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Qin Xu
and
Shouting Gao

Abstract

It is shown that the geometric shape of the cold dome in the two-layer model of cold air damming of Xu can be described approximately by a cubic polynomial and thus a set of coupled algebraic equations can be derived to quantify the scale and intensity of cold air damming as functions of the external parameters that characterize the environmental flow. In particular, these functions are easily computed and plotted in the parameter space, showing quantitatively how the cold dome width (scaled by the Rossby radius of deformation) and mountain-parallel jet speed change with the Froude number, surface roughness, inertial aspect ratio, and incident angle of the upstream inflow. The results also show that the cold dome width and mountain-parallel jet speed are insensitive to the depth of the upper-layer cross-mountain flow if the cross-mountain flow is sufficiently deep. The surface roughness and inverse inertial aspect ratio are found to have nearly the same control on the cold dome width and mountain-parallel jet speed and, thus, can be combined into a single parameter-the normalized Ekman number.

The algebraic equations are shown to be useful for diagnoses or local forecasts of cold air damming provided the external parameters are properly estimated from the operational analyses or predictions. Examples of application are given for three cases of cold air damming.

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Lingkun Ran
and
Shouting Gao

Abstract

A three-dimensional, nonhydrostatic local wave-activity relation for pseudomomentum is derived from the nonhydrostatic primitive equations in Cartesian coordinates by using an extension of the momentum–Casimir method. The stationary and zonally symmetric basic states are chosen and a Casimir function, which is the single-valued function of potential vorticity and potential temperature, is introduced in the derivation.

The wave-activity density and wave-activity flux of the local wave-activity relation for pseudomomentum are expressed entirely in terms of Eulerian quantities so that they are easily calculated with atmospheric data and do not require the knowledge of particle placements. Constructed in the ageostrophic and nonhydrostatic dynamical framework, the local wave-activity relation for pseudomomentum is applicable to diagnosing the evolution and propagation of mesoscale weather systems.

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Qin Xu
,
Ting Lei
, and
Shouting Gao

Abstract

Maximum nonmodal growths of total perturbation energy are computed for symmetric perturbations constructed from the normal modes presented in Part I. The results show that the maximum nonmodal growths are larger than the energy growth produced by any single normal mode for a give optimization time, and this is simply because the normal modes are nonorthogonal (measured by the inner product associated with the total perturbation energy norm). It is shown that the maximum nonmodal growths are produced mainly by paired modes, and this can be explained by the fact that the streamfunction component modes are partially orthogonal between different pairs and parallel within each pair in the streamfunction subspace. When the optimization time is very short (compared with the inverse Coriolis parameter), the nonmodal growth is produced mainly by the paired fastest propagating modes. When the optimization time is not short, the maximum nonmodal growth is produced almost solely by the paired slowest propagating modes and the growth can be very large for a wide range of optimization time if the parameter point is near the boundary and outside the unstable region. If the parameter point is near the boundary but inside the unstable region, the paired slowest propagating modes can contribute significantly to the energy growth before the fastest growing mode becomes the dominant component.

The maximum nonmodal growths produced by paired modes are derived analytically. The analytical solutions compare well with the numerical results obtained in the truncated normal mode space. The analytical solutions reveal the basic mechanisms for four types of maximum nonmodal energy growths: the PP1 and PP2 nonmodal growths produced by paired propagating modes and the GD1 and GD2 nonmodal growths produced by paired growing and decaying modes. The PP1 growth is characterized by the increase of the cross-band kinetic energy that excessively offsets the decrease of the along-band kinetic and buoyancy energy. The situation is opposite for the PP2 growth. The GD1 (or GD2) growth is characterized by the reduction of the initial cross-band kinetic energy (or initial along-band kinetic and buoyancy energy) due to the inclusion of the decaying mode.

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Shahzada Adnan
,
Kalim Ullah
, and
Gao Shouting

Abstract

The climatology of precipitation and drought are analyzed by using different indices in the region of south central Asia (SCA). The spatial precipitation pattern is delineated by using principal component analysis (PCA) over the period of 1951–2010, which identifies six subregions in the SCA. The monthly and annual trends of precipitation were analyzed by applying the five statistical tests: Student’s t, Mann–Kendall, and Spearman’s rho tests for linear trend and turning point analysis and Sen’s slope for randomness and slope magnitude, respectively, at the α = 0.05 significance level. The time series analysis shows data similarity between Global Precipitation Climatology Centre (GPCC) and area-weighted precipitation of 52 meteorological stations in Pakistan, which results in a high correlation (R 2 = 0.93). Two main drought periods were identified (1971 and 2000–02); also, 2001 was an extremely dry year in the SCA region. The drought in 1952 was the most severe in Pakistan; the longest drought period was 2000–02. Intense droughts were reported in the whole SCA region when the annual percent of precipitation was below 80%. It is noted that the A-5 region (northeast SCA), where 19 droughts were reported, is the most vulnerable. The monthly precipitation analysis shows a significant increasing trend in the months of September and June in the A-3 (northwest SCA) and A-5 regions, respectively, while a decreasing trend is observed in January and August in the A-4 region (east SCA). The decadal analysis shows significant decreasing trend (−21.5 mm decade−1) in region A-4, while the highest increasing trends (17.1 and 7.5 mm decade−1) are observed in Pakistan and the A-5 region respectively.

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Qin Xu
,
Shouting Gao
, and
Brian H. Fiedler

Abstract

The previously developed two-layer model of cold air damming is extended to include upstream cold air inflow. The upper layer is an isentropic cross-mountain flow. The lower layer is a cold boundary layer flow partially blocked by a two-dimensional mountain with a cold dome formed on the windward side of the mountain. The interface represents a sloping inversion layer coupling the two layers. The shape of the interface can be approximated by a cubic polynomial, and the interfacial coupling condition yields a set of algebraic equations that quantify the scale and intensity of the dammed flow as functions of the external parameters characterizing the environmental conditions. It is found that the cold dome shrinks as the Froude number increases or, to a minor degree, as the Ekman number decreases or/and the upstream inflow veers from northeasterly to southeasterly (with respect to a longitudinal mountain to the west). The mountain-parallel jet speed increases as the Ekman number decreases or/and the upstream inflow veers from southeasterly to northeasterly or, to a minor degree, as the Froude number decreases. The theoretical results are qualitatively verified by numerical simulations with a full model and interpreted physically in comparison with the results of the previous two-layer model. It is also shown that our two-dimensional model may (or may not) be applied to a quasi-two-dimensional mountain ridge if the length scale of the ridge is (or is not) significantly larger than the Rossby radius of deformation multiplied by the inverse Froude number.

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Shouting Gao
,
Lingkun Ran
, and
Xiaofan Li

Abstract

The effects of ice microphysics on rainfall and thermodynamic processes in the tropical deep convective regime are examined based on hourly zonal-mean data from a pair of two-dimensional cloud-resolving simulations: one simulation with ice clouds and the other without ice clouds. The model is integrated for 21 days with the imposed large-scale vertical velocity, zonal wind, and horizontal advections obtained from the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment. The experiment without ice clouds produces a larger amount of cloud water and a smaller surface rain rate than the experiment with ice clouds because of the exclusion of vapor deposition processes in the experiment without ice clouds. The experiment without ice clouds produces cold and moist states simply because it generates a smaller cloud heating rate and consumes a smaller amount of vapor than does the experiment with ice clouds.

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Shouting Gao
,
Yushu Zhou
, and
Xiaofan Li

Abstract

Effects of diurnal variations on tropical heat and water vapor equilibrium states are investigated based on hourly data from two-dimensional cloud-resolving simulations. The model is integrated for 40 days and the simulations reach equilibrium states in all experiments. The simulation with a time-invariant solar zenith angle produces a colder and drier equilibrium state than does the simulation with a diurnally varied solar zenith angle. The simulation with a diurnally varied sea surface temperature generates a colder equilibrium state than does the simulation with a time-invariant sea surface temperature. Mass-weighted mean temperature and precipitable water budgets are analyzed to explain the thermodynamic differences. The simulation with the time-invariant solar zenith angle produces less solar heating, more condensation, and consumes more moisture than the simulation with the diurnally varied solar zenith angle. The simulation with the diurnally varied sea surface temperature produces a colder temperature through less latent heating and more IR cooling than the simulation with the time-invariant sea surface temperature.

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Qin Xu
,
Huijuan Lu
,
Shouting Gao
,
Ming Xue
, and
Mingjing Tong

Abstract

A time-expanded sampling approach is proposed for the ensemble Kalman filter (EnKF). This approach samples a series of perturbed state vectors from each prediction run not only at the analysis time (as the conventional approach does) but also at other time levels in the vicinity of the analysis time. Since all the sampled state vectors are used to construct the ensemble, the number of required prediction runs can be much smaller than the ensemble size and this can reduce the computational cost. Since the sampling time interval can be adjusted to optimize the ensemble spread and enrich the ensemble structures, the proposed approach can improve the EnKF performance even though the number of prediction runs is greatly reduced. The potential merits of the time-expanded sampling approach are demonstrated by assimilation experiments with simulated radar observations for a supercell storm case.

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John P. Boyd
,
Difei Deng
,
Qiu-Shi Chen
, and
Shouting Gao

Abstract

Bivariate Fourier series have many benefits in limited-area modeling (LAM), weather forecasting, and meteorological data analysis. However, atmospheric data are not spatially periodic on the LAM domain (“window”), which can be normalized to the unit square (x, y) ∈ [0, 1] ⊗ [0, 1] by rescaling the coordinates. Most Fourier LAM meteorology has employed rather low-order methods that have been quite successful in spite of Gibbs phenomenon at the boundaries of the artificial periodicity window. In this article, the authors explain why. Because data near the boundary between the high-resolution LAM window and the low-resolution global model are necessarily suspect, corrupted by the discontinuity in resolution, meteorologists routinely ignore LAM results in a buffer strip of nondimensional width D, and analyze only the Fourier sums in the smaller domain (x, y) ∈ [D, 1 − D] ⊗ [D, 1 − D]. It is shown that the error in a one-dimensional Fourier series with N terms or in a two-dimensional series with N 2 terms, is smaller by a factor of N on a boundary-buffer-discarded domain than on the full unit square. A variety of procedures for raising the order of Fourier series convergence are described, and it is explained how the deletion of the boundary strip greatly simplifies and improves these enhancements. The prime exemplar is solving the Poisson equation with homogeneous boundary conditions by sine series, but the authors also discuss the Laplace equation with inhomogeneous boundary conditions.

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Li Yaodong
,
Wang Yun
,
Song Yang
,
Hu Liang
,
Gao Shouting
, and
Rong Fu

Abstract

Summer convective systems (CSs) initiated over the Tibetan Plateau identified by the International Satellite Cloud Climatology Project (ISCCP) deep convection database and associated Tropical Rainfall Measuring Mission (TRMM) precipitation for 1998–2001 have been analyzed for their basic characteristics in terms of initiation, distribution, trajectory, development, life cycle, convective intensity, and precipitation. Summer convective systems have a dominant center over the Hengduan Mountain and a secondary center over the Yaluzangbu River Valley. Precipitation associated with these CSs contributes more than 60% of total precipitation over the central-eastern area of the Tibetan Plateau and 30%–40% over the adjacent region to its southeast. The average CS life cycle is about 36 h; 85% of CSs disappear within 60 h of their initiation. About 50% of CSs do not move out of the Tibetan region, with the remainder split into eastward- and southward-moving components. These CSs moving out the Tibetan Plateau are generally larger, have longer life spans, and produce more rainfall than those staying inside the region. Convective system occurrences and associated rainfall present robust diurnal variations. The midafternoon maximum of CS initiation and associated rainfall over the plateau is mainly induced by solar heating linked to the unique Tibetan geography. The delayed afternoon–late night peak of rainfall from CSs propagating out of this region is a combined outcome of multiple mechanisms working together. Results suggest that interactions of summer Tibetan CSs with the orientation of the unique Tibetan geography and the surrounding atmospheric circulations are important for the development, intensification, propagation, and life span of these CSs.

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