Carbon: the amount of available carbon for bacteria, NaHCO3 and CO2 are the one of the available forms of carbon. TC (total carbon) is the best method to measure carbon, COD is the indirect way of measuring carbon. the amount of oxygen is required to oxidize carbon, there by you can predict the quantity of carbon.
Nitrogen: TN (Total nitrogen) test gives you complete amount of nitrogen in your sample. Nitrate, Nitrite and ammonia is the other forms of nitrogen.
in autotrophic bacteria, they fix atmospheric carbon dioxide into sugars, so it is not advisable to measure carbonates or carbon dioxide, it's better measure total carbon.
A agree with what Mr Chaitanya said and, I would like to add this:
Keep in mind two important aspects of design engineering of biological systems : stoichiometry an kinetic.
Stoichiometry is related to the concept of "mass balance": For a given quantity of substrate, a mass balance is used to determine the amount of chemicals that must be supplied to satisfy the energy, nutrient and environmental needs of the microorganisms. In addition, the amount of end products generated can be estimated. Typical formula used to represent bacteria in stoichiometric equation is: C45H83O16N9P. Given that, you can estimate the amount of substrat you need to produce the amount of product you want.
Kinetic gives two informations: How fast the microorganisms are growing ? and what is the effect of the substrat concentration on the growth rate of the used microorgnism.
If you are interested in this topic, please find more information in the book, hereafter referenced: Rittman B. E. et P.L. McCarty. 2001. Environmental Biotechnology, Principles and applications, McGraw-Hill International Editions, New York, p. 755.
All discussions conducted on the subject are of great interest and points very clear answer to your problem. I personally support those presented by Mr. Mouhamadou Nourou Dine and Lord Chaitanya Kumar LIADY.
The autotrophic bacteria fix the atmospheric carbon dioxide, so in that case you have to measure total Carbon and then TOC. COD and BOD methods are for measuring primarily DO and similarly you can measure Total N and P
1. The term C/N is practical, but unfortunately not accurate. We actually mean ORGANIC C / Total N . Carbon to be considered DOES NOT include CO2, HCO3 or CO3.
The organic C/N will determine if Ammonium is released to the water by microbial processes (C/N 10-15). As such C/N is an important tool we got to affect toxic ammonia in the pond.
C/N/P is an important parameter in oceanography and limnology, where phosphorus is commonly the factor controlling algae biomass. In our system, fed ponds, we always have more than enough phosphorus for the algae, thus this term is not important.
Photosynthetic organisms (autotrophs), such as plants, algae, and cyanobacteria, appear to be quite flexible in their growth rate and chemical composition and are able to adjust their ratios depending on availability of nutrients in the environment. Thus, plants exhibit "weak stoichiometric homeostasis," meaning that their biomass C:N:P ratios tend to track those of environmental supplies.