File:cost fig4.png

The normalized cost function J computed within inner-loops (curves) and JNL the cost function computed relative to the nonlinear model during outer-loops (open circles). The various cases shown are for a 1-day assimilation window: (30,1) no preconditioning (solid black line, black circles); (10,3) no preconditioning (solid dark blue line, blue circles); (10,3) and Ritz preconditioning using 10 Ritz vectors (dashed black curve, black asterisks); (15,2) and Ritz preconditioning using 15 Ritz vectors (green curve, green circles); and (5,6) and Ritz preconditioning using 4 Ritz vectors (red curve, red circles).The horizontal dashed blue line represents the theoretical minimum value of the cost function given by half the number of assimilated observations.