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Maurice Danard

Abstract

Methods are proposed for calculating the surface horizontal pressure gradient or geostrophic wind in a local area over elevated terrain from randomly spaced surface observations. These procedures avoid many of the problems associated with sea-level pressure. One technique is to compute pressure at the mean terrain elevation using the same procedure as for sea-level pressure. Another method, which is the main contribution of this paper, is based on sigma coordinates. Temperatures and geopotentials in a reference atmosphere are subtracted from those in the actual atmosphere to reduce the magnitudes of the compensating terms in the expression for the horizontal pressure gradient, and therefore decrease roundoff error. A geostrophic streamfunction is derived whose gradient is then determined by least squares fit to observations. Temperature gradients in the atmospheric boundary layer are also calculated in the sigma coordinates method. An iterative procedure to compute the mean and standard deviation of wind angles is presented, which can also be used in air quality applications.

The techniques are applied to southwestern Alberta using data at 0000 and 1200 UTC for January to March inclusive for 1985 and 1986. There are significant discrepancies between the geostrophic wind computed at the mean terrain elevation compared to that at sea level. Average differences between the two geostrophic winds depend on wind direction and are as much as 87° for direction and 10 m s−1 for speed. The geostrophic wind calculated from the sigma coordinates method also differs from that at the mean terrain elevation. The standard deviation of the direction difference is 18°.

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Maurice Danard

Abstract

This paper describes a diagnostic, one-level, primitive equation model for computing mesoscale influences of orography, friction and heating on surface winds, given large-scale data from synoptic or prognostic charts. The model is capable of simulating phenomena such as orographic channelling, effects due to changes in atmospheric stability, land- and sea-breezes, and anabatic and katabatic winds. It probably works best for orographic channelling. The model has been applied to Juan de Fuca and Georgia Straits in British Columbia using a grid size of 10 km. Compared to simple methods of computing surface winds, use of the model typically reduces the difference between computed and reported directions by 10–15° for land stations and 25° for exposed lighthouses. Improvement in cases of strong orographic channelling is much greater. One interesting result is the sensitivity of wind directions in Juan de Fuca and Georgia Straits when the geostrophic direction is in the ranges 220–250° or 030–060°. Slight variations of the geostrophic direction from these critical values results in abrupt 180° reversals in surface winds.

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Maurice Danard

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Maurice Danard

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Maurice Danard

Abstract

A prognostic one-dimensional bulk model of the atmospheric boundary layer is described for the surface temperature, height of the atmospheric boundary layer, and surface wind. Heat conduction into the ground is accounted for using a “force-restore” equation. Longwave and shortwave radiation are calculated for clear, overcast or partly cloudy skies. Surface fluxes of momentum, heat and water vapor are computed using generalized similarity theory. The procedures are applied to mean July conditions at Inuvik, Edmonton and Port Hardy. Integrations are performed for three days and reproduce the diurnal cycles reasonably well. Sensitivity tests show that the surface emissivity is an important variable.

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Maurice Danard

Abstract

Equations are first derived in shape-preserving coordinates for the spatial derivatives of the unit vectors, the gradient and Laplacian of a scalar, the divergence and vorticity of a vector, the advective acceleration in the equations of motion, the strain-rate tensor, and the viscous forces per unit mass. A shape-preserving projection is defined here as one in which the map scale, though spatially variable, is independent of the orientation of an infinitesimal line segment. Shape-preserving projections are also conformal. Examples are stereographic and Mercator projections. The results are then extended to the case where the map scale factors in the two horizontal coordinate directions are different.

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Maurice Danard

Abstract

A diagnostic procedure to compute the surface wind from the geostrophic wind including the effects of baroclinity is designed and tested. Expressions are derived to calculate the similarity functions A and B for use when only the surface geostrophic wind Vg0 and its vertical derivative ∂Vg/∂z are known (i.e., no atmospheric boundary-layer winds are available). The cross-isobaric angle of the surface wind has a maximum for δ=122° and a minimum for δ=300°, where δ is the angle counterclockwise from Vg0 to ∂Vg/∂z. The surface wind speed is highest for δ=30° and lowest for δ=210°. The results are compared to observations and the agreement is quite good.

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Maurice B. Danard

Abstract

A quasi-geostrophic numerical model for predicting precipitation amounts and the heights of the 1000-, 850-, 700-, 500-, and 300-mb surfaces is described. The basic equations are the vorticity and omega equations. Influences of released latent heat are incorporated in the static stability in the latter equation. Frictional and orographic effects are included in the lower boundary condition for the vertical velocity.

Numerical integrations are carried out for 36 hours in a case of intense cyclogenesis over central United States. “Moist” and “dry” predictions are made, the latter by artificially excluding effects of release of latent heat. In the “dry” prognosis, the sea-level low is moved northeastward but not intensified. By contrast, in the “moist” prediction it is rapidly deepened. Forecast precipitation amounts agree roughly in magnitude with observations. However, the occurrence of heavy convective precipitation along the cold front is not satisfactorily predicted.

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MAURICE B. DANARD

Abstract

A simple relationship is obtained between pressure changes associated with friction and the geostrophic drag coefficient. From this, the imbalance between frictionally induced mass inflow and outflow is shown to be one or two orders of magnitude smaller than either the inflow or outflow.

Numerical integrations using the primitive equations are performed for an axially symmetric autobarotropic low-pressure system. The velocity components and pressure tendencies are found to depend critically on the drag coefficient.

Two actual synoptic cases are studied using a quasi-geostrophic numerical model incorporating release of latent heat. Computations are performed with and without surface friction. When friction is excluded, the 1000-mb Highs and Lows are more intense.

Two methods of computing the surface stress are compared. One is based on variations in terrain height and the other on the nature of the vegetation. Differences are large, especially over the western part of North America.

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MAURICE B. DANARD

Abstract

An eight-level primitive equation model has been developed incorporating orography, large-scale release of latent heat, longwave radiation, and surface and internal friction. The clouds and moisture patterns used in the radiation calculations are predicted (i.e., change with time). Drag coefficients vary spatially. Thirty-six-hr predictions are performed over North America for an intense midlatitude winter cyclone.

The inclusion of longwave radiation lowers 300-mb heights by as much as 190 m after 36 hr and significantly improves the forecasts at that level. However, there is little influence at lower levels or on predicted precipitation amounts.

Less intense Highs and Lows result when surface friction is included. In the cyclone area, 1000-mb heights are raised by as much as 110 m after 36 hr. Maximum Ekman layer wind speeds are reduced from about 50 to 25 m/s. However, precipitation amounts are not significantly affected.

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