# Make categorical forecast based on a multi-model forecast with potential for calibrate This function converts a multi-model ensemble forecast into a categorical forecast by giving the probability for each category. Different methods are available to combine the different ensemble forecasting models into probabilistic categorical forecasts. Motivation: Beyond the short range, the unpredictable component of weather predictions becomes substantial due to the chaotic nature of the earth system. Therefore, predictions can mostly be skillful when used in a probabilistic sense. In practice this is done using ensemble forecasts. It is then common to convert the ensemble forecasts to occurence probabilities for different categories. These categories typically are taken as terciles from climatolgical distributions. For instance for temperature, there is a cold, normal and warm class. Commonly multiple ensemble forecasting systems are available but some models may be more competitive than others for the variable, region and user need under consideration. Therefore, when calculating the category probabilities, the ensemble members of the different forecasting system may be differently weighted. Such weighting is typically done by comparison of the ensemble forecasts with observations. Description of the tool: The tool considers all forecasts (all members from all forecasting systems) and converts them into occurrence probabilities of different categories. The amount of categories can be changed and are taken as the climatological quantiles (e.g. terciles), extracted from the observational data. The methods that are available to combine the ensemble forecasting models into probabilistic categorical forecasts are: 1) ensemble pooling where all ensemble members of all ensemble systems are weighted equally, 2) model combination where each model system is weighted equally, and, 3) model weighting. The model weighting method is described in Rajagopalan et al. (2002), Robertson et al. 2004 and Van Schaeybroeck and Vannitsem (2019). More specifically, this method uses different weights for the occurence probability predicted by the available models and by a climatological model and optimizes the weights by minimizing the ignorance score. Finally, the function can also be used to categorize the observations in the categorical quantiles. ```r CST_CategoricalEnsCombination( exp, obs, cat.method = "pool", eval.method = "leave-k-out", amt.cat = 3, k = 1, tail.out = TRUE, ... ) ``` ## Arguments - `exp`: An object of class `s2dv_cube` as returned by `CST_Load` function, containing the seasonal forecast experiment data in the element named `$data`. The amount of forecasting models is equal to the size of the `dataset` dimension of the data array. The amount of members per model may be different. The size of the `member` dimension of the data array is equal to the maximum of the ensemble members among the models. Models with smaller ensemble sizes have residual indices of `member` dimension in the data array filled with NA values. - `obs`: An object of class `s2dv_cube` as returned by `CST_Load` function, containing the observed data in the element named `$data`. - `cat.method`: Method used to produce the categorical forecast, can be either `pool`, `comb`, `mmw` or `obs`. The method pool assumes equal weight for all ensemble members while the method comb assumes equal weight for each model. The weighting method is descirbed in Rajagopalan et al. (2002), Robertson et al. (2004) and Van Schaeybroeck and Vannitsem (2019). Finally, the `obs` method classifies the observations into the different categories and therefore contains only 0 and 1 values. - `eval.method`: Is the sampling method used, can be either `"in-sample"` or `"leave-k-out"`. Default value is the `"leave-k-out"` cross validation. - `amt.cat`: Is the amount of categories. Equally-sized quantiles will be calculated based on the amount of categories. - `k`: k Positive integer. Default = 1. In method `leave-k-out`, `k` is expected to be odd integer, indicating the number of points to leave out. In method `retrospective`, `k` can be any positive integer, indicating when to start. - `tail.out`: Boolean for 'leave-k-out' method; TRUE to remove both extremes keeping the same sample size for all k-folds (e.g. sample.length = 50, k = 3, eval.dexes = 1, train.dexes = (3,49)). FALSE to remove only the corresponding tail (e.g.. sample.length = 50, k = 3, eval.dexes = 1, train.dexes = (3,50)) - `...`: other parameters to be passed on to the calibration procedure. ## Returns An object of class `s2dv_cube` containing the categorical forecasts in the element called `$data`. The first two dimensions of the returned object are named dataset and member and are both of size one. An additional dimension named category is introduced and is of size amt.cat. ## Examples ```r mod1 <- 1 : (2 * 2* 4 * 5 * 2 * 2) dim(mod1) <- c(dataset = 2, member = 2, sdate = 4, ftime = 5, lat = 2, lon = 2) mod1[2, 1, , , , ] <- NA datasets <- c("MF", "UKMO") obs1 <- 1 : (1 * 1 * 4 * 5 * 2 * 2) dim(obs1) <- c(dataset = 1, member = 1, sdate = 4, ftime = 5, lat = 2, lon = 2) lon <- seq(0, 30, 5) lat <- seq(0, 25, 5) coords <- list(lat = lat, lon = lon) attrs <- list(Datasets = datasets) exp <- list(data = mod1, coords = coords, attrs = attrs) obs <- list(data = obs1, coords = coords) attr(exp, 'class') <- 's2dv_cube' attr(obs, 'class') <- 's2dv_cube' a <- CST_CategoricalEnsCombination(exp = exp, obs = obs, amt.cat = 3, cat.method = "mmw") ``` ## References Rajagopalan, B., Lall, U., & Zebiak, S. E. (2002). Categorical climate forecasts through regularization and optimal combination of multiple GCM ensembles. Monthly Weather Review, 130(7), 1792-1811. Robertson, A. W., Lall, U., Zebiak, S. E., & Goddard, L. (2004). Improved combination of multiple atmospheric GCM ensembles for seasonal prediction. Monthly Weather Review, 132(12), 2732-2744. Van Schaeybroeck, B., & Vannitsem, S. (2019). Postprocessing of Long-Range Forecasts. In Statistical Postprocessing of Ensemble Forecasts (pp. 267-290). ## Author(s) Bert Van Schaeybroeck, bertvs@meteo.be

CST_CategoricalEnsCombination function