# Sample Lesson Plan: Intro to Satellite Altimetry

Ch. 5.2.7 Satellite Alitmetry – Torge, Wolfgang (2001) Geodesy. De Gruyter. Berlin, New York

Overview of Satellite Altimetry

Satellite Gravimetry v. Altimetry for Geoid Determination

OVERVIEW

• What is Satellite Altimetry?
• Active remote sensing
• Missions
• Application of Satellite Altimetry
• Mean Sea Surface
• Geoid Determination
• Dynamic Ocean Topography

OBJECTIVES

• Understand the basic principles of satellite altimetry (two-way measurement, footprint)
• The student should be able to break up the different components of the measurement and list the time variant and static variables.
• The assignment will help the student gain practice in creating GUIs and functions in Matlab as well as refresh their memory on satellite orbits (which should have been learned in a previous geodesy course)

WHAT IS SATELLITE ALTIMETRY?

• Satellite Altimetry is a form of active remote sensing.
• The most common form, and the one that this lecture is focused on, operates using microwave electromagnetic waves (RADAR), 13.5 GHz frequency (Ku Frequency). There are also laser altimetry which is used for polar missions that is not covered here.
• Two-way measurement (d = c/2*delta_t)
• Measures the instantaneous height of the sea surface
• If we break this up into the components we get d = r_s – r_p – (N + SST)
• Where d = measurement from satellite, r_s = the geocentric distance of the satellite, r_p = the geocentric distance to the point p where p lies on the surface of the reference ellipsoid and is contained by the vector of r_s, N is the geoid undulation at point p, and SST is the sea surface topography
• Satellite Altimetry operates by using a number of short pulses and taking the average of the pulses to filter out roughness in the sea surface.
• This translates into the footprint of the altimeter.
• Important Missions in Satellite Altimetry:
• NASA: Skylab, GOES-3, Seasat, Geosat, TOPEX/Poseidon, Jason 1,2,& 3
• ESA: ERS-1, ERS-2

POSSIBLE ASSIGNMENT

• Write a MatLab GUI that will calculate the time period of data to average from the Jason-2 satellite with an input footprint size. Use the orbital parameters for the Jason-2 satellite from NASA mission page. Assume a pulse frequency of 100 pulses/sec.

Marks (out of 10)

• Input (1 mark) the program asks for a footprint size
• Output (1 mark) the program displays a message with the resultant time
• Functions (4 marks) the student used functions/set variables rather than just one code (satellite parameters, calculate orbital speed, calculate single measurement footprint, calculate time)
• GUI (2 marks) the student produced a GUI program rather than using text-based operations
• Cycle code (2 marks) the program should be able to repeat calculations without having to restart
• Bonus (2 marks) the program has a drop down menu to select a different satellite to use and the results for those satellites are correct. (1 mark for 2 extra satellites, 2 marks for 4 extra satellites)

APPLICATION OF SATELLITE ALTIMETRY

• Limitation of satellite gravimetry in geoid determination is the resolution, satellite altimetry is of a higher resolution
• If we recall the equation d = r_s – r_p – (N + SST) we know that satellite altimetry measurements cannot directly measure the geoid as it contains the SST.
• If we set r_s – r_p to h_s which is the geodetic height of the satellite we can rearrange the equation to: h_s – d = N + SST
• we will then further simplify the equation by setting h_s – d = h which is the geodetic height of the sea surface at point p and represent SST by the symbol ζ, this gives us the equation: h = N + ζ
• Although this equation helps us visualize the situation it is not helpful for calculations
• Given this we must break N and ζ into their respective components.
• N can be broken into a long wavelength component (N_lw) and variations from the long wavelength (ΔN)
• Since satellite gravimetry measures the long wavelength of the geoid we can use a geoid model derived from such measurements as a value for N_lw in which we will call N_REF
• ζ can be broken into the mean  dynamic topography (ζ_MDT) and the temporal component of the sea surface topography from tides, atmospheric effects, wind, etc. (ζ(t))
• If we add the term e to represent the error in measured and modelled values we now have the equation: h = N_REF + ΔN + ζ_MDT + ζ(t) + e
• This equation still has 3 unknowns; ΔN, ζ_MDT, ζ(t);
• To reduce this to give us ΔN we can assume that the values of: ζ_MDT, ζ(t), and N_REF, do not fluctuate between observations so we can measure the slope of ΔN by measuring the change in the sea surface between observations: Δh_a-b = ΔN_a-b and combine these results with air- and shipborne gravity observations to define ΔN
• We can then calculate the geoid undulations using the equation N = N_REF + ΔN
• If we use the average of measurements over a long time span we may assume that the averaged value of ζ(t) = 0 and then can solve for ζ_MDT
• This then allows us to model ζ(t) based on each measurement of h from satellite altimetry.