The Impact of Uncertainties of Global Atmosphere Models on the Gravity Field Determination with GRACE

Transcription

1 The Impact of Uncertainties of Global Atmosphere Models on the Gravity Field Determination with GRACE L. Zenner 1, E. Fagiolini, F. Flechtner 3, T. Gruber 1, G. chwarz, T. Trautmann, J. Wickert 3 1 Institut für Astronomische u. hysikalische Geodäsie, TU-München Institut für Methodik der Fernerkundung, DLR, Oberpfaffenhofen 3 GeoForschungsZentrum otsdam roject: IDEAL-GRACE Improved De-ALiasing for Gravity Field Modelling with GRACE

2 Motivation The De-Aliasing process seems to be one of the main remaining uncertainty source in the GRACE data analysis. pecifically atmospheric mass variations play a major role! Uncertainties in atmosphere models have direct impact on GRACE (c.p. fig: Degree-Variances of atmosphere signal is above the error of GRACE)

3 roject Goals `IDEAL GRACE (Improved De-ALiasing for Gravity Field Modelling with GRACE) 1. Representative error measures for atmospheric and oceanic parameters shall be determined (comparison between different atmospheric models, radio occultation, remote sensing data, etc.).. The de-aliasing concept shall be improved by developing an error propagation for H the de-aliasing. Atmospheric De-Aliasing rocess L Moving satellite L improved modelling of high frequency atmospheric and oceanic effects as well as improved GRACE gravity field time series by taking into account the uncertainties of these models. Geocenter H

4 Atmospheric De-Aliasing Concept - Vertical Integration - Input arameter from ECMWF/NCE: Temperature T, pecific Humidity, urface ressure s, urface Geopot. Height Fundamental Formulas: H T v = ( T ) = a + b k + 1/ k+ 1/ k+ 1/ ==> N 1 level H = + R T j+ 1/ k+ 1/ H dry vln g j= k+ 1 j 1/ Cn m nm ( 1 ) 0 a + k n a ξ = + (n+ 1) Mg a H Earth k+ 1/ a ( 1 ) 0 a + k n a ξ = + (n+ 1) Mg a H Earth k+ 1/ a n+ 4 n+ 4 d nm(cos θ)cosmλsin θdθdλ d nm(cos θ)sin mλsinθdθdλ

5 Input-arameter Atmospheric De-Aliasing (I) 01. December 006-0h urface pecific Humidity [kg/kg] Error urface pecific Humidity [kg/kg]

6 Input-arameter Atmospheric De-Aliasing (II) 01. December 006-0h urface Difference Temperature ECMWF NCE [K] Error urface Temperature [K]

7 Input-arameter Atmospheric De-Aliasing (III) 01. December 006-0h Difference urface ressure ECMWF [ha] NCE Error urface ressure [ha]

8 Mathematical Model - Error ropagation (I) Law of error propagation (no covariances): f f f( x, y) σ f x y x σ = + y σ Error of virtual temperature: Tv Tv Tv ( T ) σ Tv T T σ = + = + σ Error of half-level pressure: k + 1/ k+ 1/ = ak+ 1/ + bk+ 1/ s σ = σ k+1/ s Error of geopot. height in half-levels : H 1/ H k + k + 1/ σ + T σ v k max RT T 1/ v j 1/ v j+ + H k + 1/ = H s + ln σ = H k+ 1/ j= k+ 1 g 45 j 1/ H k + 1/ + σ + σ j 1/ Hs j 1/ Error vertical integral : I n n+ 4 ' a N I I σ d 1 = + = + k max n n d In Hk 1/ g σ σ + 0 a H s k + 1/ a Hk + 1 / d = j+ 1/

9 Mathematical Model - Error ropagation (II) Full error propagation up to the inner integral is realized. Cn m nm ( 1+ k ) 0 n+ 4 a n a ξ = + d (n+ 1) Mg a H Earth k + 1/ a ( 1+ k ) 0 n+ 4 a n a ξ = + d (n+ 1) Mg a H Earth k + 1/ a (cos θ ) cos mλsinθdθdλ (cos θ ) sin mλsinθdθdλ implified approach for the spherical analysis (error propagation for the spherical harmonic analyses not yet implemented) nm nm Error of the potential coefficients C nm, nm due to uncertainties in the atmosphere model.

10 ropagated Errors on potential coefficients quare root of degree variances in terms of geoid heights [mm] Error in terms of geoid heights due to uncertainties in the atmosphere model (simplified approach!): Error arameter all parameter 1.8 surface pressure 1.8 Global Mean [cm] temperature 1.1 e-3 geopotential height. e-4 specific humidity 4.1 e-5 GRACE is ENITIVE to Uncertainties in Atmosphere Models!

11 Effects of the Uncertainties on the Geoid ropagated Error of all atmospheric input parameter (temperature, surface pressure, specific humidity, geopotential height) on the geoid. 01. December 006-0h Min Max Mean RM 1.73 cm 1.94 cm 1.81 cm cm [cm]

12 Conclusions Until now, the input parameters for atmospheric de-aliasing are regarded as error-free! BUT: Uncertainties in Atmospheric Models have significant impact on GRACE (for the long wavelengths up to degree 30) most significant: surface pressure almost negligible: temperature, specific humidity, geopotential height THEREFORE: To get more reliable homogenous potential coefficient series, error propagation should be included in the standard GRACE De-Aliasing process (AOD1B-roduct). Representative error measures for atmospheric and oceanic parameters have to be determined.

13 Thank you for your attention! Visit our poster: The ensitivity of atellite Gravity Field Determination to Uncertainties in Atmospheric Models E. Fagiolini, L. Zenner, F. Flechtner, T. Gruber, G. chwarz, T. Trautmann, J. Wickert oster ession B, Tuesday (Today!) 16/10 at 6 p.m