Hydrostatic Mapping Function Research Articles

Reducing ZHD–ZWD mutual absorption errors for blind ZTD model users

In precise point positioning (PPP), the zenith hydrostatic delay (ZHD) is traditionally treated as a priori value from the ZHD model but the zenith wet delay (ZWD) is treated as an unknown parameter to estimated. For some near real-time PPP tasks, priori ZHD from the blind ZHD models are often used because external meteorological measurement or information about atmospheric pressure or ZHD can not be obtained in such conditions. On the other hand, a priori ZHD errors can project into GNSS height estimates errors in the PPP analysis, because unmodeled part of the ZHD is usually absorbed into the estimated ZWD while there is the difference between the hydrostatic mapping function and the wet mapping function. In this study, we found the errors of the ZHD seasonal models are not always less than those of the ZWD seasonal models, which implies that the traditional strategy for treating ZTD (priori ZHD and estimated ZWD) is not always the best choice when using the blind zenith tropospheric delay (ZTD) models. A decision model for the ZTD blind model (DMZBM), which is a new strategy of dealing with ZTD in PPP when using blind ZTD models, was proposed. For most cases, the traditional strategy works while for some exception cases, it is recommended that priori ZWD from the blind ZWD model was set but ZHD is treated as an unknown parameter to estimated. The DMZBM can directly reduce ZHD–ZWD mutual absorption errors which potentially reduce GNSS height estimates errors due to the difference between the hydrostatic mapping function and the wet mapping function. The results show that there are significant reductions of ZHD–ZWD mutual absorption errors in polar regions when using the new ZTD-treating strategy.

Improvement on Atmospheric Hydrostatic Delay Correction at Low Elevation Angles

Observation made at low evelation angles is the trend of development of GPS (Global Positioning System) meteorology, wherein the development of highly accurate atmospheric hydrostatic delay corrections at low elevating angles is the main key technique. The comparison among three methods for calculating the atmospheric hydrostatic delay correction of the radio waves from space to the ground-based receiver is made: (1) the atmospheric hydrostatic delay obtained from the path integration of the sounding balloon data under the assumption of atmospheric spherical symmetry, (2) the atmospheric hydrostatic delay acquired from the reanalyzed data of the NCEP (National Centers for Environmental Prediction) under the assumption of atmospheric spherical symmetry and (3) the atmospheric hydrostatic delay got from Niell's atmospheric hydrostatic mapping function. The results of the comparison of them with the atmospheric hydrostatic mapping function obtained from the calculation carried out by taking advantage of the data acquired at 89 sounding balloon stations in China in 2001 show that the accuracy of the method of the path integration of the reanalyzed data of NCEP at low elevating angles (bellow 5°) is about 5 times better than that of the Niell mapping function model.

A new hydrostatic mapping function for tropospheric delay estimation

A new hydrostatic mapping function is proposed by modifying the analytical solution of the Chapman grazing incident (Chi) function. Applicability of this mapping function is evaluated over the Indian region by comparing it with the true value of mapping function estimated through ray-tracing the refractivity profile of neutral atmosphere as well as by comparing it with the Niell and Global Mapping Functions. This comparison shows that the new mapping function, agrees very well with the ray-traces values and it is in par with if not better than the other global mapping functions for very high zenith angles up to ∼88°.

Influence of mapping function parameters on global GPS network analyses: Comparisons between NMF and IMF

One major part in the error budget of GPS measurements is the imperfect modeling of the tropospheric delay. By processing a global network of 195 stations we have compared two different mapping techniques: (1) the commonly used Niell hydrostatic mapping function (NMF) and (2) the isobaric hydrostatic mapping function (IMF) based on numerical weather fields. The two solutions reveal significant differences in the derived zenith total delay (ZTD) parameters and site positions. The largest differences occur in Antarctica, where the annual mean heights differ by up to 15 mm. We infer that the significant differences are related to model deficiencies in NMF since a) IMF improves the repeatability in station heights in high southern latitudes significantly, and b) using IMF reduces the dependence of the solution on the elevation cut‐off angle by about 20%. In conclusion, the use of mapping function (MF) parameters based on meteorological data is strongly recommended for global GPS analyses.

The influence on GPS estimates of NWP-derived mapping functions

When estimating zenith total delays (ZTD) from global positioning system (GPS) signals it is assumed that the atmosphere is symmetric in the horizontal plane and that delays in the signal from one of the GPS satellites to a receiver can be mapped onto the zenith direction through a known mapping function. The generally used mapping function has only a dependence on the day of the year and the latitude of the receiver. The fact that these mapping functions do not depend on the actual weather may introduce errors in estimates of the location parameters and the estimate of the ZTD. In this paper mapping functions from numerical weather prediction (NWP) models are derived and the influence on the accuracy of location parameters and ZTD estimates is investigated during a cold front passage in the Netherlands on the 30th of October 2000. The hydrostatic mapping function computed from NWP was smaller than the Niell mapping function (0.02 at 5° elevation). The differences for the wet mapping function were much larger, and of opposite sign. However, since the hydrostatic delay is larger than the wet delay, we found that the geodetic parameters are mainly influenced by errors in the hydrostatic mapping function. Using an elevation cut-off error of 10°, we observed systematic errors in the estimated ZTD of −2.1 to −3.1 mm, in the clock error of 6.5–9.2 mm and in the height of 4.8–6.5 mm.

A simple “geometric” mapping function for the hydrostatic delay at radio frequencies and assessment of its performance

The hydrostatic mapping function, m(ε), describes the dependence of the hydrostatic path delay on the elevation angle ε. We have developed a simple mapping function, where the only free parameter is an “effective height” of the atmosphere, Hatm, corresponding to about the first two scale heights above the surface. The value of m(ε) is given by the ratio of the straight‐line ray path length within height Hatm to height Hatm itself. We used simulated delays at GPS (Global Positioning System) frequencies derived from high resolution ECMWF (European Centre for Medium‐Range Weather Forecasts) atmospheric analysis fields to assess the performance of the “geometric” mapping function relative to well established ones (the Davis, Niell, and Herring mapping functions, respectively). At elevations >6° the new mapping function generally exhibits, based on a single parameter, a performance comparable to or better than the other mapping functions.

A new “geometric” mapping function for the hydrostatic delay at GPS frequencies

The hydrostatic mapping function, m(ε), is a dimensionless factor which describes the elevation angle dependence of the hydrostatic path delay and relates the line of sight delay to the zenith delay. We have developed a simple “geometric” mapping function where the only free parameter (besides the elevation angle, ε) is the climatological pressure scale height. The value of m(ε) is given by the ratio of the straight-line ray path length within the first two scale heights above the surface and the “effective height” defined by these first two scale heights. We used simulated neutral delays at GPS frequencies derived from high resolution ECMWF (European Centre for Medium-Range Weather Forecasts) atmospheric analysis fields (T213L50, T213L60) at different latitudes to compare the new mapping function with others currently in use (we compare with the Niell and the Davis mapping function, respectively, most frequently encountered in literature).At elevations > 6° the geometric mapping function displays, without involving any meteorological data, comparable or better accuracy and precision than the other mapping functions.

Improved atmospheric mapping functions for VLBI and GPS

New mapping functions based on in situ meteorological parameters have been developed for calculating the radio path length through the atmosphere at elevations down to 3°. The hydrostatic component of the mapping function is related to the geopotential height of the 200 mb isobaric pressure level above the site and provides a factor of two improvement in accuracy and precision over previous hydrostatic mapping functions at mid-latitudes. The wet component of the mapping function is calculated from the vertical profile of wet refractivity at the site but will provide an improvement of only about twenty-five percent. However, since the effect of known errors in the hydrostatic mapping function dominates that from the wet component, except near the equator, implementation of these mapping functions should reduce the contribution of the atmosphere to errors in estimates by VLBI and GPS of both the vertical component of site position and the radio propagation delay due to water vapor in the atmosphere.

Using meteorological data assimilation models in computing tropospheric delays at micrwave frequencies

Despite improvement of space geodetic techniques, the troposphere continues to be a source of random and systematic error. We have investigated the possibility of correcting tropospheric delay models in space geodetic analysis with data from a meteorological data assimilation model. Four radiosonde sites in different climatic regions were selected for study. The precision and accuracy at a 5° elevation angle of commonly used tropospheric mapping functions and of data assimilation model delays were evaluated by comparisons with raytracings of radiosonde profiles. We determined the model delays by raytracing site profiles calculated by interpolation of the gridded (2°×2.5°) model profiles. Monthly variations in the atmospheric profile at a typical continental site result in hydrostatic mapping function delay variations at a 5° observation elevation of 50–100 mm, which results in about 12–25 mm of variation in the estimated site vertical coordinate. Rms differences between radiosonde delays and the common mapping functions delays are 9–35 mm. Rms differences between radiosonde delays and data assimilation model delays are 5–6 mm. Along with mapping function errors, unmodeled atmospheric delay gradients produce errors in geodetic analysis. The gradient delay at an elevation of 5° has an rms variation of about 45 mm over a year. For the 1990–1993 VLBI sessions using the antenna at Westford, Massachusetts, we found that the gradient vector computed from the data assimilation model is correlated with corresponding VLBI gradient vector estimates with correlation coefficients of 0.60 and 0.49 for the north and east components respectively. When the model gradient includes only the hydrostatic part of the refractivity, this correlation is reduced to 0.53 and 0.48.

Global mapping functions for the atmosphere delay at radio wavelengths

I have developed expressions for calculating the ratios (mapping functions) of the “line of sight” hydrostatic and wet atmospheric path delays to their corresponding zenith delays at radio wavelengths for elevation angles down to 3°. The coefficients of the continued fraction representation of the hydrostatic mapping function depend on the latitude and height above sea level of the observing site and on the day of the year; the dependence of the wet mapping function is only on the site latitude. By comparing with mapping functions calculated from radiosonde profiles for sites at latitudes between 43°S and 75°N, the hydrostatic mapping function is seen to be more accurate than, and of comparable precision to, mapping functions currently in use, which are parameterized in terms of local surface meteorology. When the new mapping functions are used in the analysis of geodetic very long baseline interferometry (VLBI) data, the estimated lengths of baselines up to 10,400 km long change by less than 5 mm as the minimum elevation of included data is reduced from 12° to 3°. The independence of the new mapping functions from surface meteorology, while having comparable accuracy and precision to those that require such input, makes them particularly valuable for those situations where surface meteorology data are not available.