RESEARCH ARTICLE10.1002/2013WR014836

Stochastic convective rain-field simulation usinga high-resolution synoptically conditioned weather generator(HiReS-WG)Nadav Peleg1 and Efrat Morin2

1Hydrology and Water Resources Program, Hebrew University of Jerusalem, Jerusalem, Israel, 2Department of Geography,Hebrew University of Jerusalem, Jerusalem, Israel

Abstract A new stochastic high-resolution synoptically conditioned weather generator (HiReS-WG)appropriate for climate regimes with a substantial proportion of convective rainfall is presented. The simu-lated rain fields are of high spatial (0.5 3 0.5 km2) and temporal (5 min) resolution and can be used for mosthydrological applications. The WG is composed of four modules: the synoptic generator, the motion vectorgenerator, the convective rain cell generator, and the low-intensity rainfall generator. The HiReS-WG wasapplied to a study region on the northwestern Israeli coastline in the Eastern Mediterranean, for which 12year weather radar and synoptic data were extensively analyzed to derive probability distributions of con-vective rain cells and other rainfall properties for different synoptic classifications; these distributions wereused as input to the HiReS-WG. Simulated rainfall data for 300 years were evaluated for annual rain depth,season timing, wet-/dry-period durations, rain-intensity distributions, and spatial correlations. In general, theWG well represented the above properties compared to radar and rain-gauge observations from the studiedregion, with one limitation—an inability to reproduce the most extreme cases. The HiReS-WG is a good toolto study catchments’ hydrological responses to variations in rainfall, especially small-size to medium-sizecatchments, and it can also be linked to climate models to force the prevailing synoptic conditions.

1. Introduction

A weather generator (WG) is a stochastic model that creates a synthetic time series of weather data basedon the statistical characteristics of observed weather at a specific location. The focus of the current paper isa WG for rainfall data. The WG is particularly useful in nongauged locations or when rainfall records areshort, enabling the examination of large variability in rainfall patterns. Several fields of research utilize WGs.A common use is for downscaling global circulation model (GCM) or regional circulation model (RCM) out-puts for studies on climate-change impacts. For example, Moron et al. [2008] downscaled GCM simulationsover Senegal and Wetterhall et al. [2009] used another GCM combined with a WG to generate daily precipi-tation data over Sweden. Wilby and Wigley [1997] and Wilby et al. [1998] detailed the use of different meth-ods and models for precipitation downscaling using WGs. WGs have also been used to study the effects ofextreme rainfall on catchments’ hydrological responses (e.g., see the study by Samuels et al. [2009] in theupper Jordan River). They are also frequently used in agricultural studies to assess crop yields for differentscenarios, as done by Mavromatis and Hansen [2001] who used several WGs for different locations world-wide, Soltani and Hoogenboom [2007] who compared two different WGs in Iran, Robertson et al. [2009] whoconducted a study in Indonesia, and Qian et al. [2011] who conducted a study in Canada. WG simulationsare also used for ecological and economic studies.

Several well-known WGs have been described in the literature, such as WGEN [Richardson and Wright,1984], SIMMETEO [Geng et al., 1988], LARS-WG [Racsko et al., 1991; Semenov and Barrow, 1997], MOFRBC[Bardossy and Plate, 1992; Wetterhall et al., 2009], WeatherMan [Pickering et al., 1994], MarkSim [Jones andThornton, 2000], AAFC-WG [Hayhoe, 2000; Qian et al., 2004], WM2 [Hansen and Mavromatis, 2001], and AWE-GEN [Fatichi et al., 2011, 2013; Ivanov et al., 2007]. WGEN, SIMMETEO, WeatherMan, and WM2 are based on aMarkovian process; in fact, Wilks [2010] claimed that the most commonly used stochastic precipitation gen-erator is the first-order Markov chain method. A first-order Markov chain is normally used to determine ifthe next day in a sequence will be ‘‘wet’’ or ‘‘dry’’ based on the previous day in the sequence. It was firstused by Gabriel and Neumann [1962] to estimate the daily occurrence of rainfall in Tel-Aviv (Israel); since

Special Section:Eco-hydrology of SemiaridEnvironments: ConfrontingMathematical Models withEcosystem Complexity

Key Points:� New high-resolution weather

generator for rainfall simulations ispresented� Stochastic rain fields with multiple

convective rain cells are produced� Rain data can be used for

hydrological modeling anddownscaling

Supporting Information:� WG_video

Correspondence to:N. Peleg,nadav.peleg@mail.huji.ac.il

Citation:Peleg, N., and E. Morin (2014),Stochastic convective rain-fieldsimulation using a high-resolutionsynoptically conditioned weathergenerator (HiReS-WG), Water Resour.Res., 50, doi:10.1002/2013WR014836.

Received 3 OCT 2013

Accepted 4 FEB 2014

Accepted article online 8 FEB 2014

PELEG AND MORIN VC 2014. American Geophysical Union. All Rights Reserved. 1

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then, it has been used and further developed for many cases worldwide. For example, Wilks [1999] tested thefirst-order Markov model for 30 locations across the United States; Robertson et al. [2004] used a hidden Mar-kov model to downscale daily rainfall occurrence over Northeast Brazil; Mehrotra and Sharma [2006] down-scaled rainfall around Sydney (Australia) with a nonparametric nonhomogeneous hidden Markov model. Thenonhomogeneous hidden Markov model has also been used for rainfall downscaling over Senegal [Moronet al., 2008], Greece [Kioutsioukis et al., 2008], Indramayu (Indonesia) [Robertson et al., 2009], and the upper Jor-dan River [Samuels et al., 2009]. For further information, the readers are referred to the review papers by Wilks[2010] and Wilks and Wilby [1999]. Other methods are less common but are also in use, such as the Bayesiantechnique (see example by Fatichi et al. [2013]), the K nearest neighbor (KNN) [Eum et al., 2010; Moron et al.,2008], and the multiobjective fuzzy-rule-based classification method [Wetterhall et al., 2009].

The goal of the current study was to develop a WG that would produce rain fields at the resolution requiredfor hydrological modeling of small-size to medium-size catchments (i.e., up to a few dozens of square kilo-meters). Most of the WGs listed above generate rainfall at a daily or monthly temporal resolution and lackthe ability to produce rain fields on a spatial scale of a few kilometers. One method of temporal downscal-ing of rainfall from low-resolution to high-resolution scale (e.g., daily to hourly) is by using rainfall disaggre-gation models. Pui et al. [2012] assessed four models: the canonical and microcanonical versions of thediscrete multiplicative random cascades [Molnar and Burlando, 2005], the randomized Bartlett-Lewis model[Koutsoyiannis and Onof, 2001], and the nonparametric resampling approach based on ‘‘method of frag-ment’’ [Sharma and Srikanthan, 2006], and found that the downscaled rainfall simulated the common rain-fall statistics reasonably well. Molnar and Burlando [2005] claimed that the cascade-based disaggregationmodels are easily extendible from time to space, as has been lately published by Rupp et al. [2012]. We offera new method of producing rain fields similar to those recorded by weather radars, providing rainfall dataat high spatial and temporal resolution which is suitable for most hydrological modeling purposes [Peleget al., 2013]. Therefore, the WG introduced in the current paper differs from the above WGs because it wasdeveloped based on analysis of rain fields derived from weather radar data in addition to synoptic parame-ters. Moreover, we propose a WG that explicitly represents convective rain cell elements that are known tohave a large impact on catchments’ hydrological responses in general and on flash-flood generation in par-ticular [Tarolli et al., 2012; Yakir and Morin, 2011].

In this paper, we present the high-resolution synoptically conditioned weather generator (HiReS-WG) andits application for a study region on Israel’s northwestern coastline in the Eastern Mediterranean. The paperis organized as follows: section 2 describes the WG and its four modules: the synoptic generator, the motionvector generator, the convective rain cell generator, and the low-intensity rainfall generator (Figure 1); sec-tion 3 presents the application of the HiReS-WG: it describes the study area and constructs the requiredinputs from radar and synoptic data analyses. The HiReS-WG ensembles are evaluated on different scales insection 4. The supporting information video is discussed in section 5 and a discussion of the HiReS-WG’sstrengths and weakness, and its potential applications, is presented in section 6.

2. The Weather Generator

The high-resolution synoptically conditioned weather generator (HiReS-WG) stochastically produces rainfields with high spatial (0.5 3 0.5 km2) and temporal (5 min) resolution, where each run generates thesefields for the entire year and ensembles can be generated with multiple runs. A rainstorm is first condi-tioned on the presence of synoptic conditions suitable for rainfall generation. Moreover, rainfall statisticsoften depend on the synoptic type. Therefore, the first WG module is the synoptic generator (see Figure 1for schematic description of the HiReS-WG modules). Second, given a rainstorm was initiated, a main char-acteristic is the general direction and speed of rainfall advection, which also depends on the synoptic typeand depicts the second WG module—the motion vector generator. Lastly, the advected rain is composedof convective rain cells embedded within regions of low rain intensities, generated by two more WG mod-ules: the convective rain cell generator and the low-intensity rainfall generator. All four modules areexplained in detail in the following subsections.

2.1. Synoptic Generator ModuleThis module generates, for a 1 year period, a time series of synoptic types at 6 h resolution and a series ofrain durations for each case of wet synoptic type. It should be noted that the following two modules, the

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motion vector generator module (section 2.2) and the convective rain cell generator module (section 2.3),are conditioned on synoptic type. The module receives three inputs: probability of a wet event occurringfor each 6 h period in the year, probability of synoptic type occurrence given that there is a wet event foreach 6 h period in the year, and probability distribution of rain-event durations. Accordingly, for each 6 hperiod, ‘‘dry’’ versus ‘‘wet’’ status is selected and, in the case of a ‘‘wet’’ event selection, a synoptic type andrain-event duration are selected; all selections are random based on the input distributions and are inde-pendent of each other. If the selected rain duration is longer than 6 h, the next 6 h period(s) is also markedas ‘‘wet’’ and receives the same synoptic type.

2.2. Motion Vector Generator ModuleThis module uses a first-order Markovian method to generate a time series of motion vectors (direction andvelocity) for each 5 min time step during the rain events. It receives as input for each synoptic type a transi-tion probability matrix for the motion direction at 1� resolution and an emission probability matrix for themotion velocity at 1 m s21 resolution for each selected direction. Following the first-order Markovianmethod, the direction of the motion vector in the next time step is randomly selected based on the direc-tion in the concurrent time step by applying the transition probability matrix; the motion velocity in thenext time step is then set based on the selected direction utilizing the emission probability matrix.

2.3. Convective Rain Cell Generator ModuleThis module generates, for each rainy 5 min time step, a set of convective rain cells, some new and someadvected from the previous time step; the cells are projected over a rain field at a 0.5 3 0.5 km2 resolution.This module receives the following inputs: (1) probability distributions for changes in the spatial

Figure 1. Schematic description of the HiReS-WG modules. (1) The synoptic generator produces 6 h periods of wet/dry conditions and syn-optic types (S, T), where the blue regions mark the duration of the rain event within the 6 h period. (2) The motion-vector generator pro-duces, for periods of wet events, direction, and velocity values at 5 min time steps (represented by the arrows’ direction and length). (3)and (4) The convective rain cell and low-intensity rainfall generators produce, for periods of wet events, rain fields at 5 min time steps witha spatial resolution of 0.5 3 0 5 km2. The rain fields follow the statistics of the relevant synoptic type and are advected and change alongthe corresponding motion vector. The four modules are discussed in detail in section 2.

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characteristics of advected rain cells (maximal rain intensity, mean rain intensity as a function of synoptictype, area, ellipticity, and orientation); (2) for each wet synoptic type, a probability distribution for the numberof new rain cells in a time step; (3) a pixel-based probability distribution for the location of new cells; (4) foreach wet synoptic type, probability distributions for new convective rain cells’ spatiotemporal characteristics(lifetime, maximal rain intensity, mean rain intensity, area, ellipticity, and orientation), and (5) a spatial correla-tion function for cells’ rain intensity with distance. At each rainy time step, cells from the previous time stepare advected using the motion vector while their spatial-structure parameters are altered according to thechanges sampled from the probability distributions for advected rain cells. This allows the cells to changetheir shape and intensity as they pass through. Convective rain cells that complete their lifetime do not con-tinue to the next time step; in addition, cells that are advected out of the study region and cells that are inthe last time step of a rain-event are terminated. Finally, new convective rain cells are generated. Accordingto the prevailing synoptic type, the module samples the number of new cells, their locations, and their spatialcharacteristics. The convective cell’s spatial structure is constructed in two steps: first, the cell is formed in anidealized shape, then a more realistic form is generated by a random rearrangement of rain-intensity valueswithin the cell while keeping the rain-field correlation structure. These two steps are detailed below.

The spatial pattern of the rain cells is based on the HYCELL model introduced by Feral et al. [2003]. Thismodel uses a hybrid combination of Gaussian and exponential functions to simulate an elliptical rain cellthat decays from a maximum rain intensity located in the cell’s center. Using hybrid functions, the simulatedcell represents both the large gradients of rain intensity near the cell’s core and the more moderate decaynear its margins. Ellipses give a good depiction of the shape of convective rain cells [Barnolas et al., 2010;Karklinsky and Morin, 2006; Peleg and Morin, 2012]. The HYCELL model has been used in several studies, forexample, in Feral et al. [2005, 2006], Pastoriza et al. [2011], and Yakir and Morin [2011]. A short description ofthe algorithm is given below, and detailed explanations can be found in Feral et al. [2003]. The rain-intensityfield of a cell centered at the axis origin with a zero orientation is given by:

Rðx; yÞ5

RG � exp 2x2

a2G

1y2

b2G

� �� �for R � R1

RE � exp 2x2

a2E

1y2

b2E

� �0:5" #

for R1 > R � R2

8>>>><>>>>:

9>>>>=>>>>;

(1)

where R (x, y) (mm h21) is the rain intensity for each point along the x-y plane of the convective cell’sdomain, RG and RE are the Gaussian and exponential peak rain intensity (respectively), R1 is the thresholdrain-intensity value (mm h21) from which the model shifts from a Gaussian function to an exponential solu-tion, R2 is the lower threshold for which the rainfall is simulated (a constant value of 1 mm h21 was set inthe current study), aG, aE (km) represent the decay rate along the cell’s major axis for the Gaussian andexponential function, respectively, and bG, bE are the same, but for the cell’s minor axis.

Five parameters are required to generate each cell’s rain field: rain cell’s maximal rain intensity (Rmax, mmh21), rain cell’s average rain intensity ð�Rc; mm h 21Þ, rain cell area (Ac, km2), ellipticity of the cell (Ec, kmkm21), and cell orientation (Oc, degrees in reference to the east-west axis). These parameters are sampledfrom the input probability distributions as explained above. As shown in Feral et al. [2003], the decay-rateparameters aG, aE, bG, and bE can be computed given the above parameters and the following three unknownparameters: (1) the Gaussian peak (RG) which should be close to the cell’s maximal rain intensity (Rmax); (2) theexponential peak (RE), and (3) the exponential Gaussian threshold (R1). These parameters are found by optimi-zation, where for each set of parameters examined, a rain-field cell is generated, the cell’s average rain inten-sity ð�Rm; mm h 21Þ and area (Am, km2) are determined, and the error criterion f is computed as:

f5

���� �Rc

�Rm21

����1���� Ac

Am21

����1���� Rmax

RG21

���� (2)

The optimization algorithm searches for the set of parameters that minimize f. After the cell is generated, itis rotated according to the Oc parameter and it is located in space according to its sampled coordinates.

The HYCELLL function generates idealized convective cell rain fields. In fact, this is the case for most of therain cell models: Gaussian-based models [Montopoli and Marzano, 2007; Morin et al., 2006], exponential-

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based models [Capsoni et al., 1987; Montopoli and Marzano, 2007; von Hardenberg et al., 2003], and hybridmodels that combine both Gaussian and exponential decay functions [Feral et al., 2003; Montopoli and Mar-zano, 2007]; all simulate convective cells with one rainfall peak at the cell core. In reality, rain data are muchnoisier. The shape of the convective cell and the number of rain peaks may influence the hydrologicalresponse of small-size to medium-size catchments. This is crucial in case of catchments with a high sensitiv-ity to high rain intensity for short durations, for example, in arid or urban environments. A more realisticconvective cell (e.g., without smooth decay from the center to the boundaries) can be generated, for exam-ple, by adding noise to the simulated convective cell [Pastoriza et al., 2011]. Here we apply a differentapproach in which the pixels are stochastically rearranged for each cell while preserving the spatial correla-tion of the rainfall (which is an input for this module). This requires first creating a random matrix (M1) withthe same dimensions as the generated rain cell and with data randomly sampled from a standard normaldistribution (l 5 0, r 5 1). A second matrix (M2) is formed with the same dimensions. The value for eachpixel in M2 is set based on values from M1 within a 5 pixel distance:

M2ðx; yÞ5

XkðX;YÞ2ðx;yÞk�5

M1ðX; YÞ � q kðX; YÞ2ðx; yÞkð Þd�

� �X

kðX;YÞ2ðx;yÞk�5

q kðX; YÞ2ðx; yÞkð Þd�

� � (3)

where q kðX; YÞ2ðx; yÞkð Þ is the spatial rainfall correlation at the Euclidean distance between (X, Y) and (x, y)and d* is a power parameter determined to match M2 to the spatial rainfall correlation (see an example forapplication in section 3). The HYCELL-generated rain-intensity data are now assimilated into the M2 matrix

Figure 2. An example of the convective-cell generator product. (a) A convective rain cell generated using the HYCELL model (Rmax 5 69.8 mm h21, Rc 5 l mm h21, Rc 5 27 mm h21,Ac 5 48.6 km2, Ec 5 0.52 km km21, and Oc 5 9�). (b) A random normal M1 matrix. (c) A correlated M2 matrix. (d) The same convective rain cell as in Figure 2a after pixel rearrangement.

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according to their rank: the pixel with the maximum value in M2 is set to the maximum HYCELL rain-intensity value, the pixel with the second highest value in M2 is set to the second-highest rain intensity gen-erated, and so on.

An example of a single convective rain cell generated by this module is presented in Figure 2a. The convec-tive rain cell was generated using the following parameters: Rmax 5 69.8 mm h21, R2 5 1 mm h21,�Rc 5 27 mm h 21, Ac 5 48.6 m2, Ec 5 0.52 km km21, and Oc 5 9�. The found rain decay rates are:aG 5 1.8 km, aE 5 1.27 km, bG 5 1.71 km, and bE 5 1.21 km, and the optimized cell parameters are: RG 5 69.8mm h21, RE 5 97.7 mm h21, and R1 5 19.9 mm h21. The average rain intensity �Rm 5 26:67 mm h 21, theconvective cell area Am 5 50.25 km2, and the maximum rain intensity (RG) are in close agreement with themodel inputs. The generated random M1 matrix and the correlated M2 matrix are presented in Figures 2band 2c, respectively, with d* 5 3.5 up to a distance of 0.5 km and d* 5 3 otherwise (as mentioned in section3). The cell generated after the pixels’ rearrangement is presented in Figure 2d.

2.4. Low-Intensity Rainfall Generator ModuleThis module generates regions of low rain intensity in the range of 1–10 mm h21 for each rainy time step.The module inputs are probability distributions for area and rain intensity and probability distribution forchanges in area for advected low-intensity regions. For each time step, the number of low-intensity regionsis randomly chosen with a uniform distribution between 1 and 10 and their location is also set randomlyover the rain field. The area of each region and the rain-intensity values that compose it are sampled fromthe above distributions for each time step. Similar to the convective rain cells, the low-intensity rainfallregions move along a trajectory between rain fields as dictated by the motion vector, and their area canshrink or expand. Once they exit the domain, they are terminated.

3. HiReS-WG Application

The HiReS-WG was applied to a study area in the Eastern Mediterranean, a 102 3 73 km2 domain (centeredover coordinates 34.7�E 32.5�N) located on the northwestern Israeli coastline (Figure 3). About two-thirds ofthe study area is offshore, where most of the rain cells are generated. The terrain near the coastline ismostly flat, ascending moderately eastward up to 380 m above sea level. The study area has a Mediterra-nean climate; its wet season lasts from October to May, while June to September is dry and hot. Accord-ingly, the HiReS-WG is applied only to the wet season. The annual mean rainfall near the coastline is �620mm, decreasing inland with distance from the sea. The annual rainfall variance is high, where the wettestyear (1991) recorded a total of more than 1000 mm of rainfall in the study area, whereas during the driestyear (1981), less than 400 mm was recorded. The study area is covered by the Shacham Mekorot (EMS)weather radar, located 25–120 km south of it. The radar is a non-Doppler C-band system with a temporalresolution of about 5 min per volume scan and a spatial polar resolution of 1.4� 3 1 km in space (Figure 3).In addition, NCEP/NCAR reanalysis data [Kalnay et al., 1996] at 6 h intervals for a grid point near the studyarea (35�E 32.5�N) were used for the analysis.

Radar and NCEP/NCAR data were analyzed to derive the required HiReS-WG inputs detailed in the previoussection. A large part of these inputs were based on the thorough study conducted by Peleg and Morin[2012] to characterize the spatial and temporal properties of convective rain cells for different synoptictypes over the study area. For the sake of brevity, we do not provide all of the derived inputs here, onlythose demonstrating the key features.

Radar data for 12 hydrological years (1991/1992–1997/1998, 1999/2000–2002/2003, and 2004/2005) wereanalyzed (2 years of data were excluded from the analysis due to their low quality), with a total of 191,586radar volume scans, for which segmentation and cell-tracking algorithms [Peleg and Morin, 2012] wereapplied for space-time characterization of convective rain cells. The data were divided into rain events,where a rain event begins when a rain cell first appears on the radar image and ends when there is an inter-mission of more than 1 h before the appearance of the next rain cell. This follows the procedure applied inPeleg and Morin [2012], where a similar definition for rain-event separation was used. Defining rainevents using a different window of intermission (2 h, 6 h, and so on) would obviously change theevent statistics, e.g., event duration and number of convective cells in each event. The rain eventswere classified using a hierarchical agglomerative cluster analysis technique into three synoptic types:

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(1) a Shallow low; (2) a Deep low(also known as Cyprus low); and (3)Active Red Sea Trough (ARST). Theclassification was performed usingfour variables obtained from the 6 hNCEP/NCAR reanalysis data for thestudy region: sea level pressure, spe-cific humidity at 700 hPa, geopotentialheight at 500 hPa, and zonal wind at850 hPa. The Shallow lows werefound to contribute 69% of the rainevents, the Deep lows 25%, and theARST accounted for the rest (only 6%)[Peleg and Morin, 2012]. The sampleconsisted of 1556 wet periods ofduration 6 h for the 12 years, whichis larger than the minimum requiredsample size of a few hundred rainevents calculated by Lana and Mills[1994] for a similar climatological area.The time distribution of wet/dry peri-ods and the wet synoptic types overthe observed 12 years are presentedin Figure 4a. To construct therequired distributions for the HiReS-

WG synoptic generator module, a 13 period moving average was applied for the derived distributionsto smooth the effects of large irregular components. The resulting wet-event probability of occurrenceand wet-synoptic-type probability of occurrence for each 6 h period during the wet season are pre-sented in Figures 4b and 4c, respectively. The empirical distributions of rain-event durations were com-puted and found to be similar for all three wet synoptic types, with most of the rain events (78%)lasting less than 6 h and their average and median being 265 min and 165 min, respectively. Theempirical distribution of rain-event durations, used as input for the HiReS-WG synoptic generatormodule, is presented in Figure 5a.

The motion vector data were analyzed for each synoptic type. For an extensive discussion regarding themotion vectors for the three synoptic types, the reader is referred to Peleg and Morin [2012]. The empiricaldistributions of the observed motion vectors are presented in Figure 6 for the three synoptic types, wherethe ARST type is divided into two groups due to its distinct bi-modality—one with a dominant southerncomponent and the other with a dominant western component. For each synoptic type, the transitionand emission probability matrixes (for direction and velocity computation, respectively) were computed(not shown) and served as input to the HiReS-WG motion vector generator module.

The inputs to the convective rain cell generator module were constructed based on the convective rain cellcharacteristics derived from the radar data for each synoptic type. This included the empirical distributionsof: new rain cell numbers, their locations, their lifetimes and spatial parameters, and the distributions ofchanges in spatial parameters for advected rain cells. The lifetime and spatial parameter distributions arepresented in Peleg and Morin [2012, Figures 5 and 6]. An example of the distribution of new convective cellnumbers for the Deep low synoptic type and of the distribution of changes in the cells’ maximum rainintensity between time steps are presented in Figures 5b and 5c. Empirical distributions of the low-intensityrainfall and the area it occupies are presented in Figure 5d and are used by the low-intensity rainfall genera-tor module.

Another required input to the convective rain cell generator module is the rainfall spatial correlation func-tion. This was computed from the radar data using Pearson’s product-moment correlation for a time scaleof 5 min with a lag distance of 500 m, up to a distance of 5 km. Since the average polar pixel size of the rawradar data over the region is �1.6 3 1 km2, it should be noted that the correlation values for the lower

Figure 3. Map showing the study area, weather radar location and its mesh. TheDalya (pink) and Taninim (green) catchments and marked with bright polygons.Triangles (black) represent the location of the 13 rain gauges and the blue trian-gle marks the location of the dense network of recording rain gauges [Peieget al., 2013].

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separation distances are extrapolated. The extrapolation was performed by converting the radar raw datafrom polar to Cartesian grid with pixel size of 500 3 500 m2. In addition, data acquired from a dense rain-gauge network located at the center of the domain [Peleg et al., 2013] were used to verify the curveobtained from the radar calculation for the short separation distances. Correlations were computed for rainintensities larger than 10 mm h21 up to a distance of 2 km (the network area size) and extrapolated up to adistance of 5 km. The results are plotted in Figure 7. Although the two curves are generally similar, it seemsthat the radar correlations are somewhat overestimated for the distances of 0–2.4 km, whereas for distancesof 2.4–5 km, the radar correlations are lower than those of the gauges; however, the latter are extrapolatedin this range and are less certain. The parameter d* used by the convective rain cell generator (equation (3))was calibrated and found to be dependent on the distance d (km) as: d�ðd�0:5Þ53:5 and d�ðd>0:5Þ53. It wascalibrated by generating a random M1 matrix, calculating the M2 matrix for different d* values using raindata generated by the HYCELL model, calculating the matrix spatial correlation curve, and comparing it tothe curve obtained from the radar data (Figure 7).

4. HiReS-WG Evaluation

The HiReS-WG was applied to the study region, and 300 years of synthetic rain fields at 0.5 3 0.5 km2 and 5min resolution were generated. The rain data were evaluated by examination of their climatological charac-teristics as compared to those derived from observations (rain-gauge and radar data). The following aspectswere examined and are presented below: annual rain depth, timing of the rainy season, wet-period anddry-period durations, distribution of 5 min rain intensity, and their spatial correlation. These aspects repre-sent a range of scales from the annual, to intra-annual and down to the 5 min scale.

Figure 4. (a) Classification of the observed 6 h periods derived for the study area. Colors represent the wet event’s synoptic type while dry events are unmarked. (b) Probability of wet-event occurrence for each 6 h period in the year. (c) Occurrence probabilities for the three wet synoptic types for each 6 h period during the wet season conditioned on wet-eventoccurrence.

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The annual rain depth onshore was evaluated using data from 13 rain gauges located in the study region(Figure 3), which were compared to simulated data at the gauge locations. Rain-gauge data were preferredover radar data for this purpose as they have longer records. The 300 simulated years were divided into 10ensembles of 30 years each to match the 30 years of rain-gauge records (1972–2002). We assume that the12 year data (derived from the weather radar) used for the WG application adequately represented the 30year evaluation period as rainfall’s natural variability is much higher than the systematic changes that most

Figure 5. (a) The relative frequency of rain-event durations. (b) The relative frequency of the number of new convective rain cells depend-ing on the existing rain-field area. (c) The relative frequency of a change in maximum rain intensity of the advected convective rain cells.(d) Empirical distribution of areas and rain intensity in the low-intensity rainfall regions (less than 10 mm h21).

Figure 6. A rose diagram presenting the distribution of the observed motion vector (velocity and direction) for each synoptic type.

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often imply insignificant rainfall trends in the region[e.g., Kafle and Bruins, 2009; Morin, 2011; Shohamiet al., 2011; Ziv et al., 2013]. The averaged gaugeannual rainfall and the averaged HiReS-WG annualrainfall (of each of the 10 ensembles) for the 30 yearsare presented in Figure 8. The annual measuredintragauge standard deviation (also presented in Fig-ure 8) averaged over 30 years was 68 mm yr21, closeto the 64 mm yr21 average intragauge standarddeviation calculated for the 10 ensembles (a rangeof 56–71 mm yr21). There was an up to 11% differ-ence between the 30 year observed average annualrainfall and the simulated average annual rainfall tak-ing the driest ensemble (E4) and the wettest ensem-ble (E9) into account. This difference seems to bewithin the natural variability of the rainfall as theaverage rainfall of 9 out of the 10 ensembles fellwithin the 0.95 confidence interval of the observedaverage rainfall (range of 553–684 mm yr21), whilethe one ensemble which fell outside of the confi-

dence interval (E4, 550 mm yr21) was very close to this range. Two ensembles (E6 and E8, with a meanannual rainfall of 617 mm and 620 mm, respectively) were in close agreement with the measured rainfall(annual mean of 619 mm), but the standard deviations of these ensembles were lower than those of theobserved series (137 mm and 132 mm, respectively, compared to 175 mm), and this lower variance was evi-dent in all 10 ensembles. The extreme annual rainfall of 1181 mm observed in 1991, which was not gener-ated by the HiReS-WG in any of the ensembles, is the reason for the relatively high observed standarddeviation. Excluding the data from this year, the observed mean changes to 599 mm with a standard devia-tion of 142 mm; in this case, E7, with an average annual rainfall of 599 mm and a standard deviation of 126mm, is the closest to the measured series.

The beginning and end of the rainy season, defined as the time of 5% and 95% of the annual rainfall,respectively, were evaluated by comparing the HiReS-WG data to the 30 year rain-gauge records. Similarseason timings were found from the rain gauges and the ensembles although the ensembles’ season endswere slightly delayed relative to the observed ends: the gauges’ average beginning and ending for the wetseason were 31 October and 20 March, respectively, while the ensembles’ average beginning and endingwere 2 November (with a range of 31 October to 4 November) and 27 March (with a range of 25 March to30 March), respectively. The 0.95 confidence intervals were computed and found to be 25 October to 5November for the beginning of the wet season and 14–26 March for its end. All 10 ensembles fell withinthe confidence intervals for the beginning of the wet season, but 6 out of the 10 ensembles fell outside ofthe confidence intervals for the ending of the wet season. This implies a slightly longer wet season, byabout 2 days on average.

The distribution of wet and dry periods was evaluated by testing the number and duration of the wet anddry periods in the rainy seasons. For this evaluation, 5 min rain data are needed and therefore radar datawere used for comparison, taken at the locations of the 13 rain gauges described in the beginning of thissection. In this case, 25 ensembles of 12 years (to match the radar record) were compared to the radar data.Each simulated rain field and observed radar image were marked as wet when at least one of the 13 pixelswas indicative of rain. The wet-period durations therefore represent the length (min) of continuous rain andthe dry-period durations represent the length (min) of intervals between wet periods. The statistics for the12 year radar data and for the first five simulated ensembles (out of 25 ensembles of 12 years each) aresummarized in Table 1. Both the simulated wet-period and dry-period durations were underestimated com-pared to the radar data (a bias of 0.87 and 0.96, respectively). This is explained by an overestimation of thenumber of wet periods generated by the model compared to the radar data (a bias of 1.06). Comparing thedry and wet periods by percentiles, it was determined that for the lower half of the distribution (q5–q50),the simulated dry-period and wet-period durations were close enough to the observations; for the q75

Figure 7. Correlograms of rain intensities above 10 mm h21 (5min time intervals) derived from weather radar data, a denserain-gauge network [Peieg et al., 2013] and one HiReS-WGensemble (E1).

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percentile, the simulated dry periods were shorter than expected and in the upper 5%, this phenomenonwas reversed and the simulated dry periods were much longer than the observed ones; the simulated wet-period durations seemed to match the observations up to the 75% percentile but they were too short inthe upper tail (q95). This implies that the underestimation in the average simulated wet periods is mainlycaused by the inability to generate extremely long rainfall events, which in turn could reduce the overesti-mation of the longest 5% of the dry periods.

The 5 min rain-intensity HiReS-WG data were evaluated by examining their distribution and spatial correla-tion as compared to the radar rain intensity. This examination was performed for the same onshore gaugelocations described above. Figure 9a presents the portion of the rain fields exceeding the specific rain inten-sity from the radar data (average and range) and the first 12 year ensemble (E1; average and each year).The HiReS-WG ensembles slightly overestimated areas of low rain intensity (with a maximal difference of2.65% for threshold values lower than 6 mm h21) and underestimated areas of high rain intensities (maxi-mal difference of 0.75% for threshold values above 6 mm h21). Additional evaluation of rain intensities wasperformed by comparing the cumulative distribution functions of the radar and ensemble data (Figure 9b),along with data from 1 year of observations from a dense network of rain gauges located in the sameregion [Peleg et al., 2013]. The HiReS-WG rain-intensity frequency fell, in most cases, between the frequen-cies of the radar and gauge rain-intensity data (as can be seen from the example of one ensemble plottedin Figure 9b), indicating a reasonable representation of rain-intensity distribution over the study area.

The spatial correlation of the simulated rain intensity within convective rain cells was computed and com-pared to those derived from the radar and dense rain-gauge data (Figure 7). As can be seen from the

Figure 8. Annual rainfall averaged over 13 rain gauges (upper graph) and from the simulated ensembles averaged over the gauge’s location (El–E10, two ensembles per graph); 30 yearaverage (m), standard deviation (r), maximum, and minimum are presented. Gray area in the upper graph represents the intragauge standard deviation. All units are in mm per year.

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analysis of the first ensemble’s data, shown in Figure 7, the HiReS-WG spatial correlation curve was in closeagreement with the radar data. The results from the other ensembles were similar, implying an adequatespatial correlation structure of the simulated convective rain cells.

Additional evaluation tests were applied to theprobability distributions of spatiotemporal rain cellproperties and synoptic types and they were foundto be satisfactory, but they are not shown here asthese distributions served as model inputs andtheir match to the simulated data was generallyexpected.

5. Video Example

An example of the HiReS-WG simulated rain fieldsover the study region is presented in a supportinginformation video. The video is composed of 72images of rain fields with a temporal resolution of 5min and a spatial resolution of 0.5 3 0.5 km2, simu-lating a rain event that lasted 6 h during a Deeplow synoptic type. The HiReS-WG was used in thiscase to produce rain fields precipitating over thesmall to medium upper Dalya (42 km2) and upperTaninim (48 km2) catchments (Figure 3). The catch-ments are presented in the main window, alongwith the convective and low-intensity rain thatassembles the rain field. Three virtual rain gaugeswere positioned: one in the upper part of the Dalyacatchment (blue gauge), another in the upper partof the Taninim catchment (red), and the third inthe lower part of the Taninim catchment (green).The 5 min rain intensity and the rainfall accumu-lated from the beginning of the simulation are pre-sented in two separate windows. The motionvector is presented in a fourth window, where anarrow marks the direction and velocity of the tra-jectory of the rainfall for the next image. The simu-lation starts at T5 and ends at T365; during thesimulation, new convective cells are born whileothers are terminated. The convective cells thatlasted for more than one time step changed theirintensity, area, shape and orientation between timesteps as described above. The low-intensity rainfall,

Table 1. Number of Wet Periods (# Wet), and Mean and Percentiles of Wet- and Dry-Period Durations From 12 years of Radar Data and the First Five Ensembles (E1–E5)

Mean (min) q5 (min) q25 (min) Median (min) q75 (min) q95 (min)

# Wet Wet Dry Wet Dry Wet Dry Wet Dry Wet Dry Wet Dry

Radar 11274 25.7 272.8 5 5 5 5 15 10 30 50 85 640E1 12034 21.4 254.0 5 5 5 5 10 5 25 15 70 1410E2 12117 21.8 260.2 5 5 5 5 15 5 25 15 70 1365E3 11620 23.0 296.5 5 5 5 5 15 5 30 15 75 1725E4 11996 20.7 251.7 5 5 5 5 10 5 25 15 65 1390E5 12193 22.8 270.8 5 5 5 5 15 5 30 15 75 1530

Figure 9. (a) The proportion of rain-field areas above rain-intensity thresholds (5 min time intervals) for 12 years of radardata (black hatched line represents the average, the maximumand minimum values are constrained within the red area) and onemodeled ensemble (El, blue hatched line represents the averageand gray lines represent the individual years within the ensemble)(b) Cumulative distribution functions of the rain intensity (5 mintime intervals) from the 12 years of radar data (black hatchedline), 1 year of dense rain-gauge network data [Peleg et al., 2013](red hatched line), and an example of one 12 year ensemble’sdata (El, blue hatched line). X axis for both graphs is in logarithmicscale.

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which was most of the rainfall over the catchments (in terms of both depth and occurrence) in this simula-tion, also changed its spatial distribution with time.

6. Discussion and Conclusions

The WG presented in the current paper is capable of producing rain fields at high space and time resolu-tions that are suitable for most hydrological applications. Aside from its advantages, several limitations ofthe HiReS-WG should be considered. Herein, we discuss the advantages, disadvantages, and possibleimprovements of the proposed WG.

As already stated, the main advantage of the HiReS-WG is its ability to generate heterogeneous rain fieldsover areas of a few dozen square kilometers as demonstrated in the supporting information video: at theend of the simulation, almost 12 mm of rain had accumulated in the upper virtual rain gauges in bothcatchments, while the virtual gauge in the lower part of the Taninim catchment recorded only about 8 mmof rainfall (about two-thirds of the amount that fell over the catchment head water). Large differences inrain-intensity distribution over the catchments are also evident, for example: at T80, a small convective cellhits the virtual gauge over the Dalya catchment with a maximum rain intensity of 45 mm h21, while at thesame time the virtual gauges over the Taninim catchment record only nonconvective rainfall; at T170, partof a large convective cell hits the catchments, raining over the upper parts of both catchments and missingthe lower parts. The ability of the HiReS-WG to produce nonuniform rain fields over small catchments at atemporal resolution that is smaller than their hydrological response time is what makes this WG unique andappealing.

One of the most important applications of the HiReS-WG products is as inputs for hydrological models. Ithas been shown that catchment hydrological responses are very sensitive to rainfall distribution in general[Bahat et al., 2009; Morin et al., 2006; Singh, 1997; Zoccatelli et al., 2011], and to convective rain cell proper-ties in particular [Rozalis et al., 2010; Smith et al., 2000; Yakir and Morin, 2011]. Ensembles of stochastic rainfields in which convective rain cells are explicitly and realistically represented are therefore of special inter-est, and their use in hydrological models can potentially expand the variance of flow conditions and simu-lated stream hydrographs, especially for small-size and medium-size catchments.

Moreover, the effect of climate change on small-size to medium-size catchments (changes in flood fre-quency, discharge rates, infiltration, etc.) can be examined using the HiReS-WG linked with GCMs or RCMs,forced by the atmospheric conditions from these climate models that set the synoptic type at each timestep; in this approach, the HiReS-WG serves as a stochastic downscaling method, assuming there is nochange in the statistical properties of the rainfall associated with each synoptic type. While most studiesconsider stochastic downscaling of climate models to a daily [e.g., Kioutsioukis et al., 2008; Robertson et al.,2004; Wilks, 1998] or hourly [Fatichi et al., 2011, 2013; Ivanov et al., 2007] temporal resolution, here muchsmaller time scales [�5 min; similar to Pegram and Clothier, 2001] can be obtained toward forecastingclimate-change impacts on hydrological regimes of small-size and medium-size catchments; however, fur-ther research is needed to establish this application.

Along with the clear advantages of the proposed WG, it also has some limitations. The WG was developedunder a particular set of assumptions: (1) rain fields are composed of convective rain cells in addition tolow-intensity areas; (2) all probability distributions are assumed to be independent of each other and theyare sampled independently between rain cells, between time steps and between years. In addition, most ofthe input probability distributions are spatially homogeneous; (3) the atmospheric forcing is manifestedonly by the selection of synoptic type. The first assumption limits the application of this WG to climaticregions and storms where convective rain cells form a substantial proportion of the rainfall in the region.Most of the rainfall over the study area occurs in cold fronts, which are associated with extratropical cyclo-nes over the Mediterranean Sea [Peleg and Morin, 2012; Saaroni et al., 2010]; the cloud systems in the coldair masses behind the cold front contain organized convection lines and unorganized convective clouds[Goldreich, 2003; Goldreich et al., 2004; Rosenfeld, 1980]. Analysis of the 12 years of rainfall using radar datarevealed that these convective cells contribute an average of 36% (range 23–53%) of the total precipitation.Further research is required to examine the applicability of the HiReS-WG to other regions. The secondassumption was made after examining the correlation values between the different distributions and inspace—all were found to be generally low (below 0.2). Although some low dependencies may exist, taking

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them into account would further complicate the WG and the required inputs, and we therefore decided toneglect them. The third assumption is mainly important if one considers the linkage of HiReS-WG withGCMs or RCMs, which in the current configuration cannot represent changes in rain statistical properties forthe same synoptic type. Although these limitations may be important, we believe that they can all beaddressed in future developments of the WG.

Models often tend to underestimate extremes [Deque, 2007] and therefore this aspect needs to be tested(see example by Semenov [2008]). This was also noted for the HiReS-WG, where the extreme year 1991, withobserved annual rain depth in gauges of 1181 mm, was not generated in any of the 300 simulated years.The closest simulated year accumulated 975 mm of rainfall over the gauge locations—a difference ofalmost 20%. However, the second-ranked observed annual rainfall of 920 mm (measured in 1994) wasexceeded 4 times in the 300 runs of the WG. In addition, the WG underestimated rain durations in the upper(5%) tail as compared to the radar data (q95 5 70–80 min for the HiReS-WG compared to 85 min for theradar data). This problem can be addressed by correcting the relevant distributions (as suggested, e.g., byDeque [2007]) to better represent their tails. Because this change may in turn impact the fit in the centralpart of the distribution, it should be considered in the context of the WG application.

Another issue that needs to be discussed is the complexity of the HiReS-WG. The WG requires at least 20input parameters, depending on the number of synoptic types used. Considerable time and effort areneeded to analyze the rainfall-parameter distributions in a given study area and to calibrate the WG suc-cessfully, as the derived rainfall statistical characteristics depend on several parameters and their interac-tions. Consider, for example, the rain-duration distribution, which is affected by both the distribution of therain event’s duration and the distribution of the cell’s lifetime. Furthermore, when a rain-event ends, cells inthe last time step of that event will be terminated before fulfilling their full time span, biasing rain durationsto lower values and especially affecting the tail of the distribution. Correcting one distribution during thecalibration process can affect another one.

The HiReS-WG presented in this study provides stochastically simulated rain fields with a resolution that isappropriate for hydrological modeling studies of small-size to medium-size catchments affected by rainfallwith a substantial convective component. It is therefore a useful tool for studying the catchments’ hydrologicalresponse. We used data from northwestern Israel (Mediterranean climate) as a case study, but the HiReS-WGcan be applied to other regions with similar conditions as well. The major limitation associated with applicationto other regions of the globe would be the need of a good record of high-resolution rainfall data. We intend tofurther develop the WG to downscale GCM and RCM data, and to further link the WG to hydrological models.This will aid in assessing the potential effects of different climate-change scenarios on the hydrological regime.

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AcknowledgmentsRadar data were provided by E.M.S.(Mekorot Company) and rain-gaugedata were provided by the IMS (IsraelMeteorology Service). The authorsthank Camille Vainstein for hereditorial work. The study was fundedby the Israel Water Authority, the IsraelMinistry of Environmental Protection,the Israel Ministry of Agriculture andRural Development, the KKL-JNF, theIsrael-USA. Bi-National ScienceFoundation (BSF-2008046), and theIsrael Science Foundation’s Recanatiand IDB Group Foundation (grant 332/11). We thank the Associate Editor andthe three anonymous reviewers fortheir significant contribution to thequality of the paper.

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