SC740 SEMINAR WEEK 11
TOPIC: Application of data assimilation techniques in physical oceanography
By Dr. Igor Shulman
Institute of Marine Sciences
University of Southern Mississippi
Summary and Comments : By Lee Emmanwori
Dr. Igor introduced the existing data assimilation techniques in numerical modeling of oceanic processes. He focused on three cases of application of the data assimilation techniques namely :
. Assimilation of satellite derived data into the NRL layered ocean model- a high spatial resolution with low temporal resolution.
. Assimilation of HF Doppler radar data into the hydrodynamical model of the Monterey Bay-a high spatial and temporal resolution over the small area.
. Assimilation of profilers, moored arrays- a high temporal resolution at a single point.
He described KALMAM FILTER(KF) which involves a linear stochastic system that describes
temperature, salinity and noise with linear measurements such as wind stress.
Xk+1 = FkXk + BkUk + Wk
Zk = HkXk + Vk
where
Xk is the ocean state at the time k
Z is the vector of observations
F is the model and
H is the observation operator
The noses W & V are unbiased random processes. He defined
d
x = Kd zwhere K is the Kalman gain matrix defined as
K = EbHT(HEbHT + R)-1
where Eb is the error covariance matrix of the background. The error covariance matrix of the analysis is given by
Ea = (I-KH)Eb and this equation is also called error prediction equation.
Dr. Igor also talked about Optimum Interpolation (OI) which uses the full numerical model instead of the linear state transition. He said that the OI can be implemented in the form of a relaxation method called nudging.