Judith Berner

A Spectral Stochastic Kinetic Energy Backscatter Scheme and Its Impact on Flow-Dependent Predictability in the ECMWF Ensemble Prediction System

Understanding model error in state-of-the-art numerical weather prediction models and representing its impact on flow-dependent predictability remains a complex and mostly unsolved problem. Here, a spectral stochastic kinetic energy backscatter scheme is used to simulate upscale-propagating errors caused by unresolved subgrid-scale processes. For this purpose, stochastic streamfunction perturbations are generated by autoregressive processes in spectral space and injected into regions where numerical integration schemes and parameterizations in the model lead to excessive systematic kinetic energy loss. It is demonstrated how output from coarse-grained high-resolution models can be used to inform the parameters of such a scheme. The performance of the spectral backscatter scheme is evaluated in the ensemble prediction system of the European Centre for Medium-Range Weather Forecasts. Its implementation in conjunction with reduced initial perturbations results in a better spread‐error relationship, more realistic kinetic-energy spectra, a better representation of forecast-error growth, improved flow-dependent predictability, improved rainfall forecasts, and better probabilistic skill. The improvement is most pronounced in the tropics and for largeanomaly events. It is found that whereas a simplified scheme assuming a constant dissipation rate already has some positive impact, the best results are obtained for flow-dependent formulations of the unresolved processes.

Model Uncertainty in a Mesoscale Ensemble Prediction System: Stochastic versus Multiphysics Representations

AbstractA multiphysics and a stochastic kinetic-energy backscatter scheme are employed to represent model uncertainty in a mesoscale ensemble prediction system using the Weather Research and Forecasting model. Both model-error schemes lead to significant improvements over the control ensemble system that is simply a downscaled global ensemble forecast with the same physics for each ensemble member. The improvements are evident in verification against both observations and analyses, but different in some details. Overall the stochastic kinetic-energy backscatter scheme outperforms the multiphysics scheme, except near the surface. Best results are obtained when both schemes are used simultaneously, indicating that the model error can best be captured by a combination of multiple schemes.

Impact of a quasi-stochastic cellular automaton backscatter scheme on the systematic error and seasonal prediction skill of a global climate model

The impact of a nonlinear dynamic cellular automaton (CA) model, as a representation of the partially stochastic aspects of unresolved scales in global climate models, is studied in the European Centre for Medium Range Weather Forecasts coupled ocean–atmosphere model. Two separate aspects are discussed: impact on the systematic error of the model, and impact on the skill of seasonal forecasts. Significant reductions of systematic error are found both in the tropics and in the extratropics. Such reductions can be understood in terms of the inherently nonlinear nature of climate, in particular how energy injected by the CA at the near-grid scale can backscatter nonlinearly to larger scales. In addition, significant improvements in the probabilistic skill of seasonal forecasts are found in terms of a number of different variables such as temperature, precipitation and sea-level pressure. Such increases in skill can be understood both in terms of the reduction of systematic error as mentioned above, and in terms of the impact on ensemble spread of the CAs representation of inherent model uncertainty.

Linking Nonlinearity and Non-Gaussianity of Planetary Wave Behavior by the Fokker–Planck Equation

Abstract To link prominent nonlinearities in the dynamics of 500-hPa geopotential heights to non-Gaussian features in their probability density, a nonlinear stochastic model of atmospheric planetary wave behavior is developed. An analysis of geopotential heights generated by extended integrations of a GCM suggests that a stochastic model and its associated Fokker–Planck equation call for a nonlinear drift and multiplicative noise. All calculations are carried out in the reduced phase space spanned by the leading EOFs. It is demonstrated that this nonlinear stochastic model of planetary wave behavior captures the non-Gaussian features in the probability density function of atmospheric states to a remarkable degree. Moreover, it not only predicts global temporal characteristics, but also the nonlinear, state-dependent divergence of state trajectories. In the context of this empirical modeling, it is discussed on which time scale a stochastic model is expected to approximate the behavior of a continuous dete...

The U.S. Air Force Weather Agency's mesoscale ensemble: scientific description and performance results

This work evaluates several techniques to account for mesoscale initial-condition (IC) and model uncertainty in a short-range ensemble prediction system based on the Weather Research and Forecast (WRF) model. A scientific description and verification of several candidate methods for implementation in the U.S. Air Force Weather Agency mesoscale ensemble is presented. Model perturbation methods tested include multiple parametrization suites, landsurface property perturbations, perturbations to parameters within physics schemes and stochastic ‘backscatter’ streamfunction perturbations. IC perturbations considered include perturbed observations in 10 independent WRF-3DVar cycles and the ensemble-transform Kalman filter (ETKF). A hybrid of ETKF (for IC perturbations) and WRF-3DVar (to update the ensemble mean) is also tested. Results show that all of the model and IC perturbation methods examined are more skilful than direct dynamical downscaling of the global ensemble. IC perturbations are most helpful during the first 12 h of the forecasts. Physical parametrization diversity appears critical for boundary-layer forecasts. In an effort to reduce system complexity by reducing the number of suites of physical parametrizations, a smaller set of parametrization suites was combined with perturbed parameters and stochastic backscatter, resulting in the most skilful and statistically consistent ensemble predictions.

Systematic Model Error: The Impact of Increased Horizontal Resolution versus Improved Stochastic and Deterministic Parameterizations

Long-standing systematic model errors in both tropics and extratropics of the ECMWF model run at a horizontal resolution typical for climate models are investigated. Based on the hypothesis that the misrepresentation of unresolvedscales contributes to the systematic model error, three model refinements aimed at their representation—fluctuating or deterministically—are investigated. Increasing horizontal resolution to explicitly simulate smaller-scale features, representing subgrid-scale fluctuationsbyastochasticparameterization,andimprovingthedeterministicphysicsparameterizationsalllead to a decrease in the systematic bias of the Northern Hemispheric circulation. These refinements reduce the overly zonal flow and improve the model’s ability to capture the frequency of blocking. However, the model refinements differ greatly in their impact in the tropics. While improving the deterministic and introducing stochastic parameterizations reduces the systematic precipitation bias and improves the characteristics of convectivelycoupled waves and tropicalvariabilityin general,increasing horizontal resolution has littleimpact. Thefact that differentmodel refinements can lead toreductions in systematic model erroris consistentwith the hypothesis that unresolved scales play an important role. At the same time, this degeneracy of the response to different forcings can lead to compensating model errors. Hence, if one takes the view that stochastic parameterization should be an important element of next-generation climate models, if only to provide reliable estimates of model uncertainty, then a fundamental conclusion of this study is that stochasticity should be incorporated within the design of physical process parameterizations and improvements of the dynamical core and not added a posteriori.

Linear and nonlinear signatures in the planetary wave dynamics of an AGCM : Probability density functions

Abstract To identify and quantify indications of linear and nonlinear planetary wave behavior and their impact on the distribution of atmospheric states, characteristics of a very long integration of an atmospheric general circulation model (GCM) in a four-dimensional phase space are examined. The phase space is defined by the leading four empirical orthogonal functions of 500-hPa geopotential heights. First it is established that nonlinear tendencies similar to those reported in an earlier study of the phase space behavior in this GCM have the potential to lead to non-Gaussian features in the probability density function (PDF) of planetary waves. Then using objective measures it is demonstrated that the model’s distribution of states has distinctive non-Gaussian features. These features are characterized in various subspaces of dimension as high as four. A key feature is the presence of three radial ridges of enhanced probability emanating from the mode, which is shifted away from the climatological mean...

Stochastic climate theory and modeling

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations (SSPs) as well as for model error representation, uncertainty quantification, data assimilation, and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large-scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochastic components and non-Markovian (memory) terms. Stochastic approaches in numerical weather and climate prediction models also lead to the reduction of model biases. Hence, there is a clear need for systematic stochastic approaches in weather and climate modeling. In this review, we present evidence for stochastic effects in laboratory experiments. Then we provide an overview of stochastic climate theory from an applied mathematics perspective. We also survey the current use of stochastic methods in comprehensive weather and climate prediction models and show that stochastic parameterizations have the potential to remedy many of the current biases in these comprehensive models.

Linear and Nonlinear Signatures in the Planetary Wave Dynamics of an AGCM: Phase Space Tendencies

Abstract To identify and quantify indications of linear and nonlinear planetary wave behavior, characteristics of a very long integration of an atmospheric general circulation model in a four-dimensional phase space are examined. The phase space is defined by the leading four empirical orthogonal functions of 500-hPa geopotential heights, and the primary investigated characteristic is the state dependence of mean phase space tendencies. Defining the linear component of planetary wave tendencies as that part which can be captured by a least squares fit linear operator driven by additive Gaussian white noise, the study finds that there are distinct linear and nonlinear signatures. These signatures are especially easy to see in plots of mean tendencies projected onto phase space planes. For some planes the mean tendencies are highly linear, while for others there are strong departures from linearity. The results of the analysis are found to depend strongly on the lag time used to estimate tendencies with the...

Representing Forecast Error in a Convection-Permitting Ensemble System

AbstractEnsembles provide an opportunity to greatly improve short-term prediction of local weather hazards, yet generating reliable predictions remain a significant challenge. In particular, convection-permitting ensemble forecast systems (CPEFSs) have persistent problems with underdispersion. Representing initial and or lateral boundary condition uncertainty along with forecast model error provides a foundation for building a more dependable CPEFS, but the best practice for ensemble system design is not well established.Several configurations of CPEFSs are examined where ensemble forecasts are nested within a larger domain, drawing initial conditions from a downscaled, continuously cycled, ensemble data assimilation system that provides state-dependent initial condition uncertainty. The control ensemble forecast, with initial condition uncertainty only, is skillful but underdispersive. To improve the reliability of the ensemble forecasts, the control ensemble is supplemented with 1) perturbed lateral bou...