Introduction to Data Assimilation for Scientists and Engineers

Masse conservation :

\(\displaystyle h_L (U_L - W) = h_R (U_R- W)\)

When the downstream gate is closed, \(U_r=0\) and thus:

\(\displaystyle W = - { h_L \, U_L \over h_R - h_L}\)

If \(q=h_L\, U_L\) and \(h_L\) are exactly known and \(h_R\) are measured with some incertidue, one defines the observation operator as:

\(\displaystyle W = {\cal G}(h_R) = - {q\over h_R - h_L}\)