Nadarajah Ramesh

Multi-site doubly stochastic Poisson process models for fine-scale rainfall

We consider a class of doubly stochastic Poisson process models in the modelling of fine-scale rainfall at multiple gauges in a dense network. Multi-site stochastic point process models are constructed and their likelihood functions are derived. The application of this class of multi-site models, a useful alternative to the widely-known Poisson cluster models, is explored to make inferences about the properties of fine time-scale rainfall. The proposed models, which incorporate covariate information about the catchment area, are used to analyse tipping-bucket raingauge data from multiple sites. The results show the potential of this class of models to reproduce temporal and spatial variability of fine time-scale rainfall characteristics.

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

A doubly stochastic rainfall model with exponentially decaying pulses

We develop a doubly stochastic point process model with exponentially decaying pulses to describe the statistical properties of the rainfall intensity process. Mathematical formulation of the point process model is described along with second-order moment characteristics of the rainfall depth and aggregated processes. The derived second-order properties of the accumulated rainfall at different aggregation levels are used in model assessment. A data analysis using 15 years of sub-hourly rainfall data from England is presented. Models with fixed and variable pulse lifetime are explored. The performance of the model is compared with that of a doubly stochastic rectangular pulse model. The proposed model fits most of the empirical rainfall properties well at sub-hourly, hourly and daily aggregation levels.

Doubly stochastic Poisson pulse model for fine-scale rainfall

Stochastic rainfall models are widely used in hydrological studies because they provide a framework not only for deriving information about the characteristics of rainfall but also for generating precipitation inputs to simulation models whenever data are not available. A stochastic point process model based on a class of doubly stochastic Poisson processes is proposed to analyse fine-scale point rainfall time series. In this model, rain cells arrive according to a doubly stochastic Poisson process whose arrival rate is determined by a finite-state Markov chain. Each rain cell has a random lifetime. During the lifetime of each rain cell, instantaneous random depths of rainfall bursts (pulses) occur according to a Poisson process. The covariance structure of the point process of pulse occurrences is studied. Moment properties of the time series of accumulated rainfall in discrete time intervals are derived to model 5-min rainfall data, over a period of 69 years, from Germany. Second-moment as well as third-moment properties of the rainfall are considered. The results show that the proposed model is capable of reproducing rainfall properties well at various sub-hourly resolutions. Incorporation of third-order moment properties in estimation showed a clear improvement in fitting. A good fit to the extremes is found at larger resolutions, both at 12-h and 24-h levels, despite underestimation at 5-min aggregation. The proportion of dry intervals is studied by comparing the proportion of time intervals, from the observed and simulated data, with rainfall depth below small thresholds. A good agreement was found at 5-min aggregation and for larger aggregation levels a closer fit was obtained when the threshold was increased. A simulation study is presented to assess the performance of the estimation method.

Markov modulated Poisson process models incorporating covariates for rainfall intensity

Time series of rainfall bucket tip times at the Beaufort Park station, Bracknell, in the UK are modelled by a class of Markov modulated Poisson processes (MMPP) which may be thought of as a generalization of the Poisson process. Our main focus in this paper is to investigate the effects of including covariate information into the MMPP model framework on statistical properties. In particular, we look at three types of time-varying covariates namely temperature, sea level pressure, and relative humidity that are thought to be affecting the rainfall arrival process. Maximum likelihood estimation is used to obtain the parameter estimates, and likelihood ratio tests are employed in model comparison. Simulated data from the fitted model are used to make statistical inferences about the accumulated rainfall in the discrete time interval. Variability of the daily Poisson arrival rates is studied.