State-of-the-art physical models for calculating atmospheric pressure loading effects 1 Geodätische Woche 2010 5-7 October, 2010 - Köln, Germany Dudy D.

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State-of-the-art physical models for calculating atmospheric pressure loading effects 1 Geodätische Woche October, Köln, Germany Dudy D. Wijaya, Böhm J., Schindelegger M., Karbon M., Schuh H. Institute of Geodesy and Geophysics, TU Vienna

2 1. Introduction: The Project GGOS Atmosphere at TU Vienna Provide a detailed and comprehensive knowledge how the atmosphere affects observations of the three pillars of geodesy: geometry, gravity field & rotation Contribute to a better understanding of the system Earth Purpose and significance Determine consistent and homogeneous models for a)Atmospheric Propagation Delay (Delay) : Johannes Böhm (project leader) b)Atmospheric Angular Momentum (AAM) : Michael Schindelegger c)Atmospheric Gravity Field Coefficients (AGC) : Maria Karbon d)Atmospheric Pressure Loading (APL) : Dudy D. Wijaya Main goals

3 1. Introduction: Atmospheric pressure loading (APL) Global atmospheric pressure circulation The Earth’s crust Deformation of the Earth’s crust Pressure variations The mechanism of atmospheric loading Characteristics of atmospheric loading Pressure (mbar) Vertical displ. (mm) Boulder - USA (Lat: 40 o N) DOY in DOY in 1980 Onsala - Sweden (Lat: 57 o N) Pressure (mbar) Vertical displ. (mm) (van Dam & Wahr, 1987) 2 weeks

Radial displacement at August 1, 2008, 00 UT mm 4 1. Introduction: Atmospheric pressure loading (APL) Rule of thumb : 10 hPa ≈ 3 mm radial displacement Temporal variations : annual, one to few weeks, diurnal, semidiurnal Characteristics of atmospheric loading -Petrov & Boy : -H. –G. Scherneck : -van Dam & Gegout : -TU Vienna: APL Service

5 2. APL Modeling : The basic components of APL determination The IERS recommendation: Geophysical model Reference pressure Surface pressure The Green’s function (weight function) & Tidal & non-Tidal Surface displacements U Global pressure data Atmospheric tides Oceanic response Pressure variations The basic components Earth model geometry, mechanical properties, rheology Theory & mathematical model elastic theory, boundary conditions, extension of load Load Love Numbers The Green’s function

6 2. APL Modeling : Load Love Numbers and the Green‘s functions (a) Determination of Load Love Numbers (h n, l n, k n ) The SNREI Earth model : Preliminary Earth Reference Model (PREM), Gutenberg-Bullen Model (GB-model) Fundamental theory : Free oscillations of the Earth & elastic-gravitation theory Harmonic degree n : Definition of the radial Green’s function (G R ) Love numberLegendre Formalism of the horizontal Green’s function (G h ) is similar PREM model GB model (angular distance in degree)

7 2. APL Modeling : Load Love Numbers and the Green‘s functions (b) Effect of different Earth models on APL displacements The difference of APL displacements for some VLBI sites (PREM minus GB model) Radial displacements Eastward displacements MON-PEAKALGOPARKWETTZELL The difference of the displacements due to the choice of a specific Earth model is small (< 1mm). We choose PREM model for our operational solutions.

8 2. APL Modeling : Definition of reference pressure Global Reference Pressure (GRP) Reference pressure GRP memo, GRP data and MATLAB/Fortran codes can be found at GRP model: is based on the ECMWF 40 re-analysis (ERA-40) data (monthly means) provides a reference pressure value at any point is suitable for various applications Schuh et al. (2010) GRP error (hPa)

9 2. APL Modeling : Surface pressure & non-tidal displacements (a) European Centre for Medium-range Weather Forecasts (ECMWF) Temporal resolution : 00, 06, 12, 18 UTC Spatial resolution : 1 o x 1 o Surface pressure Lat=0, Lon=50 Problem of atmospheric pressure tides in the 6 h fields Representation of atmospheric tide signals is not accurate. The 6 h fields do not permit proper resolution of the S 2 tide. Atmospheric pressure signals S 1 /S 2 should be removed and non-tidal APL displacements should be calculated (Ray & Ponte, 2003). S1S1 S2S2 Spectra x (Pa 2 /Hz)

10 European Centre for Medium-range Weather Forecasts (ECMWF) Temporal resolution : 00, 06, 12, 18 UTC Spatial resolution : 1 o x 1 o Problem of atmospheric pressure tides in the 6 h fields S1S1 S2S2 Reduced S 1 /S 2 signals 2. APL Modeling : Surface pressure & non-tidal displacements (a) Representation of atmospheric tide signals is not accurate. The 6 h fields do not permit proper resolution of the S 2 tide. Atmospheric pressure signals S 1 /S 2 should be removed and non-tidal APL displacements should be calculated (Ray & Ponte, 2003). Tide free Surface pressure With (wrong) tide Lat=0, Lon=50 Spectra x (Pa 2 /Hz)

11 Amplitude spectra of non-tidal displacements at WETTZELL 2. APL Modeling : Surface pressure & non-tidal displacements (b) Radial displacements Eastward displacements Tide freeWith (wrong) tide S1S1 S2S2 S1S1 S2S2 Spectra x 10 5 (mm 2 /Hz)

12 2. APL Modeling : Surface pressure & non-tidal displacements (c) WETT: Radial displ. WETT: Eastward displ. Non-tidal displacements at WETTZELL and ALGOPARK ALGO: Radial displ. ALGO: Eastward displ. Petrov & Boy Vienna Differences between Petrov & Boy and Vienna models are less than 10 % of total displacements

13 2. APL Modeling : Tidal displacements (a) Trigonometric model for tidal displacements Convolution with Green’s functions Pressure tide model: Tidal displacements model: Three-hourly surface pressure from ECMWF ( ) Better representation of atmospheric tide signals The 3 h fields permit proper resolution of S 2 and ter-diurnal S 3 tides S1S1 S2S2 S3S3 S4S4 Lat=0, Lon=50 Amplitude spectra (Pa 2 /Hz)

14 Tidal displacements at WETTZELL and ALGOPARK 2. APL Modeling : Tidal displacements (b) WETT: Radial displ. WETT: Eastward displ. ALGO: Radial displ. ALGO: Eastward displ. Petrov&Boy ViennaVan Dam Differences between three models are less than 50 % of total displacements

15 Current status 3. Status of APL service at TU Vienna Tidal and non-tidal displacements provided for all VLBI sites from 1980 till now. Daily calculation (at 08:15 GMT+2). Reference frame: Center of Mass (CM). Next plans Recalculation of Love numbers and the Green’s functions. Improvement of S 1 /S 2 tide corrections and oceanic response. Tidal and non-tidal displacements provided for the nodes of a global 1 degree grid. Reference frame: Center of Mass (CM) & Center of the solid Earth (CE). Download APL correction at

16 Summary and conclusion 4. Summary, conclusion and future investigations State-of-the-art physical models for APL calculations have been presented and validated with results from other providers. Differences between Petrov & Boy and Vienna results are very small, less than 10 % of the APL displacements (~20 mm) Treatment of oceanic response was not discussed in this presentation. In the calculation we assume that the oceanic response follows the inverted barometer principle. REMARKS: if the APL displacements remain uncorrected in the analysis of space geodetic data it can systematically affect other parameters as was shown by Dach et al. (2009) for GPS and Boehm et al. (2010) for VLBVI. Future investigations Further improvements regarding theoretical and technical aspects will be done. Thorough validations by VLBI observations and other space geodetic observations will be carried out.