On the role of non-random errors in inverse problems in radiative transferand other applications

The inverse solution of the radiative transfer equation-which here serves a s an example for the more general case of multi-dimensional inverse problem s-is affected by measurement noise and by uncertain model parameters. We pr opose to transform the model parameter uncertainties into the measurement d omain and include related signal uncertainties in the measurement covarianc e matrix. The solution of the inverse problem where the Jacobian is weighte d by this extended covariance matrix rather than by the pure measurement co variance matrix is shown to be equivalent to an optimal estimation solution where the uncertain parameter is treated as an additional unknown paramete r. The advantage of the proposed approach is that, contrary to the optimal estimation approach, the number of fit variables does not increase with the number of uncertain model parameters. (C) 2001 Elsevier Science Ltd. All r ights reserved.