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A pressure washer surface cleaner is probably the best tool for this job.
First prepare to power wash the tennis court by removing any debris (leaves, balls, and any object that is big enough to pick up by hand).
Secure or remove any object that could be pushed by the pressure of the jet such as trashcans, counters, or plastic chairs. Anything that is lightweight and can become a projectile should be taken out.
A pressure of 2000-2600 psi should be plenty to clean dirt and any mold that took hold on the surface. This will not only result in a safer court but will also save long term resurfacing costs by extending the life of the surface.
You may want to consider a pressure washer trailer or a trailer mounted pressure washer depending on how many courts you have in your facility.