A Minimal Model to Diagnose the Contribution of the Stratosphere to Tropospheric Forecast Skill

Abstract

Many recent studies have confirmed that variability in the stratosphere is a significant source of surface sub‐seasonal prediction skill during Northern Hemisphere winter. It may be beneficial, therefore, to think about times in which there might be windows‐of‐opportunity for skillfull sub‐seasonal predictions based on the initial or predicted state of the stratosphere. In this study, we propose a simple, minimal model that can be used to understand the impact of the stratosphere on tropospheric predictability. Our model purposefully excludes state dependent predictability in either the stratosphere or troposphere or in the coupling between the two. Model parameters are set up to broadly represent current sub‐seasonal prediction systems by comparison with four dynamical models from the Sub‐Seasonal to Seasonal Prediction Project database. The model can reproduce the increases in correlation skill in sub‐sets of forecasts for weak and strong lower stratospheric polar vortex states over neutral states despite the lack of dependence of coupling or predictability on the stratospheric state. We demonstrate why different forecast skill diagnostics can give a very different impression of the relative skill in the three sub‐sets. Forecasts with large stratospheric signals and low amounts of noise are demonstrated to also be windows‐of‐opportunity for skillfull tropospheric forecasts, but we show that these windows can be obscured by the presence of unrelated tropospheric signals.

Modulation of Atmospheric Rivers by the Arctic Stratospheric Polar Vortex

“…The associated Northern Annular Mode (NAM) anomalies in the lower stratosphere, where the e ‐folding timescale is around 4 weeks (Baldwin et al., 2003; Simpson et al., 2011), can persist for at least 2 months (Baldwin & Dunkerton, 2001). This makes the stratosphere one of the most predictable components of the extratropical atmosphere (Son et al., 2020) and can provide a boundary condition for S2S forecasts (Charlton‐Perez et al., 2021).…”

The tropical influence on sub‐seasonal predictability of wintertime stratosphere and stratosphere–troposphere coupling

“…Contribution from the stratosphere–troposphere coupling to the tropospheric forecast skill has previously been found for cases when the stratosphere is in an extreme state (Sigmond et al, 2013; Tripathi et al, 2015; Domeisen et al, 2020; Charlton‐Perez et al, 2021; Statnaia et al, 2022). The experiments used in our study can help to better quantify when and by how much the tropospheric skill is improved due to the stratospheric improvements.…”

“…Overall, the influence of the stratospheric and tropical relaxations has comparable effects on the extratropical tropospheric skill. Charlton‐Perez et al (2021) estimated that a perfect knowledge of the stratospheric conditions would increase the correlation skill score of the North Atlantic Oscillation (NAO) for week 3 from 0.49 (a representative value in the present forecast systems) to 0.56, that is, an increase of 0.07. This increase cannot be directed compared with the ACC increase of 0.03 found for STRAT during week 3 because of a different metric; however, the result found here is broadly consistent with the theoretical estimations of Charlton‐Perez et al (2021).…”

“…The experiments used in our study can help to better quantify when and by how much the tropospheric skill is improved due to the stratospheric improvements. In particular, Charlton-Perez et al (2021) showed that the NAO correlation skill score during week 3 can be improved by 0.07 due to the perfect knowledge of the stratospheric conditions. Our results demonstrate a similar level on skill improvements, although a thorough comparison has not been made.…”

Diversity of Stratospheric Error Growth Across Subseasonal Prediction Systems

“…Our model, from Charlton‐Perez et al. (2021), is as follows: $$${Y}_{S}(t)={\beta }_{y}S(t)+\varepsilon O(t),$$$ $$${X}_{Sk}(t)={\beta }_{x}S(t)+\eta {P}_{k}(t)\quad \quad \,\text{for}\,k=1,\text{\ldots },K,$$$ $$${Y}_{T}(t)={C}_{y}{Y}_{S}(t)+{\alpha }_{y}T(t)+\lambda Q(t),$$$ $$${X}_{Tk}(t)={C}_{x}{X}_{Sk}(t)+{\alpha }_{x}T(t)+\xi {R}_{k}(t)\quad \quad \hspace*{.5em}\text{for}\hspace*{.5em}k=1,\text{\ldots },K.$$$ In this model, Y ( t ) is the observed time series of the parameter of interest for forecasts made at different times, t ; X k ( t ) are the matching ensemble forecasts. An added subscript S means stratosphere and T means troposphere.…”