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Patrick A. Reinecke and Dale Durran

Abstract

The tendency of high-resolution numerical weather prediction (NWP) models to overpredict the strength of vertically propagating mountain waves is explored. Discrete analytic mountain-wave solutions are presented for the classical problem of cross-mountain flow in an atmosphere with constant wind speed and stability. Time-dependent linear numerical solutions are also obtained for more realistic atmospheric structures. On one hand, using second-order-accurate finite differences on an Arakawa C grid to model nonhydrostatic flow over what might be supposed to be an adequately resolved 8Δx-wide mountain can lead to an overamplification of the standing mountain wave by 30%–40%. On the other hand, the same finite-difference scheme underestimates the wave amplitude in hydrostatic flow over an 8Δx-wide mountain. Increasing the accuracy of the advection scheme to the fourth order significantly reduces the numerical errors associated with both the hydrostatic and nonhydrostatic discrete solutions. The Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) model is used to generate two 70-member ensemble simulations of a mountain-wave event during the Terrain-Induced Rotor Experiment. It is shown that switching from second-order advection to fourth-order advection leads to as much as a 20 m s−1 decrease in vertical velocity on the lee side of the Sierra Nevada, and that the weaker fourth-order solutions are more consistent with observations.

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Patrick A. Reinecke and Dale R. Durran

Abstract

A parameter widely used to predict topographic flow blocking is the nondimensional mountain height or, synonymously, the inverse Froude number. Predictions using this parameter are based on the morphology of flows with uniform upstream static stability and wind speed, which rarely occur in the real world. The appropriateness of applying this theory in the presence of nontrivial background stability is therefore investigated using a numerical model. Two methods were considered to estimate the low-level stability, averaging the Brunt–Väisälä frequency below the crest and using the bulk change in θ between the ground and crest level.

No single best method emerged for estimating the upstream static stability and thereby mapping the simulations with inversions onto the set of solutions with constant stratification. Instead, the best method depended on the application at hand. To predict the onset of flow stagnation, averaging the low-level stability worked best, while to predict low-level flow diversion the bulk estimate of low-level stability was most appropriate. These results are consistent across a range of inversion thicknesses and strengths. In addition, it is shown that variations in static stability above the mountain crest have little impact on flow blocking.

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Patrick A. Reinecke and Dale R. Durran

Abstract

The sensitivity of downslope wind forecasts to small changes in initial conditions is explored by using 70-member ensemble simulations of two prototypical windstorms observed during the Terrain-Induced Rotor Experiment (T-REX). The 10 weakest and 10 strongest ensemble members are composited and compared for each event.

In the first case, the 6-h ensemble-mean forecast shows a large-amplitude breaking mountain wave and severe downslope winds. Nevertheless, the forecasts are very sensitive to the initial conditions because the difference in the downslope wind speeds predicted by the strong- and weak-member composites grows to larger than 28 m s−1 over the 6-h forecast. The structure of the synoptic-scale flow one hour prior to the windstorm and during the windstorm is very similar in both the weak- and strong-member composites.

Wave breaking is not a significant factor in the second case, in which the strong winds are generated by a layer of high static stability flowing beneath a layer of weaker mid- and upper-tropospheric stability. In this case, the sensitivity to initial conditions is weaker but still significant. The difference in downslope wind speeds between the weak- and strong-member composites grows to 22 m s−1 over 12 h. During and one hour before the windstorm, the synoptic-scale flow exhibits appreciable differences between the strong- and weak-member composites. Although this case appears to be more predictable than the wave-breaking event, neither case suggests that much confidence should be placed in the intensity of downslope winds forecast 12 or more hours in advance.

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Dale R. Durran, Patrick A. Reinecke, and James D. Doyle

Abstract

The predictability of lowland snow in the Puget Sound region of the Pacific Northwest is explored by analyzing the spread in 100-member ensemble simulations for two events from December 2008. Sensitivities to the microphysical and boundary layer parameterizations in these simulations are minimized by estimating the likely precipitation type from the forecast 850-hPa temperatures and the established rain–snow climatology. Results suggest that the ensemble spread in events such as these, which were triggered by amplifying short waves, may develop a significant fraction of both rain-likely members and snow-likely members at forecast lead times as short as 36 h.

The perturbation kinetic energy of the ensemble members about the ensemble mean () is not maximized at small scales. Instead, the power in the initial spectrum of produced by the authors’ ensemble Kalman filter (EnKF) data assimilation cycle increases with increasing horizontal scale. The power in subsequently grows with time, while maintaining approximately the same spectral shape. There is no evidence of small-scale perturbations developing rapidly and transferring their influence upscale. Instead, the large-scale perturbations appear to grow more rapidly during the first 12 h than those at the smallest resolved scales.

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Daniel Hodyss, Jeffrey L. Anderson, Nancy Collins, William F. Campbell, and Patrick A. Reinecke

Abstract

It is well known that the ensemble-based variants of the Kalman filter may be thought of as producing a state estimate that is consistent with linear regression. Here, it is shown how quadratic polynomial regression can be performed within a serial data assimilation framework. The addition of quadratic polynomial regression to the Data Assimilation Research Testbed (DART) is also discussed and its performance is illustrated using a hierarchy of models from simple scalar systems to a GCM.

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