International Journal of Recent Technology and Engineering (IJRTE) ISSN: 2277-3878, Volume-8, Issue-2S2, July 2019 158 Published By: Blue Eyes Intelligence Engineering & Sciences Publication Retrieval Number: B10290782S219/19©BEIESP DOI: 10.35940/ijrte.B1029.0782S219 Abstract: In meteorological data, lots of variables have annual, seasonal or diurnal cycles. These would be based on different climatic patterns in different seasons rising sea levels. The delta change approach is one of the statistical downscaling methods that used to downscale global climate model data in order to use it as a future input for hydrological models and flood risk assessment. In this work, a non-stationary GEV model with cyclic covariate structure for modelling magnitude and variation of data series with some degrees of correlation for real-world applications is proposed. All extreme events were calculated assuming that maximum annual daily precipitations follow the GEV distribution. The method makes it possible to identify and estimate the impacts of multiple time scales-such as seasonality, interdecadal variability, and secular trends-throughout the area, scale, and shape parameters of extreme sea level probability distribution. The incorporation of seasonal effects describes a huge amount of data variability, permitting the methods involved to be estimated more efficiently. Next, the technique of delta- change was implemented to the mean annual rainfall and also the regular rainfall occurrences of 5, 10, 20, 50 and 100 years of return. The capability of the proposed model will be tested to one rainfall station in Sabah. The new model suggesting improvement over the stationary model based on the p-value which is highly significant (approximate to 0). GEV model with cyclic covariate on both location and scale parameters is able to capture the seasonality factor in rainfall data. Hence, a reliable delta-change model has been developed in this study. This could produce more accurate projection of rainfall in the future. Index Terms: covariate, cyclic, delta-change, generalized extreme value, rainfall. I. INTRODUCTION Many variables have annual, seasonal or diurnal cycles in meteorological data. These will be due to various climatic patterns in different seasons, or even due to longer-term trends due to climate change. Statistical downscaling approach is one of the approaches that is widely used to estimate the future rainfall. Statistical downscaling is a two- step process consisting of Statistical downscaling is a two- step process consisting of 1) statistical relationship development among local climate variables and large-scale predictors, 2) applying such relationships to large-scale outputs in order to simulate future local climate characteristics[1]. One of the statistical downscaling methods is called as delta-change method. Revised Manuscript Received on June 22, 2019. Syafrina Abdul Halim, Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia A common method of dealing with General Circulation Model (GCM) outputs inadequacies (known as the delta change method) is to compute differences between current and future GCM simulations and add these changes to observed time-series [e.g., 2,3]. The delta change method is the primary future scenario generation technique suggested for use in the U.S. National Assessment (see http://www.nacc.usgcrp.gov/). Applying the delta change method assumes that GCMs more reliably simulate relative changes rather than absolute values. In the modeling of cyclic changes in threshold exceedance, it is useful to specify a model with different parameters in each cycle. The generalized extreme value (GEV) distribution has been employed widely in describing flood characteristics due to its capability in analyzing hydrologic phenomena for instance flood events, which are of particular interest to the fields of engineering and water resources. Traditionally, the GEV distribution is fit assuming that the underlying process is stationary in time, with observations that are independent and identically distributed (IID). However, according to Towler et al. [4], GEV has become generally accepted that climate variability can play a significant role in the magnitude and frequency of extreme streamflow events. Natural modes of interannual and interdecadal variability (e.g., the El Niño phenomenon) have been found to influence flood frequency. Furthermore, evidence of long- term trends, such as from global warming, has undermined the long-held assumption of stationarity [4]. Accurate methods are required to accurately capture the non-stationary climate. Several studies have developed non- stationary GEV approaches in hydrological area [4]. Sarr et al. [5] has applied two different statistical downscaling techniques to the outputs of four regional climate models at six selected precipitation stations in Senegal. The stationary GEV model was presented and the estimated parameters were calculated in the study. A non-stationary GEV model with cyclic covariate structure is proposed in this work to model data series magnitude and variation with some degrees of correlation for real-world applications. All extreme events were calculated assuming that maximum annual daily precipitations follow the GEV distribution. The method makes it possible to identify and estimate the impacts of multiple time scales-such as seasonality, interdecadal variability, and secular trends-throughout the area, scale, and shape parameters of extreme sea level probability distribution. Delta Change Method with Cyclic Covariate Generalized Extreme Value Model for Downscaling Extreme Rainfall Syafrina Abdul Halim