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Elizabeth Satterfield and Istvan Szunyogh

Abstract

The performance of an ensemble prediction system is inherently flow dependent. This paper investigates the flow dependence of the ensemble performance with the help of linear diagnostics applied to the ensemble perturbations in a small local neighborhood of each model gridpoint location ℓ. A local error covariance matrix 𝗣 is defined for each local region, and the diagnostics are applied to the linear space defined by the range of the ensemble-based estimate of 𝗣. The particular diagnostics are chosen to help investigate the efficiency of in capturing the space of analysis and forecast uncertainties.

Numerical experiments are carried out with an implementation of the local ensemble transform Kalman filter (LETKF) data assimilation system on a reduced-resolution [T62 and 28 vertical levels (T62L28)] version of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS). Both simulated observations under the perfect model scenario and observations of the real atmosphere in a realistic setting are used in these experiments. It is found that (i) paradoxically, the linear space provides an increasingly better estimate of the space of forecast uncertainties as the time evolution of the ensemble perturbations becomes more nonlinear with increasing forecast time; (ii) provides a more reliable linear representation of the space of forecast uncertainties for cases of more rapid error growth (i.e., for cases of lower predictability); and (iii) the ensemble dimension (E dimension) is a reliable predictor of the performance of in predicting the space of forecast uncertainties.

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Fan Han and Istvan Szunyogh

Abstract

A new morphing-based technique is proposed for the verification of precipitation forecasts for which the location error can be described by a spatial shift. An adaptation of the structural similarity index measure (SSIM) of image processing to the precipitation forecast verification problem, called the amplitude and structural similarity index (ASSIM), is also introduced. ASSIM is used to measure both the convergence of the new morphing algorithm, which is an iterative scheme, and the amplitude and structure component of the forecast error. The behavior of the proposed technique, which could also be applied to other forecast parameters with sharp gradients (e.g., potential vorticity), is illustrated with idealized and realistic examples. One of these examples examines the predictability of the location of precipitation events associated with winter storms. It is found that the functional dependence of the average magnitude of the location error on the forecast lead time is qualitatively similar to that of the root-mean-square error of the fields of the conventional atmospheric state variables (e.g., geopotential height). Quantitatively, the average magnitude of the estimated location error is about 40 km at initial time, 110 km at day 1, 250 km at day 3, and 750 km at week 1, and it eventually saturates at about week 2.

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Fan Han and Istvan Szunyogh

Abstract

This paper describes a morphing-based approach for the verification of precipitation forecasts. This approach employs a pyramid matching algorithm to morph the precipitation features in a forecast into features that match the related precipitation features in the verifying analysis (observations) as closely as possible. The algorithm computes an optical flow (vector field) that maps the original forecast features into the morphed forecast features. The optical flow also provides quantitative information about the error in the location of the forecast features. This information, combined with information about the error in the prediction of the total precipitation over the verification domain, is used to quantify the structure error in the precipitation forecast. The proposed approach has three novel aspects compared to the published morphing-based verification strategies. First, it imposes a constraint on the pyramid matching algorithm to prevent overconvergence toward strong precipitation features during morphing. Second, it introduces an objective criterion for the selection of the subsampling parameter to avoid splitting or distorting features due to an arbitrary maximum displacement limit. Third, the proposed definitions of the location and structure errors are new. The behavior of the proposed multivariate verification metrics is investigated by applications to both idealized and numerical forecast examples.

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Nedjeljka Žagar and Istvan Szunyogh
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Elizabeth Satterfield and Istvan Szunyogh

Abstract

The ability of an ensemble to capture the magnitude and spectrum of uncertainty in a local linear space spanned by the ensemble perturbations is assessed. Numerical experiments are carried out with a reduced resolution 2004 version of the model component of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS). The local ensemble transform Kalman filter (LETKF) data assimilation system is used to assimilate observations in three steps, gradually adding more realistic features to the observing network. In the first experiment, randomly placed, noisy, simulated vertical soundings, which provide 10%% coverage of horizontal model grid points, are assimilated. Next, the impact of an inhomogeneous observing system is introduced by assimilating simulated observations in the locations of real observations of the atmosphere. Finally, observations of the real atmosphere are assimilated.

The most important findings of this study are the following: predicting the magnitude of the forecast uncertainty and the relative importance of the different patterns of uncertainty is, in general, a more difficult task than predicting the patterns of uncertainty; the ensemble, which is tuned to provide near-optimal performance at analysis time, underestimates not only the total magnitude of the uncertainty, but also the magnitude of the uncertainty that projects onto the space spanned by the ensemble perturbations; and finally, a strong predictive linear relationship is found between the local ensemble spread and the upper bound of the local forecast uncertainty.

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Christina R. Holt, Istvan Szunyogh, and Gyorgyi Gyarmati

Abstract

This study investigates the benefits of employing a limited-area data assimilation (DA) system to enhance lower-resolution global analyses in the northwest Pacific tropical cyclone (TC) basin. Numerical experiments are carried out with a global analysis system at horizontal resolution T62 and a limited-area analysis system at resolutions from 200 to 36 km. The global and limited-area DA systems, which are both based on the local ensemble transform Kalman filter algorithm, are implemented using a unique configuration, in which the global DA system provides information about the large-scale analysis and background uncertainty to the limited-area DA system. The limited-area analyses of the storm locations are, on average, more accurate than those from the global analyses, but increasing the resolution of the limited-area system beyond 100 km has little benefit. Two factors contribute to the higher accuracy of the limited-area analyses. First, the limited-area system improves the accuracy of the location estimates for strong storms, which is introduced when the background is updated by the global assimilation. Second, it improves the accuracy of the background estimate of the storm locations for moderate and weak storms. Improvements in the steering flow analysis as a result of increased resolution are modest and short lived in the forecasts. Limited-area track forecasts are more accurate, on average, than global forecasts, independently of the strength of the storms up to five days. This forecast improvement is due to the more accurate analysis of the initial position of storms and the better representation of the interactions between the storms and their immediate environment.

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Young-noh Yoon, Edward Ott, and Istvan Szunyogh

Abstract

Several localized versions of the ensemble Kalman filter have been proposed. Although tests applying such schemes have proven them to be extremely promising, a full basic understanding of the rationale and limitations of localization is currently lacking. It is one of the goals of this paper to contribute toward addressing this issue. The second goal is to elucidate the role played by chaotic wave dynamics in the propagation of information and the resulting impact on forecasts. To accomplish these goals, the principal tool used here will be analysis and interpretation of numerical experiments on a toy atmospheric model introduced by Lorenz in 2005. Propagation of the wave packets of this model is shown. It is found that, when an ensemble Kalman filter scheme is employed, the spatial correlation function obtained at each forecast cycle by averaging over the background ensemble members is short ranged, and this is in strong contrast to the much longer range correlation function obtained by averaging over states from free evolution of the model. Propagation of the effects of observations made in one region on forecasts in other regions is studied. The error covariance matrices from the analyses with localization and without localization are compared. From this study, major characteristics of the localization process and information propagation are extracted and summarized.

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Michael Oczkowski, Istvan Szunyogh, and D. J. Patil

Abstract

The complexity of atmospheric instabilities is investigated by a combination of numerical experiments and diagnostic tools that do not require the assumption of linear error dynamics. These tools include the well-established analysis of the local energetics of the atmospheric flow and the recently introduced ensemble dimension (E dimension). The E dimension is a local measure that varies in both space and time and quantifies the distribution of the variance between phase space directions for an ensemble of nonlinear model solutions over a geographically localized region. The E dimension is maximal, that is, equal to the number of ensemble members (k), when the variance is equally distributed between k phase space directions. The more unevenly distributed the variance, the lower the E dimension.

Numerical experiments with the state-of-the-art operational Global Forecast System (GFS) of the National Centers for Environmental Prediction (NCEP) at a reduced resolution are carried out to investigate the spatiotemporal evolution of the E dimension. This evolution is characterized by an initial transient phase in which coherent regions of low dimensionality develop through a rapid local decay of the E dimension. The typical duration of the transient is between 12 and 48 h depending on the flow; after the initial transient, the E dimension gradually increases with time.

The main goal of this study is to identify processes that contribute to transient local low-dimensional behavior. Case studies are presented to show that local baroclinic and barotropic instabilities, downstream development of upper-tropospheric wave packets, phase shifts of finite amplitude waves, anticyclonic wave breaking, and some combinations of these processes can all play crucial roles in lowering the E dimension.

The practical implication of the results is that a wide range of synoptic-scale weather events may exist whose prediction can be significantly improved in the short and early medium range by enhancing the prediction of only a few local phase space directions. This potential is demonstrated by a reexamination of the targeted weather observations missions from the 2000 Winter Storm Reconnaissance (WSR00) program.

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Michael A. Herrera, Istvan Szunyogh, and Joseph Tribbia

Abstract

This paper employs local linear, spatial spectral, and Lorenz curve–based diagnostics to investigate the dynamics of uncertainty in global numerical weather forecasts in the NH extratropics. The diagnostics are applied to ensembles in the THORPEX Interactive Grand Global Ensemble (TIGGE). The initial growth of uncertainty is found to be the fastest at the synoptic scales (zonal wavenumbers 7–9) most sensitive to baroclinic instability. At later forecast times, the saturation of uncertainties at the synoptic scales and the longer sustainable growth of uncertainty at the large scales lead to a gradual shift of the wavenumber of the dominant uncertainty toward zonal wavenumber 5. At the subsynoptic scales, errors saturate as predicted by Lorenz’s classic theory. While the ensembles capture the general characteristics of the uncertainty dynamics efficiently, there are locations where the predicted magnitude and structure of uncertainty have considerable time-mean errors. In addition, the magnitude of systematic errors in the prediction of the uncertainty increases with increasing forecast time. These growing systematic errors are dominated by errors in the prediction of low-frequency changes in the large-scale flow.

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Aleksey V. Zimin, Istvan Szunyogh, Brian R. Hunt, and Edward Ott

Abstract

Previously developed techniques that have been used to extract envelopes of Rossby wave packets are based on the assumption of zonally propagating waves. In this note a method that does not require such an assumption is proposed. The advantages of the new technique, both on analytical and real-world examples, are demonstrated.

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