A Stochastic Parameter Perturbation Method to Represent Uncertainty in a Microphysics Scheme

Abstract

Current state-of-the art regional numerical weather forecasts are run at horizontal grid spacings of a few kilometers, which permits medium to large-scale convective systems to be represented explicitly in the model. With the convection parameterization no longer active, much uncertainty in the formulation of subgrid-scale processes moves to other areas such as the cloud microphysical, turbulence, and land-surface parameterizations. The goal of this study is to investigate experiments with stochastically-perturbed parameters (SPP) within a microphysics parameterization and the model’s horizontal diffusion coefficients. To estimate the “true” uncertainty due to parameter uncertainty, the magnitudes of the perturbations are chosen as realistic as possible and not with purposeful intent of maximal forecast impact as some prior work has done. Spatial inhomogeneities and temporal persistence are represented using a random perturbation pattern with spatial and temporal correlations. The impact on the distributions of various hydrometeors, precipitation characteristics, and solar/longwave radiation are quantified for a winter and summer case. In terms of upscale error growth, the impact is relatively small and consists primarily of triggering atmospheric instabilities in convectively unstable regions. In addition, small in situ changes with potentially large socio-economic impacts are observed in the precipitation characteristics such as maximum hail size. Albeit the impact of introducing physically-based parameter uncertainties within the bounds of aerosol uncertainties is small, their influence on the solar and longwave radiation balances may still have important implications for global model simulations of future climate scenarios.

Sensitivity of Modeled Microphysics to Stochastically Perturbed Parameters

“…They differ however in the selection of the AR1 model class (Grunwald et al, 2000), the quantity to which the model is applied and the underlying statistical parameter distribution used for sampling the innovations at every time step. For example, the SPP scheme first formulated by Ollinaho et al (2017) and since applied in a number of other studies makes use of the Gaussian AR1 model applied to spectral coefficients of 2D horizontal Gaussian correlated noise with the innovations based on either the Log-Normal or Normal univariate distributions (Jankov et al, 2017(Jankov et al, , 2019Ollinaho et al, 2017;Stanford et al, 2019;Thompson et al, 2021). Another widely used SP scheme referred to as the Random Parameters (RP) uses a non-Gaussian linear AR1 model applied directly to spatially invariant parameters, with the innovation term based on the bounded uniform distribution (Hermoso et al, 2021;McCabe et al, 2016).…”

“…As a result, the SP schemes produce physically‐based and physically‐consistent stochastic variability to the tendencies of the resolved states. Evaluations of the SP schemes in global and regional models have shown positive impacts on the ensemble prediction skill of various degrees depending on the prediction time range, the modeling system, and verification variables (Christensen et al., 2015; Hermoso et al., 2021; Jankov et al., 2017; Leutbecher et al., 2017; McCabe et al., 2016; Ollinaho et al., 2017; Stanford et al., 2019; Thompson et al., 2021; Wang et al., 2019). In comparison to the SPPT, the impacts of the SP schemes on ensemble spread were found to be smaller, but adding value when the two approaches were combined (Christensen et al., 2015; Hermoso et al., 2021; Jankov et al., 2019; Ollinaho et al., 2017).…”

“…Over the last two decades, the inclusion of stochastic representation of unresolved variability of sub‐grid scale processes in weather and ES models has emerged as a viable approach to representing the intrinsic uncertainties of physical parameterizations in the context of improving probabilistic prediction skill using ensembles (Berner et al., 2011, 2015; Bouttier et al., 2012; Buizza et al., 1999; Charron et al., 2010; Christensen et al., 2015; Davini et al., 2017; Hermoso et al., 2021; Jankov et al., 2017; Leutbecher et al., 2017; Palmer et al., 2005, 2009; Ollinaho et al., 2017; Romine et al., 2014; Sanchez et al., 2015; Stanford et al., 2019; Thompson et al., 2021). The representations of uncertainty using this approach are commonly referred to as stochastic parameterizations (Berner et al., 2017).…”

“…Similarly, Hermoso et al (2021) demonstrated that the Random Parameters (RP) scheme (McCabe et al, 2016) applied to several microphysics parameters in a two-moment bulk microphysics scheme significantly increased ensemble variability of convective storm evolution for the studied case. Thompson et al (2021) reported important localized impacts on the precipitation properties including changes to maximum hail-size from perturbing only two microphysics parameters using the SPP scheme. These results clearly point to potential for expanding the scope of relevant impacts by including more processes within the SP framework.…”

Evaluation of the COSMO model (v5.1) in polarimetric radar space – impact of uncertainties in model microphysics, retrievals and forward operators

“…The aforementioned inconsistencies can be larger above the melting layer, where uncertainty exists in, among other things, the partitioning of the total ice water content (IWC) P. Shrestha et al: Evaluation of the COSMO model (v5.1) in polarimetric radar space across hydrometeor species -cloud ice, snow aggregates, graupel and hail -in cloud microphysics schemes (van Lier-Walqui et al, 2012;Morrison et al, 2020;Thompson et al, 2021). Morrison and Milbrandt (2015) developed an alternative scheme called P3 with only a single frozen hydrometeor class but with explicit prediction of size-dependent hydrometeor bulk densities and fall speeds based on the prognostic rimed and deposited masses.…”