Motivation Models Examples Electromagnetic Modeling for Lidar and Landsat remote sensing of forests Leland Pierce The Univ of Michigan, Radiation Lab Ann Arbor, MI 48109-2122 USA May 7, 2014 Pierce Electromagnetic Modeling
MotivationModels
Examples
Electromagnetic Modeling for Lidar and Landsatremote sensing of forests
Leland Pierce
The Univ of Michigan, Radiation LabAnn Arbor, MI 48109-2122 USA
May 7, 2014
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MotivationModels
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Scenario
Continuing from the previous presentation...
I Let’s say we are a researcherinterested in biodiversity andhabitat.
I We know forest structurematters, among other things.
I The sensors are somewhatsensitive to forest structuralattributes
I How do we use the sensors toget at biodiversity?
(Photos Courtesy of Kathleen Bergen)
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Parameter Estimation Procedure
I Since there are no “standard products” for forest structure,each researcher must estimate these.
I Regressions seem the most straighforward way.
I An alternative is to use physics-based models.
I These can provide intuition as to what is possible.
I ...and enable the intelligent use of the remotely-sensed data.
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Parameter Estimation Procedure
I Today I will provide an overview of the basic physics behindthese models.
I I will also discuss the approximations that are used, and theirpossible effects on the results.
I You will see that these are straightforward to use.
I Simulations of forests relevant to your research area canprovide clues as to how to use the measured remotely-senseddata effectively to get the structural parameters you need.
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Outline
1. Forest Geometrical Model
2. Interaction of Light with Matter
3. Ray Tracing
4. Radiative Transfer: Landsat
5. Lidar
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MotivationModels
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Fractal Tree Model
I Model developed in late 1990’s.
I Fractal pseudo-random trees.
I Use Lindenmayer System:string-rewriting rules are used togenerate realistic branchingstructures, with needles andleaves.
I Each species of tree has its ownset of rules so it looks realistic.
I Both coniferous and deciduoustrees can be modeled.
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Fractal Tree Model
Same tree with and without leaves:
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Interaction of Light with Matter
3 mechanisms:
1. reflection
2. absorption
3. transmission
Conservation of Energy:Incident Energy = Energy Reflected + Energy Absorbed + Energy Transmitted
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Raytracing
Can calculate how much of the incident energy is redirected ineach direction:
I PROSPECT is oneexample for leaves.
I Can do the same forstems, twigs, needles,bark, etc.
I Approximate withthousands of rays
Jacquemoud, Baret, “PROSPECT: A Model of Leaf Optical Properties Spectra”, Rem Sens Env, 1990.
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Radiative Transfer
For Landsat-type sensors implement the following algorithm:
I Keep track of the energy as itpropagates along each of the rays.
I Track rays through several bouncesuntil their energy is very small.
I Repeat for every object in the canopy.
I Also include the reflection from theground.
I Add up all the energy directed at oursensor.
And repeat this for every wavelength of interest. (Tree image courtesy of clipart.com)
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PROSAIL
I PROSAIL uses statistical properties of forestsI The fractal forest can be used to calculate these statistics:
I branch angle distribution,I leaf size distribution,I leaf angle distribution,I branch sizes,I densities, LAI, etc.
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Landsat-type Example
This example shows the change in the spectrum as the forest LAIis varied, as calculated by PROSAIL.
Plot from: Jacquemoud, Verhoef, Baret, Bacour, Zarco-Tejada, Asner, Francois,Ustin, “PROSPECT+SAIL models: A review of use for vegetation characterization,”Rem Sens Env, 2009.
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Lidar Model
Forest Attributes:
Biomass
Tree Species
Tree Attributes:
Height
Crown Diameter
Height to live crown
Trunk Diameter
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LIDAR Model
I Divide volume of stand into cubes.
I Each cube analyzed for verticalreflection and transmission.
I track the first reflection only (a firstapproximation)
I Radiative Transfer from cube-to-cubeto produce time-trace of LIDAR signal.
I Horizontal Gaussian pulse weightingacross the stand, with a verticalGaussian as well to obtain verticalresolution.
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Radiative Transfer for one cube
I Given power propagating from aboveand below: quantify how muchtransmitted and reflected in eachdirection.
I Update the power propagating to nextcubes.
I Can use PROSPECT or measurementsfrom literature to determine values forreflection and transmission forleaves/needles and branches.
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Radiative Transfer for one column
I Light is tracked as it propagatesdown and then up a single column ofcubes.
I At each time step one cube istraversed, with both a downgoingand an upgoing light power value.
I Ground reflectance is approximatedbased on data in literature.
I The upgoing light at the top of thecanopy is the reflected LIDAR signal.
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Short Trees
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Medium Trees
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Tall Trees
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Low Biomass
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Medium Biomass
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High Biomass
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Parameter Estimation Procedure
One possible way of using modeling for parameter estimation:
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Thanks for your attention
You can contact me at:[email protected]
Viewgraphs available at:http://www.eecs.umich.edu/~lep/lidar optical talk 2014.pdf
or:
http://tinyurl.com/lep2014models
Pierce Electromagnetic Modeling