University of Reading


A Nonhydrostatic Numerical Model in Sigma-coordinates and Simulations of Mesoscale Phenomena


Ming Xue

 A dissertation submitted in partial fulfilment

of Doctor's Degree of Philosophy in Meteorology

Department of Meteorology

July, 1989


A nonhydrostatic mesoscale numerical model is developed and simulations of various mesoscale phenomena using this model are described.

The model is based on a quasi-nonhydrostatic equation system in the normalized pressure-sigma coordinates. The system is free of vertical sound waves but contains Lamb wave modes which are however significantly retarded in nonhydrostatic regime. An integration time step comparable to that of an anelastic model system can be used when grid length is around a few kilometres. The current model includes also parameterized microphysical processes.

The solution procedure of the model is analogous to that of an anelastic system in terrain-following height-coordinates. An elliptic equation has to be solved for the geopotential height perturbation. Conventional finite differencing techniques are used except in the advection of thermodynamical variables, where the flux-corrected transport scheme (FCT) is employed. FCT eliminates the problem of 'negative water' generation and significantly improves the model accuracy. Radiative conditions are applied at the lateral boundaries, and at the upper boundary radiative condition is simulated by an absorbing layer. Subgrid scale turbulence is parameterizd using the deformation and Richardson number dependent formulation. Three water phases, i.e. water vapour, cloud water and rain water, are present in the model with Kessler's microphysics parameterizations being adopted.

A number of two dimensional mesoscale problems are studied using the model. They include, dry and moist gravity waves and related phenomena in stratified air streams flowing over a 2-D ridge, long-lived squall line systems and deep orographic convection.

Firstly, the model solutions of small amplitude mountain gravity waves in various regimes are verified against analytical solutions and good agreement is found. The model is then used to simulate the 1972 Boulder severe downslope windstorm and the results lend further support to Smith's nonlinear flow transition mechanism of severe downslope winds. Two events of mountain lee waves which occurred over the west of the British Isles are also studied. The lee wave patterns observed from satellite are well reproduced, and furthermore, the effects of mountain height and scales, orography spectrum and moisture condensation on the formation and evolution of trapped lee waves and associated clouds are examined.

A series of simulations of long-lived squall lines is performed which demonstrate in particular the role of the interaction between cold pool outflow and low-level ambient inflow, and the mechanism by which such an interaction determines and maintains an optimal state of squall line convection. It is shown that it is the momentum rather than the vorticity in the inflow that plays the key role. An optimal condition for the most intense, long-lasting squall lines is proposed based on the propagation speed of the cold pool. The sensitivities of convection to the use of FCT scheme, to spatial resolution and to diffusion are also examined.

Deep orographic convection is also studied using the sigma-coordinate model. The Big Thompson storm that remained quasi-stationary on the upwind slope of the Front Range of the Rocky Mountains and caused flash floods is simulated. An intense and quasi-stationary storm is obtained when an isolated orography profile is used. A plateau type mountain is found to produce fast-moving storm systems which is explained in terms of the cold outflow strength. Experiments showing the effect of modifications to an ambient sounding are also presented and finally the restrictions of two-dimensionality on the storm simulations discussed.


Table of Contents

Cover page and Table of Contents (PDF format) (PS format)

Chapter 1: General Introduction and the Quasi-Non-Hydrostatic Equation System (PDF format) (PS format)

Chapter 2: Model Equations and Numerical Formulation of Dynamic Processes (PDF format) (PS format)

Chapter 3: Thermodynamics, Cloud Microphysics and Subgrid Scale Mixing (PDF format) (PS format)

Chapter 4: Dry and Moist Flow over 2-D Orography: Mountain gravity waves and severe downslope winds (PDF format) (PS format)

Chapter 5: Strong, Long-lived Squall Lines: Two Dimensional Numerical Experiments (PDF format) (PS format)

Chapter 6: Deep Orographic Convection: Numerical Study on The Big Thompson Storm (PDF format) (PS format)

Chapter 7: Conclusions and Discussions (PDF format) (PS format) (PS format)

Appendix A A brief description of the leapfrog-trapezoidal transport algorithm, References and others (PDF format) (PS format)


This thesis can be referenced as:

Xue, M., 1989: A nonhydrostatic numerical model in sigma-coordinates and simulations of mesoscale phenomena. Ph.D thesis, Dept. of Meteorology, Reading University, 258pp.

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