Unbiased station grid for study of the kinetic energy balance of the atmosphere

Summary For the past several years observational studies of the northern hemisphere kinetic energy balance and related subjects have been performed by the Planetary Circulation Project of the Massachusetts Institute of Technology. Numerous integrals required were recently evaluated directly from a five-year period of observations using a network of nearly 800 stations. The stations, however, are concentrated primarily over temperate latitude continents, and the data from maritime and tropical areas were comparatively sparse. The question then arises whether the results are representative. The problem discussed in this paper is to select a subset of more uniformly spaced stations and to recompute the zonal kinetic energy balance. This is accomplished and the results are presented herewith.The research reported in this paper was sponsored by the U.S. National Science Foundation under Grant No. GA-1310X.     

A method for the study of the zonal kinetic energy balance in the atmosphere

Summary The atmospheric balance of the kinetic energy of the zonally averaged zonal motion is investigated from five years of daily data at 800 stations for the northern hemisphere. The basic equation for such energy is used, together with the simplifying assumption that the frictional destruction is due in the main to stresses acting across horizontal surfaces, being thus presumably related to the vertical shear of the mean zonal wind, although no further details are needed in the analysis. The five-year averages of various terms as well as their seasonal means appear to give reasonable results.The research reported in this paper was sponsored by the U.S. National Science Foundation under Grant No. GA-1310X.     

Satellite solar occultation sounding of the middle atmosphere

This paper discusses the principles, achievements, and prospects for satellite solar occultation sounding of the middle atmosphere. Advantages, disadvantages, and spatial and temporal coverage capabilities are described. Progress over the past 15 years is reviewed, and results from a recent satellite aerosol experiment are presented. Questions with regard to Doppler shift, atmosphric refraction, instrument pointing, pressure sensing, and measurement of diurnally active species are addressed. Two experiments now orbiting on the Nimbus-7 and AEM-B satellites, and approved experiments under development for future flights on Spacelab and the Earth Radiation Budget Satellite, are also described. In some cases more than one experiment is scheduled to be flown on the same spacecraft, and the advantages and synergistic effects of these applications are discussed.     

On the energy content of the atmosphere

Summary Vertical profiles of the content of sensible heat, potential energy, and latent heat in the atmosphere between 1000 and 100 mb, during January and July, are derived for the latitude circles 0, 10, 20, 30, 40, 50, and 60°N. Contrasts between oceans and continents are found to vary significantly with latitude and season.

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Zusammenfassung Vertikalprofile des Gehalts an fühlbarer Wärme, potentieller Energie und latenter Wärme in der Atmosphäre zwischen 1000 and 100 mb werden für Januar und Juli und die Breitenkreise 0, 10, 20, 30, 40, 50, und 60°N abgeleitet. Gegensätze zwischen Land und See ändern sich mit geographischer Breite und Jahreszeit.

     

Onset of an energy cascade and nonperiodic behaviour in the nonlinear propagation of MHD waves in the solar atmosphere

Abstract

We study the nonlinear stability of MHD waves propagating in a two-dimensional, compressible, highly magnetized, viscous plasma. These waves are driven by a weak, shear body force which could be imposed by large scale internal fluctuations present in the solar atmosphere.

The effects of anisotropic viscosity (leading to a cubic damping) and of the nonlinear coupling of the Alfven and the magnetoacoustic waves are analysed using Galerkin and multiple-scale analysis: the MHD equations are reduced to a set of nonlinear ordinary differential equations which is then suitably truncated to give a model dynamical system, representing the interaction of two complex Galerkin modes.

For propagation oblique to the background magnetic field, analytical integration shows that the low-wavenumber mode is physically unstable. For propagation parallel to the background magnetic field the high-wavenumber wave can undergo saddlenode bifurcations, in way that is similar to the van der Pol oscillator; these bifurcations lead to the appearance of a hysteresis cycle.

A numerical integration of the dynamical system shows that a sequence of Hopf bifurcations takes place as the Reynolds number is increased, up to the onset of nonperiodic behaviour. It also shows that energy can be transferred from the low- wavenumber to the high-wavenumber mode.     

Ejection and descent of matter in the solar atmosphere

The descent and ejection of matter in the solar atmosphere observed in the CaII 8498-Å line have been studied. In the NOAA active region no. 10 792 on July 30, 2005 before the flare, the dense cold gas cloud descended with a ray velocity of ～8 km/s and then ascended in the impulsive phase. The plasma ascended with an acceleration reaching 0.4 km/s² in the flare maximum. The acceleration of the matter likely continued after the flare maximum, because an acceleration of higher than 0.5 km/s² was required for the appearance of the ejection at the edge of the occulting disk of the LASCO C2 coronagraph at 0557 UT. The descent of the matter resulting in the local heating of the chromosphere was also observed in the NOAA active region no. 10656 on August 9, 2004 before the flare. The maximum descent velocity was no more than 24.7 km/s.     

General circulation of the solar atmosphere from observational evidence

Summary One of the main results of the rotating cylinder experiments ofFultz andHide is that the general flow regime in them is essentially determined by the ratio of the angular velocity of the fluid motions (relative to the cylinder) to that of the cylinder itself. Extending these results to the atmosphere of the sun, leads to the hypothesis that the layer in which spots are imbedded should exhibit a non-axially symmetric pattern, of theRossby type.The fluid motions, characteristic of such a general circulation pattern, are mainly along spherical surfaces, and have a wavelike (eddy) appearance similar to the planetary waves in the upper troposphere of the terrestrial atmosphere. These eddies transport momentum along these spherical surfaces from regions of relatively lower angular velocity to regions of higher velocity. Tracers (e.g., sunspots) imbedded is such a flow would show a correlation between their proper motions in latitude and longitude, such that spots moving equatorward will tend to have larger longitudinal motions (toward the west limb), and vice versa.Analysis of ten years (1935 to 1944) of Greenwich spot data shows a consistent, and (statistically) very significant correlation of spot group proper motions, in the proper sense. These results provide strong support for the existence of large-scale waves which are some modest fraction of the solar circumference, but larger than the sunspot groups. Moreover, these waves transport angular momentum (up the gradient of angular velocity) toward the equatorial regions from higher latitudes across at least the entire sunspot zone. It is not known, however, whether these eddies are the primary (or only) source of momentum to maintain the equatorial acceleration of the sun. However, if this source were shut off, and all other processes continued unabated, this layer of the sun between latitudes ±20° would reach solid rotation in about 51/2 rotations.Because this eddy transport of momentum is counter to the gradient of angular velocity, there is an implied transformation of the kinetic energy of the eddies into the kinetic energy of the mean east-west flow. Of possibly even more interest, however, might be the possibility of transfers of kinetic energy between eddies of all different scale sizes extending down the entire spectrum to include sunspot groups and the spots themselves. Moreover, some eddy size(s) in this layer is likely to be primarily responsible for a conversion of potential to kinetic energy.A result of subsidiary interest is the systematically higher value of solar rotation (at all latitudes) derivable from this data, which includes all spots which survive for at least two days. In contrast to the work of previous authors who used only long-lived spots, the result obtained when many small spots are used, indicates perhaps a variation of the rotation rate with height in the solar atmosphere.The results provide no evidence to indicate the existence of significant meridional circulations (latitudinal driffs).     

Solar faculae and waves propagating in the solar atmosphere

Solar faculae are among the most common manifestations of solar activity and can play an important role in the energy transfer from the lower solar atmosphere into the corona. However, the mechanisms by which energy is transferred remain insufficiently studied. Our work is based on observational data obtained with the AST telescope of the Sayan solar observatory. Simultaneous observations were performed in the Hα 6563 Å and FeI 6569 Å, BaII 4554 Å and FeI 4551.6 Å, and CaII 8542 Å and FeI 8538 Å pairs of spectral lines. The studies indicated that the spectral composition of the line-of-sight (LOS) velocity oscillations in faculae is inhomogeneous and is affected by the chromospheric network’s structural elements. The possible presence of short and low magnetic loops in the facula region makes it difficult to determine the unambiguous phase relations between chromospheric and photospheric oscillations. The LOS velocity oscillation signals registered at the chromospheric level both lead and lag behind the signals registered at the photospheric level. At the same time, signs of propagating waves are evidently registered in the chromosphere of individual faculae.     

Torque balance and energy budget for the precessionally driven dynamo

The feasibility of a precessionally driven dynamo is investigated. The relative orientation of the angular-velocity vectors of the mantle and core and the precession vector of the earth are determined from a torque balance. The core and mantle are acted upon by separate gravitational torques and mutual interaction torques resulting from pressure, viscous and magnetic stresses at the core-mantle interface. The viscous and magnetic torques are determined using the results of a detailed analysis of the Ekman-Hartmann and magnetic diffusion layers generated at the core-mantle interface by the misalignment of the mantle and core angular-velocity vectors. The dissipative torques are found to be weaker by a factor of 10^?4 than those estimated by Malkus (1968) and Stacey (1973), resulting in only 3.5 · 10⁷ W being extracted from the rotational kinetic energy of the earth by these mechanisms. Furthermore, it is found that all of this energy is dissipated in the boundary layers at the core-mantle interface and none is available to drive the geodynamo.     

Instability of a thin magnetic tube in the solar atmosphere

Abstract

The static equilibrium of a thin vertical magnetic tube embedded in the solar atmosphere is shown to be dynamically unstable against the fundamental mode of perturbation having no nodes in the vertical displacement. The instability has its origin in the convection zone, and the eigenfunction is extended further up in the stable upper layers by the magnetic field which guides the displacement mainly in the longitudinal direction. It is suggested that the downdraft observed in the solar network structure is a finite amplitude consequence of this instability. The overtone modes are found to be stable.     

A unifying framework for watershed thermodynamics: balance equations for mass,momentum, energy and entropy,and the second law of thermodynamics

The basic aim of this paper is to formulate rigorous conservation equations for mass, momentum, energy and entropy for a watershed organized around the channel network. The approach adopted is based on the subdivision of the whole watershed into smaller discrete units, called representative elementary watersheds (REW), and the formulation of conservation equations for these REWs. The REW as a spatial domain is divided into five different subregions: (1) unsaturated zone; (2) saturated zone; (3) concentrated overland flow; (4) saturated overland flow; and (5) channel reach. These subregions all occupy separate volumina. Within the REW, the subregions interact with each other, with the atmosphere on top and with the groundwater or impermeable strata at the bottom, and are characterized by typical flow time scales.The balance equations are derived for water, solid and air phases in the unsaturated zone, water and solid phases in the saturated zone and only the water phase in the two overland flow zones and the channel. In this way REW-scale balance equations, and respective exchange terms for mass, momentum, energy and entropy between neighbouring subregions and phases, are obtained. Averaging of the balance equations over time allows to keep the theory general such that the hydrologic system can be studied over a range of time scales. Finally, the entropy inequality for the entire watershed as an ensemble of subregions is derived as constraint-type relationship for the development of constitutive relationships, which are necessary for the closure of the problem. The exploitation of the second law and the derivation of constitutive equations for specific types of watersheds will be the subject of a subsequent paper.     

Perturbation equations for the time-average state of the atmosphere including the effects of transient disturbances

Summary The time-average, or «stationary», state of the atmosphere can be regarded as a forced response to large-scale transient eddy transports of heat and momentum, as well as to fixed sources and sinks of heat and momentum resulting from small-scale transient eddy processes, non-adiabatic processes (e. g., radiation and phase transformations), topography, and friction. Perturbation equations governing this response are derived and a program of research based on the equations is proposed.     

On the aquifer's integrated balance equations

A general methodology is presented for describing transport phenomena in porous media at a macroscopic level. Then, these macroscopic balance equations are integrated (or averaged) along the vertical for confined, leaky and phreatic aquifers.The results are employed to derive (averaged) aquifer equations for the flow of water and of a solute (hydrodynamic dispersion). It is shown that in all cases, the resulting equation is identical to that derived on the basis of an assumption of horizontal flow (the Dupuit assumption).Macrodispersion, occurring at the aquifer level, is discussed and appropriate coefficients are proposed.     

Analytical study of the energy rate balance equation for the magnetospheric storm-ring current

We present some results of the analytical integration of the energy rate balance equation, assuming that the input energy rate is proportional to the azimuthal interplanetary electric field, E_y, and can be described by simple rectangular or triangular functions, as approximations to the frequently observed shapes of E_y, especially during the passage of magnetic clouds. The input function is also parametrized by a reconnection-transfer efficiency factor (which is assumed to vary between 0.1 and 1). Our aim is to solve the balance equation and derive values for the decay parameter compatible with the observed Dst peak values. To facilitate the analytical integration we assume a constant value for through the main phase of the storm. The model is tested for two isolated and well-monitored intense storms. For these storms the analytical results are compared to those obtained by the numerical integration of the balance equation, based on the interplanetary data collected by the ISEE-3 satellite, with the values parametrized close to those obtained by the analytical study. From the best fit between this numerical integration and the observed Dst the most appropriate values of are then determined. Although we specifically focus on the main phase of the storms, this numerical integration has been also extended to the recovery phase by an independent adjust. The results of the best fit for the recovery phase show that the values of may differ drastically from those corresponding to the main phase. The values of the decay parameter for the main phase of each event, _m, are found to be very sensitive to the adopted efficiency factor, , decreasing as this factor increases. For the recovery phase, which is characterized by very low values of the power input, the response function becomes almost independent of the value of and the resulting values for the decay time parameter, _r, do not vary greatly as varies. As a consequence, the relative values of between the main and the recovery phase, _m/_r, can be greater or smaller than one as varies from 0.1 to 1.     

Mid-latitude summer response of the middle atmosphere to short-term solar UV changes

Temperature and wind data obtained with Rayleigh lidar since 1979 and Russian rockets since 1964 are analyzed to deduce the summer response of the middle atmosphere to short-term solar UV changes. The equivalent width of the 1083 nm He I line is used as a proxy to monitor the short-term UV flux changes. Spectral analyses are performed on 108-day windows to extract the 27-day component from temperature, wind and solar data sets. Linear regressions between these spectral harmonics show some significant correlations around 45 km at mid-latitudes. For large 27-day solar cycles, amplitudes of 2 K and 6 m s⁻¹ are calculated for temperature data series over the south of France (44°N), and on wind data series over Volgograd (49°N), respectively. Cross-spectrum analyses have indicated correlations between these atmospheric parameters and the solar proxy with a phase lag of less than 2 days. These statistically correlative results, which provide good qualitative agreement with numerical simulations, are both obtained at mid-latitude. However, the observed amplitudes are larger than expected, with numerical models suggesting that dynamical processes such as equatorial or gravity waves may be responsible.     

On conversion between potential and kinetic energy in the atmosphere

Summary The basic concept of synoptic statistical methods for construction of prognostic charts was outlined by the author in a previous paper. As a result of these investigations it was found that a high correlation exists between time and space means of contourheights of an isobaric surface (850 mb surface). As it has been shown later byPichler this result may be interpreted by assuming that the geopotential fields obeys a numerical solution of the second order homogenous differential equation for wave propagation (hyperbolic equation) provided the phase velocity is given by . SinceReuter has used for s=666 km and for t=24 hours the conclusion may be drawn that the phase velocity of the wave propagation has an order of magnitude of 5 m/sec. Actually for long waves in the westerlies such a value can be found on an average. The same method can be used for extended forecast procedures if the wave equation is set down for 5 days mean values. Theoretical considerations lead then to a prognostic formula for a 5 days mean chart (8a). This formula can be applied for a sufficient number of grid points in order to construct prognostic charts. The underlying assumption, namely that the mean geopotential field satisfies also a solution of the wave equation turns out to be quite accurate even if only average values of the phase velocity were used for the computation. The usefullness of the method is illustrated for two cases.

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Vortrag gehalten am 7. April 1961 auf der 9. Allgemeinversammlung der «Società Italiana di Geofisica e Meteorologia» (Genova, 6.8. April 1961).     

Regions of the maximal cosmic ray energy release in the atmosphere

The cosmic ray flux through the atmosphere at different levels of solar activity is simulated. The Geant program package has been used to determine the atmospheric zones where the maximal contrast of the released ray energy originates between the periods of solar minimum and maximum. The geographic coordinates and altitudes of these zones have been calculated. The results can be used to search for statistical correlations between the solar activity variations and dynamics of atmospheric transparency.