What is the significance of the mathematical bounds printed by stats mode?
The stats mode of XTide prints upper and lower bounds that are calculated based on all tidal constituents simultaneously taking on their maximum and minimum possible values in the prediction model. These are valid bounds in the mathematical sense, meaning that it is 100% guaranteed that the predicted heights for that station will always fall between those bounds. However, in practice, the mathematical bounds will be considerably more extreme than any water level predicted by the model for any particular span of time. Stats mode also determines and outputs the maximum and minimum predicted by the model within the span of time specified by the user. This provides a narrower interval than the mathematical bounds, and one that is equally valid for the span of time specified. However, these bounds will vary depending on the span of time searched, while the mathematical bounds do not. Actual observed heights may exceed any and all bounds of the prediction model (e.g., in case of tidal surge
