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Hui Liu, Jeffrey L. Anderson, Ying-Hwa Kuo, and Kevin Raeder

Abstract

The importance of multivariate forecast error correlations between specific humidity, temperature, and surface pressure in perfect model assimilations of Global Positioning System radio occultation (RO) refractivity data is examined using the Ensemble Adjustment Filter (EAF) and the NCAR global Community Atmospheric Model, version 3. The goal is to explore whether inclusion of the multivariate forecast error correlations in the background term of 3D and 4D variational data assimilation systems (3DVAR and 4DVAR, respectively) is likely to improve RO data assimilation in the troposphere. It is not possible to explicitly neglect multivariate forecast error correlations with the EAF because they are not used directly in the algorithm. Instead, the filter only makes use of the forecast error correlations between observed quantities (RO here) and model state variables. However, because the forecast error correlations for RO observations are dominated by correlations with a subset of state variable types in certain regions, the importance of multivariate forecast error correlations between state variables can be indirectly assessed. This is done by setting the forecast error correlations of RO observations and some state variables (e.g., temperature) to zero in a set of assimilation experiments. Comparing these experiments to a control in which all state variables are impacted by RO observations allows an indirect assessment of the importance of multivariate correlations between state variables not impacted by the observations and those that are impacted. Results suggest that proper specification of the multivariate forecast error correlations in 3DVAR and 4DVAR systems should improve the analysis of specific humidity, surface pressure, and temperature in the troposphere when assimilating RO data.

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

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

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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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Xiu-Qun Yang, Jeffrey L. Anderson, and William F. Stern

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An approach to assess the potential predictability of the extratropical atmospheric seasonal variations in an ensemble of atmospheric general circulation model (AGCM) integrations has been proposed in this study by isolating reproducible forced modes and examining their contributions to the local ensemble mean. The analyses are based on the monthly mean output of an eight-member ensemble of 10-yr Atmospheric Model Intercomparison Project integrations with a T42L18 AGCM.

An EOF decomposition applied to the ensemble anomalies shows that there exist some forced modes that are less affected by the internal process and thus appear to be highly reproducible. By reconstructing the ensemble in terms of the more reproducible forced modes and by developing a quantitative measure, the potential predictability index (PPI), which combines the reproducibility with the local variance contribution, the local ensemble mean over some selective geographic areas in the extratropics was shown to result primarily from reproducible forced modes rather than internal chaotic fluctuations. Over those regions the ensemble mean is potentially predictable. Extratropical potentially predictable regions are found mainly over North America and part of the Asian monsoon regions. Interestingly, the potential predictability over some preferred areas such as Indian monsoon areas and central Africa occasionally results primarily from non-ENSO-related boundary forcing, although ENSO forcing generally dominates over most of the preferred areas.

The quantitative analysis of the extratropical potential predictability with PPI has shown that the preferred geographic areas have obvious seasonality. For the 850-hPa temperature, for example, potentially predictable regions during spring and winter are confined to Alaska, northwest Canada, and the southeast United States, the traditional PNA region, while during summer and fall they are favored over the middle part of North America. It has also been shown that the boreal summer season (June–August) possesses the largest potentially predictable area, which seems to indicate that it is a favored season for the extratropical potential predictability. On the contrary, boreal winter (December–February) appears to have a minimum area of extratropical potential predictability.

The results have been compared with the more traditional statistical tests for potential predictability and with observations from the National Centers for Environmental Prediction reanalysis, which indicates that the PPI analysis proposed here is successful in revealing extratropical potential predictability determined by the external forcing.

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Nicholas F. Anderson, Cedric A. Grainger, and Jeffrey L. Stith

Abstract

Airborne in situ measurements of updrafts in tropical convective storms were analyzed to determine the similarities and differences between updrafts in a tropical continental and a tropical oceanic region. Two hundred fifteen updraft cores from the Tropical Rainfall Measuring Mission (TRMM) component of the Large Scale Biosphere–Atmosphere (LBA) experiment (tropical continental wet season) and 377 updraft cores from the Kwajalein Experiment (KWAJEX) (tropical oceanic) were analyzed in a similar manner to that of previous studies of tropical updrafts. Average speed, maximum speed, width, and mass flux of the updraft cores from the TRMM-LBA and KWAJEX were generally similar to each other and also were similar to results from previous studies of tropical updrafts.

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Lili Lei, Jeffrey L. Anderson, and Glen S. Romine

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For ensemble-based data assimilation, localization is used to limit the impact of observations on physically distant state variables to reduce spurious error correlations caused by limited ensemble size. Traditionally, the localization value applied is spatially homogeneous. Yet there are potentially larger errors and different covariance length scales in precipitation systems, and that may justify the use of different localization functions for precipitating and nonprecipitating regions. Here this is examined using empirical localization functions (ELFs). Using output from an ensemble observing system simulation experiment (OSSE), ELFs provide estimates of horizontal and vertical localization for different observation types in regions with and without precipitation. For temperature and u- and υ-wind observations, the ELFs for precipitating regions are shown to have smaller horizontal localization scales than for nonprecipitating regions. However, the ELFs for precipitating regions generally have larger vertical localization scales than for nonprecipitating regions. The ELFs are smoothed and then applied in three additional OSSEs. Spatially homogeneous ELFs are found to improve performance relative to a commonly used localization function with compact support. When different ELFs are applied in precipitating and nonprecipitating regions, performance is further improved, but varying ELFs by observation type was not found to be as important. Imbalance in initial states caused by use of different localization functions is diagnosed by the domain-averaged surface pressure tendency. Forecasts from analyses with ELFs have smaller surface pressure tendencies than the standard localization, indicating improved initial balance with ELFs.

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Man-Yau Chan, Jeffrey L. Anderson, and Xingchao Chen

Abstract

The introduction of infrared water vapor channel radiance ensemble data assimilation (DA) has improved numerical weather forecasting at operational centers. Further improvements might be possible through extending ensemble data assimilation methods to better assimilate infrared satellite radiances. Here, we will illustrate that ensemble statistics under clear-sky conditions are different from cloudy conditions. This difference suggests that extending the ensemble Kalman filter (EnKF) to handle bi-Gaussian prior distributions may yield better results than the standard EnKF. In this study, we propose a computationally efficient bi-Gaussian ensemble Kalman filter (BGEnKF) to handle bi-Gaussian prior distributions. As a proof-of-concept, we used the 40-variable Lorenz 1996 model as a proxy to examine the impacts of assimilating infrared radiances with the BGEnKF and EnKF. A nonlinear observation operator that constructs radiance-like bimodal ensemble statistics was used to generate and assimilate pseudoradiances. Inflation was required for both methods to effectively assimilate pseudoradiances. In both 800- and 20-member experiments, the BGEnKF generally outperformed the EnKF. The relative performance of the BGEnKF with respect to the EnKF improved when the observation spacing and time between DA cycles (cycling interval) are increased from small values. The relative performance then degraded when observation spacing and cycling interval become sufficiently large. The BGEnKF generated less noise than the EnKF, suggesting that the BGEnKF produces more balanced analysis states than the EnKF. This proof-of-concept study motivates future investigation into using the BGEnKF to assimilate infrared observations into high-order numerical weather models.

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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

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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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