Retrieval of Soil Moisture and Vegetation Canopy Parameters With L-band Radar for a Range of Boreal Forests Alireza Tabatabaeenejad, Mariko Burgin, and Mahta Moghaddam Radiation Laboratory Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor, MI, USA

Introduction (1/3) Soil Moisture is of fundamental importance to the study and understanding of  Cycling of Water & Energy, Runoff Potential, Flood Control  Weather and Climate  Geotechnical Engineering, Soil Erosion  Agricultural Productivity, Drought Monitoring  Human Health (mosquito-transmitted diseases in wet areas) 2/33 Courtesy of ESA

Introduction (2/3) The need to monitor soil moisture on a global scale has motivated the European Space Agency (ESA)'s Soil Moisture and Ocean Salinity (SMOS) mission and the National Aeronautics and Space Administration (NASA)'s Soil Moisture Active and Passive (SMAP) mission. 3/33 Courtesy of ESA Courtesy of JPL

Introduction (3/3) In this work,  We study the radar retrieval of soil moisture, as well as canopy parameters, in a range of boreal forests.  The forward model is a discrete scatterer radar model.  The retrieval is formulated as an optimization problem.  The optimization algorithm is a global optimization scheme known as simulated annealing. 4/33

Outline  Forward Scattering Model for Forested Area  Inverse Model  Inversion of Model Parameters  Forested Area (Synthetic Data)  Forested Area (CanEx-SM10 Data)  Conclusion 5/33

Outline 6/33  Forward Scattering Model for Forested Area  Inverse Model  Inversion of Model Parameters  Forested Area (Synthetic Data)  Forested Area (CanEx-SM10 Data)  Conclusion

Forward Model: Introduction 7/33 Soil & forest parameters Scattering coefficients Frequency, incidence angle Forward Model

Forward Model: Forest Geometry Forest Geometry 8/33 * S. L. Durden, J. J. van Zyl, and H. A. Zebker, "Modeling and observation of the radar polarization signature of forested areas," IEEE Trans. Geosci. Remote Sens., May  Forward Model: A general discrete scatterer radar model by Durden et al. *

Forward Model: Scattering Mechanisms (1/2) Canopy Layer Trunk Layer Ground b g bg tg The model identifies 4 distinct scattering mechanisms: b: branch bg: branch-ground tg: trunk-ground g: ground 9/33 * S. L. Durden, J. J. van Zyl, and H. A. Zebker, "Modeling and observation of the radar polarization signature of forested areas," IEEE Trans. Geosci. Remote Sens., May  Forward Model: A general discrete scatterer radar model by Durden et al. *

Forward Model: Scattering Mechanisms (2/2)  Forward Model: A general discrete scatterer radar model by Durden et al. *  The total backscattered power, represented by the Stokes matrix, is the sum of the powers from all contributing scatterers. 10/33 * S. L. Durden, J. J. van Zyl, and H. A. Zebker, "Modeling and observation of the radar polarization signature of forested areas," IEEE Trans. Geosci. Remote Sens., May branch contribution branch-ground contribution trunk-ground contribution ground contribution

11/33 Forward Model: Parameters  The forest floor is modeled as a rough dielectric surface with a layer of nearly vertical dielectric cylinders (representing tree trunks) on top of it. The soil dielectric constant is related to the soil moisture via the soil type*  Branches are represented by a layer of randomly oriented cylinders.  The forward model uses properties of large and small branches (dielectric constant, length, radius, density, orientation) leaves (dielectric constant, length, radius, density) trunks (dielectric constant, length, radius, density) soil (volumetric moisture content, roughness RMS height) canopy height to characterize a forested area. * N.R. Peplinski, F.T. Ulaby, and M.C. Dobson, “Dielectric properties of soils in the GHz range,” IEEE Trans. Geosci. Remote Sens., vol. 33, no. 3, pp , 1995.

Forward Model: Sensitivity 12/33  Sensitivity of several dBs to soil moisture at L-band in the presence of large amount of vegetation  Less sensitivity to soil moisture as soil moisture increases  Preserved dynamic range while canopy height increases  Increase in trunk-ground double bounce counterbalanced by an increase in attenuation by trunk layer as trunk density increases.  Dielectric constants correspond to OJP trees (CanEx-SM10) and allometric relationships are hypothetical.

Outline 13/33  Forward Scattering Model for Forested Area  Inverse Model  Inversion of Model Parameters  Forested Area (Synthetic Data)  Forested Area (CanEx-SM10 Data)  Conclusion

 The forward model has too many parameters to allow inversion 14/33 Inverse Model: Allometric relations  Allometric relations can be based on actual measurements, for example  Allometric relations are used to relate unknown parameters to each other and reduce the overall number of unknowns  Ideally, one or two stand parameters can be used as kernels to describe the entire forest stand

Inverse Model: Simulated Annealing (1/2) 15/33  Simulated annealing uses an analogy between the unknown parameters and particles in the annealing process of solids.  A small randomly-generated perturbation is applied to the current model parameters.  If ΔL<0, the new state is accepted, otherwise it is accepted with probability exp(-ΔL /T) → Metropolis criterion  This process is repeated at a sequence of decreasing temperatures.

Inverse Model: Simulated Annealing (2/2) 16/33 Temperature Current State Last accepted point of the chain Best state so far

Inverse Model: Cost Function  Cost Function L where X = state pq = polarization f = frequency θ = incidence angle σ  = calculated backscattering coefficients d = measured backscattering coefficients  HH and VV polarizations components are used in the inversion 17/33

Outline 18/33  Forward Scattering Model for Forested Area  Inverse Model  Inversion of Model Parameters  Forested Area (Synthetic Data)  Forested Area (CanEx-SM10 Data)  Conclusion

Inversion of Model Parameters: Synthetic Data (1/4) Sample inversion for a sample forest using synthetic data and hypothetical allometric relationships at L-band for four unknowns 19/33  d=2.5 m, ρ tr =0.72 #/m 2, m v =0.25, h=2 cm  Dielectric constants are from CanEx-SM10 (for an OBS forest) and allometric relationships are hypothetical.  Accurate retrieval for all unknowns (soil moisture, trunk density, canopy height, roughness RMS height)

Inversion of Model Parameters: Synthetic Data (2/4) Sample inversion for a sample forest using synthetic data and hypothetical allometric relationships at L-band for four unknowns 20/33  d=2.5 m, ρ tr =0.72 #/m 2, m v =0.25, h=2 cm  Dielectric constants are from CanEx-SM10 (for an OBS forest) and allometric relationships are hypothetical.  Accurate retrieval for all unknowns (soil moisture, trunk density, canopy height, roughness RMS height)

Inversion of Model Parameters: Synthetic Data (3/4) Sample inversion for a sample forest using synthetic data and hypothetical allometric relationships at L-band for four unknowns 21/33  d=2.5 m, ρ tr =0.72 #/m 2, m v =0.25, h=2 cm  Dielectric constants are from CanEx-SM10 (for an OBS forest) and allometric relationships are hypothetical.  Accurate retrieval for all unknowns (soil moisture, trunk density, canopy height, roughness RMS height) Absolute error in d = 0 m

Inversion of Model Parameters: Synthetic Data (4/4) Sample inversion for a sample forest using synthetic data and hypothetical allometric relationships at L-band for four unknowns 22/33 Absolute error in h = 0.2 cm  d=2.5 m, ρ tr =0.72 #/m 2, m v =0.25, h=2 cm  Dielectric constants are from CanEx-SM10 (for an OBS forest) and allometric relationships are hypothetical.  Accurate retrieval for all unknowns (soil moisture, trunk density, canopy height, roughness RMS height)

Outline 23/33  Forward Scattering Model for Forested Area  Inverse Model  Inversion of Model Parameters  Forested Area (Synthetic Data)  Forested Area (CanEx-SM10 Data)  Conclusion

Inversion of Model Parameters: Overview  The data are from CanEx-SM10 in June  Data acquisition included Old Jack Pine, Young Jack Pine, and Old Black Spruce forests, located in Saskatchewan, Canada.  NASA/JPL UAVSAR flown on a Gulfstream III aircraft acquired large swaths of fully polarimetric L-band measurements.  Soil moistures and roughness RMS height are unknowns.  The other forest parameters are assumed known from ground measurement 24/33

Inversion of Model Parameters: Three forests Old Jack Pine (OJP), Young Jack Pine (YJP), Old Black Spruce (OBS) forests Old Jack Pine: Columnar trees, dry and flat sandy loam ground, densely covered with dry lichen, which is transparent at L-band Young Jack Pine: Pyramidally-shaped trees, very dry and flat sandy ground with short and sparse ground cover Old Black Spruce: Columnar coniferous trees, wet loam ground complicated by a non-uniform moss and organic layer, water puddles, and bushy understory 25/33

Inversion of Model Parameters: Measurement transects Ground measurements included a transect of 100 m along which several measurements were taken in ~10-m intervals. 26/33

Inversion of Model Parameters: Results for OJP Inversion of soil moisture at L-band  Average error (bias) is  RMS error is (6m12m) 27/33  Average error (bias) is  RMS error is 0.03 (18m36m) mυimυi σ0iσ0i Σ σ 0 i = σ 0 mυmυ

Inversion of Model Parameters: Results for YJP Inversion of soil moisture at L-band  Average error (bias) is  RMS error is 0.02 (6m12m) 28/33  Average error (bias) is  RMS error is (18m36m) mυimυi σ0iσ0i Σ σ 0 i = σ 0 mυmυ

Inversion of Model Parameters: Results for OBS Inversion of soil moisture at L-band  Average error (bias) is 0.14  RMS error is 0.24 (6m12m) 29/33  Average error (bias) is 0.92  RMS error is 0.16 (18m36m)  Average error (bias) is 0.93  RMS error is 0.11 (18m36m) Σ σ 0 i = σ 0 m υ ( □ ) mυimυi σ0iσ0i σ0iσ0i Σ m υ i = m υ (*)

Inversion of Model Parameters: Adding more unknowns 30/33  Adding canopy height and trunk density to the unknowns (four unknowns) and cross-pol backscattering coefficient to the measured data points (three data points), the error in soil moisture would be large (0.085 cm 3 /cm 3 for OJP) due to  Unreliability of the cross-pol radar measurements  Adding only canopy height to the unknowns (three unknowns) and using only co-pol data (two data points), results in an RMS error of cm 3 /cm 3 in soil moisture.

Summary and Conclusion (1/2) 31/33  L-band retrieval of under-canopy soil moisture as well as other canopy parameters using radar data was investigated.  Simulated annealing accurately retrieved soil moisture from only a few data points. (synthesize data, four unknowns, allometric relationships)  Inversion was successful for the OJP and YJP sites. (CanEx-SM10 data, two unknowns)

Summary and Conclusion (2/2) 32/33  Error was large for the OBS forest mostly due to  small sensitivity of the forward model to soil moisture for larger moisture values  possible inaccuracies in the forest parameterization  complex nature of the forest floor  L-band radar is capable of retrieving surface soil moisture in high-biomass forests (such as OJP) where the soil moisture information is mainly carried by the trunk-ground scattering mechanism.

Questions 33/33 Thank you for your interest. Do you have any questions? Further questions: Alireza Tabatabaeenejad Mariko Burgin Mahta Moghaddam