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Zhe-Min Tan
,
Fuqing Zhang
,
Richard Rotunno
, and
Chris Snyder
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Rebecca E. Morss
,
Kerry A. Emanuel
, and
Chris Snyder

Abstract

Adaptive sampling uses information about individual atmospheric situations to identify regions where additional observations are likely to improve weather forecasts of interest. The observation network could be adapted for a wide range of forecasting goals, and it could be adapted either by allocating existing observations differently or by adding observations from programmable platforms to the existing network. In this study, observing strategies are explored in a simulated idealized system with a three-dimensional quasigeostrophic model and a realistic data assimilation scheme. Using simple error norms, idealized adaptive observations are compared to nonadaptive observations for a range of observation densities.

The results presented show that in this simulated system, the influence of both adaptive and nonadaptive observations depends strongly on the observation density. For sparse observation networks, the simple adaptive strategies tested are beneficial: adaptive observations can, on average, reduce analysis and forecast errors more than the same number of nonadaptive observations, and they can reduce errors by a given amount using fewer observational resources. In contrast, for dense observation networks it is much more difficult to benefit from adapting observations, at least for the data assimilation method used here. The results suggest that the adaptive strategies tested are most effective when the observations are adapted regularly and frequently, giving the data assimilation system as many opportunities as possible to reduce errors as they evolve. They also indicate that ensemble-based estimates of initial condition errors may be useful for adaptive observations. Further study is needed to understand the extent to which the results from this idealized study apply to more complex, more realistic systems.

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Zhe-Min Tan
,
Fuqing Zhang
,
Richard Rotunno
, and
Chris Snyder

Abstract

Recent papers by the authors demonstrated the possible influence of initial errors of small amplitude and scale on the numerical prediction of the “surprise” snowstorm of 24–25 January 2000. They found that initial errors grew rapidly at scales below 200 km, and that the rapid error growth was dependent on moist processes. In an attempt to generalize these results from a single case study, the present paper studies the error growth in an idealized baroclinic wave amplifying in a conditionally unstable atmosphere. The present results show that without the effects of moisture, there is little error growth in the short-term (0–36 h) forecast error (starting from random noise), even though the basic jet used here produces a rapidly growing synoptic-scale disturbance. With the effect of moisture included, the error is characterized by upscale growth, basically as found by the authors in their study of the numerical prediction of the surprise snowstorm.

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Lotte Bierdel
,
Chris Snyder
,
Sang-Hun Park
, and
William C. Skamarock

Abstract

Under assumptions of horizontal homogeneity and isotropy, one may derive relations between rotational or divergent kinetic energy spectra and velocities along one-dimensional tracks, such as might be measured by aircraft. Two recent studies, differing in details of their implementation, have applied these relations to the Measurement of Ozone and Water Vapor by Airbus In-Service Aircraft (MOZAIC) dataset and reached different conclusions with regard to the mesoscale ratio of divergent to rotational kinetic energy. In this study the accuracy of the method is assessed using global atmospheric simulations performed with the Model for Prediction Across Scales, where the exact decomposition of the horizontal winds into divergent and rotational components may be easily computed. For data from the global simulations, the two approaches yield similar and very accurate results. Errors are largest for the divergent component on synoptic scales, which is shown to be related to a very dominant rotational mode. The errors are, in particular, sufficiently small so that the mesoscale ratio of divergent to rotational kinetic energy can be derived correctly. The proposed technique thus provides a strong observational check of model results with existing large commercial aircraft datasets. The results do, however, show a significant dependence on the height and latitude ranges considered, and the disparate conclusions drawn from previous applications to MOZAIC data may result from the use of different subsets of the data.

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Zhiquan Liu
,
Craig S. Schwartz
,
Chris Snyder
, and
So-Young Ha

Abstract

The impact of assimilating radiance observations from the Advanced Microwave Sounding Unit-A (AMSU-A) on forecasts of several tropical cyclones (TCs) was studied using the Weather Research and Forecasting Model (WRF) and a limited-area ensemble Kalman filter (EnKF). Analysis/forecast cycling experiments with and without AMSU-A radiance assimilation were performed over the Atlantic Ocean for the period 11 August–13 September 2008, when five named storms formed. For convenience, the radiance forward operators and bias-correction coefficients, along with the majority of quality-control decisions, were computed by a separate, preexisting variational assimilation system. The bias-correction coefficients were obtained from 3-month offline statistics and fixed during the EnKF analysis cycles. The vertical location of each radiance observation, which is required for covariance localization in the EnKF, was taken to be the level at which the AMSU-A channels’ weighting functions peaked.

Deterministic 72-h WRF forecasts initialized from the ensemble-mean analyses were evaluated with a focus on TC prediction. Assimilating AMSU-A radiances produced better depictions of the environmental fields when compared to reanalyses and dropwindsonde observations. Radiance assimilation also resulted in substantial improvement of TC track and intensity forecasts with track-error reduction up to 16% for forecasts beyond 36 h. Additionally, assimilating both radiances and satellite winds gave markedly more benefit for TC track forecasts than solely assimilating radiances.

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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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Xuguang Wang
,
Dale M. Barker
,
Chris Snyder
, and
Thomas M. Hamill

Abstract

A hybrid ensemble transform Kalman filter–three-dimensional variational data assimilation (ETKF–3DVAR) system for the Weather Research and Forecasting (WRF) Model is introduced. The system is based on the existing WRF 3DVAR. Unlike WRF 3DVAR, which utilizes a simple, static covariance model to estimate the forecast-error statistics, the hybrid system combines ensemble covariances with the static covariances to estimate the complex, flow-dependent forecast-error statistics. Ensemble covariances are incorporated by using the extended control variable method during the variational minimization. The ensemble perturbations are maintained by the computationally efficient ETKF. As an initial attempt to test and understand the newly developed system, both an observing system simulation experiment under the perfect model assumption (Part I) and the real observation experiment (Part II) were conducted. In these pilot studies, the WRF was run over the North America domain at a coarse grid spacing (200 km) to emphasize synoptic scales, owing to limited computational resources and the large number of experiments conducted. In Part I, simulated radiosonde wind and temperature observations were assimilated. The results demonstrated that the hybrid data assimilation method provided more accurate analyses than the 3DVAR. The horizontal distributions of the errors demonstrated the hybrid analyses had larger improvements over data-sparse regions than over data-dense regions. It was also found that the ETKF ensemble spread in general agreed with the root-mean-square background forecast error for both the first- and second-order measures. Given the coarse resolution, relatively sparse observation network, and perfect model assumption adopted in this part of the study, caution is warranted when extrapolating the results to operational applications.

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Xuguang Wang
,
Dale M. Barker
,
Chris Snyder
, and
Thomas M. Hamill

Abstract

The hybrid ensemble transform Kalman filter–three-dimensional variational data assimilation (ETKF–3DVAR) system developed for the Weather Research and Forecasting (WRF) Model was further tested with real observations, as a follow-up for the observation system simulation experiment (OSSE) conducted in Part I. A domain encompassing North America was considered. Because of limited computational resources and the large number of experiments conducted, the forecasts and analyses employed relatively coarse grid spacing (200 km) to emphasize synoptic scales. As a first effort to explore the new system with real observations, relatively sparse observation datasets consisting of radiosonde wind and temperature during 4 weeks of January 2003 were assimilated. The 12-h forecasts produced by the hybrid analysis produced less root-mean-square error than the 3DVAR. The hybrid improved the forecast more in the western part of the domain than the eastern part. It also produced larger improvements in the upper troposphere. The overall magnitude of the ETKF ensemble spread agreed with the overall magnitude of the background forecast error. For individual variables and layers, the consistency between the spread and the error was less than the OSSE in Part I. Given the coarse resolution and relatively sparse observation network adopted in this study, caution is warranted when extrapolating these results to operational applications. A case study was also performed to further understand a large forecast improvement of the hybrid during the 4-week period. The flow-dependent adjustments produced by the hybrid extended a large distance into the eastern Pacific data-void region. The much improved analysis and forecast by the hybrid in the data void subsequently improved forecasts downstream in the region of verification. Although no moisture observations were assimilated, the hybrid updated the moisture fields flow dependently through cross-variable covariances defined by the ensemble, which improved the forecasts of cyclone development.

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Hui Liu
,
Jeffrey Anderson
,
Ying-Hwa Kuo
,
Chris Snyder
, and
Alain Caya

Abstract

A nonlocal quasi-phase radio occultation (RO) observation operator is evaluated in the assimilation of Challenging Minisatellite Payload (CHAMP) radio occultation refractivity using a Weather Research and Forecasting (WRF) ensemble data assimilation system at 50-km resolution. The nonlocal operator calculates the quasi phase through integration of the model refractivity along the observed ray paths. As a comparison, a local refractivity operator that calculates the model refractivity at the observed ray perigee points is also evaluated. The assimilation is done over North America during January 2003 in two different situations: in conjunction with dense, high-quality radiosonde observations and with only satellite cloud drift wind observations. Analyses of temperature and water vapor with the RO refractivity assimilated using the local and nonlocal operator are verified against nearby withheld radiosonde observations. The bias and RMS errors of the analyses of water vapor and temperature using the nonlocal operator are significantly reduced compared with those using the local operator in the troposphere when the only additional observations are satellite cloud drift winds. The reduction of the bias and RMS errors is reduced when radiosonde observations are assimilated.

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Thomas M. Hamill
,
Chris Snyder
, and
Jeffrey S. Whitaker

Abstract

Approximations to flow-dependent analysis-error covariance singular vectors (AEC SVs) were calculated in a dry, T31 L15 primitive-equation global model. Sets of 400-member ensembles of analyses were generated by an ensemble-based data assimilation system. A sparse network of simulated rawinsonde observations were assimilated, and a perfect model was assumed. Ensembles of 48-h forecasts were also generated from these analyses. The structure of evolved singular vectors was determined by finding the linear combination of the forecast ensemble members that resulted in the largest forecast-error variance, here measured in a total-energy norm north of 20°N latitude. The same linear combination of analyses specifies the initial-time structure that should evolve to the forecast singular vector under assumptions of linearity of error growth.

The structures of these AEC SVs are important because they represent the analysis-error structures associated with the largest forecast errors. If singular vectors using other initial norms have very different structures, this indicates that these structures may be statistically unlikely to occur. The European Centre for Medium-Range Weather Forecasts currently uses singular vectors using an initial total-energy norm [“total-energy singular vectors” or (TE SVs)] to generate perturbations to initialize their ensemble forecasts. Approximate TE SVs were also calculated by drawing an initial random ensemble with perturbations that were white in total energy and applying the same approach as for AEC SVs. Comparing AEC SVs and approximate TE SVs, the AEC SVs had maximum amplitude in midlatitudes near the tropopause, both at the initial and evolved times. The AEC SVs were synoptic in scale, deep, and did not appear to be geographically localized nor tilted dramatically upshear. This contrasts with TE SVs, which started off relatively smaller in scale, were tilted upshear, and had amplitudes typically largest in the lower to midtroposphere.

The difference between AEC SVs and TE SVs suggests that operational ensemble forecasts based on TE SVs could be improved by changing the type of singular vector used to generate initial perturbations. This is particularly true for short-range ensemble forecasts, where the structure of the forecast ensemble is more closely tied to the analysis ensemble.

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