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Joshua P. Hacker

Abstract

Predictability experiments with the Weather Research and Forecast (WRF) model as a proxy for the atmosphere are analyzed to quantify the spatial and temporal scales of boundary layer wind response to land surface perturbations. Soil moisture is chosen as the land surface variable subject to uncertainty because the atmosphere is known to be sensitive to its state. A range of experiments with spatially correlated, small-amplitude perturbations to soil moisture leads to results that show the dependence of predictability on atmospheric conditions. The primary conclusions are as follows: 1) atmospheric conditions, including static instability and the presence of deep convection, determine whether large errors and local loss of predictability are possible in response to soil moisture errors; 2) the scale of soil moisture uncertainty determines scales of PBL wind predictability when the atmosphere is resistant to upscale error transfer, but when the atmosphere is sensitive the scale and magnitude of soil moisture uncertainty are not important after a few hours; and 3) nonlinear error growth is present whether or not the atmosphere is relatively sensitive to soil moisture uncertainty, leading to doubling times of minutes to hours for finite-sized perturbations. Similar results could be expected from other land surface variables or parameters that exert time-dependent forcing on the atmosphere that is similar in magnitude and scale to that of soil moisture.

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Joshua P. Hacker and Lili Lei

Abstract

Ensemble sensitivities have proven a useful alternative to adjoint sensitivities for large-scale dynamics, but their performance in multiscale flows has not been thoroughly examined. When computing sensitivities, the analysis covariance is usually approximated with the corresponding diagonal matrix, leading to a simple univariate regression problem rather than a more general multivariate regression problem. Sensitivity estimates are affected by sampling error arising from a finite ensemble and can lead to an overestimated response to an analysis perturbation. When forecasts depend on many details of an analysis, it is reasonable to expect that the diagonal approximation is too severe. Because spurious covariances are more likely when correlations are weak, computing the sensitivity with a multivariate regression that retains the full analysis covariance may increase the need for sampling error mitigation. The purpose of this work is to clarify the effects of the diagonal approximation, and investigate the need for mitigating spurious covariances arising from sampling error. A two-scale model with realistic spatial covariances is the basis for experimentation. For most problems, an efficient matrix inversion is possible by finding a minimum-norm solution, and employing appropriate matrix factorization. A published hierarchical approach for estimating regression factors for tapering (localizing) covariances is used to measure the effects of sampling error. Compared to univariate regressions in the diagonal approximation, skill in predicting a nonlinear response from the linear sensitivities is superior when localized multivariate sensitivities are used, particularly when fast scales are present, model error is present, and the observing network is sparse.

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Joshua P. Hacker and Chris Snyder

Abstract

In situ surface layer observations are a rich data source that could be more effectively utilized in NWP applications. If properly assimilated, data from existing mesonets could improve initial conditions and lower boundary conditions, leading to the possibility of improved simulation and short-range forecasts of slope flows, sea breezes, convective initiation, and other PBL circulations.

A variance–covariance climatology is constructed by extracting a representative column from real-time mesoscale forecasts over the Southern Great Plains, and used to explore the potential for estimating the state of the PBL by assimilating surface observations. A parameterized 1D PBL model and an ensemble Kalman filter (EnKF) approach to assimilation are used to test this potential. Analysis focuses on understanding how effectively the EnKF can spread the surface observations vertically to constrain the state of the PBL model. Results confirm that assimilating surface observations can substantially improve the state of a modeled PBL. Experiments to estimate the moisture availability parameter through the data assimilation system show that the EnKF is a viable tool for parameter estimation, and may help mitigate model error in forecasting and simulating the PBL.

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Lili Lei and Joshua P. Hacker

Abstract

Objective data assimilation methods such as variational and ensemble algorithms are attractive from a theoretical standpoint. Empirical nudging approaches are computationally efficient and can get around some amount of model error by using arbitrarily large nudging coefficients. In an attempt to take advantage of the strengths of both methods for analyses, combined nudging-ensemble approaches have been recently proposed. Here the two-scale Lorenz model is used to elucidate how the forecast error from nudging, ensemble, and nudging-ensemble schemes varies with model error. As expected, an ensemble filter and smoother are closest to optimal when model errors are small or absent. Model error is introduced by varying model forcing, coupling between scales, and spatial filtering. Nudging approaches perform relatively better with increased model error; use of poor ensemble covariance estimates when model error is large harms the nudging-ensemble performance. Consequently, nudging-ensemble methods always produce error levels between the objective ensemble filters and empirical nudging, and can never provide analyses or short-range forecasts with lower errors than both. As long as the nudged state and the ensemble-filter state are close enough, the ensemble statistics are useful for the nudging, and fully coupling the ensemble and nudging by centering the ensemble on the nudged state is not necessary. An ensemble smoother produces the overall smallest errors except for with very large model errors. Results are qualitatively independent of tuning parameters such as covariance inflation and localization.

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Dorita Rostkier-Edelstein and Joshua P. Hacker

Abstract

A probabilistic verification and factor-separation analysis (FSA) elucidate skillful nowcasts of planetary boundary layer (PBL) temperature, moisture, and wind profiles with a single-column model (SCM) and ensemble filter (EF) assimilation of surface observations. Recently, an FSA showed the importance of surface assimilation versus advection and radiation on ensemble-mean skill. That work addressed the necessary complexity of the model and assimilation scheme for improving PBL nowcasts, relative to deterministic-mesoscale predictions. Here, probabilistic ensemble-based SCM forecasts are compared to a simple probabilistic postprocessing scheme termed climatological dressing (CD). CD adjusts a deterministic mesoscale forecast using surface-atmosphere 3D-climatological covariances, a 30-min persistence model, and surface-forecast errors. It also dresses the adjusted profile with an in-sample uncertainty distribution (obtained from archives) scaled by the 30-min forecast error. Superior deterministic skill from SCM/EF results during night when flow-dependent covariances are more accurate than climatological covariances. CD is deterministically more skillful for temperature and moisture profiles during daytime because SCM/PBL parameterization yields biased covariances. SCM/EF is most probabilistically skillful because (a) the EF covariances accommodate large seasonal variability, (b) the 30-min error persistence assumption fails during nighttime, and (c) vertical error covariance estimates from archived forecasts are generally poor estimates of actual error covariances. A probabilistic FSA of the SCM/EF shows the relative importance of surface assimilation, radiation parameterization, and advection during night. Results confirm surface assimilation as the most important factor. A factor can be deterministically beneficial and probabilistically detrimental, or vice versa, depending on its role in reducing mean error or improving sharpness. Assimilation results in notable probabilistic improvement for nowcasts of low-level jet structures.

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Joshua P. Hacker and Dorita Rostkier-Edelstein

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Following recent results showing the potential for using surface observations of temperature, water vapor mixing ratio, and winds to determine PBL profiles, this paper reports on experiments with real observations. A 1D column model with soil, surface-layer, and PBL parameterization schemes that are the same as in the Weather Research and Forecasting model is used to estimate PBL profiles with an ensemble filter. Surface observations over the southern Great Plains are assimilated during the spring and early summer period of 2003. To strictly quantify the utility of the observations for determining PBL profiles in the ensemble filter framework, only climatological information is provided for initialization and forcing. The analysis skill, measured against rawinsondes for an independent verification, is compared against climatology to quantify the influence of the observations. Sensitivity to changing parameterization schemes, and to prescribed values of observation error variance, is examined. Temporal propagation of skillful analyses is also assessed, separating the effects of good prior state estimates from the impact of assimilation at night when covariance is weak. Results show that accurate profiles of temperature, mixing ratio, and winds are estimated with the column model and ensemble filter assimilating only surface observations. Results are largely insensitive to choice of parameterization scheme and specified observation error variance. The effects of using different parameterization schemes within the column model depend on whether assimilation is included, showing the importance of evaluating models within assimilation systems. At night, skillful estimates are possible because the influence of the observations from the previous day is temporally propagated, and atmospheric dynamics in the residual layer operate on slow time scales. It is expected that these profiles will have applications for nowcasting and secondary models (e.g., plume dispersion models) that rely on accurate specification of PBL structure.

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Joshua P. Hacker and Daran L. Rife

Abstract

Statistical analysis arguments are used to construct an estimation algorithm for systematic error of near-surface temperatures on a mesoscale grid. The systematic error is defined as the observed running-mean error, and an averaging length of 7 days is shown to be acceptable. Those errors are spread over a numerical weather prediction model grid via the statistical analysis equation. Two covariance models are examined: 1) a stationary, isotropic function tuned with the observed running-mean errors and 2) dynamic estimates derived from a recent history of running-mean forecasts. Prediction of error is possible with a diurnal persistence model, where the error at one time of day can be estimated from data with lags of 24-h multiples. The approach is tested on 6 months of 6-h forecasts with the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) over New Mexico. Results show that for a quantity such as 2-m temperature, the systematic component of error can be effectively predicted on the grid. The gridded estimates fit the observed running-mean errors well. Cross validation shows that predictions of systematic error result in a substantial error reduction where observations are not available. The error estimates show a diurnal evolution, and are not strictly functions of terrain elevation. Observation error covariances, localization operators, and covariance functions in the isotropic case must be tuned for a specific forecast system and observing network, but the process is straightforward. Taken together, the results suggest an effective method for systematic error estimation on near-surface mesoscale grids in the absence of a useful ensemble. Correction for those errors may provide benefits to forecast users.

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Raquel Lorente-Plazas and Joshua P. Hacker

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In numerical weather prediction and in reanalysis, robust approaches for observation bias correction are necessary to approach optimal data assimilation. The success of bias correction can be limited by model errors. Here, simultaneous estimation of observation and model biases, and the model state for an analysis, is explored with ensemble data assimilation and a simple model. The approach is based on parameter estimation using an augmented state in an ensemble adjustment Kalman filter. The observation biases are modeled with a linear term added to the forward operator. A bias is introduced in the forcing term of the model, leading to a model with complex errors that can be used in imperfect-model assimilation experiments.

Under a range of model forcing biases and observation biases, accurate observation bias estimation and correction are possible when the model forcing bias is simultaneously estimated and corrected. In the presence of both model error and observation biases, estimating one and ignoring the other harms the assimilation more than not estimating any errors at all, because the biases are not correctly attributed. Neglecting a large model forcing bias while estimating observation biases results in filter divergence; the observation bias parameter absorbs the model forcing bias, and recursively and incorrectly increases the increments. Neglecting observation bias results in suboptimal assimilation, but the model forcing bias parameter estimate remains stable because the model dynamics ensure covariance between the parameter and the model state.

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Walter C. Kolczynski Jr. and Joshua P. Hacker

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An important aspect of numerical weather model improvement is the identification of deficient areas of the model, particularly deficiencies that are flow dependent or otherwise vary in time or space. Here the authors introduce the use of self-organizing maps (SOMs) and analysis increments from data assimilation to identify model deficiencies. Systematic increments reveal time- and space-dependent systematic errors, while SOMs provide a method for categorizing forecasts or increment patterns. The SOMs can be either used for direct analysis or used to produce composites of other fields. This study uses the forecasts and increments of 2-m temperature and dry column mass perturbation μ over a 4-week period to demonstrate the potential of this technique. Results demonstrate the potential of this technique for identifying spatially varying systematic model errors.

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William R. Ryerson and Joshua P. Hacker

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This work examines the viability of producing short-range (<20 h) probabilistic fog predictions in remote locations, absent an observational history, using an uncalibrated 4-km, 10-member Weather Research and Forecasting Model (WRF) ensemble configured to closely match the Air Force Weather Agency Mesoscale Ensemble Forecast Suite. Three distinct sources of error in the final predictions are considered separately to facilitate a better understanding of the total error and appropriate mitigation strategies. These include initial condition error, parameterization of subgrid-scale processes, and error in the visibility parameterization used to convert NWP model output variables to visibility. The raw WRF predictions are generally not skillful in valley and coastal regions, where they produce a shortage of light fog predictions with visibilities of 1–7 mi (1.6–11.3 km) in favor of excessive forecasts of zero cloud water, corresponding to no fog. Initial condition error and visibility parameterization error are shown to play a relatively minor role compared to error in the parameterization of subgrid-scale processes. This deficiency is caused by a negative relative humidity bias, which results from a warm overnight bias. A second-order source of error arises from an inconsistent delineation of fog and haze in the NWP model compared to the verifying observations. Results show that under most conditions it is necessary to deviate from the perfect-prog assumption, and to introduce some method of statistical postprocessing to obtain skillful visibility predictions from the ensemble.

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