environmental geodesy

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

Precision of observationsversus

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.


Surface Loading

Model predictions

Based on: - theory (continuum mechanics) - Earth model - surface loads


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?).


Depending on the Earth model, we get the following classes of Green's functions:


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:


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


Earth models: lateral heterogeneities

Now at: http://igppweb.ucsd.edu/~gabi/crust2.html



http://igppweb.ucsd.edu/~gabi/sediment.html



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)



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.

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

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

NCEPETOPO5-NCEP

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

Difference between air pressure data sets

Reference surfaces for air pressure

ECMWF: Pressure at sea surfaceNCEP: Pressure at model orography(?)

height

Comparison: at topographic heightResolution: 2.5 x 2.5 degrees

NCEP ref. surf. ECMWF ref. surf.

ECMWF-NCEP Atmospheric loading

Mean

Std

Maximum

Daily Weekly

mbar

Range of Pressure anomaly

Atmospheric loading

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

Atmospheric loading

Range:-12 to 12 mm

Time:2000.0 to 2004.o

Atmospheric loading

Atmospheric loadingOcean 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.

Atmospheric loadingOcean Tidal Loading

SchwiderskiLe Provost

Radial Displacement for M2 Tide in the Icelandic Sea

(m)

Atmospheric loadingNon-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.

Atmospheric loadingHydrological 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;

Atmospheric loadingHydrological Loading

JPL MASCON, secular trends 2003-2007, Watkins, 2008

Atmospheric loadingCryospheric 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.


- Accelerated ice melt is a problem for the reference frame


Post-glacial rebound; example sea level changes

Method: Extrapolation of predicted present-day signal in sea level;

Mean of many predictionsExample: 14 different predictionsSignal: -10 to 5 mm/yr

Uncertainty from standard deviation: Max. ± 1.2 mm/yr, relative: ~15%

Mean of 14 models

STD

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.

environmental geodesy

Documents

loading signalsplag

loading signalsdepending

atmospheric loading

snrei earth models

d models

isotrop models snrei

surface topography

surface layer