Cultivation is the paramount step of microalgae bio-processing as a concentrated and flourished biomass broth will result in higher recoveries of its metabolites. But there is scarce model development for the prediction of microalgae biomass productivity in outdoor cultivation systems under the fluctuations of process conditions. Hence, this study develops a mathematical model based on the first principles with a nonlinear approach to forecast the microalgae growth in open ponds under non-optimal cultivation conditions in respect of the location. The model accounts for the effect of temperature, solar irradiance level, availability of nutrients in the cultivation medium and the effect of local climatic conditions over the microalgae growth. The model is validated against the experimental results from literature data and model analyses have been proceeded to determine the effect of variations in process parameters on the microalgae biomass yield.