What is the total area of leaves on a tree? On the one hand, this is a pretty obvious question to ask. Leaves are the exchange surfaces of plants, absorbing light, taking in carbon dioxide and releasing oxygen and water vapour. If we want to measure the rates at which each of these occurs for an individual tree then the area of their leaves is an essential parameter.
On the other hand, the total leaf area of a tree is an extremely difficult thing to measure, which is why for the most part we don’t bother. Up until now the only way to do so would be to pull all the leaves off a tree, measure them individually, then add the areas together. This kind of destructive sampling is generally frowned upon and makes long-term monitoring impossible.
Forest ecologists have therefore developed a range of alternative metrics which capture something of the same information. The most commonly used is Leaf Area Index (LAI), which gives the average number of leaf layers in a forest stand (strictly speaking it’s an estimate of the leaf area per unit ground area). This is very useful for modelling forests at the ecosystem level, where the overall area available for transpiration or gas exchange is important. But if you’re interested in the growth of individual trees, as I am, then it’s not much help. Likewise if you care about the foliage available as either habitat or food for herbivores, or where in the canopy those leaves actually are, LAI doesn’t provide the resolution you really need.
Terrestrial laser scanning has often been touted as a grand solution to challenges such as this. A conventional scanning laser can in theory measure at 2 mm resolution up to 50 metres away, which sounds impressive. Certainly the point clouds provide stunning visualisations which always make an impact in a presentation*.
There are a number of challenges though, and some of the over-ambitious expectations for laser-scanning derive from a few misconceptions. Dealing with these is an essential first step.
The main thing to clarify is that laser scanners don’t directly measure the amount of stuff; they measure the distance to stuff. A point cloud shows the nearest thing to the laser scanner that a beam actually struck**. That beam (you might want to think of it as a vector) is a straight line from the scanner which stops when it hits something, and everything past that point is effectively invisible. We refer to this as the occlusion problem, and it causes all sorts of issues.
To use a logical argument made famous by Donald Rumsfeld, what lies behind the first point in a laser beam’s pathway are a lot of known unknowns. We know there’s nothing until the first point (known absences), until it hits an object (a known known). After that we have no information. On top of this, coverage of laser beams is never continuous, and they spread out with distance from the scanner, so even at the highest resolution there are many things that the laser beams wouldn’t ever strike anyway.
To cut a long story short, terrestrial laser scanning provides a biased sample of the amount of stuff in a habitat, not a complete picture, however seductive our visualisations appear. We know it’s biased but we don’t know how much we’re missing. If we want to use our point cloud to estimate leaf area then we need to fill in the gaps.
In our new paper we provide a proof-of-concept for doing exactly this based on a computer simulation approach. The first step was to take a set of trees for which we knew the sizes, positions and angles of every single leaf (this was a mammoth sampling effort for which credit goes to my collaborator Sylvain Pincebourde and his team). Then we reconstructed those trees using computer graphics and simulated terrestrial laser scanning in a similar fashion to what would take place in the field. The next phase, which was also relatively novel, was to develop an algorithm to convert point clouds into flat surfaces. We could then use the area of these to create a direct estimate of tree leaf area.
Why do this? Well, it allows us to quantify exactly what proportion of the true leaf area we are theoretically able to replicate, identify how much we might be missing, and work out how our coverage varies through the canopy. It varies between the five trees, unsurprisingly, but the main lesson comes from what it tells us about the effectiveness of terrestrial laser scanning overall.
Scanning a single tree from one viewing point on the ground allows us to reconstruct only around 30% of the leaf canopy. That’s not particularly great. However, with three scanning positions around the tree, we could raise coverage to around 67% of leaf area (this scanning method matches standard recommendations). Two-thirds of leaf area might not sound amazing, but it’s better than anyone else has managed, and still much easier than pulling all the leaves off! Finally, adding an airborne scan pushes the recovery rate higher still, up to a maximum of 90%, but there are practical issues that mean this is unlikely to work with current technology, at least unless the LiDAR device is mounted on something solid like a canopy crane. All these are also theoretical maximum values; in the real world problems such as moving leaves or additional obstructions will reduce coverage.
The good news, however, is that it’s possible to get a direct estimate of tree leaf area with a laser scanner, and we have a starting point to work from. As with any new technology we’re still at the outset. Lots of people have been working on using terrestrial laser scanning to measure timber volume or tree heights but leaf area remains challenging. The next step is to see how this might integrate with hand-held mobile scanning lasers. What we have provided is a platform that at last allows us to evaluate the known unknowns and find a way to compensate for them. Eventually that means we should be able to answer the original question — what’s the area of leaves on a tree — without needing to remove a single leaf.
Yun T., Cao L., An F., Chen B., Xue L., Li W., Pincebourde S., Smith M.J. and Eichhorn M.P. (2019). Simulation of multi-platform LiDAR for assessing total leaf area in tree crowns. Agricultural and Forest Meteorology, 266–277, 107610. pdf
* And would make a stunning addition to this blog post if I had paid for a full WordPress account which allowed me to include videos. But I haven’t. So look here instead.
** For simplicity let’s not talk about split beams or multiple-return LiDAR. That gets messy very quickly.