A key initial step in geophysical imaging is to devise an effective means of mapping the sensitivity of an observation to the model parameters, that is to compute its Fréchet derivatives or sensitivity kernel. In the absence of any simplifying assumptions and when faced with a large number of free parameters, the adjoint method can be an effective and efficient approach to calculating Fréchet derivatives and requires just two numerical simulations. In the Glacial Isostatic Adjustment problem, these consist of a forward simulation driven by changes in ice mass and an adjoint simulation driven by fictitious loads that are applied at the observation sites. The theoretical basis for this approach has seen considerable development over the last decade. Here, we present the final elements needed to image 3-D mantle viscosity using a dataset of palaeo sea-level observations. Developments include the calculation of viscosity Fréchet derivatives (i.e. sensitivity kernels) for relative sea-level observations, a modification to the numerical implementation of the forward and adjoint problem that permits application to 3-D viscosity structure, and a recalibration of initial sea level that ensures the forward simulation honours present-day topography. In the process of addressing these items, we build intuition concerning how absolute sea-level and relative sea-level observations sense Earth’s viscosity structure and the physical processes involved. We discuss examples for potential observations located in the near field (Andenes, Norway), far field (Seychelles), and edge of the forebulge of the Laurentide ice sheet (Barbados). Examination of these kernels: (1) reveals why 1-D estimates of mantle viscosity from far-field relative sea-level observations can be biased; (2) hints at why an appropriate differential relative sea-level observation can provide a better constraint on local mantle viscosity and (3) demonstrates that sea-level observations have non-negligible 3-D sensitivity to deep mantle viscosity structure, which is counter to the intuition gained from 1-D radial viscosity Fréchet derivatives. Finally, we explore the influence of lateral variations in viscosity on relative sea-level observations in the Amundsen Sea Embayment and at Barbados. These predictions are based on a new global 3-D viscosity inference derived from the shear-wave speeds of GLAD-M25 and an inverse calibration scheme that ensures compatibility with certain fundamental geophysical observations. Use of the 3-D viscosity inference leads to: (1) generally greater complexity within the kernel; (2) an increase in sensitivity and presence of shorter length-scale features within lower viscosity regions; (3) a zeroing out of the sensitivity kernel within high-viscosity regions where elastic deformation dominates and (4) shifting of sensitivity at a given depth towards distal regions of weaker viscosity. The tools and intuition built here provide the necessary framework to explore inversions for 3-D mantle viscosity based on palaeo sea-level data.
The effect of lateral variations in Earth structure on Last Interglacial sea level
It is generally agreed that the Last Interglacial (LIG; ∼130 – 115 ka) was a time when global average temperatures and global mean sea level were higher than they are today. However, the exact timing, magnitude, and spatial pattern of ice melt is much debated. One difficulty in extracting past global mean sea level from local observations is that their elevations need to be corrected for glacial isostatic adjustment (GIA), which requires knowledge of Earth’s internal viscoelastic structure. While this structure is generally assumed to be radially symmetric, evidence from seismology, geodynamics, and mineral physics indicates that large lateral variations in viscosity exist within the mantle. In this study, we construct a new model of Earth’s internal structure by converting shear wave speed into viscosity using parameterisations from mineral physics experiments and geodynamical constraints on Earth’s thermal structure. We use this 3D Earth structure, which includes both variations in lithospheric thickness and lateral variations in viscosity, to calculate the first 3D GIA prediction for LIG sea level. We find that the difference between predictions with and without lateral Earth structure can be meters to 10s of meters in the near field of former ice sheets, and up to a few meters in their far field. We demonstrate how forebulge dynamics and continental levering are affected by laterally varying Earth structure, with a particular focus on those sites with prominent LIG sea level records. Results from four 3D GIA calculations show that accounting for lateral structure can act to increase local sea level by up to ∼1.5 m at the Seychelles and minimally decrease it in Western Australia. We acknowledge that this result is only based on a few simulations, but if robust, this shift brings estimates of global mean sea level from these two sites into closer agreement with each other. We further demonstrate that simulations with a suitable radial viscosity profile can be used to locally approximate the 3D GIA result, but that these radial profiles cannot be found by simply averaging viscosity below the sea level indicator site.
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- NSF-PAR ID:
- 10285697
- Date Published:
- Journal Name:
- Geophysical Journal International
- ISSN:
- 0956-540X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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SUMMARY -
Glacial isostatic adjustment (GIA) simulations using earth models that vary viscoelastic structure with depth alone cannot simultaneously fit geographic trends in the elevation of marine isotope stage (MIS) 5a relative sea level (RSL) indicators across continental North America and the Caribbean and yield conflicting estimates of global mean sea level (GMSL). We present simulations with a GIA model that incorporates three-dimensional (3-D) variation in North American viscoelastic earth structure constructed by combining high-resolution seismic tomographic imaging with a new method for mapping this imaging into lateral variations in lithospheric thickness and mantle viscosity. We pair this earth model with a global ice history based on updated constraints on ice volume and geometry. The GIA prediction provides the first simultaneous reconciliation of MIS 5a North American and Caribbean RSL highstands and strengthens arguments that MIS 5a peak GMSL reached values close to that of the Last Interglacial. This result highlights the necessity of incorporating realistic 3-D earth structure into GIA predictions with continent-scale RSL data sets.more » « less
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During the last interglacial (LIG) period, global mean sea level (GMSL) was higher than at present, likely driven by greater high-latitude insolation. Past sea-level estimates require elevation measurements and age determination of marine sediments that formed at or near sea level, and those elevations must be corrected for glacial isostatic adjustment (GIA). However, this GIA correction is subject to uncertainties in the GIA model inputs, namely, Earth’s rheology and past ice history, which reduces precision and accuracy in estimates of past GMSL. To better constrain the GIA process, we compare our data and existing LIG sea-level data across the Bahamian archipelago with a suite of 576 GIA model predictions. We calculated weights for each GIA model based on how well the model fits spatial trends in the regional sea-level data and then used the weighted GIA corrections to revise estimates of GMSL during the LIG. During the LIG, we find a 95% probability that global sea level peaked at least 1.2 m higher than today, and it is very unlikely (5% probability) to have exceeded 5.3 m. Estimates increase by up to 30% (decrease by up to 20%) for portions of melt that originate from the Greenland ice sheet (West Antarctic ice sheet). Altogether, this work suggests that LIG GMSL may be lower than previously assumed.
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Site description. This data package consists of data obtained from sampling surface soil (the 0-7.6 cm depth profile) in black mangrove (Avicennia germinans) dominated forest and black needlerush (Juncus roemerianus) saltmarsh along the Gulf of Mexico coastline in peninsular west-central Florida, USA. This location has a subtropical climate with mean daily temperatures ranging from 15.4 °C in January to 27.8 °C in August, and annual precipitation of 1336 mm. Precipitation falls as rain primarily between June and September. Tides are semi-diurnal, with 0.57 m median amplitudes during the year preceding sampling (U.S. NOAA National Ocean Service, Clearwater Beach, Florida, station 8726724). Sea-level rise is 4.0 ± 0.6 mm per year (1973-2020 trend, mean ± 95 % confidence interval, NOAA NOS Clearwater Beach station). The A. germinans mangrove zone is either adjacent to water or fringed on the seaward side by a narrow band of red mangrove (Rhizophora mangle). A near-monoculture of J. roemerianus is often adjacent to and immediately landward of the A. germinans zone. The transition from the mangrove to the J. roemerianus zone is variable in our study area. An abrupt edge between closed-canopy mangrove and J. roemerianus monoculture may extend for up to several hundred meters in some locations, while other stretches of ecotone present a gradual transition where smaller, widely spaced trees are interspersed into the herbaceous marsh. Juncus roemerianus then extends landward to a high marsh patchwork of succulent halophytes (including Salicornia bigellovi, Sesuvium sp., and Batis maritima), scattered dwarf mangrove, and salt pans, followed in turn by upland vegetation that includes Pinus sp. and Serenoa repens. Field design and sample collection. We established three study sites spaced at approximately 5 km intervals along the western coastline of the central Florida peninsula. The sites consisted of the Salt Springs (28.3298°, -82.7274°), Energy Marine Center (28.2903°, -82.7278°), and Green Key (28.2530°, -82.7496°) sites on the Gulf of Mexico coastline in Pasco County, Florida, USA. At each site, we established three plot pairs, each consisting of one saltmarsh plot and one mangrove plot. Plots were 50 m^2 in size. Plots pairs within a site were separated by 230-1070 m, and the mangrove and saltmarsh plots composing a pair were 70-170 m apart. All plot pairs consisted of directly adjacent patches of mangrove forest and J. roemerianus saltmarsh, with the mangrove forests exhibiting a closed canopy and a tree architecture (height 4-6 m, crown width 1.5-3 m). Mangrove plots were located at approximately the midpoint between the seaward edge (water-mangrove interface) and landward edge (mangrove-marsh interface) of the mangrove zone. Saltmarsh plots were located 20-25 m away from any mangrove trees and into the J. roemerianus zone (i.e., landward from the mangrove-marsh interface). Plot pairs were coarsely similar in geomorphic setting, as all were located on the Gulf of Mexico coastline, rather than within major sheltering formations like Tampa Bay, and all plot pairs fit the tide-dominated domain of the Woodroffe classification (Woodroffe, 2002, "Coasts: Form, Process and Evolution", Cambridge University Press), given their conspicuous semi-diurnal tides. There was nevertheless some geomorphic variation, as some plot pairs were directly open to the Gulf of Mexico while others sat behind keys and spits or along small tidal creeks. Our use of a plot-pair approach is intended to control for this geomorphic variation. Plot center elevations (cm above mean sea level, NAVD 88) were estimated by overlaying the plot locations determined with a global positioning system (Garmin GPS 60, Olathe, KS, USA) on a LiDAR-derived bare-earth digital elevation model (Dewberry, Inc., 2019). The digital elevation model had a vertical accuracy of ± 10 cm (95 % CI) and a horizontal accuracy of ± 116 cm (95 % CI). Soil samples were collected via coring at low tide in June 2011. From each plot, we collected a composite soil sample consisting of three discrete 5.1 cm diameter soil cores taken at equidistant points to 7.6 cm depth. Cores were taken by tapping a sleeve into the soil until its top was flush with the soil surface, sliding a hand under the core, and lifting it up. Cores were then capped and transferred on ice to our laboratory at the University of South Florida (Tampa, Florida, USA), where they were combined in plastic zipper bags, and homogenized by hand into plot-level composite samples on the day they were collected. A damp soil subsample was immediately taken from each composite sample to initiate 1 y incubations for determination of active C and N (see below). The remainder of each composite sample was then placed in a drying oven (60 °C) for 1 week with frequent mixing of the soil to prevent aggregation and liberate water. Organic wetland soils are sometimes dried at 70 °C, however high drying temperatures can volatilize non-water liquids and oxidize and decompose organic matter, so 50 °C is also a common drying temperature for organic soils (Gardner 1986, "Methods of Soil Analysis: Part 1", Soil Science Society of America); we accordingly chose 60 °C as a compromise between sufficient water removal and avoidance of non-water mass loss. Bulk density was determined as soil dry mass per core volume (adding back the dry mass equivalent of the damp subsample removed prior to drying). Dried subsamples were obtained for determination of soil organic matter (SOM), mineral texture composition, and extractable and total carbon (C) and nitrogen (N) within the following week. Sample analyses. A dried subsample was apportioned from each composite sample to determine SOM as mass loss on ignition at 550 °C for 4 h. After organic matter was removed from soil via ignition, mineral particle size composition was determined using a combination of wet sieving and density separation in 49 mM (3 %) sodium hexametaphosphate ((NaPO_3)_6) following procedures in Kettler et al. (2001, Soil Science Society of America Journal 65, 849-852). The percentage of dry soil mass composed of silt and clay particles (hereafter, fines) was calculated as the mass lost from dispersed mineral soil after sieving (0.053 mm mesh sieve). Fines could have been slightly underestimated if any clay particles were burned off during the preceding ignition of soil. An additional subsample was taken from each composite sample to determine extractable N and organic C concentrations via 0.5 M potassium sulfate (K_2SO_4) extractions. We combined soil and extractant (ratio of 1 g dry soil:5 mL extractant) in plastic bottles, reciprocally shook the slurry for 1 h at 120 rpm, and then gravity filtered it through Fisher G6 (1.6 μm pore size) glass fiber filters, followed by colorimetric detection of nitrite (NO_2^-) + nitrate (NO_3^-) and ammonium (NH_4^+) in the filtrate (Hood Nowotny et al., 2010,Soil Science Society of America Journal 74, 1018-1027) using a microplate spectrophotometer (Biotek Epoch, Winooski, VT, USA). Filtrate was also analyzed for dissolved organic C (referred to hereafter as extractable organic C) and total dissolved N via combustion and oxidation followed by detection of the evolved CO_2 and N oxide gases on a Formacs HT TOC/TN analyzer (Skalar, Breda, The Netherlands). Extractable organic N was then computed as total dissolved N in filtrate minus extractable mineral N (itself the sum of extractable NH_4-N and NO_2-N + NO_3-N). We determined soil total C and N from dried, milled subsamples subjected to elemental analysis (ECS 4010, Costech, Inc., Valencia, CA, USA) at the University of South Florida Stable Isotope Laboratory. Median concentration of inorganic C in unvegetated surface soil at our sites is 0.5 % of soil mass (Anderson, 2019, Univ. of South Florida M.S. thesis via methods in Wang et al., 2011, Environmental Monitoring and Assessment 174, 241-257). Inorganic C concentrations are likely even lower in our samples from under vegetation, where organic matter would dilute the contribution of inorganic C to soil mass. Nevertheless, the presence of a small inorganic C pool in our soils may be counted in the total C values we report. Extractable organic C is necessarily of organic C origin given the method (sparging with HCl) used in detection. Active C and N represent the fractions of organic C and N that are mineralizable by soil microorganisms under aerobic conditions in long-term soil incubations. To quantify active C and N, 60 g of field-moist soil were apportioned from each composite sample, placed in a filtration apparatus, and incubated in the dark at 25 °C and field capacity moisture for 365 d (as in Lewis et al., 2014, Ecosphere 5, art59). Moisture levels were maintained by frequently weighing incubated soil and wetting them up to target mass. Daily CO_2 flux was quantified on 29 occasions at 0.5-3 week intervals during the incubation period (with shorter intervals earlier in the incubation), and these per day flux rates were integrated over the 365 d period to compute an estimate of active C. Observations of per day flux were made by sealing samples overnight in airtight chambers fitted with septa and quantifying headspace CO_2 accumulation by injecting headspace samples (obtained through the septa via needle and syringe) into an infrared gas analyzer (PP Systems EGM 4, Amesbury, MA, USA). To estimate active N, each incubated sample was leached with a C and N free, 35 psu solution containing micronutrients (Nadelhoffer, 1990, Soil Science Society of America Journal 54, 411-415) on 19 occasions at increasing 1-6 week intervals during the 365 d incubation, and then extracted in 0.5 M K_2SO_4 at the end of the incubation in order to remove any residual mineral N. Active N was then quantified as the total mass of mineral N leached and extracted. Mineral N in leached and extracted solutions was detected as NH_4-N and NO_2-N + NO_3-N via colorimetry as above. This incubation technique precludes new C and N inputs and persistently leaches mineral N, forcing microorganisms to meet demand by mineralizing existing pools, and thereby directly assays the potential activity of soil organic C and N pools present at the time of soil sampling. Because this analysis commences with disrupting soil physical structure, it is biased toward higher estimates of active fractions. Calculations. Non-mobile C and N fractions were computed as total C and N concentrations minus the extractable and active fractions of each element. This data package reports surface-soil constituents (moisture, fines, SOM, and C and N pools and fractions) in both gravimetric units (mass constituent / mass soil) and areal units (mass constituent / soil surface area integrated through 7.6 cm soil depth, the depth of sampling). Areal concentrations were computed as X × D × 7.6, where X is the gravimetric concentration of a soil constituent, D is soil bulk density (g dry soil / cm^3), and 7.6 is the sampling depth in cm.more » « less
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Abstract Paleoshorelines serve as measures of ancient sea level and ice volume but are affected by solid Earth deformation including processes such as glacial isostatic adjustment (GIA) and mantle dynamic topography (DT). The early Pliocene Epoch is an important target for sea‐level reconstructions as it contains information about the stability of ice sheets during a climate warmer than today. Along the southeastern passive margin of Argentina, three paleoshorelines date to early Pliocene times (4.8–5.5 Ma), and their variable present‐day elevations (36–180 m) reflect a unique topographic deformation signature. We use a mantle convection model to back‐advect present‐day buoyancy variations, including those that correspond to the Patagonian slab window. Varying the viscosity and initial tomography‐derived mantle buoyancy structures allows us to compute a suite of predictions of DT change that, when compared to GIA‐corrected shoreline elevations, makes it possible to identify both the most likely convection parameters and the most likely DT change. Our simulations illuminate an interplay of upwelling asthenosphere through the Patagonian slab window and coincident downwelling of the subducted Nazca slab in the mantle transition zone. This flow leads to differential upwarping of the southern Patagonian foreland since early Pliocene times, in line with the observations. Using our most likely DT change leads to an estimate of global mean sea level of 17.5 ± 6.4 m (1σ) in the early Pliocene Epoch. This confirms that sea level was significantly higher than present and can be used to calibrate ice sheet models.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/gji/ggab289
