Atmospheric Path Delay Correction Based on the Numerical Prediction Data

Kashima Space Research Center
Communications Research Laboratory
893-1 Hirai, Kashima, Ibaraki 314, Japan

1. Introduction

Atmospheric path delay is a serious error source in measurements by very long baseline interferometry (VLBI) both through ray path bending and the modification of the electromagnetic wave velocity. The delay has been separately discussed because of its causes; one is the "wet delay" due to the dipole component of water vapor and the other is the "hydrostatic delay" due to the nondipole components of atmospheric constituents. Geodesists have especially focused their attention on devising techniques for estimating the wet delay because of the significant variability of water vapor. Conventionally, the wet delay for each site has been estimated from a "zenith delay" and a "mapping function", with the latter function describing the elevation angle behavior of the atmospheric path delay (e.g. Chao, 1972; Davis et al., 1985). The zenith wet delay is estimated from (1) a model relating surface meteorological conditions to this delay (e.g. Saastamoinen, 1972), (2) observation by using a ground-based water vapor radiometer (WVR) (e.g. Hogg et al., 1983), and (3) parametric estimation by using a stochastic process such as the Kalman filtering techniques (e.g. Herring et al., 1990; Tralli et al., 1992). The mapping functions are constructed for a spherically symmetric atmosphere. On the contrary, the atmospheric water vapor, temperature, and pressure vary in various temporal scales and spatial dimensions. Consequently, we exactly require an effective method to correct the azimuthal asymmetry of the wet delay to attain sub-millimeter accuracy.

2.Atmospheric Path Delay Estimated by Numerical Prediction Data

Recently, the numerical weather prediction model has been successfully used for the purpose of the operational weather prediction. The three-dimensional grid point data set is produced from the numerical weather prediction model can be applied to estimate the wet delay. Figure 1 shows a schematic figure of the global analysis (GANL) data set by the Japan Meteorological Agency (JMA) (JMA, 1993). The GANL data are given four times a day to a 1.875-degree latitude-longitude grid system with 16 layers (surface and 15 standard pressure levels, i.e., 1000, 850, 700, 500, 400, 300, 250, 200, 150, 100, 70, 50, 30, 20, and 10 hPa). At each grid point meteorological elements, geopotential height, temperature, dewpoint depression, and wind vector are computed from the data obtained by radiosonde, aircraft, maritime and satellite observations, using a multi-variate optimum interpolation method (Lorenc, 1981) together with the forecast values. Figure 2 shows the temporal variations of the zenith wet delay based on the GANL data set and that from radiosonde observation at Tateno near Tsukuba and Hachijojima in the West Pacific during the period from April 1988 to February 1989. At both sites the zenith wet delay computed from radiosonde data varies from 5 to 20 cm in winter (January), and from 20 to 40 cm in summer (July). Moreover, the amplitude of delay variation within the period of several days reaches more than 10 cm during all seasons. The zenith wet delay based on the GANL data set is well consistent with that from radiosonde observations in both amplitude and phase through the period. It is clear that the GANL data set exhibits a good recovery of the observed meteorological conditions. JMA developed finer mesh model, named the 10 km spectral model to forecast mesoscale phenomena accurately as shown in Figure 3. The 10 km data are given on a 97 X 97 latitude-longitude grid system with 10 km intervals (at 60 degrees N) and 12 layers (surface and 11 significant pressure levels, i.e., 1000, 900, 850, 700, 500, 400, 300, 250, 200, 150, and 100 hPa) for the purpose of the numerical prediction of mesoscale phenomena of the order of 20-200 km, such as squall lines, cloud clusters and so on. The outputs from the model can be available to correct the azimuthal asymmetry of the wet delay. Figure 4 shows an example of positioning errors due to the azimuthal asymmetry of the wet delay numerically estimated by 10 km spectral model (Ichikawa et al., 1994). Minimum elevation angle of 15 degrees is assumed. According to the figure, uncertainties of baseline vectors are up to several centimeters in horizontal and more than one centimeter in vertical.

Figure 1. Grid system of the JMA (Japan Meteorological Agency) global analysis data. (after JMA(1995)).

Figure 2. Daily variation of the zenith wet delay based on the global analysis data set (solid line) and that from radiosonde observation (broken line) during the period from April 1988 to February 1989 at Tateno (upper) and Hachijojima (lower).

Figure 3. Forecast area of the JMA 10 km spectral model.

Figure 4. Estimated horizontal vectors and vertical components of the apparent displacement vectors caused by the wet delay error due to the azimuthal asymmetry of atmosphere. These apparent displacement vectors are considered to be the relative positioning errors in measurements by VLBI. Minimum elevation angles of radio sources are assumed to be 5 degrees. Frontal position is obtained from JMA operational surface analysis.

3.Proposal of New Correction Method

The estimations of the wet delay by the numerical prediction data can be easily applied to the correction of VLBI measurements considering the azimuthal asymmetry. In the field of numerical weather prediction, there has been much effort recently in developing more accurate models. These new models are devised to take account of modeling the real atmospheric motion and new meteorological observations such as satellite microwave radiometry. These model data sets always keep the three-dimensional scheme. Therefore, once an estimation system of the wet delay is established, we can easily obtain more accurate estimates of the delay when the numerical prediction model data set is up to date. This new correction method has two advantages. First, the equally-weighted correction to the delay is available wherever the VLBI measurements are conducted. Second, re-examination and re-correction of the delay for the past geodetic observations are always available by using the updated model data in the future. It is expected that this will become a powerful correction method. At present, I plan feasibility studies to evaluate the availability of the numerical prediction data for correcting VLBI measurements.


Updated on November 2, 1995.
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