Download Lab 1

Advanced Satellite Geodesy - GS 873 lab No.1
Spring Quarter 2005
Due date: May/13/2005
TA: Manman ZHANG
1. Please produce a data file of local sea level change by making a copy of Unix script
file /data2/sf/tp/src/tser873 in your working directory on geodesy SGI and run it there.
Data we used is the sea surface height (SSH) data of the TOPEX satellite. The SSH
data needed for this lab can be accessed from the “stackfile” database system of the
TOPEX radar altimeter that resides in directory /data2/sf/tp/ on geodesy SGI, a Unix
system. The lat/long of computation point of time series data are 15°N and 90°E,
respectively, specified by parameters clat and clon in the script. The path name of
output file can be specified using parameter ofile in the script too. The time series file
produced contains four columns: the first one is for a time tag in MJD, second for the
mean residual SSH in m averaged for all the 1-Hz data points within a circle of radius
3 degrees from the point (clat, clon) that are available during every 3 days, third for
the standard deviation in m corresponding to the mean, and the fourth is the number
of 1-Hz data points used for mean and standard deviation.
2. Treating short-term ocean current changes, storm effects, etc., as parts of random
data noise, set up a least-squares adjustment model of 6 (fixed) parameters to
represent the sea level changes due to long-term climate effect, solar heating cycle,
and seasonal changes of salinity that are observable in your residual SSH data over
the maximum time-span available. Define and describe your model composed of
polynomial and sinusoidal terms with the once per year harmonic as the lowest
frequency. What is the apparent annual rate of sea level rise in mm/yr? What is the
amplitude for each frequency of periodic sea level changes? What is the RMS residual
of your fit? Assume 365.25 days = 1 year in all of your computations.
3. To test the validity of your choice of two periods for solar heating cycle and
seasonal sea level change, try another adjustment model of 4 parameters without
sinusoidal terms for frequency higher than annual frequency. What is the RMS
residual of this fit? Assume 365.25 days = 1 year in all of your computations.
Please make a plot of your time series data along with your 6-parameter curve fitted
to the data and 4-parameter curve fitted to the data. The time axis should be labeled in
Julian years (e.g., year 2000.0 = MJD 51544).
Reference: The stackfile manual /data2/sf/stackfiles.pdf on geodesy SGI.
Some background information for the lab
1, For Q1, The altimeter’s 1-Hz SSH data sampled at instantaneous sub-satellite points along
the satellite’s actual ground tracks contain temporal change signals if the residual SSH above
a reference surface called the mean sea surface (MSS) is considered. The MSS, which is
assumed to be stationary or time-independent for a period of several years or so, is basically
the marine geoid vertically displaced by the ocean dynamic topography effect that is caused
by strong and steady ocean currents like the Gulf Stream and varies from location to location
with an RMS amplitude of about ±60 cm. The residual SSH above the MSS can be assumed
to be free from spatial variations.
2, For Q2, The SSH data accessible from stackfiles have been corrected for temporal
sea level changes due to tidal fluctuations and the loading effect of changing
atmospheric pressure at sea surface. Even if these corrections are perfect, which is not
true, the residual SSH data still contain the information of sea level changes including
long-term climate change effect, seasonal changes of solar heating cycle and salinity,
short-term ocean current changes, such as, eddies and gyres, and storm effects, etc.