Neyman-Scott Rectangular Pulses Research Articles

A stochastic rainfall model for the assessment of regional water resource systems under changed climatic condition

Abstract. A stochastic model is developed for the synthesis of daily precipitation using conditioning by weather types. Daily precipitation statistics at multiple sites within the region of Yorkshire, UK, are linked to objective Lamb weather types (LWTs) and used to split the region into three distinct precipitation sub-regions. Using a variance minimisation criterion, the 27 LWTs are clustered into three physically realistic groups or ‘states'. A semi-Markov chain model is used to synthesise long sequences of weather states, maintaining the observed persistence and transition probabilities. The Neyman-Scott Rectangular Pulses (NSRP) model is then fitted for each weather state, using a defined summer and winter period. The combined model reproduces key aspects of the historic precipitation regime at temporal resolutions down to the hourly level. Long synthetic precipitation series are useful in the sensitivity analysis of water resource systems under current and changed climatic conditions. This methodology enables investigation of the impact of variations in weather type persistence or frequency. In addition, rainfall model statistics can be altered to simulate instances of increased intensity or proportion of dry days for example, for individual weather groups. The input of such data into a water resource model, simulating potential atmospheric circulation changes, will provide a valuable tool for future planning of water resource systems. The ability of the model to operate at an hourly level also allows its use in a wider range of hydrological impact studies, e.g. variations in river flows, flood risk estimation etc. Keywords: water resources; climate change; impacts; stochastic rainfall model; Lamb weather types

Stochastic point process modelling of rainfall. II. Regionalisation and disaggregation

The Neyman-Scott Rectangular Pulses rainfall model is fitted to daily and hourly data taken from 112 sites scattered throughout the UK. The model is regionalised by regressing estimates of the model parameters on harmonic and site variables. This allows the model to be applied to catchments where data do not exist or are limited. Percentage errors between the second-order properties at the 112 sites and those predicted by the regionalised model were found to be less than the sampling error (expressed as a percentage of the mean) typically found in a 20 year record of historical rainfall data, which suggests that the regionalised model can be used with reasonable confidence. A method of disaggregating the hourly rainfall time series to 5 min rainfall time series is further developed and tested. Thus, the regionalised model can be used to generate data with a resolution of 5 min if required. Some validation tests carried out with storm sewer system models indicate that the performance of the model is satisfactory for its intended application.

On parameter estimation of temporal rainfall models

Characteristics and moment estimators of temporal rainfall models such as Poisson rectangular pulse (PRP), Neyman‐Scott white noise (NSWN), and Neyman‐Scott rectangular pulse (NSRP) are investigated. It is shown that PRP and NSWN have a correlation structure like that of an autoregressive moving average (ARMA) (1,1) model whereas the NSRP has a dependence structure like that of an ARMA (2, 2). The admissible regions of lag‐1 and lag‐2 autocorrelations are derived to demonstrate that in general they are more restricted than their ARMA counterparts. An additional property denoted as variance ratio, which is intimately related to the scale of fluctuation of a process, is defined and used for model comparison. The bias and mean square error properties of the moment estimators are investigated with emphasis on the NSWN model, for which it is suggested that the temporal scale T, defined by βT = 1, provides the most efficient estimators of the parameters. Parameter β defines the arrival of rain bursts relative to the origin of storm systems. All three models are fitted to an extensive data set covering hourly precipitation data at 38 stations in northeastern Colorado. The correlation and variance ratio plots are used to select the appropriate model for each month. However, it is shown that the diurnal periodicity of storm occurrence is predominant during the summer months, which is a characteristic not built into any of the temporal models used here.