Many weather web-providers supply information of this nature. Data relating to the weather can be downloaded and processed by logging onto such servers as "Weather Underground." in fact it may be possible to make a metric just by multiplying these indicators together initially. The eventual ideal would be to predict drying conditions based on the effect of prevailing weather conditions on the wet and dry weight of a patch of cloth hanging in the elements.
The patch of cloth can be weighed by a digital scale or strain gauge. Devices such as these are very common and relatively inexpensive. The weight of the patch of cloth can be monitored alongside the prevailing weather conditions in order to generate data regarding drying time and whether the weather is having a positive or negative effect on such drying time.