Representation Of Model Uncertainty Research Articles

Model Uncertainty Representation for a Convection-Allowing Ensemble Prediction System Based on CNOP-P

Formulating model uncertainties for a convection-allowing ensemble prediction system (CAEPS) is a much more challenging problem compared to well-utilized approaches in synoptic weather forecasting. A new approach is proposed and tested through assuming that the model uncertainty should reasonably describe the fast nonlinear error growth of the convection-allowing model, due to the fast developing character and strong nonlinearity of convective events. The Conditional Nonlinear Optimal Perturbation related to Parameters (CNOP-P) is applied in this study. Also, an ensemble approach is adopted to solve the CNOP-P problem. By using five locally developed strong convective events that occurred in pre-rainy season of South China, the most sensitive parameters were detected based on CNOP-P, which resulted in the maximum variations in precipitation. A formulation of model uncertainty is designed by adding stochastic perturbations into these sensitive parameters. Through comparison ensemble experiments by using all the 13 heavy rainfall cases that occurred in the flood season of South China in 2017, the advantages of the CNOP-P-based method are examined and verified by comparing with the well-utilized stochastically perturbed physics tendencies (SPPT) scheme. The results indicate that the CNOP-P-based method has potential in improving the under-dispersive problem of the current CAEPS.

Joint Estimation of Battery Parameters and State of Charge Using an Extended Kalman Filter: A Single-Parameter Tuning Approach

The joint estimation of the state of charge (SoC) and the parameters of a battery model is typically done using nonlinear extensions of the Kalman filter (KF), such as the well-known and widely used extended KF (EKF), in combination with a simple but relatively accurate equivalent-circuit model. The main limitation of the joint EKF is that extensive tuning of the covariance matrices is required when implementing the observer in an application. This tuning is a tedious task with no clear guidelines for the tuning procedure. Furthermore, the joint EKF and its extensions do not explicitly address model uncertainty and sensor noise, which may be the cause for the problematic tuning. In this article, we combine a nonlinear observer with the structured representation of model uncertainty and disturbances as typically used in a robust-observer design approach. Therefore, the joint EKF for simultaneous estimation of SoC and model parameters will be presented for the case that includes cross-correlated noises. Moreover, inspired by the conditions for enforcing convergence of the SoC estimation error, a so-called forgetting factor will be introduced to the joint EKF. These adaptations lead to an observer with a single tuning parameter. The experimental results show that tuning of the proposed observer is straightforward and the performance is similar to a regular joint EKF with a root-mean-square SoC error of 0.5%.

Representing Model Uncertainty by Multi-Stochastic Physics Approaches in the GRAPES Ensemble

To represent model uncertainties more comprehensively, a stochastically perturbed parameterization (SPP) scheme consisting of temporally and spatially varying perturbations of 18 parameters in the microphysics, convection, boundary layer, and surface layer parameterization schemes, as well as the stochastically perturbed parameterization tendencies (SPPT) scheme, and the stochastic kinetic energy backscatter (SKEB) scheme, is applied in the Global and Regional Assimilation and Prediction Enhanced System—Regional Ensemble Prediction System (GRAPES-REPS) to evaluate and compare the general performance of various combinations of multiple stochastic physics schemes. Six experiments are performed for a summer month (1–30 June 2015) over China and multiple verification metrics are used. The results show that: (1) All stochastic experiments outperform the control (CTL) experiment, and all combinations of stochastic parameterization schemes perform better than the single SPP scheme, indicating that stochastic methods can effectively improve the forecast skill, and combinations of multiple stochastic parameterization schemes can better represent model uncertainties; (2) The combination of all three stochastic physics schemes (SPP, SPPT, and SKEB) outperforms any other combination of two schemes in precipitation forecasting and surface and upper-air verification to better represent the model uncertainties and improve the forecast skill; (3) Combining SKEB with SPP and/or SPPT results in a notable increase in the spread and reduction in outliers for the upper-air wind speed. SKEB directly perturbs the wind field and therefore its addition will greatly impact the upper-air wind-speed fields, and it contributes most to the improvement in spread and outliers for wind; (4) The introduction of SPP has a positive added value, and does not lead to large changes in the evolution of the kinetic energy (KE) spectrum at any wavelength; (5) The introduction of SPPT and SKEB would cause a 5%–10% and 30%–80% change in the KE of mesoscale systems, and all three stochastic schemes (SPP, SPPT, and SKEB) mainly affect the KE of mesoscale systems. This study indicates the potential of combining multiple stochastic physics schemes and lays a foundation for the future development and design of regional and global ensembles.

Comparing the impact of environmental conditions and microphysics on the forecast uncertainty of deep convective clouds and hail

Abstract. Severe hailstorms have the potential to damage buildings and crops. However, important processes for the prediction of hailstorms are insufficiently represented in operational weather forecast models. Therefore, our goal is to identify model input parameters describing environmental conditions and cloud microphysics, such as the vertical wind shear and strength of ice multiplication, which lead to large uncertainties in the prediction of deep convective clouds and precipitation. We conduct a comprehensive sensitivity analysis simulating deep convective clouds in an idealized setup of a cloud-resolving model. We use statistical emulation and variance-based sensitivity analysis to enable a Monte Carlo sampling of the model outputs across the multi-dimensional parameter space. The results show that the model dynamical and microphysical properties are sensitive to both the environmental and microphysical uncertainties in the model. The microphysical parameters lead to larger uncertainties in the output of integrated hydrometeor mass contents and precipitation variables. In particular, the uncertainty in the fall velocities of graupel and hail account for more than 65 % of the variance of all considered precipitation variables and for 30 %–90 % of the variance of the integrated hydrometeor mass contents. In contrast, variations in the environmental parameters – the range of which is limited to represent model uncertainty – mainly affect the vertical profiles of the diabatic heating rates.

Dynamic Synchrophasor Estimation by Extended Kalman Filter

Fast synchronized measurements of the phasor, frequency, and rate of change of frequency are expected to be very important for the automated control actions in the smart grid context. In this regard, measurement latency must be kept as short as possible for an effective control implementation when networks characterized by extremely fast dynamics are concerned. Kalman filter (KF)-based estimation algorithms appear to be attractive in this context; however, the conventional implementations suffer from significant limitations in their ability to deal with different types of dynamic conditions due to approximations in the model and in the associated uncertainty. This article proposes an innovative solution, based on an extended KF algorithm using a Taylor model, which is shown to provide improved tracking ability in a vast range of dynamic conditions. A novel element in the proposed technique is the representation of model uncertainty, which takes into account the intrinsic correlation among errors that appear in the state–space description under dynamic conditions. A compatibility check between the forecast and measurement result is also introduced as an effective and metrologically sound approach to detect large unexpected changes in the tracked parameters in order to achieve a fast response of the algorithm also under those conditions. The performance of the algorithm is thoroughly investigated by means of simulation to demonstrate the significant improvement compared to other KF solutions in some conditions of practical relevance.

Identification and sampling of Bayesian posteriors of high-dimensional symmetric positive-definite matrices for data-driven updating of computational models

We propose a probabilistic methodology for data-driven updating of non-Gaussian high-dimensional symmetric positive-definite matrices involved in computational models. We cast the data-driven updating as a Bayesian identification of the symmetric positive-definite matrices. The posterior thus obtained exhibits several hyperparameters that control the dispersion of the prior and the weight of the weighted distance that represents the model-data misfit in the likelihood function. Using an identification criterion that quantifies the agreement between the predictions and the data, we identify these hyperparameters so as to obtain not only improved predictions but also a probabilistic representation of model uncertainties. The numerical implementation of the Bayesian inversion by using a Markov chain Monte Carlo (MCMC) method is computationally challenging because the support of the posterior is restricted to a set of symmetric positive-definite matrices and the dimensionality of the problem grows with the square of the matrix dimension and hence can be high. We thus use a transformation of measure to set up the Markov chain in terms of real-valued state variables whose distribution is Gaussian under the prior but non-Gaussian under the posterior. This transformation of measure allows us to sample the posterior using an Itô-SDE-based MCMC method that inherits computational efficiency in high dimension from leveraging the gradient of the posterior. We apply this methodology to a problem of a data-driven updating of a reduced-order model in computational structural dynamics.

Ensemble size: How suboptimal is less than infinity?

Ensemble forecasts are the method of choice in numerical weather prediction (NWP) to generate probabilistic forecasts. The number of members in an ensemble is an important factor in determining how well a probability distribution of a weather‐related variable can be estimated. Having only a finite number of members reduces the average skill such a probabilistic forecast can have. Increasing ensemble size is therefore desirable; however, ensemble size is also proportional to the computational cost. Having a small ensemble size limits the cost and makes other improvements, such as increases in spatial resolution, feasible.This article examines how average skill measures with metrics such as the continuous ranked probability score, the quantile score, and the Dawid–Sebastiani score converge with ensemble size. A numerical experiment with a 200 member ensemble using the European Centre for Medium‐Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS) model at a resolution of 29 km and a forecast range of 15 days provides data to compare the convergence of probabilistic skill in a current NWP system with theoretical expectations derived for perfectly reliable ensembles with exchangeable members.Results in the first part of the article can help users of operational NWP ensemble forecasts formulate their minimum requirement in terms of ensemble size. In the second part, requirements for scientists who test changes to NWP systems are examined. Using proper scores and fair scores, it is explored whether testing changes in the ensemble forecasts can be meaningful with fewer members than in the operational configuration. Results are based on medium‐range numerical experiments with 50 members. Two experiments test the activation of a representation of model uncertainty and three other experiments test changes in horizontal resolution from 29 to 18 km and from 29 to 45 km.

Toward the Improvement of Subseasonal Prediction in the National Centers for Environmental Prediction Global Ensemble Forecast System

AbstractIn order to provide ensemble‐based subseasonal (weeks 3 and 4) forecasts to support the operational mission of the Climate Prediction Center, National Centers for Environmental Prediction, experiments have been designed through the Subseasonal Experiment (SubX) project to investigate the predictability in both tropical and extratropical regions. The control experiment simply extends the current operational Global Ensemble Forecast System (GEFS; version 11) from 16 to 35 days. In addition to the control, the parallel experiments will be mainly designed to focus on three areas: (1) improving model uncertainty representation for the tropics through stochastic physical perturbations; (2) considering the impact of the ocean by using a two‐tiered sea surface temperature approach; and (3) testing a new scale‐aware convection scheme to improve the model physics for tropical convection and Madden‐Julian Oscillation (MJO) forecasts. All experiments are initialized every 5 days at 0000 UTC during the period of May 2014–May 2016 (25 months). In the tropics, MJO forecast skill has been improved from an average of 12.5 days (control) to nearly 22 days by combining all three modifications to GEFS. In the extratropics, the ensemble mean anomaly correlation of 500‐hPa geopotential height improved over weeks 3 and 4. In addition, the Continuous Ranked Probability Score (of the Northern Hemisphere raw surface temperature (land only) is improved as well. A similar result is found in the Contiguous United States precipitation, although forecast skill is extremely low. Our results imply that calibration may be important and necessary for surface temperature and precipitation forecast for the subseasonal timescale due to the large systematic model errors.

Multi-parametric variational data assimilation for hydrological forecasting

Abstract Ensemble forecasting is increasingly applied in flow forecasting systems to provide users with a better understanding of forecast uncertainty and consequently to take better-informed decisions. A common practice in probabilistic streamflow forecasting is to force deterministic hydrological model with an ensemble of numerical weather predictions. This approach aims at the representation of meteorological uncertainty but neglects uncertainty of the hydrological model as well as its initial conditions. Complementary approaches use probabilistic data assimilation techniques to receive a variety of initial states or represent model uncertainty by model pools instead of single deterministic models. This paper introduces a novel approach that extends a variational data assimilation based on Moving Horizon Estimation to enable the assimilation of observations into multi-parametric model pools. It results in a probabilistic estimate of initial model states that takes into account the parametric model uncertainty in the data assimilation. The assimilation technique is applied to the uppermost area of River Main in Germany. We use different parametric pools, each of them with five parameter sets, to assimilate streamflow data, as well as remotely sensed data from the H-SAF project. We assess the impact of the assimilation in the lead time performance of perfect forecasts (i.e. observed data as forcing variables) as well as deterministic and probabilistic forecasts from ECMWF. The multi-parametric assimilation shows an improvement of up to 23% for CRPS performance and approximately 20% in Brier Skill Scores with respect to the deterministic approach. It also improves the skill of the forecast in terms of rank histogram and produces a narrower ensemble spread.

Stochastic representations of model uncertainties at ECMWF: state of the art and future vision

Members in ensemble forecasts differ due to the representations of initial uncertainties and model uncertainties. The inclusion of stochastic schemes to represent model uncertainties has improved the probabilistic skill of the ECMWF ensemble by increasing reliability and reducing the error of the ensemble mean. Recent progress, challenges and future directions regarding stochastic representations of model uncertainties at ECMWF are described in this article. The coming years are likely to see a further increase in the use of ensemble methods in forecasts and assimilation. This will put increasing demands on the methods used to perturb the forecast model. An area that is receiving greater attention than 5–10 years ago is the physical consistency of the perturbations. Other areas where future efforts will be directed are the expansion of uncertainty representations to the dynamical core and other components of the Earth system, as well as the overall computational efficiency of representing model uncertainty.

Introducing independent patterns into the Stochastically Perturbed Parametrization Tendencies (SPPT) scheme

The Stochastically Perturbed Parametrization Tendencies (SPPT) scheme is used at weather and climate forecasting centres worldwide to represent model uncertainty that arises from simplifications involved in the parametrization process. It uses spatio‐temporally correlated multiplicative noise to perturb the sum of the parametrized tendencies. However, SPPT does not distinguish between different parametrization schemes, which do not necessarily have the same error characteristics. A generalization to SPPT is proposed, whereby the tendency from each parametrization scheme can be perturbed using an independent stochastic pattern. This acknowledges that the forecast errors arising from different parametrizations are not perfectly correlated. Two variations of this ‘independent SPPT’ (iSPPT) approach are tested in the Integrated Forecasting System (IFS). The first perturbs all parametrized tendencies independently, while the second groups tendencies before perturbation. The iSPPT schemes lead to statistically significant improvements in forecast reliability in the Tropics in medium‐range weather forecasts. This improvement can be attributed to a large, beneficial increase in ensemble spread in regions with significant convective activity. The iSPPT schemes also lead to improved forecast skill in the extratropics for a set of cases in which the synoptic initial conditions were more likely to result in European ‘forecast busts’. Longer 13 month simulations are also considered to indicate the effect of iSPPT on the mean climate of the IFS.

Ensemble superparameterization versus stochastic parameterization: A comparison of model uncertainty representation in tropical weather prediction

AbstractStochastic schemes to represent model uncertainty in the European Centre for Medium‐Range Weather Forecasts (ECMWF) ensemble prediction system has helped improve its probabilistic forecast skill over the past decade by both improving its reliability and reducing the ensemble mean error. The largest uncertainties in the model arise from the model physics parameterizations. In the tropics, the parameterization of moist convection presents a major challenge for the accurate prediction of weather and climate. Superparameterization is a promising alternative strategy for including the effects of moist convection through explicit turbulent fluxes calculated from a cloud‐resolving model (CRM) embedded within a global climate model (GCM). In this paper, we compare the impact of initial random perturbations in embedded CRMs, within the ECMWF ensemble prediction system, with stochastically perturbed physical tendency (SPPT) scheme as a way to represent model uncertainty in medium‐range tropical weather forecasts. We especially focus on forecasts of tropical convection and dynamics during MJO events in October–November 2011. These are well‐studied events for MJO dynamics as they were also heavily observed during the DYNAMO field campaign. We show that a multiscale ensemble modeling approach helps improve forecasts of certain aspects of tropical convection during the MJO events, while it also tends to deteriorate certain large‐scale dynamic fields with respect to stochastically perturbed physical tendencies approach that is used operationally at ECMWF.

Towards process‐level representation of model uncertainties: stochastically perturbed parametrizations in the ECMWF ensemble

Ensemble forecasts depend on representations of model uncertainties. Here, we introduce a model uncertainty representation where a novel approach is taken to the established methodology of perturbing model parameters. The Stochastically Perturbed Parametrizations (SPP) scheme applies spatially and temporally varying perturbations to 20 parameters and variables in the ECMWF IFS model. The perturbed quantities are chosen from the IFS parametrizations of (a) turbulent diffusion and subgrid orography, (b) convection, (c) clouds and large‐scale precipitation, and (d) radiation. The perturbations are drawn from prescribed distributions.Numerous configurations of SPP are compared in experiments with the ECMWF ensemble forecasts at TL399 resolution up to 15 day lead times. Halving the standard deviations of the perturbations considerably reduces the ensemble spread. Smaller variations of the standard deviations lead to minor changes to the ensemble spread. Experiments with different space and time correlations for the perturbations suggest optimal correlation scales of 2000 km and 72 h. SPP displays a lower skill for upper‐air variables in the medium range than the current operational model uncertainty scheme Stochastically Perturbed Parametrization Tendencies (SPPT) for a given set of fixed initial‐state perturbations. However, in short ranges the two schemes display similar skill. Moreover, verification against surface observations shows SPP is more skilful than SPPT in 2 m temperature for the first couple of forecast days. We show that the direct perturbation of cloud (and radiation) processes in SPP has a greater impact on radiative fluxes than the indirect perturbation via SPPT. SPP also produces a better model climate for a range of variables when comparing long model integrations with the two schemes, indicating the potential advantage of a physically consistent model uncertainty representation. A comparison of the tendency perturbations introduced by SPP and SPPT suggests that the two schemes represent different aspects of model uncertainty.

Representing model uncertainty in the Met Office convection‐permitting ensemble prediction system and its impact on fog forecasting

Representing model uncertainty in convection‐permitting ensemble prediction systems is a developing area of research. While methods for including variability to account for model uncertainty at the global scales are quite mature, it is not clear that these methods will necessarily be applicable at the convective scale. One such method is the Random Parameter (RP) scheme, where parameters from the physics parametrizations are perturbed at regular intervals throughout the forecast. In this work, we adapt the RP scheme to represent model uncertainty in the Met Office's convection‐permitting ensemble prediction system for the UK (MOGREPS‐UK). The revised version of the RP scheme is applied to a sub‐set of model parameters, chosen to target specific physical processes relevant to the UK forecast. Objective verification scores from two one‐month trials show particular improvements for visibility and surface temperature when the RP scheme is used. Application of the RP scheme results in a modest increase in the ensemble spread for all surface parameters. The results of low‐visibility case‐studies show that applying the RP scheme enables the ensemble to capture observed fog events otherwise missed by the forecast. Overall, the RP scheme has a positive effect on MOGREPS‐UK, and demonstrates the benefit of schemes that target known areas of model uncertainty.

Characteristic soil strength for axial pile capacity and its estimation with confidence for offshore applications

Many offshore design codes require the characteristic soil strength for axial pile capacity to be estimated with caution or conservatism, i.e. – in statistical terms – it has to be estimated with confidence. This study is concerned with a reliability-based calibration of the necessary minimum confidence for such estimation. The study demonstrates how to estimate characteristic soil strength for axial pile capacity with confidence and provides an approach to such estimation that will render an incentive to obtain more soil strength data and thereby give credit to the geotechnical designer who opts to test more. The study capitalizes on existing load and resistance models for an offshore example pile from the literature and refers to a number of relevant offshore foundation design codes. In order to accomplish the purpose, a number of prerequisites for a successful study are dealt with before the confidence calibration itself is presented.A suitable approach to represent model uncertainty associated with axial pile capacity predictions is presented and implemented in the reliability analyses that are used for the calibrations. The approach implies that the standard deviation of the ratio between true and predicted capacity is represented as a function of the pile length rather than as a constant. This approach is supported both by theory and by data.Based on stochastic models for load and resistance in conjunction with a method for prediction of axial pile capacity, a second-order reliability analysis of the example pile is carried out. With an assumption of perfect knowledge of the soil strength, with characteristic soil strength defined as the mean value and with prescribed load factors for permanent and environmental loads, the necessary requirement for the material factor on the characteristic soil strength is calibrated by tuning the reliability analysis to meet a prescribed target failure probability.With the calibrated material factor kept unchanged, the reliability analysis is repeated, now with the stochastic model for soil strength altered to include statistical uncertainty owing to limited soil data. The value of the characteristic soil strength is adjusted downward until the result of the reliability analysis again meets the prescribed target failure probability. The resulting value of the characteristic soil strength is interpreted as “the conservatively assessed value” to be used in design when soil data are limited and this value is subsequently used to find the corresponding minimum confidence for characteristic value estimation by capitalizing on the properties of the Student’s t distribution. Results are presented for target annual failure probabilities in the range 10−5–10−4.

Oceanic Stochastic Parameterizations in a Seasonal Forecast System

Stochastic parameterization provides a methodology for representing model uncertainty in ensemble forecasts. Here the impact on forecast reliability over seasonal time scales of three existing stochastic parameterizations in the ocean component of a coupled model is studied. The relative impacts of these schemes upon the ocean mean state and ensemble spread are analyzed. The oceanic variability induced by the atmospheric forcing of the coupled system is, in most regions, the major source of ensemble spread. The largest impact on spread and bias came from the stochastically perturbed parameterization tendency (SPPT) scheme, which has proven particularly effective in the atmosphere. The key regions affected are eddy-active regions, namely, the western boundary currents and the Southern Ocean where ensemble spread is increased. However, unlike its impact in the atmosphere, SPPT in the ocean did not result in a significant decrease in forecast error on seasonal time scales. While there are good grounds for implementing stochastic schemes in ocean models, the results suggest that they will have to be more sophisticated. Some suggestions for next-generation stochastic schemes are made.

Comparison of methods used for quantifying prediction interval in artificial neural network hydrologic models

The application of artificial neural network (ANN) has gained significant interest while modeling various hydrologic processes. The main reason is the ANN models have produced promising results without the detailed information of watershed characteristics as required in physics based models. Still, the uncertainty in ANN models is a major issue that cannot be ignored. There could be different forms to represent model uncertainty, in which quantification of prediction interval for the model output has been mostly reported. In this paper, three different methods [i.e. Bootstrap method, Bayesian Approach and Prediction Interval (PI) method] were employed for quantifying the prediction interval in ANN models. The modeling procedure presented in this paper, is illustrated through river flow forecasting using the data collected from Kolar basin, India. The prediction interval was quantified using the measures such as percentage of coverage and average width. The comparison between these methods indicated that PI method has resulted in relatively less prediction and parameter uncertainty, besides the improved model performance. In addition, the PI method produced accurate prediction of hydrograph peak, which is a general concern in ANN models.

A Hybrid Global Ocean Data Assimilation System at NCEP

Abstract Seasonal forecasting with a coupled model requires accurate initial conditions for the ocean. A hybrid data assimilation has been implemented within the National Centers for Environmental Prediction (NCEP) Global Ocean Data Assimilation System (GODAS) as a future replacement of the operational three-dimensional variational data assimilation (3DVar) method. This Hybrid-GODAS provides improved representation of model uncertainties by using a combination of dynamic and static background error covariances, and by using an ensemble forced by different realizations of atmospheric surface conditions. An observing system simulation experiment (OSSE) is presented spanning January 1991 to January 1999, with a bias imposed on the surface forcing conditions to emulate an imperfect model. The OSSE compares the 3DVar used by the NCEP Climate Forecast System (CFSv2) with the new hybrid, using simulated in situ ocean observations corresponding to those used for the NCEP Climate Forecast System Reanalysis (CFSR). The Hybrid-GODAS reduces errors for all prognostic model variables over the majority of the experiment duration, both globally and regionally. Compared to an ensemble Kalman filter (EnKF) used alone, the hybrid further reduces errors in the tropical Pacific. The hybrid eliminates growth in biases of temperature and salinity present in the EnKF and 3DVar, respectively. A preliminary reanalysis using real data shows that reductions in errors and biases are qualitatively similar to the results from the OSSE. The Hybrid-GODAS is currently being implemented as the ocean component in a prototype next-generation CFSv3, and will be used in studies by the Climate Prediction Center to evaluate impacts on ENSO prediction.

Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization*

Abstract It is now acknowledged that representing model uncertainty in atmospheric simulators is essential for the production of reliable probabilistic forecasts, and a number of different techniques have been proposed for this purpose. This paper presents new perturbed parameter schemes for use in the European Centre for Medium-Range Weather Forecasts (ECMWF) convection scheme. Two types of scheme are developed and implemented. Both schemes represent the joint uncertainty in four of the parameters in the convection parameterization scheme, which was estimated using the Ensemble Prediction and Parameter Estimation System (EPPES). The first scheme developed is a fixed perturbed parameter scheme, where the values of uncertain parameters are varied between ensemble members, but held constant over the duration of the forecast. The second is a stochastically varying perturbed parameter scheme. The performance of these schemes was compared to the ECMWF operational stochastic scheme, stochastically perturbed parameterization tendencies (SPPT), and to a model that does not represent uncertainty in convection. The skill of probabilistic forecasts made using the different models was evaluated. While the perturbed parameter schemes improve on the stochastic parameterization in some regards, the SPPT scheme outperforms the perturbed parameter approaches when considering forecast variables that are particularly sensitive to convection. Overall, SPPT schemes are the most skillful representations of model uncertainty owing to convection parameterization.

단기 앙상블 예보에서 모형의 불확실성 표현: 태풍 루사

The most objective way to overcome the limitation of numerical weather prediction model is to represent the uncertainty of prediction by introducing probabilistic forecast. The uncertainty of the numerical weather prediction system developed due to the parameterization of unresolved scale motions and the energy losses from the sub-scale physical processes. In this study, we focused on the growth of model errors. We performed ensemble forecast to represent model uncertainty. By employing the multi-physics scheme (PHYS) and the stochastic kinetic energy backscatter scheme (SKEBS) in simulating typhoon Rusa (2002), we assessed the performance level of the two schemes. The both schemes produced better results than the control run did in the ensemble mean forecast of the track. The results using PHYS improved by 28% and those based on SKEBS did by 7%. Both of the ensemble mean errors of the both schemes increased rapidly at the forecast time 84 hrs. The both ensemble spreads increased gradually during integration. The results based on SKEBS represented model errors very well during the forecast time of 96 hrs. After the period, it produced an under-dispersive pattern. The simulation based on PHYS overestimated the ensemble mean error during integration and represented the real situation well at the forecast time of 120 hrs. The displacement speed of the typhoon based on PHYS was closest to the best track, especially after landfall. In the sensitivity tests of the model uncertainty of SKEBS, ensemble mean forecast was sensitive to the physics parameterization. By adjusting the forcing parameter of SKEBS, the default experiment improved in the ensemble spread, ensemble mean errors, and moving speed.