A hidden Markov model segmentation procedure for hydrological and environmental time series

In this paper we present a procedure for the segmentation of hydrological and enviromental time series. We consider the segmentation problem from a purely computational point of view which involves the minimization of Huberts segmentation cost; in addition this least squares segmentation is equivalent to Maximum Likelihood segmentation. Our segmentation procedure maximizes Likelihood and minimizes Huberts least squares criterion using a hidden Markov model (HMM) segmentation algorithm. This algorithm is guaranteed to achieve a local maximum of the Likelihood. We evaluate the segmentation procedure with numerical experiments which involve artificial, temperature and river discharge time series. In all experiments, the procedure actually achieves the global minimum of the Likelihood; furthermore execution time is only a few seconds, even for time series with over a thousand terms.     

A class of hidden Markov models for regional average rainfall

Abstract

Basic hidden Markov models are very useful in stochastic environmental research but their ability to accommodate sufficient dependence between observations is somewhat limited. However, they can be modified in several ways to form a rich class of flexible models that are useful in many environmental applications. We consider a class of hidden Markov models that incorporate additional dependence among observations to model average regional rainfall time series. The focus of the study is on models that introduce additional dependence between the state level and the observation level of the process and also on models that incorporate dependence at observation level. Construction of the likelihood function of the models is described along with the usual second-order properties of the process. The maximum likelihood method is used to estimate the parameters of the models. Application of the proposed class of models is illustrated in an analysis of daily regional average rainfall time series from southeast and southwest England for the winter season during 1931 to 2010. Models incorporating additional dependence between the state level and the observation level of the process captured the distributional properties of the daily rainfall well, while the models that incorporate dependence at the observation level showed their ability to reproduce the autocorrelation structure. Changes in some of the regional rainfall properties during the time period are also studied.

Editor D. Koutsoyiannis     

基于隐马尔可夫模型平滑估计的随机噪声压制方法

以地震勘探记录去噪为目标,本文提出了一种隐马尔可夫模型平滑估计方法.它是在基本隐马尔可夫模型滤波基础之上,运用信号检测环节将带噪信号段和无信号段加以区分,构建带噪地震记录的状态转移模型,在贝叶斯框架下,利用平滑密度函数进行状态估计,从而达到压制噪声的目的.数值模拟表明,无论对信噪比还是均方误差,隐马尔可夫模型平滑估计处理后的重构信号优于常规的维纳滤波所恢复信号.我们可以期待这种方法会成为实际地震记录噪声压制的有效手段.     

Daily rainfall projections from general circulation models with a downscaling nonhomogeneous hidden Markov model (NHMM) for south‐eastern Australia

An ensemble of stochastic daily rainfall projections has been generated for 30 stations across south‐eastern Australia using the downscaling nonhomogeneous hidden Markov model, which was driven by atmospheric predictors from four climate models for three IPCC emissions scenarios (A1B, A2, and B1) and for two periods (2046–2065 and 2081–2100). The results indicate that the annual rainfall is projected to decrease for both periods for all scenarios and climate models, with the exception of a few scenarios of no statistically significant changes. However, there is a seasonal difference: two downscaled GCMs consistently project a decline of summer rainfall, and two an increase. In contrast, all four downscaled GCMs show a decrease of winter rainfall. Because winter rainfall accounts for two‐thirds of the annual rainfall and produces the majority of streamflow for this region, this decrease in winter rainfall would cause additional water availability concerns in the southern Murray–Darling basin, given that water shortage is already a critical problem in the region. In addition, the annual maximum daily rainfall is projected to intensify in the future, particularly by the end of the 21st century; the maximum length of consecutive dry days is projected to increase, and correspondingly, the maximum length of consecutive wet days is projected to decrease. These changes in daily sequencing, combined with fewer events of reduced amount, could lead to drier catchment soil profiles and further reduce runoff potential and, hence, also have streamflow and water availability implications. Copyright © 2012 John Wiley & Sons, Ltd.     

A general Bayesian framework for calibrating and evaluating stochastic models of annual multi-site hydrological data

Multi-site simulation of hydrological data are required for drought risk assessment of large multi-reservoir water supply systems. In this paper, a general Bayesian framework is presented for the calibration and evaluation of multi-site hydrological data at annual timescales. Models included within this framework are the hidden Markov model (HMM) and the widely used lag-1 autoregressive (AR(1)) model. These models are extended by the inclusion of a Box–Cox transformation and a spatial correlation function in a multi-site setting. Parameter uncertainty is evaluated using Markov chain Monte Carlo techniques. Models are evaluated by their ability to reproduce a range of important extreme statistics and compared using Bayesian model selection techniques which evaluate model probabilities. The case study, using multi-site annual rainfall data situated within catchments which contribute to Sydney’s main water supply, provided the following results: Firstly, in terms of model probabilities and diagnostics, the inclusion of the Box–Cox transformation was preferred. Secondly the AR(1) and HMM performed similarly, while some other proposed AR(1)/HMM models with regionally pooled parameters had greater posterior probability than these two models. The practical significance of parameter and model uncertainty was illustrated using a case study involving drought security analysis for urban water supply. It was shown that ignoring parameter uncertainty resulted in a significant overestimate of reservoir yield and an underestimation of system vulnerability to severe drought.     

Parameter identification in tidal models with uncertain boundary conditions

In this paper a parameter estimation algorithm is developed to estimate uncertain parameters in two dimensional shallow water flow models. Since in practice the open boundary conditions of these models are usually not known accurately, the uncertainty of these boundary conditions has to be taken into account to prevent that boundary errors are interpreted by the estimation procedure as parameter fluctuations. Therefore the open boundary conditions are embedded into a stochastic environment and a constant gain extended Kalman filter is employed to identify the state of the system. Defining a error functional that measures the differences between the filtered state of the system and the measurements, a quasi Newton method is employed to determine the minimum of this functional. To reduce the computational burden, the gradient of the criterium that is required using the quasi Newton method is determined by solving the adjoint system.     

Parameter identification in tidal models with uncertain boundary conditions

In this paper a parameter estimation algorithm is developed to estimate uncertain parameters in two dimensional shallow water flow models. Since in practice the open boundary conditions of these models are usually not known accurately, the uncertainty of these boundary conditions has to be taken into account to prevent that boundary errors are interpreted by the estimation procedure as parameter fluctuations. Therefore the open boundary conditions are embedded into a stochastic environment and a constant gain extended Kalman filter is employed to identify the state of the system. Defining a error functional that measures the differences between the filtered state of the system and the measurements, a quasi Newton method is employed to determine the minimum of this functional. To reduce the computational burden, the gradient of the criterium that is required using the quasi Newton method is determined by solving the adjoint system.