The influence of surface cover and climate on energy partitioning and evaporation in a subarctic wetland

Energy partitioning and evaporation were measured over three wetland surfaces in a subarctic coastal marsh during pre-growing and growing periods. These surfaces included an alder/willow woodland, a sedge marsh and a raised backshore sedge meadow. A combination model analysis was used to assess the relative importance of surface resistance and meteorological conditions on the magnitude of the Bowen ratio, , during the growing period.Overall, the three surfaces experienced important site-to-site and seasonal differences in and evaporation, Q _E. During the non-foliated period, Q _E was largest and was smallest for the open water marsh, while the dry backshore site experienced the smallest Q _E and largest . The non-foliated woodland assumed intermediate values of and Q _E. After the vegetation covers were established, the woodland assumed the smallest and largest Q _E flux. It was also found that at the marsh site increased with the presence of a vegetation cover.Wind direction was always an important factor in determining Q _E and at all sites. was substantially larger and Q _E was smaller for onshore winds (i.e., originating from James Bay) than for offshore winds. The combination model analysis showed that canopy resistance at all sites was largest during warm offshore winds, which were associated with large saturation deficits. However, the effect of increased canopy resistance on during offshore winds was offset by a large climatological resistance, resulting in small values and large Q _E. When winds originated from James Bay, canopy resistance was smaller than for offshore winds, but the climatological resistance also was much smaller, resulting in larger and small Q _E. The results have important implications for changes in land cover and climate on the regional water balance.     

Radiation balance in a tropical city — Delhi (India)

The impact of urbanization is assessed by comparing values of the radiation parameters at an urban location with those of a rural site. Urban Delhi was divided according to land-use and the effects of urbanization was studied on incoming short-wave (K), albedo, incoming longwave (L, outgoing longwave (L), and net radiation (Q ^*), were individually studied at four representative sites (Rural, Commercial, Residential and Industrial). MaximumK was observed in the rural and commercial areas whereas highL was observed in the commercial and industrial locations. High depletion ofK of the order of 13% was observed for the industrial location in the winter season. An increase ofL in, the industrial location is of the same order as that of the commercial location, i.e. 20%. The residential location shows quite moderate (4.6%) depletion ofK in comparison with other sites.Nomenclature U Urban - R Rural - K Incoming Short-wave radiation - L Incoming Long-wave radiation - L Outgoing Long-wave radiation - Q ^* Net Radiation - Albedo - K ^* Net Short-wave radiation - L ^* Net Long-wave radiation     

Spectral Characteristics and Correction of Long-Term Eddy-Covariance Measurements Over Two Mixed Hardwood Forests in Non-Flat Terrain

We present turbulence spectra and cospectra derived from long-term eddy-covariancemeasurements (nearly 40,000 hourly data over three to four years) and the transferfunctions of closed-path infrared gas analyzers over two mixed hardwood forests inthe mid-western U.S.A. The measurement heights ranged from 1.3 to 2.1 times themean tree height, and peak vegetation area index (VAI) was 3.5 to 4.7; the topographyat both sites deviates from ideal flat terrain. The analysis follows the approach ofKaimal et al. (Quart. J. Roy. Meteorol. Soc. 98, 563–589, 1972) whose results were based upon 15 hours of measurements atthree heights in the Kansas experiment over flatter and smoother terrain. Both thespectral and cospectral constants and stability functions for normalizing and collapsingspectra and cospectra in the inertial subrange were found to be different from those ofKaimal et al. In unstable conditions, we found that an appropriate stabilityfunction for the non-dimensional dissipation of turbulent kinetic energy is of the form ₍₎ = (1 - b^-)^-1/4 - c^-, where representsthe non-dimensional stability parameter. In stable conditions, a non-linear functionG_xy() = 1 + b_xy^c _xy (c_xy < 1) was found to benecessary to collapse cospectra in the inertial subrange. The empirical cospectralmodels of Kaimal et al. were modified to fit the somewhat more (neutraland unstable) or less (stable) sharply peaked scalar cospectra observed over forestsusing the appropriate cospectral constants and non-linear stability functions. Theempirical coefficients in the stability functions and in the cospectral models varywith measurement height and seasonal changes in VAI. The seasonal differencesare generally larger at the Morgan Monroe State Forest site (greater peak VAI) andcloser to the canopy.The characteristics of transfer functions of the closed-path infrared gas analysersthrough long-tubes for CO₂ and water vapour fluxes were studied empirically. This was done by fitting the ratio between normalized cospectra of CO₂ or watervapour fluxes and those of sensible heat to the transfer function of a first-order sensor.The characteristic time constant for CO₂ is much smaller than that for water vapour. The time constant for water vapour increases greatly with aging tubes. Three methods were used to estimate the flux attenuations and corrections; from June through August, the attenuations of CO₂ fluxes are about 3–4% during the daytime and 6–10% at night on average. For the daytime latent heat flux (Q_E), the attenuations are foundto vary from less than 10% for newer tubes to over 20% for aged tubes. Correctionsto Q_E led to increases in the ratio (Q_H + Q_E)/(Q^* - Q_G) by about 0.05 to0.19 (Q_H is sensible heat flux, Q^* is net radiation and Q_G is soil heat flux),and thus are expected to have an important impact on the assessment of energy balanceclosure.     

The use of σ T as a temperature scale in the atmospheric surface layer

The standard deviation of temperature _T is proposed as a temperature scale and as a velocity scale to describe the behaviour of turbulent flows in the Atmospheric Surface Layer (ASL), instead of _* andu _* of the Monin—Obukhov similarity theory, and ofT _f andU _f used for free convection stability conditions. On the basis of experimental evidence reported in the literature, it is shown that _T T _f andv _* U _f in the free convection region, and _{T *} andv _* U _* in nearneutral and stable conditions. This implies that the proposed scales can be applied for all stabilities. Furthermore, a new length scale is proposed and its relation with Obukhov length is given. Also, a simple semi-empirical expression is presented with which _T andv _* can be evaluated in a rather simple way. Some examples of practical applications are given, e.g., a stability classification for unstable conditions.     

Statistics of Surface-Layer Turbulence Over Terrain with Metre-Scale Heterogeneity

Refuge has patchy vegetation in sandy soil. During midday and at night, the surface sources and sinks for heat and moisture may thus be different. Although the Sevilleta is broad and level, its metre-scale heterogeneity could therefore violate an assumption on which Monin-Obukhov similarity theory (MOST) relies. To test the applicability of MOST in such a setting, we measured the standard deviations of vertical (_w) and longitudinal velocity (_u), temperature (_t), and humidity (_q), the temperature-humidity covariance (¯tq), and the temperature skewness (S_t). Dividing the former five quantities by the appropriate flux scales (u_*, _*, and q_*) yielded the nondimensional statistics _w/u_*, _u/u_*, _t/|t_*|, _q/|q_*|, and ¯tq/t_*q_*. _w/u_*, _t/|t_*|, and S_t have magnitudes and variations with stability similar to those reported in the literature and, thus, seem to obey MOST. Though _u/u_* is often presumed not to obey MOST, our _u/u_* data also agree with MOST scaling arguments. While _q/|q_*| has the same dependence on stability as _t/|t_*|, its magnitude is 28% larger. When we ignore ¯tq/t_*q_* values measured during sunrise and sunset transitions – when MOST is not expected to apply – this statistic has essentially the same magnitude and stability dependence as (_t/t_*)². In a flow that truly obeys MOST, (_t/t_*)², (_q/q_*)², and ¯tq/t_*q_* should all have the same functional form. That (_q/q_*)² differs from the other two suggests that the Sevilleta has an interesting surface not compatible with MOST. The sources of humidity reflect the patchiness while, despite the patchiness, the sources of heat seem uniformly distributed.     

Equatorial disturbances,monsoons, and 1982–1983 ENSO

Summary Interannual modes are described in terms of three-month running mean anomaly winds (u,v), outgoing longwave radiation (OLR), and sea surface temperature (T _* ). Normal atmospheric monsoon circulations are defined by long-term average winds (u _n,v _n) computed every month from January to December. Daily winds are grouped into three frequency bands, i.e., 30–60 day filtered winds (u _L,v _L); 7–20 day filtered winds (u _M,v _M); and 2–6 day filtered winds (u _S,v _S). Three-month running mean anomaly kinetic energy (signified asK _L , K _M , andK _S , respectively) is then introduced as a measure of interannual variation of equatorial disturbance activity. Interestingly, all of theseK _L , K _M , andK _S perturbations propagate slowly eastward with same phase speed (0.3 ms^–1) as ENSO modes. Associated with this eastward propagation is a positive (negative) correlation between interannual disturbance activity (K _L , K _M , K _S ) and interannualu (OLR) modes. Namely, (K _L , K _M , K _S ) becomes more pronounced than usual nearly simultaneously with the arrival of westerlyu and negativeOLR (above normal convection) perturbutions. In these disturbed areas with (K _L , K _M , K _S >0), upper ocean mixing tends to increase, resulting in decreased sea surface temperature, i.e.T _* 0. Thus, groups (not individual) of equatorial disturbances appear to play an important role in determiningT _* variations on interannual time scales. HighestT _* occurs about 3 months prior to the lowestOLR (convection) due primarily to radiational effects. This favors the eastward propagation of ENSO modes. The interannualT _* variations are also controlled by the prevailing monsoonal zonal windsu _n, as well as the zonal advection of sea surface temperature on interannual time scales. Over the central Pacific, all of the above mentioned physical processes contribute to the intensification of eastward propagating ENSO modes. Over the Indian Ocean, on the other hand, some of the physical processes become insignificant, or even compensated for by other processes. This results in less pronounced ENSO modes over the Indian Ocean.With 10 FiguresContribution No. 89-6, Department of Meteorology, University of Hawaii, Honolulu, Hawaii.     

Similarity forms for ground-source surface-layer diffusion

Past work on analyzing ground-source diffusion data in terms of surface-layer similarity theory is reviewed; these analyses assume that _z /L orh/L is a function of u ^* x/L (where h = Q/ dy). It is argued that an alternative scaling, h ^*/L versus x/L, is nearly as universal in that it is very weakly influenced by surface roughness, except for a modest influence in the free convective case (h ^* = Q/u ^* dy); the advantage of this scaling is that it eliminates the need to reassess as vertical diffusion progresses. The Prairie Grass data set is adjusted for the difference in source and sampling heights, and is plotted with this scaling. Simple analytic equations are suggested that fit the resultant data plots for stable and unstable conditions, and suggestions are made towards practical application of these results.On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.     

Boundary-layer parameterizations for applied dispersion modeling over urban areas

Many applied dispersion models require the knowledge of boundary-layer parameters such as sensible heat flux,Q _H , friction velocity,u _*, and turbulent energy components, _w and _v . Formulas are suggested for calculating these parameters over a wide variety of types of ground surfaces, based on simple observations of wind speed near the ground and fractional cloud cover, and specification of constants such as roughness length, albedo, and soil moisture availability. Observations ofu _*,Q _H , _w , and _v during field experiments in St. Louis and Indianapolis are used to test the formulas for urban sites. Relative errors of about ±20% in the predictions are seen to occur whenu _*,Q _H , _w , and _v are large. However, when these quantities are small (e.g.,u _* < 0.2 m/s), the errors in the predictions are as large as the mean value of the quantity itself.In addition, it is concluded from studies of available field data and theories that the magnitude of _w is not well-known at elevations above about 100m during the late afternoon and night. Some simple parameterizations for _w . are suggested that are consistent with the observed steady decrease in ground-level concentration in the afternoon and the sudden increase in concentration that can occur a few hours after sunset due to wind shears associated with a low-level jet, for continuous plumes emitted from moderate to tall stacks.     

Free convection frequency spectra of atmospheric turbulence over the sea

Frequency spectra of atmospheric turbulenceS (f) in the inertial subrange are considered in the free convection regime over the sea surface in a case of motionless instrument measurements (Eulerian frequency spectra). The frequency spectra formulaef _* S (f)/ ² =c (f _*/f)^5/3 for wind velocity (=1–3), temperature (=t) and humidity (=e) fluctuations are derived on the basis of similarity theory and the –5/3 law. These relations also can be derived from a consideration of convective large-scale advection of small eddies. The frequency scalef _* = (N ^{1 2}/)^1/2 (H/z ²)^1/3 is the lower bound of the inertial subrange and it is of order 10^–2 Hz.The spectra formulae are compared with direct measurements of atmospheric turbulence from the fixed research tower in the coastal zone of the Black Sea in calm weather. It is shown that these formulae are realized at least over two to three decades of the frequency range (approximately from 10^–2 to 10 Hz) and values of the numerical coefficients are found. The derived formulae can be used for calculations of sensible and latent heat fluxes by measuring the high-frequency range of spectra at a fixed point at low wind speeds when the conventional inertial dissipation method is not applicable.     

A study of the seasonal migration of ITCZ and the quasi-periodic oscillations in a simple monsoon system using an energy balance model

Summary A zonally averaged global energy balance model with feedback mechanisms was constructed to simulate (i) the poleward limits of ITCZ over the continent and over the ocean and (ii) a simple monsoon system as a result of differential heating between the continent and the ocean. Three numerical experiments were performed with lower boundary as (1) global continent, (2) global ocean and (3) continent-ocean, with freezing latitudes near the poles. Over the continent, midlatitude deserts were found and the ITCZ migrates 25° north and south with seasons. Over a global swamp ocean results do not show migration of ITCZ with time but once the ocean currents are introduced the ITCZ migrates 5° north and south with seasons. It was found that the seasonal migration of ITCZ strongly depends on the meridional distribution of the surface temperature. It was also found that continent influences the location of the oceanic ITCZ. In the tropics northward progression of quasi-periodic oscillations called events are found during the pre- and post-monsoon periods with a period of 8 to 15 days. This result is consistent with the observed quasi-periodic oscillations in the tropical region. Northward propagation of the surface temperature perturbation appears to cause changes in the sensible heat flux which in turn causes perturbations in vertical velocity and latent heat flux fields.List of Symbols vertical average - ₀ zonal average - vertical mean of the zonal average - _0s zonal average at the surface - _0a zonal average at 500 mb level - latitude We now define the various symbols used in the model rate of atmospheric heating due to convective cloud formation (K/sec) - dp/dt (N/m²/sec) - density - potential temperature (K) - rate of rotation of the earth (rad/sec) - empirical constant - humidity mixing ratio - ^* saturated humidity mixing ratio - opacity of the atmosphere - ₁,₂ factors for downward and upward effective black body long wave radiation from the atmosphere - Stefan-Boltzmann constant - emissivity of the surface - _D subsurface temperature (K) - a specific volume - _0xs ,_0ys eastward and northward components of surface frictional stress - ^* vertical velocity at the top of the boundary layer (N/m²/sec) - P Thickness of the boundary layer (mb) - nondimensional function of pressure - P pressure - P _a pressure of the model atmosphere (N/m²) - P _s pressure at the surface (N/m²) - t time (sec) - U eastward wind speed (m/sec) - V northward wind speed (m/sec) - surface water availability - T absolute temperature (K) - heat addition due to water phase changes - g acceleration due to gravity (m²/sec) - a radius of the earth (m) - R gas constant for dry air (J/Kg/K) - C _p specific heat of air at constant pressure (J/Kg/K) - k R/C _p - L latent heat of condensation (J/Kg) - f coriolis parameter (rad/sec) - H _s H _0s ⁽¹⁾ +H _0s ⁽²⁾ +H _0s ⁽³⁾ +H _0s ⁽⁴⁾ +H _0s ⁽⁵⁾ (J/m²/Sec)=sum of the rates of vertical heat fluxes per unit surface area, directed toward the surface - H _a H _0a ⁽¹⁾ +H _0a ⁽²⁾ +H _0a ⁽³⁾ +H _0a ⁽⁴⁾ (J/m²/Sec)=sum of the rates of heat additions to the atmospheric column per unit horizontal area by all processes - H _0s ⁽¹⁾ ,H _0a ⁽¹⁾ heat flux due to short wave radiation - H _0s ⁽²⁾ ,H _0a ⁽²⁾ heat flux due to long wave radiation - H _0s ⁽³⁾ ,H _0a ⁽³⁾ heat flux due to small scale convection - H _0s ⁽⁴⁾ heat flux due to evaporation - H _0a ⁽⁴⁾ heat flux due to condensation - H _0s ⁽⁵⁾ heat flux due to subsurface conduction and convection - e ^* saturation vapor pressure - R solar constant (W/m²) - r _a albedo of the atmosphere - r _s albedo of the surface - b ₂ empirical constant (J/m²/sec) - c ₂ empirical constant (J/m²/sec) - e ₂ nondimensional empirical constant - f ₂ empirical constant (J/m₂/sec) - factor proportional to the conductive capacity of the surface medium - a _s constant used in Sellers model - b _s positive constant of proportionality used in the Sellers model (kg m²/J/sec²) - K _HT coefficient for eddy diffusivity of heat (m²/sec) - K _HE exchange coefficient for water vapor (m²/sec) - h depth of the water column (m) - z height (m) - V _0ws meridional component of surface current (m/sec) - n cloud amount - G _0,n long wave radiation form the atmosphere for cloud amount n (W/m²) - B ₀ long wave radiation from the surface (W/m²) - S _0,n short wave radiation from the atmosphere for cloud amount n (W/m²) - A _n albedo factor for a cloud amount n - R _f1 large scale rainfall (mm/day) - R _f2 small scale rainfall (mm/day) With 22 Figures     

A Comparative Analysis of Transpiration and Bare Soil Evaporation

Transpiration E^v and bare soil evaporation E^b processes are comparatively analysed assuming homogeneous and inhomogeneous areal distributions of volumetric soil moisture content . For a homogeneous areal distribution of we use a deterministic model, while for inhomogeneous distributions a statistical-deterministic diagnostic surface energy balance model is applied. The areal variations of are simulated by Monte-Carlo runs assuming normal distributions of .The numerical experiments are performed for loam. In the experiments we used different parameterizations for vegetation and bare soil surface resistances and strong atmospheric forcing. According to the results theE^v()-^Eb() differences are great, especially in dry conditions. In spite of this, the available energy flux curves of vegetation A^v() and bare soil A^b() surfaces differ much less than the E^v() and ^Eb() curves. The results suggest that E^v is much more non-linearly related to environmental conditions than ^Eb. Both E^v and ^Eb depend on the distribution of , the wetness regime and the parameterization used. With the parameterizations, ^Eb showed greater variations than E^v. These results are valid when there are no advective effects or mesoscale circulation patterns and the stratification is unstable.     

Observation of lake breeze penetration and subsequent development of the thermal internal boundary layer for the Nanticoke II Shoreline Diffusion Experiment

The turbulent structure of the lake breeze penetration and subsequent development of the thermal internal boundary layer (TIBL) was observed using a kytoon-mounted ultrasonic anemometer-thermometer. The lake breeze penetrated with an upward rolling motion associated with the upward flow near the lake breeze front. After the lake breeze front passed, the behaviors of the velocity and temperature at the top of the lake breeze layer were similar to those found in convective boundary layers (CBL). Comparing _gq/_*, _u /w _* and _w /w _* between the present observation of TIBL development after the passage of the lake breeze front and CBL data from the literature, the /_* values showed reasonable agreement; however, _u /w _* and _w /W_* had smaller values in the TIBL than in the CBL at higher altitudes. This is due to the differences in the mean velocity profiles. While the CBL has a uniform velocity profile, the TIBL has a peak at lower elevation due to the lake breeze penetration; the velocity then decreases with height.Present address: The Institute of Behavioral Science, 1-35-7 Yoyogi, Tokyo 151, Japan.     

Über die mittlere lineare sukzessive Differenz und ihre Anwendung auf die Untersuchung meteorologischer Beobachtungsreihen

Zusammenfassung Eine endliche Reihe (Sequenz) wird als eine der möglichen Permutationen ihrer Glieder aufgefaßt. Es wird gezeigt, daß die Summe der absoluten Differenzen der aufeinanderfolgenden Glieder gleich ist , wo die natürliche Zahlen sind und nur von der Rangordnung der Glieder der Reihe (von der Permutation) abhängen; die _j sind von der Reihenfolge unabhängig und werden durch die Dispersion der Reihenglieder bestimmt. Die _j und die _j werden separat untersucht; der Erwartungswert der erwähnten Differenzsumme wird abgeleitet. Verschiedene bereits bekannte und auch erstmalig hier vorgeschlagene Maßzahlen werden geprüft. An Reihen jährlicher Regenmengen wird die Rolle der _j und der _j und das Verhalten der besprochenen Maßzahlen veranschaulicht.

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Summary A series ofn members can be considered as one of the possible permutations of its members. It is shown that the sum of the linear successive differences is equal to the expression , where the _j are positive integers, dependent only upon the rank-order (the permutation) of the members, while the _j are independent of the order of the succession and are determined by the dispersion of the members of the series. The factors _j and _j are separately investigated; the expected value of the sum of the linear successive differences is established. Various related statistical measures, already in usage and new ones suggested here, are discussed. Series of yearly rainfall amounts are used to show the effects of the _j and _j and to discuss the behaviour of the various measures.

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Résumé Une série, constituée parn valeurs, est regardée comme une des possibles permutations de ces valeurs. L'auteur montre que la somme des différences absolues, qui se présentent entre les valeurs consécutives de la série, est égale à l'expression . Les _j sont des nombres entiers positifs et ne dépendent que de l'ordre des membres de la série, tandis que les _j, indépendants de l'ordre, sont déterminés par la dispersion des membres. Les facteurs _j et _j sont étudiés séparément; l'espérance mathématique de la somme mentionnée est dérivée. Des paramètres statistiques déjà connus ou proposés ici pour la première fois, sont discutés. Le rôle des _j et des _j et le comportement des divers paramètres sont montrés à l'aide de séries de totaux annuels de pluies.

     

Experiments On Buoyant Plume Dispersion In A Laboratory Convection Tank

Plume dispersion in the convective boundary layer (CBL) is investigated experimentally in a laboratory convection tank. The focusis on highly-buoyant plumes that loft near or become trapped in the CBL capping inversion and resistdownward mixing. Such plumes are defined by dimensionless buoyancy fluxes F_* 0.1, where F_* = F_b/(U w_* ² z_i), F_b is the stack buoyancy flux,U is the mean wind speed, w_* is the convective velocity scale, and z_i is the CBL depth. The aim is to obtain statistically-reliable mean (C) and root-mean-square (rms, _c) concentration fields as a function of F_* and the dimensionless distance X = w_*x/(U z_i), where x is the distance downstream of the source.The experiments reveal the following mainresults: (1) For 3 X 4and F_* 0.1, the crosswind-integrated concentration (CWIC) fields exhibit distinctly uniform profiles below z_i with a CWIC maximum aloft, in contrast to the nonuniform profiles obtained earlier by Willis and Deardorff. (2) The lateral dispersion (_y) variation with X is consistent with Taylor's theory for _* 0.1 and a buoyancy-enhanced dispersion, _y/z_i F_* ^1/3X^2/3, forF_* = 0.2 and 0.4. (3) The entrapment, the plume fraction above z_i, has a mean (E) that follows a systematic variationwith X and F_*, and a variability (_e/E) that is broad ( 0.3 to 2) near the source but subsides to 0.25 far downstream. (4) Vertical profiles of the concentration fluctuation intensity (c/C) are uniform for z < z_i and X > 1.5, but exhibit significant increases: (a) at the surface and close to the source (X 1.5), and(b) in the entrainment zone. (5) The cumulative distribution functions (CDFs) of the scaled concentration fluctuations (c/_c) separate into mixed-layer and entrainment-layer CDFs for X 2, with the mixed-layer group collapsing to a single distribution independent of z.These are the first experiments to obtain all components of the lateral and vertical dispersion parameters (rms meander, relative dispersion, total dispersion) for continuous buoyant releases in a convection tank. They also are the first tank experiments to demonstrate agreement with field observations of: (1) the scaled ground-level concentration along the plume centreline, and (2) the dimensionless lateral dispersion _y/z_i of buoyant plumes.     

The dynamical range of global circulations — II

The dynamical range of global atmospheric circulations is extended to specialized parameter regions by evaluating the influence of the rotation rate () on axisymmetric, oblique, and diurnally heated moist models. In Part I, we derived the basic range of circulations by altering for moist and dry atmospheres with regular and modified surfaces. Again we find the circulations to be composed of only a few elementary forms. In axisymmetric atmospheres, the circulations consist of a single jet in the rotational midrange (^*=1/2–1) and of double jets in the high range (^*=2–4), together with one or two pairs of Hadley and Ferrel cells; where (^*=/ _E ) is the rotation rate normalized by the terrestrial value. These circulations differ from those predicted by firstorder symmetric-Hadley (SH₁) theory because the moist inviscid atmosphere allows a greater nonlinearity and prefers a higher-order meridional mode. The axisymmetric circulations do, however, resemble the mean flows of the natural system — but only in low latitudes, where they underlie the quasi-Hadley (QH) element of the MOIST flows. In midlatitudes, the axisymmetric jets are stronger than the natural jets but can be reduced to them by barotropic and baroclinic instablities. Oblique atmospheres with moderate to high tilts ( _P =25°–90°) have the equator-straddling Hadley cell and the four basic zonal winds predicted by the geometric theory for the solstitial-symmetric-Hadley (SSH) state: an easterly jet and a westerly tradewind in the summer hemisphere, and a westerly jet and an easterly tradewind in the winter hemisphere. The nonlinear baroclinic instability of the winter westerly produces a Ferrel cell and the same eddy fluxes as the quasi-geostrophic QG element, while the instability of the summer easterly jet produces a QG-Hadley (QGH) element with a unique, vertically bimodal eddy momentum flux. At high _P and low ^*, the oblique atmospheres reach a limiting state having global easterlies, a pole-to-pole Hadley cell, and a warm winter pole. At low tilts _P <10°, the oblique circulations have a mix of solstitial and equinoctial features. Diurnal heating variations exert a fundamental influence on the natural-Hadley (NH) circulations of slowly rotating systems, especially in the singular range where the zonal winds approach extinction. The diurnality just modifies the NH element in the upper singular range (1/45^*1/16), but completely transforms it into a subsolar-antisolar Halley circulation in the lower singular range (0^*<1/45). In the modified NH flows, the diurnality acts through the convection to enhance the generation of the momentum-transferring planetary waves and, thereby, changes the narrow polar jets of the nondiurnal states into broad, super-rotating currents. Circulation theory for these specialized flows remains rudimentary. It does not explain fully how the double jets and the multiple cells arise in the axisymmetric atmospheres, how the QGH element forms in the oblique atmospheres, or how waves propagate in the slowly rotating diurnal atmospheres. But eventually all theories could, in principle, be compared against planetary observation: with Mars testing the QGH elements; Jupiter, the high-range elements; Titan, the equinoctial and solstitital axisymmetric states; and Venus, the diurnally modified NH flows.     

Théorie des oscillations annuelles et diurnes de la température à la surface des continents et des océans

Résumé On détermine analytiquement les températures absoluesT (z, t) etT (z, t) dans l'air et dans le substrat terrestre, au voisinage de la surface de séparation de ces milieux, sous la condition que le rayonnement global varie dans le temps selon une fonction périodique simple ou quelconque. A cette fin, on s'attache à résoudre le système des deux équations de la chaleur dans l'air et dans le substrat terrestre en tenant compte de toutes les conditions physiques déterminantes du problème. Celles-ci interviennent dans l'équation énergétique aux limites pour le plan de séparationz=0. Un minimum d'hypothèses simplificatrices confère une plus haute valeur pratique aux résultats. Leur limitation principale réside dans le fait que les diffusivités turbulentesK etK _w de l'air et de l'Océan sont supposées constantes. On retrouve le résultat classique selon lequel l'onde thermique est déphasée sur le rayonnement global et jouit d'une amplitude proportionnelle à celle de ce rayonnement. Toutefois, l'amortissement thermique et le déphasage dépendent cette fois de la somme + des «propriétés thermiques» du substrat et de l'air, et étant alternativement dominant selon qu'il s'agit des Continents ou des Océans. Dans ce dernier cas, la théorie des oscillations thermiques est traitée d'abord en admettant l'existence d'une couche d'eau isothermique. On établit ensuite la théorie plus réaliste qui considère à la fois la diffusivité thermique turbulenteK _w et le coefficient d'extinctionq du rayonnement global dans l'Océan. Le point de départ de la théorie est l'équation de la chaleur dans un milieu semi-transparent. Les résultats montrent que l'onde thermique de surface subit un amortissement complémentaire dû au facteurq, le déphasage sur le rayonnement global pouvant atteindre 91 jours alors que cette limite n'est que de 45 jours pour les Continents. La discussion des résultats théoriques montre leur bon accord quantitatif avec les faits observés. On termine par quelques applications de la théorie; on montre notamment que celle-ci valide rationnellement la théorie astronomique des phases climatiques quaternaires.

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Summary Absolute temperaturesT (z, t) andT (z, t) near the interface of air and terrestrial substratum are analytically determined, under the condition that the total radiation varies with time according to a simple or to any other periodic function. To achieve this, the system of two equations of heat in air and terrestrial substratum is resolved in taking into account all the determining physical conditions of the problem. These conditions are considered in the energy boundary equation for the surface of separationz=0. A minimum number of simplifying hypotheses give a higher practical value to the results whose principal limitation lies in the fact that eddy conductivitiesK andK _w of air and ocean water are supposed to be constant. The classical result that the thermal wave differs in phase from the total radiation and gives an amplitude proportional to that radiation is confirmed. However, the thermal damping and the lag in phase depend here of the sum + of the thermal properties of the substratum and the air, and being preponderant for continents and oceans respectively. In the last case, the theory of thermal oscillations is first studied with the aid of the hypothesis of an isothermal water layer. Then a more realistic theory is established which considers in addition the eddy diffusivityK _w and the extinction coefficientq of the total radiation in the ocean. The basis of the theory is the heat equation for a semi-transparent medium. The results show that the surface thermal wave suffers a further damping due toq. In addition, the maximum temperature may lag behind the maximum radiation by as much as 91 days as against a maximum of 45 days for the continents. The discussion of the theoretical results shows their good quantitative agreement with the observations. Some practical applications of the theory are given. For example the validity of the astronomical theory of the climatic changes during the Quaternary period is rationally justified.

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Zusammenfassung Die absoluten TemperatureT (z, t) undT (z, t) von Luft und terrestrischer Unterlage in der Nähe der Trennschicht der beiden Medien werden analytisch bestimmt mit der Bedingung, daß die Globalstrahlung nach einer einfachen oder einer beliebigen periodischen Funktion mit der Zeit variiert. Zu diesem Zweck wird versucht, under Berücksichtigung aller bestimmenden physikalischen Bedingungen des Problems das System der beiden Wärmegleichungen für Luft und für das terrestrische Substrat zu lösen. Diese gehen in der Energiegleichung für die Grenzbédingungen der Trennflächez=0 ineinander über. Ein Minimum an vereinfachenden Hypothesen erhöht den praktischen Wert der Resultate; die Annahme der Konstanz des AustauschkoeffizientenA=K undA _w = _w A _w der Luft und des Ozeans bildet die wichtigste Einschränkung. Das klassische Resultat, nach dem die Wärmewelle zur Globalstrahlung in Phase verschoben und ihre Amplitude proportional zur Strahlungsamplitude ist, wird bestätigt. Die Abschwächung der thermischen Amplitude sowie die Phasenverschiebung hängen aber von der Summe + der thermischen Eigenschaften der Unterlage und der Luft ab; wobei oder überwiegt, je nachdem es sich um die Kontinente oder die Ozeane handelt. Für den letzteren Fall Wird die Theorie der Wärmeschwankungen zuerst unter der Annahme der Existenz einer isothermen Wasserschicht behandelt. Hernach wird die allgemeiner gültige Theorie entwickelt, welche gleichzeitig den TurbulenzaustauschA _w und den Extinktionskoeffizientenq der Globalstrahlung im Ozean in Betracht zieht. Den Ausgangspunkt für die Theorie bildet die Wärmegleichung für ein Strahlungsdurchlässiges Medium. Die Resultate zeigen, daß die Oberflächenwärmewelle eine Abschwächung entsprechend dem Faktorq erfährt; dabei kann die Phasenverschiebung gegenüber der Globalstrahlung 91 Tage erreichen, während die maximale Verschiebung für die Kontinente nur 45 Tage beträgt. Die Vergleichung der theoretischen Resultate ergibt deren gute quantitative Übereinstimmung mit den Beobachtungstatsachen. Zum Schluß werden einige Anwendungen der Theorie gebracht; so wird z. B. gezeigt, daß diese eine sinngemäße Rechtfertigung der Gültigkeit der astronomischen Theorie der quaternären klimatischen Phasen gestattet.

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Institut belge pour l'Encouragement de la Recherche Scientifique Outre-Mer (IBERSOM), 3, rue Montoyer, Bruxelles, Belgique.     

Standard deviation of vertical two-point longitudinal velocity differences in the atmospheric boundary layer

The standard deviation of vertical two-point longitudinal velocity fluctuation differences is analyzed experimentally with eleven sets of turbulence measurements obtained at the NASA 150-m ground-winds tower site at Cape Kennedy, Florida. It is concluded that /u _*0 is proportional to (fz/u _*0)^0.22, where the coefficient of proportionality is a function of fz/u _*0 and u _*0/fL ₀. The quantities f and L₀ denote the Coriolis parameter and the surface Monin-Obukhov stability length, respectively; u _*0 is the surface friction velocity; z is the vertical distance between the two points over which the velocity difference is calculated; and zz is the mean height of the mid-point of the interval z above natural grade. The results of the analysis are valid for 20<-u _*0/fL ₀<2000.     

A calculation of global radiation in The Netherlands with the aid of the relative duration of sunshine

Summary A.Ångström has assumed a linear relation between daily totals of the global radiation measured at a certain place and the corresponding daily values of the relative duration of sunshine. Other authors have applied the same relationhip, however, with a different unit of time, such as a 5-day period, a 10-day period and a month. In this paper a period of one hour is chosen as unit.Ångström's Q ₀ ^– and -values have been determined for De Bilt and for the one-hour periods L. A. T. of the mean day in each of the 60 months of the 5-year period 1954–1958. For the mean day of each of the 12 months of the year the arithmetic means of the 5Q ₀ ^– and 5 -values for the same hours have been calculated.A simple method to compute daily amounts of global radiation by means of these averageQ ₀ ^– and -values has been applied to De Bilt and Wageningen for all days of 1958. The square root of the residual variance of the thus determined daily amounts appeared to amount to 0.75 for De Bilt and to 0.82 for Wageningen compared with that computed for Wageningen fromÅngström's formula for daily amounts directly. This result shows that the average hourlyQ ₀ ^– and -values for De Bilt may be used to calculate daily amounts of global radiation for any place in the Netherlands.

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Zusammenfassung A.Ångström hat eine lineare Beziehung zwischen den Tagessummen der Globalstrahlung an einem Ort und den entsprechenden täglichen Werten der relativen Sonnenscheindauer angenommen. Andere Autoren haben dieselbe Beziehung benützt, jedoch mit verschiedenen Zeiteinheiten, wie einer Pentade, einer Dekade oder einem Monat. In der vorleigenden Untersuchung ist die Dauer einer Stunde als Einheit gewählt worden. DieÅngströmschenQ ₀ ^– und -Werte sind bestimmt worden für alle Stunden in wahrer Sonnenzeit für den mittleren Tag jedes der 60 Monate der fünfjährigen Periode 1954–1958 für De Bilt. Daraus sind die arithmetischen Mittel der 5Q ₀ ^– und der 5 -Werte für dieselben Stunden des mitteleren Tages in jedem der 12 Monate des Jahres berechnet worden.Eine einfache Methode zur Berechnung der Tagessummen der Globalstrahlung mit Hilfe der mittlerenQ ₀ ^– und -Werte wurde für De Bilt und Wageningen auf alle Tage des Jahres 1958 angewandt; dabei hat die Quadratwurzel der Restvarianz der also berechneten Tagessummen für De Bilt 0,75 mal und für Wageningen 0,82 mal den Wert der Quadratwurzel der Restvarianz der in direkter Weise mit Hilfe derÅngströmschen Formel für Wageningen berechneten Tagessummen ergeben. Daraus geht hervor, daß für jeden Ort in den Niederlanden die Tagessumme der Globalstrahlung nach der oben beschriebenen Methode mit genügender Genauigkeit berechnet werden kann.

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Résumé A.Ångström a supposé une relation linéaire entre les sommes journalières du rayonnement global observées en un lieu donné et les valuers journalières correspondantes de la durée d'insolation relative. D'autres auteurs ont admis la même relation, mais en employant des unités de temps différentes, telles que la pentade, la décade ou le mois. C'est la période d'une heure qui a été choisie ici comme unité. Les valeursQ ₀ et d'Ångström ont été déterminées pour De Bilt pour chaque heure, en temps solaire vrai, au cours d'un jour moyen de chaque mois de la période 1954–1958. Les moyennes arithmétiques de cinq valuersQ ₀ et ont été calculées pour les mêmes heures du jour moyen de chacun des douze mois de l'année.Une méthode simple de calcul des sommes journalières du rayonnement global à l'aide de ces valeurs moyennes deQ ₀ et de a été appliquée pour De Bilt et Wageningen pour tous les jours de l'année 1958. On a trouvé que le rapport de la racine carrée de la variance résiduelle des valuers journalières calculées de cette façon à celle des valeurs journalières calculées directement au moyen de la formule d'^Ångström pour Wageningen se montait à 0,75 pour De Bilt et à 0,82 pour Wageningen. Ce résultat prouve que l'on peut appliquer les valeurs horairesQ ₀ et calculées pour De Bilt au calcul des sommes journalières du rayonnement global en chaque point des Pays-Bas.

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The present investigation is treated more in detail in a Scientific Report of the Royal Netherlands Meteorological Institute No. WR-60-6.     

Les bilans énergétiques approchés en variables λ, ϕ,p ett

Résumé L'auteur montre comment il faut déduire les formes approchées des bilans énergétiques des mouvements atmosphériques en variables , ,p ett de leurs formes générales exactes. Il a tenu compte de la variabilité de la pression à la surface du globe.

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Summary It is shown how the approximate energy equations of atmospheric motions expressed with the independent variables , ,p andt must bederived from their exact general form. The variability of surface pressure has been taken into account.

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Zusammenfassung Es wird gezeigt, wie sich Näherungsformeln der Energiebilanzen der atmosphärischen Bewegungsvorgänge durch die unabhängigen Variablen , ,p undt von ihrer exakten Formulierung ableiten lassen; dabei wird der Veränderlichkeit des Luftdrucks an der Erdoberfläche Rechnung getragen.