Inverse problem and the pseudoempirical orthogonal function method of solution. 2: Use

The information content about tropospheric rural aerosol size distributions (i.e., functional form, accuracy of solution, and moments of the solution) that may be obtained from measurements of the backscattered radiation with no additional information is discussed. The need for additional information in the form of constraints is demonstrated. The resulting solution depends on these constraints and is thus not entirely objective. The accuracy of the solution will depend, to some degree, on the validity of the constraints. The influence of constraints is examined for the inverse problem of determining aerosol size distributions from multiwavelength measurements of backscattered radiation. Using the method of pseudoempirical orthogonal functions, two types of constraint are employed: positivity and positivity combined with smoothing. A discussion of the effects on the solutions of the two constraints is presented.