The 2nd law is tough to apply cleanly as truly closed systems are hard to find. But fundamentally, law #2 says heat never flows from a hotter region to a colder region. So assuming a constant atmospheric temperature, more energy (in this case evaporating water) will flow from the region of higher average temperature, given the increasing entropy that follows. Very much like an extensive explanation from JFRCalifornia on most any Powell/water topic - it may appear to be decreasing the disorder of the topic through his explanations and conclusions, but in fact the amount of energy he must input for every explanation he provides substantially increases the overall entropy involved. So for JFRC: ΔS >> 0.
