Monitoring of the refraction coefficient in the lower atmosphere using a controlled setup of simultaneous reciprocal vertical angle measurements

Abstract

[1] A great deal of empirical studies have investigated the characteristics of terrestrial refraction. However, only few of these are concerned with short-term fluctuations of refraction influences. The aim of the present work is to analyze the short-term characteristics (amplitudes and variations at scales of minutes to hours) of terrestrial refraction in the lower atmosphere around 1.8 m above the grass surface. We apply the known method of simultaneous reciprocal vertical angle measurements to derive time series of the refraction coefficient k as a measure for refraction. Our study uses a new setup of two pairs of total stations for parallel observations of the refraction coefficient along adjacent lines of sight. Such a controlled experiment not only allows us to determine refraction coefficients independently but also to assess measurement errors from the residuals between refraction coefficient pairs. Over five observation days in the summer of 2008, a total of 33 h of parallel observation data of the refraction coefficient were collected at sampling frequencies of 1 min. On one observation day, unique parallel observations of the refraction coefficient along three lines of sight with a total of six total stations were possible. For mostly sunny days, we found wave-like and sawtooth-like fluctuations of the refraction coefficient with amplitudes of 1-1.5 at time scales of 10-30 min. On cloudy days, the amplitudes of fluctuations were on the order of 0.5. Our refraction experiments show a variation range of k between −4 and +16 near the ground on sunny summer days. This equates to vertical temperature gradients between −0.5 and −0.1 K/m during the day and 1-2 K/m shortly after sunset. Cloud cover reduces the variability of k to a range of −2 to +5. Our results show that the frequently used Gaussian refraction coefficient of +0.13 is not suited for describing refraction effects in the lower atmosphere. As a conclusion, our results may be helpful to better assess the role of refraction in near-ground precision surveys, such as geometric levelling or trigonometric heighting.Citation: Hirt, C., S. Guillaume, A. Wisbar, B. Bürki, and H. Sternberg (2010), Monitoring of the refraction coefficient in the lower atmosphere using a controlled setup of simultaneous reciprocal vertical angle measurements,

Satellite-mediated quantum atmospheric links

“…This allows us to neglect the ray curvature effects in the following. This is of course an idealization and for specific daytime and meteorological conditions the accounting for ray curvature effects turns out to be important [56]. Figure 3 shows the path elongation factor due to atmospheric refraction,…”

Elementary Error Model Applied to Terrestrial Laser Scanning Measurements: Study Case Arch Dam Kops

“…By higher atmosphere, the layers from 100 m and above the ground surface are addressed. The VTG in this part of the troposphere has values around −0.006 K/m and is fairly independent of the Earth's surface temperature [54]. The next layer, the intermediate atmosphere between 20-30 m and 100 m is weakly influenced by the ground temperature and has an average value for the VTG of −0.01 K/m.…”

“…This is defined in meteorology or climate research under the name of micro-and local climate [53]. Hirt et al [54] use the terms higher, intermediate and lower atmosphere to define the variation of the vertical temperature gradient (VTG) within a given range. By higher atmosphere, the layers from 100 m and above the ground surface are addressed.…”

“…Going a level lower, the first layer, considered the lower atmosphere is where ground temperature reaches its maximum influence on the VTG. Several studies, summarized in [54], showed variations of the refraction coefficient between −3.5 and 3.5. Noteworthy are the empirical findings of Hennes [55] in which the local refraction coefficient reaches values of −2.9 (from a VTG of −0.5 K/m) leading to a concave curvature of the light path, contrasting the common belief about the chord being convex in almost all cases.…”

“…In addition to this, it was shown (cf. [48,54]) that even within a short time span, these may present strong variations and there is no straightforward method of correcting the measurement values dependent on these temporal variations. For this reason, modeling the impacts on the observations needs to be done stochastically.…”