I notice that you also have some plants in your water system in what looks like a bog filter. If these plants are rooted in garden soil, they may be adding phosphate to your water which encourages algae growth. You may want to consider re-potting the plants in coarse sand to eliminate this algae food source if that is the case. It will also be helpful to add Koi Clay to your water, as it absorbs phosphate from the water and starves the algae.

I think you've had several things at work here. You had heavy rains mingled with bright sunshine. Algae will bloom after a heavy rain quite easily as the rainwater adds massive amounts of nitrogen from the atmosphere along with whatever else it happens to pick up in the air. When you shaded the pond it helped to starve the algae of the sunlight it needed and your water cleared as a result. When you removed the shade it once again went green because the algae had what it needed (nitrogen and sunlight for photosynthesis). Adding the Trickle tower has definitely been a benefit.
Trickle towers provide you with two things. They add volume to your biofiltration as the media will colonize nitrobacters and process ammonia and nitrite together with the rest of your filtration. It has the added benefit of acting as a degassing column to rid your water of Nitrate (in the form of nitrogen) and excess carbon dioxide, which improves the oxygen carrying capacity of your water. Even though the bacteria in the TT is not doing much yet, the degassing begins immediately as your clearer water shows.