Forward Sensitivity Approach to Dynamic Data Assimilation

Algorithm 1

DO 𝑗 = 𝑁 to 1

 DO 𝑖 = 𝑁 to 𝑗

 𝜂(𝑡_𝑖)=𝑀^𝑇(𝑡_𝑗,𝑡_𝑗−1)𝜂(𝑡_𝑖)

 END

END

𝜇(1)=𝐿(𝑡₁,0)

DO 𝑖 = 2 to 𝑁

𝜇(𝑖)=𝜇(𝑖−1)+𝐿(𝑡_𝑖,𝑡_𝑖−1)

END

Grad = 0

DO 𝑖 = 1 to 𝑁

Grad = Grad + 𝜇(𝑖)𝜂(𝑡_𝑖)

END