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2. Overview and background information
The ICESat-II laser altimeter measures travel time of light that is emitted by the spacecraft,
reflected by the surface and bounced back to the satellite. In the first approximation the travel
time is the sum of distances from the emitter to the surface and from the surface to the receiver
multiplied by the speed of light in vacuum. Since the satellite is moving with respect to the surface,
the position of emitter and the receiver are different, but they can be easily computed from the
parameters of the orbit. In the second approximation the effect of propagation of light in the
atmosphere should be accounted for. The speed of light of the photon pulse, so-called group speed,
depends on the density and composition of the gaseous medium: light travels slower in a denser
gas. The relative reduction of speed of light v in the medium with respect to the speed of light in
vacuum c is conveniently to express as (c − v)/c and it will be called thereafter refractivity r. Gas
density depends on temperature, pressure, and mixing ratios of gas components. The mixing ratios
of all major gas component are fairly constant, except the mixing ratio of water vapor and ozone.
Though, the contribution of ozone to refractivity does not exceed 10
−6
of the total refractivity,
which has a negligible effect on ICESat data.
Thus, in order to compute air refractivity, one needs to know the density of dry air and density of
water vapor along the trajectory of light propagation. These densities depend on three parameters:
temperature of moist air, total atmospheric pressure, and partial pressure of water vapor. In the
presented algorithm these parameters will be computed using the output of numerical weather
model GEOS-FPIT developed by the Global Modeling and Assimilation Office at the Goddard
Space Flight Center. The model output can be used for deriving the state of the atmosphere at a
four-dimensional grid over elevation level with respect to the geoid, longitude, geodetic latitude, and
time. Air refractivity is computed for each element of the grid from the values of air temperature
of moist air, total pressure, and the partial pressure of water vapor. Then, using the set of gridded
discrete values of refractivity, the coefficients of the expansion of the refractivity field over a set of
basic functions are computed. These interpolating functions determine the refractivity field as a
continuous four-dimensional function in the bounded regions where the atmosphere is confined.
Using this expansion, the refractivity along the predicted light trajectory considered as a straight
line is computed. It will be shown that we can neglect bending in the atmosphere for processing
ICESat II data, since zenith angle of the light trajectory is supposed to be within 5 degrees.
Integrating the refractivity along the trajectory gives us path delay in the atmosphere. Using this
path delay, the estimate of the footprint altitude is corrected.
Presented algorithm has the internal precision better than 1 mm. Its accuracy is determined
by the accuracy of numerical weather models.
2.1. Parameters that describe the footprint
The following parameters describe the footprint for the purpose of atmospheric path delay
computation:
• h
ell
— altitude above the WGS-84 reference ellipsoid in meters;
• ϕ — geodetic latitude in degrees;
• λ — longitude in degrees;
• t – time stamp of the pulse emitted by the spacecraft in TAI time scale;
Release date TBD 2
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