Frontiers in Earth Science - Editor's Choice 2017 - Valerio Acocella

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Lagroix and Guyodo Decomposing Low Temperature Magnetic Behavior FIGURE 1 | The charging and discharging of the supraconducting magnet differs whether the target magnetic field is approached using the no-overshoot or oscillation modes. The difference can be monitored through the MPMS high-resolution voltmeter readings. The gray boxes delimit the time elapsed from the moment the set field command is activated to the moment the software alerts the set magnetic field is stable. Reducing a stable magnetic field of 2.5–0.3 T using the no-overshoot mode takes approximately three and a half minutes. Reducing a stable magnetic field of 0.3–0 T using the oscillate mode takes approximately 2 min. Manipulating the magnetic field as shown in the figure leads to the 300 mT peak field demagnetization of a 2.5 T IRM that can be acquired at any temperature between 2 and 400 K. laboratory of Prof. R. Lee Penn in the Chemistry Department at of a LT-SIRM acquired in a 2.5 T field at 10 K after cooling the the University of Minnesota. Component 3 is a goethite powder sample from 300 to 10 K in zero field (ZFC) or in a 2.5 T field composed of micrometer size needle crystals (30 × 350 nm) (FC) is monitored upon warming from 10 to 300 K. This protocol synthesized following the method of Schwertmann and Cornell is routinely referred to as a ZFC-FC remanence experiment. (1991) and previously used in Guyodo et al. (2003). Staking In order to test the demagnetization efficiency of the the three components with 4.2 mg of magnetite sandwiched in superconducting magnet’s oscillation mode, the individual between 74.8 mg of goethite and 102 mg of hematite formed the components and mixture samples were subjected to a step- “mixture” sample. Magnetite, goethite and hematite components wise demagnetization of an IRM acquired in a 2.5 T field, represent, respectively, 2.3, 41.3, and 56.3 wt.% of the mixed followed by a step-wise IRM acquisition up to 2.5 T and a one- sample. Further demonstrations are provided on a natural step demagnetization by charging the superconducting magnet loess sample of the penultimate glacial period (Saalian glacial down in the oscillation mode from 300 to 0 mT (Figure 3). or marine oxygen isotope stage 6) from the Dolni Vestonice The experimental sequence programmed through the MultiVu sequence in the Czech Republic (Antoine et al., 2013; Fuchs et al., software is provided as Supplementary Material. 2013) and a commercially available hematite sample from The The experimental protocol followed to generate the data of Nature Company (www.naturesowndesigns.com), which is used Figure 4, aiming at decomposing the magnetic behavior of the as a remarkably stable MD magnetite + hematite standard. All individual components within the mixture sample following samples were prepared in gelatin capsules and when necessary the acquisition of an enhanced RT-SIRM, is provided as completed with cotton to fill the volume of the capsules. For Supplementary Material. The sequence is as follows: measurements, the gelatin capsules were inserted in clear plastic 1) Acquisition of an IRM in a 2.5 T field at 300 K (RT-SIRM). straws, following common practices. 2) Measure RT-SIRM and monitor its evolution while cycling the The magnetic behavior of the individual components and temperature from 300 to 10 K and back to 300 K. of the mixture sample is characterized at room temperature 3) Apply a 2.5 T field and sweep the sample from 300 to 400 K (RT) and at low-temperature (LT) (Figure 2, Table 1). Room and back to 300 K (enhanced RT-SIRM). temperature hysteresis loops were measured on a vibrating 4) Measure the enhanced RT-SIRM and monitor its evolution sample magnetometer (VSM) in a 1.5 T maximum field. The while cycling the temperature from 300 to 10 K, 10 to 400 K, behavior of a RT saturation isothermal remanent magnetization 400 to 10 K, and 10 to 300 K. (SIRM) acquired in a 2.5 T field was monitored while cycling from 300 to 10 K and back to 300 K at a sweep rate of 5 K/min, The same experimental sequence is run on a natural sample which is the same rate used throughout. This protocol is in Figure 5. The RT-SIRM is labeled as enhanced because commonly referred to as a RT-SIRM experiment even though the sample is cooled from 400 to 300 K in a strong applied saturation of the IRM is not necessarily achieved. The behavior field. If any goethite is present, this RT-SIRM pre-treatment Frontiers in Earth Science | www.frontiersin.org July 2017 | Volume 5 | Article 61 | 9 Lagroix and Guyodo Decomposing Low Temperature Magnetic Behavior FIGURE 2 | Characterization of the magnetic behavior of the individual components, magnetite (A–C), hematite (D–F) and goethite (G–I), and the mixture (J–L) is shown. Room temperature hysteresis loops (A,D,G,J) are normalized to the uncorrected for high-field slope loop magnetization induced in the maximum 1.5 T field. Room temperature (300 K) IRM acquired in a 2.5 T field (RT-SIRM) is monitored on cooling and warming and remanence values are normalized to the initial RT-SIRM. Low temperature (10 K) IRM acquired in a 2.5 T field is monitored on warming after cooling in zero field (ZFC) or cooling in a 2.5 T field (FC) and remanence values are normalized to the initial FC value at 10 K. All normalizing values and hysteresis loop derived parameters are listed in Table 1. RT-SIRM data in (H,K) are enhanced RT-SIRM and ZFC and FC experiments in (I,L) were acquired without thermally demagnetizing the enhanced RT-SIRM. The gray ZFC (solid) and FC (dashed) curves in (I) are data acquired on the pristine goethite powder sample prior to any “enhancing” pre-treatments. Frontiers in Earth Science | www.frontiersin.org July 2017 | Volume 5 | Article 61 | 10 Lagroix and Guyodo Decomposing Low Temperature Magnetic Behavior TABLE 1 | Uncorrected hysteresis and low temperature magnetic properties of the individual components and of the three-component mixture used to validate the new method and shown in Figure 2. Parameter Units Component 1 Component 2 Component 3 Mixturec Magnetitea Hematiteb Goethite Mass mg 6.9 88.6 188.2 181.0 M(1.5T) Am2 /kg 92.1 0.413 0.252 2.34 MR Am2 /kg 16.1 1.99 × 10−2 4.99 × 10−4 0.340 MR /M(1.5T) Dimensionless 0.174 0.048 0.002 0.145 BC mT 14.0 55.6 2.56 12.8 BCR mT 26.8 138 – 25.0 BCR /BC Dimensionless 1.91 2.48 – 1.95 RT-SIRM2.5T Am2 /kg 8.64 7.31 × 10−3 2.25 × 10−4 0.190 Enhanced RT-SIRM2.5T Am2 /kg – – 1.36 × 10−2 0.194 10K ZFC Am2 /kg 13.7 2.73 × 10−2 3.50 × 10−2 0.329 2.5T 10K FC Am2 /kg 11.8 5.71 × 10−2 7.50 × 10−2 0.322 2.5T a The hysteresis loop of component 1 reached saturation. Uncorrected and corrected loops render the same MS value. b The slope defined between 1 and 1.5 T when subtracted renders an MS of 0.102 Am2 /kg. c The mixture is composed of 2.3 wt% of component 1 (magnetite), 56.3 wt% of component 2 (hematite) and 41.3 wt% of component 3 (goethite). effectively imparts a TRM on the goethite population as it cools Figure 2I). The ZFC-FC warming curves shown with open and through its Néel temperature (393 K for stoichiometric goethite) closed circles in Figure 2I where measured on the sample after an in the presence of a magnetic field. Finally, in Figure 6, we enhanced RT-SIRM (i.e., TRM) was acquired and not thermally illustrate the new capability by demagnetizing an IRM acquired demagnetized by heating to a temperature above its Néel at 20 K in the case of a ZFC-FC experiment. The experimental temperature. The 2.3 wt.% magnetite, 41.3 wt.% hematite and sequence executed to generate the data of Figure 6 is provided as 56.3 wt.% goethite mixture has magnetic data largely dominated Supplementary Material. by the 2.3% of magnetite (Figures 2J–L). Only a slight high-field slope is observed in the hysteresis loop (which would be easily discarded as a paramagnetic component in a natural sediment), RESULTS and a faint Morin transition can be observed in the RT-SIRM Magnetic Characterization: Individual curves and FC low-temperature data. The goethite component, which represents more than half of the mixture, cannot be Components and Mixture detected in these data. The three mineral components used in this study were chosen because of their significantly different low-temperature magnetic signatures, as shown in Figure 2. Component 1, the W3006 Efficiency of the Superconducting synthetic magnetite sample, shows a characteristic magnetic Magnet’s Oscillation Mode hysteresis with a saturation magnetization of 92.1 Am2 /kg The new experimental protocol utilizes the superconducting (Table 1; Figure 2A). A sharp Verwey transition is observed in magnetic oscillation mode of the MPMS to perform an both RT-SIRM and ZFC-FC curves (Figures 2B,C). Component isothermal demagnetization of the initial remanence without the 2, the hematite sample, is characterized by an open hysteresis use of an external AF demagnetizer. Testing of this method loop that does not saturate at 1.5 T, and a clear Morin transition was performed at room temperature on all three individual in both the RT-SIRM and the ZFC-FC curves (Figures 2D–F). components and the mixture (Figure 3). For the magnetite The Morin transition on cooling begins at 220 K and spreads sample, the stepwise demagnetization of the IRM acquired in over 60 K, which is compatible with the compiled data of 2.5 T results in a rapidly decreasing remanent magnetization. hematite nanoparticles in Özdemir et al. (2008). The net A peak-field of 300 mT demagnetizes 98.6% of the original separation observed between FC and ZFC curves implies that an intensity; the 1.4% remaining remanence equals to 0.128 Am2 /kg. additional remament magnetization was acquired during cooling As expected for hematite, the stepwise demagnetization of in a 2.5 T magnetic induction likely due to the progressive component 2 is spread over a larger range of peak-field and blocking of a remanence in the smaller particles of the sample’s is only complete at 2.5 T. At 300 mT, 78.7% of the initial grain-size distribution. Component 3 is a goethite sample remanence of component 2 remains. The shape of components displaying a characteristic, nearly strait and closed hysteresis 1 and 2 demagnetization curves are relatively similar to that loop (Figure 2G). The enhanced RT-SIRM cooling and warming of their IRM acquisition curves, and the single-step 300 mT curves are reversible and show a 230% increase in remanence demagnetizations are superposed to the 300 mT step of the with decreasing temperature (Figure 2H). ZFC-FC warming stepwise demagnetizations. As expected, the remanence of the curves are well separated and display the expected downward goethite component is not demagnetized (Guyodo et al., 2006). curvature upon warming (dashed and solid gray line data in The initial 300 K IRM of 1.36 × 10−2 Am2 /kg shown in Frontiers in Earth Science | www.frontiersin.org July 2017 | Volume 5 | Article 61 | 11 Lagroix and Guyodo Decomposing Low Temperature Magnetic Behavior FIGURE 3 | Experiments aimed at testing the demagnetization efficiency of the superconducting magnetic’s oscillation mode for the individual components, magnetite (A), hematite (B), goethite (C), and the mixture (D). First a RT-SIRM was imparted in a 2.5 T field (gray and white circles) and stepwise demagnetized by charging the superconducting magnet in the no-overshoot mode and back to zero in the oscillation mode from increasingly higher fields (black circles). Second, each sample was subjected to a stepwise IRM acquisition up to 2.5 T (white squares) followed by single step demagnetization from 300 mT to zero (red and pink diamonds). The low field correction corresponds to a sequence using the AC coil to cancel the magnet residual field. Each data point is the average of three measurements and its standard deviation. MPMS sequence is provided as Supplementary Material. Figure 3C is the enhanced 300 K IRM2.5T and is two orders conducted on the mixture. Its cooling and warming curves are of magnitude greater than the isothermally acquired 300 K plotted as closed and opened circles, respectively in Figure 4A. IRM2.5T value of 2.25 × 10−4 Am2 /kg. The demagnetization For clarity, only the 300 K IRM2.5T magnetization acquired after and acquisition behavior of the mixture behaves in a manner warming (300–400 K) and cooling (400–300 K) in a 2.5 T field similar to that of the magnetite sample with a non-demagnetized is plotted in Figure 4A as a gray circle. The enhanced RT- baseline slightly higher than the magnetization of component SIRM cycle data are plotted in Figure 2K. The enhanced RT- 3. Altogether, these observations demonstrate the efficiency of SIRM of the mixture is 2.6% higher than the classic RT-SIRM. the superconducting magnetic oscillation mode to demagnetize Demagnetizing the mixture’s enhanced RT-SIRM in a 300 mT samples with the appropriate coercivity spectrum. peak field with the MPMS removes 85.8% of the magnetization and is represented by the red diamond in Figures 4A,B. Cycling Validating the New Experimental Method the remaining remanent magnetization to 10 K and back to 300 K The MPMS isothermal demagnetization method is first used to (Figure 4B) reveals a clear Morin transition of the hematite separate the magnetic behavior of the individual components component and a net increase in magnetization with decreasing within the mixture sample. The MPMS experimental sequence temperatures, which is reversible at temperatures below ∼200 K. ran to generate the data of Figure 4 is provided as Supplementary Evidence of a Verwey transition is observed indicative of an Material. A classic RT-SIRM2.5T experiment was initially incomplete demagnetization of magnetite. However, the results Frontiers in Earth Science | www.frontiersin.org July 2017 | Volume 5 | Article 61 | 12 Lagroix and Guyodo Decomposing Low Temperature Magnetic Behavior FIGURE 4 | The RT-SIRM of the mixture sample is cooled to 10 K (black circles) and warmed back to 300 K (white circles). An enhanced RT-SIRM is imparted by warming the sample to 400 K and back to 300 K in the presence of a strong 2.5 T field (gray circle). The enhanced RT-SIRM is demagnetized by charging the supraconducting magnet in the no-overshoot mode to 300 mT and back to zero in the oscillation mode and measured (red diamond). The 300 mT demagnetized enhanced RT-SIRM is cooled to 10 K (black squares) and warmed to 400 K (white squares), providing a partial thermal demagnetization before cooling back to 10 K (solid triangles) and warming to 300 K (white triangles). The full experiment is shown in (A). (B) Provides a broken zoomed scale of the first and second cycling of the enhanced and partially demagnetized RT-SIRM. MPMS sequence is provided in Supplementary Material. FIGURE 5 | The same experimental protocol as in Figure 4 conducted on a natural loess sample from the penultimate glaciation (Saalian) recovered in the Dolni Vestonice sequence in the Czech Republic. Full experiment is shown in (A) and a zoomed view of the first and second enhanced RT-SIRM cycles are shown in (B). of the efficiency test presented in section Efficiency of the 2 (hematite) and 3 (goethite) respectively (Table 1). Considering Superconducting Magnet’s Oscillation Mode showed a 98.6% that magnetite constitutes only 2.3 wt.% of the mixture, the demagnetization of component 1 (magnetite) in 300 mT, which remaining magnetization after the 300 mT demagnetization in absolute value equals 0.128 Am2 /kg. Therefore, even after in the mixture should be ∼0.003 Am2 /kg. This is one tenth demagnetizing 98.6% of its initial remanence, the remaining of the mixture’s remaining enhanced RT-SIRM after 300 mT magnetization of component 1 is greater by one and two demagnetization, which is sufficient to be observed. Continued orders of magnitude than the initial acquisition of component thermal demagnetization up to 400 K above the Néel temperature Frontiers in Earth Science | www.frontiersin.org July 2017 | Volume 5 | Article 61 | 13 Lagroix and Guyodo Decomposing Low Temperature Magnetic Behavior FIGURE 6 | (A) ZFC and FC warming curves of a commercially available hematite purchased from The Nature Company, which also contains magnetite. The same sample was subjected to a new ZFC-FC acquisition where the ZFC and FC 2.5 T IRMs acquired at 20 K were partially demagnetized by charging the supraconducting magnet in the no-overshoot mode to 100 mT (B), 300 mT (C), or 500 mT (D) and further to zero in the oscillation mode. MPMS sequence is provided in Supplementary Material. of goethite removes its behavior from the final cooling and temperature dependent behavior of (partially) demagnetized warming cycle plotted as closed and open circles in Figure 4B. remanences acquired at temperatures below room temperature. The final cycle begins with a 300 K remanence of 6.47 × 10−3 Figure 6 presents ZFC–FC remanence warming curves Am2 /kg, isolating the behaviors of hematite and magnetite. conducted on a commercially available hematite containing Based on the efficiency tests of Section Efficiency of The magnetite impurities (see Section Materials and Methods). Superconducting Magnet’s Oscillation Mode (Figure 3) only The initial FC and ZFC remanences (Figure 6A) were 13.2% of hematite’s remanence would have been demagnetized by partially demagnetized in peak fields of 100, 300 or 500 mT the 300 mT peak field along with 98.6% of magnetite’s remanence (Figures 6B–D respectively) generated with the MPMS using the stated above, leading to a calculated remanence of 6.35 × 10−3 oscillation mode. The Verwey transition of the multi-domain Am2 /kg, which is only 1.8% less than the measured value. impurity magnetite is almost entirely suppressed by the 300 mT The new experimental method is also tested on a natural demagnetizing field, enabling the isolated observation of the sample of loess and results obtained from the same experimental temperature dependent behavior of the hematite component. sequence (Supplementary Material) are presented in Figure 5 following the same format as for the mixture sample (Figure 4). The classic RT-SIRM cooling and warming curves display both DISCUSSION characteristics of magnetite (Verwey transition) and goethite or maghemite (1% increasing in remanence with cooling One timeless challenge in rock magnetic studies, inclusive of trend). The enhanced RT-SIRM 300 K value of 1.39 × 10−3 paleomagnetism and environmental magnetism, is decomposing Am2 /kg is 1.8% greater than the 1.37 × 10−3 Am2 /kg 300 K a sample’s bulk magnetic behavior into its individual magnetic remanence measured in the classic RT-SIRM experiment. When mineral components. For the study of the Earth’s magnetic demagnetizing the enhanced RT-SIRM with a 300 mT peak field and its derived applications for paleogeographic, tectonic field 82% of the remanence is lost. The remaining 18% (or and geodynamic reconstructions, the breadth of useful mineral 2.50 × 10−4 Am2 /kg) when cooled and warmed back to room stoichiometry and grain size is restricted to those ordering temperature displays a reversible linearly increasing remanence magnetically at a temperature well above ambient temperature with decreasing temperature. The remanence increases by 105%, and having a grain size stable magnetically over geological which can be only be attributed to goethite. A slight irreversibility time scales. In contrast, for environmental magnetism studies between 300 and 200 K can be observed. Continued thermal the breadth of useful mineral stoichiometry and grain size is demagnetization to 400 K results in a further 6% demagnetization unrestricted. The accuracy of magnetism-based interpretations of the initial enhanced RT-SIRM at 300 K. Cycling the remaining of climate, environmental and biogeochemical processes and 12% or 1.67 × 10−4 Am2 /kg to low temperature and back change is dependent, firstly, on a comprehensive identification reveals a remanence loss transition on cooling starting at ∼250 K of all magnetic mineral compositions, no matter their magnetic which is recovered on warming with a slight thermal hysteresis ordering temperature or particle size. The other two important reminiscent of a hematite Morin transition. Superimposed is a determinations are the concentration and grain size distribution trend of increasing remanence on cooling quantified to 1% in the for each mineral composition. 30 to 170 K temperature range, which is similar to observations The magnetic data acquired on the three components and made from stoichiometric maghemite (Özdemir and Dunlop, the mixture samples used in this study (Figure 2, Table 1) 2010). illustrate fairly well the difficulties in obtaining comprehensive The new experimental method broadens our current chemical composition, and (semi-)quantitative grain size and experimental capabilities in allowing the observation of concentration estimates even for the most common of iron oxides Frontiers in Earth Science | www.frontiersin.org July 2017 | Volume 5 | Article 61 | 14 Lagroix and Guyodo Decomposing Low Temperature Magnetic Behavior (magnetite and hematite) and oxyhydroxides (goethite). Scalar of component 1 in the mixture, observed and discussed above, quantities derived from hysteresis parameters and their ratios are remain even for low-temperature thermomagnetic data. Low- the most accessible means of characterizing relative variations temperature cycling of a RT-SIRM fails to detect any change in mineral composition (e.g., S-ratio, HIRM), mean magnetic in intensity that might hint to an additional component other grain size (e.g., MRS /MS , χ/MS ), and concentration (MS , MRS , than magnetite (Figure 2K). The same is also true for the χ, χf , χHF ) (see review by Liu et al., 2012). The mixture sample, ZFC data. The only hint of a second component comes from despite being constituted of 97.7 wt% hematite + goethite and the small inflection around 220 K in the FC warming curve only 2.3 wt% magnetite has hysteresis parameters which fall on (Figure 2L). Because heating induced alterations are absent the magnetite SD-MD mixing lines of Dunlop (2002). Within a over these temperature ranges, multiple experiments can be natural bulk sample containing paramagnetic and diamagnetic conducted on the same sample. With the added new possibility minerals, and in a maximum field of 1.5 T, the magnetization of partially demagnetizing (at any temperature between 2 of component 3 (goethite) as well as 75% of the magnetization and 400 K) remanences acquired in fields up to 5, 7, or 14 T of component 2 (nano-hematite) would be lost in the high field and at temperatures as low as 2 K using the same equipment, slope corrected magnetization. Scalar parameters acquired in low experimental decomposition of a bulk sample’s thermomagnetic to moderately high fields will thus provide an incomplete picture behavior, as demonstrated and validated herein (Figures 4–6), of the ensemble of environmentally significant iron bearing becomes possible. The new experimental method presented minerals, heavily biased toward magnetite. While this statement here is currently the only means of obtaining a comprehensive is common knowledge, it is often disregarded in reports and identification of all mineral species of an ensemble of magnetic reviews of environmental magnetism studies. mineral within a bulk sample, with a minimum of assumptions Unmixing and principal component analysis of spectrum- and no a priori knowledge. type data such as remanence curves, hysteresis loops and FORC distributions can more readily provide evidence of multiple New Frontiers for Earth and Planetary components. These approaches are increasingly undertaken to Sciences through Mineral Magnetism characterize changes in contributions to the total remanent Recovering continental climate and environmental change magnetization and in magnetic grain size of sedimentary archives through the study of loess and paleosol sequences motivated of various origins from past and present continents and oceans the development of the new experimental method. The (e.g., Abrajevitch and Kodama, 2011; Lascu et al., 2012; Chen decomposition shown in Figure 5 enables the positive et al., 2014; Nie et al., 2014; Hyland et al., 2015; Fabian identification of four components: magnetite, hematite, et al., 2016; Maxbauer et al., 2016c; Zhang et al., 2016). goethite and maghemite. Relative concentrations between However, obtaining mineral compositions of an ensemble of samples can be compared given a set of assumptions albeit components via these methods is only possible indirectly through fewer than for reaching absolute concentrations. While such a series of assumptions or a priori knowledge. In addition, an analysis on all depth intervals of a loess sequence may be the fact that these analyses are isothermal, (i.e., investigating too time consuming and costly, the unambiguous observations changes in magnetization as a function of field strength at it provides is indispensible to constrain other data which a single temperature) and that the analysis temperature is can be acquired more easily and rapidly on a voluminous almost always room temperature, there is a high probability of sample suite. Such direct and comprehensive determinations incomprehensiveness of the characterization results, similarly of mineral compositions of all magnetic particle grain sizes are to scalar derived hysteresis parameters discussed above. The needed to interpret accurately routine measurements, which thermal fluctuation tomography method proposed by Jackson are intrinsically less comprehensive. The most comprehensive et al. (2006) addresses the limitation of exclusion of particles remanence data achievable with instrumentations available in with SP behavior from room temperature-derived coercivity paleomagnetic and rock magnetic laboratories today are FC distribution, and provides a means of characterizing grain warming curves. The MPMS systems can field cool a sample size distributions from variable low-temperature remanence from 400 to 2 K and thus even the smallest size particles will coercivity spectrums. Unfortunately, the method has been acquire a remanence and any mineralogy with an ordering seldom applied (e.g., Nie et al., 2013; Wang et al., 2013) likely temperature below room temperature will acquire a remanence. due to the time consuming and relatively costly nature of the The new demagnetization method presented herein permits, as analysis. shown in Figure 6, to separate FC remanence warming curves, The most direct means of identifying the chemical the most comprehensive data needing to be separated. composition of magnetic minerals is through thermomagnetic As mineral magnetism aims to broaden its reach, contributing data and the observation of magnetic ordering transitions (Curie for example to the study of the formation of the solar and Néel temperature) or other characteristic crystallographic system (e.g., Strauss et al., 2016; Wang et al., 2017), of or magnetic transitions (e.g., Verwey, Morin and Besnus deep-time terrestrial environments (e.g., Carlut et al., 2015; transitions, spin glass transition). Many transitions can be Slotznick and Fischer, 2016) or of extreme environments of observed below 400 K. In Figure 2, for instance, we observe hydrothermal vents (e.g., Toner et al., 2016), it is necessary the drastically different low temperature behavior of the three to accompany these new frontiers with experimental tools components for both the RT-SIRM and ZFC-FC experiments. adapted to the greater diversity of mineral compositions This said, the pitfalls due to the overwhelming magnetization and greater complexity of mineral assemblages resulting from Frontiers in Earth Science | www.frontiersin.org July 2017 | Volume 5 | Article 61 | 15 Lagroix and Guyodo Decomposing Low Temperature Magnetic Behavior the superposition of geological and biogeochemical processes AUTHOR CONTRIBUTIONS through time. Magnetic characterization presents the advantages of a low detection limit (order of 1 ppm) and in situ FL and YG both contributed to the experimental development, bulk sample analyses avoiding time consuming physical and the data analysis and the writing of the manuscript. chemical separation techniques shown to be biased (e.g., Lagroix et al., 2004; Wang et al., 2013). In addition, low-temperature FUNDING magnetism in addition avoids complications resulting from in situ alteration when conducting analyses at temperature above The work benefitted from financial support through research ∼200◦ C (e.g., Özdemir and Dunlop, 2000; Till et al., 2015). grants ANR-2010-BLAN-604-01, ANR-08-BLANC-0227-CSD6 The new method combines these advantages to the partial and ANR-06-JCJC-0144. demagnetization at any temperature below 127◦ C (400 K) of a remanent magnetization, especially that of magnetite, which ACKNOWLEDGMENTS due to its up to 3 orders of magnitude greater magnetization intensity and ubiquity in the geological record can completely We are grateful to R. L. Penn and D. Burleson for the synthesis mask significant mass or volume concentrations of other and use of the J-1 hematite sample. This is IPGP contribution environmentally or paleomagnetically important components. 3870. In the present study, the mixture sample contains masses of hematite and goethite that are 24 times and 18 times, SUPPLEMENTARY MATERIAL respectively, greater than that of magnetite and still were undetectable in routine room temperature rock magnetic The Supplementary Material for this article can be found analyses. The new experimental protocol circumvents the online at: http://journal.frontiersin.org/article/10.3389/feart. magnetite masks and opens the door to more comprehensive 2017.00061/full#supplementary-material magnetic mineral composition identification through direct MPMS sequence for the experimental protocol is available observations, to more accurate semi-quantitative concentration as Supplemental Material. 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Frontiers in Earth Science | www.frontiersin.org July 2017 | Volume 5 | Article 61 | 17 SECTION: HYDROSPHERE Global DEM Errors Underpredict Coastal Vulnerability to Sea Level Rise and Flooding This paper introduces the topic of the usefulness and usage of Digital Elevation Models (DEMs) for coastal flood mapping. The Authors describe the advantages and disadvantages of using the most widely used DEM, the Shuttle Radar Topography Mission (SRTM), in coastal areas. They come to the important conclusion that the errors are such that flood risks and vulnerability with respect to sea level rise are greatly underestimated. In the USA, this underestimation is as high as 60% with respect to population at risk in coastal areas. This is an important information that will have direct effect on impact assessment and management strategies of global sea level rise. Nick Van De Giesen, Specialty Chief Editor, Hydrosphere ORIGINAL RESEARCH published: 19 April 2016 doi: 10.3389/feart.2016.00036 Global DEM Errors Underpredict Coastal Vulnerability to Sea Level Rise and Flooding Scott Kulp * and Benjamin H. Strauss Climate Central, Princeton, NJ, USA Elevation data based on NASA’s Shuttle Radar Topography Mission (SRTM) have been widely used to evaluate threats from global sea level rise, storm surge, and coastal floods. However, SRTM data are known to include large vertical errors in densely urban or densely vegetated areas. The errors may propagate to derived land and population exposure assessments. We compare assessments based on SRTM data against references employing high-accuracy bare-earth elevation data generated from lidar data available for coastal areas of the United States. We find that both 1-arcsecond and 3-arcsecond horizontal resolution SRTM data systemically underestimate exposure across all assessed spatial scales and up to at least 10 m above the high tide line. At 3 m, 1-arcsecond SRTM underestimates U.S. population exposure by more than 60%, and under-predicts population exposure in 90% of coastal states, 87% of counties, and 83% of municipalities. These fractions increase with elevation, but error medians and Edited by: Guy Jean-Pierre Schumann, variability fall to lower levels, with national exposure underestimated by just 24% at 10 m. University of California, Los Angeles, Results using 3-arcsecond SRTM are extremely similar. Coastal analyses based on SRTM USA data thus appear to greatly underestimate sea level and flood threats, especially at lower Reviewed by: elevations. However, SRTM-based estimates may usefully be regarded as providing Brian C. Gunter, Georgia Institute of Technology, USA lower bounds to actual threats. We additionally assess the performance of NOAA’s Global Alessio Pugliese, Land 1-km Base Elevation Project (GLOBE), another publicly-available global DEM, but University of Bologna, Italy do not reach any definitive conclusion because of the spatial heterogeneity in its quality. *Correspondence: Scott Kulp Keywords: sea level rise, climate impacts, srtm, globe, error analysis [email protected] Specialty section: INTRODUCTION This article was submitted to Hydrosphere, Understanding the exposure of coastal nations and communities to sea level rise and coastal a section of the journal flooding is critical in informing policymakers about the potential benefits of protective strategies, Frontiers in Earth Science as well as in building awareness of the tangible effects of climate change. In recent years, a number Received: 13 December 2015 of studies have used high resolution, high vertical accuracy, bare earth digital elevation models Accepted: 23 March 2016 (DEMs) derived from lidar to produce coastal exposure estimates in individual countries, such as Published: 19 April 2016 the United States (Knowles, 2010; Strauss et al., 2012, 2015). However, since availability of lidar Citation: is limited outside of the US, many non-US and global analyses have relied on DEMs of poorer Kulp S and Strauss BH (2016) Global DEM Errors Underpredict Coastal accuracy and resolution, notably ones based on NASA’s Shuttle Radar Topography Mission (SRTM; Vulnerability to Sea Level Rise and McGranahan et al., 2007; Hallegatte et al., 2013; Hinkel et al., 2014; Neumann et al., 2015). Flooding. Front. Earth Sci. 4:36. Recent studies have investigated the absolute elevation error in SRTM (Shortridge, 2006; Tighe doi: 10.3389/feart.2016.00036 and Chamberlain, 2009; Becek, 2014), including the impacts of vegetation (LaLonde et al., 2010; Frontiers in Earth Science | www.frontiersin.org April 2016 | Volume 4 | Article 36 | 19 Kulp and Strauss SRTM Underestimates Coastal Flooding Exposure Shortridge and Messina, 2011) and urban development (Gamba may produce additional error in some marginal coastal strips. We et al., 2002) on error. As most coastal exposure analysis is expect this source of error to be minimal due to the small amount performed within the first few vertical meters above high tide of elapsed time, and the large ratios of land area to coastline lines, estimates are highly sensitive to small errors and differences length for our municipal, county, and state units of analysis. in land elevation. For example, (Hinkel et al., 2014) recently GLOBE has a much coarser horizontal resolution of 1 km found that using SRTM to compute exposed population below (roughly 30 arcseconds), and is classified to measure bare earth the 100-year flood event produces global estimates less than half elevation. However, GLOBE was developed using a patchwork those predicted by NOAA’s Global Land 1-km Base Elevation of several different data sources, collected between the 1950’s Project (GLOBE). Additionally, recent studies, such as (Kuleli, and 1998, and so its accuracy is inconsistent across the world’s 2010; Hallegatte et al., 2013; Strauss et al., 2015), have begun surface. Roughly 1/3 of the global land surface(including the to investigate global sea level rise exposure at the municipality United States), has absolute vertical RMSE ≤ 18 m, while another scale, which may be more sensitive to local noise in the DEM. 1/3 of Earth’s land surface has over 97 m vertical RMSE (Hastings While the elevation error in global DEMs has been studied, the et al., 1999). impact of these elevation errors on computed coastal exposure As distributed by NOAA, the Coastal Lidar dataset is is not well understood, making interpretation of such exposure referenced to the NAVD88 geoid. Both SRTM and GLOBE are analysis challenging. Here, we characterize bias and variability referenced to the EGM96 geoid. We convert these datasets to in exposure error based on global DEMs, including any behavior NAVD88 with a correction grid generated from geoid height with respect to flood level and spatial scale. calculators developed by NOAA (2011) and NGA (2013). Since This paper seeks to fill this need by building an error we are interested in flood exposure due to SLR and coastal storms, model from computed land and population exposure within we then convert all elevations to reference the local mean higher the contiguous United States. Over most coastal areas, high- high water (MHHW) tidal datum using NOAA’s VDatum grid quality elevation models based on lidar are available from NOAA (Parker et al., 2003) and nearest neighbor interpolation. (NOAA, 2015). Previous studies have used lidar-based DEMs as The US Census provides block boundaries and block a reference to assess the accuracy of SRTM elevation (Hofton populations (www.census.gov/geo/maps-data/data/tiger-line. et al., 2006). In this work, we similarly use NOAA’s lidar-based html), which we use to compute population and land exposed coastal DEMs as a baseline against which we can assess flood below 1–10 m MHHW in increments of 1 m for each DEM. The exposure error under SRTM and GLOBE. After converting each exposure values computed within each block are then summed DEM to the same tidal datum, we use US Census block data to across their corresponding census places (municipalities), compute population and land exposure at water levels between counties, and states. For all DEM’s, this analysis assumes uniform 1 and 10 m above local high tide lines, and sum this exposure population density within Census blocks, except for zero density up to municipality, county, state, and national scales. By treating over wetland areas, following the methodology described in exposure under lidar as ground truth, we can compute relative Strauss et al. (2012). We define a sample’s “true” exposure value error at every location, allowing us to characterize error at all (land or population), etrue , to be its computed exposure using water surface levels and spatial scales, and assess not only bias and lidar, and its “test” values, etest , as its computed exposure under variability, but how often each elevation source underestimates SRTM-1 or GLOBE. In addition to using relative error, we also (or overestimates) exposure under different conditions. define the log10-multiplier (LM10) as follows:   etrue DATA SET CHARACTERISTICS AND LM10(etrue , etest ) = log10 etest ANALYSIS METHODS NOAA maintains and makes publically available a collection This metric has advantages in error visualization, as it is of lidar-derived DEMs generated by a range of governmental centered about zero (no error), and gives equal weight, sources across the US coast, collected between 1996 and 2015. We though opposite sign, to underestimation or overestimation of use these lidar data as our baseline topography, which is classified exposure. to measure bare earth elevation, has a roughly 5 m horizontal This analysis is performed within every coastal state within resolution, and most data have published vertical errors <20 the contiguous United States (CONUS), except for Virginia and cm RMSE (NOAA, 2012). SRTM, based on a NASA mission Rhode Island, as there exist large regions of coastline within in 2000, is available globally at both 3 arcsecond (“SRTM-3”) both of these states in which SRTM elevation is unavailable. and 1 arcsecond (“SRTM-1”) horizontal resolutions (roughly Accordingly, we also do not consider VA or RI in any of the 90 and 30 m, respectively), each with a vertical RMSE <10 m lidar nor GLOBE exposure analysis discussed below. At the (Rodriguez et al., 2006; LaLonde et al., 2010). However, SRTM municipality and county levels, to prevent very large relative is an unclassified (“surface”) elevation model, and thus tall error values occurring due to exceptionally small levels of buildings and vegetation are expected to introduce significant exposure in certain locations, we only consider those places in positive bias (LaLonde et al., 2010; Shortridge and Messina, which estimated exposure under both lidar and SRTM/GLOBE 2011). Additionally, we note that coastal processes between exceeds 1% of the total population/land area of that SRTM collection and the generally more recent lidar datasets place. Frontiers in Earth Science | www.frontiersin.org April 2016 | Volume 4 | Article 36 | 20 Kulp and Strauss SRTM Underestimates Coastal Flooding Exposure RESULTS AND DISCUSSION higher accuracy, with nearly zero relative error at larger water heights. Our results present three major findings, which are discussed In our analysis, we have empirically found that SRTM-1 in detail below. First, SRTM is very likely to underestimate and SRTM-3 produce nearly identical patterns in exposure exposure at all subnational locations and scales, while GLOBE error. For the purposes of clarity and brevity, we focus exhibits more positive bias. Secondly, we see that error variability the rest of our discussion on SRTM-1, as this is the most at subnational spatial scales is high under both DEM’s, but recent and highest resolution version of SRTM currently drops considerably at higher water heights, especially under available. The complete set of tables and figures for SRTM. Finally, across CONUS as a whole, SRTM-1 underpredicts our SRTM-3 analysis is available in the Supplementary exposure by a factor as high as 2.5, while GLOBE performs with Materials. FIGURE 1 | Bar graph of percent of places underestimating population (A) and land (B) exposure under SRTM-1 and GLOBE, across Municipalities (M, orange), Counties (C, blue), and States (S, green). Frontiers in Earth Science | www.frontiersin.org April 2016 | Volume 4 | Article 36 | 21 Kulp and Strauss SRTM Underestimates Coastal Flooding Exposure FIGURE 2 | Scatter plot of LM10 vs. estimated population (rows 1 and 2) and land (rows 3 and 4) exposure at individual places. LM10 is defined as log10 ([SRTM1 or GLOBE exposure]/[lidar exposure]). Error bars for municipalities represent the 5/50/95th percentiles of LM10 values of neighboring points. County medians are also included, but error bars are removed to reduce clutter. Counties and municipalities with less than 1% exposure are not included. Frontiers in Earth Science | www.frontiersin.org April 2016 | Volume 4 | Article 36 | 22 Kulp and Strauss SRTM Underestimates Coastal Flooding Exposure UNDER/OVERPREDICTION RATES overestimates population exposure in 85% of municipalities, 83% of counties, and 81% of states (values complementary to the SRTM-1 consistently underpredicts exposure at all spatial scales underestimation rates listed in Figure 1 and Table 2). These high (Figure 1). At 1 m, no clear patterns of bias in population overestimation rates may be caused by GLOBE’s low resolution exposure error are apparent, but at 3 m, SRTM-1 underestimates and high vertical error in the DEM, causing inaccurately flooded population exposure in 83% of municipalities, 87% of counties, pixels to cover large (1 km2 ) regions of populated land, while and 90% of states. By 10 m, SRTM-1 underestimation total exposure under lidar at 1 m is much smaller. However, becomes nearly universal, with 86% of municipalities, 92% these error rates drop rapidly as water elevation rises, such of counties, and 95% of states underpredicting population that at 3 m, GLOBE overpredicts in just 61% of municipalities, exposure. Land exposure under SRTM-1 follows similar 67% of counties, and 67% of states. By the 10 m flood level, patterns of error, though is more likely to underestimate 28% of municipalities reach 100% population exposure under at 1 m. both lidar and GLOBE, implying zero error in exposure Conversely, GLOBE is more likely to overpredict exposure assessment for such locations. This causes overestimation rate in than SRTM-1, especially at smaller spatial scales. At 1 m, GLOBE municipalities to fall to 40% under GLOBE, while county and TABLE 1 | Relative error values at the 5/50/95th percentiles across exposed states, counties, and towns under SRTM-1. 1m 2m 3m 4m 5m 6m 7m 8m 9m 10 m State Population RE 5% −0.8 −0.88 −0.87 −0.83 −0.79 −0.74 −0.68 −0.62 −0.57 −0.54 50% −0.21 −0.33 −0.40 −0.42 −0.41 −0.39 −0.33 −0.32 −0.28 −0.27 95% 1.02 0.41 0.05 −0.04 −0.03 −0.02 −0.04 −0.05 −0.05 −0.04 Pct under (%) 57 86 90 95 95 95 95 95 95 95 Land RE 5% −0.85 −0.83 −0.81 −0.79 −0.77 −0.72 −0.66 −0.62 −0.59 −0.55 50% −0.47 −0.49 −0.44 −0.40 −0.37 −0.34 −0.32 −0.30 −0.27 −0.25 95% 0.24 −0.04 −0.14 −0.14 −0.14 −0.13 −0.13 −0.13 −0.12 −0.11 Pct under (%) 86 100 100 100 100 100 100 100 100 100 Number of exposed states 21 21 21 21 21 21 21 21 21 21 County Population RE 5% −0.75 −0.86 −0.85 −0.86 −0.84 −0.79 −0.73 −0.7 −0.69 −0.7 50% −0.17 −0.41 −0.43 −0.43 −0.41 −0.37 −0.33 −0.30 −0.27 −0.23 95% 2.88 0.95 0.64 0.36 0.11 0.19 0.15 0.11 0.12 0.11 Pct under (%) 58 77 87 90 91 91 91 92 93 92 Land RE 5% −0.81 −0.83 −0.82 −0.79 −0.79 −0.8 −0.77 −0.78 −0.74 −0.72 50% −0.37 −0.45 −0.41 −0.42 −0.39 −0.37 −0.35 −0.33 −0.30 −0.27 95% 1.45 0.45 0.19 0.20 0.21 0.18 0.11 0.12 0.09 0.08 Pct under (%) 70 82 89 91 91 92 93 92 93 93 Number of exposed counties 151 180 204 218 231 240 255 265 271 277 Municipality Population RE 5% −0.88 −0.93 −0.93 −0.93 −0.91 −0.87 −0.83 −0.78 −0.77 −0.74 50% −0.19 −0.46 −0.48 −0.44 −0.41 −0.35 −0.3 −0.24 −0.19 −0.14 95% 4.73 1.73 0.89 0.60 0.49 0.27 0.17 0.12 0.10 0.07 Pct Under (%) 58 77 83 86 88 88 88 88 88 86 Pct Over (%) 41 22 16 13 11 11 9 9 8 8 Land RE 5% −0.89 −0.91 −0.92 −0.9 −0.89 −0.85 −0.81 −0.77 −0.75 −0.73 50% −0.33 −0.48 −0.47 −0.44 −0.4 −0.35 −0.3 −0.25 −0.21 −0.17 95% 2.84 0.94 0.46 0.37 0.25 0.21 0.14 0.11 0.07 0.05 Pct Under (%) 66 80 86 88 89 89 90 89 89 89 Pct Over (%) 33 19 13 11 10 10 8 8 7 7 Number of exposed municipalities 1459 686 1037 1306 1521 1729 1887 2018 2137 2251 This table also lists the percentage of places in which SRTM-1 is underestimating exposure, as well as the total number of exposed places. Some municipalities see 100% exposure under both lidar and SRTM-1 (neither under- nor over-estimating), so the actual percentage of municipalities overestimating exposure is also included. Municipalities and counties in which <1% of the total are exposed in either SRTM or lidar are not considered. Frontiers in Earth Science | www.frontiersin.org April 2016 | Volume 4 | Article 36 | 23 Kulp and Strauss SRTM Underestimates Coastal Flooding Exposure TABLE 2 | Relative error values at the 5/50/95th percentiles across exposed states, counties, and towns under GLOBE. 1m 2m 3m 4m 5m 6m 7m 8m 9m 10 m State Population RE 5% −0.35 −0.63 −0.65 −0.64 −0.61 −0.55 −0.54 −0.48 −0.44 −0.44 50% 1.54 0.28 0.21 0.19 0.16 0.09 0.08 0.06 0.03 0.02 95% 5.19 2.80 1.21 1.09 0.79 0.55 0.35 0.28 0.22 0.33 Pct Under (%) 19 33 33 38 33 33 38 43 43 43 Land RE 5% −0.73 −0.66 −0.62 −0.60 −0.60 −0.58 −0.53 −0.48 −0.45 −0.40 50% −0.16 −0.40 −0.19 −0.12 −0.10 −0.08 −0.07 −0.06 −0.06 −0.06 95% 0.83 0.44 0.37 0.41 0.28 0.21 0.18 0.2 0.21 0.21 Pct under (%) 57 62 67 57 57 67 62 62 62 62 Number of exposed states 21 21 21 21 21 21 21 21 21 21 County Population RE 5% −0.62 −0.80 −0.78 −0.74 −0.74 −0.73 −0.70 −0.72 −0.69 −0.63 50% 1.52 0.50 0.21 0.26 0.18 0.11 0.07 0.04 0.03 0.02 95% 12.03 5.39 4.21 3.91 2.87 2.37 2.04 1.75 1.74 1.83 Pct under (%) 17 29 33 34 31 31 31 34 33 33 Land RE 5% −0.81 −0.82 −0.82 −0.76 −0.74 −0.72 −0.69 −0.67 −0.62 −0.56 50% 0.07 0.02 0.00 0.01 0.01 0.00 0.00 0.00 0.00 0.00 95% 5.20 2.08 1.27 0.89 0.76 0.6 0.63 0.53 0.57 0.51 Pct under (%) 46 48 49 47 44 47 48 45 46 45 Number of exposed counties 216 237 256 265 271 278 282 289 298 303 Municipality Population RE 5% −0.61 −0.8 −0.78 −0.76 −0.76 −0.77 −0.72 −0.72 −0.73 −0.68 50% 2.20 0.51 0.12 0.04 0.01 0.00 0.00 0.00 0.00 0.00 95% 27.2 11.2 9.90 8.39 5.57 5.49 4.64 4.20 3.67 3.31 Pct under (%) 14 23 27 27 26 27 27 27 27 27 Pct over (%) 85 75 68 63 60 53 50 46 43 40 Land RE 5% −0.75 −0.82 −0.81 −0.8 −0.79 −0.77 −0.75 −0.75 −0.75 −0.69 50% 0.92 0.23 0.05 0.01 0.00 0.00 0.00 0.00 0.00 0.00 95% 13.97 7.25 5.87 4.43 3.29 2.80 2.58 2.18 1.96 1.72 Pct under (%) 23 30 35 35 33 33 33 32 33 32 Pct over (%) 76 68 61 58 56 52 49 47 43 40 Number of exposed municipalities 1302 1617 1869 2069 2216 2365 2468 2556 2635 2710 This table also lists the percentage of places in which GLOBE is underestimating/overestimating exposure, as well as the total number of exposed places. Some municipalities see 100% exposure under both lidar and GLOBE (neither under- nor over-estimating), so the actual percentage of municipalities overestimating exposure is also included. Municipalities and counties in which <1% of the total are exposed in either GLOBE or lidar are not considered. state overpredict population exposure in 65 and 57% of cases, between −35 and 519% under GLOBE. Across municipalities, respectively. this variability is worse, with between −88 and 473% error under SRTM-1, and between –61 and 2720% error under GLOBE. ERROR VARIABILITY This variability shrinks at higher water elevations, particularly under SRTM-1, which at 3 m produces errors across states In Figure 2, we also see that both global elevation datasets between −87 and 5%. However, variability across municipalities produce exposure estimates of highly variable error. In under SRTM-1 remains relatively high, between −92 and 89%, Table 1(SRTM-1) and Table 2 (GLOBE), we aggregate these while error under GLOBE falls between −65 and 121% across exposure error results across each subnational spatial scale. As states, and between −78 and 990% across municipalities. municipalities and states clearly represent the high and low At 10 m, under SRTM-1, error variability drops even further ends of error variability in both DEM’s, we focus on these across states (−54 to −4%) and municipalities (−74 to 7%). two spatial scales in this discussion, and we note that error However, while GLOBE experiences smaller bias in exposure variability at the county level tends to fall between these two at 10 m, the error spread in both states (−44 to 33%), and extremes. municipalities (−68% to 331%) is much higher than SRTM-1, We see that at 1 m, even across states, 90% of population making GLOBE a less reliable option, especially at smaller spatial exposure errors fall between –80 and 102% under SRTM-1, and scales. Frontiers in Earth Science | www.frontiersin.org April 2016 | Volume 4 | Article 36 | 24 Kulp and Strauss SRTM Underestimates Coastal Flooding Exposure TABLE 3 | Population and Land exposure relative error for the contiguous USA (omitting VA and RI) under SRTM-1 and GLOBE. 1m 2m 3m 4m 5m 6m 7m 8m 9m 10 m SRTM-1 population RE −0.31 −0.60 −0.61 −0.57 −0.51 −0.45 −0.38 −0.32 −0.28 −0.24 SRTM-1 land RE −0.51 −0.50 −0.50 −0.46 −0.43 −0.39 −0.36 −0.34 −0.31 −0.28 GLOBE population RE 1.34 0.35 0.20 0.11 0.06 0.04 0.03 0.01 0.00 0.00 GLOBE land RE 0.19 0.17 0.10 0.07 0.04 0.01 0.01 0.00 −0.01 0.00 NATIONAL ERROR ASSESSMENT height, SRTM-1 underpredicts population exposure by a factor of over 2.5, as compared to estimates produced by using NOAA’s Table 3 presents a detailed summary of national-scale error more accurate Coastal Lidar. This error is most likely explained analysis of population and land for both SRTM-1 and GLOBE. the presence of vegetation and urban development causing We see that at every flood level and for both variables, SRTM-1 bias in SRTM’s surface measurements. That said, increasing underestimates exposure. At 1 m, SRTM-1 estimates 31% fewer the flood height shrinks this error and its variability across people exposed than lidar, while at 2 and 3 m, this difference rises smaller spatial scales to more reasonable levels, and may to over 61%. Rising water heights see shrinking error values, and provide lower bounds of exposure in individual nations and by 10 m, SRTM underestimates exposure by just 24%. Analysis municipalities globally. However, this also implies that global of land produces similar results, with SRTM estimating 50% less coastal threats may be even more damaging than what the exposure than lidar between 1 and 3 m, and 28% lower by 10 m. recent literature suggests, especially at low elevations. While However, we again find GLOBE overestimates national GLOBE may produce acceptable results at the wide spatial population exposure at the lower water levels, with values over scales and high water elevations, it can only be expected to 130% higher than lidar at 1 m. Between 2 and 4 m, GLOBE error perform this well across 1/3 of the earth’s land surface, where drops rapidly to 11%, and produces estimates nearly identical the highest quality data sources are used. In any other wider to lidar above 8 m. GLOBE performs noticeably better in land global-scale or narrower municipality-scale sea level rise and exposure analysis, overestimating by only 20% at 1 m, and nearly coastal flooding analysis, despite its nature of underestimating zero error above 5 m. exposure, SRTM is the most reliable DEM publically GLOBE’s excellent performance across the US as a whole available. at flood heights >5 m could be attributed to the wide spatial scale, its high quality data source in the US (Digital Terrain AUTHOR CONTRIBUTIONS Elevation Data), as well the bare-earth classification properties of this DEM, resulting in minimal elevation (and thus exposure) SK and BS designed research; SK performed research and bias. However, we note that GLOBE’s relative success in the analyzed data; SK and BS wrote the paper. US would not likely translate to most of the rest of the world, due to variable data sources and larger known errors. As such, SLR exposure analysis using GLOBE is probably only useful in ACKNOWLEDGMENTS those countries with elevation sources of known high quality, We thank Claudia Tebaldi for statistical advice and Ashton and is inappropriate for exposure analysis comparing multiple Shortridge for geoid datum conversion grids. The research countries. Additionally, as we have seen, smaller-scale locations, leading to these results received funding from the Kresge including states, generally perform worse under GLOBE than Foundation, V. Kann Rasmussen Foundation, and the Schmidt SRTM-1. Family Foundation. CONCLUSIONS SUPPLEMENTARY MATERIAL At any scale, using SRTM in sea level rise exposure analysis The Supplementary Material for this article can be found is highly likely to underestimate true vulnerability—especially online at: http://journal.frontiersin.org/article/10.3389/feart. at water surface levels of 2–3 m. For example, at 2 m flood 2016.00036 REFERENCES Gamba, P., Dell Acqua, F., and Houshmand, B. (2002). “SRTM data characterization in urban areas,” in International Archives of Photogrammetry Becek, K. (2014). Assessing global digital elevation models using the runway Remote Sensing and Spatial Information Sciences, Vol. 34.3/B, method: the advanced spaceborne thermal emission and reflection 55–58. radiometer versus the shuttle radar topography mission case. IEEE Hallegatte, S., Green, C., Nicholls, R. J., and Corfee-Morlot, J. (2013). Future flood Trans. Geosci. Remote Sens. 52, 4823–4831. doi: 10.1109/TGRS.2013.22 losses in major coastal cities.Nature Publishing Group. Nat. Clim. Chang. 3, 85187 802–806. doi: 10.1038/nclimate1979 Frontiers in Earth Science | www.frontiersin.org April 2016 | Volume 4 | Article 36 | 25 Kulp and Strauss SRTM Underestimates Coastal Flooding Exposure Hastings, D. A., Dunbar, P. K., Elphingstone, G. M., Bootz, M., Murakami, H., NOAA (2015). 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T., Zimmermann, J., and Nicholls, R. J. (2015). Future coastal population growth and exposure to sea-level rise and coastal flooding Conflict of Interest Statement: The authors declare that the research was - a global assessment. PLoS ONE 10:e0118571. doi: 10.1371/journal.pone.01 conducted in the absence of any commercial or financial relationships that could 18571 be construed as a potential conflict of interest. NGA (2013). WGS 84 Earth Gravitational Model. Available online at: http:// earth-info.nga.mil/GandG/wgs84/gravitymod/index.html (Accessed October Copyright © 2016 Kulp and Strauss. This is an open-access article distributed 28, 2015). under the terms of the Creative Commons Attribution License (CC BY). The NOAA (2011). Computation of GEOID03 Geoid Height. Available online at: http:// use, distribution or reproduction in other forums is permitted, provided the www.ngs.noaa.gov/cgi-bin/GEOID_STUFF/geoid03_prompt1.prl (Accessed original author(s) or licensor are credited and that the original publication in October 28, 2015). this journal is cited, in accordance with accepted academic practice. No use, NOAA (2012). Lidar 101: An Introduction to Lidar Technology, Data, and distribution or reproduction is permitted which does not comply with these Applications. Charleston, SC. terms. Frontiers in Earth Science | www.frontiersin.org April 2016 | Volume 4 | Article 36 | 26 SECTION: CRYOSPHERIC SCIENCES Estimating Spring Terminus Submarine Melt Rates at a Greenlandic Tidewater Glacier Using Satellite Imagery The paper is rather unique tackling a topic that has received increased attention in the last years: submarine melt rates. Submarine melt rates are very difficult to quantify, however, the authors manage to estimate these melt rates with innovative approaches. Regine Hock, Specialty Chief Editor, Hydrosphere ORIGINAL RESEARCH published: 15 December 2017 doi: 10.3389/feart.2017.00107 Estimating Spring Terminus Submarine Melt Rates at a Greenlandic Tidewater Glacier Using Satellite Imagery Alexis N. Moyer 1*, Peter W. Nienow 1 , Noel Gourmelen 1, 2 , Andrew J. Sole 3 and Donald A. Slater 1, 4 1 School of Geosciences, University of Edinburgh, Edinburgh, United Kingdom, 2 IPGS UMR 7516, Université de Strasbourg, CNRS, Strasbourg, France, 3 Department of Geography, University of Sheffield, Sheffield, United Kingdom, 4 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA, United States Oceanic forcing of the Greenland Ice Sheet is believed to promote widespread thinning at tidewater glaciers, with submarine melting proposed as a potential trigger of increased glacier calving, retreat, and subsequent acceleration. The precise mechanism(s) driving glacier instability, however, remain poorly understood, and while increasing evidence points to the importance of submarine melting, estimates of melt rates are uncertain. Edited by: Here we estimate submarine melt rate by examining freeboard changes in the seasonal Timothy C. Bartholomaus, University of Idaho, United States ice tongue of Kangiata Nunaata Sermia (KNS) at the head of Kangersuneq Fjord (KF), Reviewed by: southwest Greenland. We calculate melt rates for March and May 2013 by differencing Leigh A. Stearns, along-fjord surface elevation, derived from high-resolution TanDEM-X digital elevation University of Kansas, United States models (DEMs), in combination with ice velocities derived from offset tracking applied Twila Moon, University of Oregon, United States to TerraSAR-X imagery. Estimated steady state melt rates reach up to 1.4 ± 0.5 m d−1 David F. Porter, near the glacier grounding line, with mean values of up to 0.8 ± 0.3 and 0.7 ± 0.3 m d−1 Columbia University, United States for the eastern and western parts of the ice tongue, respectively. Melt rates decrease *Correspondence: Alexis N. Moyer with distance from the ice front and vary across the fjord. This methodology reveals [email protected] spatio-temporal variations in submarine melt rates (SMRs) at tidewater glaciers which develop floating termini, and can be used to improve our understanding of ice-ocean Specialty section: interactions and submarine melting in glacial fjords. This article was submitted to Cryospheric Sciences, Keywords: submarine melt, ice/ocean interactions, tidewater glaciers, remote sensing, TanDEM-X a section of the journal Frontiers in Earth Science Received: 01 September 2017 INTRODUCTION Accepted: 04 December 2017 Published: 15 December 2017 Acceleration of marine-terminating glaciers in Greenland in recent decades has significantly Citation: increased the contribution of the ice sheet to sea level (Enderlin et al., 2014). Many of these glaciers Moyer AN, Nienow PW, Gourmelen N, are in contact with relatively warm ocean water (Holland et al., 2008; Straneo et al., 2012; Carr et al., Sole AJ and Slater DA (2017) 2013; Motyka et al., 2013), and submarine melting at the ice-ocean interface has been proposed Estimating Spring Terminus as a potential trigger of glacier calving, retreat and acceleration (Nick et al., 2009; O’Leary and Submarine Melt Rates at a Greenlandic Tidewater Glacier Using Christoffersen, 2013; Luckman et al., 2015). The spatial distribution of submarine melting along Satellite Imagery. an ice front can impact grounding line stability and influence ice front shape by undercutting, Front. Earth Sci. 5:107. overcutting, and creating embayments (Straneo et al., 2012; Carroll et al., 2015; Fried et al., 2015). doi: 10.3389/feart.2017.00107 These changes in ice front shape likely affect calving processes and can create locations along the Frontiers in Earth Science | www.frontiersin.org 2017 | Volume 5 | Article 107 | 28 December Moyer et al. Ice Tongue Submarine Melt Rates ice front where calving preferentially occurs (Chauché et al., STUDY AREA 2014; Luckman et al., 2015). The dynamic coupling between glacier margins and upstream ice enables oceanic forcing of Located at the head of Kangersuneq Fjord (KF), Kangiata tidewater glaciers to promote widespread thinning, increased Nunaata Sermia (KNS), the largest tidewater glacier in southwest glacier retreat, calving and velocity, and consequent mass Greenland, drains ∼2% of the ice sheet (Sole et al., 2011; loss (e.g., Joughin et al., 2004; van den Broeke et al., Figure 1). The ice front is ∼4.5 km wide with a maximum 2009; Vieli and Nick, 2011; Carr et al., 2013; Goelzer grounding line depth of ∼250 m below sea level (Mortensen et al., 2013; Sundal et al., 2013; Straneo and Cenedese, et al., 2013). KNS has retreated at least 22 km from its Little Ice 2015). Age maximum extent, following increased air and sea surface Despite their potential importance for ice dynamics, temperatures (Lea et al., 2014). For the past 15 years, with submarine melt rates (SMRs) are poorly constrained, because the exception of 2011 and 2015, a thick seasonal ice tongue collecting in situ measurements near actively-calving glacier contiguous with the glacier forms by mid-winter and advances termini is both difficult and dangerous (e.g., Mortensen et al., down-fjord prior to rapid break-up in late-spring (Motyka et al., 2011, 2013; Lea et al., 2014). Numerous studies have instead 2017; Figure 2). The floating ice tongue flows directly across the used hydrographic profiles from glacial fjords to estimate the glacier grounding line (e.g., with no gap or calving processes net heat flux available for melting ice, resulting in SMRs up occurring between the grounded and floating ice) with near to 16.8 ± 1.3 m d−1 in Alaska (Motyka et al., 2003, 2013) and spatially consistent velocity (see Supplementary Figures 1, 2). On ranging from 0.7 ± 0.2 to 10.1 m d−1 in Greenland (Rignot average, the ice tongue has a length between 2 and 3 km, and et al., 2010; Sutherland and Straneo, 2012; Inall et al., 2014). decreases in freeboard with distance from the grounding line Other studies have used general circulation models or plume (Figure 2). The fjord waters adjacent to the front of the ice tongue theory to estimate SMR (e.g., Jenkins, 2011; Christoffersen are typically packed with dense ice mélange (i.e., mixture of sea et al., 2012; Sciascia et al., 2013; Xu et al., 2013; Slater et al., ice, bergy bits, and icebergs) during the winter and spring months 2015), resulting in melt rates ranging from 0.12 to 3.6 m before breaking up in late spring. d−1 in Greenland. However, most measurements used to Mortensen et al. (2011, 2013) performed detailed analyses on estimate SMR from heat flux methods or to constrain model the characteristics of the waters and heat sources entering KF parameters are taken far from the grounding line (15–80 km and reaching to within ∼4 km of the KNS terminus. Classical away) (e.g., Johnson et al., 2011; Christoffersen et al., 2012; two-layered buoyancy-driven circulation operates in the fjord Sutherland and Straneo, 2012; Inall et al., 2014), and are primarily during the spring and summer, where circulation is therefore integrating all the processes that will affect the heat driven by subglacial meltwater plumes (Figure 3). Subglacial flux between the measurement site and the terminus, including discharge exits the glacier at the grounding line, rises buoyantly heat lost to the melting of icebergs, sea ice, and mélange along the ice front due to its lower density relative to the at considerable distances from the grounding line. SMRs ambient fjord water, and flows down-fjord once neutral buoyancy estimated from fjord heat flux are also uncertain due to the is reached (Motyka et al., 2003; Jenkins, 2011; Cowton et al., temporal variability in fjord circulation, so that it is not clear 2015). In fjords with shallow glacier grounding line depths how representative an estimate is of the longer term mean (<500 m) like KNS, summer discharge meltwater plumes often (Jackson and Straneo, 2016). reach neutral buoyancy and horizontally enter the fjord within Alternative approaches to estimating glacier submarine melt the upper 100 m of the water column (Carroll et al., 2016). rate utilize remotely sensed observations. Several studies have The outflow forced by the subglacial discharge establishes an quantified SMR by accounting for ice flux divergence and estuarine circulation cell, drawing in coastal waters from the surface mass balance of floating ice shelves and tongues (e.g., shelf, which flow in a layer beneath the fresher outflow (Motyka Rignot and Jacobs, 2002; Depoorter et al., 2013; Enderlin and et al., 2003; Mortensen et al., 2011). This warm coastal water Howat, 2013; Rignot et al., 2013; Gourmelen et al., 2017). This is then entrained into the subglacial discharge plume, and approach has generated SMRs up to 0.11 m d−1 beneath ice melts the ice front and underside of the ice tongue as it shelves in Antarctica (Rignot and Jacobs, 2002) and ranging rises. from 0.03 ± 0.02 to 2.9 ± 0.65 m d−1 beneath floating glacier tongues in Greenland (Enderlin and Howat, 2013). Enderlin DATA AND METHODOLOGY and Hamilton (2014) also used remotely sensed observations to estimate submarine melt, using changes in iceberg freeboard DEM and Ice Velocity Data Generation derived from high-resolution digital elevation models (DEMs) to We used TanDEM-X and TerraSAR-X imagery from 2013 estimate iceberg volume loss, which was then used to estimate to estimate ice tongue freeboard and velocity, respectively. area-averaged iceberg SMRs. During the summers of 2011 and TerraSAR-X has a repeat period of 11 days and both satellites 2013, estimated iceberg SMR was 0.39 ± 0.17 m d−1 in Sermilik have spatial resolution on the order of a meter (Krieger Fjord, east Greenland. Here we also employ a remote sensing et al., 2007; Eineder et al., 2011), thereby providing excellent approach, using satellite radar data to estimate near-terminus temporal and spatial resolution for observing changes in ice SMR from spatial and temporal changes in seasonal ice tongue tongue velocity and freeboard. The radar platforms enabled freeboard adjacent to a large tidewater glacier in southwest us to use imagery acquired in non-daylight hours and cloudy Greenland. conditions, in contrast to optical platforms. Time lapse camera Frontiers in Earth Science | www.frontiersin.org December 2017 | Volume 5 | Article 107 | 29 Moyer et al. Ice Tongue Submarine Melt Rates FIGURE 1 | Map of study area, including Kangiata Nunaata Sermia (KNS) and Akullersuup Sermia (AS) glaciers and ice tongue and mélange, from Landsat 8 satellite image acquired for May 1, 2013 (bottom panel).The red and blue triangles indicate the locations of the University of Alaska Fairbanks (2013) and our (2009) time lapse cameras, respectively, and the black box indicates the extent of Figures 4A,B. The red and black dots in the fjord scale locator map (top right panel) indicate the locations of the Danish Meteorological Institute (DMI) and GEUS PROMICE weather stations, respectively. imagery near the terminus of KNS (Figure 1) every 4 h 2011). A vertical shift with a linear dependence on location (tilt) from January to June 2013 (courtesy of M. Truffer and M. was estimated for each DEM using a least-squares regression: Fahnestock, University of Alaska Fairbanks) was used to visually confirm the formation, presence, and break-up of the ice dh (X, Y) = a0 + a1 X + a2 Y (1) tongue. We derived two 2.5 m resolution DEMs dated 17 March and where dh are elevation differences in stable areas, X and Y the 27 May 2013 from conventional SAR interferometric processing easting and northing and ai the parameters to be estimated. This of bi-static TanDEM-X imagery (Dehecq et al., 2016). GIMPDEM shift was then subtracted at each pixel. For this step, which is (Howat et al., 2014) was used as a reference during the more sensitive to outliers, all points with a slope higher than 40◦ unwrapping stage to minimize unwrapping errors. The DEMs were excluded. The DEMs were then converted from ellipsoid to produced must be correctly aligned, both horizontally and elevation above the EIGEN-EC4 geoid. vertically, using known stable areas (e.g., bedrock outcrops) that Due to the limited coverage of the ICESat lines over non- are not covered by ice or snow. To perform this calibration, we ice terrain (see Supplementary Figure 3), an additional tilt used ICESat elevation data over non-ice terrain as defined by the in the DEMs was identified and subsequently corrected for GIMP land classification mask (Howat et al., 2014). A horizontal using Operation IceBridge (OIB) Airborne Topographic Mapper shift (3.9 and 3.3 m in the x and y directions, respectively) (ATM) L1B Elevation and Return Strength data (Krabill, 2016). between the TanDEM-X derived DEMs and ICESat over non-ice OIB ATM elevation points were acquired for three springs when covered terrain was calculated by fitting a sinusoidal relationship the seasonal ice tongue was present in the fjord (08 April 2011, between elevation differences and terrain aspect (Nuth and Kääb, 25 April 2012, and 15 April 2014). TanDEM-X elevations from Frontiers in Earth Science | www.frontiersin.org December 2017 | Volume 5 | Article 107 | 30 Moyer et al. Ice Tongue Submarine Melt Rates FIGURE 2 | Example photographs from our 2009 time lapse camera (see Figure 1 for location) demonstrating (A) the intact ice tongue on 25 May 2009 and (B) the glacier terminus on 19 July 2009, post-ice tongue disintegration. FIGURE 3 | Schematic of intact ice tongue showing buoyancy-driven circulation in the fjord, as well as the characteristic decrease in ice tongue freeboard (and thus thickness) away from the ice front. 17 March 2013 were extracted for spatially corresponding 2011 Three 20 m resolution ice tongue velocity maps were created OIB ATM points and the difference taken over open water where based on conventional feature tracking applied to TerraSAR-X the OIB data had a slope of near-zero (20 to 25 km from the ice imagery (Tedstone et al., 2014) for the following 2013 image front). The slope of the difference was taken as the trend (or tilt; pairs: 12–23 February, 8–19 April, and 30 April to 11 May. ∼0.45 m height per km distance along-fjord) in the TanDEM-X Ice velocity on 17 March (Supplemental Figure 1A), the date elevations and was removed, effectively de-trending the dataset of our first DEM, was estimated assuming a linear trend in (see Supplemental Figure 4). The same correction was applied to velocity between the velocity maps from 12–23 February to 8–19 elevations from the 27 March 2013 DEM, as the tilt was the same April, and ranges from 28.5 to 30.5 m d−1 over the ice tongue. as that for the 17 March. The last available velocity map was from 30 April to 11 May Frontiers in Earth Science | www.frontiersin.org December 2017 | Volume 5 | Article 107 | 31 Moyer et al. Ice Tongue Submarine Melt Rates FIGURE 4 | Eastern (E) and western (W) ice flowlines, overlain on TanDEM-X ice tongue freeboard from (A) 17 March 2013 and (B) 27 May 2013. Refer to Figure 1 for location. (Supplemental Figure 1B), and throughout the paper, we use this (ddfs) of 4.5 mm d−1 ◦ C−1 , as used by Slater et al. (2017) velocity epoch to correspond with our second DEM, acquired on for KNS. Air temperature (◦ C) data were acquired from the 27 May. Ice tongue velocities in May range from 20.5 to 23.5 m nearby Geological Survey of Denmark and Greenland (GEUS) d−1 . PROMICE weather station (NUK_L, 550 m a.s.l., 64◦ 28′ 55.2′′ N, 49◦ 31′ 50.88′′ W, ∼21 km from KNS) (Ahlstrom et al., 2008; Ice Flowline Construction Figure 1), using a lapse rate of 0.5◦ C per 100 m to adjust the We constructed flowlines along the ice tongue using our ice temperatures to sea level (Slater et al., 2017). Precipitation data velocity results to track flow direction. Ten points near the glacier were acquired from the Danish Meteorological Institute (DMI) grounding line were chosen from both the eastern and western weather station in Nuuk (NUUK 4250, 80 m a.s.l., 64◦ 10′ 0.12′′ N, side of the ice tongue, with ∼25 m between points in the across- 51◦ 45′ 0′′ W, ∼105 km from KNS) (Cappelen, 2016; Figure 1). flow direction (Figure 4). To accommodate temporal changes in ice velocity, two separate sets of flowlines were created, one Estimating Submarine Melt Rate (SMR) for March and one for May, using our velocity maps from 17 SMR for all ice flowlines were estimated for both steady and March and 30 April to 11 May, respectively. Velocity vectors non-steady state scenarios. A steady state scenario assumes ice were extracted for each initial point, enabling the extraction thickness at a fixed location does not change in time, whereas of flow direction, which was then taken at points every 50 m a non-steady state scenario allows for changes in ice thickness moving down-fjord until the end of the ice tongue. The points at a fixed location (e.g., thinning due to high submarine melting were then connected, creating flowlines of ice moving down- exceeding the delivery of ice across the grounding line or changes fjord away from the grounding line (Figure 4). Distance from in the thickness of ice being advected across the grounding the grounding line was averaged for each set of flowlines (i.e., line). As estimating a non-steady state scenario requires at least eastern and western), using the end of spring terminus position two elevation estimates, a steady state (i.e., ∂H/∂t = 0) is often (Figure 1) digitized from a Landsat 8 image from 10 June 2013. assumed due to lack of data (e.g., Jenkins and Doake, 1991; Smith, 1996; Johnson et al., 2011). The two scenarios are presented Estimating Ice Tongue Surface Melt Rates here for comparison purposes, in part to test the validity of our Observed reduction in ice tongue freeboard as it is advected into method for years with only one DEM, when determining SMR by the fjord can be attributed to changes in surface mass balance, assuming a steady state scenario would be the only option. For a longitudinal and lateral spreading, and submarine melting. To steady state scenario (SS), elevation values along each ice flowline assess the potential contribution from surface mass balance, were extracted from both the 17 March and 27 May 2013 DEMs. surface melt was estimated using a simple positive degree day To reduce the impact of short-length scale elevation changes, (PDD) model (Hock, 2003) with a degree day factor for snow including crevasses, in the fractured tongue (see Figure 2) on our Frontiers in Earth Science | www.frontiersin.org December 2017 | Volume 5 | Article 107 | 32 Moyer et al. Ice Tongue Submarine Melt Rates melt rate estimates, flowline elevations were smoothed using a SMRSS (Rignot et al., 2013): two-sided moving average with a 625 m window (see Figures 5A, 6A). Elevation data were then converted to ice thickness using 1HNSS SMRNSS = SMRSS − (3) ocean water (1,027 kg m−3 ; Ribergaard, 2013) and ice (900 kg 1t m−3 following Enderlin and Hamilton, 2014) densities, assuming where 1HNSS (m) is the difference in ice thickness between the the ice is floating in hydrostatic equilibrium; an assumption two dates and 1t (d) is the time between the two dates. supported by both the best available bathymetry (Mortensen Melt rates were then averaged to produce a mean SMRSS and et al., 2013; Motyka et al., 2017) and the observation of the rapid SMRNSS for the western and eastern flowlines. To capture the and total disintegration of the ice tongue within just a 4-h time general trend in melt rates, lines of best fit were applied to both window on 15 June 2013. steady and non-steady state estimates. SMRSS were calculated for both March and May, accounting for thinning due to stretching in both the flow direction (second Error Analysis term on right-hand side of Equation 2) and perpendicular to flow Potential errors were traced throughout the analysis and standard (third term on right-hand side of Equation 2): error propagation methods were used to calculate the effect of errors in both elevation and ice velocity on estimated SMR. Errors ∂H ∂vx ∂vy in elevation values are from three primary sources: (1) DEM SMRSS = −vx −H −H (2) ∂x ∂x ∂y construction (including correction using ICESat), (2) correcting TanDEM-X elevations using OIB ATM data, and (3) smoothing where H is the ice thickness (m), vx and vy are the ice velocity the elevations for melt rate calculations. Error resulting from (m d−1 ) in the along- and across-flowline direction, and x and y DEM construction is ±2 m, a general error for the TanDEM-X represent distance in the along- and across-flowline direction. derived DEMs over areas with a slope <12◦ (Rizzoli et al., 2012), Note that a term representing across-flow thinning, −vy ∂H ∂y , which is likely an overestimate over the relatively low-sloped ice does not contribute because, by definition of a flowline, vy = tongue (<0.15◦ ). As our calculations utilize the elevation gradient 0 on the flowline. The final term in Equation (2) does however and not the absolute elevation, we instead account for a gradient make a small contribution due to the convergence or divergence error of ±0.35 m over the nearly 2 km ice tongue. This gradient of different flowlines. Derivatives in Equation (2) are evaluated error was estimated over 2 km segments (the same length over using conventional finite differences with a spacing 1x = 50 m which SMRs were estimated) of a section of very thin ice mélange and 1y = 25 m. where successive OIB ATM flights show near-constant slope. For a non-steady state scenario (NSS), a linear trend of The gradient error was estimated as the largest difference in thickness change between 17 March and 27 May 2013 was slope between the corrected TanDEM-X elevation flowlines and assumed at each point on the flowlines and accounted for by the OIB ATM lines. Fitting the TanDEM-X elevations to the subtracting a daily rate of change (m d−1 ) from the estimated OIB ATM elevations results in a root mean square error of FIGURE 5 | (A) Ice freeboard and thickness (m) on 17 March and 27 May 2013 with distance from KNS terminus for the eastern flowlines, where solid lines are means from 10 flowlines (Figure 4) and dashed lines are moving averages (MAVs) of the mean; (B) Steady state estimated submarine melt rate (SMRSS ) for eastern flowlines, with dashed trendlines and shaded error ranges. Frontiers in Earth Science | www.frontiersin.org December 2017 | Volume 5 | Article 107 | 33 Moyer et al. Ice Tongue Submarine Melt Rates FIGURE 6 | (A) Ice freeboard and thickness (m) on 17 March and 27 May 2013 with distance from KNS terminus for the western flowlines, where solid lines are means from 10 flowlines (Figure 4) and dashed lines are moving averages (MAVs) of the mean; (B) Steady state estimated submarine melt rate (SMRSS ) for western flowlines, with dashed trendlines and shaded error ranges. ±0.38 m, and smoothing the flowlines results in maximum mean Another potential source of error derives from smoothing squared errors of ±0.86 and ±0.47 m for the eastern and western the ice freeboard near the glacier grounding line, where pre- flowlines, respectively. The maximum total error for any one smoothed freeboard values decrease sharply, as compared with point in elevation along the eastern and western flowlines is ±1.4 smoothed values (see Figures 5A, 6A). While smoothing out and ±0.64 m, respectively. fracturing associated with large crevasses on the ice tongue helps Following Paul et al. (2015), error in ice velocity was estimated to reduce noise in the SMR estimates, the resultant reduction as ±0.09 m d−1 , resulting from the feature tracking process in freeboard gradient significantly lowers our SMRs near the applied to stable areas of the ice tongue, where crevassing is grounding line, which should therefore be considered minimum easily trackable and ice deformation is low. Errors in velocity at estimates of melt rate in this location. locations within 150 m of the original position of the previous end of summer vertical ice-front (which likely corresponds to RESULTS the grounding line) and at the edge of the ice tongue are not considered, as we did not use any velocities from these regions SMR Estimates in Kangersuneq Fjord in our SMR estimations. The reduction in smoothed ice freeboard (and thus thickness) While the error estimates cited alongside our SMRs account with distance down-fjord from the grounded KNS terminus for errors in the DEMs and ice velocity maps, there are in the March DEM (Figures 5A, 6A for eastern and western several additional sources of error that, although difficult to flowlines, respectively), combined with the interpolated ice quantify, must be considered. The assumption of both steady velocities, results in SMRSS for the eastern and western flowline and non-state state scenarios for ice tongue thickness likely sets of up to 1.4 ± 0.5 m d−1 (mean = 0.7 ± 0.4 m d−1 ) and introduces error in our SMR estimates. We know the ice 1.0 ± 0.2 m d−1 (mean = 0.5 ± 0.2 m d−1 ), respectively (see tongue is not in steady state between March and May 2013, lines of fit in Figures 5B, 6B). Due to thickening of the ice as the glacier is slower and the ice is thicker in May than in via advection, estimated SMRNSS for each set of flowlines (not March for any given point. Since we have only two DEMs, shown) are less than those estimated for the steady state scenario, we can only assume a linear thickening trend over the time with mean decreases in melt rate of 15 and 28% for the eastern period (see Equation 3). Any deviation from this trend would and western flowlines, respectively. For all flowlines, melt rates affect our melt rate estimates. For example, if the ice tongue broadly decrease with distance from the KNS grounding line and was thickest in April, this would imply the ice tongue was moving from east to west across the ice tongue. thinning between April and May, increasing NSS melt rates SMRSS estimated in May are similar to those in March, with estimated using Equation 3. Thus, if the tongue was thickest in eastern and western flowline SMRs of up to 1.4 ± 0.2 m d−1 April, our May melt rate estimates would be an underestimate; (mean = 0.8 ± 0.3 m d−1 ) and 1.0 ± 0.1 m d−1 (mean = 0.7 however without additional DEMs we cannot address this ± 0.3 m d−1 ), respectively (see lines of fit in Figures 5B, 6B). possibility. Estimated SMRNSS for each set of flowlines are again less than Frontiers in Earth Science | www.frontiersin.org December 2017 | Volume 5 | Article 107 | 34 Moyer et al. Ice Tongue Submarine Melt Rates those estimated for the steady state scenario, decreasing by 3 and with velocity and ambient fjord temperature (e.g., Holland and 10% for eastern and western flowlines, respectively. SMRs in May Jenkins, 1999; Jenkins, 2011). Mortensen et al. (2013) investigated show the same spatial variability as seen in March. winter circulation and water properties in 2009 in KF, finding While the heavily crevassed nature of the ice tongue itself a cool surface layer (ranging from −1.4 to 1.0◦ C at 0 and 40 m is not unphysical, it leads to unphysical noise in our melt rate depth, respectively) overlaying a warmer intermediate-depth estimates. For example, the rapid decrease in thickness between layer (increasing from 1.3 to 1.8◦ C at 50 to 90 m depth), below two adjacent points over a crevasse (one on the ice tongue which temperature was relatively constant (1.8◦ C) with depth. surface and one at the bottom of the crevasse) is interpreted as Motyka et al. (2017) investigated summer fjord water properties thinning using our method, and thus the estimated SMR would in 2011, ∼22 km from the KNS ice front, again finding a cool be erroneously high (e.g., the peak in March SMR ∼570 m from surface layer (ranging from 0 to 1.0◦ C at 0 and 40 m depth, the grounding line, Figure 5B). In contrast, the rapid increase in respectively) overlaying an even warmer intermediate layer thickness between a point at the bottom of the same crevasse and (increasing from 2.0 to 2.5◦ C at 50 to 150 m depth). Therefore, ice tongue surface on the other side is interpreted as thickening the ambient fjord water entrained by any subglacial plumes will of the ice, resulting in a negative melt rate (e.g., negative March be cooler with increasing distance from the grounding line, as SMRs, Figure 5B). To exclude these anomalous melt rates, we the thinning ice tongue, and shallower draft, will be submerged use the lines of best fit as seen in Figures 5B, 6B to interpret the in shallower, colder surface water. Plume velocity also decreases broader trends in estimated SMR. As they are the same order of with distance from the ice front as the plume loses buoyancy magnitude as the non-steady state scenario, we use our steady (Jenkins, 2011). For these reasons, and as expected, our estimated state scenario melt rates in our subsequent analyses, which allows SMRs approach 0 m d−1 down-fjord of the grounding line. for comparison to melt rates estimated in years when only one The presence of thick sea ice down-fjord of the end of the ice DEM is available (i.e., assumed steady state). In addition, we tongue supports this expectation, suggesting the surface waters note again that our melt rates near the grounding line should are very cold, resulting in little or no submarine melting (or else be considered minimum estimates, as the smoothing of crevasses there would be no sea ice). This result is dissimilar to summer greatly reduces freeboard gradient here. melt rates derived from icebergs found tens of kilometers from glacier grounding lines in other Greenlandic fjords (Enderlin and Surface Melt Estimates over the Ice Hamilton, 2014), which we would expect to be higher, due to Tongue deeper iceberg keel depths (as compared to the shallow ice tongue For the study period, between 17 March and 27 May 2013, depth) and stronger buoyancy-driven circulation from higher total surface snow melt over the ice tongue was 0.48 m water subglacial discharge in the summer (Sciascia et al., 2013). equivalent and total precipitation as snow was 0.23 m. We expect SMRs also show across-fjord variability, with higher melt precipitation to be less over the ice tongue than that recorded rates in the eastern section of the main ice tongue, compared in Nuuk, given the low elevation of the ice tongue and the to the western part. Across-fjord variability may be driven by rain shadow effect of the coastal mountains. A previous study water temperature, both in the ambient water column and thus estimated spring average precipitation decreases between coastal the plume, and by the strength (i.e., velocity) of any buoyant and inland weather stations in western Greenland between ∼0.5 runoff plume present. The eastern part of the ice tongue had the and 0.8 mm per km inland (Abermann et al., 2017). Therefore, highest March surface elevation, and thus the greatest thickness if anything, by using the estimates of precipitation from Nuuk and deepest keel depth (Figure 5A). Reaching over 80 m beneath we overestimate spring snowfall. Regardless, the estimates of the fjord surface near the grounding line, ice along the eastern precipitation are still orders of magnitude lower (in terms of flowlines is exposed to relatively warm, intermediate-depth water equivalent and impact therefore on freeboard) than our waters, which promote more rapid submarine melting (Enderlin estimated SMRs. The resultant mean surface melt rate, 0.004 m and Hamilton, 2014; Enderlin et al., 2016). In comparison, ice in d−1 , taken over the 71 days of the study period, is approximately the western part of the tongue has a keel depth near the ice front two orders of magnitude less than the rate of change in ice of <70 m, which could explain, in part, the lower SMR in this area thickness over the same time period, and thus considered of the fjord, as the shallower ice keel is exposed to slightly cooler negligible. As the PDD sum for 2013 during our study period waters than the eastern part of the tongue. (16.3◦ C day) is ∼75% lower than the mean for the last decade Across-fjord variability in SMR may also reflect the strength (mean from 17 March to 27 May for 2008 to 2016 of 69.4◦ C day), and location of any subglacial meltwater plumes emerging at 2013 should be considered a low spring surface melt and runoff the glacier grounding line. Uniform across-fjord ice tongue year. SMR would be expected, if keel depths are constant, where spatially well-distributed meltwaters emerge at the grounding DISCUSSION line (Slater et al., 2015). Conversely, spatially-focused, high SMRs near the ice front may indicate a locally dominant subglacial Spatial Variability in SMR meltwater channel, which in this case could be emerging Submarine melt rates show along-fjord variability, generally preferentially under the eastern part of the ice tongue. Slater et al. decreasing with distance down-fjord from the KNS grounding (2017) inferred KNS subglacial runoff distribution using plume line. This variability is likely driven by both the velocity and observations from summer 2009 time lapse imagery, suggesting temperature of subglacial meltwater plumes, with SMR scaling that runoff likely exits under the grounding line via spatially Frontiers in Earth Science | www.frontiersin.org December 2017 | Volume 5 | Article 107 | 35 Moyer et al. Ice Tongue Submarine Melt Rates distributed channels, with sporadic focusing resulting in visible In order to investigate the potential role that basal frictional surface plumes. During the mid- to late melt season, plumes meltwater could play in driving plumes in winter, we estimate typically reach the surface to the west of the grounding line basal meltwater flux for the area of KNS between the grounding center, with infrequently visible plumes emerging on the eastern line and ∼11 km up-ice from the grounding line. As basal drag side of fjord (Slater et al., 2017). However, as the presence of is unknown for KNS, we assume drag is of a similar magnitude the ice tongue and surrounding thick ice mélange prevents the to that estimated for Jakobshavn Isbræ, ∼200 kPa (Iken et al., expression of plumes on the surface, it is difficult to interpret 1993; Funk et al., 1994), as used for Kangerdlugssuaq Glacier subglacial meltwater distribution during the winter and spring by Christoffersen et al. (2012). Using our TerraSAR-X derived months. velocities for March and May for the lower 11 km of the glacier, In addition, rotational circulation in the fjord should be an ice density of 900 kg m−3 , and a latent heat of fusion of 334 kJ considered, which could impact the across-fjord distribution of kg−1 , basal meltwater flux was estimated as 3.2 m3 s−1 , for both surface meltwater and water entering the fjord at depth (Cottier March and May. Although producing weak plumes, subglacial et al., 2010; Straneo and Cenedese, 2015), and thus the heat discharge of this magnitude can generate point source SMRs of available for melting ice. Using data from Mortensen et al. between 2 and 4 m d−1 (Slater et al., 2015). Due to their lower (2013), we assume a 30 m thick fresh surface layer of sea ice/ice velocity, weak plumes, such as those expected via basal frictional tongue/glacier meltwater overlaying transitional layers of ice melt melting, reach neutral buoyancy before reaching the fjord surface and fjord source water, which gives an internal Rossby radius of (Christoffersen et al., 2012; Slater et al., 2015; Carroll et al., 2016). ∼6 km. As the fjord width varies between 4 and 6 km, rotational However, close to the glacier grounding line, where ice tongue effects are unlikely to have a primary role in controlling fjord keel depth is greatest, weaker plumes will likely still reach and circulation. However, they may have a secondary effect, focusing melt the base of the ice tongue. In comparison, higher subglacial the flow of water toward and away from the glacier terminus to discharge (between 50 and 100 m3 s−1 ), as might be expected the right hand side in the direction of flow (e.g., Cottier et al., later in the melt season, can result in point source SMRs up to 2010; Sutherland et al., 2014). 7 m d−1 (Slater et al., 2015). These stronger plumes may reach the fjord surface before reaching neutral buoyancy, thus allowing Temporal Variability in SMR for melting of the full ice front depth (Slater et al., 2015). Estimated mean SMRs do not show significant temporal variability, potentially due to the fact that all melt rates are estimated in the spring, prior to the on-set of substantial surface Comparison with Previous SMR Estimates melt. While estimated monthly total surface snow melt from from Greenland degree day modeling was higher in May (0.26 m) than in March Submarine melt rates estimated in this study are greater than, but (0.11 m), we do not expect or see significant differences in of the same order of magnitude, as those estimated for icebergs SMRs given how small these early spring surface melt rates are. during summer in Sermilik Fjord, southeast Greenland. Using However, increased surface melt later in the melt season and the repeat high-resolution satellite imagery, Enderlin and Hamilton associated enhanced subglacial meltwater plumes, combined with (2014) estimated SMRs of 0.39 ± 0.17 m d−1 for icebergs located increased intermediate depth water temperatures (Mortensen up to 60 km from the terminus of Helheim Glacier between et al., 2013; Motyka et al., 2017) would be expected to amplify August 2011 and July 2013. Using our lines of best fit, our local SMR considerably compared to winter melting (Jackson and estimated SMRs (up to 1.4 m d−1 ) are more than double those of Straneo, 2016). Such estimates would however not be possible Enderlin and Hamilton (2014). Given the close proximity to the using our method as the ice tongue breaks up in early June each grounding line, our estimated SMRs may reflect the influence of year, and is thus absent during the summer and autumn months. melting by plumes enhanced by emerging subglacial meltwater Seasonal stratification and water temperature at depth are sourced from frictional basal melt (e.g., Christoffersen et al., highly dependent on the mode of circulation in KF (Mortensen 2012); such plumes will clearly have a diminished influence et al., 2011). In the spring, when we estimate SMR, circulation is 60 km from the ice front, where plume velocity has decreased. mainly driven by dense coastal inflows and tidal mixing, which Estimated SMRs for icebergs stuck in ice mélange in Sermilik act to cool and slightly freshen waters at intermediate depths. and Ilulissat fjords range from 0.1 to 0.8 m d−1 , and increase The presence of subglacial meltwater plumes sourced from with iceberg draft and submerged ice area (Enderlin et al., 2016). frictional basal meltwater emerging at the glacier grounding line These melt rates are more similar to ours near KNS, due both (Christoffersen et al., 2012) likely also play a role in controlling to the relatively similar distance from the grounding line to fjord circulation and submarine melting in the winter and early the icebergs (from 0 to 20 km away) and our estimates (150 to spring. In the summer, however, tidal mixing and subglacially- 2,400 m away), as well as the comparable summer intermediate driven circulation, via surface-derived meltwater plumes, are ambient water temperatures in Ilulissat (up to 2.2◦ C) (Mernild dominant and act to freshen and significantly warm the upper et al., 2015), Sermilik (up to 2◦ C) (Straneo et al., 2010, 2011), and intermediate water layer (Mortensen et al., 2013). Temperature Kangersuneq (up to 2.5◦ C) fjords. differences of nearly 2◦ C were seen at intermediate depths Estimated SMRs for the KNS ice tongue in spring 2013 are (between 120 and 150 m) between April and September 2010 one to two orders of magnitude larger than SMRs estimated (Motyka et al., 2017), an increase which would have a significant between 2000 and 2010 for the floating tongue at Petermann impact on the melting of submerged ice. Glacier (0.07 ± 0.035 m d−1 ) (Johnson et al., 2011; Enderlin Frontiers in Earth Science | www.frontiersin.org December 2017 | Volume 5 | Article 107 | 36 Moyer et al. Ice Tongue Submarine Melt Rates and Howat, 2013). The difference in melt rate magnitude in Freshwater Flux from Submarine Melting this case is likely due to both the difference in ambient ocean of the Ice Tongue temperatures at ice keel depth between the two fjords as well as Given the potential importance of meltwater generation to fjord meltwater plume dynamics. The ambient water temperatures in water properties and nutrient productivity (Meire et al., 2017), we northwest Greenland are much lower at keel depth than those here estimate the spring freshwater flux from submarine melting in southwest Greenland, peaking at 0.2◦ C at nearly 500 m depth of the ice tongue. Using grounded terminus width (∼4,500 m), in Peterman Fjord (Johnson et al., 2011), where keel depths in depth (∼250 m), and average velocity from March to May 2013 the first few km of the fjord reach ∼480 m (Wilson et al., 2017). (∼6.9 km a−1 ), spring ice flux across the KNS grounding line was In contrast, ambient water temperatures at keel depth for KNS estimated to be 246 m3 s−1 . Assuming a simplified rectangular (∼80 m near the grounding line) fall between 1.3 and 2.0◦ C, submarine configuration of the ice tongue with a width of depending on the season (Mortensen et al., 2013; Motyka et al., ∼1,800 m and a length of ∼2,500 m, total basal submerged area 2017). Plume dynamics may also fundamentally differ, with the is ∼4.5 km2 . Using spatially averaged SMRSS from our western weak melt-driven convective plumes beneath Petermann (which and eastern fjord flowlines, meltwater flux derived from the has a ∼70 km long permanent ice tongue) more akin to those ice tongue ranges from 26 to 36 m3 s−1 (11 to 15% of spring at large Antarctic ice shelves, and strong subglacial discharge- grounding line ice flux) in March, and from 36 to 42 m3 s−1 driven plumes beneath the short ice tongue at KNS giving rise to in May (15 to 17% of spring grounding line ice flux). This convection-driven melt as observed at tidewater glaciers in mid- partitioning of freshwater flux entering the fjord is comparable summer (Jenkins, 2011). In addition, the difference in velocity to that estimated by Xu et al. (2013) for Store Glacier in western between KNS and Petermann glaciers may play a secondary Greenland, where submarine melting accounted for 20% of role in controlling estimated SMRs. The average winter velocity August 2010 glacier influx. In contrast, our flux partitioning is for KNS is ∼8 km a−1 , eight times that of Petermann Glacier much lower than that estimated by Motyka et al. (2003, 2013) for (Johnson et al., 2011). A faster-flowing, warm based glacier will LeConte Glacier in Alaska, where submarine melting accounts create more basal friction and thus more basal melt (e.g., Holland for 50–67% of summer frontal ablation. Differences in flux et al., 2008; Christoffersen et al., 2012), producing more vigorous partitioning are likely due to seasonality and fjord temperatures, subglacial meltwater plumes and inducing higher SMRs even in and to terminus geometry (Truffer and Motyka, 2016). winter (Carroll et al., 2015; Cowton et al., 2015; Slater et al., While ice tongue melt only accounts for ∼11–17% of the 2015). overall spring grounding line flux, it provides a significant Utilizing summer hydrographic observations between ∼35 amount of freshwater to the fjord in spring months, when and 88 km from the Kangerdlugssuaq Glacier terminus, Inall et al. surface runoff is largely absent. As such, the associated inputs (2014) estimated heat delivery to the calving front equivalent of freshwater into the fjord at different depths from submarine to 10 m d−1 of ice melt. Motyka et al. (2017) used parameters melting may have a major impact on fjord water stratification, derived from models and hydrographic measurements 12 km circulation and associated productivity (e.g., Motyka et al., 2013; from the KNS ice front to estimate a near-terminus late-summer Sciascia et al., 2013; Sutherland et al., 2014; Meire et al., 2017). SMR of ∼3–7 m d−1 . Our empirically-derived SMRs are nearly an order of magnitude lower than those estimated by Inall et al. (2014) and the upper range estimates of Motyka et al. (2017), Potential Applications despite similar ambient fjord water temperatures (up to 2.25◦ C at We have derived SMRs using changes in the freeboard of a depth for Kangerdlugssuaq Fjord; Inall et al., 2014). It is unlikely seasonally floating ice tongue as it advances down-fjord during that hydrographic estimates taken more than 30 km from the the spring, building upon earlier work using freeboard and terminus realistically represent the heat energy used for melting ice flux divergence to estimate SMRs of floating ice tongues the ice front, as a large portion of this energy might be lost in Greenland (e.g., Motyka et al., 2011; Enderlin and Howat, to melting of any ice mélange and icebergs in the fjord before 2013). This technique has considerable potential to further our reaching the glacier (Enderlin et al., 2016). In fjords like Helheim, understanding of ice-ocean interactions and submarine melting where icebergs are large enough to cover the full fjord depth in glacial fjords. Using both satellite and time-lapse imagery, (Enderlin and Hamilton, 2014), deep water could also be cooled seasonal differences in SMR could be evaluated by estimating by the melting of icebergs at depth. Heat transport to the ice front melting throughout the year, as long as an ice tongue is present can also be reduced through vertical mixing of the water column in winter and spring, and icebergs are present in summer and via wind-driven internal seiches (e.g., Arneborg and Liljebladh, autumn sufficiently close to the ice front (following methods of 2001; Cottier et al., 2010) or by the convective overturning of Enderlin and Hamilton, 2014). In addition, analysis of seasonally water due to the release of brine from sea ice formation (Cottier floating ice tongues presents the opportunity to derive SMR et al., 2010). In addition, the presence of shallow sills in the estimates much nearer to glacier calving fronts (when compared fjord alter the fjord circulation and may prevent deeper, warm with estimates using hydrographic profiles), in the precise water from reaching the ice front (e.g., Mortensen et al., 2011, location where the key processes controlling calving dynamics 2013). This suggests that terminus melt rates derived from distal and retreat are not well resolved. We anticipate that our estimates along-fjord heat flux values may be too high unless the heat lost of SMR, and others derived using this methodology, will be to mid-fjord melting, vertical mixing, and fjord bathymetry are used to tune fjord circulation and plume models, which in considered. turn will soon be used to force ice sheet models predicting Frontiers in Earth Science | www.frontiersin.org December 2017 | Volume 5 | Article 107 | 37 Moyer et al. Ice Tongue Submarine Melt Rates the future of the Greenland Ice Sheet and its contribution to in the ice tongue draft and the temperature stratification in the sea level rise. fjord, but may also reflect the strength of any subglacial meltwater Our submarine melt rate estimates are derived from an ice plumes present. The submarine meltwater flux derived from the tongue that is already floating, thus they do not affect the annual ice tongue ranges from 26 to 42 m3 s−1 , which accounts for mass balance of the grounded portion of KNS. Nevertheless, the between 11 and 17% of the grounding line ice flux into the fjord submarine melting of the ice tongue may affect its ability to in the spring months, prior to the onset of ice sheet surface buttress the winter ice flux and discharge across the grounding melt. Our results demonstrate that using high resolution satellite line (e.g., Motyka et al., 2011; Krug et al., 2015), with potential imagery to analyze changes in freeboard at floating seasonal ice negative consequences for annual mass balance. If SMRs increase tongues has considerable potential to reveal in detail the temporal in the future as is expected under climate projections, the and spatial variations in SMR at tidewater glacier termini. residence time of seasonal ice tongues like that at KNS will decrease, effectively extending the length of the calving season AUTHOR CONTRIBUTIONS and allowing for greater mass loss from the grounded portion of the ice sheet. In addition, quantifying ice tongue melt rates AM performed all of the analysis and led the writing of the can tell us a lot about calving front melt processes. For example, manuscript. NG produced the DEMs and ice velocities. All the spatial distribution of ice front SMRs (for which our ice authors contributed ideas and methodological developments, tongue SMRs are a proxy) can influence the morphology of the and provided editorial input on the manuscript. calving front through spatially heterogeneous undercutting, with potential implications for calving frequency and style (Straneo FUNDING et al., 2012; Chauché et al., 2014; Carroll et al., 2015; Slater et al., 2017), and ultimately glacier retreat, velocity and ice flux. A better AM is supported by a Principal’s Career Development understanding of spatial variations in submarine melting of the PhD Scholarship from the University of Edinburgh. We ice front may lead to the development of a relationship between acknowledge NERC grants NE/K015249/1 (to PN) and melt distribution and calving, which is poorly understood but NE/K014609/1 (to AS), and a NERC PhD studentship (to likely of critical importance for controlling tidewater glacier DS). We also acknowledge DLR projects XTI_GLAC0296 and dynamics. LAN1534 (to NG). The research leading to these results has also received funding from the Scottish Alliance for Geoscience, CONCLUSIONS Environment and Society’s Small Grant Scheme (to AM). Improved estimates of SMR are essential to gain a better ACKNOWLEDGMENTS understanding of the processes controlling ice dynamics at tidewater glacier termini, and in particular, the potential We acknowledge M. Truffer and M. Fahnestock of the University relationship between submarine melt and tidewater glacier of Alaska, Fairbanks for the use of time lapse camera imagery, acceleration and retreat. Using high-resolution TerraSAR-X and which was acquired under the US NSF grant PLR-0909552. Data TanDEM-X satellite imagery, we have estimated SMRs of a from the Programme for Monitoring of the Greenland Ice Sheet seasonal floating ice tongue adjacent to the grounding line of (PROMICE) were provided by the Geological Survey of Denmark KNS. Changes in freeboard of the ice tongue, both with distance and Greenland (GEUS) at http://www.promice.dk and data from from the grounding line and across the fjord, have been used to the Danish Meteorological Institute (DMI) are available at http:// estimate spatial variations in melt rate. www.dmi.dk. Our estimates of spring steady state SMR near the grounding line of KNS reach 1.4 ± 0.5 m d−1 , and decrease with distance SUPPLEMENTARY MATERIAL down-fjord from the glacier grounding line, with mean rates up to 0.8 ± 0.3 and 0.7 ± 0.3 m d−1 for the eastern and western The Supplementary Material for this article can be found parts of the ice tongue, respectively. There is also considerable online at: https://www.frontiersin.org/articles/10.3389/feart. across-fjord variability in SMR which may be driven by variation 2017.00107/full#supplementary-material REFERENCES Cappelen, J. (ed.). (2016). Greenland–DMI Historical Climate Data Collection 1784- 2016. 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