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Bowen Zhou, Ming Xue, and Kefeng Zhu

Abstract

The model gray zone refers to the range of grid spacings comparable to the dominant length scale of the flow. In the gray zone, the flow is partially resolved and partially subgrid scale (SGS). Neither ensemble-averaging-based parameterizations nor turbulence closures are appropriate for parameterizing the effects of SGS motions on the resolved flow. The gray zone of the convective boundary layer (CBL) is in the range of CBL depth, typically O(1) km. A new approach that seeks explicit resolution of the unstable surface layer through a nest layer of fine grid spacing is proposed to improve CBL parameterization in the gray zone. To provide the theoretical basis for the approach, a linear analytic model is presented, and one-way nested simulations are performed to investigate the dynamical coupling between the surface layer and the mixed layer. The analytic model shows that at the onset of thermal instability, the vertical and horizontal structures of the mixed layer are set by surface-layer forcings. The nested 3D simulations extend the findings from the analytic model and further reveal potential improvements in high-order statistics and resolved convective structures both including and extending above the nest region compared to the stand-alone gray-zone simulations. This study suggests that when the most energetic scales of CBL convection are resolved in the surface layer, the overall simulation of the CBL improves at gray-zone resolutions.

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Bowen Zhou, Ming Xue, and Kefeng Zhu

Abstract

A grid-refinement-based method is implemented in a community atmospheric model to improve the representation of convective boundary layer (CBL) turbulence on gray-zone [i.e., ~O(1) km] grids. At this resolution, CBL convection is partially resolved and partially subgrid scale (SGS), such that neither traditional mesoscale planetary boundary layer (PBL) schemes nor SGS closures for large-eddy simulations (LESs) are appropriate. The proposed method utilizes two-way interactive nesting to refine the horizontal resolution of the unstable surface layer of the daytime CBL. SGS turbulent mixing in the fine nest and coarse parent grids are parameterized by an LES turbulence closure and a PBL scheme, respectively. The method does not rely on predetermined empirical functions to introduce grid (scale) dependency and in theory works with any PBL scheme. Compared to the stand-alone gray-zone simulation, the proposed approach shows improvements in terms of higher-order statistics, the timing of the onset of resolved convection, and the convective structures. A deficiency of the method exists when the nest domain is limited to the surface layer; the convective structures become gradually contaminated by spurious convection on the parent gray-zone grid. A deeper nest domain alleviates the issue at increased computational costs.

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Bowen Zhou, Kefeng Zhu, and Ming Xue

Abstract

Compared to the representation of vertical turbulent mixing through various planetary boundary layer (PBL) schemes, the treatment of horizontal turbulent mixing in the boundary layer has received much less attention. In mesoscale and convective-scale models, subgrid-scale horizontal turbulent mixing has traditionally been associated with mesoscale circulations or eddies. Its parameterization most often adopts the gradient-diffusion model, where the horizontal mixing coefficients are usually set constant, or through the 2D Smagorinsky formulation, or in some cases based on the 1.5-order turbulence kinetic energy (TKE) closure. For horizontal turbulent mixing associated with boundary layer eddies, the traditional schemes are shown to perform poorly. This work investigates the characteristic turbulence velocity and length scales based on analysis of a well-resolved, wide-domain large-eddy simulation of a convective boundary layer (CBL). To improve the representation of horizontal turbulent mixing by CBL eddies, a class of schemes is proposed with different levels of sophistication. The first two schemes can be used together with first-order PBL schemes, while the third uses TKE to define its characteristic velocity scale and can be used together with TKE-based higher-order PBL schemes. The proposed parameterizations are tested a posteriori in idealized simulations of turbulent dispersion of a passive scalar. Comparisons show improved horizontal dispersion by the proposed schemes and further demonstrate the weakness of the existing schemes.

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Bowen Zhou, Yuhuan Li, and Kefeng Zhu

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Based on a priori analysis of large-eddy simulations (LESs) of the convective atmospheric boundary layer, improved turbulent mixing and dissipation length scales are proposed for a turbulence kinetic energy (TKE)-based planetary boundary layer (PBL) scheme. The turbulent mixing length incorporates surface similarity and TKE constraints in the surface layer, and makes adjustments for lateral entrainment effects in the mixed layer. The dissipation length is constructed based on balanced TKE budgets accounting for shear, buoyancy, and turbulent mixing. A nongradient term is added to the TKE flux to correct for nonlocal turbulent mixing of TKE. The improved length scales are implemented into a PBL scheme, and are tested with idealized single-column convective boundary layer (CBL) cases. Results exhibit robust applicability across a broad CBL stability range, and are in good agreement with LES benchmark simulations. It is then implemented into a community atmospheric model and further evaluated with 3D real-case simulations. Results of the new scheme are of comparable quality to three other well-established PBL schemes. Comparisons between simulated and radiosonde-observed profiles show favorable performance of the new scheme on a clear day.

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Bowen Zhou, Shiwei Sun, Jianning Sun, and Kefeng Zhu

Abstract

The vertical turbulent velocity variance normalized by the convective velocity squared as a function of the boundary layer depth–normalized height [i.e., ] in the convective boundary layer (CBL) over a homogeneous surface exhibits a near-universal profile, as demonstrated by field observations, laboratory experiments, and numerical simulations. The profile holds over a wide CBL stability range set by the friction velocity, CBL depth, and surface heating. In contrast, the normalized horizontal turbulent velocity variance increases monotonically with decreasing stability. This study investigates the independence of the profile to changes in CBL stability, or more precisely, wind shear. Large-eddy simulations of several convective and neutral cases are performed by varying surface heating and geostrophic winds. Analysis of the turbulent kinetic energy budgets reveals that the conversion term between and depends almost entirely on buoyancy. This explains why does not vary with shear, which is a source to only. Further analysis through rotational and divergent decomposition suggests that the near-universal profile of is fundamentally related to the dynamics and interactions of local and nonlocal CBL turbulence. Specifically, the preferential interactions between local wavenumbers and the downscale energy cascade of CBL turbulence offer plausible explanations to the universal profile of .

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Shiwei Sun, Bowen Zhou, Ming Xue, and Kefeng Zhu

Abstract

In numerical simulations of deep convection at kilometer-scale horizontal resolutions, in-cloud subgrid-scale (SGS) turbulence plays an important role in the transport of heat, moisture, and other scalars. By coarse graining a 50 m high-resolution large-eddy simulation (LES) of an idealized supercell storm to kilometer-scale grid spacings ranging from 250 m to 4 km, the SGS fluxes of heat, moisture, cloud, and precipitating water contents are diagnosed a priori. The kilometer-scale simulations are shown to be within the “gray zone” as in-cloud SGS turbulent fluxes are comparable in magnitude to the resolved fluxes at 4 km spacing, and do not become negligible until ~500 m spacing. Vertical and horizontal SGS fluxes are of comparable magnitudes; both exhibit nonlocal characteristics associated with deep convection as opposed to local gradient-diffusion type of turbulent mixing. As such, they are poorly parameterized by eddy-diffusivity-based closures. To improve the SGS representation of turbulent fluxes in deep convective storms, a scale-similarity LES closure is adapted to kilometer-scale simulations. The model exhibits good correlations with LES-diagnosed SGS fluxes, and is capable of representing countergradient fluxes. In a posteriori tests, supercell storms simulated with the refined similarity closure model at kilometer-scale resolutions show better agreement with the LES benchmark in terms of SGS fluxes than those with a turbulent-kinetic-energy-based gradient-diffusion scheme. However, it underestimates the strength of updrafts, which is suggested to be a consequence of the model effective resolution being lower than the native grid resolution.

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Liping Luo, Ming Xue, Kefeng Zhu, and Bowen Zhou

Abstract

During the afternoon of 28 April 2015, a multicellular convective system swept southward through much of Jiangsu Province, China, over about 7 h, producing egg-sized hailstones on the ground. The hailstorm event is simulated using the Advanced Regional Prediction System (ARPS) at 1-km grid spacing. Different configurations of the Milbrandt–Yau microphysics scheme are used, predicting one, two, and three moments of the hydrometeor particle size distributions (PSDs). Simulated reflectivity and maximum estimated size of hail (MESH) derived from the simulations are verified against reflectivity observed by operational S-band Doppler radars and radar-derived MESH, respectively. Comparisons suggest that the general evolution of the hailstorm is better predicted by the three-moment scheme, and neighborhood-based MESH evaluation further confirms the advantage of the three-moment scheme in hail size prediction. Surface accumulated hail mass, number, and hail distribution characteristics within simulated storms are examined across sensitivity experiments. Results suggest that multimoment schemes produce more realistic hail distribution characteristics, with the three-moment scheme performing the best. Size sorting is found to play a significant role in determining hail distribution within the storms. Detailed microphysical budget analyses are conducted for each experiment, and results indicate that the differences in hail growth processes among the experiments can be mainly ascribed to the different treatments of the shape parameter within different microphysics schemes. Both the differences in size sorting and hail growth processes contribute to the simulated hail distribution differences within storms and at the surface.

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Bowen Zhou, Shiwei Sun, Kai Yao, and Kefeng Zhu

Abstract

Turbulent mixing in the daytime convective boundary layer (CBL) is carried out by organized nonlocal updrafts and smaller local eddies. In the upper mixed layer of the CBL, heat fluxes associated with nonlocal updrafts are directed up the local potential temperature gradient. To reproduce such countergradient behavior in parameterizations, a class of planetary boundary layer schemes adopts a countergradient correction term in addition to the classic downgradient eddy-diffusion term. Such schemes are popular because of their simple formulation and effective performance. This study reexamines those schemes to investigate the physical representations of the gradient and countergradient (GCG) terms, and to rebut the often-implied association of the GCG terms with heat fluxes due to local and nonlocal (LNL) eddies. To do so, large-eddy simulations (LESs) of six idealized CBL cases are performed. The GCG fluxes are computed a priori with horizontally averaged LES data, while the LNL fluxes are diagnosed through conditional sampling and Fourier decomposition of the LES flow field. It is found that in the upper mixed layer, the gradient term predicts downward fluxes in the presence of positive mean potential temperature gradient but is compensated by the upward countergradient correction flux, which is larger than the total heat flux. However, neither downward local fluxes nor larger-than-total nonlocal fluxes are diagnosed from LES. The difference reflects reduced turbulence efficiency for GCG fluxes and, in terms of physics, conceptual deficiencies in the GCG representation of CBL heat fluxes.

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Ming Xue, Jordan Schleif, Fanyou Kong, Kevin W. Thomas, Yunheng Wang, and Kefeng Zhu

Abstract

Twice-daily 48-h tropical cyclone (TC) forecasts were produced for the fall 2010 Atlantic hurricane season using the Advanced Research core of the Weather Research and Forecasting (WRF-ARW) model on a large 4-km grid covering much of the northern Atlantic. WRF forecasts initialized from operational Global Forecast System (GFS) analyses based on the gridpoint statistical interpolation (GSI) three-dimensional variational data assimilation (3DVAR) system and from experimental global ensemble Kalman filter (EnKF) analyses, and corresponding global GFS forecasts were intercompared. For the track, WRF forecasts show improvement over GFS forecasts using either set of initial conditions (ICs). The EnKF-initialized GFS and WRF are also better than the corresponding GSI-initialized forecasts, but the difference is not always statistically significant. At all lead times, the WRF track errors are comparable to or smaller than the National Hurricane Center (NHC) official track forecast error, with those of the EnKF WRF being smallest. For weaker TCs, more improvement comes from the model (resolution) than from the ICs. For hurricane intensity TCs, EnKF ICs produce better track forecasts than GSI ICs, with the best forecast coming from WRF at most lead times. For intensity, EnKF ICs consistently outperform GSI ICs in both models for weaker TCs. For hurricane-strength TCs, EnKF ICs produce forecasts statistically indistinguishable from GSI ICs in either model. For all TCs combined, WRF produces about half the error of the corresponding GFS simulation beyond 24 h, and at 36 and 48 h, the errors are smaller than those from NHC official forecasts. The improvement is even greater for hurricane-strength TCs. Overall, the WRF forecasts initialized with EnKF ICs have the smallest intensity error, and the difference is statistically significant compared to the GFS 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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