Experiments on Regional Forecasting Using a Stretched-Coordinate

263

Short- and Medium-Range Numerical Weather Prediction Collectionof Papers Presented at the VVA/O/IUGG NWP Symposium, Tokyo, 4-8 August 1986

Experiments on Regional Forecasting Using a Stretched-Coordinate General Circulation Model

By O.P. Sharma*, H. Upadhyaya*, Th. Braine-Bonnaireand R. Sadourny Laboratoire de Meteorologie Dynamique du CNRS, Ecole Normals Superieure, 75231 Paris Cedex 05 (Manuscript received 4 November

1986, in revised form 8 February 1987)

Abstract The

feasibility of regional forecasting using a stretched-coordinate global general circu-

lation model enhanced

is tested on a series of simulations of the 1979 summer

resolution (or "zoom")

over

the Indian Ocean

is found that the medium-to-long-range

monsoon

onset, using

area via a coordinate transform. It

simulations are sensitive to the formulation

of lateral

diffusion and its dependency on grid size. The present experiments, performed at relatively coarse resolution, show definite improvement of the simulated circulation and precipitation features over the monsoon

area in the medium

model; or

1. Introduction The

problem

range, du to the use of coordinate stretching.

of regional

forecasting

is

usually addressed by using limited-area finemesh models, nested in coarser-mesh general circulation models which provide the required information at lateral boundaries. The actual boundary conditions, however, are delicate to specify properly. In particular,noise tends to be easily generated in the vicinity of lateral boundaries, due to the trapping of small-scale energy in the fine-mesh area. The problem has been extensively studied {e.g. Miyakoda and Rosati, 1977; Davies, 1983), and many different approaches has been tried for specifying the boundary conditions: for example, overspecification of boundary variables associated with diffusive damping; or their relaxation towards prescribed values interpolated from the outer general circulation * Permanent address: Centre for Atmospheric and Fluid Sciences,Indian Institute of Technology, 110016 Delhi.

pseudo-radiation

conditions

for-

mulated as time-space extrapolations from grid-points within the nested grid. An alternative approach is to use a single general circulation model with space-varying mesh size, representing both the region of interest with a relatively fine mesh, and, at the same time, its surroundings with coarser resolution. If the mesh-size transition is abrupt, the approach reduces to a two-way nested grid technique with itsspecificproblems of boundary specification.The other possibility is to use a smoothly-varying mesh, like in Staniforth and Mitchell (1978). This can be implemented in a very general way by using smooth (preferably analytic) coordinate stretching, i. e.a suitably chosen mapping of the sphere onto a coordinate plane, which is scale-stretching in the area of interest.Note that this approach is easy to implement, but much less flexible than the nested-grid aproach: coordinate stretching is basically a

264

Regional forecasting using a stretched-coordinateGCM

one-dimensional technique which shows some unpleasant rigidities in higher dimension. The simpler approach for dimension two is to use the product of two one-dimensional stretching functions centered in the area of interest; this at least preserves the orthogonality of the grid. Analytic stretching also preserves the order of accuracy of the discretization scheme, which is another desirable property. We describe here how the stretched coordinate approach has been applied to the LMD general circulation model, and its impact on regional weather prediction for a single test case: the monsoon onset of the FGGE year. This case has been intensively studied by other models; see for example Krishnamurti (1985), Kershaw (1985); some results from a preliminary version of the stretched coordinate LMD GCM have been given in Sharma and Sadourny (1985). 2. The

model

a. The

stretched coordinates

In the experiments described here, coordinate stretching is aimed at improving the simulation of the Indian monsoon; it is therefore designed to increase resolution over the Indian ocean area at the expense of resolution over the eastern Pacific or the polar regions. Latitudinal stretching is performed by using y=sin;y, where y refers to latitude, as meridional coordinate. This is a relatively moderate stretching, which improves the near-equatorial meridional resolution by a factor 1.5. Longitudinal stretching is preformed by defined by

using

X=X!+X

a function X

points in the meridional direction, the stretched grid size is 312x254 Km2 in the central Indian ocean, where the regular grid size would be 624x400 Km2. Over northwestern Canada, on the opposite, the stretched mesh reaches 900x900 Km2. b. The

The basic general circulation model to which the stretching is applied is the LMD GCM (Sadourny and Laval, 1984). It is a second-order finite-difference model, and the use of an analytical stretching like (1) guarantees that the order of the discrete approximations is maintained in the process. Coordinate stretching is most easily handled by formulating the equations in terms of covariant or contravariant vector components (Sadourny, 1972, 1975; Gal Chen and Somerville,1975), respectively defined as u*=urcosydx/dX, u*=u/{r

v*=vrdy/dY;

cos ydx/dX),

― x0), (1)

v*=v/{rdy/dY).

Here r is the radius of the earth. We also define the area map factor, a=r2cosy dx/dX dy/dY, and the area-weighted surface pressure and Coriolis parameter, ps,=aps, f*=af. On Arakawa's C-grid, horizontal mass fluxes, potential vorticity and Bernoulli function respectively read

U=ps.

u*, V=ps.yV*

; Xy

Z ( ― asinix^X

discretized equations

of longitude,

for longitudinal coordinate. In (1),x longitude, 0