Showing papers in "Quarterly Journal of the Royal Meteorological Society in 1975"

Dynamics of deserts and drought in the Sahel

Abstract: It is suggested that the high albedo of a desert contributes to a net radiative heat loss relative to its surroundings and that the resultant horizontal temperature gradients induce a frictionally controlled circulation which imports heat aloft and maintains thermal equilibrium through sinking motion and adiabatic compression. In the subtropics this sinking motion is superimposed on the descending branch of the mean Hadley circulation but is more intense. Thus the desert feeds back upon itself in an important manner. If one takes into account the biosphere, this feedback mechanism could conceivably lead to instabilities or metastabilities in desert border regions. It is argued that a reduction of vegetation, with consequent increase in albedo, in the Sahel region at the southern margin of the Sahara would cause sinking motion, additional drying, and would therefore perpetuate the arid conditions. Numerical integrations with the general circulation model of NASA's Goddard Institute for Space Studies appear to substantiate this hypothesis. Increasing the albedo north of the ITCZ from 14% to 35% had the effect of shifting the ITCZ several degrees of latitude south and decreasing the rainfall in the Sahel about 40% during the rainy season.

Turbulent wind flow over a low hill

Abstract: An analytical solution is presented for the flow of an adiabatic turbulent boundary layer on a uniformly rough surface over a two-dimensional hump with small curvature, e.g. a low hill. The theory is valid in the limit L/y0 → ∞ when h/L 2k2/ln(δ/y0) where L and h are the characteristic length and height of the hump, y0 the roughness length of the surface and δ the thickness of the boundary layer. For rural terrain, taking δ ∼ 600m these conditions imply that 102 < L < 104m and h/L < 0·05. Considerations of the turbulent energy balance suggest that the eddy viscosity distribution for equilibrium flow near a wall may still be used to a good approximation to determine the changes in Reynolds stress. This result is only required in a thin layer adjacent to the surface - in the main part of the boundary layer the perturbation stresses are shown to be negligible and the disturbance to be almost irrotational. The theory shows that for a log-profile upwind the increase in wind speed near the surface of the hill is O((h/L)u0(L)) where u0(L) is the velocity of the incident wind at a height L. Thus the increase in surface winds can be considerably greater than is predicted by potential flow theory based on an upwind velocity u0(h). It is also found that, at the point above the top of a low hill at which the increase in velocity is a maximum, the velocity is approximately equal to the velocity at the same elevation above level ground upwind of the hill. The surface stress is highly sensitive to changes in the surface elevation, being doubled by a slope as small as one in five. The turning of the wind in the Ekman layer may induce a change in direction of the wind above the hill. The main object of this analysis is to show how the changes in wind speed and shear stress are related to the size and shape of the hill and to the roughness of the surface. Some comparisons are made with measurements of the natural wind and wind tunnel flows. These suggest that the theory may be useful in giving rough estimates of the effect of hills on the wind. The theory and the quoted measurements suggest that the present design recommendation for the increase in wind speeds over hills to be used in wind loading calculations may be an underestimate. It is to be hoped that this analysis will encourage more detailed measurements to be made of the wind over hills.

Variation of the sea surface drag coefficient with wind speed

Abstract: Eddy correlation measurements of wind turbulence obtained at a sand spit on Sable Island, Nova Scotia, in winds ranging from gentle breeze to strong gale force agree with other recent measurements over water. There is a significant increase in the drag coefficient with wind speed which is well described by the equation of Charnock (1955). The heat transfer coefficient is slightly lower than the drag coefficient.

A multi-layer spectral model and the semi-implicit method

Abstract: The formulaton of a multi-layer primitive equation model on the sphere is described. The horizontal representation is by means of spherical harmonics, truncated either in the triangular or rhomboidal manner. The time integration is performed using the semi-implicit method in which the linearized gravity wave terms are time averaged and thus the fast moving waves of this type are slowed. For a 5-layer hemispheric model with triangular truncation at wavenumber 21, storage of 38K words is needed and with the time scheme allowing a time-step of 90 minutes, one day's simulation requires 11 seconds of CDC 7600 time. The growth of a baroclinic wave on a simple basic state of differential solid body rotation is exhibited. The errors involved in this case in utilizing the large time-step allowed by the semi-implicit scheme are thoroughly examined by comparing wave amplitudes and phases, conservation properties and gravity wave treatment for different time-steps. These errors are found to be negligible. The conservation properties of the model are in fact extremely good. The vertical finite differencing scheme of Arakawa is studied in the same baroclinic instability simulation. The growth is similar though the conservation of angular momentum is greatly improved. The transform method used in all these integrations allows some aliasing, but this is shown to be negligible.

Global dynamics and climate - a system of minimum entropy exchange

Abstract: It is found that the mean meridional distribution of temperature, cloud cover and meridional energy flux can be predicted with extraordinary accuracy by application of a simple minimum principle to a multi-box model of the globe which contains no direct specification of the system dynamics. The minimized quantity is related to the global net rate of production of entropy. It is the sum over all latitude zones of the ratio of net radiant energy input to the effective emission temperature of the zone. The result suggests that global dynamics is something of a passive variable which alters so as to satisfy a condition akin to minimum energy dissipation.

Comparison of aerodynamic and energy budget estimates of fluxes over a pine forest

Abstract: Values of the total vertical flux of sensible and latent heat over a level forested region, obtained from aerodynamic (profile-gradient) formulae appropriate to airflow over relatively smooth surfaces, are found to fall consistently short of independent energy-balance estimates by a factor of 2 to 3 in unstable and near-neutral conditions (Richardson number, Ri, in the range −0·4 to +0·01), whereas for Ri > + 0·02 no similar discrepancy is detected. These results, based on tangents drawn to (semi-logarithmic) profiles at a height of about nine aerodynamic roughness parameters (z0) above the zero plane displacement level (d) of the forest, rely on the basic assumption that the value of d established in very nearly neutral conditions (|Ri| < 0·003), namely 0·76 mean tree heights, holds under all conditions of thermal stability. Wake diffusion and thermal seeding effects are discussed as possible additional transfer mechanisms acting to reduce profile gradients immediately over aerodynamically rough surfaces. In terms of the former mechanism (assumed to operate below d + 25z0, or so), approximate empirical formulae are derived which attempt to quantify the observed discrepancy in terms of Ri and the proximity of the surface. It is concluded that aerodynamic equations ought not to be used to give independent flux estimates close to aerodynamically rough surfaces.

Secular changes in South African rainfall: 1880 to 1972

Abstract: Analysis of time series for 157 stations with records covering the period 1910–1972 and for fewer stations with records extending back to 1880 suggests that the commonly held view that South Africa, as a whole, is undergoing progressive desiccation must be questioned. Instead the data suggest the specific regional occurrence of weak (but nonetheless readily discernible) oscillations of 16–20 and 10–12 years, the ubiquity of 3–4 year fluctuations and the spatially distinctive occurrence of a quasi-biennial oscillation.

Long‐wave radiation at the ground I. Angular distribution of incoming radiation

Abstract: The apparent emissivity of the atmosphere ϵ, defined as the ratio of incoming long-wave radiation to black-body radiation at screen temperature Ta, was measured under clear skies in the English Midlands and in the Sudan. At a zenith angle Z the emissivity was given by ϵ(Z) = a + bIn(usec Z) where u is the reduced depth of precipitable water (cm). For a set of 46 scans in England, the mean values of a and b were 0·70±0·05 and 0·090 ± 0·002. Systematic deviations about these mean values could be ascribed to: (i) temperature gradients; (ii) aerosol. The Sudan measurements gave a = 0·67 ± 0·03 and b = 0·085 ± 0·002 consistent with the English results and observations already published. There is some evidence that minimum values of a have increased over the past 50 years. Integration over the hemisphere gives the flux density (Wm−2) of atmospheric radiation as 1·06 σTa4 − 119 (T in K), where σ is Stefan's constant, or 5·5 Ta + 213 (T in °C). Radiation records by Dines and Dines (1927) for overcast skies are analysed to show that the angular distribution is the same as for cloudless skies; that the mean temperature of cloud base at their site was UK below screen temperature; and that when the mean fraction of cloud cover is c, the apparent emissivity is ϵa(c) = (1 − 0·84c)ϵa(0) + 0·84c.

The temperature dependence of the ozone concentration near the stratopause

Abstract: Using measurements from two instruments on the Nimbus 4 satellite comparisons between ozone concentration and temperature have been made at levels near 1mb during an occasion of stratospheric warming. High correlation exists between ozone concentration and temperature. Good agreement has been found with a photochemical model which incorporates ‘classical’ oxygen photochemistry together with reactions involving OH.

Penetrative convection in the absence of mean shear

Abstract: This paper reports the first large-scale observations of a developing mixed layer in which only convection can be causing the deepening. The convection arises from solar heating of water beneath lake ice. Since the water is below its temperature of maximum density, heating due to the absorption of radiation passing through the ice results in a mixed layer which increases in thickness with time. Observations taken with an electronic bathythermograph and by recording thermistor chains have permitted the estimation of that fraction of kinetic energy made available by the gravitational instability, which is converted into potential energy by entrainment of stable fluid as the convecting layer advances. Twelve independent estimates vary from 0.003 to 0.113 with an average value of 0.036. This result qualitatively agrees with the laboratory work of Deardorff, Willis and Lilly (1969) who found that only a small fraction (about 0.015) was recovered in this way. However, relatively little penetration can have a significant effect on mixed layer growth; the results obtained in the present study correspond to a mixed layer thickness 17% greater than that predicted for zero penetration in the case of a linear initial density profile.

The assignment of Rainfall stations into homogeneous groups: An application of principal component analysis

Abstract: The calculation of eigenvectors has been used to describe annual precipitation totals over an area of large extent. Rotation of the eigenvectors brought about further clarification of the system of recording stations. By noting the eigenvector of most importance to each station, delimitation of an area was made possible. Reduction in records, a necessary prelude to our future work on forecasting models, was obtained by discarding those stations most closely related to eigenvectors whose eigenvalue was less than 0·6.

A two‐dimensional mean circulation model for the atmosphere below 80km

Abstract: The paper sets out the detailed formulation of a numerical model whose purpose is the study of the interactions of dynamics, photochemistry and radiation in the stratosphere and mesosphere. Two integrations of the model for 900 days are described in which many features of the atmosphere are reproduced but with important differences of detail. The dependent variables are zonal means of the relevant meteorological quantities, held as functions of time, latitude and height (log pressure) with a resolution of μ/19 in latitude and 0.5 in pressure scale height. Eddy fluxes of heat and matter are treated by large-scale diffusion coefficients. This treatment is not applicable to momentum fluxes: these are currently specified from observations made mainly from the selective chopper radiometer on the Nimbus V spacecraft. Radiative coolings due to CO2 and O3 emission are computed from simplified expressions which are essentially cooling-to-space approximations with emissivities obtained by curve-fitting against the results of more elaborate treatments. Absorption of solar radiation by ozone is obtained from tabulations of absorption against ozone amount traversed. Radiation and latent heat release in the troposphere are specified climatologically. The photochemistry in the integrations described here is the classical ozone scheme but, with a view to investigating possible stratospheric pollution problems, integrations have been performed with the inclusion of reactions involving nitrogen and hydrogen compounds. These will be described in a later paper.

Geostrophic drag and heat transfer relations for the atmospheric boundary layer

Abstract: The empirical determinations of the similarity functions of geostrophic drag and heat transfer relations by Zilitinkevich and Chalikov (1968) and by Clarke (1970a, b) indicate large disparities between their results, raising serious doubts on the universality of these relations. Some reasons for these large differences are investigated by reanalysing the available data from the two sites (O'Neill in Nebraska, U.S.A., and Hay in New South Wales, Australia) in the same format, using the best available flux-profile relations and reasonable criteria for the selection of suitable runs. Although there is still considerable (but, much less than in previous studies) scatter of data points, when plotted in the similarity framework, we find no significant differences in the results of two sites. Thus a large part of the above noted disparities must have been spurious, probably caused by different ways of determining surface fluxes and of defining external variables by the previous investigators. Our empirical results are compared with those obtained from recent theoretical models for both stable and unstable boundary layers. Having fitted some third degree polynomials through the same, nomograms are obtained for geostrophic drag and heat transfer coefficients and also for the surface cross-isobaric angle as functions of dimensionless parameters defined in terms of easily measured ‘external’ variables. These show expected trends with stability.

The simulation of particle motion in the atmosphere by a numerical random-walk model

Abstract: Of all the models of turbulent motion that are based on a random-walk technique, the simplest are ones which simulate individual particle trajectories. The accuracies of two such models are assessed by applying them to low-level diffusion in the atmosphere. It is found that one based on a Markov-Chain principle predicts particle concentrations over short and medium ranges which are consistent with observation. Calculations are extended to include dispersion in unstable conditions, and by postulating the dependence of several important turbulence parameters on z/L, it is possible to derive a physically realistic model.

The nature of orographic rain at wintertime cold fronts

Abstract: Some of the largest falls of orographic rain in the western parts of the British Isles are associated with wintertime cold fronts. This paper contains four case studies of wet cold fronts which were all characterized by south-westerly prefrontal low-level jets but were widely different in other respects. The distribution of rainfall in England and Wales is analysed using a network of autographic raingauges, specially augmented near the coast and over the hills of south Wales, and the orographic effects are explained using data from series of hourly rawinsonde ascents from a single station. The rain is considered in three distinct regions: pre-frontal, the surface cold front, and post-frontal. Behind the front orographic effects were found to be well defined but rather slight. At the surface front orographic effects were negligible, heavy rain tending to occur regardless of topography. Ahead of the front, orographic effects varied from small to very large, depending on the existence of a moist low-level feeder cloud and seeding particles. The occurrence of heavy orographic rain ahead of the cold front is favoured by the presence of the low-level jet, since this ensures the replenishment of a high liquid water content in the feeder cloud despite its rapid depletion by washout. Low-level ascent, or at least the absence of descent, in the general airflow upwind of the hills is also needed if the feeder cloud is to have a high liquid water content. The required seeding particles in some cases originate from melted ice crystals grown aloft; alternatively they may be generated within the low-level cloud itself even in the absence of the ice phase.

Turbulent diffusion within a wheat canopy: II. Results and interpretation

Abstract: The coefficient of turbulent diffusion was measured in a 1·25m tall wheat canopy using a uniform release of nitrous oxide, the energy and momentum balance methods, and the humidity profile. The nitrous oxide profile gave the most accurate values, KN in the lower two thirds of the canopy, and a regression of the energy balance estimates, KE, against KN had a slope of 1·17 ± 0·10 with a non-significant intercept of 17cm2s−1. The mean day time profile of KN was exponential, K(z) = K(h) exp(−γ(1-z/h)) with γ = 3·9 when u(h) 1·2m s−1. But analysis of KN for the height interval 0·3 to 0·8m shows the importance of thermal stability, and the results are related to the non-dimensional stability parameter g/T(ΔT/Δz/(u(h)h2) where ΔT/Δz is the temperature gradient and u(h) is the windspeed at crop height, h. The large scatter in the results was attributed to the heterogeneity of the crop. Also the wind profile was frequently S-shaped defying a simple one-dimensional analysis and causing the momentum balance to give nonsensical results. Hence it seems unlikely that one-dimensional analysis of transfer can give values of K allowing an accurate estimate of the source and sink distributions within a dense crop canopy.

Electric field growth in thunderclouds

Abstract: We have constructed a balloon-borne instrument for measuring the magnitude of the horizontal component of the electric field in thunderclouds. It consists of two hollow, copper spheres 15cm in diameter held 2cm apart. The spheres spin about an axis that can be described as the perpendicular bisector of the line segment between the centres of the spheres. The sinusoidally-varying charge that is induced on the spheres by an electric field is amplified and telemetered to ground. The amplifier and telemetry transmitters are located inside one of the spheres. The spheres also serve as the telemetry antenna. The time behaviour of the electric field in the cloud is substantially different than that at the ground. The effects of corona discharge from the ground and of the finite conductivity of the air outside the cloud seem to be negligible in the presence of the intense field near a region of charge inside a cloud. Measurements of electric field intensities inside a cloud just before and after a lightning flash when combined with measurements at the ground can be used to obtain an approximate value for the total quantity of charge in a region of cloud just before it is partially discharged by lightning. In two cases the charge just before lightning was estimated to be −120C and −160C. During a brief interval in one of our flights the electric field at the balloon reflected the time behaviour of the electric field in the cloud; the electric field increased linearly with time between lightning flashes.

New England coastal frontogenesis

Abstract: New England coastal frontogenesis is investigated on the basis of individual and climatological case studies. The results suggest that differential friction plays the role of the synoptic scale geostrophic deformation in packing the isotherms together for this mesoscale boundary-layer frontal phenomenon. An initial temperature gradient must be present for the differential friction mechanism to be effective. Geostrophic deformation is incapable of initiating coastal frontogenesis while the maximum area of observed deformation coincides with the location of the developing front. Coastal frontogenesis is associated with a pronounced sea level cold anticyclone to the north and east of New England in all cases studied. Differential friction between the northerly inland flow and the more easterly onshore flow then sets up favourable shoreline deformation and convergence fields leading to frontogenesis in the presence of differential thermal stratification. The time scale for an order-of-magnitude increase in the horizontal temperature gradient appears to be one-half to one day depending upon the contribution of differential diabatic heating. The orientation of the New England shoreline is such as to favour frontogenesis across extreme eastern Massachusetts and Rhode Island. An axis of relatively high precipitation is noted just to the west of this favoured locale on the climatological charts, consistent with a thermally direct circulation about the front.

A representation of the effects of topography on surface rainfall within moving baroclinic disturbances

Abstract: A numerical ‘parameterization’ model has been developed in order to predict precipitation amount over hilly terrain in North Wales. The model enables calculations to be made of the vertical velocity profile resulting from orographic and large-scale baroclinic effects at grid points one kilometre apart over an area of 2400km2. In the present study the precipitation falling on an area of 103km2, and on areas of order 102km2 within the larger area has been predicted, using as the input to the model large-scale wind and humidity values derived from radiosonde ascents. Seven case studies are presented. All are examples of fast moving baroclinic systems. This type of system was chosen to minimize the effects of non-orographic mesoscale or convective mechanisms, which are not parameterized in the present model. The mean error in the predicted rainfall over 103km2 was ± 10% and over 102km2 about ± 20%.

A split semi-implict reformulation of the Bushby-Timpson 10-level model

Abstract: A split semi-implicit reformulation of the Bushby-Timpson 10–level model is described. The integration cycle is split into two main parts. Firstly, the dependent variables are advected by the wind using the explicit two-step Lax-Wendroff integration scheme with the grid staggered in time and space. Secondly, these advected values are adjusted to account for the terms that govern the motion of small amplitude inertio-gravity waves in the model, using a combination of an unconditionally stable implicit scheme and a conditionally stable explicit scheme. A novel feature of the scheme is the implicit treatment of only two of the model's ten gravity wave modes. This split semi-implicit scheme is more than four times as efficient as the original explicit scheme designed by Bushby and Timpson. The results of one semi-implicit integration to 36 hours are described and compared with an integration made with Bushby and Timpson's original explicit scheme.

The temperature structure of the Southern Hemisphere stratosphere August – October 1971

Abstract: The temperature field in the Southern Hemisphere stratosphere from 100 to 1mb during August to October 1971 is described using observations from the Selective Chopper Radiometer on the Nimbus IV spacecraft. Zonal and monthly mean wind fields for September and October 1971 deduced from these temperatures are presented and the behaviour of the zonal temperature waves with wavenumbers 1, 2 and 3 is discussed. The largest amplitudes of wavenumbers 1 and 2 in the horizontal coincide broadly with the maximum westerlies. The amplitudes of wavenumber 2 are generally smaller at around 20mb than above or below. The amplitudes of both waves are small north of 30°S. Wavenumber 1 exhibits little vertical coherence throughout August and September. In October, however, the slope of the wave with height is much less variable, in spite of a slow eastward movement in early October and a westward movement in late October. Wavenumber 2 travelled eastwards with a fairly uniform rate of approximately 15·5° longitude per day between 15 August and 7 October but less uniformly at other times. Changes in wave amplitude at strato-pause levels are associated with comparable changes near the tropopause. A maximum of wavenumber 2 amplitude on 26 September 1971 is associated with falling ZPE in the lower stratosphere and rising ZPE in the higher stratosphere. The dominant contribution to the eddy available potential energy is in the lower stratosphere. In the low stratosphere there is an inverse relationship in zonal and eddy available potential energies, rises in one form being associated with falls in the other. This inverse relationship is not well marked in the high stratosphere.

The effects of vertical wind shear on the evolution of convective clouds

Abstract: The effects of ambient wind shear Uo on the evolution of an isolated three-dimensional convective cloud are studied. Sixteen cases are considered which differ from one another both in the value of U′0 in the initial value of the energy of atmospheric instability per unit height of the unstable layer, E0. It is found that convective clouds may be grouped into two types, ‘weak’ and ‘strong’: if E0/H < 0−65 × 102cm s−2 then convection is ‘weak’; if E0 0−65 × 10−2cm s−2 then convection is ‘strong’. For ‘weak’ convective clouds there is a critical value of shear, U′0cr |U′0| < U′0crthere is an inhibiting effect on the development of convection; and for |U′0| U′0 its evolution is completely suppressed. The essential new result is that ‘strong’ convective clouds are intensified under the effect of U′0. In this case there is a resonance value of shear, U′0res at which the degree of the intensification of convection has a maximum (30–40%).

Comparison of evaporation measurements using different methods

Abstract: During the 1971 growing season continuous measurements were made (with some breaks in the record due to instrumental faults) of the evaporation from barley using five methods: (1) Bowen ratio method; (2) aerodynamic method; (3) use of the energy balance equation and the aerodynamic heat flux to obtain evaporation as the residue (for convenience called the energy balance method); (4) a weighing lysimeter; and (5) a neutron moisture meter. In this paper some estimates are made of the error expected from each method and the results of the measurements are presented. It is shown that the energy balance method is almost as good as the Bowen ratio method and has the advantage of not requiring humidity measurements.

Budget studies of heat flux profiles in the convective boundary layer over land

Abstract: Observations of the convective boundary layer over southern England using an instrumented light aircraft and radio-sondes enable its structure and development to be described for two periods of active, shallow convection. Budgeting is used to deduce the sensible heat flux as a function of height, showing a downward flux in the upper part of the boundary layer associated with entrainment of warmer air from above. For the two occasions studied results indicate that the entrained sensible heat flux is about 0·3 of the sensible heat flux at the ground. For one of the occasions a moisture budget was possible yielding a value of the mean latent heat flux at the ground.

Momentum transport by the thermal tide in the stratosphere of Venus

Abstract: The response of a stratified Boussinesq fluid subjected to a moving periodic thermal forcing is analysed and the role of thermal stratification in the generation of a mean ‘zonal’ motion discussed. In the parameter range where the phase speed of this forcing is much less than the speed of the gravest gravity wave mode, the problem may be treated as one of momentum transport by damped internal gravity waves, though the analysis does not require that the damping be small. Results from a simple model show that mean flow speeds much larger than the speed of heat source motion can be generated by this mechanism. Whilst, in the parameter range appropriate (to the best of our present knowledge) to the stratosphere of Venus, some assumptions of the analysis are violated, it is argued that mean winds of the order of 100m s−1 may be generated, thus supporting the suggestion of Schubert and Whitehead that this mechanism is responsible for the observed four-day rotation of that planet's equatorial stratosphere. It is shown that the ratio of mean wind velocity to the speed of the subsolar point is independent of the length of the solar day, and that it is largely determined by the distribution of radiative heating and cooling in the planetary atmosphere.

The effect of a warm mid‐latitude sea surface temperature anomaly on a numerical simulation of the general circulation of the southern hemisphere

Abstract: A mid-latitude Sea Surface Temperature Anomaly (SSTA) is introduced into a 9-level polar stereographic southern hemisphere model. Two 50-day anomaly integrations (SSTAR1 and SSTAR2) are compared with their respective control integrations. In SSTAR2 the anomaly is introduced 10 days later than in SSTAR1. Comparison of the two integrations reveals systematic effects in some regions of the Antarctic trough and the mid-Atlantic and Indian Oceans, but no systematic effect in the immediate area of the SSTA. The latter region shows a weak variation in SSTAR2 while SSTAR 1 is characterized by a strong variation and a blocking sequence some 20 days into the integration. The region of enhanced cyclogenesis in SSTAR1 occurs on the equatorial side of the anomaly and not the region of enhanced surface baroclinicity. One such large cyclone is a major feature of the blocking sequence. Enhanced latent heat release appears to be an important factor in these developments.

The influence of momentum advections on a well-mixed layer

Abstract: This study examines the influence of weak horizontal advections of momentum on a well-mixed planetary boundary layer. In the simple flow system examined, the direction and magnitude of flow modifications depend on the Rossby number, the nondimensional surface drag coefficient and the orientation of the geostrophic wind gradient field. It is found that advective modification of the boundary layer vertical motion field involves dependencies on the square of the local vorticity and dependencies on vorticity gradients. The mixed-layer assumptions are relaxed for a special flow case to show that these results do not depend crucially on the mixed-layer condition.

Long‐wave radiation at the ground. II. Geometry of interception by slopes, solids, and obstructed planes

Abstract: At the earth's surface, long-wave radiation received from the atmosphere in the absence of cloud may be expressed as the sum of the flux density from an isotropic source and the flux density due to anisotropy of atmospheric radiation. Separation of these components facilitates calculations of the radiative flux received by obstructed horizontal surfaces (near walls or in valleys), by sloping planes, by solid cylinders, and by spheres and prisms. Radiation received from adjacent surfaces is also considered. As the angular distribution of radiation is the same for overcast skies as for clear skies, the relationships for clear skies may be extended to derive climatological mean values for the long-wave irradiances of slopes, solids, etc.