sensing products. ERA5 is weakly different than both MERRA-2 and CPC at all significance levels, with significant coefficients at _p >_ 0 _._ 95 in 65% of regressions compared to 56% for MERRA2 and CPC. We saw in Figure 28, ERA5 had slightly higher adjusted R<sup>2</sup> values compared to the other two, though these differences did not satisfy our weak criteria.

These results raise the question of whether CHIRPS, CPC, MERRA-2, ARC2, and TAMSAT contain measurement error in precipitation and ERA5 is accurate - or whether the reverse is true. Similarly, the question exists if MERRA-2 and CPC contain measurement error in temperature and ERA5 is accurate - or, again, if the reverse is true. Based on our maintained assumption that weather metrics are significantly correlated with outcomes, we should conclude that ERA5 is more accurate than the other products in terms of both rainfall and temperature, while all the other remote sensing sources produce weather data containing measurement error. However, as CHIRPS, CPC, MERRA-2, ARC2, and TAMSAT, report roughly the same results, it could be that they are the more accurate products and ERA5 is the outlier.

This latter interpretation then begs the question of whether, if ERA5 suffers from measurement error in both rainfall and temperature, is the error classical or non-classical. Based on the descriptive evidence, it is possible that ERA5 suffers from non-classical measurement error, in that it consistently reports higher rainfall levels than most of the other precipitation products, suggesting the measurement error is not random but biased. That ERA5 produces the largest share of significant _p_ -values on rainfall metrics also suggests that if there is measurement error in the product it may be non-classical in nature. This is because the general understanding of the effects of classical measurement error is to introduce noise, not bias, meaning we would expect a product suffering from classical measurement error to produce fewer, not more, significant _p_ -values. For ERA5 temperature measurements, the picture is somewhat more muddled. The descriptive evidence for temperature from ERA5 does not reveal a larger variance, which a common indicator of classical measurement error. As with rainfall from ERA5, that the large number of significant _p_ -values produced by temperature metrics from ERA5 is the opposite of what one expects from classical measurement error, where noise introduces imprecision in coefficient estimates. Yet, neither of the descriptive statistics for temperature from ERA5 demonstrate a tendency to under- or over-report temperatures, relative to the other products, as ERA5 does for rainfall.

This leaves us with one of two options: either ERA5 is accurate and the other five precipitation products mismeasure precipitation or, alternatively, ERA5 suffers from non-classical measurement error, overestimating precipitation and thereby biasing regressions results so that rainfall appears more correlated with outcomes than it actually is in reality. Similarly, either ERA5 is accurate and MERRA-2 and CPC suffer from measurement error or MERRA-2 and CPC accurately report the objective fact of temperature, while ERA5 suffers from non-classical measurement error that results in biased coefficients that are more strongly correlated with outcomes than they should be. If the latter is true for either rainfall or temperature, then we cannot determine if those 36