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Sam Hatfield
,
Aneesh Subramanian
,
Tim Palmer
, and
Peter Düben

Abstract

A new approach for improving the accuracy of data assimilation, by trading numerical precision for ensemble size, is introduced. Data assimilation is inherently uncertain because of the use of noisy observations and imperfect models. Thus, the larger rounding errors incurred from reducing precision may be within the tolerance of the system. Lower-precision arithmetic is cheaper, and so by reducing precision in ensemble data assimilation, computational resources can be redistributed toward, for example, a larger ensemble size. Because larger ensembles provide a better estimate of the underlying distribution and are less reliant on covariance inflation and localization, lowering precision could actually permit an improvement in the accuracy of weather forecasts. Here, this idea is tested on an ensemble data assimilation system comprising the Lorenz ’96 toy atmospheric model and the ensemble square root filter. The system is run at double-, single-, and half-precision (the latter using an emulation tool), and the performance of each precision is measured through mean error statistics and rank histograms. The sensitivity of these results to the observation error and the length of the observation window are addressed. Then, by reinvesting the saved computational resources from reducing precision into the ensemble size, assimilation error can be reduced for (hypothetically) no extra cost. This results in increased forecasting skill, with respect to double-precision assimilation.

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Hajoon Song
,
Ibrahim Hoteit
,
Bruce D. Cornuelle
, and
Aneesh C. Subramanian

Abstract

A new approach is proposed to address the background covariance limitations arising from undersampled ensembles and unaccounted model errors in the ensemble Kalman filter (EnKF). The method enhances the representativeness of the EnKF ensemble by augmenting it with new members chosen adaptively to add missing information that prevents the EnKF from fully fitting the data to the ensemble. The vectors to be added are obtained by back projecting the residuals of the observation misfits from the EnKF analysis step onto the state space. The back projection is done using an optimal interpolation (OI) scheme based on an estimated covariance of the subspace missing from the ensemble. In the experiments reported here, the OI uses a preselected stationary background covariance matrix, as in the hybrid EnKF–three-dimensional variational data assimilation (3DVAR) approach, but the resulting correction is included as a new ensemble member instead of being added to all existing ensemble members.

The adaptive approach is tested with the Lorenz-96 model. The hybrid EnKF–3DVAR is used as a benchmark to evaluate the performance of the adaptive approach. Assimilation experiments suggest that the new adaptive scheme significantly improves the EnKF behavior when it suffers from small size ensembles and neglected model errors. It was further found to be competitive with the hybrid EnKF–3DVAR approach, depending on ensemble size and data coverage.

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Hajoon Song
,
Ibrahim Hoteit
,
Bruce D. Cornuelle
,
Xiaodong Luo
, and
Aneesh C. Subramanian

Abstract

A new hybrid ensemble Kalman filter/four-dimensional variational data assimilation (EnKF/4D-VAR) approach is introduced to mitigate background covariance limitations in the EnKF. The work is based on the adaptive EnKF (AEnKF) method, which bears a strong resemblance to the hybrid EnKF/three-dimensional variational data assimilation (3D-VAR) method. In the AEnKF, the representativeness of the EnKF ensemble is regularly enhanced with new members generated after back projection of the EnKF analysis residuals to state space using a 3D-VAR [or optimal interpolation (OI)] scheme with a preselected background covariance matrix. The idea here is to reformulate the transformation of the residuals as a 4D-VAR problem, constraining the new member with model dynamics and the previous observations. This should provide more information for the estimation of the new member and reduce dependence of the AEnKF on the assumed stationary background covariance matrix. This is done by integrating the analysis residuals backward in time with the adjoint model. Numerical experiments are performed with the Lorenz-96 model under different scenarios to test the new approach and to evaluate its performance with respect to the EnKF and the hybrid EnKF/3D-VAR. The new method leads to the least root-mean-square estimation errors as long as the linear assumption guaranteeing the stability of the adjoint model holds. It is also found to be less sensitive to choices of the assimilation system inputs and parameters.

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William E. Chapman
,
Luca Delle Monache
,
Stefano Alessandrini
,
Aneesh C. Subramanian
,
F. Martin Ralph
,
Shang-Ping Xie
,
Sebastian Lerch
, and
Negin Hayatbini

Abstract

Deep-learning (DL) postprocessing methods are examined to obtain reliable and accurate probabilistic forecasts from single-member numerical weather predictions of integrated vapor transport (IVT). Using a 34-yr reforecast, based on the Center for Western Weather and Water Extremes West-WRF mesoscale model of North American West Coast IVT, the dynamically/statistically derived 0–120-h probabilistic forecasts for IVT under atmospheric river (AR) conditions are tested. These predictions are compared with the Global Ensemble Forecast System (GEFS) dynamic model and the GEFS calibrated with a neural network. In addition, the DL methods are tested against an established, but more rigid, statistical–dynamical ensemble method (the analog ensemble). The findings show, using continuous ranked probability skill score and Brier skill score as verification metrics, that the DL methods compete with or outperform the calibrated GEFS system at lead times from 0 to 48 h and again from 72 to 120 h for AR vapor transport events. In addition, the DL methods generate reliable and skillful probabilistic forecasts. The implications of varying the length of the training dataset are examined, and the results show that the DL methods learn relatively quickly and ∼10 years of hindcast data are required to compete with the GEFS ensemble.

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Carolyn A. Reynolds
,
Rebecca E. Stone
,
James D. Doyle
,
Nancy L. Baker
,
Anna M. Wilson
,
F. Martin Ralph
,
David A. Lavers
,
Aneesh C. Subramanian
, and
Luca Centurioni

Abstract

Under the Atmospheric River Reconnaissance (AR Recon) Program, ocean drifting buoys (drifters) that provide surface pressure observations were deployed in the northeastern Pacific Ocean to improve forecasts of U.S. West Coast high-impact weather. We examine the impacts of both AR Recon and non-AR Recon drifter observations in the U.S. Navy’s global atmospheric data assimilation (DA) and forecast system using data-denial experiments and forecast sensitivity observation impact (FSOI) analysis, which estimates the impact of each observation on the 24-h global forecast error total energy. Considering all drifters in the eastern North Pacific for the 2020 AR Recon season, FSOI indicates that most of the beneficial impacts come from observations in the lowest quartile of observed surface pressure values, particularly those taken late in the DA window. Observations in the upper quartile have near-neutral impacts on average and are slightly nonbeneficial when taken late in the DA window. This may occur because the DA configuration used here does not account for model biases, and innovation statistics show that the forecast model has a low pressure bias at high pressures. Case studies and other analyses indicate large beneficial impacts coming from observations in regions with large surface pressure gradients and integrated vapor transport, such as fronts and ARs. Data-denial experiments indicate that the assimilation of AR Recon drifter observations results in a better-constrained analysis at nearby non-AR Recon drifter locations and counteracts the NAVGEM pressure bias. Assimilating the AR Recon drifter observations improves 72- and 96-h Northern Hemisphere forecasts of winds in the lower and middle troposphere, and geopotential height in the lower, middle, and upper troposphere.

Significance Statement

The purpose of this study is to understand how observations of atmospheric pressure at the ocean surface provided by drifting buoys impact weather forecasts. Some of these drifting buoys were deployed under a program to study atmospheric rivers (ARs) to improve forecasts of high-impact weather on the West Coast. We find that these observations are most effective at reducing forecast errors when taken in regions near fronts and cyclones. The additional drifting buoys deployed under the AR Reconnaissance project reduce forecast errors at 72 and 96 h over North America and the Northern Hemisphere. These results are important because they illustrate the potential for improving forecasts by increasing the number of drifting buoy surface pressure observations over the world oceans.

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