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

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 analyse 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 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 set-up 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 the determination of refraction coefficients independently, but also to assess measurement errors from the residuals between refraction coefficient pairs. Over five observation days in summer 2008, a total of 33 hours 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 saw-tooth-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 K/m 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.