The two-stream scheme underlying TIP is described in Pinty et al. (2006), and its source code along with further information is available at JRC. TIP (Pinty et al., 2007) implements the tangent, adjoint, and Hessian codes (Voßbeck et al., 2008) of a cost function balancing 1) the misfit between observed and modeled remote sensing fluxes and 2) the deviation from prior knowledge on the one dimensional model parameter values. This procedure delivers a Gaussian approximation of the probability density functions (PDFs) of the retrieved model parameters which characterise the radiative status of the vegetation-soil system. In this procedure the adjoint code is used to efficiently provide the derivative of the cost function with respect to the parameters to a gradient algorithm for minimisation. The propagation of uncertainties from the observations to the model parameters is achieved via the Hessian of the cost function and yields a covariance matrix of posterior parameter uncertainties. This matrix is propagated to the radiation fluxes via the model's Jacobian matrix of first derivatives. This provides a Gaussian approximation of the posterior PDFs of the transmitted, absorbed and scattered fluxes within the vegetation layer, included those that are not measured, for example, the fraction absorbed by the background below vegetation. The system is highly flexible and can assimilate any combination of narrowband, broadband or hyperspectral radiation flux observations. Another definite asset of the TIP lies in its capability to control and ultimately relax a number of assumptions that are often implicit in traditional approaches.
There is a series of successful TIP applications:
The following TIP products are available:
For non-TIP FAPAR products, please check the JRC website.