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Future use of microwave observations in support of Cryosat Authors - C. Ruiz, E. Jeansou NOVELTIS, France - J.D. Flach, K. Partington VEXCEL UK, United Kingdom - M. Drinkwater ESA-ESTEC, The Netherlands -F. Rémy, LEGOS, France Abstract: Electromagnetic models are used as the basis for a least squares inversion technique to estimate the dry snow zone surface properties of the terrestrial ice sheets from active and passive microwave satellite data. Retrieved parameters include grain size, density, layer thickness and accumulation rate. The prime motivation is to provide information of direct value to the Cryosat altimeter mission. The derived parameters can be used to convert from elevation change to snow mass change. They can also be used to predict geophysical retracking errors in altimeter data and to estimate the resulting uncertainty in the altimeter elevation measurement. With this technique, snow accumulation rate can also be estimated using passive microwave data. These data can then be compared to historical ERS altimeter data in order to assess the impact of interannual variability in accumulation rate on the significance of rates of elevation change. The technique is in the preliminary stages of assessment but is demonstrated using ERS-2 altimeter data in conjunction with spatio-temporally co-located SSM/I and QSCAT data. It is planned to apply the technique ultimately to Cryosat. Funding ESA-ESTEC Contract 16556/02/NL/GS Acknowledgement To A. Bingham from JPL that kindly provided model code for the benefit of defining the inversion algorithms Conclusion and prospects: A technique has been developed for estimating the surface properties of the dry snow zones of the ice sheets based on microwave model inversion. The model inversion technique has potential value for assisting with future radar altimeter missions including Cryosat. The technique can provide an estimate of the geophysical error resulting from surface penetration of the radar and can be used to convert surface elevation changes into a mass change. It can also be used to estimate the uncertainty in elevation estimates as a function of location via a sensitivity analysis. A more extensive validation is required using in-situ data, profiles of grain radius and density.The technique might also benefit from improved modelling of the near surface variation of snow pack properties. Stratigraphy and microwave models The inversion procedure is based on simple Rayleigh scattering based microwave models combined with a model of the dry snow zone stratigraphy. The density profile is derived from a best fit to recent shallow ice core data from the NASA Program for Arctic Regional Assessment (PARCA) : The depth to which the relationship is linear, z L, and the slope dρ/dz are determined from the surface density, ρ 0, and the slope of the power curve. The grain radius profile is determined by assuming the cross-sectional area of a grain increases linearly with time. Assuming a mean annual layer of thickness D, the depth-dependent grain radius r(z) is given by: where r 0 is the mean grain radius at the surface and K is the grain growth rate (K 0 =6.75 107 mm 2.yr -1 and E=47 kJ.mol -1 ) Firn layer temperature is computed using conventional heat-conduction theory and a seasonal sinusoidal relationship of the form : where T m and T a are the mean annual temperature and seasonal amplitude respectively, ω is the frequency and φ the phase of the seasonal variation and k is the thermal diffusivity of snow. Greenland GC-NET Automatic Weather Station data was used to derive a simple relationship, similar to that observed by Benson (1962), to determine T m and T a from elevation and latitude of each site within the Greenland dry snow zone : where Stratigraphy model Microwave models To compute brightness temperature of a multi-layered ice sheet surface, Bingham and Drinkwater (2000) adapted the model of Burke (1979). where ( ) is the power reflection coefficient and T atm accounts for atmospheric effects. L j represents the one-way power loss factor across the j th layer and 0 the incidence angle. The power reflection coefficient and one-way power loss factor, for each layer of the snow-pack, are determined from the absorption and scattering coefficients, which are themselves determined from the dielectric constant (Ulaby et al., 1981), firn density, grain radius and temperature profiles. The total backscatter from dry firn is considered as the incoherent sum of the isotropic volume backscattering components from each layer within the firn pack. Rough surface scattering effects are neglected at air-firn and firn-firn boundaries, as the impedance mismatch between firn layers is small. Following the methodology developed in Drinkwater et al. (2001), the total backscatter at an incidence angle 0 is given by: Microwave emissivity model Microwave backscatter model where where is the incident-angle dependent volume backscatter, is the transmissivity between adjacent layers, L is the one-way loss factor. D is the layer thickness, k e is the extinction coefficient and is the refracted incidence angle. Inversion technique The inversion method works by forward-modelling brightness temperatures and backscatter coefficients for realistic ranges of input parameters, which include layer thickness, surface density and grain size. A set of simulations of backscatter coefficients is carried out for all SSM/I and QuikSCAT data channels and for different combinations of input parameters, through an entire year (July 1999-July 2000), thus providing sufficient data points to support a least squares inversion using the actual observations. The set of input parameters which minimizes the RMS error between the modelled and observed brightness temperature and backscatter coefficients is selected as the best estimate of the surface properties of the ice sheets. This inversion procedure is formalised as follows. For all i m, where m is the number of sets of input parameters used in the simulations, find the minimum value of T i 2, where: is the RMS error for model simulation i generated from the i th set of input parameters, where i m, with m being the number of sets of input parameters. is the observed brightness temperature or backscatter coefficient for the j th dataset, e.g. SSM/I 19 GHz V, where j n and for day t, where t 365, the number of days in the year and n is the number of data channels. is the observed mean brightness temperature or backscatter coefficient for the j th dataset over the year (1 t 365). is the modelled microwave brightness temperature or backscatter value generated from the i th set of input parameters for the j th dataset, = function (D i, r i, i ) is the modelled mean brightness temperature or backscatter coefficient for the j th dataset over the year (1 t 365). is an optional weighting that can be applied to the j th dataset (0 j 1). Inversion of surface parameter Derived 1999/2000 snow pack parameters from the inversion technique including (c) grain size, (d) annual layer thickness, (e) surface density and (f) annual accumulation for 1999/2000, as derived using SSM/I 19, 22 and 37 GHz vertically polarised channels, for the Greenland dry snow zone Simulation of altimeter elevation errors The inverted surface parameters are used to forward-model conventional (ERS-2) radar altimeter returns over the dry snow zone of Greenland. The altimeter waveform model used is a simplified version of the Féménias model developed by Rémy and Legrésy (1997). Altimeter waveform model output derived from the inverted Greenland surface parameters for Summit. The true surface elevation corresponds to the vertical line at 27.5 range gates. The measured surface elevation corresponds to the vertical line at 28.7 range gates. The elevation (retrack) error is therefore calculated from the difference multiplied by the range gate width.

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