RTTOV – Mathematical Overview

Mathematical overview of RTTOV

[latexpage] Given a state vector, x, which describes the atmospheric/surface state and a radiance vector, y, then for all channels required to be simulated:

y = H(x)

where H is the radiative transfer model, i.e. RTTOV (also referred to as the observation operator in data assimilation parlance). This is known as the ‘direct’ or ‘forward’ model.

In addition RTTOV also computes the Jacobian matrix H which gives the change in radiance δy for a change in any element of the state vector δx assuming a linear relationship about a given atmospheric state x0:

δy = H(x0)δx


It is not always necessary to store and access the full Jacobian matrix H and so the RTTOV package also has routines to only output the tangent linear values δy, i.e. the change in top of atmosphere radiances, for a given change in atmospheric profile, δx, about an initial atmospheric state x0. The tangent linear routines all have TL as an ending. Conversely the adjoint routines (ending in AD) compute the change in the gradient of any scalar quantity with respect to the atmospheric state, x0, given a change in the gradient of that quantity with respect to the radiances, y. These routines are normally used as part of the variational assimilation of radiances.

For users only interested in the direct or forward model for radiance simulations the TL/AD/K routines are not required.