Correction on “Towards Detecting Swath Events in TerraSAR-X Time Series to Establish NATURA 2000 Grassland Habitat Swath Management as Monitoring Parameter”

We found a mistake in the swath detection rule in Section 2.4 [1]. Specifically, the percent deviation calculation in the definition of the signal changes D₁ and D₂ and axiom A₂ are altered. The correct version shall be:

Consequently, the proposed rule for the detection of swath events consists of two axioms (A₁ and A₂) that need to be satisfied. For the signal backscatter (σ°) at a specific acquisition order number (k) of the acquired scene in the time series (N), the positive or negative signal changes in percent deviation for the first (D₁) and second (D₂) acquisition after a potential swath event are considered as:

$$\begin{array}{l}{D}_1=({\sigma }^0(\text{k})-{\sigma }^0(\text{k}-1))\mathrm{\hspace{0.17em} }/\mathrm{\hspace{0.17em} }(-\hspace{0.17em}{\sigma }^0(\text{k}))\mathrm{\hspace{0.17em} }\times \mathrm{\hspace{0.17em} }100\\ D_2=({\sigma }^0(\text{k}+1)-{\sigma }^0(\text{k}))\mathrm{\hspace{0.17em} }/\mathrm{\hspace{0.17em} }(-({\sigma }^0(\text{k}))\times 100\end{array}$$

The second axiom focuses on the absolute magnitude of signal change:

$$\begin{array}{l}|D_1|\succ \frac{\sum _{i=1}^N|{\sigma }^0(\text{i}-1)-{\sigma }^0(\text{i})|}{N}/\mathrm{\hspace{0.17em} }({\sigma }^0(\text{i}))\times 100\mathrm{\hspace{0.17em} },\mathit{where}\mathrm{\hspace{0.17em} }\forall i,\mathrm{\hspace{0.17em} }{D}_1\succ \mathrm{\hspace{0.17em} }\approx 10\%\\ \mathit{AND}\\ |D_2|\succ \frac{\sum _{i=1}^N|{\sigma }^0(\text{i}-1)-{\sigma }^0(\text{i})|}{N}/\mathrm{\hspace{0.17em} }({\sigma }^0(\text{i}))\times 100\mathrm{\hspace{0.17em} },\mathit{where}\mathrm{\hspace{0.17em} }\forall i,\mathrm{\hspace{0.17em} }{D}_2\succ \mathrm{\hspace{0.17em} }\approx 5\%\end{array}$$

(A2)

If (A₁) and (A₂) are satisfied then:

$${\sigma }^0(\text{k})\Rightarrow \mathit{swath}$$