Adjoint Method Of "on-off" Problems In Four-dimensional Variational Data Assimilation System

Tangent linear and adjoint method of "on-off " switches are studied in this paper. The two analytic examples show that: if the heating and moistening due to convection at the switch-on point is much smaller than all the other terms in the tendency equation, then keeping the "on-off " switches the same as the basic state will produce the right tangent linear model and adjoint model. The results of numerical experiments, using the four-dimensional variational data assimilation system of the nonhydrostatic mesoscale model MM5, show that: the tangent linear model and adjoint model conducted by keeping the "on-off" switches the same as the basic state, can provide a good approximation of the first-order information to the NLM perturbation and a good descent direction for the minimization procedure; switching on and off at every other time step in the Kuo cumulus parameterization scheme don't impact the convergence rate of cost function; the existence of the switches don't impact improvement to the MM5 model rainfall prediction because that not only specific humidity ,but also wind, temperature and pressure are assimilated into the model.