Modelling Bottom Reflectance Image by Fred Voetsch, Death Valley, To develop an analytical model that portrays the reflectance of an irregular bottom. Goal: To develop an analytical model that portrays the reflectance of an irregular bottom. How much will bottom morphology alter the magnitude, distribution and spectral quality of the light reflected from the bottom? Uses: 1. Estimate the importance of multiple reflections on BRDFBRDF spectral quality of the reflectancespectral quality of the reflectance 2.Provide a check for Monte Carlo models 3.Framework for modeling reflectance from a textured surface. Wendy Clavano & Bill Philpot

Modelling Bottom Reflectance To develop an analytical model that portrays the reflectance of an irregular bottom. Goal: To develop an analytical model that portrays the reflectance of an irregular bottom. Assumptions: a. The bottom is locally Lambertian. b. Bottom morphology modeled using an infinitely repeating sine wave. Roughness is adjusted by adjusting the amplitude and length of the bottom sine wave. c. The solar plane is the reference azimuth. d. Shadowing and obscuration will be significant under some conditions. e. 2nd (and higher) order reflections will be significant under some conditions. f. Surface texture may be treated by adjusting the height and length of the bottom waveform (modelled as a sine wave).

Modelling Bottom Reflectance

First Order Reflectance Modelling Bottom Reflectance

First & Second Order Far-Field Reflectance Modelling Bottom Reflectance

Shadowing for 1 st and 2 nd Order Reflections Reflectance includes contribution by inter- reflections. Some parts of the waveform are not directly illuminated. Modelling Bottom Reflectance

Obscuration for 1 st and 2 nd Order Reflections Some parts of the wave, although may be illuminated, are hidden from the detector’s view. The effects of illumination and viewing angles are not equivalent. Modelling Bottom Reflectance

Results a) In the absence of shadowing and obscuration, the BRDF remains smooth and cosine-like (for a single sine wave). b) Reflectance decreases with increasing roughness c) Reduction in 1 st order reflectance due to bottom roughness is mitigated by 2 nd order reflectance for a realistic range of wave height/length ratios. Next steps a) Consider spectral characteristics in modelling water attenuation and bottom reflectance. b) Expand model structure to consider 3D sine waves both in the near-field and in the far-field, for both variable sun incidence angles and viewing angles. c) Compare results against Monte Carlo model results.

Inverting Spectral Reflectance Goal: To develop analytical or semi-analytical methods for extracting information about water properties from hyperspectral data. Peggy Imboden & Bill Philpot

Assumptions: a. Algorithm development will be most effective if guided by a radiative transfer model. b. Properly applied, spectral derivatives will be an effective method for extracting information from the spectral data.

Research Questions: a. To what extent can spectral derivatives be related to the water IOPs? b. Can we extract more information about pigment composition by considering the more subtle spectral features? c. Can phytoplankton taxa be characterized with this approach?

Reflectance Approximation: 1 st Derivative: Approximations 1) Backscattering is relatively strong, spectral dependence of scattering is very weak compared to that of absorption:  The slope of the reflectance spectrum is dominated by the absorption spectrum and if b b << a then: If

Reflectance Approximation: 1 st Derivative: Approximations 2) Backscattering is weak relative to absorption, spectral dependence of scattering is relatively strong, such that: and if b b << a then: if

Reflectance Approximation: 2 nd Derivative: Approximation: 1) Assume that the spectral dependence of scattering is relatively weak: or, with luck,

Reflectance Approximation: Using only two non-zero terms, the 1 st Derivative becomes:

Tasks: a. Formulate basic model & derivatives. (done) b. Review data for phytoplankton species that are typical for selected sites.(ongoing) c. Run Hydrolight / OOPS to model water-leaving radiance for typical water optical components over expected ranges.(in process) d. Sensitivity analysis. e. Develop algorithms for analyzing spectral water-leaving radiance. Need: - pigment composition (w/ relative concentrations) for major phytoplankton taxa.