An application of the A-4DEnVar to coupled parameter optimization

In variational methods,coupled parameter optimization(CPO) often needs a long minimization time window(MTW) to fully incorporate observational information,but the optimal MTW somehow depends on the model nonlinearity.The analytical four-dimensional ensemble-variational(A-4DEnVar) considers model nonlinearity well and avoids adjoint model.It can theoretically be applied to CPO.To verify the feasibility and the ability of the A-4DEnVar in CPO,“twin” experiments based on A-4DEnVar CPO are conducted for the first time with the comparison of four-dimensional variational(4D-Var).Two algorithms use the same background error covariance matrix and optimization algorithm to control variates.The experiments are based on a simple coupled oceanatmosphere model,in which the atmospheric part is the highly nonlinear Lorenz-63 model,and the oceanic part is a slab ocean model.The results show that both A-4DEnVar and 4D-Var can effectively reduce the error of state variables through CPO.Besides,two methods produce almost the same results in most cases when the MTW is less than 560 time steps.The results are similar when the MTW is larger than 560 time steps and less than 880 time steps.The largest MTW of 4 D-Var and A-4DEnVar are 1 200 time steps.Moreover,A-4DEnVar is not sensitive to ensemble size when the MTW is less than 720 time steps.A-4DEnVar obtains satisfactory results in the case of highly nonlinear model and long MTW,suggesting that it has the potential to be widely applied to realistic CPO.

Optimizing water and nitrogen inputs for winter wheat cropping system on the Loess Plateau,China

Optimal use of water and fertilizers can enhance winter wheat yield and increase the efficiencies of water and fertilizer usage in dryland agricultural systems. In order to optimize water and nitrogen （N） management for winter wheat, we conducted field experiments from 2006 to 2008 at the Changwu Agro-ecological Experimental Station of the Chinese Academy of Sciences on the Loess Plateau, China. Regression models of wheat yield and evapotranspiration （ET） were established in this study to evaluate the water and fertilizer coupling effects and to determine the optimal coupling domain. The results showed that there was a positive effect of water and N fertilizer on crop yield, and optimal irrigation and N inputs can significantly increase the yield of winter wheat. In the drought year （2006-2007）, the maximum yield （Yma~） of winter wheat was 9.211 t/hm2 for the treatment with 324 mm irriga- tion and 310 kg/hm2 N input, and the highest water use efficiency （WUE） of 16.335 kg/（hm2.mm） was achieved with 198 mm irrigation and 274 kg/hm2 N input. While in the normal year （2007-2008）, the maximum winter wheat yield of 10.715 t/hm2 was achieved by applying 318 mm irrigation and 291 kg/hm2 N, and the highest WUE was 18.69 kg/（hm2.mm） with 107 mm irrigation and 256 kg/hm2 N input. Crop yield and ET response to irrigation and N inputs followed a quadratic and a line function, respectively. The optimal coupling domain was determined using the elas- ticity index （El） and its expression in the water-N dimensions, and was represented by an ellipse, such that the global maximum WUE （WUErnax） and Ymax values corresponded to the left and right end points of the long axis, respectively. Considering the aim to get the greatest profit in practice, the optimal coupling domain was represented by the lower half of the ellipse, with the Yma~ and WUE^ax on the two end points of the long axis. Overall, we found that the total amount of irrigation for winter wheat should not exceed 324 ram. In addition, our optimal coupling domain visually reflects the optimal range of water and N inputs for the maximum winter wheat yield on the Loess Plateau, and it may also provide a useful reference for identifying appropriate water and N inputs in agricultural applications.

Optimal Markovian Couplings and Applications

This paper is devoted to studying a new topic:optimal Markovian couplings,mainly for time-continuous Markov processes.The study emphasizes the analysis of the coupling opera- tors rather than the processes.Some constructions of optimal Markovian couplings for Markov chains and diffusions are presented,which are often unexpected.Then,the results are applied to study the L^2-convergence for Markov chains and for a diffusion on compact manifold.The estimate of the convergent rate provided by this method can be sharp.

Optimal Markovian Coupling and Exponential Convergence Rate for the TCP Process

In this work, by constructing optimal Markovian couplings we investigate exponential convergence rate in the Wasserstein distance for the transmission control protocol process. Most importantly, we provide a variational formula for the lower bound of the exponential convergence rate.