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

CHAPTER 1. OVERVIEW 24
1.6.3 Cell and Subcell Relative Errors
Under the assumption that the separation between two points is small enough so that long wavelength
errors are identical for both points (as will be the case for the SRTM cells and subcells, by definition),
the average (over the high frequency process, but not over the envelope) relative error variance can
be written as
(δh(x) − δh(x ′ )) 2
≈ σ 2 (x) + σ 2 (x ′ ) − 2σ(x)σ(x ′ )C(|x − x ′ |) (1.16)
and, if the separation between x and x ′ is greater than the correlation length, as will be the case for
most points inside a cell or subcell, we have that
(δh(x) − δh(x ′ )) 2
≈ σ 2 (x) + σ 2 (x ′ ) (1.17)
i.e., the relative error variance is the sum of the variances of the high frequency process. (Notice
that this approximation is equivalent to assuming that the correlation function is a delta function).
The average value of the relative error variance over a cell or subcell box is then given by
(δh(x) − δh(x ′ )) 2
(1.18)
B ≈ σ 2 (x) + σ 2 (x ′ )
B = 2 σ 2 (x)
Making the same assumptions as for the absolute error, the 90% relative error over a cell or
subcell is given by
Relative Error = 1.64 2 〈σ2 (x)〉 B
B
(1.19)