risk. We will illustrate the various approaches using streamflow data of some streams in Colorado.
H52A-03 11:10h
Stochastic Models of Long-Term Hydrological Data using a Bayesian Approach: The Challenges of Multi-site Data
Multi-site stochastic simulations of long-term rainfall and streamflow are used as hydrological inputs for water resource allocation models used to estimate drought risks. A general framework for evaluating the performance of competing multi-site stochastic model parameterisations has been developed. This framework includes a Bayesian approach to quantify parameter uncertainty. Diagnostics used to evaluate model performance are their ability to reproduce important extreme observed statistics and Bayes Factors to calculate model probabilities. Current models included in this framework are the lag-one autoregressive model and the two-state hidden Markov model. The challenges in implementing a Bayesian approach for these multi-site stochastic models will be outlined. The case study used is the hydrological data from Sydney's main water supply catchment; the Warragamba Catchment. The practical impact of evaluating parameter uncertainty is confirmed by illustrating that extreme drought risks are significantly underestimated if parameter uncertainty is ignored.
H52A-04 11:25h
Comparison by Simulation of Two Methods for Frequency Analysis of Annual Flood Data When Flow Records are Fragmented.
The frequency analysis of flood events is made more difficult where flow records are fragmented. The problem is particularly acute in developing countries, where it is essential for planning purposes to utilize to the full whatever records are found to exist. When a flow record is fragmented, a "peaks over a threshold" analysis is one possible approach, but the choice of threshold is not always straightforward. This paper adopts the alternative approach in which annual maximum discharges are used, considered as censored where years are incomplete. A new method for the analysis of fragmented flow records is compared by simulation with a well-known alternative. In both methods, a GEV distribution is used to model the frequency of annual maximum discharges; estimates of floods with T-year return period, given by the two methods, are compared, together with the results of tests for time-trend in the data when discharges are censored. Extension to the multi-site case is discussed, for which preliminary results are given.
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H52A-05 INVITED 11:40h
Stochastic Modelling of Monthly Runoff From Multiple Sites in a Semi-arid Region
The identification, estimation and generation of a multivariate time series model for monthly runoff from eight sub-catchments of the Mupfure catchment in Zimbabwe have been accomplished taking into account the fact that entire years of zero runoff may occur. The occurrence of years with no runoff at four of the eight sub-catchments was acknowledged in the simulation model through conditional probabilities for zero runoff and subsequent adjustments due to the fact that zero runoff is more likely in dry than in wet years. The model in its present state cannot encompass correlation between successive years. The expected occurrence of months with zero flow during the dry season in all the sub-catchments has led to the adoption of a non-parametric disaggregation method, the method of fragments, for generation of monthly flow based on the generated annual flow. In this study, a multivariate extension of the method of fragments has been implemented. The stochastic simulation model has been verified and validated, and the statistical properties of the historical streamflows are shown to be satisfactorily reproduced.
H52A-06 INVITED 11:55h
A Stochastic Nonparametric Technique for Space-Time Disaggregation of Streamflows
Stochastic disaggregation models are widely used to simulate streamflows at several sites preserving their spatial dependencies. Traditional approaches to this problem involve transforming the streamflow data of each month and at every location to a Gaussian structure and subsequently fitting a linear model in the transformed space; the simulations are then back transformed to the original space. The main drawbacks of the traditional linear models are (i) the number of parameters to be estimated grows exponentially with increase in space or time components, (ii) transforming the monthly data at each location to normality can be cumbersome and may not be satisfactory and, (iii) restricted to capturing only linear dependency. The approach broadly has three steps:(i) Annual flow at the index gauge z is generated from an appropriate model (e.g., AR1 or a nonparametric model). (ii) A vector u is resampled from the conditional probability density function (pdf) f(U | Z), where U is the transformed matrix of the historic monthly flows at the index gauge. (iii) The resampled u is back transformed to obtain monthly flows at the index gauge x. (iv) A vector s' is resampled from the conditional pdf f(S' | X), where S' is the transformed matrix of the spatial locations, and the vector s of monthly flows at all the D locations is obtained upon back transformation. The resampling from the conditional pdfs is based on a K-nearest neighbor bootstrap approach. The method is extremely parsimonious, as the only parameter to estimate is K (the number of nearest neighbors to be used in resampling). Simulating space-time flow scenarios conditioned upon large-scale climate information (e.g., ENSO, etc.) can be easily achieved unlike the traditional methods. We demonstrate the utility of this methodology by applying it for space-time disaggregation of streamflows in the Upper Colorado River basin. The method appropriately captures the distributional and spatial dependency properties at all the gauges.