Cumulate rocks record the magmatic and cooling processes during formation of Earth’s igneous crust. Extracting the information of these two processes from mineral records, however, is often convoluted by various extents of diffusive resetting during cooling subsequent to main stages of crystallization. Accordingly, for cumulate rocks at diffusive closure, the apparent “equilibrium” temperatures derived from geothermometers are generally lower than the crystallization temperatures. Using analytical or numerical models, geospeedometers can extract cooling rates from the closure temperatures (or profiles) but only if the initial temperatures are determined independently. Here I summarize the general framework of geothermometry and geospeedometry from a trace element perspective. The Mg and REE-based exchange geothermometers for mafic cumulate rocks are reviewed as examples of the geothermometer design. Based on the observed differential diffusive closures of Mg and REE in oceanic gabbros, I outline a general resolution to uniquely determine the initial crystallization temperature and cooling rate of a cumulate rock. The basic idea is further demonstrated using the recently developed Mg-REE coupled geospeedometer for mafic cumulate rocks. Finally, I use the Hess Deep gabbros as a case study to show that this two-element coupled geospeedometer is particularly useful to delineate the igneous accretion and cooling styles during crust formation. This two-element (or multi-element) coupled approach outlined here can also be readily extended for decoding comprehensive thermal histories of other petrological systems at various geological settings or other rocky planetary bodies.
Studying diffusion of hydrogen in nominally anhydrous minerals (NAMs), like clinopyroxene, at low temperatures is a challenging task due to experimental and analytical difficulties. We applied a combination of hydrogen implantation to produce concentration gradients in natural diopside crystals with Nuclear Resonance Reaction Analysis (NRRA) measurements of nanoscale diffusion profiles. Thereby, we were able to conduct experiments at temperatures between 195 – 400 °C. Obtained diffusion rates show a consistent Arrhenius relation Ｄн = 5.47 (± 13.98) ·10⁻⁸ · exp (-115.64 (±11.5) kJ mol⁻¹/RT) m²s⁻¹. Notably, our results lie well within the range of extrapolations from high temperature experiments (≥ 600 °C) of previous studies. This implies that fast diffusion of hydrogen (compared to other elements) extends to low temperatures. We used these results in a non-isothermal diffusion model that simulates the ascent of crystals (0.5, 1.0, and 2.0 mm) along two representative geotherms (oceanic and continental) from 600 to 100 °C, to assess potential re-equilibration of H contents in clinopyroxene at low temperatures. Our model highlights the need to carefully consider boundary conditions, which are a function of P-T-𝘧O₂, that control the concentration gradient at the crystal’s rim. The results from this model allow an assessment when re-equilibration in dependence of crystal size and cooling rate must be considered. Fast ascent (e.g., kimberlitic melt) preserves initial hydrogen contents even in 0.5 mm size clinopyroxene crystals. However, dwelling at low temperatures (e.g., 300 °C) for several thousands of years (e.g., serpentinization) leads to extensive re-equilibration in 2 mm crystals.
The flow of organic matter (OM) along rivers and its retention within floodplains are fundamental to the function of aquatic and riparian ecosystems and are significant components of terrestrial carbon storage and budgets. Carbon storage and ecosystem processing of OM largely depends upon hydrogeomorphic characteristics of streams and valleys. To examine the role of channel complexity on carbon dynamics in mountain streams, we (1) quantify organic carbon (OC) storage in sediment and wood along 24 forested stream reaches in the Rocky Mountains of CO, U.S.A., (2) employ six years of logjam surveys and examine related morphological factors that regulate sediment and carbon storage, and (3) utilize fluorescence spectroscopy to examine how the composition of OM in surface water and floodplain soil leachates is influenced by valley and channel morphology. We find that lower-gradient stream reaches in unconfined valley segments at high elevations store more OC per area than higher-gradient reaches in more confined valleys, and those at lower elevations. We find that limited storage of fine sediment and increased mineralization of OC in multithread channel reaches decrease storage per area compared to simpler single-thread channel reaches. Results suggest that the positive feedbacks between channel complexity and persistent channel-spanning logjams that force multiple channels to flow across valley bottoms limit the aggradation of floodplain fine sediment, and promote hotspots for the transformation of OM. These multithread hotspots likely increase ecosystem productivity and ecosystem services by filtering dissolved organic carbon with potential to decrease contaminants associated with organic matter from surface water.
Soluble and total trace metals were measured in 4 size fractionated aerosol samples collected over the tropical eastern Atlantic Ocean. In samples that were dominated by Saharan dust, the size distributions of total iron, aluminium, titanium, manganese, cobalt and thorium were very similar to one another and to the size distributions of soluble manganese, cobalt and thorium. Finer particle sizes (< ~3 µm) showed enhanced soluble concentrations of iron, aluminium and titanium, possibly as a result of interactions with acidic sulfate aerosol during atmospheric transport. The difference in fine particle solubility between these two groups of elements might be related to the hyperbolic increase in the fractional solubility of iron, and a number of other elements, during the atmospheric transport of Saharan dust, which is not observed for manganese and its associated elements. In comparison to elements whose solubility varies during atmospheric transport, the stability of thorium fractional solubility should reduce uncertainties in the use of dissolved concentrations of this element in seawater as a proxy for dust deposition, although this topic requires further work.
We present thermophysical, biological, and chemical observations of ice and brine samples from five compositionally diverse hypersaline lakes in British Columbia's interior plateau. Possessing a spectrum of magnesium, sodium, sulfate, carbonate and chloride salts, these low-temperature high-salinity lakes are analogs for planetary ice-brine environments, including the ice shells of Europa and Enceladus, and ice-brine systems on Mars. As such, understanding the thermodynamics and biogeochemistry of these systems can provide insight into the evolution, habitability, and detectability of high priority astrobiology targets. We show that biomass is typically concentrated in a layer near the base of the ice cover, but that chemical and biological impurities are present throughout the ice. Coupling bioburden, ionic concentration and seasonal temperature measurements, we demonstrate that impurity entrainment in the ice is directly correlated to ice formation rate and parent fluid composition. We highlight unique phenomena including brine supercooling, salt hydrate precipitation, and internal brine layers in the ice cover, important processes to consider for planetary ice-brine environments. These systems can be leveraged to constrain the distribution, longevity, and habitability of low-temperature solar system brines -- relevant to interpreting spacecraft data and planning future missions in the lens of both planetary exploration and planetary protection.
Microcosm experiments using microbial mats can be useful at times to understand mineral precipitation induced by microorganisms and their extracellular polymeric substances (EPS). Currently, the existing knowledge limits our ability to elucidate the interactions between microbes, which form communities as microbial mats, and minerals that precipitate in natural environments (e.g., lagoons, rivers, springs, soils). Much of the prior research did not consider entire microbial communities, despite recent evidence that microorganisms interact in a community-based way. This is especially relevant in extreme environments where the entire microbial communities are not yet known despite their relevance to biosignatures exploration on other planets. Here, we grew microbial mats on natural substrates in the laboratory to monitor changes in mat texture and mineral paragenesis. Several analytical techniques were used to compare mineral paragenesis in association with and without microbes. This paragenesis included major phases of chemical sedimentary deposits, such as gypsum, calcium carbonate, and some silicates, whose formation is traditionally linked to evaporative processes but was not in these experiments. In addition, some of the phases only precipitated within microbial mat samples and there were differences in mineral fabrics between mat samples and abiotic controls.
Minerals are information-rich materials that offer researchers a glimpse into the evolution of planetary bodies. Thus it is important to extract, analyze, and interpret this abundance of information in order to improve our understanding of the planetary bodies in our solar system and the role our planet’s geosphere played in the origin and evolution of life. Over the past decades, data-driven efforts in mineralogy have seen a gradual increase. The development and application of data science and analytics methods to mineralogy, while extremely promising, has also been somewhat ad-hoc in nature. In order to systematize and synthesize the direction of these efforts, we introduce the concept of “Mineral Informatics”. Mineral Informatics is the next frontier for researchers working with mineral data. In this paper, we present our vision for Mineral Informatics, the X-Informatics underpinnings that led to its conception, the needs, challenges, opportunities, and future directions. The intention of this paper is not to create a new specific field or a sub-field as a separate silo, but to document the needs of researchers studying minerals in various contexts and fields of study, to demonstrate how the systemization and increased access to mineralogical data will increase cross- and interdisciplinary studies, and how data science and informatics methods are a key next step in integrative mineralogical studies.
Iron is a key micronutrient controlling phytoplankton growth in vast regions of the global ocean. Despite its importance, uncertainties remain high regarding external iron source fluxes and internal cycling on a global scale. In this study, we used a global dissolved iron dataset, including GEOTRACES measurements, to constrain source and scavenging fluxes in the marine iron component of a global ocean biogeochemical model. Our model simulations tested three key uncertainties: source inputs of atmospheric soluble iron deposition (varying from 1.4–3.4 Gmol/yr), reductive sedimentary iron release (14–117 Gmol/yr), and compared a variable ligand parameterization to a constant distribution. In each simulation, scavenging rates were tuned to reproduce the observed global mean iron inventory for consistency. The variable ligand parameterization improved the global model-data misfit the most, suggesting that heterotrophic bacteria are an important source of ligands to the ocean. Model simulations containing high source fluxes of atmospheric soluble iron deposition (3.4 Gmol/yr) and reductive sedimentary iron release (114 Gmol/yr) further improved the model most notably in the surface ocean. High scavenging rates were then required to maintain the iron inventory resulting in relatively short surface and global ocean residence times of 0.83 and 7.5 years, respectively. The model simulates a tight spatial coupling between source inputs and scavenging rates, which may be too strong due to underrepresented ligands near source inputs, contributing to large uncertainties when constraining individual fluxes with dissolved iron concentrations. Model biases remain high and are discussed to help improve global marine iron cycle models.
The paleogeographic evolution of the western USA Great Basin from the Late Cretaceous to the Cenozoic is critical to understanding how the Cordillera at this latitude transitioned from Mesozoic shortening to Cenozoic extension. According to a widely applied model, Cenozoic extension was driven by collapse of elevated crust supported by crustal thicknesses that were potentially double the present ~30–35 km. This model is difficult to reconcile with more recent estimates of moderate regional extension (≤ 50%) and the discovery that most high-angle, basin–range faults slipped rapidly ca. 17 Ma, tens of millions of years after crustal thickening occurred. Here we integrate new and existing geochronology and geologic mapping in the Elko area of northeast Nevada, one of the few places in the Great Basin with substantial exposures of Paleogene strata. We improve age control for strata that have been targeted for studies of regional paleoelevation and paleoclimate across this critical time span. In addition, a regional compilation of the ages of material within a network of middle Cenozoic paleodrainages developed across the Great Basin shows that the age of basal paleovalley fill decreases southward roughly synchronous with voluminous ignimbrite flareup volcanism that swept south across the region ca. 45–20 Ma. Integrating these datasets with the regional record of faulting, sedimentation, erosion, and magmatism, we suggest that volcanism was accompanied by an elevation increase that disrupted drainage systems and shifted the continental divide east into central Nevada from its Late Cretaceous location along the Sierra Nevada arc. The north–south Eocene–Oligocene drainage divide defined by mapping of paleovalleys may thus have evolved as a dynamic feature that propagated southward with magmatism. Despite some local faulting, the northern Great Basin became a vast, elevated volcanic tableland that persisted until dissection by Basin and Range faulting that began ca. 21–17 Ma. Based on this more detailed geologic framework, it is unlikely that Basin and Range extension was driven by Cretaceous crustal overthickening; rather, pre-existing crustal structure was just one of several factors that that led to Basin and Range faulting after ca. 17 Ma—in addition to thermal weakening of the crust associated with Cenozoic magmatism, thermally supported elevation, and changing boundary conditions. Because these causal factors evolved long after crustal thickening ended, during final removal and fragmentation of the shallowly subducting Farallon slab, they are compatible with normal (~45–50 km) thickness crust beneath the Great Basin prior to extension and do not require development of a strongly elevated, Altiplano-like region during Mesozoic shortening.
Reducing uncertainty in the global carbon budget requires better quantification of ocean CO2 uptake and its temporal variability. Several methodologies for reconstructing air-sea CO2 exchange from sparse pCO2 observations indicate larger decadal variability than estimated using ocean models. We develop a new application of multiple Large Ensemble Earth system models to assess these reconstructions’ ability to estimate spatiotemporal variability. With our Large Ensemble Testbed, pCO2 fields from 25 ensemble members each of four independent Earth system models are subsampled as the observations and the reconstruction is performed as it would be with real- world observations. The power of a testbed is that the perfect reconstruction is known for each of the 100 original model fields; thus, reconstruction skill can be comprehensively assessed. We find that a commonly used neural-network approach can skillfully reconstruct air-sea CO2 fluxes when and where it is trained with sufficient data. Flux bias is low for the global mean and Northern Hemisphere, but can be regionally high in the Southern Hemisphere. The phase and amplitude of the seasonal cycle are accurately reconstructed outside of the tropics, but longer-term variations are reconstructed with only moderate skill. For Southern Ocean decadal variability, insufficient sampling leads to a 39% [15%:58%, interquartile range] overestimation of amplitude, and phasing is only moderately correlated with known truth (r=0.54 [0.46:0.63]). Globally, the amplitude of decadal variability is overestimated by 21% [3%:34%]. Machine learning, when supplied with sufficient data, can skillfully reconstruct ocean properties. However, data sparsity remains a fundamental limitation to quantification of decadal variability in the ocean carbon sink.
Identifying fluid flow maldistribution in planar geometries is a well-established problem in subsurface science/engineering. Of particular importance to the thermal performance of Engineered (or “Enhanced”) Geothermal Systems (EGS) is identifying the existence of non-uniform (i.e., heterogeneous) permeability and subsequently predicting advective heat transfer. Here, machine learning via a Genetic Algorithm (GA) identifies the spatial distribution of an unknown permeability field in a two-dimensional Hele-Shaw geometry (i.e., parallel-plates). The inverse problem is solved by minimizing the L2-norm between simulated Residence Time Distribution (RTD) and measurements of an inert tracer breakthrough curve (BTC) (C-Dot nanoparticle). Principal Component Analysis (PCA) of spatially-correlated permeability fields enabled reduction of the parameter space by more than a factor of ten and restricted the inverse search to reservoir-scale permeability variations. Thermal experiments and tracer tests conducted at the mesoscale Altona Field Laboratory (AFL) demonstrate that the method accurately predicts the effects of extreme flow channeling on heat transfer in a single bedding-plane rock fracture. However, this is only true when the permeability distributions provide adequate matches to both tracer RTD and frictional pressure loss. Without good agreement to frictional pressure loss, it is still possible to match a simulated RTD to measurements, but subsequent predictions of heat transfer are grossly inaccurate. The results of this study suggest that it is possible to anticipate the thermal effects of flow maldistribution, but only if both simulated RTDs and frictional pressure loss between fluid inlets and outlets are in good agreement with measurements.
Coastal nitrogen (N) enrichment is a global environmental problem that can influence acidification, deoxygenation, and subsequent habitat loss in ways that can be synergistic with global climate change impacts. In the Southern California Bight, an eastern boundary upwelling system, modeling of wastewater discharged through ocean outfalls has shown that it effectively doubles N loading to urban coastal waters. However, effects of wastewater outfalls on biogeochemical rates of primary production and respiration, key processes through which coastal acidification and deoxygenation are manifested, have not been directly linked to observed trends in ambient chlorophyll a, oxygen and pH. In this paper, we compare observations of nutrient concentrations and forms, as well as rates of biogeochemical cycling, in areas within treated wastewater effluent plumes compared to areas spatially distant from ocean outfalls where we expected minimum influence of the plume. We document that wastewater nutrient inputs have an immediate, local effect on nutrient stoichiometry, elevating ammonium and nitrite concentrations by a mean of 4 µM and 0.2 µM, respectively, increasing dissolved nitrogen: phosphorus ratios by a mean of 7 and slightly increasing chlorophyll a by a mean of 1 µg L-1 in the upper 60 m of the watercolumn, as well as increasing rates of nitrification within the plume by a mean of 17 nmol L-1 day-1 and increasing δ13C and δ15N of suspended particulate matter, an integrated measure of primary production, by a mean of 1.3 ‰ and 1 ‰, respectively. We did not observe a significant near plume effect on δ18O and δ15N of the dissolved nitrate+nitrite, an indicator of nitrate+nitrite assimilation into the biomass, instantaneous rates of primary production and respiration, or dissolved oxygen concentration, suggesting any potential impact from wastewater on these is moderated by other factors, notably mixing of water masses. These results indicate that a “reference-area” approach, wherein stations within or near the zone of initial dilution (ZID) from the wastewater outfall are compared to stations farther afield (reference areas) to assess contaminant impacts, may be insufficient to document regional scale impacts of nutrients.
Alkalinity, the excess of proton acceptors over donors, plays a major role in ocean chemistry, in buffering and in calcium carbonate precipitation and dissolution. Understanding alkalinity dynamics is pivotal to quantify ocean carbon dioxide uptake during times of global change. Here we review ocean alkalinity and its role in ocean buffering as well as the biogeochemical processes governing alkalinity and pH in the ocean. We show that it is important to distinguish between measurable titration alkalinity and charge-balance alkalinity that is used to quantify calcification and carbonate dissolution and needed to understand the impact of biogeochemical processes on components of the carbon dioxide system. A general treatment of ocean buffering and quantification via sensitivity factors is presented and used to link existing buffer and sensitivity factors. The impact of individual biogeochemical processes on ocean alkalinity and pH is discussed and quantified using these sensitivity factors. Processes governing ocean alkalinity on longer time scales such as carbonate compensation, (reversed) silicate weathering and anaerobic mineralization are discussed and used to derive a close-to-balance ocean alkalinity budget for the modern ocean.
The stability, structure, and elastic properties of pyrite-type (FeS2 structured) FeO2H were determined using density functional theory-based computations with a self-consistent Coulombic self-interaction term (Ueff). The properties of pyrite-type FeO2H are compared to that of pyrite-type AlO2H with which it likely forms a solid solution at high temperature, as well as the respective lower pressure CaCl2-type polymorphs of both endmembers: e-FeOOH and d-AlOOH. Due to substantial differences in the CaCl2-type to pyrite-type structural transition pressures of these endmembers, the stabilities of the (Al,Fe)O2H solid solution polymorphs are anticipated to be compositionally driven at lower mantle pressures. As the geophysical properties of (Al,Fe)OOH are structurally dependant, interpretations regarding the contribution of pyrite-type FeO2H to seismically observed features must take into account the importance of this broad phase loop. With this in mind, Fe-rich pyrite-type (Al,Fe)OOH may coexist with Al-dominant CaCl2-type d-(Al,Fe)OOH in the deep Earth. Furthermore, pyrite-type (Al0.5-0.6,Fe0.4-0.5)O2H can reproduce the reduced compressional and shear velocities characteristic of seismically observed Ultra Low Velocity Zones (ULVZs) in the Earth’s lowermost mantle while Al-dominant but Fe-bearing CaCl2-type d-(Al,Fe)OOH may contribute to Large Low Shear Velocity Provinces (LLSPs).
We investigate if the commonly neglected riverine detrital carbonate fluxes might balance several chemical mass balances of the global ocean. Particulate inorganic carbon (PIC) concentrations in riverine suspended sediments, i.e., carbon contained by these detrital carbonate minerals, was quantified at the basin and global scale. Our approach is based on globally representative datasets of riverine suspended sediment composition, catchment properties and a two-step regression procedure. The present day global riverine PIC flux is estimated at 3.1 ± 0.3 Tmol C/y (13% of total inorganic carbon export and 4 % of total carbon export), with a flux-weighted mean concentration of 0.26 ± 0.03 wt%. The flux prior to damming was 4.1 ± 0.5 Tmol C/y. PIC fluxes are concentrated in limestone-rich, rather dry and mountainous catchments of large rivers in Arabia, South East Asia and Europe with 2.2 Tmol C/y (67.6 %) discharged between 15 °N and 45 °N. Greenlandic and Antarctic meltwater discharge and ice-rafting additionally contribute 0.8 ± 0.3 Tmol C/y. This amount of detrital carbonate minerals annually discharged into the ocean implies a significant contribution of calcium (~ 4.75 Tmol Ca/y) and alkalinity fluxes (~ 10 Tmol(eq)/y) to marine mass balances and moderate inputs of strontium (~ 5 Gmol Sr/y), based on undisturbed riverine and cryospheric inputs and a dolomite/calcite ratio of 0.1. Magnesium fluxes (~ 0.25 Tmol Mg/y), mostly hosted by less-soluble dolomite, are rather negligible. These unaccounted fluxes help elucidating respective marine mass balances and potentially alter conclusions based on these budgets.
Debate abounds regarding the composition of the deep (middle + lower) continental crust. Studies of medium and high grade metamorphic lithologies guide us but encompass mafic (< 52 wt.%) to felsic (> 68 wt.%) compositions. This study presents a global compilation of geochemical data on amphibolite (n = 6500), granulite (n = 4000), and eclogite (n = 200) facies lithologies and quantifies systematic trends, uncertainties, and sources of bias in the deep crust sampling. The continental crust’s Daly Gap is well documented in amphibolite and most granulite facies lithologies, with eclogite facies lithologies and granulite facies xenoliths having mostly mafic compositions. Al2O3, Lu, and Yb vary little from the top to bottom of the crust. In contrast, SiO2 and incompatible elements show a wider range of abundances. Because of oversampling of mafic lithologies, our predictions are a lower bound on middle crustal composition. The distinction between granulite facies terrains (intermediate SiO2, high heat production, high incompatibles) or granulite facies xenoliths (low SiO2, low heat production, low incompatibles) as being the best analogs of the deep crust remains disputable. We incorporated both, along with amphibolite facies lithologies, to define a deep crustal composition that approaches 57.6 wt.% SiO2. This number, however, represents a compositional middle ground, as seismological studies indicate a general increase in density and seismic velocity with increasing depth. Future studies should analyze more closely the depth dependent trends in deep crustal composition so that we may develop compositional models that are not limited to a three-layer crust.
The potential commonality of prebiotic chemical processes on Titan and the primitive Earth makes Titan a prime body of astrobiological interest. Amino acid synthesis can occur if the abundant simple organics on Titan’s surface can mix with liquid water. Because events that melt surface ice, such as impacts, are rare, it is essential to recognize how long the synthesized molecules remain intact on Titan’s surface. The degradation of biomolecules in extraterrestrial environments can be estimated by combining theoretical work about energy deposition on the surface with experimental results from irradiation of organic molecules. We modelled the destruction of amino acids on the surface of Titan, something absent in current literature. We chose Glycine, Alanine, and Phenylalanine as our molecules of interest due to relevant experimental results for their radiation stability at Titan temperatures. Titan’s thick atmosphere prevents solar radiation and energetic particles trapped in Saturn’s magnetosphere from reaching the surface. The dominant source of energetic radiation at the surface of Titan is the diminished flux of Galactic Cosmic Rays (GCR’s) that penetrate the atmosphere. Sittler Jr et al. (Icarus, 2019) modeled surface GCR flux to be ~10^-9 ergs/cm^3/s. Using the GCR flux, in conjunction with the half-life doses at T=100 K from Gerakines et al. (Icarus, 2012), we estimate the half-lives to be 7.69 x 10^12;, 5.07 x 10^12, and 5.82 x 10^12 years for Glycine, Alanine and Phenylalanine, respectively. These extraordinarily long half-lives on Titan’s surface, as compared to similar calculations for amino acids on Mars, Europa, or Pluto, are directly the result of reduced energy deposition due to the atmosphere. We thus conclude that the degradation of these three amino acids by GCR flux is insignificant over geological time, and will not be an essential factor in interpreting the chemistry from Titan’s surface samples from future missions, such as Dragonfly.
Lead (Pb) is a neurotoxicant that particularly harms young children. Urban environments are often plagued with elevated Pb in soils and dusts, posing a health exposure risk from inhalation and ingestion of these contaminated media. Thus, a better understanding of where to prioritize risk screening and intervention is paramount from a public health perspective. We have synthesized a large national dataset of Pb concentrations in household dusts from across the United States (U.S.), part of a community science initiative called “DustSafe.” Using these results, we have developed a straightforward logistic regression model that correctly predicts whether Pb is elevated (> 80 ppm) or low (< 80 ppm) in household dusts 75% of the time. Additionally, our model estimated 18% false negatives for elevated Pb, displaying that there was a low probability of elevated Pb in homes being misclassified. Our model uses only variables of approximate housing age and whether there is peeling paint in the interior of the home, illustrating how a simple and successful Pb predictive model can be generated if researchers ask the right screening questions. Scanning electron microscopy supports a common presence of Pb paint in several dust samples with elevated bulk Pb concentrations, which explains the predictive power of housing age and peeling paint in the model. This model was also implemented into an interactive mobile app that aims to increase community-wide participation with Pb household screening. The app will hopefully provide greater awareness of Pb risks and a highly efficient way to begin mitigation.