The air-sea interface is one of the most physically active interfaces of the Earth's environments and significantly impacts the dynamics in both the atmosphere and ocean. In this doctoral dissertation, developments are made to two types of Data Assimilation (DA) applied to this interface: Lagrangian Data Assimilation (LaDA) and Coupled Data Assimilation (CDA).

LaDA is a DA method that specifically assimilates position information measured from Lagrangian instruments such as Argo floats and surface drifters. To make a better use of this Lagrangian information, an augmented-state LaDA method is proposed using Local Ensemble Transform Kalman Filter (LETKF), which is intended to update the ocean state (T/S/U/V) at both the surface and at depth by directly assimilating the drifter locations. The algorithm is first tested using "identical twin" Observing System Simulation Experiments (OSSEs) in a simple double gyre configuration with the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model version 4.1 (MOM4p1). Results from these experiments show that with a proper choice of localization radius, the estimation of the state is improved not only at the surface, but throughout the upper 1000m. The impact of localization radius and model error in estimating accuracy of both fluid and drifter states are investigated.

Next, the algorithm is applied to a realistic eddy-resolving model of the Gulf of Mexico (GoM) using Modular Ocean Model version 6 (MOM6) numerics, which is related to the 1/4-degree resolution configuration in transition to operational use at NOAA/NCEP. Atmospheric forcing is first used to produce the nature run simulation with forcing ensembles created using the spread provided by the 20 Century Reanalysis version 3 (20CRv3). In order to assist the examination on the proposed LaDA algorithm, an updated online drifter module adapted to MOM6 is developed, which resolves software issues present in the older MOM4p1 and MOM5 versions of MOM. In addition, new attributions are added, such as: the output of the intermediate trajectories and the interpolated variables: temperature, salinity, and velocity. The twin experiments with the GoM also show that the proposed algorithm provides positive impacts on estimating the ocean state variables when assimilating the drifter position together with surface temperature and salinity.

Lastly, an investigation of CDA explores the influence of different couplings on improving the simultaneous estimation of atmosphere and ocean state variables. Synchronization theory of the drive-response system is applied together with the determination of Lyapunov Exponents (LEs) as an indication of the error convergence within the system. A demonstration is presented using the Ensemble Transform Kalman Filter on the simplified Modular Arbitrary-Order Ocean-Atmosphere Model, a three-layer truncated quasi-geostrophic model. Results show that strongly coupled data assimilation is robust in producing more accurate state estimates and forecasts than traditional approaches of data assimilation.