Here is link to many discussions about what causes algae (FA) and how to deal with it.
http://forums.pondboss.com/ubbthreads.php?ubb=showflat&Number=257088#Post257088I suggest two methods, one for the hair algae(aka FA) and one for the chara. 1. depending on your preference for use of the heavy metal copper algaecide, a simple common way to temporarily kill it for your 0.1 ac pond is take a 1 cup of copper sulfate (CuSO4); best type to use is the form with particles 1/4"-3/4" size pieces. Divide the cup into 2 to 3 equal parts because you don't want it all dissolving quickly as you circle the pond applying esp when using the small fine sugar size particles. Put the chemical portions in some sort of small cloth bag or old fine mesh sock attached to a long handled garden? rake. Drag this unit quickly alone the shoreline as far out as the rake reaches. You should be able to dose one shoreline with the 1st dose. Refill the sock and do the other shoreline. etc until the entire 1 cup is consumed/dissolved. Another option is to use copper based Cutrine-Plus or similar brand of buffered copper product. Copper sulfate will not control Chara. Don't waste CuSo4 on Chara. Another common non copper product is GreenClean Pro - aka granular hydrogen peroxide. Follow instructions of the bag as a dissolved spray or granular spread technique.
2. Non algacidal method it control FA and Chara is to use tilapia. Chara can be manually removed by raking in a small pond. See an excellent tool called Lake Rake. Chara can be used as garden fertilizer and mulch.
Tilapia work very very good consuming lots of algae and Chara IF you add enough numbers of tilapia to consume the volume or amount of the
problem plants over the course of 4 to 8 weeks. Grass carp (white amur) also will consume Chara but will not eat much algae, some but not lots. Remember each fish can only eat just so much food per day. So amount that needs to be consumed, is dependent on how big the problem is. IMPORTANT - Tilapia work best when a significant amount of algae is removed (manually or chemically) before the tilapia are introduced. This way they don't have a HUGE backlog(stockpiles) of algae to eat. Also note big predators will eat small size tilapia so be sure you are not just feeding your big bass expensive snacks.