Stochastic Kinetic Energy Backscatter Research Articles

Testing Stochastic and Perturbed Parameter Methods in an Experimental 1-km Warn-on-Forecast System Using NSSL’s Phased-Array Radar Observations

Abstract The success of the National Severe Storms Laboratory’s (NSSL) experimental Warn-on-Forecast System (WoFS) to provide useful probabilistic guidance of severe and hazardous weather is mostly due to the frequent assimilation of observations, especially radar observations. Phased-array radar (PAR) technology, which is a potential candidate to replace the current U.S. operational radar network, would allow for even more rapid assimilation of radar observations by providing full-volumetric scans of the atmosphere every ∼1 min. Based on previous studies, more frequent PAR data assimilation can lead to improved forecasts, but it can also lead to ensemble underdispersion and suboptimal observation assimilation. The use of stochastic and perturbed parameter methods to increase ensemble spread is a potential solution to this problem. In this study, four stochastic and perturbed parameter methods are assessed using a 1-km-scale version of the WoFS and include the stochastic kinetic energy backscatter (SKEB) scheme, the physically based stochastic perturbation (PSP) scheme, a fixed perturbed parameters (FPP) method, and a novel surface-model scheme blending (SMSB) method. Using NSSL PAR observations from the 9 May 2016 tornado outbreak, experiments are conducted to assess the impact of the methods individually, in different combinations, and with different cycling intervals. The results from these experiments reveal the potential benefits of stochastic and perturbed parameter methods for future versions of the WoFS. Stochastic and perturbed parameter methods can lead to more skillful forecasts during periods of storm development. Moreover, a combination of multiple methods can result in more skillful forecasts than using a single method. Significance Statement Phased-array radar technology allows for more frequent assimilation of radar observations into ensemble forecast systems like the experimental Warn-on-Forecast System. However, more frequent radar data assimilation can eventually cause issues for prediction systems due to the lack of ensemble spread. Thus, the purpose of this study is to explore the use of four stochastic and perturbed parameter methods in a next-generation Warn-on-Forecast System to generate ensemble spread and help prevent the issues from frequent radar data assimilation. Results from this study indicate the stochastic and perturbed parameter methods can improve forecasts of storms, especially during storm development.

A new approach to represent model uncertainty in the forecasting of tropical cyclones: The orthogonal nonlinear forcing singular vectors

AbstractTropical cyclone (TC) track forecasting has been considerably improved in recent decades, while TC intensity forecasting remain challenging. In this study, orthogonal nonlinear forcing singular vectors (O‐NFSVs) for emulating the impact of model uncertainties are used to conduct TC ensemble forecasting experiments with the Weather Research and Forecasting (WRF) model, with a focus on improving TC intensity forecasting skill. The O‐NFSVs approach is compared with the traditional stochastic kinetic‐energy backscatter (SKEB) and stochastically perturbed parametrization tendency (SPPT) schemes. The results demonstrate that the O‐NFSVs ensembles generally provide a better representation of the model uncertainties affecting TC intensification, with much better deterministic and probabilistic skills. These results also extend to the ability to forecast TC track, although the perturbations have not been optimized for that specific purpose. The O‐NFSVs are therefore appropriate perturbation structures for describing the uncertainties of the TC intensity and track forecasting and are also favourable for recognizing the rapid intensification process.

The Impact of Stochastic Perturbations in Physics Variables for Predicting Surface Solar Irradiance

We present a probabilistic framework tailored for solar energy applications referred to as the Weather Research and Forecasting-Solar ensemble prediction system (WRF-Solar EPS). WRF-Solar EPS has been developed by introducing stochastic perturbations into the most relevant physical variables for solar irradiance predictions. In this study, we comprehensively discuss the impact of the stochastic perturbations of WRF-Solar EPS on solar irradiance forecasting compared to a deterministic WRF-Solar prediction (WRF-Solar DET), a stochastic ensemble using the stochastic kinetic energy backscatter scheme (SKEBS), and a WRF-Solar multi-physics ensemble (WRF-Solar PHYS). The performances of the four forecasts are evaluated using irradiance retrievals from the National Solar Radiation Database (NSRDB) over the contiguous United States. We focus on the predictability of the day-ahead solar irradiance forecasts during the year of 2018. The results show that the ensemble forecasts improve the quality of the forecasts, compared to the deterministic prediction system, by accounting for the uncertainty derived by the ensemble members. However, the three ensemble systems are under-dispersive, producing unreliable and overconfident forecasts due to a lack of calibration. In particular, WRF-Solar EPS produces less optically thick clouds than the other forecasts, which explains the larger positive bias in WRF-Solar EPS (31.7 W/m2) than in the other models (22.7–23.6 W/m2). This study confirms that the WRF-Solar EPS reduced the forecast error by 7.5% in terms of the mean absolute error (MAE) compared to WRF-Solar DET, and provides in-depth comparisons of forecast abilities with the conventional scientific probabilistic approaches (i.e., SKEBS and a multi-physics ensemble). Guidelines for improving the performance of WRF-Solar EPS in the future are provided.

Multivariate ensemble sensitivity analysis applied for an extreme rainfall over Indian subcontinent

Ensemble sensitivity analysis (ESA) uses sample statistics of ensemble forecasts to estimate relationships between forecast metrics and initial conditions. The ensemble sensitivity analysis is often considered as a simple univariate regression as it includes an approximation of analysis covariance matrix with corresponding diagonal elements. In this work, univariate ensemble sensitivity is extended to multivariate ensemble sensitivity that incorporates the contribution from the full covariance matrix in the sensitivity calculations. The performance of multivariate ensemble sensitivity over univariate is examined for meso- and convective scale ensemble forecasts of a heavy rainfall event that happened over the Chennai city in India in December 2015. The ensemble forecasts and analyses are generated using the Advanced Research - Weather Research and Forecasting (WRF) model Data Assimilation Research Testbed (DART) based Ensemble Kalman Filter (EnKF). Multivariate ensemble sensitivity shows organized sensitivity patterns, while the sensitivity values are found to be broadly distributed in univariate ensemble sensitivity. Both the methods are validated using a perturbed initial condition approach, and the results indicate that the multivariate ensemble sensitivity method is effective in predicting the forecast response closest to the actual model response compared to the univariate ensemble sensitivity. The impact of model error on sensitivity calculations is examined by generating a new set of ensembles that uses the Stochastic Kinetic Energy Backscatter Scheme (SKEBS). In the presence of added model error, the forecast response estimated by multivariate using SKEBS ensembles compares better with the actual response. It is found that the performance of the multivariate approach depends on the optimal choice of localization radius, and if insufficient localization is applied, the spurious long-distance correlation contaminates the performance of the multivariate ensemble sensitivity method. The impact of various forecast lead times on the univariate and multivariate ensemble sensitivity analysis indicates that responses using multivariate ensemble sensitivity are more accurate than univariate, especially at longer lead times when nonlinearity becomes significant. The performance of univariate and multivariate methods in convection-permitting scale is examined by using the high-resolution ensemble forecasts, and it is found that the multivariate sensitivity with localization substantially improves the estimates in finer scales.

The Development of the NCEP Global Ensemble Forecast System Version 12

Abstract The Global Ensemble Forecast System (GEFS) is upgraded to version 12, in which the legacy Global Spectral Model (GSM) is replaced by a model with a new dynamical core—the Finite Volume Cubed-Sphere Dynamical Core (FV3). Extensive tests were performed to determine the optimal model and ensemble configuration. The new GEFS has cubed-sphere grids with a horizontal resolution of about 25 km and an increased ensemble size from 20 to 30. It extends the forecast length from 16 to 35 days to support subseasonal forecasts. The stochastic total tendency perturbation (STTP) scheme is replaced by two model uncertainty schemes: the stochastically perturbed physics tendencies (SPPT) scheme and stochastic kinetic energy backscatter (SKEB) scheme. Forecast verification is performed on a period of more than two years of retrospective runs. The results show that the upgraded GEFS outperforms the operational-at-the-time version by all measures included in the GEFS verification package. The new system has a better ensemble error–spread relationship, significantly improved skills in large-scale environment forecasts, precipitation probability forecasts over CONUS, tropical cyclone track and intensity forecasts, and significantly reduced 2-m temperature biases over North America. GEFSv12 was implemented on 23 September 2020.

Potential of the Coupled WRF/WRF-Hydro Modeling System for Flood Forecasting in the Ouémé River (West Africa)

Since the beginning of the 2000s, most of the West-African countries, particularly Benin, have experienced an increased frequency of extreme flood events. In this study, we focus on the case of the Ouémé river basin in Benin. To investigate flood events in this basin for early warning, the coupled atmosphere–hydrology model system WRF-Hydro is used, and analyzed for the period 2008–2010. Such a coupled model allows exploration of the contribution of atmospheric components into the flood event, and its ability to simulate and predict accurate streamflow. The potential of WRF-Hydro to correctly simulate streamflow in the Ouémé river basin is assessed by forcing the model with operational analysis datasets from the European Centre for Medium-Range Weather Forecasts (ECMWF). Atmospheric and land surface processes are resolved at a spatial resolution of 5 km. The additional surface and subsurface water flow routing are computed at a resolution of 500 m. Key parameters of the hydrological module of WRF-Hydro are calibrated offline and tested online with the coupled WRF-Hydro. The uncertainty of atmospheric modeling on coupled results is assessed with the stochastic kinetic energy backscatter scheme (SKEBS). WRF-Hydro is able to simulate the discharge in the Ouémé river in offline and fully coupled modes with a Kling–Gupta efficiency (KGE) around 0.70 and 0.76, respectively. In the fully coupled mode, the model captures the flood event that occurred in 2010. A stochastic perturbation ensemble of ten members for three rain seasons shows that the coupled model performance in terms of KGE ranges from 0.14 to 0.79. Additionally, an assessment of the soil moisture has been developed. This ability to realistically reproduce observed discharge in the Ouémé river basin demonstrates the potential of the coupled WRF-Hydro modeling system for future flood forecasting applications.

Lateral terrestrial water flow contribution to summer precipitation at continental scale – A comparison between Europe and West Africa with WRF‐Hydro‐tag ensembles

AbstractIt is well accepted that summer precipitation can be altered by soil moisture condition. Coupled land surface – atmospheric models have been routinely used to quantify soil moisture – precipitation feedback processes. However, most of the land surface models (LSMs) assume a vertical soil water transport and neglect lateral terrestrial water flow at the surface and in the subsurface, which potentially reduces the realism of the simulated soil moisture – precipitation feedback. In this study, the contribution of lateral terrestrial water flow to summer precipitation is assessed in two different climatic regions, Europe and West Africa, for the period June–September 2008. A version of the coupled atmospheric‐hydrological model WRF‐Hydro with an option to tag and trace land surface evaporation in the modelled atmosphere, named WRF‐Hydro‐tag, is employed. An ensemble of 30 simulations with terrestrial routing and 30 simulations without terrestrial routing is generated with random realizations of turbulent energy with the stochastic kinetic energy backscatter scheme, for both Europe and West Africa. The ensemble size allows to extract random noise from continental‐scale averaged modelled precipitation. It is found that lateral terrestrial water flow increases the relative contribution of land surface evaporation to precipitation by 3.6% in Europe and 5.6% in West Africa, which enhances a positive soil moisture – precipitation feedback and generates more uncertainty in modelled precipitation, as diagnosed by a slight increase in normalized ensemble spread. This study demonstrates the small but non‐negligible contribution of lateral terrestrial water flow to precipitation at continental scale.

A new stochastic ocean physics package and its application to hybrid‐covariance data assimilation

AbstractGenerating optimal perturbations is a key requirement of several data assimilation schemes. Here, we present a newly developed stochastic physics package for ocean models, implemented in the NEMO ocean general circulation model. The package includes three schemes applied simultaneously: stochastically perturbed parametrization tendencies (SPPT), stochastically perturbed parameters (SPP) and stochastic kinetic energy backscatter (SKEB) schemes. The three schemes allow for different temporal and spatial perturbation scales. Within a limited‐area ocean model configuration, ensemble free‐running simulations were performed to assess the impact and reliability of the schemes. They prove complementary in increasing the ensemble spread at different scales and for different diagnostics. The ensemble spread appears reliable; for instance, it proves consistent with the root‐mean‐square differences with respect to higher‐resolution (sub‐mesoscale) simulations that here represent the “truth” (in the sense that it includes “unresolved physics”). Interestingly, both the SPPT and the SKEB schemes lead to an increase of eddy kinetic energy at small spatial scales (2–10 km), and contribute to modify the ensemble mean state, mitigating warm biases near the thermocline due to the enhancement of the upper ocean vertical mixing. As an application of the stochastic packages, the ensemble anomaly covariances coming from the ensemble free‐running simulations are used to feed large‐scale anisotropic covariances that complement smaller‐scale ones in a hybrid‐covariance regional analysis and forecast system in the Mediterranean Sea. Ensemble‐derived covariances are formulated as slowly varying three‐dimensional low‐resolution empirical orthogonal functions (EOFs). The improvements due to the addition of such covariances to the stationary ones are found significant in real‐data experiments, within verification skill scores against glider profile data, remotely sensed observations and current speed measurements from drifters, radar and moorings.

Towards a Better Design of Convection-Allowing Ensembles for Precipitation Forecasts over Ensenada, Baja California, Mexico

Convective ensembles promise to increase forecast accuracy while at the same time providing information on the probability of the forecast. A vast number of different methods of ensemble creation have been developed over time. Here, initial conditions and model error uncertainties are represented by a convective-allowing ensemble with more than 50 members. The results are analyzed using one case study with relatively high precipitation over Ensenada, Baja California, Mexico. The ensemble members are perturbed using random initial perturbations, breeding, and the Stochastic Kinetic Energy Backscatter parameterization (SKEBS) within the Weather Research and Forecasting (WRF) model. The aim is to improve the high-resolution ensemble design provided in a previous study for the same region by maximizing the spread of an ensemble with low member count. To this end, a comparative analysis of the members is performed using perturbation growth rates and information entropy. In addition, a comparative verification is performed using observations from one automatic meteorological station and satellite-derived precipitation data. It was found that the growth rates and the one-dimensional power spectral density of the initial perturbation fields are clustered depending on each member’s origin and the methods used to generate the breeding members. An inverse relationship was observed between these two variables, which can be useful for selecting appropriate initial condition perturbations. The dynamical injections of energy, introduced as perturbations to the numerical fields by the SKEBS method, were essential to maintain positive growth rates during the simulation period. Evaluation of the information entropy suggests that a selection of a set of members generated by the SKEBS method is best for increasing the ensemble spread while saving computer resources.

Assessment of the Forecast Skill of Multiphysics and Multistochastic Methods within the GRAPES Regional Ensemble Prediction System in the East Asian Monsoon Region

Abstract To more comprehensively and accurately address model uncertainties in the East Asia monsoon region, a single-physics suite, where each ensemble member uses the same set of physics parameterizations as the control member in combination with multiple stochastic schemes, is developed to investigate if the multistochastic schemes that combine different stochastic schemes together can be an alternative to a multiphysics suite, where each ensemble member uses a different set of physics parameterizations (e.g., cumulus convection, boundary layer, surface layer, microphysics, and shortwave and longwave radiation). For this purpose, two experiments are performed for a summer monsoon month over China: one with a multiphysics suite and the other with a single-physics suite combined with multistochastic schemes. Three stochastic schemes are applied: the stochastically perturbed parameterizations (SPP) scheme, consisting of temporally and spatially varying perturbations of 18 parameters in the microphysics, convection, boundary layer, and surface layer parameterization schemes; the stochastically perturbed parameterization tendencies (SPPT) scheme; and the stochastic kinetic energy backscatter (SKEB) scheme. The combination of the three stochastic schemes is compared with the multiphysics suite in the Global and Regional Assimilation and Prediction Enhanced System–Regional Ensemble Prediction System with a horizontal grid spacing of 15 km. Verification results show that, overall, a single-physics suite that combines SPP, SPPT, and SKEB outperforms the multiphysics suite in precipitation verification and verification for upper-air weather variables, 10-m zonal wind, and 2-m temperature in the East Asian monsoon region. The indication is that a single-physics suite combining SPP, SPPT, and SKEB may be an appropriate alternative to a multiphysics suite. This finding lays a foundation for the development and design of future regional and global ensembles.

Sensitivity of a Bowing Mesoscale Convective System to Horizontal Grid Spacing in a Convection-Allowing Ensemble

The bow echo, a mesoscale convective system (MCS) responsible for much hail and wind damage across the United States, is associated with poor skill in convection-allowing numerical model forecasts. Given the decrease in convection-allowing grid spacings within many operational forecasting systems, we investigate the effect of finer resolution on the character of bowing-MCS development in a real-data numerical simulation. Two ensembles were generated: one with a single domain of 3-km horizontal grid spacing, and another nesting a 1-km domain with two-way feedback. Ensemble members were generated from their control member with a stochastic kinetic-energy backscatter scheme, with identical initial and lateral-boundary conditions. Results suggest that resolution reduces hindcast skill of this MCS, as measured with an adaptation of the object-based Structure–Amplitude–Location method. The nested 1-km ensemble produces a faster system than in both the 3-km ensemble and observations. The nested 1-km simulation also produced stronger cold pools, which could be enhanced by the increased (fractal) cloud surface area with higher resolution, allowing more entrainment of dry air and hence increased evaporative cooling.

Sensitivity Analysis of the Spatial Structure of Forecasts in Mesoscale Models: Noncontinuous Model Parameters

AbstractIn a recent work, a sensitivity analysis methodology was described that allows for a visual display of forecast sensitivity, with respect to model parameters, across a gridded forecast field. In that approach, sensitivity was assessed with respect to model parameters that are continuous in nature. Here, the analogous methodology is developed for situations involving noncontinuous (discrete or categorical) model parameters. The method is variance based, and the variances are estimated via a random-effects model based on 2k−p fractional factorial designs and Graeco-Latin square designs. The development is guided by its application to model parameters in the stochastic kinetic energy backscatter scheme (SKEBS), which control perturbations at unresolved, subgrid scales. In addition to the SKEBS parameters, the effect of daily variability and replication (both, discrete factors) are also examined. The forecasts examined are for precipitation, temperature, and wind speed. In this particular application, it is found that the model parameters have a much weaker effect on the forecasts as compared to the effect of daily variability and replication, and that sensitivities, weak or strong, often have a distinctive spatial structure that reflects underlying topography and/or weather patterns. These findings caution against fine-tuning methods that disregard 1) sources of variability other than those due to model parameters, and 2) spatial structure in the forecasts.

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.

2D turbulence closures for the barotropic jet instability simulation

AbstractIn the present work the possibility of turbulence closure applying to improve barotropic jet instability simulation at coarse grid resolutions is considered. This problem is analogous to situations occurring in eddy-permitting ocean models when Rossby radius of deformation is partly resolved on a computational grid. We show that the instability is slowed down at coarse resolutions. As follows from the spectral analysis of linearized equations, the slowdown is caused by the small-scale normal modes damping arising due to numerical approximation errors and nonzero eddy viscosity. In order to accelerate instability growth, stochastic and deterministic kinetic energy backscatter (KEBs) parameterizations and scale-similarity model were applied. Their utilization led to increase of the growth rates of normal modes and thus improve characteristic time and spatial structure of the instability.

Medium‐range global ensemble prediction system at 12 km horizontal resolution and its preliminary validation

AbstractForecasts of high‐impact weather systems require sufficiently high resolution of state‐of‐the‐art numerical models in order to resolve the small‐scale features. At the National Centre for Medium Range Weather Forecasting (NCMRWF) in India, a global ensemble prediction system (EPS—called the NEPS) has been implemented operationally at 12 km horizontal grid size. The NEPS configuration is based on the UK Met Office Global and Regional Ensemble Prediction System (MOGREPS). Initial condition perturbations are generated by the ensemble transform Kalman filter (ETKF) method. Model uncertainties are taken care of by stochastic kinetic energy backscatter (SKEB) and random parameters (RP) schemes. Forecast perturbations obtained from 6 hr short forecasts of 22 ensemble members are updated by the ETKF four times a day (0000, 0600, 1200 and 1800 UTC). Perturbations of surface parameters such as sea‐surface temperature, soil moisture content and soil temperature are also included in the new NEPS. The NEPS aims to provide 10 day probabilistic long forecasts using 23 ensemble members (22 perturbed plus one control). The long forecast provided at 0000 UTC is the combination of 11 members from the 0000 UTC cycle and lagged 11 members from the 1200 UTC cycle. The new NEPS shows improvements in terms of forecast agreement among the members in comparison with the previously operational NEPS that was running at 33 km horizontal grid size with 44 perturbed members. The ratio between the root mean square error of the ensemble mean and ensemble spread as a function of lead time has improved in both the Northern and Southern Hemispheres in the new NEPS.

Diurnal Effects of Regional Soil Moisture Anomalies on the Great Plains Low-Level Jet

AbstractThe Great Plains (GP) low-level jet (GPLLJ) contributes to GP warm season water resources (precipitation), wind resources, and severe weather outbreaks. Past research has shown that synoptic and local mesoscale physical mechanisms (Holton and Blackadar mechanisms) are required to explain GPLLJ variability. Although soil moisture–PBL interactions are central to local mechanistic theories, the diurnal effect of regional soil moisture anomalies on GPLLJ speed, northward penetration, and propensity for severe weather is not well known. In this study, two 31-member WRF-ARW stochastic kinetic energy backscatter scheme ensembles simulate a typical warm season GPLLJ case under CONUS-wide wet and dry soil moisture scenarios. In the GP (24°–48°N, 103°–90°W), ensemble mean differences in sensible heating and PBL height of 25–150 W m−2 and 100–700 m, respectively, at 2100 UTC (afternoon) culminate in GPLLJ 850-hPa wind speed differences of 1–4 m s−1 12 hours later (0900 UTC; early morning). Greater heat accumulation in the daytime PBL over dry soil impacts the east–west geopotential height gradient in the GP (synoptic conditions and Holton mechanism) resulting in a deeper thermal low in the northern GP, causing increases in the geostrophic wind. Enhanced daytime turbulent mixing over dry soil impacts the PBL structure (Blackadar mechanism), leading to increased ageostrophic wind. Overnight geostrophic and ageostrophic winds constructively interact, leading to a faster nocturnal GPLLJ over dry soil. Ensemble differences in CIN (~50–150 J kg−1) and CAPE (~500–1000 J kg−1) have implications for severe weather predictability.

Validation of Snow Multibands in the Comma Head of an Extratropical Cyclone Using a 40-Member Ensemble

Abstract This paper investigates the ability of the Weather Research and Forecasting (WRF) Model in simulating multiple small-scale precipitation bands (multibands) within the extratropical cyclone comma head using four winter storm cases from 2014 to 2017. Using the model output, some physical processes are explored to investigate band prediction. A 40-member WRF ensemble was constructed down to 2-km grid spacing over the Northeast United States using different physics, stochastic physics perturbations, different initial/boundary conditions from the first five perturbed members of the Global Forecast System (GFS) Ensemble Reforecast (GEFSR), and a stochastic kinetic energy backscatter scheme (SKEBS). It was found that 2-km grid spacing is adequate to resolve most snowbands. A feature-based verification is applied to hourly WRF reflectivity fields from each ensemble member and the WSR-88D radar reflectivity at 2-km height above sea level. The Method for Object-Based Diagnostic Evaluation (MODE) tool is used for identifying multibands, which are defined as two or more bands that are 5–20 km in width and that also exhibit a >2:1 aspect ratio. The WRF underpredicts the number of multibands and has a slight eastward position bias. There is no significant difference in frontogenetical forcing, vertical stability, moisture, and vertical shear between the banded versus nonbanded members. Underpredicted band members tend to have slightly stronger frontogenesis than observed, which may be consolidating the bands, but overall there is no clear linkage in ambient condition errors and band errors, thus leaving the source for the band underprediction motivation for future work.

Stochastic and deterministic kinetic energy backscatter parameterizations for simulation of the two-dimensional turbulence

AbstractThe problem of modelling 2D isotropic turbulence in a periodic rectangular domain excited by the forcing pattern of prescribed spatial scale is considered. This setting could be viewed as the simplest analogue of the large scale quasi-2D circulation of the ocean and the atmosphere. Since the direct numerical simulation (DNS) of this problem is usually not possible due to the high computational costs we explore several possibilities to construct coarse approximation models and corresponding subgrid closures (deterministic or stochastic). The necessity of subgrid closures is especially important when the forcing scale is close to the cutoff scale of the coarse model that leads to the significant weakening of the inverse energy cascade and large scale component of the system dynamics.The construction of closures is based on thea priorianalysis of the DNS solution and takes into account the form of a spatial approximation scheme used in a particular coarse model. We show that the statistics of a coarse model could be significantly improved provided a proper combination of deterministic and stochastic closures is used. As a result we are able to restore the shape of the energy spectra of the model. In addition the lagged auto correlations of the model solution as well as its sensitivity to external perturbations fit the characteristics of the DNS model much better.

The Taiwan WRF Ensemble Prediction System: Scientific Description, Model-Error Representation and Performance Results

The Taiwan mesoscale ensemble prediction system (EPS) based on the Weather Research and Forecast model (WRF), also called WEPS, is designed to provide reliable ensemble forecasts for the East Asian region centered on Taiwan. The most skillful ensemble is obtained if model-uncertainty is represented in addition to initial condition uncertainty. A number of numerical prediction experiments are conducted to obtain the optimal configuration consisting of multiple physics-schemes, and two stochastic parameterization schemes: The Stochastic-Kinetic Energy Backscatter (SKEB) Scheme and the Stochastically Perturbed of Physics-Tendency (SPPT) scheme. The performance of the best configuration of WEPS is objectively verified against ECMWF reanalysis and a high-resolution simulation. Further analysis finds little impact of the stochastic schemes on quantitative precipitation forecasts and a single Typhoon case study. We conclude that for best performance over the East Asian domain, stochastic parameterizations alone are not sufficient to represent model-uncertainty and need to be augmented with a multi- physics suite.

A methodology for sensitivity analysis of spatial features in forecasts: the stochastic kinetic energy backscatter scheme

Stochastic kinetic energy backscatter schemes (SKEBSs) are introduced in numerical weather forecast models to represent uncertainties related to unresolved subgrid‐scale processes. These schemes are formulated using a set of parameters that must be determined using physical knowledge and/or to obtain a desired outcome. Here, a methodology is developed for assessing the effect of four factors on spatial features of forecasts simulated by the SKEBS‐enabled Weather Research and Forecasting model. The four factors include two physically motivated SKEBS parameters (the determining amplitude of perturbations applied to stream function and potential temperature tendencies), a purely stochastic element (a seed used in generating random perturbations) and a factor reflecting daily variability. A simple threshold‐based approach for identifying coherent objects within forecast fields is employed, and the effect of the four factors on object features (e.g. number, size and intensity) is assessed. Four object types are examined: upper‐air jet streaks, low‐level jets, precipitation areas and frontal boundaries. The proposed method consists of a set of standard techniques in experimental design, based on the analysis of variance, tailored to sensitivity analysis. More specifically, a Latin square design is employed to reduce the number of model simulations necessary for performing the sensitivity analysis. Fixed effects and random effects models are employed to assess the main effects and the percentage of the total variability explained by the four factors. It is found that the two SKEBS parameters do not have an appreciable and/or statistically significant effect on any of the examined object features.