Non-linear regression of air-water temperature for modelling surface heat fluxes in waterbodies: A case study of Laurance Lake, US

Abstract

Surface heat exchange is essential in water quality modelling. It is necessary to provide water surface temperature data for determining the air-water heat fluxes. In this paper, air-water temperature relationship was developed statistically by using the non-linear logistic regression. The model outcome made water temperature easy to calculate depending on air temperature data, which is available from the close by weather stations. The regression development and analysis were performed based on meteorological and water temperature data measured at Laurance Lake, Oregon US. The air-water relationship impact on surface heat fluxes (short and long radiation, back radiation, evaporation, conduction) was used to evaluate the regression function goodness in conjugate with error statistics. Results showed that the regression can reproduce the total heat flux wave without curve shifting. For one-day computational time, MAE, RMSE, and NSE recorded 0.552, 6.936, and 0.902 Watt/m2, respectively using the logistic regression. The regression kept the same behaviour when running over longer period of time, matching the real total flux (When a maximum value of 774.21 Watt/m2 was estimated based on measured water temperature, the logistic modelling gave a value of 752.52 Watt/m2 corresponding to water temperature of 15.642 °C and 15.637 °C, respectively).