Algal needs a specific range of temperature for blooming. In my view, thermal remote sensing is applicable in this case. Calculate sea surface temperature (SSE) and then zone the study area into uniform polygons with degree of potential value in terms of blooming! Next, try existing vegetation indices in above mentioned polygons to achieve more accurate results!
I strongly recomendo you to take a look at these papers for a good start:
Gitelson, A. a., Dall’Olmo, G., Moses, W., Rundquist, D. C., Barrow, T., Fisher, T. R., … Holz, J. (2008). A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: Validation. Remote Sensing of Environment, 112(9), 3582–3593. http://doi.org/10.1016/j.rse.2008.04.015
Gitelson, A. A., Schalles, J. F., & Hladik, C. M. (2007). Remote chlorophyll-a retrieval in turbid, productive estuaries: Chesapeake Bay case study. Remote Sensing of Environment. http://doi.org/10.1016/j.rse.2007.01.016
Le, C., Li, Y., Zha, Y., Sun, D., Huang, C., & Zhang, H. (2011). Remote estimation of chlorophyll a in optically complex waters based on optical classification. Remote Sensing of Environment, 115(2), 725–737. http://doi.org/10.1016/j.rse.2010.10.014
Mishra, S., & Mishra, D. R. (2012). Normalized difference chlorophyll index: A novel model for remote estimation of chlorophyll-a concentration in turbid productive waters. Remote Sensing of Environment, 117, 394–406. http://doi.org/10.1016/j.rse.2011.10.016
Moses, W. J., Gitelson, A. A., Berdnikov, S., & Povazhnyy, V. (2009). Estimation of chlorophyll-a concentration in case II waters using MODIS and MERIS data—successes and challenges. Environmental Research Letters. http://doi.org/10.1088/1748-9326/4/4/045005
Augusto-Silva, P. B., Ogashawara, I., Barbosa, C., de Carvalho, L., Jorge, D., Fornari, C., & Stech, J. (2014). Analysis of MERIS Reflectance Algorithms for Estimating Chlorophyll-a Concentration in a Brazilian Reservoir. Remote Sensing, 6(12), 11689–11707. http://doi.org/10.3390/rs61211689
I am not sure MODIS data present what you need to estimate chlorophyll in turbid productive waters. Techniques based on red and around 700 nm bands may be helpful however there is no 700 nm band in MODIS data. I do suggest to use Sentinel-2 and -3 and (for years 2001-2009, if I am not wrong) MERIS data with band near 700 nm, which is required for accurate chlorophyll estimation.
If you are planning to use MODIS I agree with Petala' suggestion about Moses et al. (2009) paper.
Moreover, you can also use CI spectral shape algorithm (Wynne et al. 2008 and Wynne et al., 2013) which is currently being use on NOAA HAB's Bulletin.
References:
Wynne, T. T., R. P. Stumpf, M. C. Tomlinson, R. A. Warner, P. A. Tester, J. Dyble, and G. L. Fahnenstiel. 2008. “Relating Spectral Shape to Cyanobacterial Blooms in the Laurentian Great Lakes.” International Journal of Remote Sensing 29: 3665–3672.
Wynne, T. T., R. P. Stumpf, T.O. Briggs. 2013. “Comparing MODIS and MERIS spectral
shapes for cyanobacterial bloom detection.” International Journal of Remote Sensing 34:19, 6668-6678.
I second the recommendation to use the NDCI or Normalized Difference Chlorophyll Index for MERIS/MODIS. The concern is always the resolution when it comes to many inland waters, which tend to be small. Another index is the FAI or Floating Algal Index, see here:
A Novel Algorithm to Estimate Algal Bloom Coverage
to Subpixel Resolution in Lake Taihu
Yuchao Zhang, Ronghua Ma, Hongtao Duan, Steven A. Loiselle, Jinduo Xu, and Mengxiao Ma