  A baroclinic model for the atmospheric jet at middle-latitudes is used as
stochastic generator of non-stationary time series of the total energy of the
system. A linear time trend is imposed on the parameter $T_E$, descriptive of
the forced equator-to-pole temperature gradient and responsible for setting the
average baroclinicity in the model. The focus lies on establishing a
theoretically sound framework for the detection and assessment of trend at
extreme values of the generated time series. This problem is dealt with by
fitting time-dependent Generalized Extreme Value (GEV) models to sequences of
yearly maxima of the total energy. A family of GEV models is used in which the
location $\mu$ and scale parameters $\sigma$ depend quadratically and linearly
on time, respectively, while the shape parameter $\xi$ is kept constant. From
this family, a model is selected by using diagnostic graphical tools, such as
probability and quantile plots, and by means of the likelihood ratio test. The
inferred location and scale parameters are found to depend in a rather smooth
way on time and, therefore, on $T_E$. In particular, power-law dependences of
$\mu$ and $\sigma$ on $T_E$ are obtained, in analogy with the results of a
previous work where the same baroclinic model was run with fixed values of
$T_E$ spanning the same range as in this case. It is emphasized under which
conditions the adopted approach is valid.
