Dario Papale Contributi: Vern Vanderbilt, TA- Quinn Hart, M. Meroni, CCRS

1. Remote sensing and modeling in forestry Lecture 11 Models Dario Papale Contributi: Vern Vanderbilt, TA- Quinn Hart, M. Meroni, CCRS

2. What is affecting canopy reflectance 1. Absorption and reflection of the canopy elements at different wavelengths (leaves, branches, trunks, flowers, fruits, understory, soil etc.) 2. Canopy architecture (overstory biomass, LAI, leaves distribution, degree of coverage, etc.) 3. Remote sensing system (geometry Sun-target-sensor, atmosphere interaction etc.)

3. Δ A β Vegetation indexes For this reason the vegetation indexes are based in particular on reflectance in red and NIR

4. Intrinsic indexes SR (Simple Ratio) It is the easiest VI. It can have values between 0 and infinite, in particular between 0 and 1 for soils and between 6 and 10 for green vegetation. NDVI (Normalized Difference Vegetation Index) The most used and common. Values between -1 and 1, in particular less than 0 for water, just above 0 for bare soils and between 0.4 and 0.7 for vegetation. Only very dense vegetations reach NDVI = 0.8.

5. Use of vegetation indexes for spatialization Satellite images Variable of interest measured with geographic position (GPS) Georeferencing VIs calculation at the ground Measurement points Regression VIs/variable Best VI selection VI calculated on the full image Regression application Map ofthe variable

6. Vegetation Index LAI, biomass, … Saturation One of the most important limits of the vegetation indexes is that above a certain limit they saturate. For this reason they are more indicated for sparse vegetation The alternative to the VIs are the models, in particular the models based on the physics of the reflection processes of leaves and canopy

7. Models Models are simplifies representations of the real world (Wainwright and Mulligan 2004) Models don’t include all the characteristics of the process that want to reproduce and try to include all the most important and characteristic. Models in remote sensing, differently from vegetation indexes, are often based on some knowledge ofthe process of interest or of the relation between reflectance and chemical/physical properties of the object, trying to maximize the use of data and knowledge.

8. Models All the models are however based on some assumptions because there are aspects of the real world unknown or difficult to replicate and that needs to be simplified. In the models there are three main entities Constants: values that don’t change with the system that we want to model (e.g. the Solar constant or the speed of light in vacuum) Parameters: elements that can change their value but are fix in the single application or system (e.g. ratio between height and diameter of a specific forest analyzed) Variables: are the model input and a free to change in the simulations (e.g. diameter value used to calculate the heights using a H-Diam function)

9. Empirical and process models Empirical or statistical • Relations between input and output are defined using the data without imposing them and also without knowing the process • Very efficient and quite easy • Problems in the extrapolation or where the data used don’t represent all the most important conditions Process-oriented • The system under study is re-built in order to simulate its behavior • Based on scientific knowledge of the processes and system • In general complex • Can be applied in extrapolation Input Output Black box Input Output Glass box

10. Remote sensing and carbon balance The epsilon-models or radiation use efficiency models GPP = g (Qa) Qa = absorbed radiation Qa = Qi x %ass = FAPAR Qi = incirent radiation %ass = absorbed percentage

11. Remote sensing and carbon balance The epsilon-models or radiation use efficiency models FAPAR can be estimated for remote sensing, generally using models but it is also strongly correlated with vegetation indexes. For example in 1982 Kumar and Monteith proposed for AVHRR data the equation: FAPAR = 1.08 x NDVI – 0.08 So our equation become GPP = g (PAR x FAPAR)

12. Remote sensing and carbon balance The epsilon-models or radiation use efficiency models It has been demonstrated (e.g. Monteith 1972) that the g function is almost linear so: ε, known also as RUE, is the radiation use efficiency: GPP = ε x PAR x FAPAR

13. Remote sensing and carbon balance The epsilon-models or radiation use efficiency models GPP = ε x PAR x FAPAR What is influencing the value of epsilon? ε = εmax x f1 x f2 x f3 x … Linear reduction factors (between 0 and 1) linked to the environmental conditions: Ta, Ts, VPD, SWC, … Maximum potential efficiency in optimal conditions

14. Absorbed Photosynthetically Active Radiation Radiation Use Efficiency GPP = (Rnet*0.45*Fpar) * {max* [mTmin] [mvpd] } Mod15 (remote sensing) NEP=GPP – Reco L’esempio del MOD17+ GPP = APAR * 

15. Additional independent measured true data New model & parameters Validation Others data (e.g. at different spatial resolution Model-data-fusion-validation Model (Structure, Assumptions) Measured true data Model improvement parameterization

16. Importance of parameterization and validation in different conditions Wellwateredconditions 0.2 Eddy cov. (a) (b) 0.18 Sap flow 0.16 Modelled 0.14 0.12 H2O flux [mm/h] 0.1 0.08 0.06 0.04 0.02 0 Eddy cov. (c) (d) 12 Modelled 10 8 6 CO2 flux of GPP [µmol m-2 s-1] 4 2 0 -2 0 4 8 12 16 20 24 0 4 8 12 16 20 24 Local time [hr] Local time [hr] Droughtstressedconditions Reichstein, Tenhunen et al., Global Change Biology, 2002

17. Target region The multiple constrain Reichstein et al. 2003, JGR

18. Example of the RUEmax parameterization using measuremetns in the MOD17 model 1.8 1.6 1.4 1.2 1 RUE [gC / MJ APAR] 0.8 0.6 0.4 0.2 0 ENF EBF DBF MF Sav Oshrub Crop

19. Leaf reflectance Radiative transfer models Based on models that can reproduce the spectral reflectance of a single leaf and a canopy Leaf reflectance model- LRM Simulate spectral reflectance, absorbance and transmittance of a single leaf starting from its chemical and physical characteristics • Leaf characteristics • Clorophyll • Water • Structure LRM

20. Leaf reflectance Canopy reflectance Radiative transfer models Based on models that can reproduce the spectral reflectance of a single leaf and a canopy Canopy reflectance models - CRM Simulate the spectral reflectance of the canopy starting from the leaves characteristics, canopy structure, soil spectral reflectance of the soil, light conditions, data acquisition system etc. CRM • Data acquisition • Light • Geometry • Canopy characteristics • Structure • Soil • LAI

21. Leaf reflectance Canopy reflectance Models inversion • Leaf characteristics • Clorophyll • Water • Structure • Canopy characteristics • Structure • Soil • LAI • Data acquisition • Light • Geometry LRM Join models Inverted models CRM