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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

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

No abstract available.

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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 V g0 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 V g0 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 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

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

Abstract

No abstract available.

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Maurice B. Danard

Abstract

The influences of release of latent heat on the vertical motion and production of kinetic energy and low- level vorticity in a major winter cyclone over the central United States have been investigated. The vertical velocity was obtained by solving the customary (diagnostic) ω-equation, and the results were compared with values determined by kinematical techniques. It proved necessary to make allowance for horizontal variations of the static stability and release of latent heat in order to obtain satisfactory agreement between the two sets of data.

Numerical solutions, with and without inclusion of released latent heat, were used to obtain ageostrophic wind components and their effect upon the production of kinetic energy and vorticity. The following results emerged: a) the influence of released latent heat was of the same order of magnitude as the effect of dry-adiabatic circulations; b) the amplification of the vertical motion that resulted from released latent heat was accompanied by intensification of the low-level convergence and high-level divergence; c) the ageostrophic winds associated with these fields of convergence and divergence had components toward lower pressure, thus giving positive contributions to the production of kinetic energy both at low and high levels; d) the computed rate of production of low-level vorticity exceeded the observed rate, and evidence suggests that frictional effects may be important.

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Meenu Bhargava
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Maurice Danard

Abstract

Optimum interpolation is a procedure that allows the combination of observations with preliminary trial fields of the same quantities in order to produce an updated field in which the error variance is minimized. In this paper, an operational method is described to analyze observed precipitation amounts based on optimum interpolation. Since the area dealt with is topographically complex, this factor has been included in the operational method. The trial fields are provided by a three-dimensional numerical weather prediction model. This paper presents an estimation of the covariances of observational and trial field errors. Two mathematical assumptions are made: 1) trial field errors and observational errors are not correlated with each other; 2) observational errors and the deviations of the trial field values from the observations are uncorrelated. The first assumption is customarily made in any application of optimum interpolation. The second assumption is specific to this paper. These two statements together imply that observational errors are uncorrelated. A technique is derived to determine which observations influence a given grid point and their respective weights. The selection of influencing observations is done by calculating the spatial dependence of r, the trial field error covariance. A cutoff point is determined on the smoothed curve where the r value is a small fraction of the r value at the origin. The procedure is applied to the heavy rainstorm of 11–13 July 1983 in the upper Columbia River watershed in southeastern British Columbia. Certain practical problems do arise in the implementation. The noncoincidence of model day and climate day tends to introduce systematic errors within the observations. This result conflicts with the assumption that observational errors am uncorrelated. Additionally, the observing system is not designed to make allowance for topographical detail. Errors are thus introduced in the observations from a variety of sources.

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Maurice B. Danard

Abstract

Numerical models have been designed to compute carbon monoxide concentrations in the vicinity of a plane highway and a depressed highway in Toronto. The non-steady two-dimensional diffusion equation is integrated in time until steady conditions are attained. Diffusivities vary both horizontally and vertically. Near the highway, diffusivities are higher over the highway (20 m2 sec−1) than to the sides. At higher levels, diffusivities are greater for cold air advection (9 m2 sec−1) than for warm (3 m2 sec−1). Winds vary logarithmically with height in the lowest 10 m and linearly above that level. The highway is treated as an area source.

Computed concentrations at a fixed measuring site (15 m north of the plane highway and 2 m above the ground) have simple correlation coefficients of 0.82–0.94 with observed concentrations. Numerical simulations show that the order of importance of various factors is, with the most significant one first, low-level diffusivities wind component perpendicular to the highway, mixing height, and type of advection.

Particular attention is paid to the decrease of concentration with distance from the highway. For both models, the reduction is relatively small with light winds or low mixing heights. As expected, the decrease with distance is larger for the depressed highway than for the plane highway.

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