  If $X=X(t,\xi)$ is the solution to the stochastic porous media equation in
$\cal O\subset\mathbb{R}^d$, $1\le d\le 3,$ modelling the self-organized
criticaity and $X_c$ is the critical state, then it is proved that
$\int^\9_0m(\cal O\setminus\cal O^t_0)dt<\9,$ $\mathbb{P}{-a.s.}$ and
$\lim_{t\to\9}\int_{\cal O}|X(t)-X_c|d\xi=\ell<\9,\ \mathbb{P}{-a.s.}$ Here,
$m$ is the Lebesgue measure and $\cal O^t_c$ is the critical region
$\{\xi\in\cal O;$ $ X(t,\xi)=X_c(\xi)\}$ and $X_c(\xi)\le X(0,\xi)$ a.e.
$\xi\in\cal O$. If the stochastic Gaussian perturbation has only finitely many
modes (but is still function-valued), $\lim_{t\to\9}\int_K|X(t)-X_c|d\xi=0$
exponentially fast for all compact $K\subset\cal O$ with probability one, if
the noise is sufficiently strong. We also recover that in the deterministic
case $\ell=0$.
