Atmospheric pressure loading in GPS height estimates

Available Pergamon www.elsevier.com/locate/asr online at www.sciencedirect.com SCll?NCE DIRECT. doi: lO.l016/SO273-1177(03)00157-l ATMOSPHERIC PRESSURE LOADING IN GPS HEIGHT ESTIMATES M. Brondeel’ and T. Willems’ ‘Ghent University, Department of Geography, Krijgslaan 281 - S8, B-9000 Ghent, Belgium 2Ghent University, Department of Applied Mathematics and Computer Science, Krijgslaan 281B-9000 Ghent, Belgium S9, ABSTRACT Atmospheric pressure loading is known to generate noise in GPS vertical time series. Even weekly solutions of GPS determined vertical coordinates are correlated with atmospheric loading in more than 70% of the stations investigated. When correcting the GPS coordinates resulting from the different GPS processing centres for atmospheric loading, different variance reductions or augmentations for the same station are found. However, stations in Central and Southern Asia show high variance reductions, whereas nearly all coastal stations and island stations sometimes show a small augmentation in the variance, possibly due to the small variances of the loading signal itself. 0 2003 COSPAR. Published by Elsevier Science Ltd. All rights reserved. INTRODUCTION Global Positioning System (GPS) receiver hardware and data analysis software and techniques allow for the determination of weekly averaged vertical crustal motions with a precision of a few millimeters at the best determined sites (Grenerczy et al., 2000). This level of measurement precision allows us to measure long wavelength (global and continental scale) crustal motions on the order of a few millimeters per year as is required for investigating earth processes associated with postglacial rebound, the mass changes of the ice sheets, geocenter motions, crustal stability at tide gauges, etc. Whatever the proposed application, interpretations of GPS measured changes in station positions need to assessthe role of position changes due to loading phenomena. This is particularly important when the geodetic signal of interest is of the same order of magnitude as the amplitude of the loading signal itself. In this case, erroneous conclusions may be drawn with regard to the causes of station height variations. In addition, the precision of vertical positioning is such that interpretations of this parameter become sensitive to different realisations of the reference frame. This is less the case for the horizontal positioning as the reference frames are much better determined in these directions. Atmospheric pressure loading can be described as the vertical displacement of the earth’s crust due to changing atmospheric pressure. In this paper, we consider the effects of atmospheric pressure loading on precise GPS measurements. We compare estimates of atmospheric pressure loading with GPS geodetic station positions determined by four different analyses: global weekly solutions from the Center for Orbit Determination in Europe (CODE), from Jet Propulsion Laboratory (JPL) and from the Scripps Institute of Oceanography (SIG) and the freenetwork global weekly solutions calculated by IGS. The length of the time series compared depends on the length of the time series of GPS data and is in average 110 weeks. Data for more than 80 stations are considered (see Figure 1). Adv. Space Res. Vol. 31, No. 8, pp. 1959-1964.2003 0 2003 COSPAR. Published by Elsevier Science Ltd. All rights Printed in Great Britain 0273-l 177/03 $30.00 + 0.00 reserved 1960 M. Brondeel Fig. 1. Stations ATMOSPHERIC LOADING and T. Willems used in the analysis. EFFECTS Calculation Method The effects of atmospheric pressure loading are computed by convolving Farrell’s elastic Green’s functions (Farrell, 1972) with 6-hourly global surface pressure values (1” x 1” grid) provided by the European Centre for Medium Range Weather Forecasts (ECMWF) operational analyses. These data are downloaded daily from ECMWF. The ECMWF pressure fields are derived from a Global Objective Analysis (GANL) using global satellite data, global free-atmosphere data, oceanic data and land data as input. Since we are using surface pressure values, variations in pressure due to the effects of surface topography are already taken care of. The details of the technique used to model the pressure loading effects by convolving the atmosphere data with the Green’s functions, are described in van Dam and Wahr (1987), van Dam and Herring (1994a) and van Dam and Wahr (1998). Only slight differences between these analyses and the one used in this paper due to different atmospheric data can be noticed. Order of Magnitude Figure 2 shows the standard deviation in a grid of 2.5” x 2.5” of the vertical displacement due to atmospheric pressure, calculated using the CONV-IBO method. This method convolves the ground pressure data with Farrell’s Green’s functions (Farrell, 19972) and models the ocean’s response as an inverted barometer. Although for island and coastal stations the RMS of GPS heights can be very large, these large values are probably not due to atmospheric pressure loading. Due to the used ocean model, the atmospheric loading effects for island or coastal stations are small. Incorrect modeling of the oceans in the calculation of the theoretical atmospheric pressure loading can still be a problem. 6 3 -6 Fig. 2. Distribution observation (1999). -I&O-Ii0 -60 -do of the standard deviation -do 6 3'0 [m] of the atmospheric $0 Ii0 pressure 160 loading 0.006 0.0055 0.005 0.0045 0.004 0.0035 0.003 0.0025 0.002 0.0015 0.001 0.0005 0 E:ffects over 1 year of Atmospheric Pressure Loading 1961 and GPS In global, the variance of the atmospheric loading for stations at more or less the same latitude increases with increasing distance to the sea because atmospheric pressure highs and lows over the oceans are not accounted for in the Inverted Barometer Ocean (IBO) modeling for coastal stations. On the other hand, pressure variations are biggest at mid-latitude, which makes the atmospheric loading variance of mid-latitude continental stations the largest. CORRELATION HEIGHTS BETWEEN ATMOSPHERIC PRESSURE LOADING AND GPS DETERMINED Figure 3 and Figure 4 represent the time series for the vertical component of the atmospheric pressure loading effect on one hand and the GPS determined coordinates for different stations on the other hand. The GPS results derive from the IGS weekly processing strategy. Juxtaposing the two time series reveals the degree to which the GPS residuals track temporal variations in atmospheric pressure loading. For some stations, the two time series are highly correlated (e.g. the station KOSG (Kootwijk) in the Netherlands with a correlation coefficient of 0.49). Other stations, island or coastal equatorial stations like FORT (Fortalesa) in Brazil or ASCl (Ascension Island) show very small variances in the atmospheric loading (variance of 3.13* 10m9mZ compared to a variance of 6.07*10”m2 for KOSG) due to very small atmospheric ground pressure variances (see Figure 4). However, for these stations the ocean tide loading effects are generally large, so that the remaining variance of the GPS height signal after correcting for atmospheric loading is most likely due to remaining ocean tide loading effects. -0.015 i- ~ -y-G50400 50500 50600 50700 50800 50900 51000 50400 50500 50600 MJD /-GPS -atm 50700 50800 50900 51000 MJD loading 1 Fig. 3. Time series of the vertical displacement of the atmospheric loading together with the vertical coordinate determined by GPS for the station KOSG (Kootwijk); MJD= Modified Julian Date. --c GPS --+- atm loading Fig. 4. Time series of the vertical displacement of the atmospheric loading together with the vertical coordinate determined by GPS for the station ASCI (Ascension Island); MJD = Modified Julian Date. For the processing centres CODW, JPLW and SIOW, more than 70% of the stations investigated show a positive correlation between both time series. In the weekly processing of IGS, even 80% of the stations have positive correlations. For this processing, for 18% of the stations investigated, the correlation coefficient is larger than 0.4. Keeping in mind all possible errors of the GPS measurements, correlations are high. Except for the weekly processing of CODE, more or less 45% of the stations investigated are statistically correlated (with a confidence interval of 95%). For the processing CODW, this percentage mounts up to 60%. When investigating the spatial distribution of the correlation coefficient, most continental stations in Central and East Europe, Northern America and Asia show high positive correlations. All island and most coastal stations have small negative correlations. The stations investigated in South America do not show coherent distributions in the different processing methods. Most of these stations in South America are coastal stations where a negative correlation can be expected. There are not enough stations in Africa to draw coherent conclusions. 1962 CORRECTING M. BrondeelandT. Willems FOR ATMOSPHERIC PRESSURE LOADING IN GPS TIME SERIES Examining the Variance Reduction after Correction for the Atmospheric Loading There are a number of different ways to correct GPS height residuals for atmospheric loading and to test their effectiveness. In this article we have chosen to investigate the variance reduction of the GPS heights after correcting the GPS time series with the calculated values of the vertical displacement due to atmospheric,loading. Because correction of the atmospheric loading effect was done only after the GPS processing, estimation of existing errors in the processing of GPS data (like the estimation of tropospheric delay) might possibly be influenced by atmospheric pressure effects. In future the atmospheric loading corrections will be implemented in the GPS processing. To examine the variance reductions, the statistical analysis developed by van Dam et al. (1994b) is used. Variance calculations provide only estimates of the standard deviation of the observed quantities and are, as any other quantities, affected by noise. Van Dam and Herring (1994a) assume that the pressure loading corrections consist of a true loading signal and a noise component. When examining the variance after correcting the GPS heights with the atmospheric pressure loading, per processing centre approximately 55% of the stations show a variance reduction (see Table 1). Keeping in mind the central limit theorem of statistics, a variance reduction is quite rare to observe when subtracting two independent signals. Obtaining variance reductions for more than 50% of the stations investigated is an indication of the two signals not being independent, which shows that applying atmospheric loading corrections isjustified. When investigating Table 1, giving the variance reduction for several processing centres, discrepancies between the different processing centres can be detected. Although all processing centres are examined for the same stations, IGS and SIO weekly processing show less stations with variance reduction (ca. 50%) than the weekly processing of CODE or JPL (ca. 59%). The explanation of these phenomena surely lies in the different processing methods and software but is hard to point out exactly. Because IGS weekly processing is an assembly of different information gathered from different processing centres, it is quite possible that the global processing of IGS might be affected by not including effects like ocean loading in the calculation of some processing centres. Table 1. Order of magnitude of the variance reduction of GPS heights after correcting for atmospheric loading; comparison between different processing centres Var reduction >20 mm’ 10mm2<x<20mmz 5mm*<x< 10mm2 Ommz<x<5mm2 -5mm*<x<Omm* -10mm2<x<-5mm* -20mm2<x<-lOmm* < -20 mm2 Regional Distribution CODW 8% 12 % 9% 30% 23 % 6% 4% 8% JPLW 6% 8% 8% 37 % 25 % 8% 0% 8% SIOW 5% 5% 8% 32 % 25 % 11% 6% 8% IGSW 4% 11% 3% 34 % 28 % 8% 9% 3% of the Variance Reduction Per processing centre the spatial distribution of the variance reduction has been investigated. Figure 5 and 6 map the variance reduction for the stations investigated for the weekly processing of CODE and IGS. Open symbols indicate a variance reduction, whereas filled symbols are the indication of variance augmentations. The same figures were made for the processing centres JPL and SCRIPPS, but the results for these processing centres are comparable to those of IGS. Nearly all the coastal and island sites show a small increase in variance. For these stations the standard deviation of the loading signal itself is small (see Figure 2) and the GPS position variances are more affected by ocean loading signals. The discrepancy between the results for different ocean models is not big enough to explain the lack of variance reduction for these stations. In addition, most processing software (e.g. Bernese) did not include ocean tide loading corrections. As these effects are biggest for island and coastal sites and can easily amount more than a few centimeters, it is possible that the atmosphere weakens the ocean effects and thus correcting only for the atmospheric effects can even worsen the GPS results. Atmospheric Pressure Loading 1963 and GPS Different processing centres show different distributions for the variance reduction. In global, one cannot identify a station,or a region where correcting for atmospheric loading will surely lead to a variance reduction in the GPS heights. However, stations in Central and Southern Asia show high variance reductions whereas stations in Northern Europe mostly have to deal with variance augmentations. 0 0 *a I 1 : CODW c20 -20 to -1c -10 to -5 -5 to 0 ” . :,; ““‘ Fig. 5. Distribution of the variance reduction [mm21 for the processing centre CODW. IGSW c20 -20 to -1t -10 to -5 Because the computations were made with the same time span for every processing centre, the reason for the different distributions has to be searched in the different processing techniques of the GPS data (e.g. choice of stations included in the processing, choice of fixed or heavily constrained stations, tropospherical corrections, ocean loading corrections, etc.). Noise in the pressure data or erroneous calculation of the atmospheric loading effects would propagate for different processing centres in the same way. Further investigation in the different processing centres will be imperative. CONCLUSIONS Our analysis shows that GPS height results are affected by atmospheric pressure loading effects. Time series of more than 80 stations and 4 different processing centres were investigated. For coastal or island sites, the variance of the atmospheric loading effect is too small, particularly compared to the variance of the ocean loading effect, to have a significant impact on the time series of the GPS vertical position 1964 M. Brondeel and T. Willems observations. However, for almost 55% of the stations investigated a variance reduction of the GPS heights can be found after correcting the GPS results with the atmospheric loading signal. Different processing centres lead to different distribution patterns of the variance reduction. However, nearly all coastal stations and island stations show an augmentation in the variance, due to the small variances of the loading signal itself. Stations in Central and South Asia mostly show high variance reductions whereas stations in Northern Europe show variance augmentations. The distribution for the stations in America and Central Europe differs in different processing centres. The reason for this is not clear at this time but may be found in the different processing methods. When determining station velocities this effect should be kept in mind. ACKNOWLEDGMENTS The authors would like to thank the processing centres of CODE, JPL and SCRIPPS for providing us with the GPS height time series. We would like to thank the Royal Observatory of Belgium where part of this study has been financed and the ECMWF and the Royal Institute for Meteorology for providing the atmospheric pressure data. REFERENCES Farrell, W. E., Deformation of the earth by surface loads, Rev. Geophys., 10(3), 761-797, 1972. Grenerczy, G., A. Kenyeres, and I. Fejes, Present crustal movement and strain distribution in Central Europe inferred from GPS measurements, 3: Geophys. Res., 105(B9), 2 1835-2 1846,200O. van Dam, T. M., and J. Wahr, Displacements of the earth’s surface due to atmospheric loading: Effects on gravity and baseline measurements, J: Geophys. Rex, 92@2), 128 1- 1286, 1987. van Dam, T. M., and T. A. Herring, Detection of atmospheric pressure loading using very long baseline interferometry measurements, J. Geophys. Res., 99(B3), 4505-45 17, 1994a. van Dam, T. M., G. Blewitt, and M. B. Heflin, Atmospheric pressure loading effects on Global Positioning System coordinate determinations, J. Geophys. Res., 99(B 12), 23939-23950, 1994b. van Dam, T. M., and J. Wahr, Modeling environment loading effects: A review, Phys Chem. Earth, 23(9-IO), 1077-1087, 1998. E-mail address of M. Brondeel Mariike.Brondeel@rurr.ac.be T. Willems Tom. WillemsO.rue.ac.be Manuscript received 19 October 2002; revised 5 March 2003; accepted 14 March 2003