Linking space–time variability of river runoff and rainfall fields: a dynamic approach

Statistical self-similarity in the spatial and temporal variability of rainfall, river networks, and runoff processes has been observed in many empirical studies. To theoretically investigate the relationships between the various time and space scales of variability in rainfall and runoff process we propose a simplified, yet physically based model of a catchment–rainfall interaction. The channel network is presented as a random binary tree, having topological and hydraulic geometry properties typically observed in real river networks. The continuous rainfall model consists of individual storms separated by dry periods. Each given storm is disaggregated in space and time using the random cascade model. The flow routing is modelled by the network of topologically connected nonlinear reservoirs, each representing a link in the channel network. Running the model for many years of synthetic rainfall time series and a continuous water balance model we generate an output, in the form of continuous time series of water discharge in all links in the channel network. The main subject of study is the annual peak flow as a function of catchment area and various characteristics of rainfall. The model enables us to identify different physical processes responsible for the empirically observed scaling properties of peak flows.     

A transport‐distance approach to scaling erosion rates: 1. Background and model development

The process basis of existing soil‐erosion models is shown to be ill‐founded. The existing literature builds directly or indirectly on Bennett's (1974) paper, which provided a blueprint for integrated catchment‐scale erosion modelling. Whereas Bennett recognized the inherent assumptions of the approach suggested, subsequent readings of the paper have led to a less critical approach. Most notably, the assumption that sediment movement could be approximated by a continuity equation that related to transport in suspension has produced a series of submodels that assume that all movement occurs in suspension. For commonly occurring conditions on hillslopes, this case is demonstrably untrue both on theoretical grounds and from empirical observations. Elsewhere in the catchment system, it is only partially true, and the extent to which the assumption is reasonable varies both spatially and temporally. A second ground‐breaking paper – that of Foster and Meyer (1972) – was responsible for subsequent uncritical application of a first‐order approximation to deposition based on steady‐state analysis and again a weak empirical basis. We describe in this paper an alternative model (Mahleran – Model for Assessing Hillslope‐Landscape Erosion, Runoff And Nutrients) based upon particle‐travel distance that overcomes existing limitations by incorporating parameterizations of the different detachment and transport mechanisms that occur in water erosion in hillslopes and small catchments. In the second paper in the series, we consider the sensitivity and general behaviour of Mahleran , and test it in relation to data from a large rainfall‐simulation experiment. The third paper of the sequence evaluates the model using data from plots of different sizes in monitored rainfall events. From this evaluation, we consider the scaling characteristics of the current form of Mahleran and suggest that integrated modelling, laboratory and field approaches are required in order to advance the state of the art in soil‐erosion modelling. Copyright © 2008 John Wiley & Sons, Ltd.     

Multifractal analysis as a tool for validating a rainfall model

A multifractal analysis was carried out in order to validate the simulation of hourly rainfall records of a local climate model for the Iberian Peninsula. Observed and simulated hourly rainfall data from four locations in Andalusia (southern Spain) were used to carry out the study. In order to detect the influence of the length of the data series on the results, two different sizes were used for the real data: 4 years, and 20 years. The results show that algebraic tails are required to fit the probability distribution of extreme rain event sizes, and rain and dry event durations for both kinds of rainfall data. Similar results are found for the extreme rain event sizes and dry event durations fits when the real and synthetic data are considered. Nevertheless, some differences appear in the cases of rain event durations. The detection of the presence of a first‐order multifractal phase transition associated with a critical moment in the empirical moment scaling exponent function and the results of the extreme rain event sizes fits, reveal that real rainfall is a self‐organized criticality (SOC) process. That behaviour is less evident in the simulated rainfall series. The same ‘synoptic maximum’ value was found for each place with both types of rainfall data. A time clustering analysis was carried out applying the count‐based periodogram and the Fano factor methods. Some periodicities have been detected in the periodograms, especially for the longest real rainfall data series. Copyright © 2007 John Wiley & Sons, Ltd.     

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     

Variable power‐law scaling of hillslope Hortonian rainfall–runoff processes

Hydrological studies focused on Hortonian rainfall–run‐off scaling have found that the run‐off depth generally declines with the plot length in power‐law scaling. Both the power‐law proportional coefficient and the scaling exponent show great variability for specific conditions, but why and how they vary remain unclear. In the present study, the scaling of hillslope Hortonian rainfall–run‐off processes is investigated for different rainfall, soil infiltration, and hillslope surface characteristics using the physically based cell‐based rainfall‐infiltration‐run‐off model. The results show that both temporally intermittent and steady rainfalls can result in prominent power‐law scaling at the initial stage of run‐off generation. Then, the magnitude of the power‐law scaling decreases gradually due to the decreasing run‐on effect. The power‐law scaling is most sensitive to the rainfall and soil infiltration parameters. When the ratio of rainfall to infiltration exceeds a critical value, the magnitude of the power‐law scaling tends to decrease notably. For different intermittent rainfall patterns, the power‐law exponent varies in the range of ?1.0 to ?0.113, which shows an approximately logarithmic increasing trend for the proportional coefficient as a function of the run‐off coefficient. The scaling is also sensitive to the surface roughness, soil sealing, slope angle, and hillslope geometry because these factors control the run‐off routing and run‐on infiltration processes. These results provide insights into the variable scaling of the Hortonian rainfall–run‐off process, which are expected to benefit modelling of large‐scale hydrological and ecological processes.     

Selecting the best IDF model by using the multifractal approach

In this work, the multifractal properties of hourly rainfall data recorded at a location in Southern Spain have been related to the scale properties of the corresponding intensity–duration–frequency (IDF) curves. Four parametric models for the IDF curves have been fitted to the quantiles of rainfall obtained using the generalized Pareto frequency distribution function with the extreme data series obtained for the same place. The scaling of the rainfall intensity moments has been analysed, and the empirical moments scaling exponent function has been obtained. The corresponding values of q₁ and γ₁ have been empirical and theoretically calculated and compared with some characteristics of the different IDF models. Thus, the scaling behaviour of IDF curves has been analysed, and the best model has been selected. Copyright © 2012 John Wiley & Sons, Ltd.     

Scaling and self‐similarity in one‐dimensional unsteady open channel flow

The conditions under which the Saint Venant equations system for unsteady open channel flow, as an initial–boundary value problem, becomes self‐similar are investigated by utilizing one‐parameter Lie group of point scaling transformations. One of the advantages of this methodology is that the self‐similarity conditions due to the initial and boundary conditions can also be investigated thoroughly in addition to the conditions due to the governing equation. The obtained self‐similarity conditions are compared with the scaling relationships that are derived through the Froude similitude. It is shown that the initial–boundary value problem of a one‐dimensional unsteady open channel flow process in a prototype domain can be self‐similar with that of several different scaled domains. However, the values of all the flow variables (at specified time and space) under different scaled domains can be upscaled to the same values in the prototype domain (at the corresponding time and space), as shown in this study. Distortion in scales of different space dimensions has been implemented extensively in physical hydraulic modelling, mainly because of cost, space and time limitations. Unlike the traditional approach, the distinction is made between the longitudinal–horizontal and transverse–horizontal length scales in this study. The scaled domain obtained by the proposed approach, when scaling ratios of channel width and water depth are equal, is particularly important for the similarity of flow characteristics in a cross‐section because the width‐to‐depth ratio and the inclination angles of the banks are conserved in a cross‐section. It is also shown that the scaling ratio of the roughness coefficient under distorted channel conditions depends on that of hydraulic radius and longitudinal length. The proposed scaling relations obtained by the Lie group scaling approach may provide additional spatial, temporal and economical flexibility in setting up physical hydraulic models. Copyright © 2013 John Wiley & Sons, Ltd.     

Is a chaotic multi‐fractal approach for rainfall possible?

An Erratum has been published for this article in Hydrological Processes 15 (12) 2001, 2381–2382. Applications of the ideas gained from fractal theory to characterize rainfall have been one of the most exciting areas of research in recent times. The studies conducted thus far have nearly unanimously yielded positive evidence regarding the existence of fractal behaviour in rainfall. The studies also revealed the insufficiency of the mono‐fractal approaches to characterizing the rainfall process in time and space and, hence, the necessity for multi‐fractal approaches. The assumption behind multi‐fractal approaches for rainfall is that the variability of the rainfall process could be directly modelled as a stochastic (or random) turbulent cascade process, since such stochastic cascade processes were found to generically yield multi‐fractals. However, it has been observed recently that multi‐fractal approaches might provide positive evidence of a multi‐fractal nature not only in stochastic processes but also in, for example, chaotic processes. The purpose of the present study is to investigate the presence of both chaotic and fractal behaviours in the rainfall process to consider the possibility of using a chaotic multi‐fractal approach for rainfall characterization. For this purpose, daily rainfall data observed at the Leaf River basin in Mississippi are studied, and only temporal analysis is carried out. The autocorrelation function, the power spectrum, the empirical probability distribution function, and the statistical moment scaling function are used as indicators to investigate the presence of fractal, whereas the presence of chaos is investigated by employing the correlation dimension method. The results from the fractal identification methods indicate that the rainfall data exhibit multi‐fractal behaviour. The correlation dimension method yields a low dimension, suggesting the presence of chaotic behaviour. The existence of both multi‐fractal and chaotic behaviours in the rainfall data suggests the possibility of a chaotic multi‐fractal approach for rainfall characterization. Copyright © 2001 John Wiley & Sons, Ltd.     

A two steps disaggregation method for highly seasonal monthly rainfall

 The need for high resolution rainfall data at temporal scales varying from daily to hourly or even minutes is a very important problem in hydrology. For many locations of the world, rainfall data quality is very poor and reliable measurements are only available at a coarse time resolution such as monthly. The purpose of this work is to apply a stochastic disaggregation method of monthly to daily precipitation in two steps: 1. Initialization of the daily rainfall series by using the truncated normal model as a reference distribution. 2.␣Restructuring of the series according to various time series statistics (autocorrelation function, scaling properties, seasonality) by using a Markov chain Monte Carlo based algorithm. The method was applied to a data set from a rainfall network of the central plains of Venezuela, in where rainfall is highly seasonal and data availability at a daily time scale or even higher temporal resolution is very limited. A detailed analysis was carried out to study the seasonal and spatial variability of many properties of the daily rainfall as scaling properties and autocorrelation function in order to incorporate the selected statistics and their annual cycle into an objective function to be minimized in the simulation procedure. Comparisons between the observed and simulated data suggest the adequacy of the technique in providing rainfall sequences with consistent statistical properties at a daily time scale given the monthly totals. The methodology, although highly computationally intensive, needs a moderate number of statistical properties of the daily rainfall. Regionalization of these statistical properties is an important next step for the application of this technique to regions in where daily data is not available.     

Uncertainty,entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling / Incertitude,entropie, effet d'échelle et propriétés stochastiques hydrologiques. 1. Propriétés distributionnelles marginales des processus hydrologiques et échelle d'état

Abstract

The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation (CV) and lag one autocorrelation. In this first part of the study, the marginal distributional properties of hydrological variables and the state scaling behaviour are investigated. Application of the ME principle under these very simple conditions results in the truncated normal distribution for small values of CV and in a nonexponential type (Pareto) distribution for high values of CV. In addition, the normal and the exponential distributions appear as limiting cases of these two distributions. Testing of these theoretical results with numerous hydrological data sets on several scales validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes. Both theoretical and empirical results show that the state scaling is only an approximation for the high return periods, which is merely valid when processes have high variation on small time scales. In other cases the normal distributional behaviour, which does not have state scaling properties, is a more appropriate approximation. Interestingly however, as discussed in the second part of the study, the normal distribution combined with positive autocorrelation of a process, results in time scaling behaviour due to the ME principle.     

Applying multifractality and the self‐organized criticality theory to describe the temporal rainfall regimes in Andalusia (southern Spain)

A multifractal analysis of hourly and daily rainfall data recorded at four locations of Andalusia (southern Spain) was carried out in order to study the temporal structure of rainfall and to find differences between both time resolutions. The results show that an algebraic tail is required to fit the probability distribution of the extreme rain events for all the cases. The presence of a multifractal phase transition associated with a critical moment in the empirical moments scaling exponent function was also detected. Both facts indicate that the rainfall process is a case of self‐organized criticality (SOC) dynamics, although the results differ for each place according to the time resolution and the nature of the rainfall, either convective or frontal. This SOC behaviour is related to a statistically steady state that implies the presence of clusterization in the time‐occurrence sequence of rain events. Such fluctuations have been shown by performing the analysis of the Fano and Allan factors and the count‐based periodogram. The values for the “synoptic maximum”, the typical lifetime of planetary scale atmospheric structures, have been obtained for each place and some important periodicities have been detected when dealing with extremes. Copyright © 2007 John Wiley & Sons, Ltd.     

A parallel,scalable and memory efficient inversion code for very large‐scale airborne electromagnetics surveys

Over the past decade the typical size of airborne electromagnetic data sets has been growing rapidly, along with an emerging need for highly accurate modelling. One‐dimensional approximate inversions or data transform techniques have previously been employed for very large‐scale studies of quasi‐layered settings but these techniques fail to provide the consistent accuracy needed by many modern applications such as aquifer and geological mapping, uranium exploration, oil sands and integrated modelling. In these cases the use of more time‐consuming 1D forward and inverse modelling provide the only acceptable solution that is also computationally feasible. When target structures are known to be quasi layered and spatially coherent it is beneficial to incorporate this assumption directly into the inversion. This implies inverting multiple soundings at a time in larger constrained problems, which allows for resolving geological layers that are undetectable using simple independent inversions. Ideally, entire surveys should be inverted at a time in huge constrained problems but poor scaling properties of the underlying algorithms typically make this challenging. Here, we document how we optimized an inversion code for very large‐scale constrained airborne electromagnetic problems. Most importantly, we describe how we solve linear systems using an iterative method that scales linearly with the size of the data set in terms of both solution time and memory consumption. We also describe how we parallelized the core region of the code, in order to obtain almost ideal strong parallel scaling on current 4‐socket shared memory computers. We further show how model parameter uncertainty estimates can be efficiently obtained in linear time and we demonstrate the capabilities of the full implementation by inverting a 3327 line km SkyTEM survey overnight. Performance and scaling properties are discussed based on the timings of the field example and we describe the criteria that must be fulfilled in order to adapt our methodology for similar type problems.     

Fractal analysis of rainfall observed in two different climatic regions

Abstract

The importance of high-resolution rainfall data to understand the intricacies of the dynamics of hydrological processes and describe them in a sophisticated and accurate way has been increasingly realized. The present study investigates the general suitability of fractal (or scaling) theory for understanding the rainfall behaviour and transforming rainfall data from one time scale to another. The study, employing a multi-fractal approach, follows the research undertaken earlier by the author (Sivakumar, 2000) employing a mono-fractal approach in which some preliminary indication as to the possibility of existence of (multi-) fractals was obtained. Rainfall data of three different resolutions, six-hourly, daily, and weekly, observed over a period of 25 years in two different climatic regions: a subtropical climatic region (Leaf River basin, Mississippi, USA); and an equatorial climatic region (Singapore) are analysed. The existence of multi-fractal behaviour in the rainfall data is investigated using (a) the power spectrum method; (b) the empirical probability distribution function (PDF) method; (c) the statistical moment scaling method; and (d) the probability distribution multiple scaling (PDMS) method. The results achieved from all these methods for the six different rainfall data sets considered indicate the existence of multi-fractal behaviour of rainfall observed in Leaf River basin and Singapore, providing further support to the results obtained using the mono-fractal approach (Sivakumar, 2000). The suitability of a multi-fractal framework to characterize the behaviour of rainfall observed in the above two significantly different climatic regions, subtropical and equatorial, seems to suggest the general suitability of the fractal theory for transforming rainfall from one time scale to another. Investigations with rainfall data from several other climatic regions are underway with a view to strengthening the above conclusions.     

Conceptually-based shot noise modeling of streamflows at short time interval

A conceptual-stochastic approach to short time runoff data modelling is proposed, according to the aim of reproducing the hydrological aspects of the streamflow process and of preserving as much as possible the dynamics of the process itself. This latter task implies preservation of streamflow characteristics at higher scales of aggregation and, within a conceptual framework, involves compatibility with models proposed for the runoff process at those scales. At a daily time scale the watershed response to the effective rainfall is considered as deriving from the response of three linear reservoirs, respectively representing contributions to streamflows of large deep aquifers, with over-year response lag, of aquifers which run dry by the end of the dry season and of subsurface runoff. The surface runoff component is regarded as an uncorrelated point process. Considering the occurrences of effective rainfall events as generated by an independent Poisson process, the output of the linear system represents a conceptually-based multiple shot noise process. Model identification and parameter estimation are supported by information related to the aggregated runoff process, in agreement to the conceptual framework proposed, and this allows parameter parsimony, efficient estimation and effectiveness of the streamflow reproduction. Good performances emerged from the model application and testing made with reference to some daily runoff series from Italian basins.     

Conceptually-based shot noise modeling of streamflows at short time interval

A conceptual-stochastic approach to short time runoff data modelling is proposed, according to the aim of reproducing the hydrological aspects of the streamflow process and of preserving as much as possible the dynamics of the process itself. This latter task implies preservation of streamflow characteristics at higher scales of aggregation and, within a conceptual framework, involves compatibility with models proposed for the runoff process at those scales. At a daily time scale the watershed response to the effective rainfall is considered as deriving from the response of three linear reservoirs, respectively representing contributions to streamflows of large deep aquifers, with over-year response lag, of aquifers which run dry by the end of the dry season and of subsurface runoff. The surface runoff component is regarded as an uncorrelated point process. Considering the occurrences of effective rainfall events as generated by an independent Poisson process, the output of the linear system represents a conceptually-based multiple shot noise process. Model identification and parameter estimation are supported by information related to the aggregated runoff process, in agreement to the conceptual framework proposed, and this allows parameter parsimony, efficient estimation and effectiveness of the streamflow reproduction. Good performances emerged from the model application and testing made with reference to some daily runoff series from Italian basins.     

Addressing uncertainty in reflectivity‐rainfall relations in mountain watersheds during summer convection

The use of precipitation estimates from weather radar reflectivity has become widespread in hydrologic predictions. However, uncertainty remains in the use of the nonlinear reflectivity–rainfall (Z‐R) relation, in particular for mountainous regions where ground validation stations are often lacking, land surface data sets are inaccurate and the spatial variability in many features is high. In this study, we assess the propagation of rainfall errors introduced by different Z‐R relations on distributed hydrologic model performance for four mountain basins in the Colorado Front Range. To do so, we compare spatially integrated and distributed rainfall and runoff metrics at seasonal and event time scales during the warm season when convective storms dominate. Results reveal that the basin simulations are quite sensitive to the uncertainties introduced by the Z‐R relation in terms of streamflow, runoff mechanisms and the water balance components. The propagation of rainfall errors into basin responses follows power law relationships that link streamflow uncertainty to the precipitation errors and streamflow magnitude. Overall, different Z‐R relations preserve the spatial distribution of rainfall relative to a reference case, but not the precipitation magnitude, thus leading to large changes in streamflow amounts and runoff spatial patterns at seasonal and event scales. Furthermore, streamflow errors from the Z‐R relation follow a typical pattern that varies with catchment scale where higher uncertainties exist for intermediate‐sized basins. The relatively high error values introduced by two operational Z‐R relations (WSR‐57 and NEXRAD) in terms of the streamflow response indicate that site‐specific Z‐R relations are desirable in the complex terrain region, particularly in light of other uncertainties in the modelling process, such as model parameter values and initial conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

A transport‐distance approach to scaling erosion rates: 3. Evaluating scaling characteristics of Mahleran

In the two previous papers of this series, we demonstrated how a novel approach to erosion modelling (Mahleran – Model for Assessing Hillslope‐Landscape Erosion, Runoff And Nutrients) provided distinct advantages in terms of process representation and explicit scaling characteristics when compared with existing models. A first evaluation furthermore demonstrated the ability of the model to reproduce spatial and temporal patterns of erosion and their particle‐size characteristics on a large rainfall‐simulation plot. In this paper, we carry out a more detailed evaluation of the model using monitored erosion events on plots of different size. The evaluation uses four plots of 21·01, 115·94, 56·84 and 302·19 m², with lengths of 4·12, 14·48, 18·95 and 27·78 m, respectively, on similar soils to the rainfall‐simulation plot, for which runoff and erosion were monitored under natural rainfall. Although the model produces the correct ranking of the magnitude of erosion events, it performs less well in reproducing the absolute values and particle‐size distributions of the eroded sediment. The implications of these results are evaluated in terms of requirements for process understanding and data for parameterization of improved soil‐erosion models. We suggest that there are major weaknesses in the current understanding and data underpinning existing models. Consequently, a more holistic re‐evaluation is required that produces functional relationships for different processes that are mutually consistent, and that have appropriate parameterization data to support their use in a wide range of environmental conditions. Copyright © 2008 John Wiley & Sons, Ltd.     

An analysis of the impact of spatial variability in rainfall on runoff and sediment predictions from a distributed model

This paper investigates the effect of introducing spatially varying rainfall fields to a hydrological model simulating runoff and erosion. Pairs of model simulations were run using either spatially uniform (i.e. spatially averaged) or spatially varying rainfall fields on a 500‐m grid. The hydrological model used was a simplified version of Thales which enabled runoff generation processes to be isolated from hillslope averaging processes. Both saturation excess and infiltration excess generation mechanisms were considered, as simplifications of actual hillslope processes. A 5‐year average recurrence interval synthetic rainfall event typical of temperate climates (Melbourne, Australia) was used. The erosion model was based on the WEPP interrill equation, modified to allow nonlinear terms relating the erosion rate to rainfall or runoff‐squared. The model results were extracted at different scales to investigate whether the effects of spatially varying rainfall were scale dependent. A series of statistical metrics were developed to assess the variability due to introducing the spatially varying rainfall field. At the catchment (approximately 150 km²) scale, it was found that particularly for saturation excess runoff, model predictions of runoff were insensitive to the spatial resolution of the rainfall data. Generally, erosion processes at smaller sub‐catchment scales, particularly when the sediment generation equation had non linearity, were more sensitive to spatial rainfall variability. Introducing runon infiltration reduced the total runoff and sediment yield at all scales, and this process was also most sensitive to the rainfall resolution. Copyright © 2011 John Wiley & Sons, Ltd.     

Evidence for inherent nonlinearity in temporal rainfall

We examine the underlying structure of high resolution temporal rainfall by comparing the observed series with surrogate series generated by a invertible nonlinear transformation of a linear process. We document that the scaling properties and long range magnitude correlations of high resolution temporal rainfall series are inconsistent with an inherently linear model, but are consistent with the nonlinear structure of a multiplicative cascade model. This is in contrast to current studies that have reported for spatial rainfall a lack of evidence for a nonlinear underlying structure. The proposed analysis methodologies, which consider two-point correlation statistics and also do not rely on higher order statistical moments, are shown to provide increased discriminatory power as compared to standard moment-based analysis.     

Evaluation of a spatial rainfall generator for generating high resolution precipitation projections over orographically complex terrain

Space–time variability of precipitation plays a key role as driver of many environmental processes. The objective of this study is to evaluate a spatiotemporal (STG) Neyman–Scott Rectangular Pulses (NSRP) generator over orographically complex terrain for statistical downscaling of climate models. Data from 145 rain gauges over a 5760-km² area of Cyprus for 1980–2010 were used for this study. The STG was evaluated for its capacity to reproduce basic rainfall statistical properties, spatial intermittency, and extremes. The results were compared with a multi-single site NRSP generator (MSG). The STG performed well in terms of average annual rainfall (+1.5 % in comparison with the 1980–2010 observations), but does not capture spatial intermittency over the study area and extremes well. Daily events above 50 mm were underestimated by 61 %. The MSG produced a similar error (+1.1 %) in terms of average annual rainfall, while the daily extremes (>50-mm) were underestimated by 11 %. A gridding scheme based on scaling coefficients was used to interpolate the MSG data. Projections of three Regional Climate Models, downscaled by MSG, indicate a 1.5–12 % decrease in the mean annual rainfall over Cyprus for 2020–2050. Furthermore, the number of extremes (>50-mm) for the 145 stations is projected to change between ?24 and +2 % for the three models. The MSG modelling approach maintained the daily rainfall statistics at all grid cells, but cannot create spatially consistent daily precipitation maps, limiting its application to spatially disconnected applications. Further research is needed for the development of spatial non-stationary NRSP models.