# Presentation: 276665

## BIOPHYSA PHYSICALLY-BASED CONTINUOUS FIELDS ALGORITHMand Climate and Carbon Models

- FORREST G. HALL, FRED HUEMMRICH
- Joint Center for Earth Systems Technology (JCET)
- NASA's Goddard Space Flight Center
- Greenbelt, MD 20771
- Derek Peddle
- Lethbridge University
- Alberta, Canada
- David Landis
- SSAI
- Lanham, MD

**Notes:**
Chris asked me if I would give a brief update on the work that Fred, Derek, Dave and I are doing. As this title suggests, we are developing a physically-based approach to directly infer spatial fields of vegetation structure (canopy cover fraction, leaf area, leaf angle distribution and so on) from MODIS.  This work is outgrowth from work started years ago, I won’t say just quite how many, to move satellite image analysis away from purely empirical techniques, and toward physically-based techniques grounded in canopy radiative transfer theory.  I believe that what makes this a real possibility today is the improvement in satellite calibration and atmospheric correction and the improvements in computer processing speed, retrieval algorithms, and especially computer memory.

## The Chasm

-      si = (LAD, LOP, BOP, h/w,
- LAIC, LAIb, CC)

- NDVI

- CANOPY
- MODELER

- Climate, Carbon
- Modeler

**Notes:**
Before I get to the nuts and bolts, I’d like to show  this cartoon to remind us of where we have been in algorithm development. You don’t see a lot of computer modelers that look like Bill Gate’s Powerpoint clipart version, but they make the point that the 30+ years of research in developing canopy radiative transfer models still have not completely found their way into remote sensing algorithms. Over those 30 years, The CRT modeler has managed to accurately calculate a number of canopy optical and structural parameters in terms of the BRDF,   yet the C&C modeler usually has one thought on his mind when it comes to remote sensing of land surface properties.  

## Remote Sensing

- Algorithms
- Fapar = F(si| LC)
- Land Cover (LC) Classification

- Climate, Carbon Models

- Parameter
- Maps
- (Fpar, LC)
- LAI = F (Fpar, LC)

- Satellite
- (spectral, angular, temporal)
- si (Ωi)

- , Fpar, gc, Zo, Pv,NPv, LAI
- B Cndtns, Validation, Assimilation

- LOP&BOP= leaf&background
-  	optical properties
- Cg = Canopy geometry
- LAIC = Crown leaf area index
- LAIb = Branch leaf area index
- CC = fractional crown cover

- Classification Algorithms (CA)
- LC = CA(si)

- si (Ωi) =(LOP, BOP,Cg,
-        h/w, LAIC, LAIb, CC)

- = F (LAI, Fpar, LC)

- Problems
- Algorithm Locality: Spectral change with illumination view geometry, background, season etc.affects robustness.
- “Chicken & Egg Syndrome”: Radiance correction for view and illumination angle to infer biophysical parameters depends on the parameters.
- Parameter Inconsistency: Different algorithms for different parameters.
- Error structures: Error, uncertainty characterization  approximate, empirical.
- Model utility: Inability to directly assimilate satellite radiances in CWE models.

**Notes:**
What the climate and carbon modelers usually want are parameters like these shown here; albedo, Fpar, stomatal conductance, surface roughness, leaf area, photosynthetic and non-photosynthetic vegetation fraction. But  surface reflectance inferred by satellites is not directly related to any of these,  rather the optical and structural properties of the canopy. Canopy reflectance is determined by photon transfer through the canopy whereas manyof the CWE parameters are determined by canopy molecular transport. For example, the roughness length parameter modelers want is an expression of the strength of the rate of turbulent transfer of momentum,  between the wind and the canopy as air molecules, not photons, pass through the canopy.  Zo is of course larger for tall trees with lots of leaf area than for grasses.  A putting green for example. So the same parameters that affect momentum transfer also affect photon transfer, but not in the same way.  Thus Zo must be computed within the CWE model using a different set of equations that utilize LAI and canopy geometry as inputs. The key thing is that the modeler doesn’t care about the land cover type.  She only cares about the LAI and canopy geometry values needed to compute Zo.  The same kind of logic goes for the rest of these CCM  parameter.  Each can be computed using parameters that affect and can be inferred from canopy reflectance.  Remote sensing algorithms for the most part don’t use this progression from photon transport to CCM parameters.  Rather they compute the CCM parameters from empirical relationships, regression-derived in essence, as a function of reflectance, mostly vegetation indices, where the regression parameters are  dependent upon the land cover type.  The land cover type is in turn  derived from the same reflectance, using various statistical or rule-based classification algorithms which must be trained using training sites.  Biophysical parameters and landcover type are then passed to the climate carbon models as parameter maps, which the modelers must then map back to the parameters they really need.  If its trees they select one set of parameters to compute Zo.  If it’s a putting green, another. The well-known MODIS products such as land cover, Fpar, LAI etc.  In the case of the current MODIS algorithm, Fpar, LAI are physically based on a radiative transfer model, but require land cover type labels derived from separate algorithms.   This method has a number of problems . PROBLEMS which I would like to cite here.   

## BIOPHYSAn Analysis Framework linking 30+ Years of Canopy Radiative Transfer Model Research Directly to Biophysical Parameter Retrieval

**Notes:**
 Now how do we propose to address these problems?  BIOPHYS is not so much an algorithm, but an analysis and research framework that will allow us to link directly the knowledge of how vegetation affects radiation, expressed in the form of CRT models, within the CWE model structures.  And that knowledge I might add is pretty substantial at this point.

## Satellites

- (spectral, angular, temporal)
- si (Ωi)

- CANOPY CRT MODEL (Tables)
- {si}= (LOP,BOP,Cg,LAIC,LAIb,CC)
- Satellite Measurement (L2)
- {si±∆ si}i i bands, angles, dates
- Table Lookup
- {LOP,BOP,Cg,LAIC,LAIb,CC }k  {si±∆ si }i
- Compute Parameter Statistics
- <{LOP,BOP, Cg ,LAIC,LAIb, CC}>
- Model Parameters
- , Fpar, gc, Zo, Pv,NPv=
- F(<LOP,BOP, Cg,LAIC,LAIb, CC>)

- Biophys Framework

- Numerical, Non-analytic

**Notes:**
 And in this slide, in a somewhat abstract way I will describe the framework, which we have chosen to implement in a numerical rather than an analytic form,  and in the next couple of slides get less abstract by discussing the particular form of this framework within our effort.  As before, we begin with satellite LII observations of surface reflectance at different viewing and illumination angles Ωi, and in different bands Si.      DESCRIBE FRAMEWORK.  Now, some of you will note that this is not very different from the approaches we have heard described in this meeting to retrieve water vapor, atmospheric co2, aerosols and the like.  What is new here perhaps is the application to vegetated surfaces.

## BIOPHYS 

- Multi-Date BRDF Values
- (Xi,Ωi)
- Canopy Parameter Values
- LADi,LOPi,BOPi,hi/wi,LAICi,LAIbi, CCi

- CANOPY CRT
- MODELS
- GOMS, GORT, 5-scale

- MODIS
- MEASURED BRDF
- (i Ωi,ti)

- MODIS SURFACE
- Multi-Date BRDF Values
- (Xi,Ωi)
- Canopy Parameter Values
- LADi,LOPi,BOPi,hi/wi,LAICi,LAIbi, CCi

- BIOPHYS

- LookUp
- Table

- CWE Parameters
- , Fpar, gc, Zo, Pv,NPv...
- Canopy RT Parameters
- LAD,LOP,BOP,h/w,LAIC,LAIb, CC

- Climate, Carbon
- Models

- MODIS SURFACE
- Multi-Date BRDF Values
- (Xi,Ωi)
- Canopy Parameter Values
- LADi,LOPi,BOPi,hi/wi,LAICi,LAIbi, CCi

- MODIS SURFACE
- Multi-Date BRDF Values
- (Xi,Ωi)
- Canopy Parameter Values
- LADi,LOPi,BOPi,hi/wi,LAICi,LAIbi, CCi

- MODIS SURFACE
- Multi-Date BRDF Values
- (i,Ωi)
- Canopy Parameter Values
- LADi,LOPi,BOPi,hi/wi,LAICi,LAIbi, CCi

**Notes:**
As promised then, lets get a little more down to reality and describe the earthly form of BIOPHYS, and some preliminary results of our work so far.   As I’ve just said, BIOPHYS in grounded in canopy radiative transfer models and its structure directly links CRT models with CCM models and in fact could be incorporated directly in them.  We are in the process of running and testing models now and will quickly need to settle on one. But note the framework can incorporate any model. Anyway,  for each combination of parameters in the model we generate  reflectance (i,Ωi), for each sensor band a view and illumination angle ΩI .  We will then generate a table, which can be thought of as having a single column with lots of rows.  Each row will contain the particular values of parameters input into the CRM, the particular view and illumination angle chosen to generate a model reflectance value, and the reflectance in each sensor band.  In this chart, each row is represented by a card.  Each card corresponds to a particular set of biophysical parameters.  Think of the reflectance values and the view and illumination angle values as a phone number.  If we have 5 bands and 8 combinations of view and illumination angles that will be a phone number with 40 digits.  Now for this particular view-illumination angle configuration we will generate reflectance values for each combination of biophysical parameters in the model.  In the example here, I have 8 unknowns and 13 measurements, so in principle I can solve for the unknown biophysical parameters.  

Now, suppose I make a reflectance measurement in 5 bands at 8 different look and illumination angles.  All I need to do is look in the table and find the card or cards who have that set of reflectance values (the phone number), then look on the card to see what canopy model parameters I used to generate that set of reflectance values.  In this simple example, I have shown three cards that match.  But which one is the right answer?  In fact, I can’t tell based on the spectral measurements alone, so I am faced with either taking some kind of average of these answers, or using non spectral information, such as slope or aspect on which the pixel resides, to further constrain the solutions.  For example, if I have a topo map that locates bogs and fens,  I know that I won’t be finding aspen in those areas and can eliminate some possible solutions.  But the best I might be able to do is to recognize there is some uncertainty in the solution and examine the statistics of the possible solutions to obtain a best answer.  Note though that the distribution of the possible solutions automatically provides me the error structure of the estimate.  More about that in a moment.

## BIOPHYS/MFM

- Multi-Date BRDF Values
- (Xi,Ωi)
- Canopy Parameter Values
- LADi,LOPi,BOPi,hi/wi,LAICi,LAIbi, CCi

- CANOPY CRT
- MODELS
- GOMS, 5-scale

- MODIS
- MEASURED BRDF
- (i Ωi)

- MODIS SURFACE
- Multi-Date BRDF Values
- (Xi,Ωi)
- Canopy Parameter Values
- LADi,LOPi,BOPi,hi/wi,LAICi,LAIbi, CCi

- SIMPLE, ELEGANT

- Can Use Non-Spectral
- Data (e.g. slope, aspect,
- biome, time, GDD)
- to Further
- Constrain Solutions

- LookUp
- Table

- CWE Parameters
- , Fpar, gc, Zo, Pv,NPv...
- Canopy RT Parameters
- LAD,LOP,BOP,h/w,LAIC,LAIb, CC

- Climate, Carbon
-  Models
-  Fpar, gc, Zo, Pv,NPv...
- Fi (LAD,LOP,BOP,h/w,LAIC,LAIb, CC)

- Climate, Carbon
- Models

- Compute
- Parameter
- Statistics

- MODIS SURFACE
- Multi-Date BRDF Values
- (Xi,Ωi)
- Canopy Parameter Values
- LADi,LOPi,BOPi,hi/wi,LAICi,LAIbi, CCi

- MODIS SURFACE
- Multi-Date BRDF Values
- (Xi,Ωi)
- Canopy Parameter Values
- LADi,LOPi,BOPi,hi/wi,LAICi,LAIbi, CCi

- MODIS SURFACE
- Multi-Date BRDF Values
- (i,Ωi)
- Canopy Parameter Values
- LADi,LOPi,BOPi,hi/wi,LAICi,LAIbi, CCi

- _TABLE LOOKUP _
- RETURN ALL ROWS FROM LOOK UP TABLE : SELECT*FROM TABLE WHERE
-  (SCENE_REFL_RED_SZA30 BETWEEN 0.0487-0.01 AND 0.0487+0.01 AND SCENE_REFL_NIR_SZA30 BETWEEN 0.2172-0.01 AND 0.2172+0.01)
- AND (SCENE_REFL_RED_SZA45 BETWEEN 0.0372-0.01 AND 0.0372+0.01 AND SCENE_REFL_NIR_SZA45 BETWEEN 0.1730-0.01 AND 0.1730+0.01)
- AND (SCENE_REFL_RED_SZA50 BETWEEN 0.0458-0.01 AND 0.0458+0.01 AND SCENE_REFL_NIR_SZA50 BETWEEN 0.1474-0.01 AND 0.1474+0.01);

- MEASUREMENT= [(RED =  0.0487& NIR = 0.2172 at SZA = 30o),
-                     (RED = 0.0372 & NIR = 0.1730 at SZA = 45o),
-                     (RED = 0.0458 & NIR = 0.1474 at SZA = 50o)]

**Notes:**
With that context then, of what we are trying to accomplish, the goal we are trying to reach, let me describe the broad outlines of BIOPHYS, and some preliminary results of our work so far.  I think you will find that the concept is extremely simple, extremely powerful, and I think quite elegant.  As I said earlier, BIOPHYS in grounded in canopy radiative transfer models.  We are considering two possibilities for the MODIS version of BIOPHYS, GOMS, developed by Boston University, and 5-Scale developed by Jing Chen and colleagues.  For each combination of parameters in the model we generate reflectance i, for each sensor band a view and illumination angle ΩI .  We will then generate a table, which can be thought of as having a single column with lots of rows.  Each row will contain the particular values of parameters input into the CRM, the particular view and illumination angle chosen to generate a model reflectance value, and the reflectance in each sensor band.  In this chart, each row is represented by a card.  Think of the reflectance values and the view and illumination angle values as a phone number.  If we have 5 bands and 8 view and illumination angles (back and forward scatter and four  solar zenith angles) that will be a phone number with 11 values.  Now for this particular view-illumination angle configuration we will generate reflectance values for each combination of biophysical parameters in the model.  In the example here, I have 8 unknowns and 13 measurements, so in principle I can solve for the unknown biophysical parameters.  

Now, suppose I make a reflectance measurement in 5 bands at 8 different look and illumination angles.  All I need to do is look in the table and find the card or cards who have that set of reflectance values (the phone number), then look on the card to see what canopy model parameters I used to generate that set of reflectance values.  In this simple example, I have shown three cards that match.  But which one is the right answer?  In fact, I can’t tell based on the spectral measurements alone, so I am faced with either taking some kind of average of these answers, or using non spectral information, such as slope or aspect on which the pixel resides, to further constrain the solutions.  For example, if I have a topo map that locates bogs and fens,  I know that I won’t be finding aspen in those areas and can eliminate some possible solutions.  But the best I might be able to do is to recognize there is some uncertainty in the solution and examine the statistics of the possible solutions to obtain a best answer.  Note though that the distribution of the possible solutions automatically provides me the error structure of the estimate.  More about that in a moment.

## Canopyvis, nir

- LADi,LOPi,BOPi,hi/wi,LAICi,LAIbi, CCi

- SIMPLE EXAMPLE
- USING GEOSAIL

- Canopyvis, nir
- Canopy Parameters

- LAIavg within
- (±0.5%) vis, nir  cells

- Canopy vis, nir
- Canopy Parameters

- Canopy vis, nir
- Canopy Parameters

- Canopyvis, nir
- Canopy Parameters

- 70,000 values

- LAIi = LAICiXCCi

- # Obs within a
- (±0.5%) vis, nir cell
- SZA = 30o

- Standard Deviation of LAIavg within
- (±0.5%) vis, nir  cells

**Notes:**
First, I want to illustrate the general concept that I have just outlined, with a simple example using GeoSail, the canopy reflectance model developed by Fred.

## Initial Retrieval TestLandsat, vis, nir (± 0.01)16 sites,3 solar angles (3 dates)1983 Superior National Forest

## Retrieval TestLandsat, vis, nir, 3SZA’s Crown Green LAI

- Three SZA retrievals drastically reduced the number of records returned.
- For only one SZA, generally the maximum SZA returned more records.
- With two SZA either the low pair or the high pair returned the most records.

- Number of retrieved records

**Notes:**
The more constraints one puts on the retrieval, the fewer number of records are returned, with thousands of records returned for a single SZA, around 500 records returned for two SZA, and a couple of hundred or less for three SZA.  For only one SZA, generally the maximum SZA returns more records.  With two SZA either the low pair or the high pair may return the most records.

## Average Retrieved Crown Green LAI

- Average Retrieved Crown Green LAI varied little using 2 or more SZAs.

- Average Crown Green LAI

## Average Retrieved Crown Cover Fraction

- Average Retrieved Crown Cover Fraction Sensitive to SZA

- Average Fractional Canopy Cover

## Retrieval Precision vs Number of Records Retrieved-Crown Green LAI

-  Crown Green LAI

## Retrieval Precision vs Number of Records Retrieved-Crown Cover

-  Crown Fractional Canopy Cover

## Distribution of LAI Retrievals16 sites,3 solar angles (3 dates)1983 Superior National Forest

- Distribution of LAI Retrievals16 sites,3 solar angles (3 dates)1983 Superior National Forest

## Retrieval ResultsDistribution of Site LAI Retrievals

- Retrieval ResultsDistribution of Site LAI Retrievals

## Retrieval ResultsDistribution of Canopy Component Retrievals - Crown LAI and CC

- Retrieval ResultsDistribution of Canopy Component Retrievals - Crown LAI and CC

- LAI = LCi X CCi

## Retrieval ResultsAll SNF Spruce Sites

- Accuracies roughly equivalent to empirical approach
- Error structure automatically retrieved

## BIOPHYS

- Algorithm Locality: Physically-based retrievals incorporate reflectance responses to exogenous variables.
- “Chicken & Egg Syndrome”: BIOPHYS uses spectral dependence on view and illumination angle to improve retrieval accuracies.
- Parameter Inconsistency: BIOPHYS Parameter retrievals from a single algorithm using common input data.
- Error structures: Error, uncertainty an integral part of the retrieval.
- Model utility: BIOPHYS structure can assimilate data directly from within CWE models.

- Problems
- Algorithm Locality: Spectral change with illumination view geometry, background, season etc.affects robustness.
- “Chicken & Egg Syndrome”: Radiance correction for view and illumination angle to infer biophysical parameters depends on the parameters.
- Parameter Inconsistency: Different algorithms for different parameters.
- Error structures: Error, uncertainty characterization  approximate, empirical.
- Model utility: Inability to directly assimilate satellite radiances in CWE models.

## BIOPHYS FRAMEWORK & OSSEs

- OBSERVING SYSTEM SIMULATION EXPERIMENT (OSSE)
- OSSEs compute sensor/platform reqts in terms of biophysical parameter reqts.
- BIOPHYS FRAMEWORK provides a physically-based framework for computing
- Retrieval precision as a function of sensor S/N
- Retrieval bias as a function of sensor cal bias
- Retrieval error as a function of band selection
- Retrieval error as a function of CRT models

## Finally

- BIOPHYS Framework Can Bridge the Chasm
- What’s Next
- Wrap up exploratory work
- Investigate convergence of mean to actual
- Select RT Model (GOMS, GORT ...). Build the LUTs
- Complete MODIS BIOPHYS Algorithm
- Evaluate  MODIS Products and Iterate
- PRODUCE PROVISIONAL DATA SETS WITH BIOPHYS OVER SELECTED STUDY REGIONS.
- PLACE PROVISIONAL DATA SETS ONLINE; INITIATE USER EVALUATION.

**Notes:**
Selecting the RT model to be used is a bit of a problem for us.  Imost RT models are parameterized with variables that can be used in turn compute the parameteric input to CWE models.  But in my opinion, there has not yet been a conclusive evaluation of the many available RT models against independent observations of surface BRDF for the significant surface types required globally.  Micheal Verstrats effort to compare model outputs to each other has been quite useful.  

## The Chasm

- CANOPY RT
- MODELER

- Climate, Carbon
- Modeler

- 2000 MODIS LAI, FPAR

- Circa 1972- Modeling

- Circa 1980 - Inversion

- Circa 1996 Physically -Based Classification/MFM
- For Landsat

- BIOPHYS