1. SWOT Hydrology Workshop Ka-band Radar Scattering From Water and Layover Issues Delwyn Moller Ernesto Rodriguez Contributions from Daniel Esteban-Fernandez & Michael Durand

2. SWOT Hydrology Workshop Overview and Context Instrument simulation for SWOT shows that hydrology requirements are achievable for nominal operation Focus on SWOT performance and capabilities in potentially limiting scenarios: —Establish realistic performance and their dependencies (e.g. environmental, regional etc). —In limiting scenarios identify possible mitigations, either operational or algorithmic. —Help specific science interests develop realistic plans for data interpretation. Discuss here the evaluation of two phenomena that can impact the SWOT data product for terrestrial hydrology science: 1.Temporal decorrelation of the water surface 2.Layover due to topography of the surrounding region

3. SWOT Hydrology Workshop Temporal Decorrelation Impact For a synthetic aperture system the scene must remain correlated over the aperture synthesis time in order to achieve full resolution. Note: this does not effect the height error - just the spatial along-track resolution Since there is little by way of Ka-band correlation measurements over surface water we collected some initial data from which we were able to derive this quantity v L1L1 L2L2 r a1 r a2

4. SWOT Hydrology Workshop Temporal Coherence Results Correlation times ranging from 3ms to 44ms were found with the higher wind measurements producing the shorter correlations. For a 950km orbit the effect of decorrelation time on the achievable alongtrack resolution is shown to the right. -At the shortest anticipated decorrelation times a resolution of ~45m results. -This may limit our ability to estimate the width (not the height).

5. SWOT Hydrology Workshop A simple test “river” was generated” 80m wide No topography (flush with land) Running at a 55 degree angle to the radar 10m (4.4 look) posting along-track, 1 look in range Realistic thermal and speckle noise Classification based on power threshold alone A Simple Test Case Classification for Perfect Coherence Classification (  c = 7ms) Widening due to Finite (7ms Correlation Time Algorithm “robustness” issues can occur due to the narrowness of the river (in # of pixels)

6. SWOT Hydrology Workshop Ability to Estimate Width: Results Little averaging is required to converge on a mean width estimate This is relatively independent of water decorrelation time Note: We are ultimately limited by finite pixel sizes in estimating width even as the decorrelation -> infinity. Approaches to correcting for bias shall be investigated next Width Estimation Variability for an 80m River Width Estimation Bias due to Decorrelation Width Estimation Bias(m)

7. SWOT Hydrology Workshop Reaches of a few hundred meters are sufficient to average for the estimate of mean width to converge Bias is not a function of river width so for very large rivers the percent bias is less The next step is to work on an algorithm and sensitivity analysis for correcting the bias -Radar point-target response can be characterized -In the mission we may be able to process to different aperture lengths to estimate the correlation time from the azimuth widths Temporal decorrelation needs to be better understood and characterized => important to get more experimental data/statistics Temporal Decorrelation Impact Summary

8. SWOT Hydrology Workshop Effects of Topographic Layover: Revisited Layover due to topography occurs when a topographic feature occurs at the same range as the water and thus the energy from both the water and the land occur at the same time and cannot be distinguished

9. SWOT Hydrology Workshop 47 45 46 -124-123-122 Sample Region for Layover Study: Pacific Northwest Data Sources DEM: NED 10m posting Water mask: SRTM water bodies database For simplicity we have assumed the spacecraft velocity is constant in longitude. For each water pixel, every land pixel who’s range is within the radar range resolution is located When layover occurs, the proportional increase of the height error is calculated as follows: And the relative power ratio accounts for: 1.projected area of the land relative to the water 2.The dot product between the normal to the 2d facet and the incident wave. 3.The relative  0 between the land and water. Note a 10dB water/land  0 ratio is assumed at nadir which is then corrected for the local angle of incidence

10. SWOT Hydrology Workshop Layover Simulation Results Note: layover regions are spatially localized and predictable

11. SWOT Hydrology Workshop Layover Statistics Height error “scaling” factor The impact of topographic layover is geographically isolated (and could be predictably removed ) The magnitude of the additive error is typically very small (>99% of pixels have l r <1.1)

12. SWOT Hydrology WorkshopSummary Temporal decorrelation of water-bodies can be rapid and consequently limit along-track resolution and our ability to accurately determine the spatial boundaries of the water. However greater statistical knowledge is needed to bound expectations and we will investigate algorithmic approaches to produce a methodology for correction. Layover due to topography is usually small and geographically isolated so is not expected to have any significant performance impact.

13. SWOT Hydrology Workshop Backups

14. SWOT Hydrology Workshop Width Finding Algorithm X axis Y axis x0x0 x1x1 y1y1 y0y0 (x c,y c ) w  d x = x 1 -x 0 d y = y 1 -y 0 Width finding algorithm: For each i: 1.Starting from y i, scan along x until you find start and end x for intersection. Calculate d x and x c. 2.Starting (x c,y i ), find y 0 and y 1 by scanning up and down. Compute d y and y c. 3.Compute the tangent of the angle, d y /d x. Note that the sign is positive if (y 1 -y c )/(x c -x 0 )>0, negative otherwise. 4.Compute the width using the square root formula 5.Save center, width, angle 6.Given the direction of the slope, move to the next neighboring point that is classified water, and repeat. Mark used points as you go. 7.Once a river is completed, restart process with unused water pixels. 8.Smooth center and width along the reach