The distribution shapes of air and water temperatures are basic and essential information, which determine the frequency patterns of their occurrence. It is also very useful to understand the changes in long-term air and water temperatures with respect to climate change. The typical distribution shapes of air and water temperatures cannot be well fitted using widely used/accepted normal distributions because their shapes show multimodal distributions. In this study, Gaussian mixture distributions and kernel distributions are suggested as the more suitable models to fit their distribution shapes. Based on the results, the tail shape exhibits different patterns. The tail is long in higher temperature regions of water temperature distribution and in lower temperature regions of air temperature distribution. These types of shape comparisons can be useful to identify the patterns of long-term air and water temperature changes and the relationship between air and water temperatures. It is nearly impossible to identify change patterns using only mean-temperatures and normal distributions.
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