# Parabola and horizontal line detection in inland water radargrams

**CoAuthors**

**Event: **2019 Ocean Surface Topography Science Team Meeting

**Session: **Science IV: Altimetry for Cryosphere and Hydrology

**Presentation type: **Type Poster

Since few years, recent altimetric missions allow us to get valid measurements over inland water. However, most measures remain difficult to analyze and several physical effects were observed, especially the hooking effect with LRM mode in Jason3 mission (e.g. Quartly, Tournadre, … etc). Actually, this artifact appears when the altimeter continues to measure a reflective surface that it just flew over while it is no more located above this one. So, the height estimated at this location is smaller than it should and we can observe parabola in the height measurements. Therefore, the presence of parabola in height measurements is really significant of water detection and the detection of these parabola is quite important to deduce a real height estimation.

To detect these parabola in height measurements, the algorithm used is an adaptation of the Hough transform [2]. This method allows to detect objects with simple shape, like lines, circles, …, in binary image. It is more used in medical imaging and remote sensing and has the great advantage of supporting incomplete or overlapping objects. The principle of the Hough transform is to build a parabola in a new plan (the plane of parameters) for each point of the initial parabola. So, there are as many parabola in the new plan as there are points in the initial plan. In this new plan, a large majority of parabola will cross into a single point which represents the parabola in the initial plan and therefore we can deduce from it the estimated height that we are looking for. It is also possible to detect multiple parabola representing many objects, or even half parabola generally representing river banks. The same principle allows to identify horizontal line that can represent extensive water areas, lakes, flood plains, wide rivers with two half parabola separated by an horizontal segment … etc.

This algorithm detect today 60 ± 5 % of cases with at least one parabola, 70 ± 14 % with at least one horizontal line and 87 ± 28 % with at least one object (parabola or horizontal line) among 1056 overpasses. The error is determined with visual analysis on 384 overpasses. Furthermore, a method has been developed to calculate an error estimation on the height and on the position found by the algorithm and we got 12.4 cm for the height and 112 m for the position.

Today, the process needs to be further improved, optimized, tested and validated, however it already allows us to have a first encouraging results, especially for parabola. The addition of the horizontal line detection is a real asset in the analysis of altimetry measurements. This process of parabola detection can also serve to analyze and validate OLTC results. It can also be used to create a new retracker or to improve the current retracker, to analyze the temporal series, the power evolution received along track, the radargrams … etc. Actually, many projects could be developed around this algorithm of parabola and horizontal line detection.

To detect these parabola in height measurements, the algorithm used is an adaptation of the Hough transform [2]. This method allows to detect objects with simple shape, like lines, circles, …, in binary image. It is more used in medical imaging and remote sensing and has the great advantage of supporting incomplete or overlapping objects. The principle of the Hough transform is to build a parabola in a new plan (the plane of parameters) for each point of the initial parabola. So, there are as many parabola in the new plan as there are points in the initial plan. In this new plan, a large majority of parabola will cross into a single point which represents the parabola in the initial plan and therefore we can deduce from it the estimated height that we are looking for. It is also possible to detect multiple parabola representing many objects, or even half parabola generally representing river banks. The same principle allows to identify horizontal line that can represent extensive water areas, lakes, flood plains, wide rivers with two half parabola separated by an horizontal segment … etc.

This algorithm detect today 60 ± 5 % of cases with at least one parabola, 70 ± 14 % with at least one horizontal line and 87 ± 28 % with at least one object (parabola or horizontal line) among 1056 overpasses. The error is determined with visual analysis on 384 overpasses. Furthermore, a method has been developed to calculate an error estimation on the height and on the position found by the algorithm and we got 12.4 cm for the height and 112 m for the position.

Today, the process needs to be further improved, optimized, tested and validated, however it already allows us to have a first encouraging results, especially for parabola. The addition of the horizontal line detection is a real asset in the analysis of altimetry measurements. This process of parabola detection can also serve to analyze and validate OLTC results. It can also be used to create a new retracker or to improve the current retracker, to analyze the temporal series, the power evolution received along track, the radargrams … etc. Actually, many projects could be developed around this algorithm of parabola and horizontal line detection.