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Future use of microwave observations in support
of 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

• 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.
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.
Stratigraphy model
Microwave models

• The density profile is derived from a best fit to
  recent shallow ice core data from the NASA
  Program for Arctic Regional Assessment (PARCA)

Microwave emissivity model

• To compute brightness temperature of a
  multi-layered ice sheet surface, Bingham and
  Drinkwater (2000) adapted the model of Burke
  (1979).

The depth to which the relationship is linear,
zL, and the slope d?/dz are determined from the
surface density, ?0, and the slope of the power
curve.
where ?(?) is the power reflection coefficient
and Tatm accounts for atmospheric effects. Lj
represents the one-way power loss factor across
the jth 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 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
where r0 is the mean grain radius at the surface
and K is the grain growth rate (K06.75 107
mm2.yr-1 and E47 kJ.mol-1)
Microwave backscatter model

• Firn layer temperature is computed using
  conventional heat-conduction theory and a
  seasonal sinusoidal relationship of the form

• 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

where Tm and Ta are the mean annual temperature
and seasonal amplitude respectively, ? is the
frequency and f the phase of the seasonal
variation and k is the thermal diffusivity of
snow.
where
Greenland GC-NET Automatic Weather Station data
was used to derive a simple relationship, similar
to that observed by Benson (1962), to determine
Tm and Ta from elevation and latitude of each
site within the Greenland dry snow zone
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, ke is the extinction
coefficient and ? is the refracted incidence
angle.
Inversion technique
Inversion of surface parameter
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 Ti2,
where
is the RMS error for model simulation i
generated from the ith 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
jth 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 jth dataset
over the year (1 ? t ? 365). is the modelled
microwave brightness temperature or backscatter
value generated from the ith set of input
parameters for the jth dataset, function (Di,
r0i, r0i) is the modelled mean brightness
temperature or backscatter coefficient for the
jth dataset over the year (1 ? t ? 365). is
an optional weighting that can be applied to the
jth dataset (0 ? wj ? 1).
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).

• 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.

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.