Light refraction by mean temperature gradients in the near-earth atmosphere

Visible light ray paths in the atmospheric surface layer are numerically computed by division of 500- to 5000-m ranges into small intervals so that the ray path height and thus refractive index gradient is nearly constant for each step. Meteorological conditions are varied by using different combinations of sensible heat fluxes, surface stresses, and surface roughnesses. Although the effect of water vapor gradients can be substantial, their effect is not included here. The results are confined to heights of less than 5 m because of the restrictive values chosen for the ratio of the eddy diffusivity of heat to that of momentum. Mirages hide lower portions of images and the minimum height seen varies approximately inversely proportionally to the observer height. Image distortion and laser beam displacement or angle of arrival can be used to determine the mean refractive index gradient, which determines the temperature gradient in the absence of large moisture gradients along the propagation path. A simple, non-iterative formula relating laser beam displacement or angle of arrival to the average temperature gradient can be used only if the beam height varies less than 10% throughout the path.     

Determining surface roughness and displacement height

Vertical flux densities of momentum and sensible heat, obtained from simultaneous wind speed and air temperature profiles in the surface layer, depend on the displacement height of the profile system and the surface roughness. A criterion for selecting the displacement height and the surface roughness is introduced, which requires a minimum value for the error squares between the observed and a calculated wind speed profile as determined by diabatic surface layer theory. Values of displacement height and surface roughness, which provide a minimum error squares fit within a desired tolerance, are selected by the rule of false position. The method is programmed for digital computer solution and applied to a total number of 628 profiles obtained during a 7-day period at a micrometeorological test site near Davis, California, using five measurement levels to 160 cm height.     

The effect of time-variable fluxes on mean wind and temperature profile structure

Synthetic wind speed and air temperature profiles based on the sensible heat flux density and stress at the surface are averaged for the four possible ways in which the suface stress and heat flux density can vary maintaining the same average values. The analysis of the averaged wind and temperature profiles shows that, when the surface stress and/or heat flux density are time-variable, and wind speed and air temperature are averaged linearly, an erroneous estimate of surface roughness, surface stress, heat flux density and profile structure parameters will result.     

Conversion of profile difference quotients to true gradients at the geometric mean height in the surface layer

Theoretical profiles of wind speed and air temperature can provide synthetic measurements at discrete levels which may be compared with actual field measurements. In addition to wind and temperature gradients at any height, profile theory permits us to determine the difference quotients from measurements at discrete levels. It is shown that corrections are required to obtain the gradients at the geometric mean height of the two discrete levels of measurement. The correction factor depends on the measurement height and spacing, profile structure, surface roughness and the measured Richardson number. The correction can be reduced by close spacing of the measurement levels.     

Estimates of the position of sea level between 140,000 and 75,000 years ago

The absolute elevations of sea level 103,000 and 82,000 years ago have been estimated as ?15 and ?13 m, respectively, from the present elevations of emergent reefs on Barbados (Broecker et al., 1968; Matthews, 1973; Bloom et al., 1974). The “Barbados model” requires two assumptions: (1) that sea level was +6 m 124,000 years ago, and (2) that rates of uplift on short individual traverses have been uniform during the last 125,000 years.A test of the derived values on Barbados itself does not yield uniform rates of uplift between 124,000 and 82,000 years ago. Less reliably dated strand line features on less uplifted coasts suggest that sea level 124,000 years ago differed from sea levels 103,000 and 82,000 years ago by smaller amounts than those suggested by the “Barbados model.” Such smaller differences yield more uniform rates of uplift between 124,000 and 82,000 years ago, on New Guinea as well as on Barbados, than do the larger. The “Barbados model” is not sufficiently precise to yield close estimates of past elevations of sea level. Better values will eventually be derived from low uplift coasts, when stratigraphic and radiometric data from them have achieved the credibility of data from moderate to high uplift coasts.