An experiment is described in which microwave Doppler is used to determine very small changes in path length to spacecraft tracked by the Deep Space Tracking Network (DSN). The experiment was carried out to test the detection capabilities of the DSN system to gravitational radiation of very low frequency (10−2–10−4 Hz). In this work spectral analysis of Doppler variations were performed for periods over 4 hours and more.

These results indicated that one of major sources of noise was due to rapid variations in tropospheric refraction. The results obtained a differential path length variation, ΔL/L, of 1 part in 1014 for periods between 100 and 1 000 seconds.

Doppler spectra are shown and a general discussion of the experiment is given.

Pathlength variations due to refraction changes in the troposphere may impose a severe limitation to VLB experiments (like random clock drifts). In connection with a VLB experiment Moran and Penfield (1976) analysed surface values of water vapor density, data of several hundred radiosonde launches and of measurements of sky brightness near the water vapor line at λ = 1.3 cm. They found that the surface values allow to estimate the pathlength to an accuracy of 5 cm in summer and 2 cm in winter. Sky brightness data give a prediction accuracy of 1.5 cm for all weather conditions, but for cloudfree conditions the accuracy was 0.3 cm.

Corrections which are dependent on the atmosphere include the first and second velocity corrections and the curvature correction in EDM, and the refraction correction for trigonometric heighting. Generalised correction formulae have been developed to make use of variable values of the refractivity N and the coefficient of refraction k. There are no universally applicable values of these parameters, so atmospheric models of the temperature gradient and, for microwaves, the humidity gradient, are needed to represent the very significant variations. The models should take into account variations due to meteorological factors, surface conditions and the height above the surface. Many models for the vertical gradients have been produced. That of Brocks (1948) is very important and has been widely used and developed by researchers. More recently Monin and Obukhov, basing their work on the physics of the lower atmosphere and dimensional analysis, have included equations for the vertical gradients in their turbulence theory. The Turbulent Transfer Model, which embodies later results in this theory, is currently being refined and developed for geodetic applications.

The assumption of a generalized model of the composition of random and systematic errors of measurements can constitute a basis for the estimation of the influence of the environment on the results of geodetic observations in the course of their numerical elaboration. The method of the estimation of systematic errors on the basis of the analysis of an empiric distribution of the results of observations has been established on the assumption of such a model, which permits also to estimate systematic errors in the course of the adjustment of observations, these errors being treated as additional unknowns in the system.

The merits of two refraction methods are discussed with the result that the line refraction method is appropriate for elaboration of trigonometric leveling traverses whereas the station refraction method is comparatively more convenient for trigonometric and three-dimensional networks of a larger extent especially those designed in high mountain regions.

When investigating refraction in trigonometrical traverses, additional observations for vertical angles have made it possible to evaluate the coefficient of refraction for each station. The improvement in elevation accuracy was substantial in traverses with longer distances (about 4 km) between stations.

To investigate the accuracy of the determination of terrestrial refraction from reciprocal zenith angles and astronomical latitudes and longitudes at both ends of a line a test net with lines from 4 km to 23 km was observed and three dimensionally adjusted. As the measurements of the zenith angles were repeated every hour 40 times in an average the adjusted values were taken as a substitute for the true values. It is shown, that the mean refraction coefficient k, which is changing from k = 0.10 at day up to k = 0.34 at night, and the corresponding refraction angle can be determined very accurately, if both angles are measured simultaneously. Observations with day light are better than observations in the night. For observations with day light the mean difference between the true refraction angle at the observation station and the mean refraction angle of the observed line was smaller than ± 1″ independent of the length of the line. That means that the mean deviation of the true effective refraction coefficient in the observation station and the mean refraction coefficient of the observed line was inverse proportional to the distance.

The fluctuations of refraction coefficients can be described by a stochastic process: a two-component process. One component of the process is caused by short-periodic (daily) climatic variations. The other component is influenced by long-periodic (yearly) climatic variations. The central moments of these two components are used to estimate the covariance matrix of time series of refraction coefficients. Different functional and stochastic models are tested in connexion with time averaging of refraction coefficients.

A theory is developed for evaluating the vertical refraction angle from the variance of the angle-of-arrival fluctuations, assuming a horizontally homogeneous turbulent atmospheric surface layer. The vertical refraction angle is mainly a function of the vertical temperature gradient, and the variance of the angle-of-arrival is related to the temperature structure parameter CT2. However, surface layer similarity theory states that both the mean vertical temperature gradient and CT2 are functions of the same scaling temperature T* and a thermal stability parameter. This therefore provides an indirect method of determining the vertical refraction angle from a measurement of the variance of the angle-of-arrival and an estimate of the thermal stability parameter. Advantages of this method over other techniques of evaluating vertical refraction are discussed.

The NPL instrument to correct for angular refraction in geodesy measures the small dispersion between images of red (633 nm) and blue (442 nm) laser sources formed by a telescope. It uses a rotating chopper disc in association with an optical compensator plate and a phase null meter. The instrument and some early field tests have been described in detail elsewhere (Williams, D.C., 1978).

Absolute tests of the prototype have recently been made over a 4 km suburban range at an average height of 30 m. The apparent elevation of the red laser was observed with a T3 theodolite and corrected for refraction, the laser and theodolite being referred to local bench marks with a known height difference determined by spirit levelling.

On an occasion in late May 1978, the effects of turbulence were particularly small. The refraction-corrected theodolite readings then agreed with the expected value to within one sexagesimal second. Other results obtained during the preceding two months indicate that increasing turbulence causes the dispersion angle to appear too large, the greatest error observed being about 3 seconds of refraction. It is thought that most of the turbulence was due to effluent from chimneys, and that the apparent error may be due to an instrumental effect which has not yet been identified.

The performance of the instrument has also been evaluated on a 20 km range near Uppsala during the present Symposium, by kind invitation of Prof. E. Tengström. The principal difference from the 4 km range was that the intensity scintillations of the red and blue signals were no longer correlated when the refraction was large. Independent compensation of red and blue signals for this effect should enable good results to be obtained over this distance.

The author wishes to acknowledge the help of S-G. Mårtensson and S. Eklund (University of Uppsala) and A.J. Griffiths (NPL) in performing the tests.

IDM measurements carried out in Uppsala sometimes show violent changes in refraction over short periods of time.

The explanation for these changes might be found if the dynamics of atmospheric turbulence is taken into consideration.

It is too early to make scientific conclusions from the material collected so far, but observations show the way this particular problem can be handled in the future.

The paper presented, reflects some of the turbulence effects achieved by the IDM instrument constructed by prof. E. Tengström.

The main purpose of the IDM research of prof. Tengström was to confirm the possibility of determining instrumentally the refraction angle in the field even over long distances.

An appreciable increase of the accuracy could only be achieved by further improvement of the instrument. Even with the first laboratory model it seems possible to achieve an increase of the accuracy in the final results. This paper discusses the above possibilities and proposes some methods to achieve this improvement in the accuracy.

Terrestrial refraction effect has been of considerable interest to many geodesists for many decades and there is a rich litterature on the subject, of long standing. Due to its local character this problem is still topical. Geodetic determination of how far terrestrial refraction influences geodetic observations is, therefore, very often studied.

The parallactic refraction correction should be applied to the photographic observations of the light signals carried either by artificial satellites or by meteorological balloons. The correction to the right ascension and declination are made with the equations

where ϕ is the latitude of the observation station, z the zenith distance, α the right ascension, δ the declination and h the hour angle of the light signal. Parallactic refraction is denoted by Δζ.

When I had to start the Second Levelling of Finland, 43 years ago, after the first observing summer I made one important and happy finding. The vibration of the image in the levelling instrument made the levelling difficult in middle summer while in spring and autumn this trouble was not so bad. So I proposed that levelling work must be interrupted for the six weeks from the midsummer to the beginning of August and that was accepted. The fact that just these weeks are the best vacation time in Finland made our colleagues in the institute jealous, but it was not our fault, and we were happy.

A method is described for determining one and only one parameter governing the refraction effect of levelling. The central idea is that this parameter is determined not by (temperature) measurements during the observation but by adding one more element in the Least Squares Adjustment of the levelling network.

Furthermore is described an experiment where it was found that this parameter differed significantly from zero and a tentative first value is suggested.

Refraction error is often regarded as the most serious problem with geodetic leveling. Its accumulation depends on the slope of the terrain being leveled, length of sight, and the vertical temperature gradient. Refraction error can be minimized by limiting and balancing sight lengths, and by not reading the portion of the level rod which is within 0.5 meter of the ground where air density changes most rapidly. The remaining refraction error should be removed by application of a correction to leveling data, otherwise heights and crustal motion may be determined so weakly that meaningful conclusions or interpretations cannot be inferred from the data by geophysicists.

A brief description of photogrammetric procedures are made to show how it has been and today is possible to make correction to photogrammetric measurements for the effect of refraction.

Then a review of how refractional effects have been calculated is made.

Finally some suggestions are made of how to meet the demands for improved accuracy in photogrammetric measurements.