Forward Sensitivity Approach to Dynamic Data Assimilation

Figure 1

Evolution of the solution of 𝑥(𝑡) and its sensitivities to 𝑐=(𝑥(0),𝑥_𝑠,𝑘)=(1.0,11.0,0.25).

(a) Solution 𝑥(𝑡)

(b) Sensitivity of 𝑥(𝑡) w.r.t. 𝑥(0)

(c) Sensitivity of 𝑥(𝑡) w.r.t. 𝑘

(d) Sensitivity of 𝑥(𝑡) w. r. t 𝑥_𝑠