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Maurice B. Danard

Abstract

Numerical integrations with a 5-level quasi-geostrophic model incorporating effects of released latent heat were carried out for three cases of winter cyclogenesis. For purposes of comparison, calculations were also performed for each case with an initially dry atmosphere. The following typical features were noted:

In areas of predicted precipitation, the “moist” prognoses yielded heights at 1000 mb up to 150 m lower than those of the “dry” forecasts. Furthermore, the heights of the cyclone centers were more accurately predicted by the “moist” scheme than by the “dry.” At 300 mb the differences were similar in magnitude to those at 100 mb but opposite in sign. Precipitation associated with the frontal waves was predicted with some success but convective rainfall along and ahead of the cold fronts was inadequately forecast. The above characteristics were also observed in a fourth case study described in an earlier paper by the author.

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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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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

Some results obtained from double-theodolite measurements of the wind variability near Shilo, Manitoba, are presented. Wind variability [σ(s,t)] is defined here as the standard vector deviation of the difference between two winds at the same height measured at different points in space (s) and/or time (t). The investigation is restricted to winds below 10,000 ft above terrain and to intervals of distance and time of 0 to 30 mi and 0 to 3 hr, respectively. Observational error is assessed by direct measurement. Increase of error with height and wind speed is noted.

Theoretical justification is advanced for expecting the spatial variability to obey the formula &sigma2 (s,0) = a+bs 2+cs 4. By defining s = t |V̄| where V̄ the mean wind, temporal as well as spatial variabilities an used to determine the regression coefficients of the best-fitting 4th order polynomial given above. The regression coefficients are then classified according to surface wind speed, Richardson number and height. Results suggest that the polynomial may be appropriate in cases of small wind speeds and large Richardson numbers, but In other, conditions the time-scale of the motion is so small that the quadratic and quartic terms appear to be of minor importance.

Increase of wind variability with increasing surface wind speed and height above terrain is clearly demonstrated. This may, however, be due in larger part to observational error.

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MAURICE B. DANARD

Abstract

A simple method of computing longwave radiative cooling in the troposphere associated with water vapor is described. The procedure may readily be incorporated into a tropospheric numerical prediction model. Radiation from ozone and carbon dioxide is not considered. However, influences of arbitrary vertical distributions of cloud and moisture are included.

Average annual cooling rates along a meridional cross section are calculated for a cloudless atmosphere. The results agree fairly well with the total radiative cooling (longwave and shortwave) as given by Manabe and Möller except in the lower troposphere at low latitudes. Here shortwave absorption by water vapor is appreciable.

The three-dimensional distribution of longwave radiative cooling is also computed in a case of a developing cyclone for comparison with that of release of latent heat. The largest cooling occurs at cloud top and can be a significant fraction of the amount of energy released as latent heat in the upper troposphere. Computations also show that in this case study the longwave cooling tends to reduce the available potential energy, especially in the upper troposphere.

Synoptic-scale precipitation amounts resulting from destabilization of clouds by longwave cooling are computed. These range up to 1.4 mm in 12 hr. This destabilizing effect may be important in explaining the nocturnal maximum of precipitation over the sea. It may also contribute significantly to cyclone development.

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Maurice B. Danard

Abstract

Using quasi-geostrophic theory, equations are derived separating from other factors the contribution of release of latent heat to changes in the available potential energy. A synoptic case study of a major winter cyclone and an examination of the equation for the amplification of the vertical velocity associated with release of latent heat both suggest the same conclusion: in the lower and middle troposphere, the positive contribution of heating is normally significantly larger than the negative effect arising from the enhanced vertical motion. Thus release of latent heat should lessen the tendency for vertical circulations to destroy existing temperature contrasts.

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Maurice B. Danard

Abstract

A form of the thermodynamic equation with variable static stability and ageostrophic advection is derived. The effects of these two terms are then computed for four synoptic cases. Whereas the two influences tend to cancel in stable areas, this is not so in unstable regions. Since the two terms generally combine to produce minima in the effective stability in the areas where cyclogenesis took place, it is suggested that the derived equation would be useful in prognoses.

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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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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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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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