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The integral length scale measures the correlation distance of a process in terms of space or time.

The mathematical expressions for integral scales are:

$$ \Tau = \int_{0}^{\infty} \rho (\tau) d\tau $$

$$ L = \int_{0}^{\infty} \rho (r) dr $$

Where $$\tau$$ is the integral time scale, L is the integral length scale, and $$\rho(\tau)$$ and $$\rho(r)$$ are the autocorrelation with respect to time and space respectively.