There are quite a number of water quality models for simulating the water quality of a lake. The turbulent diffusion approach and the mixed-layer approach are the two approaches commonly used to model water temperature and DO in a lake. The assumption with one-dimensional models is that all inflow quantities and constituents are instantaneously dispersed throughout the horizontal layers. Most of the time, lakes are simulated using one-dimensional models that assume well mixed or uniform conditions along horizontal layers and only recognize major variations in water quality along the vertical (depth) direction. In the later part of the twentieth century, due to the advent of modern computers, various numerical models have been developed to predict water quality parameters in different types of waterbodies such as riverine systems, estuaries, lakes, and reservoirs. Water temperature and dissolved oxygen (DO) are the two most important water quality parameters for aquatic systems since temperature affects DO and the availability of DO in lakes affects freshwater fish species and populations. Water quality of natural water systems is of great concern in the modern world because of the importance of water in human life and the environment. The hourly model includes direct solar radiation heating to the bottom sediment that decreases magnitude of heat flux from or to the sediment. The hourly model uses variable hourly wind speeds to determine the turbulent diffusion coefficient in the epilimnion and produces more hours of temperature and DO stratification including stratification that lasted several hours on some of the days. The RMSEs of temperature and DO simulations from MINLAKE2018 decreased by 17.3% and 18.2%, respectively, and Nash-Sutcliffe efficiency increased by 10.3% and 66.7%, respectively indicating the hourly model performs better in comparison to daily MINLAKE2012. The root-mean-square errors (RMSEs) of simulated hourly surface temperatures in five lakes range from 1.19 to 1.95 ☌ when compared with hourly data over 4–8 years. A maximum diurnal water temperature variation of 11.40 ☌ and DO variation of 5.63 mg/L were simulated. To understand and model diurnal-nocturnal variations, a deterministic, one-dimensional hourly lake water quality model MINLAKE2018 was modified from daily MINLAKE2012, and applied to five shallow lakes in Minnesota to simulate water temperature and dissolved oxygen (DO) over multiple years. In shallow lakes, water quality is mostly affected by weather conditions and some ecological processes which vary throughout the day.
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