We believe that the situation depicted in this experiment is a common situation for meteorological normalization, since i) badly extrapolating tree-based models are quite common hypothesis classes F and ii) meteorological variables are indeed often 220 correlated with Julian date. A model that has not been trained on snow, or low temperatures (X), for summer days (T ) will behave unpredictably during meteorological normalization, where such combinations of X and T will be sampled with high probability (if R is large). We believe that, hence, this example is particularly relevant for understanding the limitations of meteorological normalization. In this work we have investigated meteorological normalization from a mathematical perspective and showed that, given certain conditions, the result of meteorological normalization coincides with the expected value of the response variable conditioned on the non-meteorological features. These conditions include i) successful learning in the sense that the model used for meteorological normalization is itself (close to) an expected value, and ii) that meteorological and non-meteorological variables are 230 marginally independent. While the first condition is unproblematic in settings for which sufficient data is available, the second condition appears to be critical in many situations of practical interest. Indeed, in many such settings there is substantial statistical dependence between these variables, especially if the non-meteorological variables contain a notion of absolute time (such as Julian day): Meteorological factors such as temperature, humidity, precipitation levels, etc. change seasonally and are, thus, strongly dependent on time.