We consider a kappa-epsilon model reduced to a 1D in the radial direction with self-consistent transport. The evolution of the two fields k-epsilon is governed by local dynamics and transverse / parallel transport. It depends on numerous parameters, including diffusion coefficients, effective growth rates of the local evolution, a Kubo parameter, and the initial states of the variables kappa and espilon. We call p the set of those parameters. We assume that we have already available target trajectories for kappa and epsilon that we want to reproduce. For a given set p of model parameters we define the cost function j as a distance between the values of kappa and epsilon computed with the current parameters and the target trajectories. Minimising the cost function j allows us to identify the best parameters p, in the sense that the corresponding trajectory of the kappa-epsilon model is as close as possible to the target values. The minimisation is performed using a quasi-Newton algorithm, the routine m1qn3, and the gradient of the cost function is obtained by automatic differentiation with the software tapenade. The identification procedure has been tested on 2 different test cases: spreading with variation of the growth rate quotient, and spreading with variation of growth rate and different diffusion coefficients for kappa and epsilon. Parameters are globally very well estimated in both cases.