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M. Tugrul Yilmaz and Timothy DelSole

Abstract

This paper tests whether seasonal mean precipitation is predictable using a new method that estimates and analyzes joint probabilities. The new estimation method is to partition the globe into boxes, pool all data within the box to estimate a single joint probability of precipitation for two consecutive seasons, and then apply the resulting joint probability to individual pixels in the box. Pooling data in this way allows joint probabilities to be estimated in relatively small sample sizes; however, the new method assumes that the transition probabilities of pixels in a box are homogeneous and stationary. Joint probabilities are estimated from the Global Precipitation Climatology Project dataset in 21 land boxes and 5 ocean boxes during the period 1979–2008. The state of precipitation is specified by dry, wet, or normal terciles of the local climatological distribution. Predictability is quantified by mutual information, which is a fundamental measure of predictability that allows for nonlinear dependencies, and is tested using bootstrap methods. Predictability was verified by constructing probabilistic and quantitative forecasts directly from the transition probabilities and showing that they have superior cross-validated skills than forecasts based on climatology, persistence, or random selection. Spring was found to be the most predictable season, whereas summer was the least predictable season. Analysis of joint probabilities reveals that although the probabilities are close to climatology, the predictability of precipitation arises from a slight tendency of the state to persist from one season to the next, or if a transition occurs, then it is more often from one extreme to normal than from one extreme to the other.

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Timothy M. Delsole and Brian F. Farrell

Abstract

Dynamical mechanisms underlying the equilibration of absolute instability are examined in a nonlinear, quasigeostrophic, two-layer model. The key to understanding the nonlinear equilibration is in recognizing that linear absolute instabilities can be stabilized both by a reduction of the vertical shear and by enhancement of the mean barotropic velocity. In a localized domain, the equilibration process proceeds with the creation of locally convectively unstable regions downstream, which encroach onto the locally absolutely unstable region until the local instability is suppressed. That local instabilities exist only if absolutely unstable regions span a minimum size is verified by eigenvalue calculations of three-dimensional flows. Numerical examples suggest that this critical size is at least 9000 km for a wide range of parameter values chosen to investigate the midlatitude storm tracks. Fluctuations arising from local absolute instability obtain maximum amplitude in the downstream convectively unstable regions rather than in the absolutely unstable regions themselves. Together, these results suggest that if an equilibrated absolute instability were to occur in midlatitudes, a zonal band of surface easterlies exceeding 9000 km would be required and the associated enhanced variances would not be found coincident with the regions of absolute instability.

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M. Tugrul Yilmaz, Timothy DelSole, and Paul R. Houser

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It is well known that the ensemble Kalman filter (EnKF) requires updating each ensemble member with perturbed observations in order to produce the proper analysis-error covariances. While increased accuracy in a mean square sense may be preferable in many applications, less accuracy might be preferable in other applications, especially if the variables being assimilated obey certain conservation laws. In land data assimilation, for instance, the update in soil moisture often produces a water balance residual, in the sense that the input water is not equal to output water. This study shows that suppressing the perturbation of observations in the EnKF and in the weakly constrained ensemble Kalman filter significantly improves the water balance residuals without significantly increasing the state errors.

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M. Tugrul Yilmaz, Timothy DelSole, and Paul R. Houser

Abstract

A weak constraint is introduced in ensemble Kalman filters to reduce the water budget imbalance that occurs in land data assimilation. Two versions of the weakly constrained filter, called the weakly constrained ensemble Kalman filter (WCEnKF) and the weakly constrained ensemble transform Kalman filter (WCETKF), are proposed. The strength of the weak constraint is adaptive in the sense that it depends on the statistical characteristics of the forecast ensemble. The resulting filters are applied to assimilate synthetic observations generated by the Noah land surface model over the Red Arkansas River basin. The data assimilation experiments demonstrate that, for all tested scenarios, the constrained filters produce analyses with nearly the same accuracy as unconstrained filters, but with much smaller water balance residuals than unconstrained filters.

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David M. Schultz, Timothy M. DelSole, Robert M. Rauber, and Walter A. Robinson
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David M. Schultz, Timothy M. DelSole, Robert M. Rauber, and Walter A. Robinson
Open access
David M. Schultz, Timothy M. DelSole, Robert M. Rauber, and Walter A. Robinson
Open access
David M. Schultz, Timothy M. DelSole, Robert M. Rauber, and Walter A. Robinson
Open access
David M. Schultz, Timothy M. DelSole, Robert M. Rauber, and Walter A. Robinson
Open access
David M. Schultz, Timothy M. DelSole, Robert M. Rauber, and Walter A. Robinson
Open access