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     

Analysis and modelling of rainfall fields at different resolutions in southern Italy

Abstract

The spatial and temporal variability of the scaling properties and correlation structure of a data set of rainfall time series, aggregated over different temporal resolutions, and observed in 70 raingauges across the Basilicata and Calabria regions of southern Italy, is investigated. Two types of random cascade model, namely canonical and microcanonical models, were used for each raingauge and selected season. For both models, different hypotheses concerning dependency of parameters on time scale and rainfall height can be adopted. In particular, a new approach is proposed which consists of several combinations of models with a different scale dependence of parameters for different temporal resolutions. The goal is to improve the modelling of the main features of rainfall time series, especially for cases where the variability of rainfall changes irregularly with temporal aggregation. The results obtained with the new methodology showed good agreement with the observed data, in particular, for the summer months. In fact, during this season, rainfall heights aggregated at fine temporal resolutions (from 5 to 20 min) are more similar (relative to the winter season) to the values cumulated on 1 or 3 h (due to convective phenomena) and, consequently, the process of rainfall breakdown is nearly stationary for a range of finer temporal resolutions.

Editor D. Koutsoyiannis; Associate editor A. Montanari     

Transfer function noise modelling of groundwater level fluctuation using threshold rainfall-based binary-weighted parameter estimation approach

Considerable uncertainty occurs in the parameter estimates of traditional rainfall–water level transfer function noise (TFN) models, especially with the models built using monthly time step datasets. This is due to the equal weights assigned for rainfall occurring during both water level rise and water level drop events while estimating the TFN model parameters using the least square technique. As an alternative to this approach, a threshold rainfall-based binary-weighted least square method was adopted to estimate the TFN model parameters. The efficacy of this binary-weighted approach in estimating the TFN model parameters was tested on 26 observation wells distributed across the Adyar River basin in Southern India. Model performance indices such as mean absolute error and coefficient of determination values showed that the proposed binary-weighted approach of fitting independent threshold-based TFN models for water level rise and water level drop scenarios considerably improves the model accuracy over other traditional TFN models.

EDITOR D. Koutsoyiannis

ASSOCIATE EDITOR A. Fiori     

An evaluation of numerical weather prediction based rainfall forecasts

ABSTRACT

Assessment of forecast precipitation is required before it can be used as input to hydrological models. Using radar observations in southeastern Australia, forecast rainfall from the Australian Community Climate Earth-System Simulator (ACCESS) was evaluated for 2010 and 2011. Radar rain intensities were first calibrated to gauge rainfall data from four research rainfall stations at hourly time steps. It is shown that the Australian ACCESS model (ACCESS-A) overestimated rainfall in low precipitation areas and underestimated elevated accumulations in high rainfall areas. The forecast errors were found to be dependent on the rainfall magnitude. Since the cumulative rainfall observations varied across the area and through the year, the relative error (RE) in the forecasts varied considerably with space and time, such that there was no consistent bias across the study area. Moreover, further analysis indicated that both location and magnitude errors were the main sources of forecast uncertainties on hourly accumulations, while magnitude was the dominant error on the daily time scale. Consequently, the precipitation output from ACCESS-A may not be useful for direct application in hydrological modelling, and pre-processing approaches such as bias correction or exceedance probability correction will likely be necessary for application of the numerical weather prediction (NWP) outputs.

EDITOR M.C. Acreman ASSOCIATE EDITOR A. Viglione     

On the potential of Bartlett Lewis rectangular pulse models for simulating rainfall in Peninsular Malaysia

Abstract

The applicability of two versions of the Bartlett Lewis rectangular pulse model, the original and the modified model, is discussed for describing the temporal and spatial variation of rainfall patterns observed at 15 raingauge stations in Peninsular Malaysia over the period 1971–2008; 17 different sets of moment combinations are fitted to these models based on the generalized method of moments approach. The common statistics included in all sets are the mean, variance, lag-1 autocorrelation and the probability of dry based on the hourly rainfall data. The analysis was carried out on hourly rainfall data from all 15 stations for all months of the year. Two stations, Petaling Jaya and Kemaman, located on the west and east coasts of the Peninsula, respectively, are considered for illustration of the results, taking the months of July and November, which correspond to the driest and wettest months, corresponding to the southwest monsoon (May–August) and northeast monsoon (November–February), respectively. The best moment combination found for the illustrative results is based on the common statistics, as well as the mean and variance based on 24-h aggregated rainfall data, the inclusion of which successfully improved the model performance; the errors were significantly reduced. It was also found that the performance of the fitted models based on the mean absolute deviate error varies according to the type of Bartlett Lewis model applied: errors are much smaller for the fitted model based on the modified model as compared to the original model. In addition, the fitted statistics: mean, lag-1 autocorrelation and probability of dry are quite well fitted for several aggregated time scales; however, the variances are underestimated in both models for all aggregated time scales, particularly in the case of the original model. The results of extreme value analysis indicate that the modified model failed to reproduce the annual hourly and daily rainfall extremes satisfactorily.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Hanaish, I.S., Ibrahim, K., and Jemain, A.A., 2013. On the potential of Bartlett Lewis rectangular pulse models for simulating rainfall in Peninsular Malaysia. Hydrological Sciences Journal, 58 (8), 1690–1703.     

Modelling streamflow trends for a watershed with limited data: case of the Litani basin,Lebanon

Abstract

Streamflow variability in the Upper and Lower Litani basin, Lebanon was modelled as there is a lack of long-term measured runoff data. To simulate runoff and streamflow, daily rainfall was derived using a stochastic rainfall generation model and monthly rainfall data. Two distinct synthetic rainfall models were developed based on a two-part probabilistic distribution approach. The rainfall occurrence was described by a Markov chain process, while the rainfall distribution on wet days was represented by two different distributions (i.e. gamma and mixed exponential distributions). Both distributions yielded similar results. The rainfall data were then processed using water balance and routing models to generate daily and monthly streamflow. Compared with measured data, the model results were generally reasonable (mean errors ranging from 0.1 to 0.8?m³/s at select locations). Finally, the simulated monthly streamflow data were used to investigate discharge trends in the Litani basin during the 20th century using the Mann-Kendall and Sen slope nonparametric trend detection methods. A significant drying trend of the basin was detected, reaching a streamflow reduction of 0.8 and 0.7 m³/s per decade in January for the Upper and Lower basin, respectively.

Editor D. Koutsoyiannis; Associate editor Sheng Yue

Citation Ramadan, H.H., Beighley, R.E., and Ramamurthy, A.S., 2012. Modelling streamflow trends for a watershed with limited data: case of the Litani basin, Lebanon. Hydrological Sciences Journal, 57 (8), 1516–1529.     

Simulation and spatio-temporal disaggregation of multi-site rainfall data for urban drainage applications

Abstract

For urban drainage and urban flood modelling applications, fine spatial and temporal rainfall resolution is required. Simulation methods are developed to overcome the problem of data limitations. Although temporal resolution higher than 10–20 minutes is not well suited for detailed rainfall—runoff modelling for urban drainage networks, in the absence of monitored data, longer time intervals can be used for master planning or similar purposes. A methodology is presented for temporal disaggregation and spatial distribution of hourly rainfall fields, tested on observations for a 10-year period at 16 raingauges in the urban catchment of Dalmuir (UK). Daily rainfall time series are simulated with a generalized linear model (GLM). Next, using a single-site disaggregation model, the daily data of the central gauge in the catchment are downscaled to an hourly time scale. This hourly pattern is then applied linearly in space to disaggregate the daily data into hourly rainfall at all sites. Finally, the spatial rainfall field is obtained using inverse distance weighting (IDW) to interpolate the data over the whole catchment. Results are satisfactory: at individual sites within the region the simulated data preserve properties that match the observed statistics to an acceptable level for practical purposes.     

Contribution to hydrological modelling of small Amazonian catchments: application of rainfall–runoff models to simulate flow duration curves

Abstract

The objective of this study is to analyse three rainfall–runoff hydrological models applied in two small catchments in the Amazon region to simulate flow duration curves (FDCs). The simple linear model (SLM) considers the rainfall–runoff process as an input–output time-invariant system. However, the rainfall–runoff process is nonlinear; thus, a modification is applied to the SLM based on the residual relationship between the simulated and observed discharges, generating the modified linear model (MLM). In the third model (SVM), the nonlinearity due to infiltration and evapotranspiration is incorporated into the system through the sigmoid variable gain factor. The performance criteria adopted were a distance metric (δ) and the Nash-Sutcliffe coefficient (R²) determined between simulated and observed flows. The good results of the models, mainly the MLM and SVM, showed that they could be applied to simulate FDCs in small catchments in the Amazon region.

Editor D. Koutsoyiannis; Associate editor A. Montanari

Citation Blanco, C.J.C., Santos, S.S.M., Quintas, M.C., Vinagre, M.V.A., and Mesquita, A.L.A., 2013. Contribution to hydrological modelling of small Amazonian catchments: application of rainfall–runoff models to simulate flow duration curves. Hydrological Sciences Journal, 58 (7), 1–11.     

A spatial temporal downscaling approach to development of IDF relations for Perth airport region in the context of climate change

ABSTRACT

Downscaling of climate projections is the most adapted method to assess the impacts of climate change at regional and local scales. This study utilized both spatial and temporal downscaling approaches to develop intensity–duration–frequency (IDF) relations for sub-daily rainfall extremes in the Perth airport area. A multiple regression-based statistical downscaling model tool was used for spatial downscaling of daily rainfall using general circulation models (GCMs) (Hadley Centre’s GCM and Canadian Global Climate Model) climate variables. A simple scaling regime was identified for 30 minutes to 24 hours duration of observed annual maximum (AM) rainfall. Then, statistical properties of sub-daily AM rainfall were estimated by scaling an invariant model based on the generalized extreme value distribution. RMSE, Nash-Sutcliffe efficiency coefficient and percentage bias values were estimated to check the accuracy of downscaled sub-daily rainfall. This proved the capability of the proposed approach in developing a linkage between large-scale GCM daily variables and extreme sub-daily rainfall events at a given location. Finally IDF curves were developed for future periods, which show similar extreme rainfall decreasing trends for the 2020s, 2050s and 2080s for both GCMs.

Editor M.C. Acreman; Associate editor S. Kanae     

Regionalization of heavy rainfall to improve climatic design values for infrastructure: case study in Southern Ontario,Canada

Abstract

Southern Ontario, Canada, has been impacted in recent years by many heavy rainfall and flooding events that have exceeded existing historical estimates of infrastructure design rainfall intensity–duration–frequency (IDF) values. These recent events and the limited number of short-duration recording raingauges have prompted the need to research the climatology of heavy rainfall events within the study area, review the existing design IDF methodologies, and evaluate alternative approaches to traditional point-based heavy rainfall IDF curves, such as regional IDF design values. The use of additional data and the regional frequency analysis methodology were explored for the study area, with the objective of validating identified clusters or homogeneous regions of extreme rainfall amounts through Ward's method. As the results illustrate, nine homogeneous regions were identified in Southern Ontario using the annual maximum series (AMS) for daily and 24-h rainfall data from climate and rate-of-rainfall or tipping bucket raingauge (TBRG) stations, respectively. In most cases, the generalized extreme value and logistic distributions were identified as the statistical distributions that provide the best fit for the 24-h and sub-daily rainfall data in the study area. A connection was observed between extreme rainfall variability, temporal scale of heavy rainfall events and location of each homogeneous region. Moreover, the analysis indicated that scaling factors cannot be used reliably to estimate sub-daily and sub-hourly values from 24- and 1-h data in Southern Ontario.

Citation Paixao, E., Auld, H., Mirza, M.M.Q., Klaassen, J. & Shephard, M.W. (2011) Regionalization of heavy rainfall to improve climatic design values for infrastructure: case study in Southern Ontario, Canada. Hydrol. Sci. J. 56(7), 1067–1089.     

Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

Integration of gauge and radar rainfall to enable best simulation of hydrological parameters

This study is about use of spatially distributed rain in physically based hydrological models. In recent years, spatially distributed radar rainfall data have become available. The distributed radar rain is used to precisely model hydrologic processes and it is more realistic than the past practice of distribution methods like Thiessen polygons. Radar provides a highly accurate spatial distribution of rainfall and greatly improves the basin average rainfall estimates. However, quantification of the exact amount of rainfall from radar observation is relatively difficult. Thus, the fundamental idea of this study is to apply hourly gauge and radar rainfall data in a distributed hydrological model to simulate hydrological parameters. Hence the comparison is made between the outcomes of the WetSpa model from radar rainfall distribution and gauge rainfall distributed by the Thiessen polygon technique. The comparative plots of the hydrograph and the results of hydrological components such as evapotranspiration, surface runoff, soil moisture, recharge and interflow, reflect the spatially distributed radar input performing well for model outflow simulation.

EDITOR D. Koutsoyiannis

ASSOCIATE EDITOR F. Pappenberger     

Using data-derived perturbations to incorporate uncertainty in generating stochastic areal rainfall from point rainfall

Abstract

Raingauge measurements are commonly used to estimate daily areal rainfall for catchment modelling. The variation of rainfall between the gauges is usually inadequately captured and areal rainfall estimates are therefore very uncertain. A method of quantifying these uncertainties and incorporating them into ensembles of areal rainfall is demonstrated and tested. The uncertainties are imposed as perturbations based on the differences in areal rainfall that result when half of the raingauges are alternately omitted. Also included is a method of: (a) estimating the proportion rainfall that falls on areas where no gauges are located that are consequently computed as having zero rain, and (b) replacing them with plausible non-zero rainfalls. The model is tested using daily rainfall from two South African catchments and is found to exhibit the expected behaviour. One of the two parameters of the model is obtained from the rainfall data, while the other has direct physical interpretation.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Ndiritu, J., 2013. Using data-derived perturbations to incorporate uncertainty in generating stochastic areal rainfall from point rainfall. Hydrological Sciences Journal, 58 (8), 1704–1717.     

Hydrological response characteristics of Mediterranean catchments at different time scales: a meta-analysis

ABSTRACT

This work examines 140 hydrological studies conducted in the Mediterranean region. It identifies key characteristics of the hydrological responses of Mediterranean catchments at various time scales and compares different methods and modelling approaches used for individual-catchment studies. The study area is divided into the northwestern (NWM), eastern (EM) and southern (SM) Mediterranean. The analysis indicates regional discrepancies in which the NWM shows the most extreme rainfall regime. A tendency for reduced water resources driven by both anthropogenic and climatic pressures and a more extreme rainfall regime are also noticeable. Catchments show very heterogeneous responses over time and space, resulting in limitations in hydrological modelling and large uncertainties in predictions. However, few models have been developed to address these issues. Additional studies are necessary to improve the knowledge of Mediterranean hydrological features and to account for regional specificities.

Editor D. Koutsoyiannis Associate editor A. Efstratiadis     

Simulating hourly rainfall occurrence within an equatorial rainforest,Borneo Island / Simulation de l'occurrence de pluie horaire au sein de la forêt équatoriale,Ile de Bornéo

Abstract

The ability to simulate characteristics of the diurnal cycle of rainfall occurrence, and its evolution over the seasons is important to the forecasting of hydrological impacts resulting from land-use and climate changes within the humid tropics. This stochastic modelling study uses a generalized linear model (GLM) solution to second-order Markov chain models, as these discrete models are better at describing binary occurrence processes on an hourly time-scale than continuous-time approaches such as stochastic state-space models. We show that transition probabilities derived by the Markov chain method need to be time-varying rather than stationary to simulate the evolution of the diurnal cycle of rainfall occurrence over a Southeast Asian monsoon sequence. The conceptual and pragmatic links between discrete diurnal processes and continuous processes occurring over seasonal periods are thereby simulated within the same model.     

Sensitivity of hydrological models to uncertainty in rainfall input

Abstract

Different approaches used in hydrological modelling are compared in terms of the way each one takes the rainfall data into account. We examine the errors associated with accounting for rainfall variability, whether in hydrological modelling (distributed vs lumped models) or in computing catchment rainfall, as well as the impact of each approach on the representativeness of the parameters it uses. The database consists of 1859 rainfall events, distributed on 500 basins, located in the southeast of France with areas ranging from 6.2 to 2851 km². The study uses as reference the hydrographs computed by a distributed hydrological model from radar rainfall. This allows us to compare and to test the effects of various simplifications to the process when taking rainfall information (complete rain field vs sampled rainfall) and rainfall–runoff modelling (lumped vs distributed) into account. The results appear to show that, in general, the sampling effect can lead to errors in discharge at the outlet that are as great as, or even greater than, those one would get with a fully lumped approach. We found that small catchments are more sensitive to the uncertainties in catchment rainfall input generated by sampling rainfall data as seen through a raingauge network. Conversely, the larger catchments are more sensitive to uncertainties generated when the spatial variability of rainfall events is not taken into account. These uncertainties can be compensated for relatively easily by recalibrating the parameters of the hydrological model, although such recalibrations cause the parameter in question to completely lose physical meaning.

Citation Arnaud, P., Lavabre, J., Fouchier, C., Diss, S. & Javelle, P. (2011) Sensitivity of hydrological models to uncertainty of rainfall input. Hydrol. Sci. J. 56(3), 397–410.     

Simulation of daily rainfall scenarios with interannual and multidecadal climate cycles for South Florida

Concerns about the potential effects of anthropogenic climate change have led to a closer examination of how climate varies in the long run, and how such variations may impact rainfall variations at daily to seasonal time scales. For South Florida in particular, the influences of the low-frequency climate phenomena, such as the El Nino Southern Oscillation (ENSO) and the Atlantic Multi-decadal Oscillation (AMO), have been identified with aggregate annual or seasonal rainfall variations. Since the combined effect of these variations is manifest as persistent multi-year variations in rainfall, the question of modeling these variations at the time and space scales relevant for use with the daily time step-driven hydrologic models in use by the South Florida Water Management District (SFWMD) has arisen. To address this problem, a general methodology for the hierarchical modeling of low- and high-frequency phenomenon at multiple rain gauge locations is developed and illustrated. The essential strategy is to use long-term proxies for regional climate to first develop stochastic scenarios for regional climate that include the low-frequency variations driving the regional rainfall process, and then to use these indicators to condition the concurrent simulation of daily rainfall at all rain gauges under consideration. A newly developed methodology, called Wavelet Autoregressive Modeling (WARM), is used in the first step after suitable climate proxies for regional rainfall are identified. These proxies typically have data available for a century to four centuries so that long-term quasi-periodic climate modes of interest can be identified more reliably. Correlation analyses with seasonal rainfall in the region are used to identify the specific proxies considered as candidates for subsequent conditioning of daily rainfall attributes using a Non-homogeneous hidden Markov model (NHMM). The combined strategy is illustrated for the May–June–July (MJJ) season. The details of the modeling methods and results for the MJJ season are presented in this study.