Simulating Bottom Reflectance Retrievals Using an Analytical Solution for the Two-Flow Irradiance Models
Existing analytical solutions to the two-flow irradiance equations are used to obtain new relations for simulating hyperspectral bottom reflectance signatures. Synthetic bottom reflectance signatures are compared to measured bottom reflectance signatures in order to test the model equation limitations of the formulations. Measured hyperspectral bottom reflectance signatures for a dead reef, Elkhorn coral, seagrass and sand, sand, and turtle grass are used. Estimated collimated and diffuse irradiances are inputs needed to run model formulations. Also, specific absorption, specific backscattering coefficients, and water depth for ocean, coastal, and estuarine waters are used as inputs to simulate bottom reflectance retrievals. The specific coefficients are coupled with estimates of dissolved organic matter (DOM), seston (SM), and chlorophyll (CHL) concentrations, pure water absorption, and backscattering coefficients. Resulting hyperspectral synthetic bottom reflectances are used to test the depth limitations for predicting bottom reflectances. Model results suggest that in clear natural water the Case I and Case II model can be used to estimate bottom reflectances down to 15 m in a water column between 440 and 560 nm with a 95% confidence level. In water types that include dissolved organic matter, seston, and chlorophyll both models lose the ability to predict the bottom type with an acceptable confidence level at depths of greater than 1-2 m depending upon the constituent concentrations. Surface reflectances provided by aircraft, satellite, or vessels can provide the essential input data needed to retrieve bottom water reflectances. Application of the results may provide a means to help assess water quality and shallow water bottom types through the mathematical inversion techniques developed for bottom feature detection and mapping of seagrasses, coral reef types, sand, and mud bottoms.