Statistical Post-processing Techniques Research Articles

Improving short-term sea ice concentration forecasts using deep learning

Abstract. Reliable short-term sea ice forecasts are needed to support maritime operations in polar regions. While sea ice forecasts produced by physically based models still have limited accuracy, statistical post-processing techniques can be applied to reduce forecast errors. In this study, post-processing methods based on supervised machine learning have been developed for improving the skill of sea ice concentration forecasts from the TOPAZ4 prediction system for lead times from 1 to 10 d. The deep learning models use predictors from TOPAZ4 sea ice forecasts, weather forecasts, and sea ice concentration observations. Predicting the sea ice concentration for the next 10 d takes about 4 min (including data preparation), which is reasonable in an operational context. On average, the forecasts from the deep learning models have a root mean square error 41 % lower than TOPAZ4 forecasts and 29 % lower than forecasts based on persistence of sea ice concentration observations. They also significantly improve the forecasts for the location of the ice edges, with similar improvements as for the root mean square error. Furthermore, the impact of different types of predictors (observations, sea ice, and weather forecasts) on the predictions has been evaluated. Sea ice observations are the most important type of predictors, and the weather forecasts have a much stronger impact on the predictions than sea ice forecasts.

Statistical post-processing of precipitation forecasts using circulation classifications and spatiotemporal deep neural networks

Abstract. Statistical post-processing techniques are widely used to reduce systematic biases and quantify forecast uncertainty in numerical weather prediction (NWP). In this study, we propose a method to correct the raw daily forecast precipitation by combining large-scale circulation patterns with local spatiotemporal information such as topography and meteorological factors. Particularly, we first use the self-organizing map (SOM) model to classify large-scale circulation patterns for each season, then we build the convolutional neural network (CNN) model to extract spatial information (e.g., elevation, specific humidity, and mean sea level pressure) and the long short-term memory network (LSTM) model to extract time series (e.g., t, t−1, t−2), and we finally correct local precipitation for each circulation pattern separately. Furthermore, the proposed method (SOM-CNN-LSTM) is compared with other benchmark methods (i.e., CNN, LSTM, and CNN-LSTM) in the Huaihe River basin with a lead time of 15 d from 2007 to 2021. The results show that the proposed SOM-CNN-LSTM post-processing method outperforms other benchmark methods for all lead times and each season with the largest correlation coefficient improvement (32.30 %) and root mean square error reduction (26.58 %). Moreover, the proposed method can effectively capture the westward and northward movement of the western Pacific subtropical high (WPSH), which impacts the basin's summer rain. The results illustrate that incorporating large-scale circulation patterns with local spatiotemporal information is a feasible and effective post-processing method to improve forecasting skills, which would benefit hydrological forecasts and other applications.

Distributional regression and its evaluation with the CRPS: Bounds and convergence of the minimax risk

The theoretical advances in the properties of scoring rules over the past decades have broadened the use of scoring rules in probabilistic forecasting. In meteorological forecasting, statistical postprocessing techniques are essential to improve the forecasts made by deterministic physical models. Numerous state-of-the-art statistical postprocessing techniques are based on distributional regression evaluated with the continuous ranked probability score (CRPS). However, the theoretical properties of such evaluations with the CRPS have solely considered the unconditional framework (i.e. without covariates) and infinite sample sizes. We extend these results and study the rate of convergence in terms of the CRPS of distributional regression methods. We find the optimal minimax rate of convergence for a given class of distributions and show that the k-nearest neighbor method and the kernel method reach this optimal minimax rate.

Improving Probabilistic Quantitative Precipitation Forecasts Using Short Training Data through Artificial Neural Networks

Abstract Conventional statistical postprocessing techniques offer limited ability to improve the skills of probabilistic guidance for heavy precipitation. This paper introduces two artificial neural network (ANN)-based, geographically aware, and computationally efficient postprocessing schemes, namely, the ANN-multiclass (ANN-Mclass) and the ANN–censored, shifted gamma distribution (ANN-CSGD). Both schemes are implemented to postprocess Global Ensemble Forecast System (GEFS) forecasts to produce probabilistic quantitative precipitation forecasts (PQPFs) over the contiguous United States (CONUS) using a short (60 days), rolling training window. The performances of these schemes are assessed through a set of hindcast experiments, wherein postprocessed 24-h PQPFs from the two ANN schemes were compared against those produced using the benchmark quantile mapping algorithm for lead times ranging from 1 to 8 days. Outcomes of the hindcast experiments show that ANN schemes overall outperform the benchmark as well as the raw forecast over the CONUS in predicting probability of precipitation over a range of thresholds. The relative performance varies among geographic regions, with the two ANN schemes broadly improving upon quantile mapping over the central, south, and southeast, and slightly underperforming along the Pacific coast where skills of raw forecasts are the highest. Between the two schemes, the hybrid ANN-CSGD outperforms at higher rainfall thresholds (i.e., >50 mm day−1), though the outperformance comes at a slight expense of sharpness and spatial specificity. Collectively, these results confirm the ability of the ANN algorithms to produce skillful PQPFs with a limited training window and point to the prowess of the hybrid scheme for calibrating PQPFs for rare-to-extreme rainfall events.

Development of a NWP based Integrated Block Level Forecast System (IBL-FS) using statistical post-processing technique for the state Jharkhand (India)

A statistical post-processing forecast system for medium range predictions using the GFS model has been developed for Jharkhand (India) with the aim of improving rainfall and temperature predictions for agricultural applications. The basis of the integrated block level forecast system (IBL-FS) build includes (i) Decaying weighted mean (DWM) bias correction technique, (ii) Value addition and (iii) Inverse distance squared weighted (IDSW) interpolation. In the first step, model bias corrected district level forecast for 24 districts of Jharkhand is generated from the output of numerical GFS model (T1534L64) by applying DWM bias correction technique. In the second step, these bias corrected forecasts are value-added using forecast from various NWP models and synoptic methods. Finally in the third step, the IDSW interpolation method is used to generate the forecast at an unmeasured block from the value-added district level forecast of the surrounding districts. The value-added forecast for 263 blocks for the state Jharkhand is prepared up to medium range time scale (120h). The performance skill of IBL-FS is evaluated for rainfall during monsoon season 2018 and 2019, for minimum temperature during winter season 2019, and for maximum temperature during summer season 2019 using different statistical metrics. The skill of IBL-FS is found to be higher than the direct model forecast (DMFC) by 15% to 43% for minimum temperature, by 18% to 41% for maximum temperature, and by 22% to 30% for rainfall forecast for day1 to day5 forecasts. This study concludes that the integrated approach is more skillful than DMFC for real time forecasts and useful for farming for the blocks of Jharkhand.

Probabilistic fire-danger forecasting: A framework for week-two forecasts using statistical post-processing techniques and the Global ECMWF Fire Forecast System (GEFF)

AbstractWildfire guidance two weeks ahead is needed for strategic planning of fire mitigation and suppression. However, fire forecasts driven by meteorological forecasts from numerical weather prediction models inherently suffer from systematic biases. This study uses several statistical-postprocessing methods to correct these biases and increase the skill of ensemble fire forecasts over the contiguous United States 8–14 days ahead. We train and validate the post-processing models on 20 years of European Centre for Medium-range Weather Forecast (ECMWF) reforecasts and ERA5 reanalysis data for 11 meteorological variables related to fire, such as surface temperature, wind speed, relative humidity, cloud cover, and precipitation. The calibrated variables are then input to the Global ECMWF Fire Forecast (GEFF) system to produce probabilistic forecasts of daily fire-indicators which characterize the relationships between fuels, weather, and topography. Skill scores show that the post-processed forecasts overall have greater positive skill at Days 8–14 relative to raw and climatological forecasts. It is shown that the post-processed forecasts are more reliable at predicting above- and below-normal probabilities of various fire indicators than the raw forecasts and that the greatest skill for Days 8–14 is achieved by aggregating forecast days together.

Space–time calibration of wind speed forecasts from regional climate models

Numerical weather predictions (NWPs) are systematically subject to errors due to the deterministic solutions used by numerical models to simulate the atmosphere. Statistical postprocessing techniques are widely used nowadays for NWP calibration. However, time-varying bias is usually not accommodated by such models. The calibration performance is also sensitive to the temporal window used for training. This paper proposes space–time models that extend the main statistical postprocessing approaches to calibrate NWP model outputs. Trans-Gaussian random fields are considered to account for meteorological variables with asymmetric behavior. Data augmentation is used to account for the censoring of the response variable. The benefits of the proposed extensions are illustrated through the calibration of hourly 10-m height wind speed forecasts in Southeastern Brazil coming from the Eta model.

Truncated generalized extreme value distribution‐based ensemble model output statistics model for calibration of wind speed ensemble forecasts

AbstractIn recent years, ensemble weather forecasting has become a routine at all major weather prediction centers. These forecasts are obtained from multiple runs of numerical weather prediction models with different initial conditions or model parametrizations. However, ensemble forecasts can often be underdispersive and also biased, so some kind of postprocessing is needed to account for these deficiencies. One of the most popular state of the art statistical postprocessing techniques is the ensemble model output statistics (EMOS), which provides a full predictive distribution of the studied weather quantity. We propose a novel EMOS model for calibrating wind speed ensemble forecasts, where the predictive distribution is a generalized extreme value (GEV) distribution left truncated at zero (TGEV). The truncation corrects the disadvantage of the GEV distribution‐based EMOS models of occasionally predicting negative wind speed values, without affecting its favorable properties. The new model is tested on four datasets of wind speed ensemble forecasts provided by three different ensemble prediction systems, covering various geographical domains and time periods. The forecast skill of the TGEV EMOS model is compared with the predictive performance of the truncated normal, log‐normal and GEV methods and the raw and climatological forecasts as well. The results verify the advantageous properties of the novel TGEV EMOS approach.

A Physically Based Stochastic Boundary Layer Perturbation Scheme. Part II: Perturbation Growth within a Superensemble Framework

AbstractConvection-permitting forecasts have improved the forecasts of flooding from intense rainfall. However, probabilistic forecasts, generally based upon ensemble methods, are essential to quantify forecast uncertainty. This leads to a need to understand how different aspects of the model system affect forecast behavior. We compare the uncertainty due to initial and boundary condition (IBC) perturbations and boundary layer turbulence using a superensemble (SE) created to determine the influence of 12 IBC perturbations versus 12 stochastic boundary layer (SBL) perturbations constructed using a physically based SBL scheme. We consider two mesoscale extreme precipitation events. For each, we run a 144-member SE. The SEs are analyzed to consider the growth of differences between the simulations, and the spatial structure and scales of those differences. The SBL perturbations rapidly spin up, typically within 12 h of precipitation commencing. The SBL perturbations eventually produce spread that is not statistically different from the spread produced by the IBC perturbations, though in one case there is initially increased spread from the IBC perturbations. Spatially, the growth from IBC occurs on larger scales than that produced by the SBL perturbations (typically by an order of magnitude). However, analysis across multiple scales shows that the SBL scheme produces a random relocation of precipitation up to the scale at which the ensemble members agree with each other. This implies that statistical postprocessing can be used instead of running larger ensembles. Use of these statistical postprocessing techniques could lead to more reliable probabilistic forecasts of convective events and their associated hazards.

ARPEGE Cloud Cover Forecast Postprocessing with Convolutional Neural Network

AbstractCloud cover provides crucial information for many applications such as planning land observation missions from space. It remains, however, a challenging variable to forecast, and numerical weather prediction (NWP) models suffer from significant biases, hence, justifying the use of statistical postprocessing techniques. In this study, ARPEGE (Météo-France global NWP) cloud cover is postprocessed using a convolutional neural network (CNN). CNN is the most popular machine learning tool to deal with images. In our case, CNN allows the integration of spatial information contained in NWP outputs. We use a gridded cloud cover product derived from satellite observations over Europe as ground truth, and predictors are spatial fields of various variables produced by ARPEGE at the corresponding lead time. We show that a simple U-Net architecture (a particular type of CNN) produces significant improvements over Europe. Moreover, the U-Net outclasses more traditional machine learning methods used operationally such as a random forest and a logistic quantile regression. When using a large number of predictors, a first step toward interpretation is to produce a ranking of predictors by importance. Traditional methods of ranking (permutation importance, sequential selection, etc.) need important computational resources. We introduced a weighting predictor layer prior to the traditional U-Net architecture in order to produce such a ranking. The small number of additional weights to train (the same as the number of predictors) does not impact the computational time, representing a huge advantage compared to traditional methods.

The development and prudent application of climate-based forecasts of seasonal malaria in the Limpopo province in South Africa

Seasonal Climate Forecasting (SCF) in South Africa has a history spanning several decades. During this period a number of SCF systems have been developed for the prediction of seasonal-to-interannual variability of rainfall and surface temperatures. Areas of highest predictability, albeit relatively modest, have also been identified. The north-eastern parts of South Africa that includes the Limpopo province has been demonstrated to be one of the areas of highest SCF skill in the country. Statistical post-processing techniques applied to global climate model output were part of this forecast system development, and were subsequently successfully used in the construction of forecasts systems for applications in sectors which are associated with ENSO-driven climate variability, such as dry-land crop yields and river flows. Here we follow a similar post-model processing approach to test SCF systems for application to the incidence of seasonal malaria in Limpopo. The malaria forecast system introduced here makes use of the seasonal rainfall output fields of one of the North American Multi-Model Ensemble (NMME) climate models, which is then linked statistically through multiple linear regression to observed malaria incidence. The verification results as calculated over a 20-year hindcast period show that the season of highest malaria incidence forecast skill is during the austral mid-summer time of December to February. Moreover, the hindcasts based on the NMME model outscore those of statistical forecast models that separately use Indian and Pacific Ocean sea-surface temperatures as predictors, thus justifying the use of physical global climate models for this kind of application. Additional results indicate that model skill levels may include quasi-decadal variability, that the periods over which forecast verification is performed strongly influences forecast skill, and that poorly predicted malaria seasons may have serious financial implications on public health operations.

Configuration of Statistical Postprocessing Techniques for Improved Low-Level Wind Speed Forecasts in West Texas

Abstract The wind energy industry needs accurate forecasts of wind speeds at turbine hub height and in the rotor layer to accurately predict power output from a wind farm. Current numerical weather prediction (NWP) models struggle to accurately predict low-level winds, partially due to systematic errors within the models due to deficiencies in physics parameterization schemes. These types of errors are addressed in this study with two statistical postprocessing techniques—model output statistics (MOS) and the analog ensemble (AnEn)—to understand the value of each technique in improving rotor-layer wind forecasts. This study is unique in that it compares the techniques using a sonic detection and ranging (SODAR) wind speed dataset that spans the entire turbine rotor layer. This study uses reforecasts from the Weather Research and Forecasting (WRF) Model and observations in west Texas over periods of up to two years to examine the skill added to forecasts when applying both MOS and the AnEn. Different aspects of the techniques are tested, including model horizontal and vertical resolution, number of predictors, and training set length. Both MOS and the AnEn are applied to several levels representing heights in the turbine rotor layer (40, 60, 80, 100, and 120 m). This study demonstrates the degree of improvement that different configurations of each technique provides to raw WRF forecasts, to help guide their use for low-level wind speed forecasts. It was found that both AnEn and MOS show significant improvement over the raw WRF forecasts, but the two methods do not differ significantly from each other.

Comparison of statistical post-processing methods for probabilistic NWP forecasts of solar radiation

The increased usage of solar energy places additional importance on forecasts of solar radiation. Solar panel power production is primarily driven by the amount of solar radiation and it is therefore important to have accurate forecasts of solar radiation. Accurate forecasts that also give information on the forecast uncertainties can help users of solar energy to make better solar radiation based decisions related to the stability of the electrical grid. To achieve this, we apply statistical post-processing techniques that determine relationships between observations of global radiation (made within the KNMI network of automatic weather stations in the Netherlands) and forecasts of various meteorological variables from the numerical weather prediction (NWP) model HARMONIE-AROME (HA) and the atmospheric composition model CAMS. Those relationships are used to produce probabilistic forecasts of global radiation. We compare 7 different statistical post-processing methods, consisting of two parametric and five non-parametric methods. We find that all methods are able to generate probabilistic forecasts that improve the raw global radiation forecast from HA according to the root mean squared error (on the median) and the potential economic value. Additionally, we show how important the predictors are in the different regression methods. We also compare the regression methods using various probabilistic scoring metrics, namely the continuous ranked probability skill score, the Brier skill score and reliability diagrams. We find that quantile regression and generalized random forests generally perform best. In (near) clear sky conditions the non-parametric methods have more skill than the parametric ones.

Assessment of Storm Wind Speed Prediction Using Gridded Bayesian Regression Applied to Historical Events With NCAR's Real‐Time Ensemble Forecast System

AbstractThis study presents the development and application of gridded Bayesian linear regression (GBLR) as a new statistical postprocessing technique to improve deterministic numerical weather prediction of storm wind speed forecasts over the northeast United States. GBLR products are produced by interpolating regression coefficients deduced from modeled‐observed pairs of historical storms at meteorological stations to grid points, thus producing a gridded product. The GBLR model is developed for the 10 members of the National Center for Atmospheric Research (NCAR) real‐time dynamic ensemble prediction system for a database composed of 92 storms, using leave‐one‐storm‐out cross validation. GBLR almost eliminates the bias of the raw deterministic prediction and achieves average coefficient of determination (R2) improvement of 36% and root‐mean‐square error reduction of 29% with respect to the ensemble mean for individual storm forecasts. Moreover, verification using leave‐one‐station‐out cross validation indicates that the GBLR model provides acceptable forecast improvements for grid points where no observations are available. The GBLR technique contributes to improving gridded storm wind speed forecasts using past event‐based data and has the potential to be implemented in real time.

Multi-model seasonal forecasts for the wind energy sector

An assessment of the forecast quality of 10 m wind speed by deterministic and probabilistic verification measures has been carried out using the original raw and two statistical bias-adjusted forecasts in global coupled seasonal climate prediction systems (ECMWF-S4, METFR-S3, METFR-S4 and METFR-S5) for boreal winter (December–February) season over a 22-year period 1991–2012. We follow the standard leave-one-out cross-validation method throughout the work while evaluating the hindcast skills. To minimize the systematic error and obtain more reliable and accurate predictions, the simple bias correction (SBC) which adjusts the systematic errors of model and calibration (Cal), known as the variance inflation technique, methods as the statistical post-processing techniques have been applied. We have also built a multi-model ensemble (MME) forecast assigning equal weights to datasets of each prediction system to further enhance the predictability of the seasonal forecasts. Two MME have been created, the MME4 with all the four prediction systems and MME2 with two better performing systems. Generally, the ECMWF-S4 shows better performance than other individual prediction systems and the MME predictions indicate consistently higher temporal correlation coefficient (TCC) and fair ranked probability skill score (FRPSS) than the individual models. The spatial distribution of significant skill in MME2 prediction is almost similar to that in MME4 prediction. In the aspect of reliability, it is found that the Cal method has more effective improvement than the SBC method. The MME4_Cal predictions are placed in close proximity to the perfect reliability line for both above and below normal categorical events over globe, as compared to the MME2_Cal predictions, due to the increase in ensemble size. To further compare the forecast performance for seasonal variation of wind speed, we have evaluated the skill of the only raw MME2 predictions for all seasons. As a result, we also find that winter season shows better performance than other seasons.

Application of Artificial Neural Networks for Accuracy Enhancements of Real-Time Flood Forecasting in the Imjin Basin

Hydrometeorological forecasts provide future flooding estimates to reduce damages. Despite the advances and progresses in Numerical Weather Prediction (NWP) models, they are still subject to many uncertainties, which cause significant errors forecasting precipitation. Statistical postprocessing techniques can improve forecast skills by reducing the systematic biases in NWP models. Artificial Neural Networks (ANNs) can model complex relationships between input and output data. The application of ANN in water-related research is widely studied; however, there is a lack of studies quantifying the improvement of coupled hydrometeorological model accuracy that use ANN for bias correction of real-time rainfall forecasts. The aim of this study is to evaluate the real-time bias correction of precipitation data, and from a hydrometeorological point of view, an assessment of hydrological model improvements in real-time flood forecasting for the Imjin River (South and North Korea) is performed. The comparison of the forecasted rainfall before and after the bias correction indicated a significant improvement in the statistical error measurement and a decrease in the underestimation of WRF model. The error was reduced remarkably over the Imjin catchment for the accumulated Mean Areal Precipitation (MAP). The performance of the real-time flood forecast improved using the ANN bias correction method.

Multi-Model Approaches for Improving Seasonal Ensemble Streamflow Prediction Scheme with Various Statistical Post-Processing Techniques in the Canadian Prairie Region

Hydrologic models are an approximation of reality, and thus, are not able to perfectly simulate observed streamflow because of various sources of uncertainty. On the other hand, skillful operational hydrologic forecasts are vital in water resources engineering and management for preparedness against flooding and extreme events. Multi-model techniques can be used to help represent and quantify various uncertainties in forecasting. In this paper, we assess the performance of a Multi-model Seasonal Ensemble Streamflow Prediction (MSESP) scheme coupled with statistical post-processing techniques to issue operational uncertainty for the Manitoba Hydrologic Forecasting Centre (HFC). The Ensemble Streamflow Predictions (ESPs) from WATFLOOD and SWAT hydrologic models were used along with four statistical post-processing techniques: Linear Regression (LR), Quantile Mapping (QM), Quantile Model Averaging (QMA), and Bayesian Model Averaging (BMA)]. The quality of MSESP was investigated from April to July with a lead time of three months for the Upper Assiniboine River Basin (UARB) at Kamsack, Canada. While multi-model ESPs coupled with post-processing techniques improve predictability (in general), results suggest that additional avenues for improving the skill and value of seasonal streamflow prediction. Next steps towards an operational ESP system include adding more operationally used models, improving models calibration methods to reduce model bias, increasing ESP sample size, and testing ESP schemes at multiple lead times, which, once developed, will not only help HFCs in Canada but would also help Centers South of the Border.

Combining predictive distributions for the statistical post-processing of ensemble forecasts

Statistical post-processing techniques are now used widely for correcting systematic biases and errors in the calibration of ensemble forecasts obtained from multiple runs of numerical weather prediction models. A standard approach is the ensemble model output statistics (EMOS) method, which results in a predictive distribution that is given by a single parametric law, with parameters that depend on the ensemble members. This article assesses the merits of combining multiple EMOS models based on different parametric families. In four case studies with wind speed and precipitation forecasts from two ensemble prediction systems, we investigate the performances of state of the art forecast combination methods and propose a computationally efficient approach for determining linear pool combination weights. We study the performance of forecast combination compared to that of the theoretically superior but cumbersome estimation of a full mixture model, and assess which degree of flexibility of the forecast combination approach yields the best practical results for post-processing applications.

Adaptive Kalman Filtering for Postprocessing Ensemble Numerical Weather Predictions

Forecasts from numerical weather prediction models suffer from systematic and nonsystematic errors, which originate from various sources such as subgrid-scale variability affecting large scales. Statistical postprocessing techniques can partly remove such errors. Adaptive MOS techniques based on Kalman filters (here called AMOS), are used to sequentially postprocess the forecasts, by continuously updating the correction parameters as new ground observations become available. These techniques, originally proposed for deterministic forecasts, are valuable when long training datasets do not exist. Here, a new adaptive postprocessing technique for ensemble predictions (called AEMOS) is introduced. The proposed method implements a Kalman filtering approach that fully exploits the information content of the ensemble for updating the parameters of the postprocessing equation. A verification study for the region of Campania in southern Italy is performed. Two years (2014–15) of daily meteorological observations of 10-m wind speed and 2-m temperature from 18 ground-based automatic weather stations are used, comparing them with the corresponding COSMO-LEPS ensemble forecasts. It is shown that the proposed adaptive method outperforms the AMOS method, while it shows comparable results to the member-by-member batch postprocessing approach.

Analog‐Based Postprocessing of Navigation‐Related Hydrological Ensemble Forecasts

AbstractInland waterway transport benefits from probabilistic forecasts of water levels as they allow to optimize the ship load and, hence, to minimize the transport costs. Probabilistic state‐of‐the‐art hydrologic ensemble forecasts inherit biases and dispersion errors from the atmospheric ensemble forecasts they are driven with. The use of statistical postprocessing techniques like ensemble model output statistics (EMOS) allows for a reduction of these systematic errors by fitting a statistical model based on training data. In this study, training periods for EMOS are selected based on forecast analogs, i.e., historical forecasts that are similar to the forecast to be verified. Due to the strong autocorrelation of water levels, forecast analogs have to be selected based on entire forecast hydrographs in order to guarantee similar hydrograph shapes. Custom‐tailored measures of similarity for forecast hydrographs comprise hydrological series distance (SD), the hydrological matching algorithm (HMA), and dynamic time warping (DTW). Verification against observations reveals that EMOS forecasts for water level at three gauges along the river Rhine with training periods selected based on SD, HMA, and DTW compare favorably with reference EMOS forecasts, which are based on either seasonal training periods or on training periods obtained by dividing the hydrological forecast trajectories into runoff regimes.