Spatial-temporal rainfall modelling for flood risk estimation

Some recent developments in the stochastic modelling of single site and spatial rainfall are summarised. Alternative single site models based on Poisson cluster processes are introduced, fitting methods are discussed, and performance is compared for representative UK hourly data. The representation of sub-hourly rainfall is discussed, and results from a temporal disaggregation scheme are presented. Extension of the Poisson process methods to spatial-temporal rainfall, using radar data, is reported. Current methods assume spatial and temporal stationarity; work in progress seeks to relax these restrictions. Unlike radar data, long sequences of daily raingauge data are commonly available, and the use of generalized linear models (GLMs) (which can represent both temporal and spatial non-stationarity) to represent the spatial structure of daily rainfall based on raingauge data is illustrated for a network in the North of England. For flood simulation, disaggregation of daily rainfall is required. A relatively simple methodology is described, in which a single site Poisson process model provides hourly sequences, conditioned on the observed or GLM-simulated daily data. As a first step, complete spatial dependence is assumed. Results from the River Lee catchment, near London, are promising. A relatively comprehensive set of methodologies is thus provided for hydrological application.     

A fine-scale point process model of rainfall with dependent pulse depths within cells

Abstract

A cluster point process model is considered for the analysis of fine-scale rainfall time series. The model is based on three Poisson processes. The first is a Poisson process of storm origins, where each storm has a random (exponential) lifetime. The second is a Poisson process of cell origins that occur during the storm lifetime, terminating when the storm finishes. Each cell has a random lifetime that follows an exponential distribution (or terminates when the storm terminates, whichever occurs first). During cell lifetimes, a third Poisson process of instantaneous pulses occurs. The model is essentially an extension of the well-known Bartlett-Lewis rectangular pulses model, with the rectangular profiles replaced with a Poisson process of instantaneous pulse depths to ensure more realistic rainfall profiles for fine-scale series. Model equations, derived in Cowpertwait et al. (2007 Cowpertwait, P., Isham, V. and Onof, C. 2007. Point process models of rainfall: developments for fine-scale structure. Proceedings of the Royal Society of London, Series A, 463: 2569–2587. [Crossref], [Web of Science ®] , [Google Scholar]), are used to fit different sets of properties to a 60 year record of 5-min data taken from Kelburn, New Zealand. As in the previous work, two superposed processes are used to account for two main and distinct precipitation types (convective and stratiform). By treating the within-cell pulses as dependent random variables, it is found, by simulation, that improved fits to extreme values and the proportion of dry intervals are obtained.

Citation Cowpertwait, P. S. P., Xie, G., Isham, V., Onof, C. & Walsh, D. C. I. (2011) A fine-scale point process model of rainfall with dependent pulse depths within cells. Hydrol. Sci. J. 56(7), 1110–1117.     

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.     

Elevation effects on rainfall: A stochastic model

The variation in point precipitation with elevation is investigated using an event-based stochastic model of thunderstorm rainfall and empirical data. Parameters of the model correspond to the number of events per unit of time and the depth of rainfall per event. An increase in precipitation with elevation may be due to an increase in the number of events, in the amount of rainfall per event or to some combination of both possibilities. The distribution of the number of events per season is assumed to be a Poisson variate while the distribution of point rainfall depths may be taken as geometric. The summation of a random number of random variables is used to represent seasonal point precipitation. Assuming that the two parameters of the model increase linearly with elevation, then total seasonal rainfall increases as a quadratic polynomial with elevation. The use of the model allows one to obtain the return period of storm rainfall of a given magnitude despite a short historical record. An independent set of data was used to verify the procedure.     

Stochastic generation of hourly rainstorm events

Occurrence of rainstorm events can be characterized by the number of events, storm duration, rainfall depth, inter-event time and temporal variation of rainfall within a rainstorm event. This paper presents a Monte-Carlo based stochastic hourly rainfall generation model considering correlated non-normal random rainstorm characteristics, as well as dependence of various rainstorm patterns on rainfall depth, duration, and season. The proposed model was verified by comparing the derived rainfall depth–duration–frequency relations from the simulated rainfall sequences with those from observed annual maximum rainfalls based on the hourly rainfall data at the Hong Kong Observatory over the period of 1884–1990. Through numerical experiments, the proposed model was found to be capable of capturing the essential statistical features of rainstorm characteristics and those of annual extreme rainstorm events according to the available data.     

A cascade approach to continuous rainfall data generation at point locations

High-resolution temporal rainfall data sequences serve as inputs for a range of applications in planning, design and management of small (especially urban) water resources systems, including continuous flow simulation and evaluation of alternate policies for environmental impact assessment. However, such data are often not available, since their measurements are costly and time-consuming. One alternative to obtain high-resolution data is to try to derive them from available low-resolution information through a disaggregation procedure. This study evaluates a random cascade approach for generation of high-resolution rainfall data at a point location. The approach is based on the concept of scaling in rainfall, or, relating the properties associated with the rainfall process at one temporal scale to a finer-resolution scale. The procedure involves two steps: (1) identification of the presence of scaling behavior in the rainfall process; and (2) generation of synthetic data possessing same/similar scaling properties of the observed rainfall data. The scaling identification is made using a statistical moment scaling function, and the log–Poisson distribution is assumed to generate the synthetic rainfall data. The effectiveness of the approach is tested on the rainfall data observed at the Sydney Observatory Hill, Sydney, Australia. Rainfall data corresponding to four different successively doubled resolutions (daily, 12, 6, and 3 h) are studied, and disaggregation of data is attempted only between these successively doubled resolutions. The results indicate the presence of multi-scaling behavior in the rainfall data. The synthetic data generated using the log–Poisson distribution are found to exhibit scaling behaviors that match very well with that for the observed data. However, the results also indicate that fitting the scaling function alone does not necessarily mean reproducing the broader attributes that characterize the data. This observation clearly points out the extreme caution needed in the application of the existing methods for identification of scaling in rainfall, especially since such methods are also prevalent in studies of the emerging satellite observations and thus in the broader spectrum of hydrologic modeling.     

Exploring the effect of data assimilation by WRF‐3DVar for numerical rainfall prediction with different types of storm events

The mesoscale Numerical Weather Prediction (NWP) model is gaining popularity among the hydrometeorological community in providing high‐resolution rainfall forecasts at the catchment scale. Although the performance of the model has been verified in capturing the physical processes of severe storm events, the modelling accuracy is negatively affected by significant errors in the initial conditions used to drive the model. Several meteorological investigations have shown that the assimilation of real‐time observations, especially the radar data can help improve the accuracy of the rainfall predictions given by mesoscale NWP models. The aim of this study is to investigate the effect of data assimilation for hydrological applications at the catchment scale. Radar reflectivity together with surface and upper‐air meteorological observations is assimilated into the Weather Research and Forecasting (WRF) model using the three‐dimensional variational data‐assimilation technique. Improvement of the rainfall accumulation and its temporal variation after data assimilation is examined for four storm events in the Brue catchment (135.2 km²) located in southwest England. The storm events are selected with different rainfall distributions in space and time. It is found that the rainfall improvement is most obvious for the events with one‐dimensional evenness in either space or time. The effect of data assimilation is even more significant in the innermost domain which has the finest spatial resolution. However, for the events with two‐dimensional unevenness of rainfall, i.e. the rainfall is concentrated in a small area and in a short time period, the effect of data assimilation is not ideal. WRF fails in capturing the whole process of the highly convective storm with densely concentrated rainfall in a small area and a short time period. A shortened assimilation time interval together with more efficient utilisation of the weather radar data might help improve the effectiveness of data assimilation in such cases. Copyright © 2012 John Wiley & Sons, Ltd.     

Effect of rainfall uncertainty on the performance of physically based rainfall–runoff models

This paper analyses the effect of rain data uncertainty on the performance of two hydrological models with different spatial structures: a semidistributed and a fully distributed model. The study is performed on a small catchment of 19.6 km² located in the north‐west of Spain, where the arrival of low pressure fronts from the Atlantic Ocean causes highly variable rainfall events. The rainfall fields in this catchment during a series of storm events are estimated using rainfall point measurements. The uncertainty of the estimated fields is quantified using a conditional simulation technique. Discharge and rain data, including the uncertainty of the estimated rainfall fields, are then used to calibrate and validate both hydrological models following the generalized likelihood uncertainty estimation (GLUE) methodology. In the storm events analysed, the two models show similar performance. In all cases, results show that the calibrated distribution of the input parameters narrows when the rain uncertainty is included in the analysis. Otherwise, when rain uncertainty is not considered, the calibration of the input parameters must account for all uncertainty in the rainfall–runoff transformation process. Also, in both models, the uncertainty of the predicted discharges increase in similar magnitude when the uncertainty of rainfall input increase.     

Sensitivity of the Weather Research and Forecasting (WRF) model to downscaling ratios and storm types in rainfall simulation

Accurate information of rainfall is needed for sustainable water management and more reliable flood forecasting. The advances in mesoscale numerical weather modelling and modern computing technologies make it possible to provide rainfall simulations and forecasts at increasingly higher resolutions in space and time. However, being one of the most difficult variables to be modelled, the quality of the rainfall products from the numerical weather model remains unsatisfactory for hydrological applications. In this study, the sensitivity of the Weather Research and Forecasting (WRF) model is investigated using different domain settings and various storm types to improve the model performance of rainfall simulation. Eight 24‐h storm events are selected from the Brue catchment, southwest England, with different spatial and temporal distributions of the rainfall intensity. Five domain configuration scenarios designed with gradually changing downscaling ratios are used to run the WRF model with the ECMWF 40‐year reanalysis data for the periods of the eight events. A two‐dimensional verification scheme is proposed to evaluate the amounts and distributions of simulated rainfall in both spatial and temporal dimensions. The verification scheme consists of both categorical and continuous indices for a first‐level assessment and a more quantitative evaluation of the simulated rainfall. The results reveal a general improvement of the model performance as we downscale from the outermost to the innermost domain. Moderate downscaling ratios of 1:7, 1:5 and 1:3 are found to perform better with the WRF model in giving more reasonable results than smaller ratios. For the sensitivity study on different storm types, the model shows the best performance in reproducing the storm events with spatial and temporal evenness of the observed rainfall, whereas the type of events with highly concentrated rainfall in space and time are found to be the trickiest case for WRF to handle. Finally, the efficiencies of several variability indices are verified in categorising the storm events on the basis of the two‐dimensional rainfall evenness, which could provide a more quantitative way for the event classification that facilitates further studies. It is important that similar studies with various storm events are carried out in other catchments with different geographic and climatic conditions, so that more general error patterns can be found and further improvements can be made to the rainfall products from mesoscale numerical weather models. Copyright © 2011 John Wiley & Sons, Ltd.     

Dynamic geomagnetic field models

A review of modern dynamic models of the Earth’s magnetosphere (the A2000 paraboloid model and Tsyganenko’s T01 model) is presented. For the magnetic storm of January 9–11, 1997, the results of joint calculations of the magnetospheric magnetic field are presented and contributions of the large-scale magnetospheric currents to the D _st variations are analyzed. Both models were shown to be well consistent with measurement data; the contribution of the magnetotail current system to D _st is comparable to the contribution of the ring current. At the same time, the relative dynamics of magnetospheric current systems are different in different models. The differences in the magnetic field variation profiles for various current systems calculated by the A2000 and T01 models are explained by model parameterizations.     

The 20–30-day oscillation of the global circulation and heavy precipitation over the lower reaches of the Yangtze River valley

Based on the observational data in summer, the variations of intraseasonal oscillation (ISO) of the daily rainfall over the lower reaches of the Yangtze River valley (LYRV) were studied by using the non-integer spectrum analysis. The NCEP/NCAR reanalysis data for the period of 1979–2005 were analyzed by principal oscillation pattern analysis (POP) to investigate the spatial and temporal characteristics of principal ISO patterns of the global circulation. The relationships of these ISO patterns to the rainfall ISO and the heavy precipitation process over LYRV were also discussed. It is found that the rainfall over LYRV in May–August is mainly of periodic oscillations of 10–20, 20–30 and 60–70 days, and the interannual variation of the intensity of its 20–30-day oscillation has a strongly positive correlation with the number of the heavy precipitation process. Two modes (POP1, POP2) are revealed by POP for the 20–30-day oscillation of the global 850 hPa geopotential height. One is a circumglobal teleconnection wave train in the middle latitude of the Southern Hemisphere (SCGT) with an eastward propagation, and the other is the southward propagation pattern in the tropical western Pacific (TWP). The POP modes explain 7.72% and 7.66% of the variance, respectively. These two principal ISO patterns are closely linked to the low frequency rainfall and heavy precipitation process over LYRV, in which the probability for the heavy precipitation process over LYRV is 54.9% and 60.4% for the positive phase of the imaginary part of POP1 and real part of POP2, respectively. Furthermore, the models of the global atmospheric circulation for the 20–30-day oscillation in association with or without the heavy precipitation process over LYRV during the Northern Hemisphere summer are set up by means of the composite analysis method. Most of the heavy precipitation processes over LYRV appear in Phase 4 of SCGT or Phase 6 of TWP. When the positive phases of 20–30-day oscillations for the rainfall over LYRV are associated with (without) the heavy precipitation process, a strong westerly stream appears (disappears) from the Arabian Sea via India and Bay of Bengal (BOB) to southern China and LYRV for the global 850 hPa filtered wind field during Phase 4 of SCGT. This situation is favorable (unfavorable) for the forming of the heavy precipitation process over LYRV. Similarly, a strong (weak) western wind belt forms from India through BOB to southern China and LYRV and the subtropical northwestern Pacific and central and eastern equatorial Pacific during Phase 6 of TWP for the cases with (without) the heavy precipitation process. The evolutions of these ISO patterns related to the 20–30-day oscillation are excited by either the interaction of extratropical circulation in both hemispheres or the heat source forcing in Asia monsoon domain and internal interaction of circulation in East Asia. These two global circulation models might therefore provide valuable information for the extended-range forecastof the heavy precipitation process over LYRV during the 10–30 days.     

Statistical characterization of temporal structure of storms

The authors present a statistical procedure to estimate the probability distributions of storm characteristics. The approach uses recent advances in stochastic hydrological modeling. The temporal dynamics of rainfall are modeled via a reward alternating renewal process that describes wet and dry phases of storms. In particular, the wet phase is modeled as a rectangular pulse process with dependent random duration and intensity; the global dependence structure is described using multidimensional copulas. The marginal distributions are described by Generalized Pareto laws. The authors derive both the storm volume statistics and the rainfall volume distribution within a fixed temporal window preceding a storm. Based on these results, they calculate the antecedent moisture conditions. The paper includes a thorough discussion of the validity of the assumptions and approximations introduced, and an application to actual rainfall data. The models presented here have important implications for improved design procedures of water resources and hydrologic systems.     

Point process models for fine-resolution rainfall

Abstract

In a recent development in the literature, a new temporal rainfall model, based on the Bartlett-Lewis clustering mechanism and intended for sub-hourly application, was introduced. That model replaced the rectangular rain cells of the original model with finite Poisson processes of instantaneous pulses, allowing greater variability in rainfall intensity over short intervals. In the present paper, the basic instantaneous pulse model is first extended to allow for randomly varying storm types. A systematic comparison of a number of key model variants, fitted to 5-min rainfall data from Germany, then generates further new insights into the models, leading to the development of an additional model extension, which introduces dependence between rainfall intensity and duration in a simple way. The new model retains the original rectangular cells, previously assumed inappropriate for fine-scale data, obviating the need for the computationally more intensive instantaneous pulse model.

Editor D. Koutsoyiannis     

A conceptually based stochastic point process model for daily stream‐flow generation

Based on the stochastic and phenomenological aspects of hydrological processes, a conceptually based stochastic point process (SPP) model for daily stream‐flow generation is proposed in this paper. In which, storms are defined by a stochastic point process with marked values. All the random variables defining the process are assumed to be mutually independent, which constitutes a compound Poisson point process. The direct surface runoff is regarded as occurring from storage in a cascade of surface linear reservoirs and is responsible for the short‐term variation of the daily stream flows. The baseflow component is considered as coming from subsurface/groundwater storage and is responsible for the long‐term persistence of the storm time‐series. This type of model is proposed as a more realistic model of daily stream flow than models based on pure stochastic processes. Studies on the instantaneous unit hydrograph and the mechanism of baseflow could thereby provide some parameters for this model. Copyright © 2002 John Wiley & Sons, Ltd.     

RESEARCH ON FORECASTING STORM DEBRIS FLOWS

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Design rainfall estimation in Australia: a case study using L moments and Generalized Least Squares Regression

Design rainfall is an important input to rainfall runoff models and is used for many other water resources planning and design applications. The estimation of design rainfall is generally done by applying a regional frequency analysis technique that uses data from a large number of rainfall stations in the region. This paper presents a regional rainfall frequency analysis technique that uses an L moments based index method coupled with Generalized Least Squares Regression (GLSR). The particular advantages of the GLSR method are that it accounts for the differences in record lengths across various sites in the region and inter-station correlation in deriving regional prediction equations. The proposed method has been applied to a data set consisting of 203 rainfall stations across Australia. It has been found that the proposed method can be applied successfully in deriving reasonably accurate design rainfall estimates from 1 to 72 h durations. It has also been found that the proposed method provides quite consistent estimates where a third order polynomial is adequate in smoothing the intensity–frequency–duration (IFD) curves. The method can readily be extended to a larger data set of Australia and other countries to derive generalized IFD data.     

Bayesian comparison of different rainfall depth–duration–frequency relationships

Depth–duration–frequency curves estimate the rainfall intensity patterns for various return periods and rainfall durations. An empirical model based on the generalized extreme value distribution is presented for hourly maximum rainfall, and improved by the inclusion of daily maximum rainfall, through the extremal indexes of 24 hourly and daily rainfall data. The model is then divided into two sub-models for the short and long rainfall durations. Three likelihood formulations are proposed to model and compare independence or dependence hypotheses between the different durations. Dependence is modelled using the bivariate extreme logistic distribution. The results are calculated in a Bayesian framework with a Markov Chain Monte Carlo algorithm. The application to a data series from Marseille shows an improvement of the hourly estimations thanks to the combination between hourly and daily data in the model. Moreover, results are significantly different with or without dependence hypotheses: the dependence between 24 and 72 h durations is significant, and the quantile estimates are more severe in the dependence case.     

Storm‐coverage effect on dynamic flood‐frequency analysis: empirical data analysis

In this study, a dynamic flood‐frequency analysis model considering the storm coverage effect is proposed and applied to six sub‐basins in the Pyungchang River basin, Korea. The model proposed is composed of the rectangular pulse Poisson process model for rainfall, the Soil Conservation Service curve number method for infiltration and the geomorphoclimatic instantaneous unit hydrograph for runoff estimation. Also, the model developed by Marco and Valdes is adopted for quantifying the storm‐coverage characteristics. By comparing the results from the same model with and without the storm‐coverage effect consideration, we could quantify the storm‐coverage effect on the flood‐frequency analysis. As a result of that, we found the storm‐coverage effect was so significant that overestimation of the design flood was unavoidable without its consideration. This also becomes more serious for larger basins where the probability of complete storm coverage is quite low. However, for smaller basins, the limited number of rain gauges is found to hamper the proper quantification of the storm‐coverage characteristics. Provided with a relationship curve between the basin size and the storm coverage (as in this study), this problem could be overcome with an acceptable accuracy level. Copyright © 2003 John Wiley & Sons, Ltd.