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- Author or Editor: Stéphane Vannitsem x
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Abstract
A hydrological ensemble prediction system, integrating a water balance model with ensemble precipitation forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS), is evaluated for two Belgian catchments. The skill of streamflow forecast for high flows is analyzed using a 6-yr period of archived EPS forecasts. The probabilistic skill of this hydrological prediction system is much better than the one based on historical precipitation inputs and extends beyond 9 days for both catchments. The skill is larger in winter than in summer. The use of this approach for operational forecasts is briefly discussed.
Abstract
A hydrological ensemble prediction system, integrating a water balance model with ensemble precipitation forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS), is evaluated for two Belgian catchments. The skill of streamflow forecast for high flows is analyzed using a 6-yr period of archived EPS forecasts. The probabilistic skill of this hydrological prediction system is much better than the one based on historical precipitation inputs and extends beyond 9 days for both catchments. The skill is larger in winter than in summer. The use of this approach for operational forecasts is briefly discussed.
Abstract
In data assimilation, observations are combined with the dynamics to get an estimate of the actual state of a natural system. The knowledge of the dynamics, under the form of a model, is unavoidably incomplete and model error affects the prediction accuracy together with the error in the initial condition. The variational assimilation theory provides a framework to deal with model error along with the uncertainties coming from other sources entering the state estimation. Nevertheless, even if the problem is formulated as Gaussian, accounting for model error requires the estimation of its covariances and correlations, which are difficult to estimate in practice, in particular because of the large system dimension and the lack of enough observations. Model error has been therefore either neglected or assumed to be an uncorrelated noise. In the present work, an approach to account for a deterministic model error in the variational assimilation is presented. Equations for its correlations are first derived along with an approximation suitable for practical applications. Based on these considerations, a new four-dimensional variational data assimilation (4DVar) weak-constraint algorithm is formulated and tested in the context of a linear unstable system and of the three-component Lorenz model, which has chaotic dynamics. The results demonstrate that this approach is superior in skill to both the strong-constraint and a weak-constraint variational assimilation that employs the uncorrelated noise model error assumption.
Abstract
In data assimilation, observations are combined with the dynamics to get an estimate of the actual state of a natural system. The knowledge of the dynamics, under the form of a model, is unavoidably incomplete and model error affects the prediction accuracy together with the error in the initial condition. The variational assimilation theory provides a framework to deal with model error along with the uncertainties coming from other sources entering the state estimation. Nevertheless, even if the problem is formulated as Gaussian, accounting for model error requires the estimation of its covariances and correlations, which are difficult to estimate in practice, in particular because of the large system dimension and the lack of enough observations. Model error has been therefore either neglected or assumed to be an uncorrelated noise. In the present work, an approach to account for a deterministic model error in the variational assimilation is presented. Equations for its correlations are first derived along with an approximation suitable for practical applications. Based on these considerations, a new four-dimensional variational data assimilation (4DVar) weak-constraint algorithm is formulated and tested in the context of a linear unstable system and of the three-component Lorenz model, which has chaotic dynamics. The results demonstrate that this approach is superior in skill to both the strong-constraint and a weak-constraint variational assimilation that employs the uncorrelated noise model error assumption.
Abstract
Extended logistic regression is used to calibrate areal precipitation forecasts over two small catchments in Belgium computed with the European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS) between 2006 and 2010. The parameters of the postprocessing are estimated from the hindcast database, characterized by a much lower number of members (5) than the EPS (51). Therefore, the parameters have to be corrected for predictor uncertainties. They have been fitted on the 51-member EPS ensembles, on 5-member subensembles drawn from the same EPS, and on the 5-member hindcasts. For small ensembles, a simple “regression calibration” method by which the uncertain predictors are corrected has been applied. The different parameter sets have been compared, and the corresponding extended logistic regressions have been applied to the 51-member EPS. The forecast probabilities have then been validated using rain gauge data and compared with the raw EPS. In addition, the calibrated distributions are also used to modify the ensembles of precipitation traces.
The postprocessing with the extended logistic regression is shown to improve the continuous ranked probability skill score relative to the raw ensemble, and the regression calibration to remove a large portion of the bias in parameter estimation with small ensembles. With a training phase limited to a 5-week moving window, the benefit lasts for the first 2 forecast days in winter and the first 5 or 6 days in summer. In general, substantial improvements of the mean error and of the continuous ranked probability score have been shown.
Abstract
Extended logistic regression is used to calibrate areal precipitation forecasts over two small catchments in Belgium computed with the European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS) between 2006 and 2010. The parameters of the postprocessing are estimated from the hindcast database, characterized by a much lower number of members (5) than the EPS (51). Therefore, the parameters have to be corrected for predictor uncertainties. They have been fitted on the 51-member EPS ensembles, on 5-member subensembles drawn from the same EPS, and on the 5-member hindcasts. For small ensembles, a simple “regression calibration” method by which the uncertain predictors are corrected has been applied. The different parameter sets have been compared, and the corresponding extended logistic regressions have been applied to the 51-member EPS. The forecast probabilities have then been validated using rain gauge data and compared with the raw EPS. In addition, the calibrated distributions are also used to modify the ensembles of precipitation traces.
The postprocessing with the extended logistic regression is shown to improve the continuous ranked probability skill score relative to the raw ensemble, and the regression calibration to remove a large portion of the bias in parameter estimation with small ensembles. With a training phase limited to a 5-week moving window, the benefit lasts for the first 2 forecast days in winter and the first 5 or 6 days in summer. In general, substantial improvements of the mean error and of the continuous ranked probability score have been shown.
Abstract
The ensemble spread is often used as a measure of forecast quality or uncertainty. However, it is not clear whether the spread is a good measure of uncertainty and how the spread–error relationship can be properly assessed. Even for perfectly reliable forecasts the error for a given spread varies considerably in amplitude and the spread–error relationship is therefore strongly heteroscedastic. This implies that the forecast of the uncertainty based only on the knowledge of spread should itself be probabilistic.
Simple probabilistic models for the prediction of the error as a function of the spread are introduced and evaluated for different spread–error metrics. These forecasts can be verified using probabilistic scores and a methodology is proposed to determine what the impact is of estimating uncertainty based on the spread only. A new method is also proposed to verify whether the flow-dependent spread is a realistic indicator of uncertainty. This method cancels the heteroscedasticity by a logarithmic transformation of both spread and error, after which a linear regression can be applied. An ensemble system can be identified as perfectly reliable with respect to its spread.
The approach is tested on the ECMWF Ensemble Prediction System over Europe. The use of spread only does not lead to skill degradation, and replacing the raw ensemble by a Gaussian distribution consistently improves scores. The influences of non-Gaussian ensemble statistics, small ensemble sizes, limited predictability, and different spread–error metrics are investigated and the relevance of binning is discussed. The upper-level spread–error relationship is consistent with a perfectly reliable system for intermediate lead times.
Abstract
The ensemble spread is often used as a measure of forecast quality or uncertainty. However, it is not clear whether the spread is a good measure of uncertainty and how the spread–error relationship can be properly assessed. Even for perfectly reliable forecasts the error for a given spread varies considerably in amplitude and the spread–error relationship is therefore strongly heteroscedastic. This implies that the forecast of the uncertainty based only on the knowledge of spread should itself be probabilistic.
Simple probabilistic models for the prediction of the error as a function of the spread are introduced and evaluated for different spread–error metrics. These forecasts can be verified using probabilistic scores and a methodology is proposed to determine what the impact is of estimating uncertainty based on the spread only. A new method is also proposed to verify whether the flow-dependent spread is a realistic indicator of uncertainty. This method cancels the heteroscedasticity by a logarithmic transformation of both spread and error, after which a linear regression can be applied. An ensemble system can be identified as perfectly reliable with respect to its spread.
The approach is tested on the ECMWF Ensemble Prediction System over Europe. The use of spread only does not lead to skill degradation, and replacing the raw ensemble by a Gaussian distribution consistently improves scores. The influences of non-Gaussian ensemble statistics, small ensemble sizes, limited predictability, and different spread–error metrics are investigated and the relevance of binning is discussed. The upper-level spread–error relationship is consistent with a perfectly reliable system for intermediate lead times.
Abstract
In this paper, a new nonlinear forcing singular vector (NFSV) approach is proposed to provide mutually independent optimally combined modes of initial perturbations and model perturbations (C-NFSVs) in ensemble forecasts. The C-NFSVs are a group of optimally growing structures that take into account the impact of the interaction between the initial errors and the model errors effectively, generalizing the original NFSV for simulations of the impact of the model errors. The C-NFSVs method is tested in the context of the Lorenz-96 model to demonstrate its potential to improve ensemble forecast skills. This method is compared with the orthogonal conditional nonlinear optimal perturbations (O-CNOPs) method for estimating only the initial uncertainties and the orthogonal NFSVs (O-NFSVs) for estimating only the model uncertainties. The results demonstrate that when both the initial perturbations and model perturbations are introduced in the forecasting system, the C-NFSVs are much more capable of achieving higher ensemble forecasting skills. The use of a deep learning approach as a remedy for the expensive computational costs of the C-NFSVs is evaluated. The results show that learning the impact of the C-NFSVs on the ensemble provides a useful and efficient alternative for the operational implementation of C-NFSVs in forecasting suites dealing with the combined effects of the initial errors and the model errors.
Significance Statement
A new ensemble forecasting method for dealing with combined effects of initial errors and model errors, i.e., the C-NFSVs, is proposed, which is an extension of the NFSV approach for simulating the model error effects in ensemble forecasts. The C-NFSVs provide mutually independent optimally combined modes of initial perturbations and model perturbations. This new method is tested for generating ensemble forecasts in the context of the Lorenz-96 model, and there are indications that the optimally growing structures may provide reliable ensemble forecasts. Furthermore, it is found that a hybrid dynamical–deep learning approach could be a potential avenue for real-time ensemble forecasting systems when perturbations combine the impact of the initial and the model errors.
Abstract
In this paper, a new nonlinear forcing singular vector (NFSV) approach is proposed to provide mutually independent optimally combined modes of initial perturbations and model perturbations (C-NFSVs) in ensemble forecasts. The C-NFSVs are a group of optimally growing structures that take into account the impact of the interaction between the initial errors and the model errors effectively, generalizing the original NFSV for simulations of the impact of the model errors. The C-NFSVs method is tested in the context of the Lorenz-96 model to demonstrate its potential to improve ensemble forecast skills. This method is compared with the orthogonal conditional nonlinear optimal perturbations (O-CNOPs) method for estimating only the initial uncertainties and the orthogonal NFSVs (O-NFSVs) for estimating only the model uncertainties. The results demonstrate that when both the initial perturbations and model perturbations are introduced in the forecasting system, the C-NFSVs are much more capable of achieving higher ensemble forecasting skills. The use of a deep learning approach as a remedy for the expensive computational costs of the C-NFSVs is evaluated. The results show that learning the impact of the C-NFSVs on the ensemble provides a useful and efficient alternative for the operational implementation of C-NFSVs in forecasting suites dealing with the combined effects of the initial errors and the model errors.
Significance Statement
A new ensemble forecasting method for dealing with combined effects of initial errors and model errors, i.e., the C-NFSVs, is proposed, which is an extension of the NFSV approach for simulating the model error effects in ensemble forecasts. The C-NFSVs provide mutually independent optimally combined modes of initial perturbations and model perturbations. This new method is tested for generating ensemble forecasts in the context of the Lorenz-96 model, and there are indications that the optimally growing structures may provide reliable ensemble forecasts. Furthermore, it is found that a hybrid dynamical–deep learning approach could be a potential avenue for real-time ensemble forecasting systems when perturbations combine the impact of the initial and the model errors.
Abstract
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.
Abstract
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.
Abstract
Accurate streamflow simulations rely on good estimates of the catchment-scale soil moisture distribution. Here, we evaluated the potential of Sentinel-1 backscatter data assimilation (DA) to improve soil moisture and streamflow estimates. Our DA system consisted of the Noah-MP land surface model coupled to the HyMAP river routing model and the water cloud model as a backscatter observation operator. The DA system was set up at 0.01° resolution for two contrasting catchments in Belgium: (i) the Demer catchment dominated by agriculture and (ii) the Ourthe catchment dominated by mixed forests. We present the results of two experiments with an ensemble Kalman filter updating either soil moisture only or soil moisture and leaf area index (LAI). The DA experiments covered the period from January 2015 through August 2021 and were evaluated with independent rainfall error estimates based on station data, LAI from optical remote sensing, soil moisture retrievals from passive microwave observations, and streamflow measurements. Our results indicate that the assimilation of Sentinel-1 backscatter observations can partly correct errors in surface soil moisture due to rainfall errors and overall improve surface soil moisture estimates. However, updating soil moisture and LAI simultaneously did not bring any benefit over updating soil moisture only. Our results further indicate that streamflow estimates can be improved through Sentinel-1 DA in a catchment with strong soil moisture–runoff coupling, as observed for the Ourthe catchment, suggesting that there is potential for Sentinel-1 DA even for forested catchments.
Significance Statement
The purpose of this study is to improve streamflow estimation by integrating soil moisture information from satellite observations into a hydrological modeling framework. This is important preparatory work for operational centers that are responsible for producing the most accurate flood forecasts for the society. Our results provide new insights into how and where streamflow forecasting could benefit from high-spatial-resolution Sentinel-1 radar backscatter observations.
Abstract
Accurate streamflow simulations rely on good estimates of the catchment-scale soil moisture distribution. Here, we evaluated the potential of Sentinel-1 backscatter data assimilation (DA) to improve soil moisture and streamflow estimates. Our DA system consisted of the Noah-MP land surface model coupled to the HyMAP river routing model and the water cloud model as a backscatter observation operator. The DA system was set up at 0.01° resolution for two contrasting catchments in Belgium: (i) the Demer catchment dominated by agriculture and (ii) the Ourthe catchment dominated by mixed forests. We present the results of two experiments with an ensemble Kalman filter updating either soil moisture only or soil moisture and leaf area index (LAI). The DA experiments covered the period from January 2015 through August 2021 and were evaluated with independent rainfall error estimates based on station data, LAI from optical remote sensing, soil moisture retrievals from passive microwave observations, and streamflow measurements. Our results indicate that the assimilation of Sentinel-1 backscatter observations can partly correct errors in surface soil moisture due to rainfall errors and overall improve surface soil moisture estimates. However, updating soil moisture and LAI simultaneously did not bring any benefit over updating soil moisture only. Our results further indicate that streamflow estimates can be improved through Sentinel-1 DA in a catchment with strong soil moisture–runoff coupling, as observed for the Ourthe catchment, suggesting that there is potential for Sentinel-1 DA even for forested catchments.
Significance Statement
The purpose of this study is to improve streamflow estimation by integrating soil moisture information from satellite observations into a hydrological modeling framework. This is important preparatory work for operational centers that are responsible for producing the most accurate flood forecasts for the society. Our results provide new insights into how and where streamflow forecasting could benefit from high-spatial-resolution Sentinel-1 radar backscatter observations.
Abstract
Statistical postprocessing techniques are nowadays key components of the forecasting suites in many national meteorological services (NMS), with, for most of them, the objective of correcting the impact of different types of errors on the forecasts. The final aim is to provide optimal, automated, seamless forecasts for end users. Many techniques are now flourishing in the statistical, meteorological, climatological, hydrological, and engineering communities. The methods range in complexity from simple bias corrections to very sophisticated distribution-adjusting techniques that incorporate correlations among the prognostic variables. The paper is an attempt to summarize the main activities going on in this area from theoretical developments to operational applications, with a focus on the current challenges and potential avenues in the field. Among these challenges is the shift in NMS toward running ensemble numerical weather prediction (NWP) systems at the kilometer scale that produce very large datasets and require high-density high-quality observations, the necessity to preserve space–time correlation of high-dimensional corrected fields, the need to reduce the impact of model changes affecting the parameters of the corrections, the necessity for techniques to merge different types of forecasts and ensembles with different behaviors, and finally the ability to transfer research on statistical postprocessing to operations. Potential new avenues are also discussed.
Abstract
Statistical postprocessing techniques are nowadays key components of the forecasting suites in many national meteorological services (NMS), with, for most of them, the objective of correcting the impact of different types of errors on the forecasts. The final aim is to provide optimal, automated, seamless forecasts for end users. Many techniques are now flourishing in the statistical, meteorological, climatological, hydrological, and engineering communities. The methods range in complexity from simple bias corrections to very sophisticated distribution-adjusting techniques that incorporate correlations among the prognostic variables. The paper is an attempt to summarize the main activities going on in this area from theoretical developments to operational applications, with a focus on the current challenges and potential avenues in the field. Among these challenges is the shift in NMS toward running ensemble numerical weather prediction (NWP) systems at the kilometer scale that produce very large datasets and require high-density high-quality observations, the necessity to preserve space–time correlation of high-dimensional corrected fields, the need to reduce the impact of model changes affecting the parameters of the corrections, the necessity for techniques to merge different types of forecasts and ensembles with different behaviors, and finally the ability to transfer research on statistical postprocessing to operations. Potential new avenues are also discussed.
