A Comparison of Sensitivity Analyses from Three methods: An adjoint, a Very Large Ensemble, and a New Method of Random Perturbations

In this work, we compare the efficiency and accuracy of three methods of obtaining sensitivity fields of a mesoscale model forecast to the initial conditions. The three methods are: the use of an adjoint (the most common method), the use of a very large ensemble (VLE) of forward model runs, and the use of an ensemble of randomly perturbed model runs, which is an entirely new technique. For the VLE method, small patches in the initial model domain are perturbed systematically. The impact of these perturbations at the forecast time are mapped to obtain forecast sensitivity fields. For the method of random perturbations, a large ensemble of model runs is made in which each member of the ensemble has the initial condition fields randomly perturbed at every grid point. Defined forecast response functions are then linearly regressed against the initial perturbations to obtain the sensitivity fields. The use of randomly perturbed model runs to calculate forecast sensitivity is analogous to the use of such model runs in an ensemble Kalman filter for the calculation of error co-variances. The same set of randomly perturbed model runs could be used in principle to calculate either co-variances or sensitivities.

The accuracy of an ensemble method depends on the size of the ensemble, while the accuracy of an adjoint is limited only by numerical precision. Ensemble methods are also sensitive to non-linearities, unlike an adjoint, which can be an advantage, and are much easier to implement.

In this paper, we calculate sensitivity fields of a mesoscale forecast of precipitation and thermodynamics for all three methods for the same cases. We also explore different ways of applying the initial random perturbations. We find that the method of random perturbations is easy to implement and highly accurate if a large enough ensemble is used, and has many advantages over the other two methods. The principal disadvantage of the two perturbation methods is the need for the computational resources required to run an ensemble of moderate or large size; however, all the methods require substantial computational resources.