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Rebecca E. Morss, Chris Snyder, and Richard Rotunno

Abstract

Results from homogeneous, isotropic turbulence suggest that predictability behavior is linked to the slope of a flow’s kinetic energy spectrum. Such a link has potential implications for the predictability behavior of atmospheric models. This article investigates these topics in an intermediate context: a multilevel quasigeostrophic model with a jet and temperature perturbations at the upper surface (a surrogate tropopause). Spectra and perturbation growth behavior are examined at three model resolutions. The results augment previous studies of spectra and predictability in quasigeostrophic models, and they provide insight that can help interpret results from more complex models. At the highest resolution tested, the slope of the kinetic energy spectrum is approximately at the upper surface but −3 or steeper at all but the uppermost interior model levels. Consistent with this, the model’s predictability behavior exhibits key features expected for flow with a shallower than −3 slope. At the highest resolution, upper-surface perturbation spectra peak below the energy-containing scales, and the error growth rate decreases as small scales saturate. In addition, as model resolution is increased and smaller scales are resolved, the peak of the upper-surface perturbation spectra shifts to smaller scales and the error growth rate increases. The implications for potential predictive improvements are not as severe, however, as in the standard picture of flows exhibiting a finite predictability limit. At the highest resolution, the model also exhibits periods of much faster-than-average perturbation growth that are associated with faster growth at smaller scales, suggesting predictability behavior that varies with time.

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Hyun Mee Kim, Michael C. Morgan, and Rebecca E. Morss

Abstract

The structure and evolution of analysis error and adjoint-based sensitivities [potential enstrophy initial singular vectors (SVs) and gradient sensitivities of the forecast error to initial conditions] are compared following a cyclone development in a three-dimensional quasigeostrophic channel model. The results show that the projection of the evolved SV onto the forecast error increases during the evolution.

Based on the similarities of the evolved SV to the forecast error, use of the evolved SV is suggested as an adaptive observation strategy. The use of the evolved SV strategy for adaptive observations is evaluated by performing observation system simulation experiments using a three-dimensional variational data assimilation scheme under the perfect model assumption. Adaptive strategies using the actual forecast error, gradient sensitivity, and initial SV are also tested. The observation system simulation experiments are implemented for five simulated synoptic cases with two different observation spacings and three different configurations of adaptive observation location densities (sparse, dense, and mixed), and the impact of the adaptive strategies is compared with that of the nonadaptive, fixed observations.

The impact of adaptive strategies varies with the observation density. For a small number of observations, several of the adaptive strategies tested reduce forecast error more than the nonadaptive strategy. For a large number of observations, it is more difficult to reduce forecast errors using adaptive observations. The evolved SV strategy performs as well as or better than the adjoint-based strategies for both observation densities. The impact of using the evolved SVs rather than the adjoint-based sensitivities for adaptive observation purposes is larger in the situation of a large number of observation stations for which the forecast error reduction by adjoint- based adaptive strategies is difficult.

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Rebecca E. Morss, Kerry A. Emanuel, and Chris Snyder

Abstract

Adaptive sampling uses information about individual atmospheric situations to identify regions where additional observations are likely to improve weather forecasts of interest. The observation network could be adapted for a wide range of forecasting goals, and it could be adapted either by allocating existing observations differently or by adding observations from programmable platforms to the existing network. In this study, observing strategies are explored in a simulated idealized system with a three-dimensional quasigeostrophic model and a realistic data assimilation scheme. Using simple error norms, idealized adaptive observations are compared to nonadaptive observations for a range of observation densities.

The results presented show that in this simulated system, the influence of both adaptive and nonadaptive observations depends strongly on the observation density. For sparse observation networks, the simple adaptive strategies tested are beneficial: adaptive observations can, on average, reduce analysis and forecast errors more than the same number of nonadaptive observations, and they can reduce errors by a given amount using fewer observational resources. In contrast, for dense observation networks it is much more difficult to benefit from adapting observations, at least for the data assimilation method used here. The results suggest that the adaptive strategies tested are most effective when the observations are adapted regularly and frequently, giving the data assimilation system as many opportunities as possible to reduce errors as they evolve. They also indicate that ensemble-based estimates of initial condition errors may be useful for adaptive observations. Further study is needed to understand the extent to which the results from this idealized study apply to more complex, more realistic systems.

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