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S. Sokolovskiy, Y-H. Kuo, and W. Wang

Abstract

In this study a nonlocal, linear observation operator for assimilating radio occultation data is evaluated. The operator consists of modeling the excess phase, that is, integrating the refractivity along straight lines tangent to rays, below a certain height. The corresponding observable is the excess phase integrated through the Abel-retrieved refractivity, along the same lines, below the same height. The operator allows very simple implementation (computationally efficient) while accurately accounting for the horizontal refractivity gradients. This is due to significant cancellation of the linearization and discretization errors when modeling the observable. Evaluation of the operator with Challenging Minisatellite Payload (CHAMP) radio occultation data and grid refractivity fields from high-resolution regional analysis over the continental United States showed reduction of the observation error in the troposphere (below 7 km) 1.5–2 times, compared to the error of local refractivity. The operator is useful for the assimilation of radio occultation data by high-resolution weather models in the troposphere.

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Kingtse C. Mo, X. L. Wang, and M. S. Tracton

Abstract

The impact of the sea surface temperature (SST) anomalies on predictions in the extratropics has been studied by comparing circulation changes in general circulation model experiments generated with observed and climatological sea surface temperatures for warm and cold Southern Oscillation events. The small samples may be insufficient for drawing firm conclusions, but results suggest that the linkage between tropical and extratropical circulations in the model resembles observed relationships.

As the atmosphere responds to the warm (cold) tropical SSTs, the convection in the Pacific intensifies (diminishes). The enhanced (suppressed) convection in the tropics enhances (suppresses) the local Hadley circulation and changes the position and strength of the divergent outflow. This in turn changes the position, shape, and strength of the upper-level subtropical jet streams. After the jets move to their new positions, synoptic eddies organize themselves at the exit regions of the jets.

The response time for the upper-level streamfunction in the tropics is about 10 days, but the changes in the position of the subtropical jets occur after 15–20 days. The largest impact on predictions is located in the tropics and downstream in the Pacific-North America and the Pacific-South America regions.

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L. Peng, S.-T. Wang, S.-L. Shieh, M.-D. Cheng, and T.-C. Yeh

Abstract

Surface tracks of some cross-Taiwan tropical cyclones were discontinuous as a result of the blockage of the north-northeast–south-southwest-oriented Central Mountain Range (CMR). This paper tries to identify the variables that may be used to diagnose track continuity in advance. The track records of 131 westbound cross-Taiwan tropical cyclones between 1897 and 2009 are examined. It is found that the track continuity of a westbound cross-Taiwan tropical cyclone depends mostly upon the landfall location (YLF), the approaching direction (ANG), and the maximum wind (VMX) of the cyclone. According to the empirical probability of track continuity estimated from the data, the dependence on YLF, which is nonlinear and remarkably asymmetric with respect to the midpoint of the east coast, may be well approximated by a quadratic function of YLF. The nonlinearity and asymmetry can be interpreted in terms of the length scale of the CMR and the north–south antisymmetry of the cyclonic flow. The estimated dependence of track continuity on cyclone intensity and size may be approximated by a linear function of VMX. The estimated dependence of track continuity on ANG may be approximated by a single term of the modified variable DIR (=|ANG − 110|, where 110 is the direction, in degrees, perpendicular to the CMR’s long axis).

Using the 64 tracks between 1944 and 1996 as the training sample, a logistic regression equation model, built in terms of YLF, YLF square, DIR, and VMX gives an overall accuracy score of 89%. As to the probability estimates of individual tracks, 49 of the 64 tracks have estimated probabilities outside the (0.5 − 0.127, 0.5 + 0.127) RMS error range and are correctly classified. A prediction test using another set of 67 tracks not included in the model-training sample, scores a success rate of 82%. As to the probability predictions for individual tracks, 49 of the 67 tracks have predicted probabilities outside the RMS error range and are correctly predicted. These results confirm the appropriateness of the model and moreover demonstrate that the three parameters, YLF, DIR, and VMX, primarily control the surface track continuity of a westbound tropical cyclone crossing Taiwan.

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Laura C. Slivinski, Gilbert P. Compo, Jeffrey S. Whitaker, Prashant D. Sardeshmukh, Jih-Wang A. Wang, Kate Friedman, and Chesley McColl

Abstract

Given the network of satellite and aircraft observations around the globe, do additional in situ observations impact analyses within a global forecast system? Despite the dense observational network at many levels in the tropical troposphere, assimilating additional sounding observations taken in the eastern tropical Pacific Ocean during the 2016 El Niño Rapid Response (ENRR) locally improves wind, temperature, and humidity 6-h forecasts using a modern assimilation system. Fields from a 50-km reanalysis that assimilates all available observations, including those taken during the ENRR, are compared with those from an otherwise-identical reanalysis that denies all ENRR observations. These observations reveal a bias in the 200-hPa divergence of the assimilating model during a strong El Niño. While the existing observational network partially corrects this bias, the ENRR observations provide a stronger mean correction in the analysis. Significant improvements in the mean-square fit of the first-guess fields to the assimilated ENRR observations demonstrate that they are valuable within the existing network. The effects of the ENRR observations are pronounced in levels of the troposphere that are sparsely observed, particularly 500–800 hPa. Assimilating ENRR observations has mixed effects on the mean-square difference with nearby non-ENRR observations. Using a similar system but with a higher-resolution forecast model yields comparable results to the lower-resolution system. These findings imply a limited improvement in large-scale forecast variability from additional in situ observations, but significant improvements in local 6-h forecasts.

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Kefeng Zhu, Yujie Pan, Ming Xue, Xuguang Wang, Jeffrey S. Whitaker, Stanley G. Benjamin, Stephen S. Weygandt, and Ming Hu

Abstract

A regional ensemble Kalman filter (EnKF) system is established for potential Rapid Refresh (RAP) operational application. The system borrows data processing and observation operators from the gridpoint statistical interpolation (GSI), and precalculates observation priors using the GSI. The ensemble square root Kalman filter (EnSRF) algorithm is used, which updates both the state vector and observation priors. All conventional observations that are used in the operational RAP GSI are assimilated. To minimize computational costs, the EnKF is run at ⅓ of the operational RAP resolution or about 40-km grid spacing, and its performance is compared to the GSI using the same datasets and resolution. Short-range (up to 18 h, the RAP forecast length) forecasts are verified against soundings, surface observations, and precipitation data. Experiments are run with 3-hourly assimilation cycles over a 9-day convectively active retrospective period from spring 2010. The EnKF performance was improved by extensive tuning, including the use of height-dependent covariance localization scales and adaptive covariance inflation. When multiple physics parameterization schemes are employed by the EnKF, forecast errors are further reduced, especially for relative humidity and temperature at the upper levels and for surface variables. The best EnKF configuration produces lower forecast errors than the parallel GSI run. Gilbert skill scores of precipitation forecasts on the 13-km RAP grid initialized from the 3-hourly EnKF analyses are consistently better than those from GSI analyses.

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Yujie Pan, Kefeng Zhu, Ming Xue, Xuguang Wang, Ming Hu, Stanley G. Benjamin, Stephen S. Weygandt, and Jeffrey S. Whitaker

Abstract

A coupled ensemble square root filter–three-dimensional ensemble-variational hybrid (EnSRF–En3DVar) data assimilation (DA) system is developed for the operational Rapid Refresh (RAP) forecasting system. The En3DVar hybrid system employs the extended control variable method, and is built on the NCEP operational gridpoint statistical interpolation (GSI) three-dimensional variational data assimilation (3DVar) framework. It is coupled with an EnSRF system for RAP, which provides ensemble perturbations. Recursive filters (RF) are used to localize ensemble covariance in both horizontal and vertical within the En3DVar. The coupled En3DVar hybrid system is evaluated with 3-h cycles over a 9-day period with active convection. All conventional observations used by operational RAP are included. The En3DVar hybrid system is run at ⅓ of the operational RAP horizontal resolution or about 40-km grid spacing, and its performance is compared to parallel GSI 3DVar and EnSRF runs using the same datasets and resolution. Short-term forecasts initialized from the 3-hourly analyses are verified against sounding and surface observations. When using equally weighted static and ensemble background error covariances and 40 ensemble members, the En3DVar hybrid system outperforms the corresponding GSI 3DVar and EnSRF. When the recursive filter coefficients are tuned to achieve a similar height-dependent localization as in the EnSRF, the En3DVar results using pure ensemble covariance are close to EnSRF. Two-way coupling between EnSRF and En3DVar did not produce noticeable improvement over one-way coupling. Downscaled precipitation forecast skill on the 13-km RAP grid from the En3DVar hybrid is better than those from GSI 3DVar analyses.

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Chaing Chen, Wei-Kuo Tao, Pay-Liam Lin, George S. Lai, S-F. Tseng, and Tai-Chi Chen Wang

Abstract

During the period of 21–25 June 1991, a mei-yu front, observed by the post–Taiwan Area Mesoscale Experiment, produced heavy precipitation along the western side of the Central Mountain Range of Taiwan. Several oceanic mesoscale convective systems were also generated in an area extending from Taiwan to Hong Kong. Numerical experiments using the Penn State–NCAR MM5 mesoscale model were used to understand the intensification of the low-level jet (LLJ). These processes include thermal wind adjustment and convective, inertial, and conditional symmetric instabilities.

Three particular circulations are important in the development of the mei-yu front. First, there is a northward branch of the circulation that develops across the upper-level jet and is mainly caused by the thermal wind adjustment as air parcels enter an upper-level jet streak. The upper-level divergence associated with this branch of the circulation triggers convection.

Second, the southward branch of the circulation, with its rising motion in the frontal region and equatorward sinking motion, is driven by frontal vertical deep convection. The return flow of this circulation at low levels can produce an LLJ through geostrophic adjustment. The intensification of the LLJ is sensitive to the presence of convection.

Third, there is a circulation that develops from low to middle levels that has a slantwise rising and sinking motion in the pre- and postfrontal regions, respectively. From an absolute momentum surface analysis, this slantwise circulation is maintained by conditionally symmetric instability located at low levels ahead of the front. The presence of both the LLJ and moisture is an essential ingredient in fostering this conditionally symmetric unstable environment.

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Yonggang G. Yu, Ning Wang, Jacques Middlecoff, Pedro S. Peixoto, and Mark W. Govett

Abstract

A single software framework is introduced to evaluate numerical accuracy of the A-grid (NICAM) versus C-grid (MPAS) shallow-water model solvers on icosahedral grids. The C-grid staggering scheme excels in numerical noise control and total energy conservation, which results in exceptional stability for long time integration. Its weakness lies in the lack of model error reduction with increasing resolution in specific test cases (especially the root-mean-square error). The A-grid method conserves well potential enstrophy and shows a linear reduction of error with increasing resolution. The gridpoint noise manifests itself clearly on A-grid, but much less on C-grid. We show that the Coriolis force term on C-grid has a larger error than on A-grid. To treat the Coriolis term and kinetic energy gradient on an equal footing on C-grid, we propose combining these two quantities into a single tendency term and computing its value by a linear combination operation. This modification alone reduces numerical errors but still fails to converge the maximum error with resolution. The method of Peixoto can solve the maximum-error nonconvergence problem on C-grid but degrades the numerical stability. For the steady-state thin-layer test (0.01 m in depth), the A-grid method is less susceptible than C-grid methods, which are presumably disrupted by the Hollingsworth instability. The effect of horizontal diffusion on model accuracy and energy conservation is shown in detail. Programming experience shows that software implementation and optimization can strongly influence computational performance for models, although memory requirement and computational load of the two schemes are comparable.

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Xuguang Wang, Thomas M. Hamill, Jeffrey S. Whitaker, and Craig H. Bishop

Abstract

A hybrid ensemble transform Kalman filter (ETKF)–optimum interpolation (OI) analysis scheme is described and compared with an ensemble square root filter (EnSRF) analysis scheme. A two-layer primitive equation model was used under perfect-model assumptions. A simplified observation network was used, and the OI method utilized a static background error covariance constructed from a large inventory of historical forecast errors. The hybrid scheme updated the ensemble mean using a hybridized ensemble and static background-error covariance. The ensemble perturbations in the hybrid scheme were updated by the ETKF scheme. The EnSRF ran parallel data assimilation cycles for each member and serially assimilated the observations. The EnSRF background-error covariance was estimated fully from the ensemble.

For 50-member ensembles, the analyses from the hybrid scheme were as accurate or nearly as accurate as those from the EnSRF, depending on the norm. For 20-member ensembles, the analyses from the hybrid scheme were more accurate than analyses from the EnSRF under certain norms. Both hybrid and EnSRF analyses were more accurate than the analyses from the OI. Further reducing the ensemble size to five members, the EnSRF exhibited filter divergence, whereas the analyses from the hybrid scheme were still better than those updated by the OI. Additionally, the hybrid scheme was less prone to spurious gravity wave activity than the EnSRF, especially when the ensemble size was small. Maximal growth in the ETKF ensemble perturbation space exceeded that in the EnSRF ensemble perturbation space. The relationship of the ETKF ensemble variance to the analysis error variance, a measure of a spread–skill relationship, was similar to that of the EnSRF ensemble. The hybrid scheme can be implemented in a reasonably straightforward manner in the operational variational frameworks, and the computational cost of the hybrid is expected to be much less than the EnSRF in the operational settings.

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Xuguang Wang, Thomas M. Hamill, Jeffrey S. Whitaker, and Craig H. Bishop

Abstract

A hybrid analysis scheme is compared with an ensemble square root filter (EnSRF) analysis scheme in the presence of model errors as a follow-up to a previous perfect-model comparison. In the hybrid scheme, the ensemble perturbations are updated by the ensemble transform Kalman filter (ETKF) and the ensemble mean is updated with a hybrid ensemble and static background-error covariance. The experiments were conducted with a two-layer primitive equation model. The true state was a T127 simulation. Data assimilation experiments were conducted at T31 resolution (3168 complex spectral coefficients), assimilating imperfect observations drawn from the T127 nature run. By design, the magnitude of the truncation error was large, which provided a test on the ability of both schemes to deal with model error. Additive noise was used to parameterize model errors in the background ensemble for both schemes. In the first set of experiments, additive noise was drawn from a large inventory of historical forecast errors; in the second set of experiments, additive noise was drawn from a large inventory of differences between forecasts and analyses. The static covariance was computed correspondingly from the two inventories. The hybrid analysis was statistically significantly more accurate than the EnSRF analysis. The improvement of the hybrid over the EnSRF was smaller when differences of forecasts and analyses were used to form the random noise and the static covariance. The EnSRF analysis was more sensitive to the size of the ensemble than the hybrid. A series of tests was conducted to understand why the EnSRF performed worse than the hybrid. It was shown that the inferior performance of the EnSRF was likely due to the sampling error in the estimation of the model-error covariance in the mean update and the less-balanced EnSRF initial conditions resulting from the extra localizations used in the EnSRF.

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