A comparison of sensitivity fields from an adjoint and from a random perturbation technique

The adjoint of a numerical model is basically the derivative of a model forecast to earlier or initial conditions. When the model forecast is defined as some forecast scalar value, then an integration of the adjoint model will produce the sensitivity of this scalar value to the model initial fields. Such sensitivity fields can also be constructed by a large number of forward model runs using random perturbations. In this case, statistical regression is used to arrive at an estimate of the sensitivity fields. At each spatial location, the forecast is regressed against the random perturbation at that location in the initial condition. The adjoint result is exact for an infinitesimal perturbation, while the statistical result is correct for finite perturbations. Because models are non-linear, these two answers will generally differ, with the difference growing as the length of time of the forecast is increased. In this study, we compare and contrast nominally identical sensitivity fields obtained from these two techniques with a mesoscale model involving convective initiation along the dryline. The adjoint can be more efficient to compute, but is less efficient to implement. Also, the adjoint method requires large amounts of computer memory,whereas the statistical method only requires the value of the scalar forecast function from each randomly perturbed ensemble member. As the non-linearity of the model becomes important with increasing forecast times, the adjoint sensitivity values, while exactly correct, decrease in physical meaning.