Coastal oceans as highly productive components of the global ocean play crucial roles in global carbon cycle and climate change. The wide continental shelf off US east coast is a typical coastal environment that serves as a buffer zone between human activities and open oceans. This thesis investigates the dispersal pattern of Hudson River outflow in the New York Bight (NYB). It applies adjoint sensitivity, Incremental Strong Constraint 4D Variational Data Assimilation (IS4DVAR) and representer-based optimal observation to integrate coastal ocean modeling and observation capabilities. Firstly, analysis of a 2-year model simulation identifies three freshwater pathways: along (i) the New Jersey coast, (ii) the Long Island coast, and (iii) a Mid-shelf Pathway. It is shown that the New Jersey coast Pathway dominates winter months and the Mid-shelf Pathway summer months. It is also demonstrated that wind is the primary force for spreading freshwater into mid- and outer-shelf and presence of the Hudson Valley strengthens freshwater recirculation in the New York Apex area. Secondly, the Constituent-oriented Age and Residence time Theory is implemented to simulate the age and residence time of the Hudson River plume. Analysis shows strong seasonality of surface mean age and residence time consistent with seasonal variation of the circulation. Time series analysis shows that spatial and temporal variations of the time scales in NYB are largely buoyancy- and wind-driven. Thirdly, adjoint sensitivity analysis applied on the New Jersey inner shelf identifies water sources and quantitatively compares the contributions of different variables to a chosen oceanic process. Fourthly, IS4DVAR is used to assimilate observational data collected by all instrument types during spring 2006. It reduces the model-observation misfit by 60% and improves forecast of temperature, salinity and velocity. Finally, a representer-based optimal observation system is applied to identify the optimal sampling locations for predicting salt transport within the Hudson Shelf Valley. The system is then used to compare the influence area of existing observations. This work prototypes the integration of observation and modeling in a coastal environment and demonstrates the use of traditional and variational tools to reveal the physical processes in a shelf region.