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  1. null (Ed.)
    We prove that the values of discrete directed polymer partition functions involving multiple non-intersecting paths remain invariant under replacing the background weights by their images under the geometric RSK correspondence. This result is inspired by a recent and remarkable identity proved by Dauvergne, Orthmann and Virag which is recovered as the zero-temperature, semi-discrete limit of our main result. 
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  2. Abstract

    Four state-of-the-science numerical weather prediction (NWP) models were used to perform mountain wave (MW)-resolving hindcasts over the Drake Passage of a 10-day period in 2010 with numerous observed MW cases. The Integrated Forecast System (IFS) and the Icosahedral Nonhydrostatic (ICON) model were run at Δx≈ 9 and 13 km globally. The Weather Research and Forecasting (WRF) Model and the Met Office Unified Model (UM) were both configured with a Δx= 3-km regional domain. All domains had tops near 1 Pa (z≈ 80 km). These deep domains allowedquantitativevalidation against Atmospheric Infrared Sounder (AIRS) observations, accounting for observation time, viewing geometry, and radiative transfer. All models reproduced observed middle-atmosphere MWs with remarkable skill. Increased horizontal resolution improved validations. Still, all models underrepresented observed MW amplitudes, even after accounting for model effective resolution and instrument noise, suggesting even at Δx≈ 3-km resolution, small-scale MWs are underresolved and/or overdiffused. MW drag parameterizations are still necessary in NWP models at current operational resolutions of Δx≈ 10 km. Upper GW sponge layers in the operationally configured models significantly, artificially reduced MW amplitudes in the upper stratosphere and mesosphere. In the IFS, parameterized GW drags partly compensated this deficiency, but still, total drags were ≈6 times smaller than that resolved at Δx≈ 3 km. Meridionally propagating MWs significantly enhance zonal drag over the Drake Passage. Interestingly, drag associated with meridional fluxes of zonal momentum (i.e.,) were important; not accounting for these terms results in a drag in the wrong direction at and below the polar night jet.

    Significance Statement

    This study had three purposes: to quantitatively evaluate how well four state-of-the-science weather models could reproduce observed mountain waves (MWs) in the middle atmosphere, to compare the simulated MWs within the models, and to quantitatively evaluate two MW parameterizations in a widely used climate model. These models reproduced observed MWs with remarkable skill. Still, MW parameterizations are necessary in current Δx≈ 10-km resolution global weather models. Even Δx≈ 3-km resolution does not appear to be high enough to represent all momentum-fluxing MW scales. Meridionally propagating MWs can significantly influence zonal winds over the Drake Passage. Parameterizations that handle horizontal propagation may need to consider horizontal fluxes of horizontal momentum in order to get the direction of their forcing correct.

     
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