NDVI= Reflection in (Near Infrared – Red) / Reflection in (Near Infrared +Red) bands of Electromagnetic spectrum

i.e ratio between difference IR/Red bands vs Sum of NIR and RED bands, varies from ​​from -1.0 to 1.0, In simple definition, the NDVI measures of the state of plant health based on how the plant reflects light /absorb at the given band. Where in Chlorophyll (a health indicator) strongly absorbs visible light, and the cellular structure of the leaves strongly reflect near-infrared light. Healthy, unhealthy vegetation dry (dehydrated), spongy layer of the plant absorbs more of the near-infrared light, rather than reflecting it. Thus, observing change in NIR to red light provides indication of the presence of chlorophyll, which correlates with plant health.

The normalized difference vegetation index (NDVI) is a simple numerical (mapping) indicator that can be used to analyze remote sensing measurements, and interpret whether the target being observed contains live green vegetation or not. To estimate phytoplankton concentration you would have to relate your NDVI numbers to field collected measurements of phytoplankton concentration, you can put your numbers@ in a graph and see if there is a linear or simolar correlations between the NDVI and phytoplankton concentration in your area of study. See figure 3 of Article Is catchment productivity a useful predictor of taxa richnes...

Md. Ashfaq Sadat ArcGIS 10x has an in-build NDVI function through its Image Analysis window. Alternatively, you could use the Raster Calculator.

There is an excellent workflow that details this at this link:

https://gisgeography.com/how-to-ndvi-maps-arcgis/

Additionally, to provide a tl;dr overview consider that plankton bloom will be seen but the seasonal values may be masked with other factors such as sea-surface or water-surface temperature and reflectivity. Consider a multi-sensor approach, with an explanation here:

https://gisgeography.com/spectral-signature/

One of the GIS textbooks for a class I took last year also discussed such a project. I'll look for it and repost later if I find the discussion relevant.

Md. Ashfaq Sadat in a simple way indicates whether there is live green vegetation or not. But I am not sure whether it is suitable in your case or not.