Fractional Canopy Cover from LAI

If $e^{-kL}$ is the fraction of light a canopy lets through, then $1 - e^{-kL}$ is the fraction it stops, and that is fractional canopy cover: the share of the ground the leaves shade. It is the same equation as canopy extinction, read from the other side, and it is a proportion — a number between zero and one, spoken as a percentage, which is why this page offers the % unit that leaf area index deliberately does not.

The shape of the curve is the useful thing. Cover climbs steeply at low LAI and then flattens hard. At $k = 0.5$, going from LAI 1 to LAI 2 buys about 15 points of cover; going from LAI 5 to LAI 6 buys 3. That flattening is exactly the same fact, seen from a different instrument, as NDVI saturating somewhere above LAI 3 or 4 — once a canopy is nearly closed, adding leaf changes almost nothing that a sensor above it can detect. It also explains why remote sensing is good at telling bare ground from vegetation and poor at telling a dense forest from a slightly denser one.

And it never reaches 100 %. An exponential approaches its asymptote and does not arrive, so no finite leaf area index gives full cover on this equation. That is not a defect of the model; it is true of real canopies. Stand under the densest forest you can find on a bright day and there are still sunflecks moving across the litter, because leaves are not opaque tiles laid edge to edge. When a field measurement reports exactly 100 % cover, it has hit the resolution of the instrument, not the ceiling of the canopy. Those sunflecks matter more than their area suggests: in a deep forest understorey they can supply the majority of the daily photon total, arriving in bursts a seedling has to be biochemically ready to use.

The word "cover" is where this page most often goes wrong in practice, because three different quantities share it. Canopy cover is the vertical projection of crowns onto the ground, which is what this equation gives. Canopy closure is the fraction of the whole sky hemisphere blocked from a point on the floor — always the larger number, because it counts crowns off to the side as well as directly overhead. And crown cover, as a forester maps it from a photograph, usually treats each crown as a solid polygon with the gaps inside it counted as covered, so it exceeds both. Three instruments, three answers, one word, and papers that do not say which they used.

Run backwards to recover LAI from a cover measurement, the relation degrades badly at the top. Below about 80 % cover it is usefully sensitive. Above 95 % you are inverting a number that has almost stopped moving, so a single point of measurement error swings the LAI by a whole unit or more; above 98 % the answer is effectively unbounded. If the canopy is closed, measure leaf area directly and do not back it out of cover.