Thermal variations of water in the Nam Song stream/Mekong river: I. A mathematical model

River water temperature affects nearly every physical property related to water quality management. Therefore, anthropogenic change of water temperature is often undesirable. The objectives of this study were to develop an analytical model describing the thermal regime of a river–dam system. The model will be tested in a second manuscript using data from the Nam Song Basin in East Asia. The model incorporates three stages: (a) short time water heating process, (b) longer time water heating and (c) water cooling. Unified and continuous presentation of the above three solutions describes the complete thermal cycle. It showed that the longer the travel time from a dam (the Nam Song dam in this study) to the measuring point (slow flow rate), the larger the amount of energy absorbed and the higher its associated water temperature. According to the model the temperature of a water volume increases at a rate of ~1.2 °C/km downstream when water flow rate is 1 km/h. When water flows at a rate of 4 km/h, temperature increases at a rate of ~0.25 °C/km downstream. The model turns out to be a simple case of the kinematic wave theory, which is much easier to solve than large-scale computer simulation. For successful test of the model the specific parameters of the Nam Song River were used. Naturally, these parameters are changed from one river to another. Thus, to use the model for prediction of thermal regime in other rivers, their local specific parameters should be taken.