An Assessment of the SRTM Topographic Products - Jet Propulsion ...

CHAPTER 1. OVERVIEW 20
error is a good predictor of the random component of the error. Section 4.1 shows the details
of this relationship.
e- After removing the height error high and medium frequency components, the residual
height error is still significant and exhibits very long wavelength behavior.
These errors are due to residual motion errors, and are further discussed in section 3.1.
f- The horizontal resolution of the SRTM data is about 45 m. The resolution is defined as
the separation between two measurements such that the correlation between the errors drops
to a value of 0.5. This is documented in Chapters 3 and 6.
1.5 SRTM Error Model
A height error model consistent with these observations can be written as
δh(x) = L(x) + σ(x)n(x) (1.3)
where L(x) represents the long wavelength error: a function neither homogeneous nor stationary;
σ(x) represents the spatially varying standard deviation of the high frequency error, which
depends on the THED values; and n(x) represents the high frequency error, a unit variance homogeneous
stationary random process, statistically independent of L(x), with the following statistical
characteristics
〈n(x)〉 = 0 (1.4)
〈n(x)n(x ′ )〉 = C(|x − x ′ |) (1.5)
where C(|x − x ′ |) represents a correlation function whose correlation length is less than approximately
100 m–400 m (see Section 3.3).
The preceding error model is physically justified as follows: The long wavelength error component
corresponds to residual roll (AODA) errors. The envelope function, σ(x) corresponds to either
modulations of the surface brightness due to surface variability, or the presence of slopes due to
topography. Finally, n(x) represents the speckle noise, which decorrelates with a distance given by
the width of the system impulse responses, after all spatial filtering has been included.
Notice that given these properties, the error variance is given by
δh 2 (x) = δL 2 (x) + δσ 2 (x)
This implies that if the total height variance is known over a continent, and the average height
variance is known over a DTED cell, the long wavelength variance can be obtained by subtracting
the two known quantities, provided the THED variance does not have much power for wavelengths
outside the cell size.
Notice that this proposed error model function is consistent with the results presented in the
previous section, but is by no means uniquely determined. It is introduced here for convenience in
interpreting the results presented in the next sections.
The structure function for this error model can then be shown to be given by
(1.6)