Rotting wood and mushrooms would lower the fertility by upping the acidity of the pond, which could be counteracted by liming if the alkalinity got below 20 ppm. What does your water look like when it hasn't just had 3.5 inches of rain? Right now it looks turbid, which is to be expected. If it doesn't get a nice green color to it during the warm months when it's not raining, then your pond may not be as fertile as another pond twenty or a hundred miles away. As Esshup noted, it's a pretty simple matter to measure visibility with a secchi disk, as you're aware of; if you have a plankton bloom that limits visibility to 18" or less, you don't need to fertilize. If your water typically stays clear enough to see more than 18" down, then your fish are not growing as fast as they could be with a plankton bloom, which could be achieved by fertilizing. Hope you grow some huge fish.
