Data Assimilation
 3DVAR: the MM5/WRF 3DVAR assimilation system was used in simulation study of Arctic extreme weather events. Customized model background error was obtained by utilizing the NMC method over a particular model domain. New observation types were introduced into the 3DVAR system, including MODIS and ATOVS retrievals;
 Arctic System Reanalysis: an ongoing project in which the MM5/WRF 3DVAR assimilation of various observations is included;
 4DVAR: the MM5 4DVAR assimilation system was used in simulation study of China heavy rain cases in the Yangtze River basin;
 MM5 “Hot Start” assimilation of MODIS data: Developed the assimilation approach and assimilated MODIS data for model cloud initialization;
 Newtonian Nudging: developed an observation nudging package and studied both observation and analysis nudging with different nudging coefficients;
 Intermittent data assimilation (IDA): based on objective analysis, the MM5 model was modified to perform intermittent data assimilation;
 IDA with Bratseth analysis scheme: introduced the Bratseth analysis method into MM5 to perform intermittent data assimilation, which achieves the results of optimal interpolation (OI) but costs less;
 Remote sensing data: the data that have been utilized in the above mentioned data assimilation studies includes: 1) MODIS data from NASA satellites Terra and Aqua; 2) TOVS/ATOVS data and AVHRR data from NOAA satellites; 3) GOES data.

Theoretical study of variational data assimilation based on a simplified climate model:
a) In the view of the two difficulties in numerical prediction caused by model error and incomplete initial conditions, three kinds of inverse problems of numerical prediction are put forward to improve prediction through retrieving initial values and model parameters to emend numerical model by using the historical data;
b) Three kinds of numerical solutions are put forward to solve the three inverse problems:
1) The gradients of cost function with respect to the initials are simply given by their definitions, and then the minimizing algorithm is used to get optimal initial conditions;
2) The gradients of cost function with respect to the model parameters are determined iteratively, and then the minimizing algorithm is used to get optimal model parameters;
3) The gradients of cost function with respect to initial conditions and model parameters are got by using variational method. The tangent linear model and the adjoint model of the forecast model are derived from the linear and adjoint equations.