A PROBABILISTIC APPROACH TO ESTIMATE THE GROWTH STAGE OF RICE CROPS - PCE METAMODELS AND GLOBAL SENSITIVITY ANALYSIS -
Onur YÜZÜGÜLLÜ1, Stefano MARELLI2, Esra ERTEN3, Bruno SUDRET2, Irena HAJNSEK1,4 (1) (2) (3) (4)
Institute of Environmental Engineering, ETH Zurich, CH-8093 Zurich, Switzerland Institute of Civil Engineering, ETH Zurich, CH-8093 Zurich, Switzerland Faculty of Civil Engineering, Istanbul Technical University, TR-34469 Istanbul, Turkey Microwaves and Radar Institute, German Aerospace Center (DLR), Wessling 82234, Germany
Introduction
MAIN GOAL
WHY
Determining the growth stage of rice fields based on a realistic morphology scattering model and understand their backscattering behaviour
Rice growth stage monitoring provides information about plant health and yield
HOW
WITH
WHERE
Probabilistic Search Algorithm over a Simulated Solution Space using a Complex EM Scattering Model
X-Band Polarimetric Synthetic Aperature Radar (PolSAR) data (HH/VV)
The border of Turkey and Greece by the Maritsa (a.k.a. Meriç, Evros) river.
Problem
Backscattering characteristics of the rice canopies
Phenological growth stage
Morphology of the rice plant
(e.g. Leaf and tiller number, panicle emergence)
(e.g. Stalk height and diameter, leaf length)
Methodology
Statistical Pre-Classification
?
Polarimetric SAR Data
Growth Scale
SITUATION •
Different growth stages may have similar polarimetric signatures
•
Polarimetric parameters have specific temporal trends
•
High dynamic range
•
Machine learning techniques need to be trained for each new campaign
PRE-CLASSIFICATION METHOD •
3 parameters are used (VV intensity, absolute co-polar coherence and co-polar phase difference)
•
5 stages are aimed based on the IRRI scale • Stage 1,5: Coherence and phase difference • Stage 2-4: Temporal gradient of the VV intensity of two consequtive acquisitions
IRRI © Figure above from: Erten, E., Rossi, C., Yuzugullu, O. 2015, IEEE Geoscience and Remote Sensing Letters, 12, 7
Methodology
EM Scattering Model
?
Crop Morphology
Polarimetric SAR Data
SITUATION •
Physical structure vs. scattering behaviour
•
Morphological changes should be observed polarimetrically R2 = 0.87 RMSE= 2.04 dB
MORPHOLOGY BASED SCATTERING MODEL • •
Based on the morphology of the rice plant [I,II,III] Coherent sum of 4 scattering mechanisms to estimate σHH and σVV intensities 𝐸𝑞𝑠 𝑟 =
•
𝑒 𝑖𝑘𝑟 𝑟
𝑆1 + 𝑆2 + 𝑆3 + 𝑆4 𝐸𝑝𝑖
Backscattering model successfully estimates the trend of intensities through vegetative and reproductive stages.
[I] Le Toan, T., Ribbes, F., Wang, L., et al. 1997, IEEE Trans. Geosci. Remote Sens., 35, 41 [II] Karam, M., Fung, A., & Antar, Y. 1988, IEEE Trans. Geosci. Remote Sens., 26, 799 [III] Karam, M. A. & Fung, A. K. 1989, IEEE Trans. Geosci. Remote Sens., 27, 687
R2 = 0.84 RMSE= 1.84 dB
Early Vegetative
Late Vegetative Early Reproductive
In the figure above, different colors represent different fields.
Methodology
PCE Metamodel
Crop Morphology
Scattering model (Faster?)
SITUATION •
•
•
Scattering model is computationally expensive, therefore slow…
POLYNOMIAL CHAOS EXPENSION METAMODEL
GLOBAL SENSITIVITY ANALYSIS
•
Substitutes the backscattering model with a polynomial approximation called metamodel [I]
•
Estimates the the uncertainty in the model output…
•
For a given input (X),output vector (Y) and unknown coefficients (𝛾𝑘 )
•
It can be calculated by means of variance…
•
This variance is decomposed into effect of each model input and group of inputs.
•
Sobol’ indices explain the decomposed total variance.
•
Higher the Total Sobol’ indice means more significant the parameter in the model output.
The important morphological parameters are not clearly known… A global sensitivity analysis is needed…
Polarimetric SAR Data
∞
𝑌=𝑓 𝑋 = •
𝑗=0
𝛿 is minimized with the derived metamodel (ℳ) 𝛿 = 𝑎𝑟𝑔𝑚𝑖𝑛
•
𝑦𝑗 𝛾𝑘 𝑋
1 𝑁
𝑁
𝒀𝑘 − ℳ𝑘 (𝑿)
2
𝑘=1
The PCE metamodel for the backscattering model has lowest R2 value of 0.80 and highest RMSE of 1.93 dB.
[I] Blatman, G. & Sudret, B. 2010, Reliability Engineering & System Safety 95, 11
Methodology
Probabilistic Model Inversion
Polarimetric SAR Data
?
SITUATION
PROBABILISTIC MODEL INVERSION
•
Single backscattering signature may represent more that one crop morphology…
•
Focuses on the set of possible morphologies for a measured backscattering value over a parameter space.
•
Small changes in the model, results in multiple similar solutions…
•
Approach is able to handle any size of samples. To detect in-field heterogeneity pixel sized samples, to detect general behaviour field mean is used.
•
Thus, analytical optimization is not possible…
•
The data is classified previously a coarse growth stage using the statistical pre-classification…
Solution space is bounded by both backscattering intensity and morphological consistency
•
Output is the probability distribution for each morphological parameter
•
Crop Morphology
Methodology
Probabilistic Model Inversion
Crop Morphology
?
Growth Stage
SITUATION • • •
Every crop is a complex structure and morphology is not fully covered by phenology BBCH: A quantitative universal growth scale for several crops. It varies between 1 and 99. Therefore, there is no direct relation between plant morphology and BBCH growth scale
Morphology Parameters • • • •
BBCH Parameters
Stalk height and diameter Leaf length and width Panicle length and diameter Number of tillers, leaves and panicles for each plant
vs.
• • • • •
Number of leaves unfolded Number of tillers detectable % Panicle emerged Visibility of flowers Grain condition (Early, medium, late) R2=0.92
Plant Morphology nTraining = 200
PCE Metamodel
BBCH Growth Stage nTest = 200
Methodology
Polarimetric SAR Data
Summary
Statistical Pre-Classification
IRRI Growth Stage
Probabilistic Inversion with EM Metamodel
Morphology & BBCH Metamodel
BBCH Growth Stage
Materials SAR Campaign • • • • •
TerraSAR-X (TSX) [9.65 GHz] Dual-pol SLC [HH,VV] Incidence angle: 31° Ascending April to October 2014 6 acquisitions
Ground Campaign • Average sampling interval: 11 days • May to September 2014 • 6 independent rice fields
Total Intensity (30/05/14)
Materials SAR Campaign • • • • •
TerraSAR-X (TSX) [9.65 GHz] Dual-pol SLC [HH,VV] Incidence angle: 31° Ascending April to October 2014 6 acquisitions
Ground Campaign • Average sampling interval: 11 days • May to September 2014 • 6 independent rice fields
Results
Statistical Pre-classification
Measurement Data FALSE 14%
S2
6
1
85.7
S2
19
100
S3
1
S4
3
S1
Classifier Result TRUE 86%
S3
S4
6
100
79.2
0 100
•
36 test data
•
79.2 % lowest classification accuracy
•
86.0 % total classification accuracy with κ=0.762
85.7
S5 User Accuracy (%)
S5
Precision (%)
S1
-
0 0
-
-
κ=0.762
IRRI Growth Phases
Results Early vegetative σHH&σVV: stalk height
σHH: stalk diameter
Global Sensitivity Analysis Late vegetative σHH&σVV: vertical
density and the canopy height
σVV: stalk diameter
Early reproductive
Late reproductive
Maturative
σHH&σVV : stalk height
σHH&σVV: stalk height
σHH: vertical density
σHH: vertical density
σHH: vertical density
σVV: stalk height and panicle density
σVV: panicle width and
σVV: panicle density
density
Stalk height (sh)
Stalk diameter (sd)
Leaf length (ll)
Leaf width (lw)
Number of stalk /m2 (ns)
Number of tiller/m2 (nt)
Number of leaf/m2 (nl)
Panicle length (pl)
Panicle width (pw)
Number of panicle/m2 (np)
Results
• Each morphological parameter as output is a distribution…
• Provided morphologies are consistent… • Example: Example field from late vegetative stage
Probabilistic Search Space Algorithm
Results
•
Similar to output morphologies, BBCH is a distribution as well
•
For the test fields the PCE has R2 value of 0.94 with RMSE of 5.80
•
Handling in-field heterogeneity
•
Growth maps are created using the mean values from the fields
Growth Stage Estimation
Summary GOAL
Determining the growth stage of rice fields
PROBLEM
Relation between the scattering behaviour and the growth stage of rice crops are challenging
METHOD
Statistical pre-classification followed by a probabilistic inversion of an electromagnetic scattering model
PROS
• Recuded computational cost • Possible to observe in-field heterogeneities • It is possible to estimate plant morphology and phenology
CONS
• Scattering model is incoherent • Up to now, only valid for rice crops in X-band • Needs morphological boundaries for the plant (Available from the agriculture experts)
NEXT
• Tests in different frequency and polarizations for rice crop • Tests in different crops
