  This article is concerned with the \emph{asymptotically autonomous
robustness} (almost surely and in probability) of non-autonomous random
attractors for two stochastic versions of 3D convective Brinkman-Forchheimer
(CBF) equations defined on the whole space $\mathbb{R}^3$:
  $$\frac{\partial\boldsymbol{v}}{\partial t}-\mu
\Delta\boldsymbol{v}+(\boldsymbol{v}\cdot\nabla)\boldsymbol{v}
+\alpha\boldsymbol{v}+ \beta|\boldsymbol{v}|^{r-1}\boldsymbol{v}+\nabla
p=\boldsymbol{f}(t)+``\mbox{stochastic terms}",\quad
\nabla\cdot\boldsymbol{v}=0,$$
  with initial and boundary vanishing conditions, where $\mu,\alpha,\beta >0$,
$r\geq1$ and $\boldsymbol{f}(\cdot)$ is a given time-dependent external force
field. By the asymptotically autonomous robustness of a non-autonomous random
attractor $ \mathscr{A}=\{ \mathscr{A}(\tau,\omega): \tau\in\mathbb{R},
\omega\in\Omega\}$ we mean its time-section $\mathscr{A}(\tau,\omega)$ is
robust to a time-independent random set as time $\tau$ tends to negative
infinity according to the Hausdorff semi-distance of the underlying space. Our
goal is to study this topic, almost surely and in probability, for the
non-autonomous 3D CBF equations when the stochastic term is a linear
multiplicative or additive noise, and the time-dependent forcing converges
towards a time-independent function. Our main results contain two cases: i)
$r\in(3,\infty)$ with any $\beta,\mu>0$; ii) $r=3$ with $2\beta\mu\geq1$. The
main procedure to achieve our goal is how to justify that the usual pullback
asymptotic compactness of the solution operators is uniform on some
\emph{uniformly} tempered universes over an \emph{infinite} time-interval
$(-\infty,\tau]$. This can be done by a method based on Kuratowski's measure of
noncompactness.
