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Do we really understand the backscatter-biomass curve?

To misquote Muhammad Ali:  Anyone who views the world the same at forty five as he did at thirty has wasted fifteen years of his life.

When I was thirty I used to explain the radar backscatter-biomass curve like this:

When radar backscatter is plotted against forest above ground biomass[1], there is a good positive correlation at first, but then the graph saturates as the biomass gets higher.  This can be explained by the simplified water cloud model, WCM, (or latterly the random volume over a ground model, RVoG) – forests at higher biomass have higher opacity (they have more “stuff”) and when the radar waves are no longer penetrating right through the canopy, the signal is no longer sensitive to further increases in biomass, hence the saturation.  Longer wavelengths penetrate more, so they saturate at higher biomass. That is why you get the very tight relationships observed by the very long wavelength (VHF) Carabas system flown by the Swedes, thus confirming the model.

This is the “standard model” for understanding radar measurements of forests. It may be slightly modified in presentation by explaining that the longer wavelength penetration also means the microwaves interact with the larger structures of the forest (and these are more indicative of total biomass), but the basic deductive model remains the same.

Now that I am forty five I no longer believe this explanation to be adequate.  Matthew Brolly (now at UMD) and I have just published an alternative deductive model that we call the “matchstick model” (Brolly and Woodhouse 2012) and it leads to some very interesting conclusions that are quite contrary to the standard model.

Our model has been developed for long wavelength radar only. It is very similar to the models that Smith and Ulander (2000) use for modelling the VHF signals from Carabas.  We completely remove the tree crowns and only consider the stems.   Unlike the Carabas model, we are only interested in looking at trends, not absolute values, and we use macroecological scaling relationships (Woodhouse 2006) to model variability in stem sizes and number densities[2]. (See Appendix below for typical technical questions).

So, how has our understanding changed as a consequence of this model?

Firstly, the tight relationship observed by VHF from Carabas is a red herring.  These good results certainly benefit from the very long wavelengths, but the reason the relationship is so tight is because they only have one stem per pixel.  As soon as you have poorer spatial resolution, you are at the mercy of the number density variations and you get a relationship that looks more like Figure 1.

Fig 1. When you take into account the variability in number density and calculate even simple backscatter values, there is a very poor relationship. If the number density variation is related to biomass then you can get a strong relationship, but its not consistent across forests with different thinning rates.

(This possibly explains the rather unconvincing results in Imhoff 2001 which are from a much lower resolution VHF system).  Note that the Carabas team themselves know this, and indeed have tried to compensate for it (Smith and Ulander, 2007).  But it is interesting how the VHF results are often used as evidence to support the “standard model” when in fact they do no such thing.

Secondly, in this simple model you can get saturation even without increasing the opacity. Why?  Well, imagine this special case.  Each stem is now large enough that the backscatter from each of them is only increasing in proportion to the physical cross section of the stems.  Yet the number of stems is decreasing in proportion to the physical cross section of the stems.  Result? No increase in backscatter even as the total volume of the forest continues to increase – ie, saturation.

Fig 2. The magic number here is when the thinning rate is 2 (solid line), typical of managed plantation forests and natural full-cover forests. This is when saturation happens even when the opacity of the canopy layer is ignored. Saturation doesn’t occur when thinning rates are much less (typical of natural forests at high latitude).

Such a relationship is a special case, but its very typical of high latitude managed forests (where most of the pioneering work on radar measurements of biomass are based).  The structural changes that are associated with a changes in forest biomass are very important and vary depending on the forest biome.

It is this variability of structure and its relation to the total biomass that we believe is key to this model. It is remarkable how few published articles on forest biomass measurements with SAR actually explain why the biomass is different for different plots (and I have been guilty of that myself).  It is as if this didn’t matter – that the biomass was all that was driving the backscatter, not the structure.  But biomass can increase for a number of different reasons (see explanation with Figure 3).

So, perhaps our general understanding of backscatter from forests is not complete.  The Matchstick Model may not be perfect for all scenarios, but it does raise some questions about the assumptions we typically make when looking at backscatter from forests.   Certainly I now view forest backscatter differently to how I did fifteen years ago.

Fig 3. This is possibly the most important figure from the paper. It shows the different ways in which a forest can vary in biomass (volume). In each case the biomass increases from left to right. At the top, the biomass variability is driven by resource availability, so that biomass increases with increasing number of trees. The next scenario is typical of new growth (or regrowth) – tree numbers remain static but the trees are growing; competition for resources hasn’t yet kicked in. The last two cases are where thinning is occurring. The last scenario has a thinning factor of 2, so that basal area remains constant as the trees grow (the biomass still increases from left to right since the trees grow in height).


Matchstick Model Paper Reference

M. Brolly and I. H. Woodhouse, A “Matchstick Model” of microwave backscatter from a forest, Ecological Modelling 237–238 (2012) 74–87 http://dx.doi.org/10.1016/j.ecolmodel.2012.04.014 (This is a fee-based journal. If you don’t have access please email the authors for a proof)

Other references

Imhoff, M. L.et al. (2001) VHF radar mapping of forest biomass in Panama, Geoscience and Remote Sensing Symposium, 2001. IGARSS ’01.  Vol 1: 121-122..

Imhoff, M. L. (1995) A Theoretical-Analysis of the Effect of Forest Structure on Synthetic-Aperture Radar Backscatter and the Remote-Sensing of Biomass. IEEE Transactions on Geoscience and Remote Sensing 33, 341-352.

G. Smith, L.M.H. Ulander, (2000) A model relating VHF-band backscatter to stem volume of coniferous boreal forest, IEEE Transactions on Geoscience and Remote Sensing, 38:728–740.

G. Smith-Jonforsen, et al. (2007) Effects of forest biomass and stand consolidation on P-band backscatter. IEEE Geoscience and Remote Sensing Letters, 4,: 669.

Woodhouse, I.H. (2006) Predicting backscatter-biomass and height-biomass trends using a macroecology model. IEEE Transactions on GeoScience and Remote Sensing. 44:871-877.

Technical Appendix: Typical reasons why you won’t like the Matchstick Model

–  The structure is too simple – real forests aren’t like that.  That’s true. It’s a deductive model aimed at simplifying as far as possible to allow us to understand what is going on, without making it unnecessarily complex.  It is meant to be simple.  Remember, the other deductive models consider a forest to be either a layer of water droplets or a layer of equally sized, randomly oriented cylinders.  So, for long wavelengths a layer of matchsticks is not such a bad simplification.

–  The scattering models are too simple.   We can talk well into the night if you want about the details of exactly which model should be used for what, and whether our assumption of smoothing over the Mie scattering is really justified.  But this is meant to be a simple model for deductive reasoning and the simple truth is that a rate of increase of backscatter for an “optical” scatterer is substantially less than a Rayleigh scatterer.  The backscatter from forest elements therefore increases less rapidly after it has reached some critical size.  And that critical size is just in the region we might expect for the size of large tree stems at P-band.

–  You might get away with no crowns at VHF wavelengths, but not at P-band.  We agree that it is harder to argue this at P-band. But the other deductive models have the opposite problem in that while they do a better job at representing the canopy as a whole, they fail to account for the impact of the largest elements.  The WCM and the RVoG both completely ignore the impact of stem size and number density.  We are sure its somewhere between the two extremes for P-band.

–       You have modelled volume not biomass.  We could model biomass simply by assigning a wood density. We decided not to as it is rather arbitrary.  Again this is no different from the other deductive models.

–       If it’s just the number density that drives the backscatter variability, then can you simply divide through by the number of trees in a pixel?  Well, we like these kinds of questions. It doesn’t seem to be that simple at P-band, so it probably is a combination of both stems and crown, but its an interesting avenue to pursue based on this model.

[1] Henceforth, loosely referred to as just “biomass”.

[2] That the radius-to-length ratio of the cylinders is important has been known since Imhoff’s 1995 paper on the subject.



7 thoughts on “Do we really understand the backscatter-biomass curve?

  1. Thank you for the information and the link to the journal, it is an interesting subject.

    Posted by jalmiburung | May 24, 2012, 8:05 am
  2. Hi Iain,

    I look forward to reading the paper in more detail.

    This paper helps to put another part of the jigsaw together.

    The idea will certainly help with field verification and validation of retrievals as you go through the process of demonstrating the models potential. It could really help with verification studies if P-band observations are available.

    What might be useful is to hypothesise further into the implications for L-band and S-band of the model.

    You might also explain on the blog what you next steps are to further calibrate and develop the model?

    Do you have adequate observations of different forest types at the wavelengths you need.

    With your matchstick model, are we using the right descriptors of what we see in a pixel (volume/biomass/cross sectional area)?

    How does this develop into observations of coherence with interferometry?

    I hope these comments help.

    Posted by Kevin Tansey | May 28, 2012, 9:19 am
  3. The matchstick model is an interesting concept for understanding the SAR signal over forests for longer wavelengths (P-band and VHF probably). For long wavelengths the simple canopy structure is likely to be adequate, because the signal originates mostly from stems and the ground. Matchsticks are certainly a more realistic representation of a canopy than the water cloud model under the long-wavelength assumption.
    The paper also raises an important issue: Should we be retrieving forest biomass from SAR at all, or should we try to estimate other biophysical parameters from the signal? Perhaps in future we will see the development of maps of stem density, average diameter at breast height or similar quantities.

    Posted by Heiko Balzter | June 6, 2012, 10:40 am


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