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DOE OSTI2024

Bayesian calibration and uncertainty quantification of a rate-dependent cohesive zone model for polymer interfaces

In this work we present a rate-dependent cohesive zone model for the fracture of polymeric interfaces and performs a Bayesian calibration, an uncertainty quantification, and a sensitivity analysis for the model. The proposed cohesive zone model accounts for both reversible elastic and irreversible rate-dependent separation sliding deformation at the interface. The viscous dissipation due to the irreversible opening at the interface is modeled using elastic-viscoplastic kinematics that incorporates the effects of strain rate. Inverse calibration of parameters for such complex models through trial and error is challenging due to the large number of parameters of the model. Moreover, the calibrated parameter values are often non-unique and uncertain when the available experimental data is limited. To tackle this challenge, we employ a Bayesian calibration approach to identify parameters from experimental data, the resulting parameters significantly enhance the accuracy of the model. To quantify the uncertainty associated with the inverse parameter estimation, a modular Bayesian approach is employed to calibrate the unknown model parameters, accounting for the parameter uncertainty of the cohesive zone model. The advantages of the Bayesian calibration over a deterministic parameter fit are demonstrated. Further, to quantify the model uncertainties, such as incorrect assumptions or missing physics, a discrepancy function is introduced, which significantly improves the model’s prediction. Finally, the total uncertainty of the model is quantified in a predictive setting. A sensitivity analysis is performed to assess how changes in the input variables of the model affect the peak load, facilitating the identification of a concise set of highly influential parameters. The present approach can be used for calibration and uncertainty quantification for other complex computational mechanics models. It should also facilitate the designing of interface materials under uncertainty.

42 ENGINEERING↗

DOE OSTI2023

Compensating attenuation effects in full-waveform inversion with dissipation-dispersion decoupling

Seismic attenuation poses challenges to velocity model building from acoustic/elastic full-waveform inversion (FWI). In particular, when constructing the FWI gradient for velocity inversion, recent studies have indicated that the high-attenuation structure could distort the gradient by damping the amplitudes and shifting the kinematic phases, resulting in an imbalanced update and thus unreliable velocity model. These Q effects are particularly significant in the reflection acquisition geometry due to the “double-damping” issue. Here, we develop a Q-compensated FWI algorithm for constructing a Q-free FWI gradient. By using a recently developed viscoacoustic wave propagator, this compensation can be done conveniently by keeping the dispersion term and flipping the dissipation term in the wave equation when we simulate the forward and time-reversed adjoint wavefields. The resultant gradient obtained by interacting these two wavefields has correct kinematics and Q-free amplitudes. This Q-compensated FWI can balance the update between Q- and no- Q-areas, which we determine using synthetic examples. In addition, we illustrate how to take advantage of the dissipation-dispersion decoupling to determine the anomalous Q value in the Q model building workflow via Q-compensated reverse time migration.

Geochemistry & Geophysics↗

DOE OSTI2022

Proxy-Based Bayesian Inversion Of Poroelastic Simulations To Interpret Strain Tensor Data Measured During Well Testing

The long runtimes of 3D poroelastic numerical simulators makes it impractical to interpret deformation datasets using many inversion schemes. Recent advances in instrumentation have made it possible to measure the strain tensor during well testing, but the lack of robust inversion methods is limiting the ability to interpret these data. We have developed an inversion workflow that reduces the number of computations required to complete a Bayesian inversion using DREAMzs. The workflow trains a KNN model using output from the poroelastic simulator, and then uses the KNN model as a proxy for the simulator during inversion. The workflow also includes a strategy for ensuring the results from the proxy model converge to the results from the simulator, ensuring the accuracy of the final results. An idealized example configured to represent a well test in a deep aquifer is used to verify that the workflow correctly identifies parameters and characterizes noise. Field data measured using strainmeters during an injection test at an oil reservoir in Oklahoma are used to evaluate performance with a real dataset. The workflow identified 265 history matching solutions out of 1240 total simulation runs (21% acceptance ratio), and the results are used to characterize posterior parameter distribution and evaluate the prediction uncertainty. This approach makes it feasible to invert strain data measured during well testing and this has the potential to improve the characterization of aquifers and reservoirs.

Roudini, Soheil↗

DOE OSTI2021

Spatial distributions of X CO 2 seasonal cycle amplitude and phase over northern high-latitude regions

Satellite-based observations of atmospheric carbon dioxide (CO 2 ) provide measurements in remote regions, such as the biologically sensitive but undersampled northern high latitudes, and are progressing toward true global data coverage. Recent improvements in satellite retrievals of total column-averaged dry air mole fractions of CO 2 (X CO 2 ) from the NASA Orbiting Carbon Observatory 2 (OCO-2) have allowed for unprecedented data coverage of northern high-latitude regions, while maintaining acceptable accuracy and consistency relative to ground-based observations, and finally providing sufficient data in spring and autumn for analysis of satellite-observed X CO 2 seasonal cycles across a majority of terrestrial northern high-latitude regions. Here, we present an analysis of X CO 2 seasonal cycles calculated from OCO-2 data for temperate, boreal, and tundra regions, subdivided into 5° latitude by 20° longitude zones. We quantify the seasonal cycle amplitudes (SCAs) and the annual half drawdown day (HDD). OCO-2 SCAs are in good agreement with ground-based observations at five high-latitude sites, and OCO-2 SCAs show very close agreement with SCAs calculated for model estimates of X CO 2 from the Copernicus Atmosphere Monitoring Services (CAMS) global inversion-optimized greenhouse gas flux model v19r1 and the CarbonTracker2019 model (CT2019B). Model estimates of X CO 2 from the GEOS-Chem CO 2 simulation version 12.7.2 with underlying biospheric fluxes from CarbonTracker2019 (GC-CT2019) yield SCAs of larger magnitude and spread over a larger range than those from CAMS, CT2019B, or OCO-2; however, GC-CT2019 SCAs still exhibit a very similar spatial distribution across northern high-latitude regions to that from CAMS, CT2019B, and OCO-2. Zones in the Asian boreal forest were found to have exceptionally large SCA and early HDD, and both OCO-2 data and model estimates yield a distinct longitudinal gradient of increasing SCA from west to east across the Eurasian continent. In northern high-latitude regions, spanning latitudes from 47 to 72° N, longitudinal gradients in both SCA and HDD are at least as pronounced as latitudinal gradients, suggesting a role for global atmospheric transport patterns in defining spatial distributions of X CO2 seasonality across these regions. GEOS-Chem surface contact tracers show that the largest X CO 2 SCAs occur in areas with the greatest contact with land surfaces, integrated over 15–30d. The correlation of X CO 2 SCA with these land surface contact tracers is stronger than the correlation of X CO 2 SCA with the SCA of CO 2 fluxes or the total annual CO 2 flux within each 5° latitude by 20° longitude zone. This indicates that accumulation of terrestrial CO 2 flux during atmospheric transport is a major driver of regional variations in X CO 2 SCA.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

BayesMT: A Probabilistic Bayesian Framework for the Seismic Moment Tensor

Moment tensors (MTs) have long been used in earthquake and explosion source analysis, and there has been a renewed interest in how they can inform us about the seismic source, particularly in the geophysical monitoring community due to its application in event identification and yield analysis. However, parameter uncertainties in seismic MT inversion are rarely available. The inverse procedure often does not quantify MT model errors such as event location, data noise and Earth model that are essential for estimating solution robustness. To address this need, we propose to adopt the Bayesian probabilistic framework to incorporate uncertainties in MT inversions. In this study, we present the theoretical background of a probabilistic Bayesian framework for MT inversion accounting for model and measurements errors and illustrate the implementation of the method using a synthetic example.

58 GEOSCIENCES↗

NASA NTRS1994

Microbial community structure at the U.S.-Joint Global Ocean Flux Study Station ALOHA: Inverse methods for estimating biochemical indicator ratios

Modeling biogeochemical fluxes in the marine plankton requires the application of factors for extrapolation of biomass indicators measured in the field (chlorophyll a, adenosine triphosphate, bacterial counts) to biomass carbon or nitrogen. These are often inferred from culture studies and are poorly constrained for natural populations. At least squares inverse method with a simple linear model constrains the values of several common indicator ratios, giving self-consistent solutions that provide useful information about the structure of the microbial community at our North Pacific Ocean study site (Station ALOHA (A Long-term Oligotrophic Habitat Assessment)). These results indicate that the fraction of the microbial biomass that is autotrophic (pigmented) is greater in the mixed layer than at the deep chlorophyll maximum layer and that heterotrophic bacteria are a significant but not necessarily predominant component of the microbial community in the euphotic zone.

Christian, James R.↗

NASA NTRS2002

Clues to Coral Reef Health: Integrating Radiative Transfer Modeling and Hyperspectral Data

An important contribution to coral reef research is to improve spectral distinction between various health states of coral species in areas subject to harmful anthropogenic activity and climate change. New insights into radiative transfer properties of corals under healthy and stressed conditions can advance understandings of ecological processes on reefs and allow better assessments of the impacts of large-scale bleaching and disease events, Our objective was to examine the spectral and spatial properties of hyperspectral sensors that may be used to remotely sense changes in reef community health. We compare in situ reef environment spectra (healthy coral, stressed coral, dead coral, algae, and sand) with airborne hyperspectral data to identify important spectral characteristics and indices. Additionally, spectral measurements over a range of water depths, relief, and bottom types are compared to help quantify bottom-water column influences. In situ spectra were collected in July and August 2002 at the Long Rock site in the Andros Island, Bahamas coastal zone coral reef. Our primary emphasis was on Acropora palmata (or elkhorn coral), a major reef building coral, which is prevalent in the study area, but is suffering from white band disease. A. palmata is currently being, proposed as an endangered species because its populations have severely declined in many areas of the Caribbean. In addition to the A. palmata biotope, we have collected spectra of at least seven other coral biotopes that exist within the study area, each with different coral community composition, density of corals, relief, and size of corals. Coral spectral reflectance was then input into a radiative transfer model, CORALMOD (CM1), which is based on a leaf radiative transfer model. In CM1, input coral reflectance measurements produce modeled reflectance through an inversion at each visible wavelength to provide the absorption spectrum. Initially, we imposed a scattering baseline that is the same regardless of the coral condition and that coral is optically thick and no light is transmitted through coral. Here we will focus on methodology, experimental design, and initial findings of the in situ spectral measurements and preliminary output from the radiative transfer model.

Guild, Liane↗

DOE OSTI2024

The key role of forest disturbance in reconciling estimates of the northern carbon sink

Northern forests are an important carbon sink, but our understanding of the driving factors is limited due to discrepancies between dynamic global vegetation models (DGVMs) and atmospheric inversions. We show that DGVMs simulate a 50% lower sink (1.1 ± 0.5 PgC yr –1 over 2001–2021) across North America, Europe, Russia, and China compared to atmospheric inversions (2.2 ± 0.6 PgC yr –1 ). We explain why DGVMs underestimate the carbon sink by considering how they represent disturbance processes, specifically the overestimation of fire emissions, and the lack of robust forest demography resulting in lower forest regrowth rates than observed. We reconcile net sink estimates by using alternative disturbance-related fluxes. We estimate carbon uptake through forest regrowth by combining satellite-derived forest age and biomass maps. We calculate a regrowth flux of 1.1 ± 0.1 PgC yr –1 , and combine this with satellite-derived estimates of fire emissions (0.4 ± 0.1 PgC yr –1 ), land-use change emissions from bookkeeping models (0.9 ± 0.2 PgC yr –1 ), and the DGVM-estimated sink from CO 2 fertilisation, nitrogen deposition, and climate change (2.2 ± 0.9 PgC yr –1 ). The resulting ‘bottom-up’ net flux of 2.1 ± 0.9 PgC yr –1 agrees with atmospheric inversions. The reconciliation holds at regional scales, increasing confidence in our results.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1990

On the dynamic and thermodynamic structures of marine stratocumulus

Latent heating effects on stratocumulus circulations were studied successfully with a nine-coefficient spectral model of two-dimensional shallow Boussinesq convection (Laufersweiler and Shirer, 1989). Further, more realistic investigations are being performed currently with a larger, 18-coefficient spectral model, in which the effects of cloud top radiational cooling and in-cloud radiational heating are also being represented. Because assuming a rigid lid at the inversion base may have affected previous results significantly, the domain top was raised to include the lower portion of the capping inversion. As in the previous model, a uniform cloud base is assumed and latent heating effects are included implicitly such that the motions in the sub- and above-cloud regions are dry adiabatic and the motions in the cloud region are moist adiabatic. The effects of forcing by radiational heating profiles that are tied to the cloud layer, such as the one used by Nicholls will be investigated, as will profiles measured during the FIRE experiment. One concern of using truncated spectral models is that the phenomena are so poorly represented that they can change dramatically as the number of spectral coefficients is increased. The efficacy of the nine-coefficient model results is checked by examining the steady state solutions of the 18-coefficient model for parameter values used by Laufersweiler and Shirer (1989), which corresponds to the case of a moderately deep cloud and no capping inversion. The horizontally asymmetric circulation patterns that have narrow downdraft areas and broad updraft areas are virtually the same as those found in the smaller spectral model. Also captured in the case of weaker heating is an elevated circulation centered at cloud base. Thus, the results of the smaller model are substantiated. Since one of the goals of studying the new model is to represent a more realistic domain, the second test of the model is to investigate whether the steady solutions are suppressed in the case of an inversion with no cloud.

Laufersweiler, Mark J.↗

DOE OSTI2024

Monitoring spatiotemporal evolution of fractures during hydraulic stimulations at the first EGS collab testbed using anisotropic elastic-waveform inversion

The EGS Collab project acquired continuous active-source seismic monitoring (CASSM) data before, during, and after hydraulic stimulations at the first testbed at the depth of 4850 ft (1478 m) at the Sanford Underground Research Facility in Lead, South Dakota, for monitoring fracture creation and evolution. CASSM acquisition was conducted using 24 hydrophones, 18 accelerometers, and 17 piezoelectric sources within four fracture-parallel wells and two orthogonal wells. 3D anisotropic traveltime tomography and anisotropic elastic-waveform inversion of the campaign cross-borehole seismic data show that the rock within the stimulation region is a heterogeneous horizontal transverse isotropic medium. Here we use these inversion results as the initial models and apply 3D anisotropic first-arrival traveltime tomography and 3D anisotropic elastic-waveform inversion to the CASSM data acquired after each stimulation in May, 2018 and December, 2018. We observe the spatiotemporal evolution of seismic velocities and anisotropic parameters caused by hydraulic fracture stimulations, showing the regions of rock alternation caused by hydraulic fracture stimulation.

15 GEOTHERMAL ENERGY↗

NASA NTRS1993

A general rough-surface inversion algorithm: Theory and application to SAR data

Rough-surface inversion has significant applications in interpretation of SAR data obtained over bare soil surfaces and agricultural lands. Due to the sparsity of data and the large pixel size in SAR applications, it is not feasible to carry out inversions based on numerical scattering models. The alternative is to use parameter estimation techniques based on approximate analytical or empirical models. Hence, there are two issues to be addressed, namely, what model to choose and what estimation algorithm to apply. Here, a small perturbation model (SPM) is used to express the backscattering coefficients of the rough surface in terms of three surface parameters. The algorithm used to estimate these parameters is based on a nonlinear least-squares criterion. The least-squares optimization methods are widely used in estimation theory, but the distinguishing factor for SAR applications is incorporating the stochastic nature of both the unknown parameters and the data into formulation, which will be discussed in detail. The algorithm is tested with synthetic data, and several Newton-type least-squares minimization methods are discussed to compare their convergence characteristics. Finally, the algorithm is applied to multifrequency polarimetric SAR data obtained over some bare soil and agricultural fields. Results will be shown and compared to ground-truth measurements obtained from these areas. The strength of this general approach to inversion of SAR data is that it can be easily modified for use with any scattering model without changing any of the inversion steps. Note also that, for the same reason it is not limited to inversion of rough surfaces, and can be applied to any parameterized scattering process.

Moghaddam, M.↗

DOE OSTI2022

Manifold Learning-Based Polynomial Chaos Expansions for High-Dimensional Surrogate Models

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantities of interest of the computational or analytical model. For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner. Polynomial chaos expansion is then used to construct a mapping between the stochastic input parameters and the diffusion coordinates of the reduced space. An adaptive clustering technique is proposed to identify an optimal number of clusters of points in the latent space. The similarity of points allows us to construct a number of geometric harmonic emulators which are finally utilized as a set of inexpensive pretrained models to perform an inverse map of realizations of latent features to the ambient space and thus perform accurate out-of-sample predictions. Thus, the proposed method acts as an encoder-decoder system which is able to automatically handle very high-dimensional data while simultaneously operating successfully in the small-data regime. The method is demonstrated on two benchmark problems and on a system of advection-diffusion-reaction equations which model a first-order chemical reaction between two species. In all test cases, the proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.

42 ENGINEERING↗

NASA NTRS1981

Calculation of atmospheric loss from microwave radiometric noise temperature measurements

Microwave propagation loss in the atmosphere can be inferred from microwave radiometric noise temperature measurements. The relevant equations are given and a derivation and calculation is made assuming various physical models. Comparison is made with the commonly used lumped element atmospheric model (isothermal and uniform loss) and the model with linear temperature and exponential loss distributions. The results are useful for estimating the integral inversion differences due to the model selection. This indicates that the commonly used lumped element atmospheric model is a very good approximation with judicious choice of the effective physical temperature. For the worst case comparison, the lumped element model agrees with the variable parameter model within 0.2 dB up to a propagation loss of 3 dB.

Stelzried, C.↗

DOE OSTI2021

Enhanced mechanical property evaluation using innovative data analytics capability

This report focuses on efforts to improve Multiphysics Object-Oriented Simulation Environ-ment (MOOSE) for mechanical property evaluation using data analytics. These efforts involveimprovements to the stochastic tools module (STM) for stochastic simulations of MOOSE mul-tiphysics model and the development of inverse optimization capabilities. The report gives anoverview of the STM and describes recent updates to its core capabilities and theory on itsreduced-order model (ROM) schemes. Examples are also provided showing the impact of theseupdates and exhibits the usefulness of ROMs. An overview of the gradient based inverse opti-mziation algorithms are given along with examples of their application to source identification.Inverse optimization will provide a new methodology in STM for fitting model parameters toexperimental data.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2009

Exploring Alternate Parameterizations for Snowfall with Validation from Satellite and Terrestrial Radars

Increases in computational resources have allowed operational forecast centers to pursue experimental, high resolution simulations that resolve the microphysical characteristics of clouds and precipitation. These experiments are motivated by a desire to improve the representation of weather and climate, but will also benefit current and future satellite campaigns, which often use forecast model output to guide the retrieval process. Aircraft, surface and radar data from the Canadian CloudSat/CALIPSO Validation Project are used to check the validity of size distribution and density characteristics for snowfall simulated by the NASA Goddard six-class, single-moment bulk water microphysics scheme, currently available within the Weather Research and Forecast (WRF) Model. Widespread snowfall developed across the region on January 22, 2007, forced by the passing of a midlatitude cyclone, and was observed by the dual-polarimetric, C-band radar King City, Ontario, as well as the NASA 94 GHz CloudSat Cloud Profiling Radar. Combined, these data sets provide key metrics for validating model output: estimates of size distribution parameters fit to the inverse-exponential equations prescribed within the model, bulk density and crystal habit characteristics sampled by the aircraft, and representation of size characteristics as inferred by the radar reflectivity at C- and W-band. Specified constants for distribution intercept and density differ significantly from observations throughout much of the cloud depth. Alternate parameterizations are explored, using column-integrated values of vapor excess to avoid problems encountered with temperature-based parameterizations in an environment where inversions and isothermal layers are present. Simulation of CloudSat reflectivity is performed by adopting the discrete-dipole parameterizations and databases provided in literature, and demonstrate an improved capability in simulating radar reflectivity at W-band versus Mie scattering assumptions.

Molthan, Andrew L.↗

NASA NTRS2009

Exploring Alternative Parameterizations for Snowfall with Validation from Satellite and Terrestrial Radars

Increases in computational resources have allowed operational forecast centers to pursue experimental, high resolution simulations that resolve the microphysical characteristics of clouds and precipitation. These experiments are motivated by a desire to improve the representation of weather and climate, but will also benefit current and future satellite campaigns, which often use forecast model output to guide the retrieval process. The combination of reliable cloud microphysics and radar reflectivity may constrain radiative transfer models used in satellite simulators during future missions, including EarthCARE and the NASA Global Precipitation Measurement. Aircraft, surface and radar data from the Canadian CloudSat/CALIPSO Validation Project are used to check the validity of size distribution and density characteristics for snowfall simulated by the NASA Goddard six-class, single moment bulk water microphysics scheme, currently available within the Weather Research and Forecast (WRF) Model. Widespread snowfall developed across the region on January 22, 2007, forced by the passing of a mid latitude cyclone, and was observed by the dual-polarimetric, C-band radar King City, Ontario, as well as the NASA 94 GHz CloudSat Cloud Profiling Radar. Combined, these data sets provide key metrics for validating model output: estimates of size distribution parameters fit to the inverse-exponential equations prescribed within the model, bulk density and crystal habit characteristics sampled by the aircraft, and representation of size characteristics as inferred by the radar reflectivity at C- and W-band. Specified constants for distribution intercept and density differ significantly from observations throughout much of the cloud depth. Alternate parameterizations are explored, using column-integrated values of vapor excess to avoid problems encountered with temperature-based parameterizations in an environment where inversions and isothermal layers are present. Simulation of CloudSat reflectivity is performed by adopting the discrete-dipole parameterizations and databases provided in literature, and demonstrate an improved capability in simulating radar reflectivity at W-band versus Mie scattering assumptions.

Molthan, Andrew L.↗

NASA NTRS1979

Elastic lithosphere thickness on the moon from mare tectonic features - A formal inversion

The thickness (T) of the lunar elastic lithosphere at the time (3.6 to 3.8 billion years ago) of the earliest preserved basalt flows in circular mare basins can be estimated by inverting the observed locations of extensional tectonic features in and surrounding the maria. In performing the inversion, the lithosphere is modeled as an elastic shell with a liquid interior, and the basalt load for each mare is approximated by a set of concentric cylinders. To permit solving the forward problem of placing radial limits on the positions of the rilles around a given mare, an additional parameter F, the ratio of the radial stress at the radial limits to the maximum radial stress, is introduced. T and F are chosen to give the best weighted-squares fit of the radial limits to the observations, and are used as the initial values in a linearized matrix inversion to check the resolution and estimate errors. The application of the procedure to three maria with prominent extensional features, Humorum, Orientale, and Serenitatis, gives values of T from about 40 + or - 10 to 50 + or - 10 km, and in each case the linearized matrix equation has an exact inverse.

Comer, R. P.↗

NASA NTRSDate not supplied

Regional variability of dust single scattering albedo due to mineral composition

Nearly all Earth System Models (ESMs) assume globally homogeneous dust aerosols, neglecting regional variations of the imaginary refractive index (IRI) due to varying mineral composition. This has led to a range of single scattering albedo (SSA) and direct radiative forcing (DRF) estimates, as models assign global properties using dust measurements from different regions. We use model and observational data to assess to what extent regionally varying mineral composition affects visible-band SSA and short-wave DRF of dust. We run global simulations with NASA GISS ModelE2.1, using optical properties for minerals based on laboratory-derived empirical relationships between dust IRI at visible wavelengths and the mineral content of iron oxides. When allowing mineral variations instead of homogeneous dust, we find regional differences in dust SSA up to ~0.06 and consequent variations in DRF up to ~6 and ~5 W/m2, at surface and top-of-atmosphere respectively. We compare model SSA with AERONET inversion data (Version 3.0, Level 2), filtered by aerosol size and optical properties to identify pure dust scenes. To investigate possible contamination by biomass burning aerosols, we use the dataset of Schuster et al. (2016, doi:10.5194/acp-16-1565-2016), who separately calculated the contribution of iron oxides and carbonaceous species to AERONET extinction and absorption optical depths. Our results show that: (1) the range of observed SSA (even without carbonaceous species) is larger than that resulting from homogeneous dust; (2) residual amounts of fine mode black and brown carbon may affect AERONET SSA even in seasons with limited biomass burning; (3) model SSA from our mineral scheme exceeds the AERONET range, possibly due also to an uncertain treatment of goethite. In summary, homogeneous dust cannot explain the variability of observed SSA, so regionally varying optical properties based on mineral content are necessary. Higher accuracy in soil mineralogy maps is needed to better reproduce SSA variations at regional scales. Also, distinct soil maps for hematite and goethite are required, given the high sensitivity of model SSA to their extreme optical properties.

V. Obiso↗