Declines in pan evaporation have been reported across the USA, former Soviet Union, India, China, Australia, New Zealand and Canada, among other places. The trend is large – approximately an order of magnitude larger than model-based estimates of top of the atmosphere radiative forcing. The pan evaporation trend also has a different sign (i.e. decline) from commonly held conceptions. These are a remarkably interesting set of observations. In the first article of this two-part series, we discussed the measurements themselves and then presented summaries of the worldwide observations. In this, the second article, we outline the use of energy balance methods to attribute the observed changes in pan evaporation to changes in the underlying physical variables, namely, radiation, temperature, vapour pressure deficit and wind speed. We find that much of the decline in pan evaporation can be attributed to declines in radiation (i.e. dimming) and/or wind speed (i.e. stilling). We then discuss the interpretation of changes in the terrestrial water balance. This has been an area of much misunderstanding and confusion, most of which can be rectified through use of the familiar and longstanding supply/demand framework. The key in using the pan evaporation data to make inferences about changes in the terrestrial water balance is to distinguish between water- and energy-limited conditions where different interpretations apply.