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Ming Fang and Ka Kit Tung

Abstract

The classical problem of viscosity-driven, axially symmetric meridional circulation, partly solved only for the midlatitudes by Charney, is solved here analytically in the whole globe and for any value of viscosity coefficient ν. The solution satisfies Hide's theorem for any Ekman number when Ro < 80E 2, where Ro is the Rossby number and E is the Ekman number. For Ro > 80E 2, the linear solution ceases to be asymptotically valid. The nonlinear, nearly inviscid regime of Held and Hou presumably is a subset of the second regime (for E → 0+ and Ro fixed).

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Ming Fang and Ka Kit Tung

Abstract

The time-dependent Hadley circulation is studied numerically in a nonlinear, nearly inviscid, axially symmetric primitive equation model, with the heating varying periodically on an annual cycle. The annual average of the Hadley circulation strength in this model with time-dependent heating is about a factor of 2 stronger than the steady-state response to the annual mean heating and is closer to the observed strength in the real atmosphere. This is caused by the fact that heating centered off-equator tends to produce stronger meridional circulation in the winter hemisphere than in the case when the heating maximum is located at the equator, as pointed out previously by Lindzen and Hou. However, unlike the steady-state solutions, there is no abrupt change as the heating center is moved off the equator.

The temperature response in this time-dependent model is simple to understand. In the tropical region, where there is a variable, but persistent, Hadley circulation, the temperature is homogenized latitudinally. In the high-latitude region, where there is no meridional circulation (in the absence of the eddies), the temperature response goes through an annual cycle with a phase lag relative to the phase of the heating. This response is as predicted by the simple time-dependent temperature equation in the absence of meridional circulation.

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Ming Fang and Richard J. Doviak

Abstract

Contrary to accepted usage, the second central moment of the Doppler spectrum is not the sum of the second central moments of individual spectral broadening mechanisms. A rigorous theoretical derivation of the spectrum width observed with short dwell times reveals that the sum cannot strictly be taken for the variances associated with various spectral broadening mechanisms and that an added-term coupling shear with turbulence is needed. Furthermore, shear and antenna rotation are coupled. The theoretical expressions derived herein apply to radars with fixed or scanning beams.

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Ming Fang and Ka Kit Tung

Abstract

Simple analytic solutions are constructed for an axially symmetric, nonlinear, slightly viscous circulation in a Boussinesq atmosphere in the presence of intense convection at an intertropical convergence zone. The latitude–height extent of the Hadley circulation is obtained, as well as its streamfunction, zonal wind, and temperature distribution. Numerical solutions of the viscous primitive equations are also obtained to verify the analytic solutions. The strength of the circulation is stronger than previous results based on dry models and is now close to the observed value. The extent of the Hadley region is also quite realistic.

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Ming Fang and Ka Kit Tung

Abstract

Analytic and numerical solutions are found for the nonlinear Hadley circulation problem with respect to the dependence of the strength and the extent of the Hadley circulation on the thermal relaxation time. The dependence on the thermal relaxation time is a crucial parameter to investigate since the simplifications used in previous studies assumed a large thermal relaxation time, to justify the geostrophic assumption, but in the presence of moist convection, thermal relaxation may be fast in the convection regions. In this study, a primitive equation model is used to investigate the effect of different latitudinal distribution of thermal relaxation time on the extent of the circulation cells, the zonal wind, the temperature distribution, and the strength of the meridional circulations. It is found that the extent of the Hadley circulation is insensitive to the value of the thermal relaxation time τ, while the strength of the circulation is very sensitive to τ (but in a way that is predictable based on the 1/τ scaling).

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Ming Fang, Richard J. Doviak, and Valery Melnikov

Abstract

Spectrum widths, one of the three moments measured and displayed by the Weather Surveillance Radar-1988 Doppler (WSR-88D), are categorized for various weather conditions showing both expected and unexpected results. Weather phenomena are classified into seven categories based on radar observations, and the statistics of the censored spectrum width fields for each of the categories are obtained. Daytime fair weather without birds, stratiform rain and snow, and isolated tornadic storms produce weather signals that have the smallest volumetric median values of spectrum widths (i.e., < 2 m s−1). Surprisingly, the median spectrum width values in the isolated tornadic storms are as low (i.e., <2 m s−1) as in the fair weather (without the presence of echoes from birds). The median spectrum width value from fair weather regions contaminated with bird echoes is larger (i.e., 3.0 m s−1). The largest median spectrum width values, ranging from 4.0 to 5.4 m s−1, are associated with embedded areal squall lines. Clusters of severe storms and storms along broken squall lines appear to have median spectrum width values between these two regimes. Spectrum width fields are also shown to be more prone to errors than fields of reflectivity and velocity. Errors mainly result from overlaid echoes, improper automatic gain control (AGC) settings, low signal-to-noise ratios, and incorrect estimates of noise power. Thus spectrum width data fields require extensive censoring. The most persistent errors appear to be those related to overlaid weather signals and low signal-to-noise ratios.

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Bruce Albrecht, Ming Fang, and Virendra Ghate

Abstract

Observations made at the Atmospheric Radiation Measurement (ARM) Program’s Southern Great Plains (SGP) site during uniform nonprecipitating stratocumulus cloud conditions for a 14-h period are used to examine cloud-top entrainment processes and parameterizations. The observations from a vertically pointing Doppler cloud radar provide estimates of vertical velocity variance and energy dissipation rate (EDR) terms in the parameterized turbulent kinetic energy (TKE) budget of the entrainment zone. Hourly averages of the vertical velocity variance term in the TKE entrainment formulation correlated strongly (r = 0.72) with the dissipation rate term in the entrainment zone, with an increased correlation (r = 0.92) when accounting for the nighttime decoupling of the boundary layer. Independent estimates of entrainment rates were obtained from an inversion-height budget using the local time derivative and horizontal advection of cloud-top height together with large-scale vertical velocity at the boundary layer inversion from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis model. The mean entrainment rate from the inversion-height budget during the 14-h period was 0.74 ± 0.15 cm s−1 and was used to calculate bulk coefficients for entrainment parameterizations based on convective velocity scale w* and TKE budgets of the entrainment zone. The hourly values of entrainment rates calculated using these coefficients exhibited good agreement with those calculated from the inversion-height budget associated with substantial changes in surface buoyancy production and cloud-top radiative cooling. The results indicate a strong potential for making entrainment rate estimates directly from radar vertical velocity variance and the EDR measurements.

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Xiaomin Chen, Ming Xue, and Juan Fang

Abstract

The notable prelandfall rapid intensification (RI) of Typhoon Mujigae (2015) over abnormally warm water with moderate vertical wind shear (VWS) is investigated by performing a set of full-physics model simulations initialized with different sea surface temperatures (SSTs). While all experiments can reproduce RI, tropical cyclones (TCs) in cooler experiments initiate the RI 13 h later than those in warmer experiments. A comparison of structural changes preceding RI onset in two representative experiments with warmer and cooler SSTs (i.e., CTL and S1) indicates that both TCs undergo similar vertical alignment despite the moderate VWS. RI onset in CTL occurs ~8 h before the full vertical alignment, while that in S1 occurs ~5 h after. In both experiments precipitation becomes more symmetrically distributed around the vortex as vortex tilt decreases. In CTL, precipitation symmetricity is higher in the inner-core region, particularly for stratiform precipitation. All experiments indicate that RI onset occurs when the radius of maximum wind (RMW) contraction reaches a certain degree measured in terms of local Rossby number. The contraction occurs much earlier in CTL, leading to earlier RI. These results suggest that vertical alignment, albeit necessary, is not an effective RI indicator under different SSTs, while a more immediate cause of RI is the formation of a strong/compact inner core with high precipitation symmetry. Diagnoses using the Sawyer–Eliassen equation indicate that in CTL the enhanced microphysical diabatic heating of additional midlevel and deep convection along with surface friction contribute to stronger boundary layer inflow near/inside the RMW, facilitating earlier RMW contraction.

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Xiaomin Chen, Yuqing Wang, Juan Fang, and Ming Xue

Abstract

In Part I of this study, the role of environmental monsoon flow in the onset of rapid intensification (RI) of Typhoon Vicente (2012) was discussed. In this Part II, key inner-core processes that effectively resist environmental vertical wind shear during RI onset are investigated. The convective precipitation shield (CPS) embedded in the downshear convergence zone plays a vital role in preconditioning the tropical cyclone (TC) vortex before RI. The CPS induces a mesoscale positive vorticity band (PVB) characterized by vortical hot tower structures upstream and shallower structures (~4 km) downstream. Multiple mesovortices form successively along the PVB and are detached from the PVB at its downstream end, rotating cyclonically around the TC center. The sufficient amount of vorticity anomalies in the PVB facilitates the upscale growth of a mesovortex into a reformed inner vortex, which eventually replaces the parent TC vortex (i.e., downshear reformation), leading to RI onset. The timing of downshear reformation is closely related to the gradually enhancing convective activity in the CPS, which is likely triggered/enhanced by increased surface heat fluxes in the downshear-left quadrant. Results from vorticity budget analyses suggest that convection in the CPS contributes to the vertical development of the tilted reformed inner vortex largely through tilting horizontal vorticity and advecting vorticity upward. The enhanced midlevel inner vortex precesses more quickly into the upshear flank and is concurrently advected toward the low-level inner vortex, resulting in vertical alignment of the reformed inner vortex and parent TC vortex at the end of downshear reformation.

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Fang-Ching Chien, Ying-Hwa Kuo, and Ming-Jen Yang

Abstract

This study presents precipitation verification, in the Taiwan area, for a real-time Pennsylvania State University–National Center for Atmospheric Research Fifth-Generation Mesoscale Model (MM5) system during the 1998 Mei-yu season. The highest equitable threat score (ETS) of precipitation forecasts, verified against observed precipitation, was about 0.2 at the 2.5-mm threshold for this nearly 2-month period. The complex and steep terrain in this region presented great challenges to the 15-km model in predicting realistic rainfall because the precipitation was driven by local forcings such as thermal effects and orographic lifting. In addition, the lack of observational data over the surrounding ocean greatly limited the quality of the model's initial data. It was found that the model system more accurately simulated nighttime rainfall than daytime precipitation. This was caused by the model underforecasting the rainfall events that resulted from solar heating and orographic lifting over the mountain slopes during the daytime hours. Precipitation, however, was overforecast over the high mountain regions (>1200 m). Further, the analysis of ETS with regard to the terrain height indicated that the model performed better over the lowlands than over the mountainous areas (slopes and highlands). It was discovered that the ETSs were much higher for precipitation forecasts after the onset of the east Asia summer monsoon than prior to the onset. Overall, the model more accurately predicted precipitation for the rainfall events associated with the Mei-yu front and the accompanying mesoscale convective systems than it predicted precipitation associated with the local forcings.

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