A cloud tomographic retrieval algorithm relying on (i) the spherical harmonics discrete ordinate method for radiative transfer calculation and (ii) the adjoint radiative transfer theory for computing the gradient of the objective function has been designed. In order to escape local minima and to increase the efficiency of the retrieval algorithm, the computation of the gradient of the objective function by the adjoint method has been combined with that of the gradient of a surrogate function. The retrieval algorithm uses regularization and accelerated projected gradient methods endowed with a step length procedure. The performances of the retrieval algorithm as compared to those of a retrieval algorithm based on the surrogate minimization method are analyzed on a few synthetic problems.
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