  (Abridged) We derive an analytical formula which provides estimates on
multiscale gravitational energy distribution using the observed surface density
PDF. Our analytical formalism also enables one to convert the observed column
density PDF into an estimated volume density PDF, and to obtain average radial
density profile $\rho(r)$. For a region with $N_{\rm col} \sim N^{-\gamma_{\rm
N}}$, the gravitational energy spectra is $E_{\rm p}(k)\sim k^{-4(1 -
1/\gamma_{\rm N})}$. We apply the formula to observations of molecular clouds,
and find that a scaling index of $-2$ of the surface density PDF implies that
$\rho \sim r^{-2}$ and $E_{\rm p}(k) \sim k^{-2}$. The results are valid from
the cloud scale (a few parsec) to around $\sim 0.1 \;\rm pc$. Because of the
resemblance the scaling index of the gravitational energy spectrum and the that
of the kinetic energy power spectrum of the Burgers turbulence (where $E\sim
k^{-2}$), our result indicates that gravity can act effectively against
turbulence over a multitude of physical scales. This is the critical scaling
index which divides molecular clouds into two categories: clouds like Orion and
Ophiuchus have shallower power laws, and the amount of gravitational energy is
too large for turbulence to be effective inside the cloud. Because gravity
dominates, we call this type of cloud g-type clouds. On the other hand, clouds
like the California molecular cloud and the Pipe nebula have steeper power
laws, and turbulence can overcome gravity if it can cascade effectively from
the large scale. We call this type of cloud t-type clouds. The analytical
formula can be used to determine if gravity is dominating cloud evolution when
the column density probability distribution function (PDF) can be reliably
determined.
