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Jeffrey L. Anderson and Huug M. van den Dool

Abstract

The skill of a set of extended-range dynamical forecasts made with a modern numerical forecast model is examined. A forecast is said to be skillful if it produces a high quality forecast by correctly modeling some aspects of the dynamics of the real atmosphere; high quality forecasts may also occur by chance. The dangers of making a conclusion about model skill by verifying a single long-range forecast are pointed out by examples of apparently high “skill” verifications between extended-range forecasts and observed fields from entirely different years.

To avoid these problems, the entire distribution of forecast quality for a large set of forecasts as a function of lead time is examined. A set of control forecasts that clearly have no skill is presented. The quality distribution for the extended-range forecasts is compared to the distributions of quality for the no-skill control forecast set.

The extended-range forecast quality distributions are found to be essentially indistinguishable from those for the no-skill control at leads somewhat greater than 12 days. A search for individual forecasts with a “return of skill” at extended ranges is also made. Although it is possible to find individual forecasts that have a return of quality, a comparison to the no-skill controls demonstrates that these return of skill forecasts occur only as often as is expected by chance.

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Joshua P. Hacker, Jeffrey L. Anderson, and Mariusz Pagowski

Abstract

Strategies to improve covariance estimates for ensemble-based assimilation of near-surface observations in atmospheric models are explored. It is known that localization of covariance estimates can improve conditioning of covariance matrices in the assimilation process by removing spurious elements and increasing the rank of the matrix. Vertical covariance localization is the focus of this work, and two basic approaches are compared: 1) a recently proposed hierarchical filter approach based on sampling theory and 2) a more commonly used fifth-order piecewise rational function. The hierarchical filter allows for dynamic estimates of localization functions and does not place any restrictions on their form. The rational function is optimized for every analysis time of day and for every possible observation and state variable combination. The methods are tested with a column model containing PBL and land surface parameterization schemes that are available in current mesoscale modeling systems. The results are expected to provide context for assimilation of near-surface observations in mesoscale models, which will benefit short-range mesoscale NWP applications. Results show that both the hierarchical and rational function approaches effectively improve covariance estimates from small ensembles. The hierarchical approach provides localization functions that are irregular and more closely related to PBL structure. Analysis of eigenvalue spectra show that both approaches improve the rank of the covariance matrices, but the amount of improvement is not always directly related to the assimilation performance. Results also show that specifying different localization functions for different observation and state variable combinations is more important than including time dependence.

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Robert Pinkel, Jeffrey Sherman, Jerome Smith, and Steven Anderson

Abstract

In this work a profiling CTD, operated from the research platform FLIP, is used to monitor the fine-scale density field as a function of both depth and time. A sequence of 10 000 CTD profiles from the surface to 560 m is examined. The data were obtained off the Southern California coast in the 1986 PATCHEX experiment. The vertical separation between successive isopycynal surfaces is tracked. The separation is related to the vertical derivative of vertical displacement, and is here referred to as the strain. The purpose of this work is to present a simple picture of the fine scale strain field as it evolves in time as well as depth.

When viewed in isopycnal following coordinates, the qualitative nature of the strain field depends on the characteristic vertical scale over which it is estimated. The “20 m strain” field has a wavelike character, dominated by inertial and semidiurnal tidal motion. Wavelike fluctuations are seen in the 20 m strain field even at subinertial frequencies. This suggests that nonlinear processes are significant even at these relatively large vertical scales. The “2 m strain” more closely resembles the classic picture of fine structure. Lenses of low density gradient fluid are separated by sheets of higher gradient water. The lenses are seen to persist up to eight hours. They can propagate with respect to the density field over tens of meters. The low gradient regions evolve into regions of high gradient and visa versa. The probability density function (PDF) of isopycnal separation is Gaussian for isopycnal pairs of large (∼20 m) mean separation. As mean separation distance is decreased, the skewness of the distribution increases.

Since all scalar fields in the sea are strained by the same velocity field, fluctuations in the fine-scale vertical gradients of a variety of quantities are correlated. Averages of the products of fine scale gradients can differ significantly from products of the averages.

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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

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

Abstract

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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Tobias Necker, Martin Weissmann, Yvonne Ruckstuhl, Jeffrey Anderson, and Takemasa Miyoshi

Abstract

State-of-the-art ensemble prediction systems usually provide ensembles with only 20–250 members for estimating the uncertainty of the forecast and its spatial and spatiotemporal covariance. Given that the degrees of freedom of atmospheric models are several magnitudes higher, the estimates are therefore substantially affected by sampling errors. For error covariances, spurious correlations lead to random sampling errors, but also a systematic overestimation of the correlation. A common approach to mitigate the impact of sampling errors for data assimilation is to localize correlations. However, this is a challenging task given that physical correlations in the atmosphere can extend over long distances. Besides data assimilation, sampling errors pose an issue for the investigation of spatiotemporal correlations using ensemble sensitivity analysis. Our study evaluates a statistical approach for correcting sampling errors. The applied sampling error correction is a lookup table–based approach and therefore computationally very efficient. We show that this approach substantially improves both the estimates of spatial correlations for data assimilation as well as spatiotemporal correlations for ensemble sensitivity analysis. The evaluation is performed using the first convective-scale 1000-member ensemble simulation for central Europe. Correlations of the 1000-member ensemble forecast serve as truth to assess the performance of the sampling error correction for smaller subsets of the full ensemble. The sampling error correction strongly reduced both random and systematic errors for all evaluated variables, ensemble sizes, and lead times.

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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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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.

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