A good sensitivity analysis (SA) practice must consider the diverse requirements and limitations of the practice both for the purpose of the analysis in the model design process and from a methodology perspective. Complex mechanistic models are often organized with several modules dynamically describing the diverse multi-physical processes. They are also characterized by a significant number of control factors. The strong interactions between the factors or the modules are crucial for understanding the model complexity. A comprehensive methodology must be devised to meet not only the classical objective of parameter screening for parameter estimation but also the objective of performing model diagnosis by qualitatively and quantitatively checking the module importance and interactions. In this paper, we proposed a comprehensive SA methodology adapted to complex mechanistic models characterized by several interacting processes with modules describing each of them. In this methodology, we successively perform the analysis of model nonlinearity, module importance ranking and its evolution with time, module-by-module parameter screening, quantitative analysis of both intra- and inter-module interactions, and the analysis of the complete model with a reduced number of parameters due to parameter screening. The numerical implementation strategy and computational cost analysis are also presented. A case study is presented on the Nitrogen Economy Model within plant Architecture (NEMA), which is a typical model organized into modules describing the multi-biophysical processes of plant growth. The results demonstrate that our methodology can help to reveal the importance evolution and interactions between biophysical processes described by the model modules. The reduction in the number of influential parameters to estimate from 83 to 17 by SA is also a significant step forward for the NEMA model parameterization improvement process.