ENVIRONMENTAL CONSEQUENCES in rocky mountain coniferous ...

or, by rearrangement,
AX. I afi Ax,tt-~t
1.t = AXi,t-~t + - + -2
r
af. Ax&t-~t +. . .
~t nt I ax, nt ax2 at
ax, at ax j
Instead of dealing with ,rates of change, we can rewrite equation 8 to facilitate
predictions of change per -
se, or -
where AXi ,t-At represents the change in state of the jth environmental characteris-
tic during the previous time interval from t-At to t; and AXi,, represents the pre-
dicted change in state of the ith environmental characteristic during the next time
interval from t to t + At. Of course, the time intervals (At) are equal in each
iteration. That is
At = t-(t-At)
and At = (t+At) - t .
afi/aX . is the partial derivative of the rate of change in Xi with respect to X
"l Y
during the interval from t to t+At (see fig. 12).
At
Figme 12. --Chunge in dX;/dt given a
change in Xj onty .