---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - Red Sea region in Egypt considered as an arid region, which suffered from sudden storms causes extremes flash floods. The Lack of the **rainfall** data and the difficulty of collecting of watersheds characteristics are the obstacles to achieve the success of hydrological models application in Wadi system. This research aims to provide 1000 realizations of daily- predicted **rainfall** **time** **series** for next 100 years providing an innovative approach of disaggregating the monthly **rainfall** data into daily **time** **series** data. The Stochastic Analysis Modelling and Simulation (SAMS 2007) was used to generate these realizations of monthly data. The ground observations (2004-2014) were used to evaluate and choose the most accurate product of the three **rainfall** gridded distribution data; Climate Research Unit data (CRU), Global Precipitation Climate Center data (GPCC) and European Center for Medium Range Weather Forecast (ECMWF)-**Rainfall** Re Analysis-Interim data (ERA- Interim). The later daily data was utilized to create the pattern of disaggregation. The evaluation results show that the GPCC monthly data perform the best among the other products for most of stations, which was used to generate data for next 100 years. The various prediction realizations were disaggregated into daily **time** **series**. The analysis of the 1000 realizations of the daily **rainfall** show that the upper limit for the 26 points is between the ranges of (4.5-15.07) mm/day.

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large changes tend to follow large changes, and small changes tend to follow small changes (Laux et al., 2011). One of the most prominent tools for capturing such changing variance was the Autoregressive Conditional Heteroskedasticity (ARCH) and Generalized ARCH (GARCH) models developed by Engle (1982), and later extended by Bollerslev (1986). Two important characteristics within **rainfall** **time** **series** are highly skewed or kurtotic distributions (Villarini et al., 2010) and volatility clustering, which can be captured by the GARCH family models. Volatility clustering can be thought of as clustering of the variance of the error term over **time**: if the regression error has a small variance in one period, its variance tends to be small in the next period, too. In other words, volatility clustering implies that the error exhibits **time**-varying heteroskedasticity that is, unconditional standard deviations are not constant.

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model the temporal characteristics of **rainfall** **time** **series**; and compare the performance of Seasonal ARIMA models and State space models with applications to two monthly **rainfall** **series** in peninsular Malaysia. The versatile and fully automatic ETS framework requires neither stationary nor strict linearity to produce contemporaneous **time** **series** forecasts for variable **time** horizons. Consequently, it is extensively employed in, e.g., econometrics and inventory control where automatic forecasts are required for a large number of diverse **time** **series**. This forecasting framework, whose performance was recently and favourably compared to those of several forecasting techniques across thousands of **time** **series** (Makridakis and Hibon, 2000), adapts to underlying alterations in **series** dynamics and automatically revises forecasts as new observations. We adapt two approaches in modelling and forecasting **rainfall** in this paper. The first is the state space model based on exponential smoothing methods and the second is Box Jenkins model building technique. The rest of the paper is organized as follows: Section Two gives the methodology employed in this paper; Section Three gives discusses the results of the finding and Section Four gives the Conclusion and Recommendations. The algorithms and modelling frameworks for automatic univariate **time** **series** forecasting which we employed in this work are implemented in the forecast package in R software version 2.14.1.

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developed during the last decade (Strebelle, 2002; Allard et al., 2006; Zhang et al., 2006; Arpat and Caers, 2007; Honarkhah and Caers, 2010; Straubhaar et al., 2011; Tah- masebi et al., 2012), MPS is a family of geostatistical tech- niques widely used in spatial-data simulations and particu- larly suited to pattern reproduction. MPS algorithms use a training image; i.e., a data set to evaluate the probability dis- tribution (pdf) of the variable simulated at each point (in **time** or space), conditionally to the values present in its neighbor- hood. In the particular case of the DS technique, the con- cept of training image is taken to the limit by avoiding the computation of the conditional pdf and making a random sampling of the historical data set where a pattern similar to the conditioning data is found. If the training data set is representative enough, these techniques can easily reproduce high-order statistics of complex natural processes at different scales. MPS has already been successfully applied to the sim- ulation of spatial **rainfall** occurrence patterns (Wojcik et al., 2009). In this paper, we test the DS technique on the simula- tion of daily **rainfall** **time** **series**. The aim is to reproduce the complexity of the **rainfall** signal up to the decennial scale, simulating the occurrence and the amount at the same **time** with the aid of a multivariate data set. Similar algorithms per- forming a multivariate simulation had been previously de- veloped by Young (1994) and Rajagopalan and Lall (1999) using a bootstrap-based approach. As discussed in detail in Sect. 2.3, the advantage of DS with respect to the mentioned techniques is the possibility to have a variable high-order **time**-dependence, without incurring excessive computation since the estimation of the n-dimensional conditional pdf is not needed. Moreover, we propose a standard setup for rain- fall simulation: an ensemble of auxiliary variables and fixed values for the main parameters required by the direct sam- pling algorithm, suitable for the simulation of any stationary **rainfall** **time** **series**, without the need of calibration. The tech- nique is tested on three **time** **series** from different climatic regions of Australia. The paper is organized as follows: in Sect. 2 the DS algorithm is introduced and compared with the existing resampling techniques. The data set used, the proposed setup and the method of evaluation are described in Sect. 3. The statistical analysis of the simulated **time** **series** is presented and discussed in Sect. 4 and Sect. 5 is dedicated to the conclusions.

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The data analyzed in this study are from three 5-min **rainfall** **series** recorded in three stations (Castel Cellesi (CCE), Mon- tefiascone (MFI), and Viterbo (VIT)) located in the Viterbo province (central Italy), by tipping bucket rain gauges with 0.2 mm resolution. The VIT **time** **series** spans from 1995 to 2005 (11 years), while CCE is available for 10 years (1995 to 2000, 2002, 2003, 2005, 2006) and MFI for eight years (1995 to 1997, 1999, 2002 to 2005). The corresponding daily se- ries were studied and modeled by Serinaldi (2009), and the annual summary statistics are shown in Table 1. The lack of long continuous **rainfall** data at a fine **time** scale moti- vates the research on **rainfall** modeling and disaggregation to obtain the information required in hydrological studies. As disaggregation methods are often applied to downscale daily **rainfall** **series**, scales ranging from 5 min to 1280 min are used here because the latter is the scale closest to the 1440-min daily scale, achievable by aggregating 5-min se- ries with b = 2 (e.g., Molnar and Burlando, 2005). For CUM simulation, this limitation does not apply; however, the same range of scales is used for the sake of comparison. Moreover, only results referring to the MFI data are presented in the fol- lowing discussion, as similar conclusions hold for CCE and VIT **series**.

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Besides the extreme value overestimation for some stations, the overall high accuracy of model disaggregated data supports its potential usefulness in hydrological applications. Some open questions are related to the **time** scales of applicability. The present study was confined to the range 1 day to 1 hour but useful disaggregation may be possible to even smaller scales. Another workable experiment is to calibrate the model using only a daily **time** **series** and evaluate up to which resolution disaggregation of the same **series** can be performed accurately. This possibility is a notable advantage of the present model compared with existing alternatives. Finally, besides assessing the quality of disaggregated data solely by comparison with observations, tests using the disaggregated data in hydrological modelling are required to evaluate their practical value. Early tests of cascade-disaggregated **rainfall** from daily to hourly **time** intervals with a simple runoff modelling approach (Calver, 1996) suggest that, over periods of the length used in the testing above, water resource issues are likely to be covered adequately by cascaded **rainfall**. It is, however, in the modelling of floods, particularly the more extreme events, that synthetic **rainfall** may introduce error. This comment should, however, be set in the context that other sources contribute to error in flood frequency modelling, notably in model structure and parameter identifiability. Moreover, an accurate description of not only the temporal but also the spatial **rainfall** distribution is crucial for successful hydrological modelling. Assessing the potential of the cascade methodology in this respect is an important area of future research.

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results with those of a standard fit with a single threshold. In order to evaluate the performances on synthetic samples that can be considered representative of our daily **rainfall** records, we preliminarily evaluated the GPD parameters on the longest **time** **series** belonging to the dataset described in Sect. 2: namely, 217 **time** **series** with more than 40 com- plete years of records. With this aim, the MTM presented in Sect. 4 was first applied on these **time** **series** with a range of thresholds between 2.5 and 12.5 mm and using three differ- ent GPD parameters estimators: the Simple Moments (SM), the Probability Weighted Moments (PWM), and the Maxi- mum Likelihood (ML) methods based on the expression re- ported in Hosking and Wallis (1987), Stedinger et al. (1993), and Grimshaw (1993). The MTM estimates of ξ M and α M 0 parameters obtained for each station using the three estima- tors are shown in the scatterplot of Fig. 5. We can observe how the ξ M estimates derived from the SM method are never larger than 0.35: this can be explained by the bias of the estimator related to the divergence of ordinary moments on heavy tailed distributions (Hosking and Wallis, 1987), thus we discarded the SM approach for our analysis. We can also observe that the ξ M estimates by ML are slightly more spread than the PWM ones. We investigated the issue to some de- tail and the largest ML estimates should be due to the higher sensitivity of the ML method to the presence of outliers or to convergence problems as argued by Hosking and Wallis (1987). We also visually inspected the CDFs of the few **time** **series** with a negative shape parameter and found that they can be reliably described by exponential distributions (ξ = 0). On the basis of this preliminary analysis, we decided to explore the MTM performances with the ML estimator on Monte Carlo samples generated by Eq. (10) with the follow- ing 7 couples (ξ , α 0 ) of GPD parameters (displayed in Fig. 5

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the fact the **series** takes on nonzero and zero values throughout the entire length of the record (Figure 6). In the same context, Figure 8 shows inter-annual decadal variation in the **rainfall** **series**; long-term trend pat- tern is seemingly not evident. However, there is large variability among the monthly values of **rainfall** of differ- ent years, with the period 1995-2009 showing slight increases in the storm event during the peak seasons. On the other hand, Figure 9, Figure 10 shows the presence of seasonality in the moments, meaning that monthly statis- tics for dry season are significantly different from those of the wet season period. Unlike intermittent stream flow process, the seasonal means have higher values than the seasonal deviations throughout the year. As noted in Figure 10, the coefficient of variation varies from 0.3234 in the month of June to 3.4227 in December (i.e., period of incipient rains, moderate-peak to late rains). The variance is maximum during the period of late rains and incipient dry season; more or less the interfacing period. This indicates atmospheric instability during this watershed period; i.e., the fringes of the raining season going to full harmattan period. Similarly, as shown in Table 3, values of the skewness coefficient (g) for the periods of incipient dry season (late rains) to full dry season are generally larger than the corresponding periods for the wet season over an annual cycle. This indi- cates that the data in the former seasons depart more from normality than those in the later (early to full wet season period). The variability in the **time** **series** regime leads to model structural uncertainty; especially if the hydrologic evolution of the generating mechanism is not appropriately understood and captured in the model formulation.

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The multifractal analysis of **rainfall** has been widely used to describe its temporal and spatial distribution (Schertzer and Lovejoy, 1987; Fraedrich and Larnder, 1993; Ladoy et al., 1993; Tessier et al., 1993, 1996; Over and Gupta, 1994; Svensson et al., 1996; de Lima and Grasman, 1999; Kiely and Ivanova, 1999; Sivakumar, 2001; Labat et al., 2002; Veneziano and Furcolo, 2002; Olsson and Burlando, 2002; Kantelhardt et al., 2006; Langousis and Veneziano, 2007). The universal multifractal model (UM) which uses the formalism of turbulence, was developed by Schertzer and Lovejoy (1987) to model the variability of **rainfall** by a multiplicative cascade process, in which the flux of water is transferred from larger to small regions (scales) of the atmosphere (Over and Gupta, 1994), in a similar way to what happens in turbulence models, where the transfer of energy from larger to smaller scales is assumed. This multifractal approach has been used to carry out multiple analyses of **rainfall** and related topics (Hubert et al., 1993; Ladoy et al., 1993; Tessier et al., 1993, 1996; Svensson et al., 1996; de Lima and Grassman, 1999; Lilley et al., 2006; Lovejoy and Schertzer, 2006; Lashermes and Foufoula-Georgiou, 2007).

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All the hydrological studies in a river basin depend primarily on how accurately the **rainfall** is recorded and its distribution over the basin is estimated both temporally and spatially. As it is often seen, gaps do occur in the **rainfall** **time** **series** due to various reasons. Of the two methods primarily used for estimating the missing **rainfall** viz., stochastic modeling of **rainfall** sequences and interpolation based methods (Villazon and Willems, 2010), the later has been seen many applications in the literature which are implemented starting from simpler techniques like

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ABSTRACT **Time** **series** clustering technique was used in this study to categorize the locations in Peninsular Malaysia according to the similarity of **rainfall** distribution patterns. Daily **rainfall** **time** **series** data from 12 meteorological observation stations across Peninsular Malaysia have been considered for this study. Four dissimilarity measure methods were examined and compared in terms of accuracy and suitability, namely Euclidean distance (ED), complexity- invariant distance (CID), correlation-based distance (COR) and integrated periodogram-based distance (IP). The average silhouette width (ASW) was used to determine the optimal group number for the **rainfall** **time** **series** data. Using Ward’s hierarchical clustering method, this study found that the **rainfall** **time** **series** in Peninsular Malaysia can be divided into four regions of homogeneous climate zones. Based on the results, the IP was the most suitable dissimilarity measures for clustering **rainfall** **time** **series** data in Peninsular Malaysia, except during the Southwest Monsoon where the COR performed better.

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Hughes et al. (2014) refer to a previous approach to incorpo- rating climate change uncertainties into hydrological mod- elling. This was based on the use of **rainfall** and tempera- ture data for 9 downscaled GCMs obtained from the Climate Systems Analysis Group (CSAG) of the University of Cape Town (Hewitson and Crane, 2006). These consist of daily **rainfall**, maximum and minimum temperature for baseline (1961 to 2000), near-future (2046 to 2065) and far-future (2081 to 2100) periods. As the statistical characteristics of the baseline **rainfall** simulations are very different, across the 9 GCMs, to the available historical data, Hughes et al. (2014) proposed a bias correction approach to generate corrected near-future **rainfall** **time** **series** that could be used with a hy- drological model established using historical **rainfall** data. There was less difference in the predicted temperature sce- narios across the 9 models. There are three potential practical problems with this approach. The first is that the sequences of near-future simulated flows for the 9 GCMs cannot be com- pared because they all have different starting conditions. The second is that the near-future simulations are only 20 years compared with the 85 year (1920 to 2005) historical data simulations that are currently used in South Africa for wa- ter resources availability assessments. The third is that there is quite a lot of data preparation and the hydrological model has to be run 9 times.

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domains can be derived, and the identification of the possi- ble linkages with local terrain characteristics and dominant synoptic circulation becomes problematic. In this paper, we attempt to overcome these limitations by characterizing inter- mittency of **rainfall** intensity and support on the island of Sar- dinia (Italy) using **time** **series** collected by 201 tipping-bucket gauges, with tipping accuracy of 0.2 mm of **rainfall** depth at **time** precision of 1 s. Specifically, we pursue the following main objectives. First, we apply several techniques to inves- tigate the intermittency properties of the **rainfall** **time** **series** recorded at each station aiming at the following: (a) assess- ing the effectiveness of each technique to characterize diverse aspects of **rainfall** intermittency; (b) identifying the presence of multiple scaling regimes and computing, for each of them, a number of metrics that permit intermittency quantification related to the fluctuations of **rainfall** intensity and the frag- mentation or clusterization of its support; and (c) investi- gating the relative contribution to the intermittency proper- ties due to **rainfall** intensity fluctuations and support frag- mentation. Second, for each scaling regime, we explore the possible existence of spatial patterns for the metrics and we search for linkages with the dominant synoptic circulations that affect the pluviometric regimes of the island and the topographic features of the gauge location.

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The Pettitt test identified significant change points or change of the median of the OND **rainfall** at three out of the 40 stations (Fig. 4). These change points were identified for the 1946/1947 season at two stations (Plumtree, Kezi) lo- cated on the western part, and in 1986/1987 for a northern station (Banket). Conway et al. (2008) also found a change point occurring in 1945 for the annual **rainfall** at Victoria Falls which is in the northwest. Significant change points for the JFM **rainfall** were identified at six stations with four of these being located on the eastern part of the country (Fig. 4). These change points have been identified for different years with the exception of two stations. The occurrence of change points in different years suggests that these changes are not due to a regional change of physical processes responsible for **rainfall** formation such as the atmospheric circulations. These change points could be due to changes in the exposure of rain gauges (Stott, et al., 2010). No significant change points in annual **rainfall** were identified except for three stations for the following periods 1926/1927, 1980/1981, 1994/1995 (Fig. 4). Stations for which change points have been identified in the OND, JFM, and in annual **rainfall** **time** **series**, are not located in geographically contiguous areas, while neighbouring stations do not have similar changes in the median. The change points have been identified at few stations, 7 to 14% of the total number of stations analysed which raises doubts about the physical significance of these changes.

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Abstract: For several decades, climate change and climate variability issues and their impacts on the hydrological regime of rivers have constituted a major topic for hydroclimatological sciences research and water resources planning policies. Understanding of these issues needs enough long **time** **series** of **rainfall** and runoff data covering a large period, and a comprehensive diagnosis of the existing trends and shifts in these **time** **series** of data. This can be done by applying robust statistical tests to relevant **rainfall** and runoff **time** annual **series**. The aim of this paper is to highlight the effect of climate change in the Gambia River Basin and its impacts on the availability of the water resources of this basin. To reach this objective, we have selected runoff **time** **series** of the Gambia River Basin at Mako, Kedougou Diaguéri streamgauges and **rainfall** **time** **series** at Koulountou’s rain gauge. Statistical tests for shift detection presented in the Khronostat software, such as Pettit, Hubert and Buishand ellipse tests are first used, Mann Kendall test for annual trend are then applied to check whether trends exist or not in these times **series**. When the null hypothesis of no trend is rejected, the non parametric Sen’s test is then applied to validate the Mann Kendall trend test and to estimate the magnitude of the trend and its direction. Tests for homogeneity show an increasing shift for **rainfall** **time** **series** of Koulountou raingauge and for runoff **time** **series** of Mako and Diaguéri and a decreasing shift for Kedougou streamgauge. According to the Mann Kendall trend test, there is an upward trend for Koulountou **rainfall** **time** **series**, and Mako and Diaguéri runoff **time** **series**, and a downward trend for Kedougou annual runoff **time** **series**. The Buishand ellipse and the Hubert test indicate generally the same year of the beginning of the shift. Interesting perspectives for decision makers in evaluation and precise management of water resources and water projects in the Gambia River basin are offered as well.

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The Hydrological Predictions for the Environment (HYPE) is a hydrological model for small-scale and large-scale assessments of water resources and water quality developed by the Swedish Meteorological and Hydrological Institute in between 2005–2007. This is a recently developed semi-distributed, conceptual model which imitates multi-basins, covering broad variations in sediment types, land and shape. HYPE integrates landscape elements and hydrological spaces along with nutrient transport along the flow path. The model divides a river watershed into number of small watersheds and each small watershed is further divided into sub-category depending upon soil type and vegetative cover. For each sub-category, the model imitates snowmelt, runoff, soil erosion, drainage, groundwater escape from different soil layers, nutrient in soil and transport to rivers and lakes. Calculations are made on a daily **time** step in linked small watersheds. The model parameters are related with land use, soil type. Due to this linking of parameters, it is best suited for imitations in ungauged watersheds also. This model takes input of maximum of ten data files independent of size and domain and all the input and output files are in ASCII format. There are some different HYPE models which are developed for the individual countries like S-HYPE model (S for Sweden) was employed for the country of Sweden to imitate daily **rainfall** runoff and nutrient concentrations. Similarly, E- HYPE model (E for Europe) for the continent of Europe, BALT-HYPE model was used for the whole Baltic Sea basin. LPB-HYPE model was applied on the La Plata Basin, Niger-HYPE model for imitating on Niger River in Africa and Arctic-HYPE model for imitating hydrological variables for the entire Arctic region. Similarly, development of In-HYPE model for simulating hydrological variables for the Indian region is in progress. 3.4 WinSRM

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For the evaluation of the presence of deterministic chaos in the dynamical systems Lyapunov exponents were used, for which it was necessary to reconstruct the phase space with the Method of **Time**-Delay, which finds the appropriate values of the **time** delay (τ) and embedding dimension (m) to capture the attractor dynamics. The autocorrelation function and the mutual information were used for the selection of the **time** delay, and the embedding dimension was selected using the correlation dimension method, the False Nearest Neighbors method (FNN) and Cao’s method, which were successfully used in (Gallego, 2010), (Hernández, 2009) and (Siek, 2011).

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Abstract: Moroccan economy is largely based upon **rainfall**, use of water resources and crop productivity, for that it’s considered as an agricultural country. It’s more required and more important for any farmer to forecast **rainfall** prediction in order to analyze crop productivity. Predicting the atmosphere or forecasting the state of the weather is considered as challenge for scientific research. The prediction of **rainfall** monthly or/and seasonal **time** scales is the application of science and technology to invent and to schedule the agriculture strategies. Recently different research articles achieve to forecast and/or predict **rainfall** monthly or seasonal **time** scales using different techniques. The methodology followed in this work, be focused on automating **time** **series** analysis to forecast / predict precipitation daily, monthly or seasonal in Aguelmam Sidi Ali basin in Morocco for last 32 years ago from 1975 to 2007. We first have to study the **rainfall** data theoretically using the simplest form statistical analysis, which is the univariate analysis, as long as only one variable is involved in our case study. To get the selected and suitable model of **time** **series** to automate, we used different autocorrelation methods based on various criterion such as: Akaike Information Criterion (AIC), estimation of parameters using Yule-Walker (YW) and Maximum Likelihood Estimation (MLE). The results of our experiment show that it is possible using our system to obtain accurate **rainfall** prediction, with a more details and with a very fast way. It shows also that it’s possible to predict for next months or next years. To minimize the risk of floods and natural disasters within a basin in general and within the Aguelmam Sidi Ali basin in particular, accurate and timely **rainfall** forecasting is required.

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Any minor changes in **rainfall** intensity or amount impose a severe challenge on the rural people since its main livelihood depends on agriculture which mostly relies on summer monsoon. This is because modeling or predicting climate change impact on predominantly sub- sistent farmers at global level is a very difficult task due to the lack of ordinary descriptions, lack or difficulty to get benchmark data, unique location, and the households’ ability to integrate on-farm and off-farm activities, and lastly the farmers’ susceptibility to a range of stressors (IPCC 2007b). The overall objective of this research was, therefore, to fill such research gaps thorough analyzing **time** **series** temperature and **rainfall** trends in the high- lands of Ethiopia and LTSB in particular.

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Runoff estimation in ungauged catchment is a challenge for the hydrological engineers and planners. For any hydrological study on an ungauged watershed, a methodology has to be appropriately selected for the determination of runoff at its outlet. Several methods have been used to estimate the runoff from a watershed. GIS and Remote Sensing techniques seem to be accurate and sensitive that includes several important properties of watershed namely, soil permeability, landuse and antecedent soil moisture conditions. In this study the estimation of runoff in the Perumal catchment, Tamilnadu State, India, by using GIS based SCS-CN method is presented. Land sat image (1:25000), Survey of India (SOI) topographic map, soil map and landuse map data were used. GIS software was used for data generation, storage, manipulation and integration to estimate the curve number from which the daily runoff was estimated for twenty eight water years from 1981-82 to 2008-09. The high R-squared values obtained for the linear equations and second degree polynomials fitted to annual **rainfall**-runoff **series** and seasonal **rainfall**-runoff **series** for all the seasons indicate that the observed runoff and runoff estimated using the fitted equations are highly correlated.

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