A mathematical procedure to estimate solar absorptance of shallow water ponds

In this article, a mathematical procedure is developed for estimating solar absorption of shallow water ponds with different pond floor based on the fact that the solar radiation trapped inside the water layer undergoes multiplicative reflection and absorption and on that the solar absorption of water is selective. Theoretical model indicates that the solar absorption of a water pond is related to the reflectivity of the pond floor, the solar spectrum and the water depth. To validate the mathematical model, a concrete water pond measuring 3 x 3 x 0.24 m was constructed. Experimental results indicate that solar reflectivity calculated based on the mathematical model proposed in this work were in good agreement with those measured. For water ponds with a water-permeable floor, such as concrete floor, theoretical calculations of the solar absorptance of a water pond should be done based on the reflectivity of full wet floor, whereas for water ponds with a non-water-permeable floor, theoretical calculations should be done based on the fact that solar reflection on the floor is neither perfect specular reflection nor prefect isotropic diffuse reflection. Results of numerical calculation show that theoretical calculations of solar absorption of a water pond by dividing solar spectrum into six bands were pretty agreement with those by dividing solar spectrum into 20 bands.