There are two methods commonly used to estimate cloud cover. Cloud cover, therefore, is used as the only remaining alternative for long-wave input data to DYRESM-CAEDYM, together with air temperature and humidity. Direct and indirect long-wave radiation measurements are often not available due to the expense and maintenance required for these instruments. Short-wave radiation (waveband 280–2800 nm) is usually measured directly whilst long-wave radiation (waveband >2800 nm) may also be measured directly as an incident or net value, or indirectly from cloud cover, air temperature and humidity (Tennessee Valley Authority, 1972). These exchanges include heating due to short-wave radiation penetration into the lake, latent heat (i.e., evaporative cooling), sensible heat (i.e., convection of heat between the water surface and the atmosphere), long-wave radiation and wind stress (Gal et al., 2003). Surface exchanges are responsible for the majority of the energy for heating, mixing and stratifying the lake. It uses heat balance equations to determine water temperature within each of the water layers. The hydrodynamic model (DYRESM) is based on a Lagrangian architecture that models a lake as a series of horizontal layers with uniform properties (e.g., temperature and salinity Romero et al., 2004). The one-dimensional water quality model (DYRESM-CAEDYM) is commonly used to simulate water temperature, salinity, density and water quality in lakes and reservoirs (Hamilton and Schladow, 1997, Schladow and Hamilton, 1997, Gal et al., 2003). Therefore the model’s good performance and broad applicability will contribute to the DYRESM-CAEDYM accuracy of water temperature simulation when long-wave radiation is not available. The model was also tested at Queenstown (South Island of New Zealand) and it provided satisfactory results compared to the measurements (RMSE = 0.16, r = 0.67, p > 0.01, n = 61). Values of TC derived from the model at the Lake Rotorua site gave a reasonable prediction of the observed values (RMSE = 0.10, r = 0.86, p > 0.01, n = 61). The validation of this cloud cover estimation model was conducted with observed short-wave solar radiation and TC at two sites. A regression equation between (1 − E 0/ E c) and TC produced a correlation coefficient value of 0.99 ( p > 0.01, n = 71). The downloaded hourly cloudiness measurements from 15 November 1991 to 20 February 2009 was used to calculate the daily values for this period and then the calculated daily values over the 17 years were used to calculate the average values for each ordinal date over one year. Comparison between these daily observed values and the modelled clear-sky solar radiation over one year was in close agreement (Pearson correlation coefficient, r = 0.995 and root mean squared error, RMSE = 12.54 W m −2). A more than 17-year (15 November 1991 to 20 February 2009) hourly solar irradiance data set was used to estimate the peak solar irradiance for each ordinal date over one year, which was assumed to be representative of solar irradiance in the absence of cloud.
Long-wave radiation is often not measured directly so a method to determine TC from commonly measured short-wave solar irradiance ( E 0) and theoretical short-wave solar irradiance under a clear sky ( E c) has broad application. The model requires inputs of surface short-wave radiation and long-wave radiation or total cloud cover fraction ( TC). The DYRESM-CAEDYM model is a valuable tool for simulating water temperature for biochemical studies in aquatic ecosystem.
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