Stochastic Parameterization of Subgrid-Scale Velocity Enhancement of Sea Surface Fluxes

Abstract

Subgrid-scale (SGS) velocity variations result in gridscale sea surface flux enhancements that must be parameterized in weather and climate models. Traditional parameterizations are deterministic in that they assign a unique value of the SGS velocity flux enhancement to any given configuration of the resolved state. In this study, we assess the statistics of SGS velocity flux enhancement over a range of averaging scales (as a proxy for varying model resolution) through systematic coarse-graining of a convection-permitting atmospheric model simulation over the Indian Ocean and west Pacific warm pool. Conditioning the statistics of the SGS velocity flux enhancement on 1) the fluxes associated with the resolved winds and 2) the precipitation rate, we find that the lack of a separation between “resolved” and “unresolved” scales results in a distribution of flux enhancements for each configuration of the resolved state. That is, the SGS velocity flux enhancement should be represented stochastically rather than deterministically. The spatial and temporal statistics of the SGS velocity flux enhancement are investigated by using basic descriptive statistics and through a fit to an anisotropic space–time covariance structure. Potential spatial inhomogeneities of the statistics of the SGS velocity flux enhancement are investigated through regional analysis, although because of the relatively short duration of the simulation (9 days) distinguishing true inhomogeneity from sampling variability is difficult. Perspectives for the implementation of such a stochastic parameterization in weather and climate models are discussed.

Flow‐dependent stochastic coupling for climate models with high ocean‐to‐atmosphere resolution ratio

“…In the case of coupled climate models, subgrid‐scale surface field information is in fact available, as part of it is resolved by the oceanic model component. Similar to coarse‐graining methods (Jung et al ., ; Bessac et al ., ; Christensen, ), this information can be used in a stochastic coupling scheme to better represent the statistical properties of the unresolved scales in the atmospheric model component. Using this information can improve the representation of spatial variability of surface fluxes.…”

Constraining stochastic parametrisation schemes using high‐resolution simulations

“…As summarised in Figure 1, the starting point for all stochastic parametrisation schemes should be identifying a source of uncertainty in a forecast model at a given resolution. Examples include the error in the representation of a specific process such as subgrid-scale turbulent mixing (Nie and Kuang, 2012;Gentine et al, 2013;Sušelj (Romps and Kuang, 2010), variability in air-sea fluxes (Bessac et al, 2019), or the error in a collection of processes, such as uncertainty in the net parametrised physics tendency (Buizza et al, 1999). Having identified the model error that leads to uncertainty in the forecast, the characteristics of that model error must be predicted through theory or assessed through measurements.…”

“…The availability of such datasets opens up the option of using high‐resolution simulations as a proxy for the “true atmosphere” and identifying the difference between a low‐resolution forecast model and a high‐resolution simulation as the model error that a stochastic parametrisation seeks to represent (Shutts and Palmer, ; Shutts and Pallares, ). This allows for the derivation of data‐driven stochastic representations of this subgrid variability (Dorrestijn et al ., ; Porta Mana and Zanna, ; Cooper and Zanna, ; Bessac et al ., ). To date, this approach has been used to construct stochastic parametrisation schemes that are independent from (i.e., an alternative to) existing deterministic parametrisations.…”

Scale‐Aware Space‐Time Stochastic Parameterization of Subgrid‐Scale Velocity Enhancement of Sea Surface Fluxes

“…These SGS velocity variations result in a systematic enhancement of air-sea fluxes relative to estimates obtained from bulk formulae using the "resolved" wind (e.g. Bessac et al, 2019;Blein et al, 2020;Godfrey & Beljaars, 1991;Mahrt & Sun, 1995;Redelsperger et al, 2000;Vickers & Esbensen, 1998;Williams, 2001;Zeng et al, 2002). A standard approach accounts for the difference between the space-time grid-box averaged wind speed and the norm of the average horizontal wind vector due to SGS velocity variations through a SGS velocity flux enhancement term, s SGS :…”

“…Section 2 presents the high-resolution numerical model outputs and the coarse-graining setup used to generate realizations at various resolutions as well as to define a ground "truth." In Section 3, we present the regression used in Bessac et al (2019) and its extension to a scale-aware regression. We also propose a model for the regression residuals that embeds scale information in the spatiotemporal structure of the residuals.…”