1. Environmental Geodesy Lecture 11 (April 4, 2011): Loading - Predicting loading signals - Atmospheric loading - Ocean tidal loading - Non-tidal ocean loading - Hydrological loading - Cryospheric loading - Summary

2. Precision of observations versus Precision of model predictions Predicting Loading Signals Observations: For example: 3-D surface displacements or deformation from geodetic measurements; gravity changes from absolute and superconducting gravimeters; gravity variations from satellite missions. Time scales from less than 1 hour up to decades Model predictions: Based on: theory (continuum mechanics); Earth model; surface loads.

3. Predicting Loading Signals Surface Loading Model predictions Based on: - theory (continuum mechanics) - Earth model - surface loads

4. Predicting Loading Signals Model predictions: Mostly used: Green's function approach (boundary value problem) Basic assumption concerning the load: thin mass distribution Widely used earth model: spherically symmetric, non-rotating, elastic, isotrop (SNREI) elastic parameters: Preliminary Reference Earth Model (PREM) Advantage of SNREI: Green's function depends only on angular distance between load and observer. Problems: boundary undulations (e.g., surface topography, core-mantel boundary); lateral heterogeneities (density, bulk modulus, shear modulus); global ocean; elastic (up to what time scale?).

5. Predicting Loading Signals Depending on the Earth model, we get the following classes of Green's functions:

6. Predicting Loading Signals Computation of Love Numbers for Spherically symmetric, non rotating, elastic, isotrop models (SNREI): - PREM or ? - PREM: surface layer: 3 km ocean - PREM: frequency-dependent shear modulus: elastic module? - PREM: parameterization of depth- dependency Green's Functions for SNREI Earth Models:

7. Predicting Loading Signals Plag et al. (1998) proposed to use surface loading to constrain Earth models Blewitt et al., (2005) proposed to use surface loading to constrain surface mass redistribution (in particular hydrological mass). Depends on sensitivity to Earth model, mass, and theoretical approximations. We will look at: - Earth model; - loads

8. Predicting Loading Signals Earth models: lateral heterogeneities Now at: http://igppweb.ucsd.edu/~gabi/crust2.html

9. Predicting Loading Signals Earth models: lateral heterogeneities http://igppweb.ucsd.edu/~gabi/sediment.html

10. Predicting Loading Signals Earth models: lateral heterogeneities http://igppweb.ucsd.edu/~gabi/rem.dir/rem.home.html: Towards a 3D Reference Earth Model Five high-resolution mantel models available: - Masters et al. (SIO) - Dziewonski et al. (HRV) - Romanowicz et al. (Berkeley) - Grand (UT Austin) - Ritsema et al (Caltech)

11. Predicting Loading Signals Earth models: lateral heterogeneities

12. Predicting Loading Signals Earth models: lateral heterogeneities

13. Predicting Loading Signals Earth models: lateral heterogeneities Status: - SNREI most likely not sufficient; - 3-D Earth modes are developing, transition from PREM (SNREI) to REM (3-D) seems feasible; - But: still considerable difference between existing 3-D models. Not discussed: - anisotropy; - non-hydrostatic pre-stress; - thin-load assumption.

14. Surface loads Relevant surface loads: - atmospheric loading; - ocean loading (tidal and non-tidal); - continental water storage (lakes, rivers, soil moisture, groundwater, reservoirs); - land-based ice masses (glaciers, ice caps, and ice sheets); - man-made mass relocation (mining, etc.) Data sets: - atmosphere: global surface pressure, 6 hours; ocean response? - tidal ocean: ocean tide models; - non-tidal ocean: circulation models (e.g., 6 hours), satellite altimetry (e.g., 10 days); - continental water storage: observations and models - ice: global data bases

15. Difference between model orography and surface topography ETOPO5 versus NCEP Resolution:2.5 x 2.5 degrees NCEP ref. surf. ECMWF ref. surf. ECMWF-NCEP Atmospheric loading ETOPO5 NCEP ETOPO5-NCEP

16. Steps to compute atmospheric loading signal: - pressure field at topography: geopotential heights - anomaly: reference pressure field - convolution with Green's function SLP SUP REP PAN UP Atmospheric loading

17. Difference between air pressure data sets Reference surfaces for air pressure ECMWF:Pressure at sea surface NCEP: Pressure at model orography(?) height Comparison: at topographic height Resolution:2.5 x 2.5 degrees NCEP ref. surf. ECMWF ref. surf. ECMWF-NCEP Atmospheric loading

18. Mean Std Maximum Daily Weekly mbar Range of Pressure anomaly Atmospheric loading

19. 1960-1969 1970-1979 1980-1989 1990-1999 Differences between Decadal Mean and Long-term Mean Range: -4 to 4 mbar Left: Mean 1958 - 2002 Decadal variability of Surface Pressure Atmospheric loading

20. Range: -12 to 12 mm Time: 2000.0 to 2004.o Atmospheric loading

21. Ocean Tidal Loading - Load depends on frequency - Standard approach: - use a (low) number of tidal constituents; GIPSY: M2, S2, N2, K2, K1, O1, P1, Q1, MF, MM, SSA. - compute station-dependent loading coefficients for each constituent - available at http://froste.oso.chalmers.se/loading// - Problems: - many different ocean tide models; still considerable inter-model differences; - Incomplete representation of harmonic potential; - In some areas, shallow-water constituents not considered.

22. Atmospheric loading Ocean Tidal Loading SchwiderskiLe Provost Radial Displacement for M2 Tide in the Icelandic Sea (m)

23. Atmospheric loading Non-Tidal Ocean Loading - Load (mass distribution and ocean bottom pressure) needs to be modeled; - Standard approach: - use ocean circulation model output; IERS products: * Global OAM mass and motion terms (c20010701) * Global OAM mass and motion terms (ECCO_50yr) * Global OAM mass and motion terms (ECCO_kf049f) * Global OAM mass and motion terms (Johnson 2001) * Global OAM mass and motion terms (Ponte 1998) * Measurements of ocean bottom pressure (GLOUP) * Model for ocean bottom pressure (ECCO) * Model for oceanic center-of-mass (c20010701) * Model for oceanic center-of-mass (Dong MICOM 1997) * Model for oceanic center-of-mass (Dong MOM 1997) * Model for oceanic center-of-mass (ECCO_50yr) * Model for oceanic center-of-mass (ECCO_kf049f) - Problems: - many different models; still considerable inter-model differences; - mass conservation (due to Bousinesque approximation) - large latency.

24. Atmospheric loading Hydrological Loading - Load is a result of complex processes with different spatial and temporal scales; - Standard approach: - use output of land water storage models; IERS Geophysical Fluids: * Continental water flux data (monthly) * Continental water storage data (monthly) * Hydrological Excitations of EOP Variations (daily) * List of Global Major Artificial Reservoirs * Water Storage Change from Grace (monthly) * Water Storage Data from CPC (monthly) * Water Storage Data from ECMWF (daily) * Water Storage Data from GLDAS (daily) * Water Storage Data from NCEP/NCAR (daily) - Problems: - large inter-model differences; - data with large latencies;

25. Atmospheric loading Hydrological Loading JPL MASCON, secular trends 2003-2007, Watkins, 2008

26. Atmospheric loading Cryospheric Loading - Load history is important because of large changes in the past: postglacial rebound and response to current changes - Standard approach: - separate post-glacial and current changes; - post-glacial: geophysical models; - current changes: mass balance from satellite altimetry, GRACE, in situ observations, models; - Problems: - PGR models are uncertain due to rheology, lateral heterogeneities, rotational effects, ice history - errors in PGR map into errors in current mass changes; - conversion of ice surface elevation changes into mass changes.

27. Atmospheric loading Cryospheric Loading - Accelerated ice melt is a problem for the reference frame

28. Atmospheric loading Cryospheric Loading Post-glacial rebound; example sea level changes Method: Extrapolation of predicted present- day signal in sea level; Mean of many predictions Example: 14 different predictions Signal: -10 to 5 mm/yr Uncertainty from standard deviation: Max. ± 1.2 mm/yr, relative: ~15% Mean of 14 models STD

29. Atmospheric loading Cryospheric Loading

30. Summary Potential sources of disagreement: - lateral heterogeneities in the Earth model not taken into account; - errors in GPS estimates of tropospheric delay, i.e., loading signal partly absorbed by estimated delays; - errors/uncertainties in surface loads/pressure: - for air pressure, deviations of the ocean response to atmospheric forcing from Inverted Barometer (IB); - air pressure at high latitudes; - non-tidal ocean loading: mass conservation of ocean models; - land water storage: soil moisture and groundwater changes; - ice loads: separation of signals from past and current mass changes. - annual signals in time series of station heights due to other processes than loading. Many studies aiming at validation of predictions of surface loading signals in space-geodetic observations. General conclusion: some improvement of the RMS at some sites, but also considerable disagreement between model predictions and observations.