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Mohamad El Gharamti
,
Kevin Raeder
,
Jeffrey Anderson
, and
Xuguang Wang

Abstract

Sampling errors and model errors are major drawbacks from which ensemble Kalman filters suffer. Sampling errors arise because of the use of a limited ensemble size, while model errors are deficiencies in the dynamics and underlying parameterizations that may yield biases in the model’s prediction. In this study, we propose a new time-adaptive posterior inflation algorithm in which the analyzed ensemble anomalies are locally inflated. The proposed inflation strategy is computationally efficient and is aimed at restoring enough spread in the analysis ensemble after assimilating the observations. The performance of this scheme is tested against the relaxation to prior spread (RTPS) and adaptive prior inflation. For this purpose, two model are used: the three-variable Lorenz 63 system and the Community Atmosphere Model (CAM). In CAM, global refractivity, temperature, and wind observations from several sources are incorporated to perform a set of assimilation experiments using the Data Assimilation Research Testbed (DART). The proposed scheme is shown to yield better quality forecasts than the RTPS. Assimilation results further suggest that when model errors are small, both prior and posterior inflation are able to mitigate sampling errors with a slight advantage to posterior inflation. When large model errors, such as wind and temperature biases, are present, prior inflation is shown to be more accurate than posterior inflation. Densely observed regions as in the Northern Hemisphere present numerous challenges to the posterior inflation algorithm. A compelling enhancement to the performance of the filter is achieved by combining both adaptive inflation schemes.

Open access
Jonathan Poterjoy
,
Ryan A. Sobash
, and
Jeffrey L. Anderson

Abstract

Particle filters (PFs) are Monte Carlo data assimilation techniques that operate with no parametric assumptions for prior and posterior errors. A data assimilation method introduced recently, called the local PF, approximates the PF solution within neighborhoods of observations, thus allowing for its use in high-dimensional systems. The current study explores the potential of the local PF for atmospheric data assimilation through cloud-permitting numerical experiments performed for an idealized squall line. Using only 100 ensemble members, experiments using the local PF to assimilate simulated radar measurements demonstrate that the method provides accurate analyses at a cost comparable to ensemble filters currently used in weather models. Comparisons between the local PF and an ensemble Kalman filter demonstrate benefits of the local PF for producing probabilistic analyses of non-Gaussian variables, such as hydrometeor mixing ratios. The local PF also provides more accurate forecasts than the ensemble Kalman filter, despite yielding higher posterior root-mean-square errors. A major advantage of the local PF comes from its ability to produce more physically consistent posterior members than the ensemble Kalman filter, which leads to fewer spurious model adjustments during forecasts. This manuscript presents the first successful application of the local PF in a weather prediction model and discusses implications for real applications where nonlinear measurement operators and nonlinear model processes limit the effectiveness of current Gaussian data assimilation techniques.

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Jeffrey L. Anderson
,
Bruce Wyman
,
Shaoqing Zhang
, and
Timothy Hoar

Abstract

An ensemble filter data assimilation system is tested in a perfect model setting using a low resolution Held–Suarez configuration of an atmospheric GCM. The assimilation system is able to reconstruct details of the model’s state at all levels when only observations of surface pressure (PS) are available. The impacts of varying the spatial density and temporal frequency of PS observations are examined. The error of the ensemble mean assimilation prior estimate appears to saturate at some point as the number of PS observations available once every 24 h is increased. However, increasing the frequency with which PS observations are available from a fixed network of 1800 randomly located stations results in an apparently unbounded decrease in the assimilation’s prior error for both PS and all other model state variables. The error reduces smoothly as a function of observation frequency except for a band with observation periods around 4 h. Assimilated states are found to display enhanced amplitude high-frequency gravity wave oscillations when observations are taken once every few hours, and this adversely impacts the assimilation quality. Assimilations of only surface temperature and only surface wind components are also examined.

The results indicate that, in a perfect model context, ensemble filters are able to extract surprising amounts of information from observations of only a small portion of a model’s spatial domain. This suggests that most of the remaining challenges for ensemble filter assimilation are confined to problems such as model error, observation representativeness error, and unknown instrument error characteristics that are outside the scope of perfect model experiments. While it is dangerous to extrapolate from these simple experiments to operational atmospheric assimilation, the results also suggest that exploring the frequency with which observations are used for assimilation may lead to significant enhancements to assimilated state estimates.

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Jeffrey Anderson
,
Huug van den Dool
,
Anthony Barnston
,
Wilbur Chen
,
William Stern
, and
Jeffrey Ploshay

A statistical model and extended ensemble integrations of two atmospheric general circulation models (GCMs) are used to simulate the extratropical atmospheric response to forcing by observed SSTs for the years 1980 through 1988. The simulations are compared to observations using the anomaly correlation and root-mean-square error of the 700-hPa height field over a region encompassing the extratropical North Pacific Ocean and most of North America. On average, the statistical model is found to produce considerably better simulations than either numerical model, even when simple statistical corrections are used to remove systematic errors from the numerical model simulations. In the mean, the simulation skill is low, but there are some individual seasons for which all three models produce simulations with good skill.

An approximate upper bound to the simulation skill that could be expected from a GCM ensemble, if the model's response to SST forcing is assumed to be perfect, is computed. This perfect model predictability allows one to make some rough extrapolations about the skill that could be expected if one could greatly improve the mean response of the GCMs without significantly impacting the variance of the ensemble. These perfect model predictability skills are better than the statistical model simulations during the summer, but for the winter, present-day statistical forecasts already have skill that is as high as the upper bound for the GCMs. Simultaneous improvements to the GCM mean response and reduction in the GCM ensemble variance would be required for these GCMs to do significantly better than the statistical model in winter. This does not preclude the possibility that, as is presently the case, a statistical blend of GCM and statistical predictions could produce a simulation better than either alone.

Because of the primitive state of coupled ocean–atmosphere GCMs, the vast majority of seasonal predictions currently produced by GCMs are performed using a two-tiered approach in which SSTs are first predicted and then used to force an atmospheric model; this motivates the examination of the simulation problem. However, it is straightforward to use the statistical model to produce true forecasts by changing its predictors from simultaneous to precursor SSTs. An examination of the decrease in skill of the statistical model when changed from simulation to prediction mode is extrapolated to draw conclusions about the skill to be expected from good coupled GCM predictions.

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Thomas M. Hamill
,
Jeffrey S. Whitaker
,
Jeffrey L. Anderson
, and
Chris Snyder
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Robert Pincus
,
Robert J. Patrick Hofmann
,
Jeffrey L. Anderson
,
Kevin Raeder
,
Nancy Collins
, and
Jeffrey S. Whitaker

Abstract

This paper explores the degree to which short-term forecasts with global models might be improved if clouds were fully included in a data assimilation system, so that observations of clouds affected all parts of the model state and cloud variables were adjusted during assimilation. The question is examined using a single ensemble data assimilation system coupled to two present-generation climate models with different treatments of clouds. “Perfect-model” experiments using synthetic observations, taken from a free run of the model used in subsequent assimilations, are used to circumvent complications associated with systematic model errors and observational challenges; these provide a rough upper bound on the utility of cloud observations with these models. A series of experiments is performed in which direct observations of the model’s cloud variables are added to the suite of observations being assimilated. In both models, observations of clouds reduce the 6-h forecast error, with much greater reductions in one model than in the other. Improvements are largest in regions where other observations are sparse. The two cloud schemes differ in their complexity and number of degrees of freedom; the model using the simpler scheme makes better use of the cloud observations because of the stronger correlations between cloud-related and dynamical variables (particularly temperature). This implies that the impact of real cloud observations will depend on both the strength of the instantaneous, linear relationships between clouds and other fields in the natural world, and how well each assimilating model’s cloud scheme represents those relationships.

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Michael K. Tippett
,
Jeffrey L. Anderson
,
Craig H. Bishop
,
Thomas M. Hamill
, and
Jeffrey S. Whitaker

Abstract

Ensemble data assimilation methods assimilate observations using state-space estimation methods and low-rank representations of forecast and analysis error covariances. A key element of such methods is the transformation of the forecast ensemble into an analysis ensemble with appropriate statistics. This transformation may be performed stochastically by treating observations as random variables, or deterministically by requiring that the updated analysis perturbations satisfy the Kalman filter analysis error covariance equation. Deterministic analysis ensemble updates are implementations of Kalman square root filters. The nonuniqueness of the deterministic transformation used in square root Kalman filters provides a framework to compare three recently proposed ensemble data assimilation methods.

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Nedjeljka Žagar
,
Jeffrey Anderson
,
Nancy Collins
,
Timothy Hoar
,
Kevin Raeder
,
Lili Lei
, and
Joseph Tribbia

Abstract

Global data assimilation systems for numerical weather prediction (NWP) are characterized by significant uncertainties in tropical analysis fields. Furthermore, the largest spread of global ensemble forecasts in the short range on all scales is in the tropics. The presented results suggest that these properties hold even in the perfect-model framework and the ensemble Kalman filter data assimilation with a globally homogeneous network of wind and temperature profiles. The reasons for this are discussed by using the modal analysis, which provides information about the scale dependency of analysis and forecast uncertainties and information about the efficiency of data assimilation to reduce the prior uncertainties in the balanced and inertio-gravity dynamics.

The scale-dependent representation of variance reduction of the prior ensemble by the data assimilation shows that the peak efficiency of data assimilation is on the synoptic scales in the midlatitudes that are associated with quasigeostrophic dynamics. In contrast, the variance associated with the inertia–gravity modes is less successfully reduced on all scales. A smaller information content of observations on planetary scales with respect to the synoptic scales is discussed in relation to the large-scale tropical uncertainties that current data assimilation methodologies do not address successfully. In addition, it is shown that a smaller reduction of the large-scale uncertainties in the prior state for NWP in the tropics than in the midlatitudes is influenced by the applied radius for the covariance localization.

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Ting-Chi Wu
,
Christopher S. Velden
,
Sharanya J. Majumdar
,
Hui Liu
, and
Jeffrey L. Anderson

Abstract

Recent studies have shown that assimilating enhanced satellite-derived atmospheric motion vectors (AMVs) has improved mesoscale forecast of tropical cyclones (TC) track and intensity. The authors conduct data-denial experiments to understand where the TC analyses and forecasts benefit the most from the enhanced AMV information using an ensemble Kalman filter and the Weather Research and Forecasting Model. The Cooperative Institute for Meteorological Satellite Studies at the University of Wisconsin provides enhanced AMV datasets with higher density and temporal resolution using shorter-interval image triplets for the duration of Typhoon Sinlaku and Hurricane Ike (both 2008). These AMV datasets are then spatially and vertically subsetted to create six parallel cycled assimilation-forecast experiments for each TC: all AMVs; AMVs withheld between 100 and 350 hPa (upper layer), between 350 and 700 hPa (middle layer), and between 700 and 999 hPa (lower layer); and only AMVs within (interior) and outside (exterior) 1000-km radius of the TC center. All AMV subsets are found to be useful in some capacity. The interior and upper-layer AMVs are particularly crucial for improving initial TC position, intensity, and the three-dimensional wind structure along with their forecasts. Compared with denying interior or exterior AMVs, withholding AMVs in different tropospheric layers had less impact on TC intensity and size forecasts. The ensemble forecast is less certain (larger spread) in providing accurate TC track, intensity, and size when upper-layer AMVs or interior AMVs are withheld. This information could be useful to potential targeting scenarios, such as activating and focusing satellite rapid-scan operations, and decisions regarding observing system assessments and deployments.

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Soyoung Ha
,
Chris Snyder
,
William C. Skamarock
,
Jeffrey Anderson
, and
Nancy Collins

Abstract

A global atmospheric analysis and forecast system is constructed based on the atmospheric component of the Model for Prediction Across Scales (MPAS-A) and the Data Assimilation Research Testbed (DART) ensemble Kalman filter. The system is constructed using the unstructured MPAS-A Voronoi (nominally hexagonal) mesh and thus facilitates multiscale analysis and forecasting without the need for developing new covariance models at different scales. Cycling experiments with the assimilation of real observations show that the global ensemble system is robust and reliable throughout a one-month period for both quasi-uniform and variable-resolution meshes. The variable-mesh assimilation system consistently provides higher-quality analyses than those from the coarse uniform mesh, in addition to the benefits of the higher-resolution forecasts, which leads to substantial improvements in 5-day forecasts. Using the fractions skill score, the spatial scale for skillful precipitation forecasts is evaluated over the high-resolution area of the variable-resolution mesh. Skill decreases more rapidly at smaller scales, but the variable mesh consistently outperforms the coarse uniform mesh in precipitation forecasts at all times and thresholds. Use of incremental analysis updates (IAU) greatly decreases high-frequency noise overall and improves the quality of EnKF analyses, particularly in the tropics. Important aspects of the system design related to the unstructured Voronoi mesh are also investigated, including algorithms for handling the C-grid staggered horizontal velocities.

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