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 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.     

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.     

Modelling point rainfall occurrences with the modified Bartlett-Lewis rectangular pulses model

A six parameter stochastic point process model, known as the modified Bartlett-Lewis Rectangular Pulses Model, is applied to fairly long hourly rainfall data recorded at Valentia (relatively a wet location) and Shannon Airport (relatively a dry location), Ireland. Five different sets of statistics of the rainfall data of each month, assuming local stationarity within the month, are used to estimate the parameters and to simulate model output. The problems of parameter stability/sensitivity and identification are discussed and it has been shown that the sensitivity of the model parameters to the choice of six statistics can be avoided by estimating the six parameters by optimization from 16 statistics namely mean, variance, lag-1 autocorrelation corfficient and proportion dry of hourly, 6-hourly, 12-hourly, and 24-hourly rainfalls. Some useful properties of the rainfall depth process are analysed using the notion of event-based statistics. The conditional distributions of rainfall depth and maximum intensity, mean event profiles, and various other features of the rainfall depth process obtained from the model simulated samples compare favourably with the historical ones.     

Study of discontinuities in hydrological data using catastrophe theory

Abstract

Modelling and prediction of hydrological processes (e.g. rainfall–runoff) can be influenced by discontinuities in observed data, and one particular case may arise when the time scale (i.e. resolution) is coarse (e.g. monthly). This study investigates the application of catastrophe theory to examine its suitability to identify possible discontinuities in the rainfall–runoff process. A stochastic cusp catastrophe model is used to study possible discontinuities in the monthly rainfall–runoff process at the Aji River basin in Azerbaijan, Iran. Monthly-averaged rainfall and flow data observed over a period of 20 years (1981–2000) are analysed using the Cuspfit program. In this model, rainfall serves as a control variable and runoff as a behavioural variable. The performance of this model is evaluated using four measures: correlation coefficient, log-likelihood, Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results indicate the presence of discontinuities in the rainfall–runoff process, with a significant sudden jump in flow (cusp signal) when rainfall reaches a threshold value. The performance of the model is also found to be better than that of linear and logistic models. The present results, though preliminary, are promising in the sense that catastrophe theory can play a possible role in the study of hydrological systems and processes, especially when the data are noisy.

Citation Ghorbani, M. A., Khatibi, R., Sivakumar, B. & Cobb, L. (2010) Study of discontinuities in hydrological data using catastrophe theory. Hydrol. Sci. J. 55(7), 1137–1151.     

Application of Fourier series in managing the seasonality of convective and monsoon rainfall

ABSTRACT

This study assesses the performance of Fourier series in representing seasonal variations of the tropical rainfall process in Malaysia. Fourier series are incorporated into a spatial-temporal stochastic model in an attempt to make the model parsimonious and, at the same time, capture the annual variation of rainfall distribution. In view of Malaysia’s main rainfall regime, the model is individually fitted for two regions with distinctive rainfall profiles: one being an urban area receiving rainfall from convective activities whilst the other receives rainfall from monsoonal activities. Since both regions are susceptible to floods, the study focuses on the rainfall process at fine resolution. Fourier series equations are developed to represent the model’s parameters to describe their annual periodicity. The number of significant harmonics for each parameter is determined by inspecting the cumulative fraction of total variance explained by the significant harmonics. Results reveal that the number of significant harmonics assigned for the parameters is slightly higher in the region with monsoonal rains. The overall simulation results show that the proposed model is capable of generating tropical rainfall series from convective and monsoonal activities.

Editor D. Koutsoyiannis Associate editor K. Hamed     

Hydroclimate variability and long-lead forecasting of rainfall over Thailand by large-scale atmospheric variables

Abstract

The development of statistical relationships between local hydroclimates and large-scale atmospheric variables enhances the understanding of hydroclimate variability. The rainfall in the study basin (the Upper Chao Phraya River Basin, Thailand) is influenced by the Indian Ocean and tropical Pacific Ocean atmospheric circulation. Using correlation analysis and cross-validated multiple regression, the large-scale atmospheric variables, such as temperature, pressure and wind, over given regions are identified. The forecasting models using atmospheric predictors show the capability of long-lead forecasting. The modified k-nearest neighbour (k-nn) model, which is developed using the identified predictors to forecast rainfall, and evaluated by likelihood function, shows a long-lead forecast of monsoon rainfall at 7–9 months. The decreasing performance in forecasting dry-season rainfall is found for both short and long lead times. The developed model also presents better performance in forecasting pre-monsoon season rainfall in dry years compared to wet years, and vice versa for monsoon season rainfall.

Editor Z.W. Kundzewicz

Citation Singhrattna, N., Babel, M.S. and Perret, S.R., 2012. Hydroclimate variability and long-lead forecasting of rainfall over Thailand by large-scale atmospheric variables. Hydrological Sciences Journal, 57 (1), 26–41.     

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.     

Hydrological model for urban catchments – analytical development using copulas and numerical solution

Abstract

A model based on analytical development and numerical solution is presented for estimating the cumulative distribution function (cdf) of the runoff volume and peak discharge rate of urban floods using the joint probability density function (pdf) of rainfall volume and duration together with information about the catchment's physical characteristics. The joint pdf of rainfall event volume and duration is derived using the theory of copulas. Four families of Archimedean copulas are tested in order to select the most appropriate to reproduce the dependence structure of those variables. Frequency distributions of runoff event volume and peak discharge rate are obtained following the derived probability distribution theory, using the functional relationship given by the rainfall–runoff process. The model is tested in two urban catchments located in the cities of Chillán and Santiago, Chile. The results are compared with the outcomes of continuous simulation in the Storm Water Management Model (SWMM) and with those from another analytical model that assumes storm event duration and volume to be statistically independent exponentially distributed variables.

Citation Zegpi, M. & Fernández, B. (2010) Hydrological model for urban catchments – analytical development using copulas and numerical solution. Hydrol. Sci. J. 55(7), 1123–1136.     

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.     

Comparison of an artificial neural network and a conceptual rainfall–runoff model in the simulation of ephemeral streamflow

ABSTRACT

The rainfall–runoff process is governed by parameters that can seldom be measured directly for use with distributed models, but are rather inferred by expert judgment and calibrated against historical records. Here, a comparison is made between a conceptual model (CM) and an artificial neural network (ANN) for their ability to efficiently model complex hydrological processes. The Sacramento soil moisture accounting model (SAC-SMA) is calibrated using a scheme based on genetic algorithms and an input delay neural network (IDNN) is trained for variable delays and hidden layer neurons which are thoroughly discussed. The models are tested for 15 ephemeral catchments in Crete, Greece, using monthly rainfall, streamflow and potential evapotranspiration input. SAC-SMA performs well for most basins and acceptably for the entire sample with R² of 0.59–0.92, while scoring better for high than low flows. For the entire dataset, the IDNN improves simulation fit to R² of 0.70–0.96 and performs better for high flows while being outmatched in low flows. Results show that the ANN models can be superior to the conventional CMs, as parameter sensitivity is unclear, but CMs may be more robust in extrapolating beyond historical record limits and scenario building.

EDITOR M.C. Acreman; ASSOCIATE EDITOR not assigned     

G) Personalia

Abstract

This paper proposes a framework for identifying the parameters of a lumped routing model in small to medium sized catchments where lateral inflows can be large but poorly defined. In a first step, a priori estimates of the parameters are made based on topography, aerial photographs, flood marks and field surveys. In a second step, runoff data are analysed of reservoir release events and convective events where no rainfall in the direct catchments occurred. In a third step the routing model is calibrated to the results of hydrodynamic models for scenarios of different magnitudes. In a fourth step, these pieces of information are combined, allowing for soft expert judgement to be incorporated. In a fifth step, the routing parameters are fine tuned to observed flood events where lateral inflows are estimated by a rainfall—runoff model. The framework is illustrated by the Kamp flood forecasting system in Austria that has been in operational use since 2006.     

Uncertainty and sensitivity analysis of runoff and sediment yield in a small agricultural watershed with KINEROS2 / Analyse d'incertitude et de sensibilité des simulations d'écoulement et de transport solide de KINEROS2 dans un petit bassin versant agricole

Abstract

Using the Monte Carlo (MC) method, this paper derives arithmetic and geometric means and associated variances of the net capillary drive parameter, G, that appears in the Parlange infiltration model, as a function of soil texture and antecedent soil moisture content. Approximate expressions for the arithmetic and geometric statistics of G are also obtained, which compare favourably with MC generated ones. This paper also applies the MC method to evaluate parameter sensitivity and predictive uncertainty of the distributed runoff and erosion model KINEROS2 in a small experimental watershed. The MC simulations of flow and sediment related variables show that those parameters which impart the greatest uncertainty to KINEROS2 model outputs are not necessarily the most sensitive ones. Soil hydraulic conductivity and wetting front net capillary drive, followed by initial effective relative saturation, dominated uncertainties of flow and sediment discharge model outputs at the watershed outlet. Model predictive uncertainty measured by the coefficient of variation decreased with rainfall intensity, thus implying improved model reliability for larger rainfall events. The antecedent relative saturation was the most sensitive parameter in all but the peak arrival times, followed by the overland plane roughness coefficient. Among the sediment related parameters, the median particle size and hydraulic erosion parameters dominated sediment model output uncertainty and sensitivity. Effect of rain splash erosion coefficient was negligible. Comparison of medians from MC simulations and simulations by direct substitution of average parameters with observed flow rates and sediment discharges indicates that KINEROS2 can be applied to ungauged watersheds and still produce runoff and sediment yield predictions within order of magnitude of accuracy.     

Non-stationary frequency analysis of heavy rainfall events in southern France

Abstract

Heavy rainfall events often occur in southern French Mediterranean regions during the autumn, leading to catastrophic flood events. A non-stationary peaks-over-threshold (POT) model with climatic covariates for these heavy rainfall events is developed herein. A regional sample of events exceeding the threshold of 100 mm/d is built using daily precipitation data recorded at 44 stations over the period 1958–2008. The POT model combines a Poisson distribution for the occurrence and a generalized Pareto distribution for the magnitude of the heavy rainfall events. The selected covariates are the seasonal occurrence of southern circulation patterns for the Poisson distribution parameter, and monthly air temperature for the generalized Pareto distribution scale parameter. According to the deviance test, the non-stationary model provides a better fit to the data than a classical stationary model. Such a model incorporating climatic covariates instead of time allows one to re-evaluate the risk of extreme precipitation on a monthly and seasonal basis, and can also be used with climate model outputs to produce future scenarios. Existing scenarios of the future changes projected for the covariates included in the model are tested to evaluate the possible future changes on extreme precipitation quantiles in the study area.

Editor Z.W. Kundzewicz; Associate editor K. Hamed

Citation Tramblay, Y., Neppel, L., Carreau, J., and Najib, K., 2013. Non-stationary frequency analysis of heavy rainfall events in southern France. Hydrological Sciences Journal, 58 (2), 280–294.     

Rainfall–runoff response and event-based runoff coefficients in a humid area (northwest Spain)

Abstract

The hydrological response of a small agroforestry catchment in northwest Spain (Corbeira catchment, 16 km²) is analysed, with particular focus on rainfall events. Fifty-four rainfall–runoff events, from December 2004 to September 2007, were used to analyse the principal hydrological patterns and show which factors best explain the hydrological response. The nonlinearity between rainfall and runoff showed that the variability in the hydrological response of the catchment was linked to the seasonal dynamics of the rainfall and, to a lesser extent, to evapotranspiration. The runoff coefficient, estimated as the ratio between direct runoff and rainfall volume, on an event basis, was analysed as a function of rainfall characteristics (amount and intensity) and the initial catchment state conditions prior to an event, such as pre-event baseflow and antecedent rainfall index. The results revealed that the hydrological response depends both on the soil humidity conditions at the start of the event and on rainfall amount, whereas rainfall intensity presented only a significant correlation with discharge increment. The antecedent conditions seem to be a key point in runoff production, and they explain much of the response. The hydrographs are characterized by a steep rising limb, a relatively narrow peak discharge and slow recession limb. These data and the observations suggest that the subsurface flow is the dominant runoff process.

Editor Z.W. Kundzewicz; Associate editor T. Wagener

Citation Rodríguez-Blanco, M.L., Taboada-Castro, M.M. and Taboada-Castro, M.T., 2012. Rainfall–runoff response and event-based runoff coefficients in a humid area (northwest Spain). Hydrological Sciences Journal, 57 (3), 445–459.     

Reliability assessment of water structures subject to data scarcity using the SCS-CN model

ABSTRACT

When discharge measurements are not available, design of water structures relies on using frequency analysis of rainfall data and applying a rainfall–runoff model to estimate a hydrograph. The Soil Conservation Service (SCS) method estimates the design hydrograph first through a rainfall–runoff transformation and next by propagating runoff to the basin outlet via the SCS unit hydrograph (UH) method. The method uses two parameters, the Curve Number (CN) and the time of concentration (T_c). However, in data-scarce areas, the calibration of CN and T_c from nearby gauged watersheds is limited and subject to high uncertainties. Therefore, the inherent uncertainty/variability of the SCS parameters may have considerable ramifications on the safety of design. In this research, a reliability approach is used to evaluate the impact of incorporating the uncertainty of CN and T_c in flood design. The sensitivity of the probabilistic outcome against the uncertainty of input parameters is calculated using the First Order Reliability Method (FORM). The results of FORM are compared with the conventional SCS results, taking solely the uncertainty of the rainfall event. The relative importance of the uncertainty of the SCS parameters is also estimated. It is found that the conventional approach, used by many practitioners, might grossly underestimate the risk of failure of water structures, due to neglecting the probabilistic nature of the SCS parameters and especially the Curve Number. The most predominant factors against which the SCS-CN method is highly uncertain are when the average rainfall value is low (less than 20 mm) or its coefficient of variation is not significant (less than 0.5), i.e. when the resulting rainfall at the design return period is low. A case study is presented for Egypt using rainfall data and CN values driven from satellite information, to determine the regions of acceptance of the SCS-CN method.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR A. Efstratiadis     

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.     

Rainfall–runoff simulation using a normalized antecedent precipitation index

Abstract

The normalized antecedent precipitation index (NAPI) model by Heggen for the prediction of runoff yield is analytically derived from the water balance equation. Heggen's model has been simplified further to a rational form and its performance verified with the Soil Conservation Service Curve Number (SCS-CN) model. The simplified model has three coefficients specific to a watershed, and requires two inputs: rainfall and the derived parameter, NAPI. The characteristic behaviour of the NAPI has resonance with the curve number (CN) of the SCS model. The proposed NAPI model was applied to three watersheds in the semi-arid region of India to simulate runoff yield. The model showed improved correlation between the observed and predicted runoff data compared to the SCS-CN model. The F test and paired t test also confirmed the reliability of the model with significance levels of 0.01 and 0.001%, respectively. The proposed model could be used successfully for rainfall–runoff modelling in a watershed.

Citation Ali, S., Ghosh, N. C. & Singh, R. (2010) Rainfall–runoff simulation using a normalized antecedent precipitation index. Hydrol. Sci. J. 55(2), 266–274.     

Estimation of rainfall elasticity of streamflow in Australia

Abstract

Estimates of rainfall elasticity of streamflow in 219 catchments across Australia are presented. The rainfall elasticity of streamflow is defined here as the proportional change in mean annual streamflow divided by the proportional change in mean annual rainfall. The elasticity is therefore a simple estimate of the sensitivity of long-term streamflow to changes in long-term rainfall, and is particularly useful as an initial estimate of climate change impact in land and water resources projects. The rainfall elasticity of streamflow is estimated here using a hydrological modelling approach and a nonparametric estimator. The results indicate that the rainfall elasticity of streamflow (? _P ) in Australia is about 2.0–3.5 (observed in about 70% of the catchments), that is, a 1% change in mean annual rainfall results in a 2.0–3.5% change in mean annual streamflow. The rainfall elasticity of streamflow is strongly correlated to runoff coefficient and mean annual rainfall and streamflow, where streamflow is more sensitive to rainfall in drier catchments, and those with low runoff coefficients. There is a clear relation-ship between the ? _P values estimated using the hydrological modelling approach and those estimated using the nonparametric estimator for the 219 catchments, although the values estimated by the hydrological modelling approach are, on average, slightly higher. The modelling approach is useful where a detailed study is required and where there are sufficient data to reliably develop and calibrate a hydrological model. The nonparametric estimator is useful where consistent estimates of the sensitivity of long-term streamflow to climate are required, because it is simple to use and estimates the elasticity directly from the historical data. The nonparametric method, being model independent, can also be easily applied in comparative studies to data sets from many catchments across large regions.     

Rainfall downscaling in time: theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades

Abstract

During recent decades, intensive research has focused on techniques capable of generating rainfall time series at a fine time scale that are (fully or partially) consistent with a given series at a coarser time scale. Here we theoretically investigate the consequences on the ensemble statistical behaviour caused by the structure of a simple and widely-used approach of stochastic downscaling for rainfall time series, the discrete Multiplicative Random Cascade. We show that synthetic rainfall time series generated by these cascade models correspond to a stochastic process which is non-stationary, because its temporal autocorrelation structure depends on the position in time in an undesirable manner. Then, we propose and theoretically analyse an alternative downscaling approach based on the Hurst-Kolmogorov process, which is equally simple but is stationary. Finally, we provide Monte Carlo experiments which validate our theoretical results.

Editor Z.W. Kundzewicz

Citation Lombardo, F., Volpi, E., and Koutsoyiannis, D., 2012. Rainfall downscaling in time: theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades. Hydrological Sciences Journal, 57 (6), 1052–1066.