Abstract: This article reviews the historical development of statistical weather models, from simple analyses of runs of consecutive rainy and dry days at single sites, through to multisite models of daily precipitation. Weather generators have been used extensively in water engineering design and in agricultural, ecosystem and hydrological impact studies as a means of in-filling missing data or for producing indefinitely long synthetic weather series from finite station records. We begin by describing the statistical properties of the rainfall occurrence and amount processes which are necessary precursors to the simulation of other (dependent) mete-orological variables. The relationship between these daily weather models and lower-frequency variations in climate statistics is considered next, noting that conventional weather generator techniques often fail to capture wholly interannual variability. Possible solutions to this deficiency – such as the use of mixtures of slowly and rapidly varying conditioning variables – are discussed. Common applications of weather generators are then described. These include the modelling of climate-sensitive systems, the simulation of missing weather data and statistical downscaling of regional climate change scenarios. Finally, we conclude by considering ongoing advances in the simulation of spatially correlated weather series at multiple sites, the downscaling of interannual climate variability and the scope for using nonparametric techniques to synthesize weather series. Key words: climate change, impact assessment, stochastic model, time series, weather generator. I

Ethiopian agriculture and Nile River flows are heavily dependent upon the Kiremt season (June– September) precipitation in the upper Blue Nile basin, as a means of rain-fed irrigation and streamflow contribution, respectively. Climate diagnostics suggest that the El Niño–Southern Oscillation phenomenon is a main driver of interannual variability of seasonal precipitation in the basin. One-season (March–May) lead predictors of the seasonal precipitation are identified from the large-scale ocean–atmosphere–land system, including sea level pressures, sea surface temperatures, geopotential height, air temperature, and the Palmer Drought Severity Index. A nonparametric approach based on local polynomial regression is proposed for generating ensemble forecasts. The method is data driven, easy to implement, and provides a flexible framework able to capture any arbitrary features (linear or nonlinear) present in the data, as compared to traditional linear regression. The best subset of predictors, as determined by the generalized cross-validation (GCV) criteria, is selected from the suite of potential large-scale predictors. A simple technique for disaggregating the seasonal precipitation forecasts into monthly forecasts is also provided. Cross-validated forecasts indicate significant skill in comparison to climatological forecasts, as currently utilized by the Ethiopian National Meteorological Services Agency. This ensemble forecasting framework can serve as a useful tool for water resources planning and management within the basin. 1.

Abstract. A methodology is proposed for coupling stochastic models of hydrologic processes applying to different time scales so that time series generated by the different models be consistent. Given two multivariate time series, generated by two separate (unrelated) stochastic models of the same hydrologic process, each applying to a different time scale, a transformation is developed (referred to as a coupling transformation) that appropriately modifies the time series of the lower-level (finer) time scale so that this series be consistent with the time series of the higher-level (coarser) time scale without affecting the second-order stochastic structure of the former and also establishing appropriate correlations between the two time series. The coupling transformation is based on a developed generalized mathematical proposition, which ensures preservation of marginal and joint second-order statistics and of linear relationships between lower- and higher-level processes. Several specific forms of the coupling transformation are studied, from the simplest single variate to the full multivariate. In addition, techniques for evaluating parameters of the coupling transformation based on second order moments of the lower-level process are studied. Furthermore, two methods are proposed to enable preservation of the skewness of the processes, in addition to that of second-order statistics. The overall methodology can be applied to problems involving disaggregation of annual to seasonal and seasonal to subseasonal time scales, as well as problems involving finer time scales (e.g. daily – hourly), under the only requirement that a specific stochastic model is available for each involved time scale. The performance of the methodology is demonstrated by means of a detailed numerical example. 1

A Bayesian methodology is used to assess the information content of categorical, probabilistic forecasts of specific variables derived from a general circulation model (GCM) forecast ensemble, and to combine a ‘‘prior’’ forecast (climatological probabilities of each category) with a categorical probabilistic forecast derived from a GCM ensemble to develop posterior, or ‘‘regularized’ ’ categorical probabilities. The combination algorithm assigns a weight to a particular model forecast and to climatology. The ratio of the sample likelihood of the model based on the posterior categorical probabilities, to that based on climatological probabilities, computed over the period of record of historical forecasts, provides a measure of the skill or information content of a candidate model. The weight given to a GCM forecast serves as a secondary indicator of its information content. Model weights are determined by maximizing the likelihood ratio. Results using the so-called ranked probability skill score as an objective function are also obtained, and are found to be very similar to the likelihood-based results. The procedure is extended to the optimal combination of forecasts from multiple GCMs. An application of the method is presented for global, seasonal precipitation and temperature forecasts in two different seasons, based on 41 yr of observational and model simulation data. The multimodel combination skill is significantly

A nonparametric bootstrap procedure is proposed for stochastic processes which follow a general autoregressive structure. The procedure generates bootstrap replicates by locally resampling the original set of observations reproducing automatically its dependence prop-erties. It avoids an initial nonparametric estimation of process characteristics in order to generate the pseudo-time series and the bootstrap replicates mimic several of the properties of the original process. Applications of the procedure in nonlinear time series analysis are considered and theoretically justi ed; some simulated and real data examples are discussed.

disaggregation of streamflows

This paper describes the development of a statistical forecasting method for summer monsoon rainfall over Thailand. Predictors of Thailand summer (August-October) monsoon rainfall are identified from the large-scale ocean-atmospheric circulation variables (i.e., sea surface temperature and sea level pressure) in the Indo-Pacific region. The identified predictors are part of the broader El Niño Southern Oscillation (ENSO) phenomenon. The predictors exhibit significant relationship to the summer rainfall only during the post-1980 period when the Thailand summer rainfall also shows a relationship with ENSO. Two methods for generating ensemble forecasts are adapted. The first is the traditional linear regression, and the second is a local polynomial based non-parametric method. The associated predictive standard errors are used for generating ensembles. Both the methods exhibit significant comparable skills in a cross-validated mode. However, the nonparametric method shows improved skill during extreme years (i.e. wet and dry years). Furthermore, the models provide useful skill at 1~3 month lead time that can have strong impact on resources planning and management.

One of the important stages of data mining is preprocessing, where the data is prepared for different mining tasks. Often, the real-world data tends to be incomplete, noisy, and inconsistent. It is very common that the data are not obtainable for every observation of every variable. So the presence of missing variables is obvious in the data set. A most important task when preprocessing the data is, to fill in missing values, smooth out noise and correct inconsistencies. This paper presents the missing value problem in data mining and evaluates some of the methods generally used for missing value imputation. In this work, three simple missing value imputation methods are implemented namely (1) Constant substitution, (2) Mean attribute value substitution and (3) Random attribute value substitution. The performance of the three missing value imputation algorithms were measured with respect to different rate or different percentage of missing values in the data set by using some known clustering methods. To evaluate the performance, the standard WDBC data set has been used.

The knowledge of sea state and wind conditions is of central importance for many offshore or nearshore operations. In this paper, we make a complete survey of stochastic models for sea state and wind time series. We begin the presentation with methods based on Gaussian processes and non parametric resampling methods for time series are introduced followed by various parametric models. Finally we propose an original statistical method, based on Monte Carlo goodness-of-fit tests, for model validation and comparison. The use of this method is illustrated by an example on wind speed data in North Atlantic.

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