  We present the construction of an original stochastic model for the
instantaneous turbulent kinetic energy at a given point of a flow, and we
validate estimator methods on this model with observational data examples.
Motivated by the need for wind energy industry of acquiring relevant
statistical information of air motion at a local place, we adopt the Lagrangian
description of fluid flows to derive, from the $3$D+time equations of the
physics, a $0$D+time-stochastic model for the time series of the instantaneous
turbulent kinetic energy at a given position. Specifically, based on the
Lagrangian stochastic description of a generic fluid-particles, we derive a
family of mean-field dynamics featuring the square norm of the turbulent
velocity. By approximating at equilibrium the characteristic nonlinear terms of
the dynamics, we recover the so called Cox-Ingersoll-Ross process, which was
previously suggested in the literature for modelling wind speed. We then
propose a calibration procedure for the parameters employing both direct
methods and Bayesian inference. In particular, we show the consistency of the
estimators and validate the model through the quantification of uncertainty,
with respect to the range of values given in the literature for some physical
constants of turbulence modelling.
