Virtual temperature

Abstract: An eddy-correlation system is presented that was designed with special focus on long-term measurements of turbulent fluxes in the atmospheric boundary layer. It consists of a SOLENT sonic anemometer, a fast temperature sensor, and a LI-COR LI 6262 closed-path infrared gas analyser. The use of a fast temperature sensor turned out to be necessary because of errors in the sound virtual temperature measured by the sonic anemometer at high wind speeds. The components are combined with special attention paid to protection against lightning and other environmental stresses. The data acquisition program SOLCOM runs on standalone systems or in a network environment and performs ‘quasi on-line’ data processing, on-line graphical display of single data and fluxes, and on-line correction of the raw data. Raw data can be stored continuously on DAT tapes. All data handling can be done by remote access, thus only a minimum amount of m situ maintenance is required. Power spectra of vertical and longitudinal wind speed, air temperature, air humidity and carbon dioxide concentration showed to follow the -2/3 law quite well. There was some noise in the high frequency range of the carbon dioxide spectrum. However, the corresponding cross spectra with the vertical wind component showed less deviation from a straight line in the high frequency range. The sum of convective heat fluxes and soil heat flux showed good agreement with the measured net radiation for several months and it was concluded that the system described here constitute a good platform for long-term flux measurements over forest.

Abstract: In a paper with the above title Professor G. I. Taylor offers some criticisms of a paper of mine on the winds produced in the atmosphere by differences of temperature and humidity. As they seem to depend in part on a misunderstanding, and as other meteorologists have expressed analogous difficulties to me in conversation, I think some further explanation is desirable. My problem was to find the periodic winds associated with a given periodic variation of temperature or of virtual temperature, the latter being a modification of the actual temperature to allow for the effect of humidity on the density. In these conditions we have as unknowns the three components of velocity and the density; given the density and the virtual temperature, the pressure is known. Thus we have four un­knowns, which satisfy the three equations of motion and the equation of continuity, and the problem is therefore determinate. It is necessary to notice that the virtual temperature is taken as known from observation as a function of position and time.

Abstract: The potential vorticity principle for a nonhydrostatic, moist, precipitating atmosphere is derived. An appropriate generalization of the well-known (dry) Ertel potential vorticity is found to be P 5 r21(2 V1 = 3 u )· =ur, where r is the total density, consisting of the sum of the densities of dry air, airborne moisture (vapor and cloud condensate), and precipitation; u is the velocity of the dry air and airborne moisture; and ur 5 Tr is the virtual potential R /c aP a (p /p) 0 temperature, with Tr 5 p/(rRa) the virtual temperature, p the total pressure (the sum of the partial pressures of dry air and water vapor), p0 the constant reference pressure, Ra the gas constant for dry air, and cPa the specific heat at constant pressure for dry air. Since ur is a function of total density and total pressure only, its use as the thermodynamic variable in P leads to the annihilation of the solenoidal term, that is, =ur ·( =r 3 =p) 5 0. In the special case of an absolutely dry atmosphere, P reduces to the usual (dry) Ertel potential vorticity. For balanced flows, there exists an invertibility principle that determines the balanced mass and wind fields from the spatial distribution of P. It is the existence of this invertibility principle that makes P such a fundamentally important dynamical variable. In other words, P (in conjunction with the boundary conditions associated with the invertibility principle) carries all the essential dynamical information about the slowly evolving balanced part of the flow.

Abstract: The temperature attained in the reversible and pseudo-adiabatic expansion of air saturated with respect to liquid water is taken as a reference; the temperatures attained in the following expansions from the same initial state are then compared with it: (a) the ice-saturation pseudo-adiabatic process (b) the water-saturation adiabatic process (c) the ice-saturation adiabatic process. The results of these comparisons are summarized in Figs. 1 to 5 of this paper. Similarly, the cloud virtual temperature, the virtual temperature adjusted for the weight of suspended particles, attained in water-saturation adiabatic expansion, is compared with that attained in water-saturation pseudo-adiabatic expansion; Fig. 6. The implications of these calculations for the properties and behaviour of cumulus are commented upon.