Performing meteorological normalization with the trained decision tree f shows that M (t) and E Y ∼p Y |t [Y ] disagree substantially, see Figure . This disagreement is caused by the fact that meteorological normalization, via resampling, breaks any statistical dependence between X and T , which under model ( ) reinforces the response (see also (12a)). Indeed, both X and T have monotonic effects on Y thanks to their positive coefficients α and β, and their strong positive correlation ensures that both variables assume values in similar ranges. There is, however, also a noticeable disagreement between meteorological normalization M (t) and the expected direct effect E η [Y direct (t)], especially for extreme values of T . The reason for this is that meteorological normalization resamples values of X according to (4), which corresponds to evaluating f on a circular, instead of an elliptic domain (see Figure ). Hence, even though the model f was successfully learned, it does not extrapolate well to combinations of (X, T ) values unseen during training. In this particular case, small values of T would require sampling only 215 small values of X; but according to Proposition 1, meteorological normalization will sample X from a zero-mean Gaussian distribution that is independent of T . As a consequence, and with reference to Figure , for small values of T , a large sample for X will lead to a situation where f overestimates the response, explaining the discrepancy in Figure .