Modeling sub-sea permafrost in the East Siberian Arctic Shelf: The Laptev Sea region

Authors


Abstract

[1] Models of sub-sea permafrost evolution vary significantly in employed physical assumptions regarding the paleo-geographic scenario, geological structure, thermal properties, initial temperature distribution, and geothermal heat flux. This work aims to review the underlying assumptions of these models as well as to incorporate recent findings, and hence develop an up-to-date model of the sub-sea permafrost dynamics at the Laptev Sea shelf. In particular, the sub-sea permafrost model developed here incorporates thermokarst and land-ocean interaction theory, and shows that the sediment salinity and a temperature-based parametrization of the unfrozen water content are critical factors influencing sub-sea permafrost dynamics. From the numerical calculations, we suggest development of open taliks may occur beneath submerged thaw lakes within a large area of the shelf.

1. Introduction

[2] The Arctic region contains extensive amounts of carbon, accumulated over millennia in terrestrial and sub-sea permafrost, that can be re-introduced back into the present-day atmosphere and biosphere biogeochemical cycle [ACIA, 2004], and thus feedback processes affecting global climate dynamics may be accelerated. One of the feedback processes is related to destabilization of significant quantities of the gas hydrate deposits [Makogon et al., 2007] and to consequent production of methane that can seep to the water column through pathways in sub-sea permafrost.

[3] The state of permafrost in Arctic is a potential key to understanding whether and how methane, preserved in seabed reservoirs, can escape to the atmosphere. Unlike the terrestrial permafrost in the Arctic which experienced a change in its thermal regime caused by the 6–7°C mean annual air temperature increase since the last Glacial Maximum [Frenzel et al., 1992], sub-sea permafrost has been subjected to additional drastic transformations, e.g., inundation by the ocean, resulting in warming of the permafrost environment by as much as 17–20°C [Soloviev et al., 1987; Kim et al., 1999; Romanovskii and Hubberten, 2001; Gavrilov and Tumskoy, 2003; Romanovskii et al., 2005].

[4] As opposed to slow and gradual release of carbon from thawing terrestrial permafrost, Shakhova and Semiletov [2009] and Shakhova et al. [2010a, 2010b]hypothesize that large quantities of carbon sequestered beneath and within the sub-sea permafrost can be released to the atmosphere rather quickly. Moreover,Shakhova et al. [2010b] recently reported extensive methane venting at some locations on the East Siberian Arctic Shelf (ESAS), and Nicolsky and Shakhova [2010]demonstrated that open taliks can occur under the Dmitry Laptev strait region. These recent findings prompt us to re-examine current understanding of the thermal state and stability of submarine permafrost in the ESAS, consisting of the Laptev and East Siberian seas. Because of the geological difference of the settings of these two seas, in this work we focus on modeling the sub-sea permafrost dynamics within the Laptev Sea shelf. Research on the East Siberian shelf is forthcoming.

[5] We emphasize that because of the sparsely distributed measurements of the sub-sea permafrost temperature, salinity, and distribution [Ponomarev, 1940; Grigoriev, 1962; Molochushkin and Gavrilyev, 1970; Soloviev et al., 1987; Rachold et al., 2007], the present understanding of the current thermal state of sub-marine permafrost in the Laptev Sea shelf is primarily based on modeling results [Molochushkin and Gavrilyev, 1970; Danilov and Zhigarev, 1977; Soloviev et al., 1987; Fartyshev, 1993; Kim et al., 1999; Delisle, 2000; Romanovskii and Hubberten, 2001; Romanovskii et al., 2005]. These previously developed models significantly vary in the underlying assumptions, producing different results regarding the age, thickness and temperature of the sub-sea permafrost.

[6] A review of sub-sea permafrost measurements and development of sub-sea permafrost models for the ESAS can be found inVigdorchik [1978], Fartyshev [1993], Zhigarev [1997] and Gavrilov et al. [2001]. Outside of ESAS, research on the sub-sea permafrost on the Beaufort Shelf of the North American Arctic was conducted byMackay [1972] and Osterkamp and Harrison [1985]. Several researchers such as Nixon [1986] and Taylor et al. [1996]attempted modeling sub-sea permafrost dynamics on the Beaufort Shelf.

[7] Two basic mechanisms of the sub-sea permafrost degradation are prelevant in models: the upward and downward. The former more prominently results from the geothermal heat flux in fault zones [e.g.,Romanovskii and Hubberten, 2001], while the latter is due to the surface warming, e.g., by large rivers [Delisle, 2000]. A key question to be answered by the models is existence of open taliks - a body of unfrozen ground connecting sub- and supra-permafrost waters - through which the gases can escape to the water column. We note that the modeling results byRomanovskii and Hubberten [2001], limits existence of open taliks to the areas of fault zones, occupying less than 5% of the Laptev and East Siberian Seas. At the same time, the modeling results by Zhigarev [1997] show existence of the open taliks outside of the fault zones by considering both the downward and upward degradation of permafrost within the Laptev Sea.

[8] We hypothesize that a possible mechanism for the formation of open taliks outside of the fault zones is the thawing of permafrost beneath thaw lakes submerged several thousand years ago during the ocean transgression. Such thaw lakes were abundant on the Laptev Sea coastal plain and their interaction with the ocean is described in Romanovskii et al. [2000] and Gavrilov and Tumskoy [2003]. The existence of open taliks underneath submerged thaw lakes was investigated by Romanovskii et al. [2004], who concluded that no open taliks can develop outside of the fault zones even underneath the submerged thaw lakes. Here, we re-evaluate the assumptions that led to this conclusion. In particular, we note that a key distinction of several modeling studies [e.g.,Nixon, 1986; Taylor et al., 1996] from those by Romanovskii is parametrization of the unfrozen liquid water by a level of the salt intrusion into permafrost. We hypothesize that modeling sub-sea permafrost on the Laptev Sea shelf with a correct parametrization of the unfrozen liquid water content can bring new insights into the current permafrost distribution.

[9] We emphasize that because of the insufficient measurements of the thermal properties, salinity, unknown dynamics of the ocean regressions/transgressions, and lack of the pre-historic temperatures, all models of the sub-sea permafrost dynamics are based on some hypotheses and assumptions regarding the shelf properties and physical processes during previous glacial cycles. Thus, in order to construct the most sound and substantialized set of parameters to simulate the permafrost dynamics within the Laptev Sea shelf, we review previous studies and modeling results for this region. We highlight major assumptions byFartyshev [1993], Taylor et al. [1996], Romanovskii et al. [2005], and Gavrilov et al. [2006], combine their ideas, and develop a refreshed sub-sea permafrost model. We indicate that some structural geology (horst and grabens) probably influence the permafrost dynamics and its present temperature distribution. We show that degradation of the salt-bearing sub-sea permafrost may lead to formation of open taliks outside of the fault zones in the Laptev Sea Region. The existence of such taliks can serve as pathways for gas in the sub-sea permafrost, providing an explanation for widespread methane observations in the Laptev Sea [Shakhova et al., 2005; Shakhova and Semiletov 2007].

2. Study Area and Permafrost Observations

[10] The Laptev Sea is an Arctic sea that is bounded by the Taimyr Peninsula on the west and the Novosibirsk Islands on the east, see Figure 1. The sea is characterized by extensive shallow regions, where the depth is typically less than 30 meters. The even bathymetry hides paleoriver canyons [Shpolyanskaya and Rozenbaum, 2004], ancient coastal terraces [Danilov et al., 1998], as well as neotectonic features caused by the ultra-slow spreading Gakkel Ridge [Grachev et al., 1970; Drachev et al., 1998; Sekretov, 1999]. It is believed that the Gakkel Ridge, which represents a boundary between the North America and Eurasia Plates in the Eurasia Basin, propagates under the Laptev Sea and has resulted in the development of geomorphological structures that comprise the Laptev Rift System (LRS) [Drachev et al., 1998].

Figure 1.

Primary structural elements of the Laptev Rift System (LRS), after Drachev et al. [1998], Sekretov [1999] and Franke et al. [2001]. The yellow circles mark locations of the deep coastal boreholes where temperature measurements are available. The dashed green line shows a transect, along which the sub-sea permafrost is modeled. The question marks are associated with areas where there is no sufficient data to determine boundaries of the structural elements. The following abbreviations are introduced: SLRB - South Laptev rift basin, LTU - Lena–Taimyr uplift, TH - Trofimov horst, ULRB - Ust' Lena rift basin, MH - Minim horst, UYH - Ust' Yana horst, ShH - Shiroston horst, ELH - East Laptev horst, SH - Stolbovoi horst, BSNRB - Bel'kov-Svyatoi Nos rift basin, KH - Kigilyakh horst, and KU - Kotel'nyi uplift. The numerals next to the abbreviations show values of the assumed geothermal heat flux in 60−3 Wm−2, used to model the reference case. The heat flux values are based on the studies by Kholodov et al. [1999], and Romanovskii and Hubberten [2001] and are discussed in Section 4.4.

[11] The present-day understanding of the LRS is based on multichannel seismic reflection data allowing for delineation of major rifts and faults [Drachev et al., 1998; Sekretov, 1999; Franke et al., 2001]. The LRS consists of a series of deep sedimentary basins (grabens, or rift basins) and highstanding blocks (horsts) aligned with the boundary between North American and Eurasian lithospheric plates. Figure 1 shows schematic locations of the primary structural elements of the LRS. The reader is encouraged to inspect the figure caption, which gives a complete list of geographical abbreviations. The sedimentary cover on the uplifts is significantly reduced and generally does not exceed 1 km in thickness.

[12] In the absence of drilling on the continental shelf, limited data from onshore boreholes provide the only clues to the stratigraphy and lithology of the Laptev Sea shelf. Fartyshev [1993] and Drachev et al. [1998] provide two complimentary accounts of the Cenozoic history of the shelf. The sedimentary cover in the North American Arctic has been studied by Blasco et al. [1990] and Blasco [1995], who found layering of marine and continental sediments in the Canadian Beaufort Shelf. The layers are identified within a 467-meter deep borehole near the Mackenzie River Delta. The data extracted from core samples show eight distinct regressive/transgressive fluvial sand/marine mud cycles [e.g.,Osterkamp, 2001]. We hypothesize that the Laptev Shelf subsidence, superimposed with the pre-Quaternary and Quaternary sea level changes, has resulted in a complicated stratigraphy of the sediments both marine and continental in origin.

[13] An extensive study of the frozen sub-sea sediments in the Laptev Sea Shelf was initiated by an expedition ofPonomarev [1940], who explored deposits of the rock salts in Kozhevnikov Bay (110°25′E, 73°40′N). During this expedition, several layers of frozen ground were discovered in boreholes distant from the ocean shore. The layers were separated by three water-bearing horizons, within which the water had sub-zero temperature in °C. These facts were sensational and led to further exploration of sub-sea permafrost. In the 1950s, Grigoriev supervised expeditions to sub-aqueous parts of the Lena, Yana, and Indigirka Deltas, Laptev Strait, and Van'kina Gulf. Based on the collected data, it was established that the frozen sub-sea sediments occur over shallow parts of the continental shelf where the land-fast ice forms [Grigoriev, 1962, 1966]. Later Usov [1965] and Ivanov [1969]joined Grigoriev and obtained similar results at locations beyond the extent of the land-fast ice. Frozen sediments were located underneath a 2.5–5.0 meter-thick cryopeg layer - a strata of the salt-bearing ground material in which water is unfrozen at temperatures less than 0°C.

[14] In 1960s, under the guidance of Molochushkin, an extensive research was conducted near the outcropping shores of Muostakh Island (130°00′E, 71°33′N) and in the Van'kina Gulf (139°44′E, 72°10′N) of the Laptev Sea. Molochushkin discovered cryopegs within the frozen sub-sea sediments. It was also found that the zone of the contemporary accumulation of sediment in the Laptev Sea had bottom deposits not cemented by ice at a temperature up to −6°C.

[15] In 1971, Grigoriev discovered ice-rich rocky material 86 meters below the sea bottom in Van'kina Gulf and showed that the sub-sea permafrost exists even in locations with a positive mean annual benthic temperature at the large depth. A decade later, several expeditions to the Novosibirsk Islands were launched. More than 60 boreholes, with depths up to 215 meters, were drilled by “SevMorGeologia” expeditions in the straits between the islands [Fartyshev, 1993]. None of the boreholes penetrated through the entire layer of permafrost, but showed that frozen ground material typically underlies unfrozen sediments. We point out that the terrestrial permafrost thickness in this region is believed to be around 400–600 meters, although no borehole has yet penetrated the whole layer of permafrost.

3. Development of Sub-sea Permafrost Maps

[16] Based on general concepts of the ocean transgression and extremely limited factual data on the sub-sea permafrost distribution,Baranov [1960]identified a boundary of the ice-bonded sub-sea permafrost distribution on the Arctic Shelf. The boundary was drawn along an isobath of 100 meters. In the 1970s, new observations became available, and Tolstikhin and Soloviev, and later Fotiev, further developed maps of the sub-sea permafrost extension that qualitatively agree with the map by Baranov. An interested reader is referred toGavrilov et al. [2001]for a comparison of the sub-sea permafrost distribution maps. Later,Neizvestnov [1981]noted that the temperature of phase change transition mainly depends on the salinity of water in soil pores and revised published sub-sea permafrost maps.

[17] The first attempt to model permafrost temperature at the Laptev Shelf after a marine transgression was attempted by Molochushkin [1970]. Water integrators - analog computers that used fluids to model heat transfer - were utilized to model temperature dynamics in a two-layer column while taking into account the latent heat of fusion of ice in Quaternary sediments. The icy sediments were assumed to have a thickness of 50 meters and were lying above a layer representing the bedrock. During the transgression, the ground surface temperature was specified to change instantly from −11°C to 0°C. On the basis of these numerical experiments, the sub-sea permafrost degradation can take from 8 to 14 thousand years [Molochushkin, 1973]. Molochushkin [1973]also considered various levels of the ground salinity and found that the saline permafrost destabilizes much faster. We emphasize that Molochushkin was one of the first scientists to consider necessary ingredients for modeling the sub-sea permafrost dynamics.

[18] In North America, Mackay [1972], Hunter et al. [1976], Lachenbruch and Marshall [1977], Osterkamp and Harrison [1985], and many other scientists also conducted research on the sub-sea permafrost in the Arctic. For instance,Nixon [1986], Taylor et al. [1996] and Osterkamp [2001]simulated the sub-sea permafrost dynamics on the Beaufort Sea Shelf. For the sake of brevity, we focus on modeling the sub-sea permafrost within the Laptev Sea shelf. We mention important related findings on the sub-sea permafrost in Beaufort Sea. Numerical modeling of the sub-sea permafrost within the Laptev Sea region was attempted byDanilov and Zhigarev [1977], Antipina et al. [1978], Soloviev [1981], Neizvestnov [1981], Fartyshev [1993], Zhigarev [1997], Romanovskii and Hubberten [2001], and Romanovskii et al. [2005]. In this section, we briefly review several Laptev Sea shelf sub-sea permafrost models in order to develop a sound set of parameters to simulate the current sub-sea permafrost distribution.

3.1. Modeling Permafrost Dynamics Since the Kargian Transgression

[19] The ocean transgressions and regressions, which occurred in the past, have influenced development of permafrost on the Laptev Sea shelf. Among all ocean regressions/transgressions, the most recent sequence of 80 and 0 kya, have primarily defined the present temperature distribution and sub-sea permafrost temperature and thickness. Usually, four intervals are considered since the last interglacial epoch: Zyryanian stadial/regression (80–50 kya), Kargian interstadial/transgression (50–25 kya), Sartanian stadial/regression (25–12 kya), and Holocene interglacial/transgression (12–0 kya). Among these intervals, the most arguable until recently were the extents of Kargian transgression and the retreat of Sartanian regression.

[20] Developing the original ideas of Molochushkin, Antipina et al. [1978], and then Fartyshev and Antipina [1982] attempted to model the freezing of the Laptev Shelf since the Kargian transgression, i.e., since 25,000 years ago. Similarly to Danilov and Zhigarev [1977], Fartyshev conjectured that the sea level during the Kargian epoch was higher than the current level. Following studies by Kaplina and Kuznetsova [1975], Fartyshev assumed that during the Sartanian regression, the ground surface temperature was −22°C. During the Holocene transgression, the ground surface temperature was thought to rise to −12°C and then lower to its present-day value ofT′ = −13°C. The assumed water level dynamics and temperature anomaly with respect to T′ are shown by green lines with square symbols in Figures 2 and 3, respectively.

Figure 2.

Reconstructed sea level dynamics, used to model the sub-sea permafrost in the Laptev Sea Region. Durations of the Zyryanian stadial, Kargian interstadial, Sartanian stadial, and Holocene interglacial are shown by segments with letters Z, K, S, and H, respectively.

Figure 3.

Reconstructed ground temperature anomaly in the Laptev Sea Region, adopted from Gavrilov and Tumskoy [2003]. The original and corrected paleotemperature reconstructions are shown by the lines marked with hollow and filled triangles, respectively. The regional paleotemperature data is according to Kaplina and Kuznetsova [1975], Kaplina and Chekhovsky [1987], Balobaev [1991], and Konishchev [1998]. Durations of the Zyryanian stadial, Kargian interstadial, Sartanian stadial, and Holocene interglacial are shown by segments with letters Z, K, S, and H, respectively.

[21] Unlike previous investigators, Fartyshev [1993]pays special attention to the structural geology of the Laptev Sea shelf. In his two-layer soil column, the ground material is associated with either a graben or horst. The top layer is composed of Quaternary deposits with the freezing temperature of up to −2.6°C. The ground material of the deeper layer, associated with grabens is considered to be salt-bearing and have a −1°C freezing temperature. The ground material in horsts, is assumed to have a 0°C freezing temperature and a negligibly small gravimetric water content 3% (volumetric water content ≈6%). In the following discussion, all considered numerical models exploit the volumetric water content, while the gravimetric water content is given in many references dealing with measurements. Thus, unless otherwise noted, we state values of both types of the water content with an estimated value of the volumetric content in parentheses. A conversion between two types of the water content can be found inHillel [2004].

[22] Despite a realistic parametrization of the thermal properties and the correct extent of the Sartanian regression, the value of the geothermal heat flux seems to be underestimated in this numerical model, which leads to inaccurate predictions of a present-day sub-sea permafrost thickness between 250 and 1400 meters.Fartyshev [1993] estimates that the flux ranges between 17 ⋅ 10−3 Wm−2 and 24 ⋅ 10−3 Wm−2. These values are extremely low, not adequately substantiated, and have led to the belief that relict sub-sea permafrost several hundreds of meters thick occurs over the entire shelf [Romanovskii and Hubberten, 2001].

3.2. Modeling Permafrost Dynamics Under the Influence of Long-Term Climate Fluctuations and Glacio-eustatic Sea Level Variations

[23] In 1970s and 1980s, a concept of glacio-eustatic oscillation of the sea level gained an acceptance and allowed for construction of a paleogeographical scenario of the Laptev Sea shelf development since the Kazantsevian inter-glacial, or since 110,000 years ago [Romanovskii et al., 1998]. The assumed relative sea level change is shown in Figure 2. The paleogeographic scenario together with advances in computer modeling permitted for the modeling permafrost dynamics over the hundreds of thousands of years [Tipenko et al., 1999; Romanovskii and Hubberten, 2001]. In these modeling studies, it was assumed that heat conduction is a dominant process, and the soil temperature T [°C] can be simulated by a heat equation with phase change:

display math

where the quantities C = C(T, x) [Jm−3 K−1] and λ = λ(T, x) [Wm−1 K−1] stand for the volumetric heat capacity and thermal conductivity of soil, respectively; η is the soil volumetric porosity; L [Jm−3] is the volumetric latent heat of fusion of water, and θ is the liquid pore water fraction. The thawed and completely frozen ground correspond to θ = 1 and θ = 0, respectively. Note that this equation is applicable when migration of water is negligible, there are no internal sources or sinks of heat, and frost heave is insignificant.

[24] While reconstructing the paleoclimate within the Laptev Sea shelf, Romanovskii and Hubberten [2001], Gavrilov and Tumskoy [2003], and Romanovskii et al. [2005]assumed that long-term temperature oscillations are synchronous over the entire globe. Therefore, the regionally corrected paleotemperature reconstruction from the Vostok ice core was assumed to adequately describe the ground temperature dynamics at the Laptev Sea shelf over the last 400,000 years. This allowed a relatively new approach for the development of the smooth temperature reconstruction during several glacial periods. Another assumption in the development of the paleoclimate scenario was a latitudinal temperature zonation, i.e., the mean annual temperature decreases 1.5°C per one degree of latitude. We argue inSection 4.1 that the zonation might not have existed within the Laptev shelf during the previous glacial periods.

[25] We emphasize that a proper parametrization of the geothermal heat flux is essential for realistic determination of the lower boundary of the permafrost [e.g., Kudryavtsev, 1978; Romanovskii, 1993]. Unfortunately, there is still little known regarding the heat flux distribution on the Laptev Shelf. Most of the heat flux measurements were completed either on the continental slope or in nearby coastal areas [Drachev et al., 2003]. Hence, Romanovskii and Hubberten [2001] and Romanovskii et al. [2005] proposed to parameterize the heat flux in the LRS similarly to continental rift systems, e.g., the Momsky and Baikalsky rifts and the rift structures of the basement of the West Siberian Plate. The flux within undisturbed blocks of the Moma and Baikal rifts can range from 40 ⋅ 10−3 to 80 · 10−3 Wm−2, while in the active faults the flux can reach as much as 100 ⋅ 10−3 Wm−2 [c.f. Lysak, 1988; Duchkov et al., 1997]. At the same time, the geothermal heat flux within the continental slope is estimated to be between 85 ⋅ 10−3 and 117 ⋅ 10−3 Wm−2, according to Drachev et al. [2003].

[26] Similarly to Soloviev [1981] and Zhigarev [1997], Romanovskii and Hubberten [2001]assumed that the ocean bottom temperature varies within limits of −0.5°C to −1.8°C with a predominance from −1.0°C to −1.5°C. We will discuss the implications of selecting different ocean bottom temperatures on modeling the sub-sea permafrost later inSection 6.1.

4. Current Sub-Sea Permafrost Dynamics Model for the Laptev Sea Shelf

[27] According to Kudryavtsev, Romanovskii, Are, Danilov, and Zhigarev, the duration of the transgression/regression cycle, air temperature, temperature of the ocean bottom water, the geothermal heat flux, and salinity of the pore water in sediments are among the most important factors influencing the sub-sea permafrost distribution. Therefore, uncertainties in all these quantities are to be addressed in order to establish a realistic permafrost distribution on the Laptev Sea shelf.

[28] Before describing the presented model, we note that the shelf experienced numerous sea level oscillations, which lead to abrupt changes in the permafrost temperature dynamics. Namely, during ocean regressions the permafrost aggregated under the influence of cold Arctic climate, while in the course of transgressions the relatively warm ocean induced degradation of the permafrost. The most recent “abrupt” change started to occurred approximately by 14,000 years ago and is associated with the Late Pleistocene transgression.

4.1. Development of the Paleogeographic Scenario

[29] A difficulty in modeling the present-day ground temperature and permafrost distribution lies in specifying a retrospective climate scenario, including the ground surface temperature dynamics.Romanovskii and Hubberten [2001], Gavrilov and Tumskoy [2003], and Romanovskii et al. [2005] assumed that mean annual ground surface temperature within Yakutian coastal lowlands can be obtained by correcting air temperature reconstructed from Vostok ice core data [Petit et al., 1999] according to the regional data [Kaplina and Kuznetsova, 1975; Kaplina and Chekhovsky, 1987; Balobaev, 1991; Konishchev, 1998]. An interested reader is referred to Schirrmeister et al. [2002], Andreev et al. [2009], and Kaplina [2009, and references therein] for techniques of the regional climate reconstruction. The original and corrected paleotemperature reconstructions are shown in Figure 3 by the lines marked with hollow and filled triangles, respectively. We note that in Romanovskii and Hubberten [2001] and Romanovskii et al. [2005], the reconstructed ground surface temperature was extended to the entire shelf by assuming the latitudinal temperature zonation, e.g., 1.5°C cooling per one degree increase in the latitude, within the Laptev Sea Shelf.

[30] We claim that the conclusion utilizing the latitudinal temperature zonation within the Laptev Sea shelf is not valid for the glacial periods for the following reasons. Due to the significant extent of the Scandinavian and Laurentide ice sheets and permanent ice coverage of the Arctic Ocean, a boundary of the anti-cyclonic circulation during glacial periods was south of its present location. We hypothesize that the lower boundary of the Arctic circulation was coincident with the southern extent of the ice sheets, and hence the Laptev Sea shelf was well inside the Arctic air mass circulation. Current temperature measurements within the Canadian High Arctic show that the latitudinal temperature zonation within the Arctic anticyclonic circulation zone is negligibly small: the interested reader is referred toRomanovsky et al. [2008, Figure 4] where the measured temperatures at the Isachsen Arctic research site, Mould Bay and Banks Island (within the land-fast ice region and Arctic anti-cyclonic circulation zone) is compared to temperature data along a transect of the North Slope of Alaska. We thus claim that the ground temperature within the entire Laptev Sea Shelf could be modeled without the modern zonality of permafrost temperatures primarily observed in 60–70°N latitudes at the boundary of the modern day anti-cyclonic circulation.

[31] We define the ground temperature, Tg, as the temperature just below the bottom of the active layer - a layer of ground that is subject to annual thawing and freezing in areas underlain by permafrost. The present-day mean annual ground temperature,Tp, is −12°C at the coast of Dmitry Laptev Strait, and so we assume that Tg during the last several glacial cycles is well approximated by

display math

where Tv is a regionally corrected temperature anomaly in relation to Tp [Romanovskii and Hubberten, 2001; Gavrilov and Tumskoy, 2003]. The plot of Tv and of the paleotemperature reconstruction from the Vostok ice core data [Petit et al., 1999] is shown in Figure 3. Note that the regional effects related to the thermal insulation of snow and the thermal offset by the organically enriched mineral soil are already accounted for in Tv by correction to the paleotemperature data collected in the coastal lowlands [Kaplina and Kuznetsova, 1975; Balobaev, 1991; Velichko, 1999].

4.2. Analysis of the Benthic Temperature

[32] When a point on the shelf is inundated, we assume that the ground/bottom surface temperature is determined by the ocean bottom water temperature. In early investigations by Fartyshev [1993] and Zhigarev [1997], it was found that the benthic temperature depends on the water depth, proximity to the river deltas, and salinity. In shallow lagoons and inlets, the water temperature can be as high as 10–12°C during the summer, while the winter water temperature is primarily determined by the salinity. In areas close to large river deltas, e.g., Lena Delta, an inflow of warm fresh water can drastically increase the benthic temperature. We thus consider the study area region as two subregions: the first is near the Lena River Delta, while the second represents areas of the shelf away from major rivers.

[33] In Figure 4, we show locations of the summer benthic temperature measurements collected during 1999–2009 summer hydrographic surveys by the International Siberian Shelf Study (ISSS) institutions, including the Laboratory of Arctic Research, Pacific Oceanological Institute of the Far Eastern Branch of Russian Academy of Science; the International Arctic Research Center, University of Alaska Fairbanks; Stockholm University; and Gothenburg University. The temperature measurements in the Lena River Region and the General Shelf Region are marked by crosses and triangles, respectively. In the same figure we show by circles the locations where the water temperatures collected by the Arctic and Antarctic Research Institute (AARI) during the winters and summers of 1920s–2007 are available.

Figure 4.

Locations of the International Siberian Shelf Study (ISSS) benthic temperature measurements (crosses and triangles) and Arctic and Antarctic Research Institute (AARI) temperature observations (circles) in Laptev and East Siberian Sea. The red crosses mark the region within which a warming effect of the Lena River outflow is significant.

[34] All available temperature measurements are plotted in Figure 5. The AARI data are shown by small rectangles, while the 1999–2009 summer data are marked by triangles. The left plot displays the temperatures in the Lena Delta Region, while the right plot shows the temperatures in the General Shelf Region. We note that the temperatures collected during the ISSS expeditions in the Lena Delta Region are much higher than those in the General Shelf Region.

Figure 5.

Dependence of the benthic temperature with the ocean depth in the (left) Lena River Region and (right) General Shelf Region. The ISSS benthic temperature during summer is marked by red triangles. The blue and red rectangles show the AARI benthic temperature during winter and summer, respectively. The dashed red and blue lines display the summer and winter benthic temperature climatology, respectively. The dashed black line represents the annually averaged-benthic temperature climatology.

[35] Based on in-situ temperature measurements of bottom sediments up to 1 meter depth below the seafloor, it was shown byShakhova and Semiletov [2007] that in areas remote from the direct influence of the Lena river outflow (e.g., Dmitry Laptev Strait), mean annual temperature of surface sediments were above 0°C. Thereafter, it was shown [Holemann et al., 2011] that wind-driven mixture of the shelf water can reach 40 meters below the sea surface. Recent data obtained during the summer ISSS-2011 expedition showed propagation of warmer surface water up to a 50–60 meter depth. Analysis of the Laptev Sea Shelf temperatures variability performed byDmitrenko et al. [2011] demonstrate a warming temperature trend in the coastal zone (depths less than 10 meters) since 1980s. Figure 6 shows the coastal zone temperature within Laptev Sea [Dmitrenko et al., 2011]. The solid line corresponds to the 1999–2009 mean temperature, while the dashed line marks the mean for 1920–2009 temperature data in the coastal zone.

Figure 6.

Mean summer temperature in the coastal zone (depths less than 10 meters) of Laptev Sea over 1920s–2007 [Dmitrenko et al., 2011]. The dash-dotted line marks mean temperature over the entire period of observations, while the solid line corresponds to the 1999–2009 interval.

[36] Because of the recent warming, the 1999–2009 nearshore ISSS data need to be adjusted to reflect a mean summer temperature for the entire period of measurements. For the sake of analyzing sensitivity of the sub-sea permafrost to the benthic temperature, we consider two different cases for the post-transgression bottom temperature. In the “100-yr mean” case, we assume that an average temperature over the first 10 meters is equal to the 100-yr mean bottom temperature, ≈1.5°C, in the coastal zone (IARC, G. Panteleev, personal communications, 2010). The summer benthic temperature is shown by dash-dotted line inFigure 5. The “1999–2009 mean” case relies on the 1999–2009 summer ISSS hydrographic surveys, and its summer climatology is plotted by a solid red line. Consequently, assuming that the summer lasts four months, the mean annual benthic temperature, Tb(z), can be derived by weight averaging the summer and winter distributions. The benthic temperatures for the first and second case are plotted by dash-dotted and solid black lines, respectively.

4.3. Model of the late Pleistocene Transgression

[37] To determine when a certain part of the shelf was dry or inundated by the ocean, we use the global sea level reconstructions by Fleming et al. [1998] and Lea et al. [2002]. If at time t ∈ (−∞, 0) the sea level is below the ground surface at point x, we assume that this point is dry and then define the ground temperature by Tg(t); otherwise the surface temperature is equal to the benthic temperature Tb(d, x), where d is the ocean depth d = d(x, t) at point xon the shelf. One of the difficulties in the sub-sea permafrost modeling is to find the moment of time when the pointxwas inundated during the transgression. In all previous permafrost modeling efforts, it was assumed that the latest ocean transgression proceeded over the present-day bathymetry, and thus temporal changes in topography/bathymetry are not considered [e.g.,Romanovskii et al., 2005]. In this section, we review major physical processes shaping the most recent transgression on the Laptev Sea shelf. A numerical implementation of the model simulating changes in the bathymetry/topography is presented in Appendix A.

[38] In the Late Pleistocene, most of the shelf was dry and vast territories of the eastern Arctic Shelf were subject to formation of the ice complex - a type of the permafrost stratum with an ice content of 50–90% by volume that can reach tens of meters in thickness. Most of the ice complex that covered the Laptev Sea shelf has disintegrated due to thermokarst, thermal erosion, and coastal abrasion processes during the last transgression, while some of its remnants became inundated by the ocean [Romanovskii et al., 2000; Gavrilov et al., 2006; Overduin et al., 2007a]. Thus, the time when a certain area was flooded depends not only on its present-day elevation (below the sea level), but also on past rates of the thermal coastal abrasion, erosion, and the thermokarst development.

[39] According to Romanovskii et al. [2000] and Gavrilov et al. [2006], at the beginning of the ocean transgression, approximately 15,000 years ago, the first thermokarst lakes had appeared. However, the lakes were sparsely distributed due to low mean annual temperature. By 13,000 year ago, numerous thermokarst depressions had formed along the river valleys and grabens, resulting in a decrease of the ice complex within the grabens. Thermokarst depressions also occurred on horsts, but their sloping terrain promoted thermokarst lakes to drain and to leave a remaining alass depression - a large depression of the ground surface produced by thawing of a large area of very thick and exceedingly ice-rich permafrost [Kasymskaya, 2010]. The horsts were subject to thermal erosion that resulted in lowering their terrain with a slower rate. On massive horst complexes, e.g., Kotelnyi Uplift, with rather flat topography, the thermokarst lakes and thermal erosion additionally played a role in lowering the ground surface.

[40] Development of the thermokarst lakes within grabens was a widespread phenomena; it is estimated that more than 50% of their area was affected. It is thought that 10–20 meter deep lakes formed in the ice complex, and that the lakes were interconnected by a series of channels and rivers. During the ocean transgression, the lakes became inundated and the transgression within grabens became a quickly proceeding ingression. By the end of 8,000 years ago when the sea level almost reached its present-day position, nearly all the surface of the grabens was inundated by the ocean, while the ice complex on horsts comprised narrow peninsulas protruding further offshore.

[41] The extended coast line and warm water temperature in the shallow inlets resulted in extensive thermal abrasion of the coast. Gavrilov et al. [2006] estimate that during the thermal optimum, the thermal abrasion could have reached the speed as much as 4–6 meter/year, while its averaged speed is estimated to be 3–4 meters/year. Thermal abrasion is considered to be the primary mechanism of degradation of the icy sediments constituting the peninsulas. It is estimated that for the last 5,000–8,000 years, the coast line may have retreated by 20–35 kilometers and completely erased these peninsulas on the narrow horsts. The rates of the thermal abrasion agree with predictions by Are [1988], who also considered physical requirements of the shore erosion. In this work, we do not take into account such requirements and the future work on their numerical implementation is required. Modeled dynamics of the ice complex disintegration is shown in Figure 7.

Figure 7.

The simulated disintegration of the ice complex over the present-day Laptev Sea shelf, according to the scenario ofGavrilov et al. [2006].

4.4. Parametrization of the Thermal Properties, Porosity, Salinity and Geothermal Heat Flux

[42] The expeditions conducted at various locations through out the East Siberian Arctic shelf extracted samples of the ocean bottom sediments from various boreholes and extensively analyzed them. We note that the majority of boreholes did not penetrate more than 60 meters into the seabed and were often drilled not further than 20–30 km offshore. For example, Molochushkin and Gavrilyev [1970] and Fartyshev [1993]provide detailed information regarding the distribution of the mineralization and water content with depth. Both authors conclude that the top 1–2 meter of the bottom sediments forms a sludge-like layer that has a large water content, i.e., 50%(≈57%), with the salinity of the pore water exceeding the salinity level of the near-bottom ocean water. Below the sludge boundary layer, the water content significantly decreases and varies between 20%(≈35%) and 25%(≈40%). Moreover, analyzing core samples up to the depth of 70 meters below the ocean bottom,Fartyshev [1993] determined that the ocean sediments have a water content between 10%(≈20%) and 26%(≈41%), and the salinity of pore water between 21‰ and 48‰. The latter result was independently supported by Marchenko [1966] and Neizvestnov and Semenov [1973].

[43] The reported values of the salinity are in agreement with the findings of Molochushkin and Gavrilyev [1970] and Zhigarev [1997] and also with data on the salinity of the seabed soils obtained from boreholes drilled offshore in the Beaufort Sea [Mackay, 1972; Sellman and Chamberlain, 1980; Miller and Bruggers, 1980]. As illustration, the salinity tests by Miller and Bruggers [1980] show that the freezing point depression is −1.8 ± 1.0°C for the unfrozen sediments, agreeing with −1.9°C as determined by Page and Iskander [1978] for the Prudhoe Bay area. For the frozen sediments, the freezing point depression ranged between −0.6°C and −3.1°C, with an average value of −1.5°C. According to Nixon [1986], the data by Sellman and Chamberlain [1980]indicate the freezing-point depression of about −2.0°C to −2.2°C that is relatively constant with depth. Recall that the freezing temperature of the seawater with the salinity of 30‰ is −1.8°C. On the basis of these data and observations, it is reasonable to conclude that an average salinity of the ocean sediments along the entire borehole depth (up to 100 meter depth) and deeper is approximately constant [Nixon, 1986; Osterkamp and Fei, 1993].

[44] Following Molochushkin and Gavrilyev [1970], Danilov and Zhigarev [1977] and Fartyshev [1993], we consider a two-layer soil column. The top layer in our model is 30 meters thick and represent the Quaternary era sediments which presumably have originated during a series regressions/transgressions, and hence have the largest water content and mineralization. The bottom layer is associated with the properties of either the pre-Quaternary clastic deposits or the undisturbed ground material. FollowingFartyshev [1993], we propose that the horsts and tectonic uplifts are primary composed of the undisturbed consolidated ground material - the bedrock, while the grabens are filled with the clastic deposits. A schematic diagram of layers in grabens and horsts is shown inFigure 8. The distributions of the horsts and grabens is shown in Figure 1. We note that horsts and tectonic uplifts have a relatively small water content, while the grabens have a larger water content. Assumed values of the volumetric porosity η for each type of ground material are listed in Table 1 together with values of the thermal conductivity λf and volumetric heat capacity Cf for the completely frozen material. The thermal conductivity and heat capacity depend on the unfrozen liquid water content θ and are computed in methodological accordance with Appendix A.

Figure 8.

Schematic diagrams of layers in (a) grabens and (b) horsts. (c) An alternative layering in horsts employed in the sensitivity study.

Table 1. Properties of the Ground Material
   Quaternary SedimentsPre-Quaternary Clastic DepositsBedrock
Volumetric porosity,η,[m3 m−3]0.350.250.05
Thermal conductivity,λf,[Wm−1 K−1]2.22.53.0
Volumetric heat capacity,Cf,[Jm−3 K−1]1.2 ⋅ 1061.2 ⋅ 1061.2 ⋅ 106
Pore water salinity,σ,403010

[45] As in Romanovskii and Hubberten [2001], we parameterize the heat flux variability on the shelf by the lateral extents of the geological structures constituting the LRS. Within the undisturbed blocks, e.g the SLRB, we assume that the heat flux is 45 ⋅ 10−3 Wm−2, while within tectonically active zones, e.g., the ULRB, ELH, SH, and BSNRB, we hypothesize that an average value of the geothermal heat flux is 60 ⋅ 10−3 Wm−2. The KU is assumed to have a relatively low heat flux of 50 ⋅ 10−3 Wm−2. The geothermal heat flux on the continental slope is assumed to be 90 ⋅ 10−3 Wm−2. The spatial distribution of the geothermal heat flux values is shown in Figure 1. We note that our values of the geothermal heat flux for the grabens are slightly larger than those of Kholodov et al. [1999], but within a range of the natural variability and the values in Romanovskii and Hubberten [2001] and Romanovskii et al. [2005].

4.5. Parametrization of the Unfrozen Liquid Water Content

[46] Investigations have led to the conclusion that thermal properties of thawed bottom sediments are primarily determined by the liquid water content. For the partially frozen ground, the thermal properties also depend on the ratio of ice to the unfrozen liquid water. Commonly used to measure liquid water below freezing temperature is the volumetric unfrozen water content [Williams, 1967; Anderson et al., 1973; Osterkamp and Romanovsky, 1997; Romanovsky and Osterkamp, 2000].

[47] An early investigation of dependence of sub-sea permafrost temperature dynamics on the liquid water content was carried byNixon [1986]. By analyzing the simulations of Molochushkin [1973] and Lachenbruch and Marshall [1977], it was found that within a period of about 2,000 years following submergence, the permafrost temperature increases to within a fraction of a degree of the freezing point depression. This phenomena was explained by the fact that the employed permafrost models, as well as other models [Fartyshev, 1993; Zhigarev, 1997], assumed the phase change occurs at the freezing point depression Tp. These simulated temperatures seemed to contradict measurements by Weaver and Stewart [1982] and Collett and Bird [1993], who reported significantly lower temperatures at 400 meter depth below the seabed. By proposing that the unfrozen liquid water content be parameterized according to the sodium chloride - water binary phase diagram,Nixon [1986] derived a qualitatively better fit to the measurements.

[48] In this work, we follow Nixon [1986] and assume that the unfrozen liquid pore water fraction θ = θ(T) can be parameterized, according to the sodium chloride - water binary phase diagram. This parametrization was reviewed and compared to unfrozen liquid water observations in different soils byHivon and Sego [1990, 1995]. For the intermediate and fine-grained soils such as silts and clays, the parametrization according to the binary phase diagram underestimates the liquid moisture content, as the adsorbtion effects are not considered. However, the latter effects can be taken into account by considering a slightly higher “effective” salinity of the sediments.

[49] We assume that the layer of Quaternary sediments has the highest salinity, 40‰, due to diffusion of salutes to the near-bottom sediments during periodic ocean transgressions. During the regressions, the marine sediments freeze and salutes are redistributed between the marine and continental sediments due to salt rejection upon freezing and sinking due to gravity. Salinities of the ground material in horsts and grabens are assumed to be 10‰ and 30‰, respectively. The dependence ofθ(T) for three different salt concentrations is shown in Figure 9. We emphasize that θ(T) shows that the freezing point of soils, and hence the latent heat content, is distributed over a range of temperatures. This mechanism is accommodated in the exploited modeling technique, described in Appendix A. For example, ground material with salinities of 40‰, 30‰, and 10‰ have the freezing point depression of −2.05°C, −1.54°C and −0.55°C, respectively. Note that at any temperature, ground material with a 30‰ pore water salinity has a large liquid pore water fraction θ(T) compared to that with a 10‰ concentration. We say that the ground is frozen if its temperature is lower than the temperature of freezing point depression Tp.

Figure 9.

Liquid pore water fraction θ(T) as a function of temperature T.The curves marked by triangles, circles and squares are related to the ground material with 40‰, 30‰ and 10‰ salt concentration of the pore water, respectively. The line plotted by hollow triangles show the liquid pore water fraction used to model sub-sea permafrost inRomanovskii and Hubberten [2001]. The curve marked by rectangles and circles parameterize the unfrozen water content in horsts and grabens, respectively.

[50] Comparison of the unfrozen liquid water content functions, plotted in Figure 9, reveals that in the previous modeling study by Romanovskii and Hubberten [2001], all sediments were considered to have a small salinity of 10‰. In this work, we employ parametrization of the unfrozen liquid water content based on the structural geology (horst and grabens) and evaluate its impact on permafrost dynamics.

5. Modeling Sub-sea Permafrost

[51] We model permafrost dynamics on the Laptev Shelf by computing the ground temperature on a grid of points spaced uniformly in longitudinal and latitudinal directions, with a resolution of 6 arc-minutes. The vertical extent of the numerical domain is set to be 2.5 km below the ground/shelf surface. We note that the chosen thickness of the soil column is sufficient to adequately model permafrost dynamics and thickness even during the Sartanian thermal minimum, when permafrost thickness was greatest. Since the lateral dimensions of the grid cell are much larger than the assumed thickness, lateral heat transfer effects are not included in the presented modeling study. Thus, at the center of each grid cell we numerically solve the 1-D non-linear heatequation (1) by a finite element method, as described in Nicolsky et al. [2009].

[52] The boundary conditions are set according to the developed paleogeographic scenario, while the initial condition is set in a manner so as to reduce the influence of uncertainties on the modeled present-day temperature distribution as suggested inTipenko et al. [1999]. In particular, the initial temperature distribution is equal to a steady state temperature approximately 360,000 years ago. This initial value is consistent with, and reflects, the geothermal gradient and ground surface temperature when the shelf was frozen in the middle of a glacial period. Recall that the temperature anomaly is shown in Figure 3. During the periods when the shelf was inundated, we assume that dependence of the benthic temperature with depth is set according to the “100-year mean” climatology. A brief mathematical description of the numerical model is provided inAppendix A.

[53] Due to a rapid temperature increase 12,000–13,000 years ago, numerous thermokarst depressions started to develop in the ice complex. It is thought that almost 50–60% of the graben surface area was covered by thermokarst lakes. Therefore, at each grid cell, we consider two subcells: Lake-type and InterLake-type sub-cells. For the sake of brevity, we call the Lake-type sub-cells “L”-sub-cells. Similarly, we name InterLake-type sub-cells the “I”-sub-cells.

[54] In the “I”-sub-cell, we simulate the permafrost dynamics outside of the thermokarst depressions. While the “I”-sub-cell is dry its surface temperature is set according to formula(2). However, once the cell is inundated the surface temperature at the “I”-sub-cell is set according to the dependence of the benthic temperature with the ocean depth over the cell.

[55] We similarly model the surface temperature at the “L”-sub-cells until 12,500 years ago, when thermokarst lakes widely appeared on the shelf. For the “L”-sub-cells that are located in grabens and that are thought to be dry 12,500 years ago, the surface temperature is assumed to rise over the course of a few centuries until it reaches 1°C and then the temperature remains constant until the grid cell became inundated by the ocean. We emphasize that within horsts and tectonic uplift areas, the thermokarst lakes are assumed to be missing, and thus the surface boundary condition for the “L”-sub-cells within horsts is identical to the boundary condition of its sibling “I”-sub-cell. Finally, we note that the assumed temperature of 1°C at the bottom of the lake is a conservative - in the sense of the potential permafrost degradation - estimate of water temperature observations, asBurn [2002] reported the water bottom temperatures up to 4°C at the bottom of some lakes of the Canadian Arctic.

5.1. Modeled Permafrost Distribution Beneath and Outside the Thermokarst Depressions

[56] To analyze the results of our numerical modeling, we present the computed ground temperature and unfrozen water content at a profile transecting the Laptev Shelf along the 74°30′N latitude and the 130°E longitude, identified by dashed lines in Figure 1. The cross-section starts in the east near Kozhevnikov Bay and cuts across several geological features in the Laptev Shelf.

[57] Figures 10 and 11display the computed results along the 74°30′N latitude and the 130°E longitude cross-sections, respectively. The ground temperature and unfrozen liquid water content are displayed at two instances. The top plot corresponds to the Sartanian thermal minimum 18,000 years ago - a time when the temperature distribution at the sub-cell scale is the same before the lakes began to form. The middle and bottom plots display the modeled present-day permafrost distribution for “I”-sub-cells and “L”-sub-cells, respectively. Locations of grabens and horsts along the first cross section are marked by their abbreviations, introduced in the caption ofFigure 1. The ground surface is marked by a yellow line. The calculated ground temperature isotherms are plotted over contours of the unfrozen liquid water content. Completely thawed ground material (θ = 1) is marked by gray colors. We emphasize that 0°C isotherm does not represent the boundary between frozen and thawed ground due to the freezing point temperature depression.

Figure 10.

Modeled ground temperature (line contours) and liquid pore water fraction (shaded color contours) along the 75°30′N cross-section. Blue-to-red contours represent partially frozen ground. The gray color marks areas with the thawed ground material. (top) The results related to the Sartanian thermal minimum. The modeled present-day permafrost distribution in the (middle) “I”-sub-cells and (bottom) “L”-sub-cells. The key parameters used to simulate the permafrost dynamics are listed inTable 2. Typically, the permafrost thickness is higher within horsts, due to their thermal properties.

Figure 11.

Modeled ground temperature (line contours) and liquid pore water fraction (shaded color contours) along the 75°30′N cross-section. The reader is referred to the caption ofFigure 10 for the explanation of the color code.

[58] The permafrost thickness reached its maximum by the end of the Sartanian cryochron about 18,000 years ago, after a prolonged subaerial cooling over several tens-of-thousands of years. We note that the temperature distribution at this time can be well approximated by a steady state temperature solution which depends on the surface temperature, thermal conductivity, and geothermal heat flux. Recall that the ground surface temperature across the entire shelf was approximately −24°C at that time, and the thermal conductivity of the ground material within the horsts is greater than that within the grabens, as listed inTable 1. Therefore, the computed permafrost thickness within the horsts is typically up to several hundred meters deeper than within the grabens at the Sartanian cryochron, as easily noted in Figure 10(top). Note that the 130°E longitude cross-section lies entirely within the ULRB, and hence the modeled permafrost thickness, displayed inFigure 11 (top), does not show variations associated with the horsts.

[59] Our numerical calculations also suggest that the permafrost has severely degraded after the most recent transgression, as shown at the middle and bottom plots in Figures 10 and 11. The degradation occurred not only from the bottom-up, but from the top-down as well since the bottom ocean temperature became higher than the freezing point temperature depression of the top layer, i.e., the Quaternary sediments. Within some shallow regions of the shelf, thawing from the top reached into the second layer. This phenomena is especially pronounced in the ULRB region, where the ocean bottom temperature is warmer due to its proximity to large rivers. Within the horsts where the ice complex has remained longer than within the grabens, the permafrost primarily thawed from the bottom-up, under the effect of the geothermal heat flux.

[60] We emphasize that our modeling results for the “I”-sub-cells suggest that the permafrost cover still exists within the continental shelf, but that a significant portion of the pore water in grabens is liquid. This means that in regions such as the ULRB where 50-60% of pore water is liquid, the permafrost is significantly weakened in mechanical strength, as a result of higher model temperatures relative to the unfrozen water content curve, shown inFigure 9. In contrast, most of the pore water is frozen and permafrost reaches a significant thickness within uplifts, e.g., near Kozhevnikov Bay, the TH, and KU. Comparison of the middle and bottom plots reveals that under the inundated thermokarst lakes, i.e., within “L”-sub-cells, the amount of the unfrozen liquid water content is much higher than outside of the thermokarst lakes, and thus the permafrost is more significantly degraded beneath the lakes than outside them, i.e., in “I”-sub-cells.

[61] As mentioned previously, offshore boreholes have not penetrated through the entire permafrost layer and hence are not available for quantitative comparison with the modeling results. Coastal boreholes have reached a significant depth, but also fail to reach the lower boundary of permafrost in Laptev Sea Region. Some temperature measurements are available onshore along the coast near Kozhevnikov Bay, Uryung-Tumus Peninsula (Nordvik), Chay-Tumus (Lena Mouth) and Tiksi Bay, and as shown inFigure 12. These temperature values allow for estimation of the permafrost depth near Kozhevnikov Bay at 500–800 meter range [Ponomarev, 1960]. Assuming an influence of several water horizons at significant depths below the ground surface, Fartyshev [1993]calculated that the permafrost thickness ranges between 875 and 1125 meters at the Kozhevnikov Bay. Similar results are reported near the Uryung-Tumus peninsula and Lena delta. Extrapolation of the Tiksi Bay borehole data suggests the permafrost thickness is approximately 650 meters. At the same time, the Chay-Tumus data suggests it may reach 800 to 1000 meters.

Figure 12.

Measured ground temperature at several locations along the coast of Laptev Sea [Grigoriev, 1966], adopted from Vigdorchik [1978] and Fartyshev [1993].

[62] According to the 2-D seismic surveys carried out by the German/Russian cooperative expedition (BGR, Germany and Russian institution SMNG, Murmansk), a strong reflective sequence is found between 300 and 850 meters near the KU [Hinz et al., 1998]. It is thought that this sequence represents the vertical boundary of the sub-sea permafrost. The numerical results of this case show that permafrost thickness is between 800 and 1000 meters, as shown in the middle and bottom plots onFigure 10. Recall that the thermokarst lakes are thought not to be occurring on horsts/uplifts, and thus the permafrost distribution within the horst structures for the corresponding “I”- and “L”-sub-cells is the same, as illustrated in the middle and bottom plots. The similar thickness of the permafrost within the KU is also reported inRomanovskii et al. [2005]. Given large uncertainties in the conducted seismic work, the model compares well with the observations. However, the permafrost thickness could be also overestimated because of the relatively high thermal conductivity used to model the permafrost dynamics in horsts.

6. Sensitivity Study

[63] In the presented model, the largest uncertainties are associated with the benthic temperature, the geothermal heat flux, and mineralization and porosity of sediments, geological structure of the LRS elements and the dynamics of the recent transgression. In Table 2, we briefly list the key model parameters used to simulate the current permafrost distributions. For the sake of brevity, we analyze sensitivity of the modeled permafrost thickness with respect to the model parameters only along the 74°30′N latitude cross-section. The reference case is shown inFigure 10 (bottom), and also in Figure 13 (top). Note that this plot is provided twice to facilitate comparison of the reference case with the results of the sensitivity study provided in Figure 13.

Table 2. Key Parameters in the Model on Which the Sub-sea Permafrost Dynamics Depends On
TypeDescriptionReference
Tectonic elementsGrabens and horstsFigure 1
Ground temperatureThe corrected Vostok ice core reconstructionFigure 3
Benthic temperatureThe “100-yr mean” caseFigure 5
Recent transgressionLate Pleistocene ice complex disintegrationFigure 7
Soil propertiesQuaternary and pre-Quaternary deposits, bedrockTable 1
Soil columnThe 1st layer - fine-grained deposits:Section 4.4
Silt/sandy silt
The 2nd layer - coarse-grained deposits:
Sand/gravel (grabens); bedrock (horsts)
Geothermal heat flux45 · 10−3 … 60 ⋅ 10−3 Wm−2 in the LRSSection 4.4
Figure 13.

Modeled present-day ground temperature (line contours) and liquid pore water fraction (shaded color contours) along the 75°30′N cross-section in the “L”-sub-cells. Blue-to-red contours represent partially frozen ground. The gray color marks areas with the thawed ground material. Typically, the permafrost thickness is higher within horsts, due to their thermal properties. The top plot shows the reference case that is coincide with the bottom plot inFigure 10. Other plots are related to cases considered in the sensitivity study in Section 6.

[64] In the presented sensitivity study, we analyze changes of the modeled current permafrost distribution underneath the inundated thermokarst depressions, i.e., only for the “L”-sub-cells, with respect to a change in a single parameter. For example, while modifying either the benthic temperature parametrization, or a value of the geothermal heat flux, the rest of the parameters are unchanged and equal to the ones used to compute the reference case distribution.

6.1. Case A: Changes in the Benthic Temperature

[65] In view of the recent benthic temperature warming [Dmitrenko et al., 2011], we analyze how the warm “1999–2009 mean” parametrization of the bottom temperature with depth, shown by a solid line in Figure 4, can affect the modeling results. In this case, we assume the warmer benthic temperatures are enforced not only the last 20 years, but during the entire period of computer simulations. The simulated permafrost thickness within the “L”-sub-cells across the 74°E latitude cross-section is shown in the second plot from the top inFigure 13. We note that the degradation of sub-sea permafrost within the whole soil column is not significantly increased compared to the reference case. Recall that the top plot corresponds to the reference case.

6.2. Case B: Response to Changes in the Salinity

[66] Salinity of the pore water depends on depth, proximity to river deltas, geological structure of the tectonic elements and the previous history of the shelf. We recall that in the reference case, the salinity of the clastic deposits constituting the grabens is thought to be 30‰,corresponding to the −1.54°C freezing point temperature depression. In the previously reviewed literature, the temperature depression for clastic deposits ranges from −0.7°C to −2°C [e.g., Fartyshev, 1993; Zhigarev, 1997]. The lower the temperature depression, higher the salinity of the ground material and more liquid water can stay unfrozen at the fixed temperature, as shown in Figure 9. From the conducted numerical experiments, we observe that for higher salinity of clastic deposits, the simulated permafrost degradates more severely. For the sake of brevity, we only consider a conservative case of the permafrost degradation as follows.

[67] We assume that salinity of the clastic deposits is 20‰ which corresponds to a −1.0°C depression temperature, while all other parameters in the numerical experiment are left the same as in the reference case. The computed permafrost distribution within the “L”-sub-cells is shown in the third plot from the top inFigure 13. The simulated permafrost underneath the inundated thermokarst lake is considerably thicker and its unfrozen water content is approximately 50%, which is lower than that in the reference case.

6.3. Case C: Response to Changes in the Layering of Sediments

[68] Recall that following Fartyshev [1993], we consider the two-layer soil column and parameterize thermal properties of the second layer according to tectonic elements constituting the LRS. The layering in the reference case is illustrated by inFigures 7a and 7b. The second layer is assumed to be below the 30-meter-thick Quaternary deposit layer and its properties are attributed either to clastic deposits (grabens) or to bedrock (horsts). According to findings byDrachev et al. [1998], Sekretov [1999], and Franke et al. [2001] a layer of sediments might be covering the bedrock within horsts. Therefore, we analyze sensitivity of the permafrost dynamics with respect to addition of an additional sedimentary cover on top of the bedrock in horsts. In this case we assume that the layering in horsts is according to column C. For the sake of brevity, we consider only one case in which the additional sedimentary cover is assumed to be 100 meters thick. Similar numerical results can be obtained in the case when the sedimentary cover is 200–300 meters thick.

[69] The computed present-day permafrost distribution is shown at the fourth plot from the top inFigure 13. The top layer of the permafrost within horsts is weakened, by the wedge-like structures of ice-bonded permafrost remain below 100 meter depth.

6.4. Case D: Response to Changes in the Porosity

[70] From the conducted numerical experiments, we observe that the sub-sea permafrost is sensitive to change in the porosity of the ground material. In the reference case, we assumed that the volumetric porosity of the clastic deposits and bedrock are 25% and 5%, respectively. In this case, we consider that the corresponding values are 20% and 0%, respectively. The numerical results show severe permafrost degradation underneath the thermokarst lakes in grabens. The permafrost within the horsts is also almost completely thawed despite our assumption that the thermokarst lakes do not form on them during the transgression.

6.5. Case E: Response to Changes in the Recent Transgression

[71] One of the largest uncertainties in the modeling study is related to the dynamics of the most recent transgression and changes in the shelf bathymetry/topography. In the reference case, we exploit the ice complex disintegration model by Gavrilov et al. [2006], who reconstructed the shoreline location at several key moments during the Holocene. Note that the modeled coastlines do not match the bathymetry contours. Also recall that in the reference case, the ice complex remained on top of the horsts (thermal coastal erosion was a primary mechanism for the ice complex disintegration within the tectonic uplifts) and the permafrost was stable as long as it was not inundated by the ocean.

[72] In this case, we assume that no ice complex has formed over the shelf and the inundation proceeded over the current bathymetry [Jakobsson et al., 2008]. The simulated inundation occurs more rapidly and the horsts as well as the tectonic uplifts are flooded at the same time as nearby grabens. Consequently, the simulated present-day permafrost within the horsts is more severely degradated, e.g., Kotel'nyi Uplift (KU), if compared to the reference case. Recall that contrary to grabens, no lakes formed within the horsts. The permafrost within the graben shows a similar level of degradation as in the reference case. An explanation is that in both computer experiments, the cells within grabens were inundated almost at the same time.

6.6. Case F: Response to Changes in the Geothermal Heat Flux

[73] Unfortunately, there are no direct measurements of the geothermal heat flux on the shelf. Several reported measurements were completed just below the sea bottom and have large uncertainties [e.g., Soloviev et al., 1987]. Romanovskii et al. [2005] argues that the geothermal heat flux can be parameterized by similar onshore structures such as the Moma Rift, where the base heat flux varies between 40 · 10−3 and 80 · 10−3 Wm−2. Therefore, in this case we consider a slightly elevated heat flux of 70 · 10−3 Wm−2 in the ULRB, MH, UYH, ShH, ELH, SH, KH, and BSNRB. We emphasize that the assumed values of the geothermal heat flux are within the natural range of variability for the undisturbed blocks; e.g., we emphasize that Romanovskii et al. [2005] assumed the value of 70 ⋅ 10−3 Wm−2 to model the minimum thickness of relict permafrost. The results of our simulations, shown in the bottom plot in Figure 13, reveal that open taliks develop in shallow areas of the modeled shelf.

[74] Finally, Figure 14 shows possible locations of open taliks on the Laptev Shelf, based on the 70 ⋅ 10−3 Wm−2flux in case of “100-yr mean” and “1999–2009 year” benthic temperature parametrization with depth. The continental slope is characterized by high values of the geothermal heat flux as well as subject to the warm Atlantic-based ocean circulation, and is thus prone to widespread development of open taliks.

Figure 14.

Modeled locations of open taliks in the Laptev Sea Shelf. Locations of the open taliks in the case of (left) “100-yr mean” and (right) “1999–2009 mean” parameterization of the benthic temperature. The geothermal heat flux within the ULRB, MH, UYH, ShH, ELH, SH, KH, and BSNRB is assumed to be 70 · 10−3 Wm−2.

7. Discussion

[75] In this paper, we concentrate on numerical modeling of sub-sea permafrost observation in the Laptev Sea Region. We emphasize that the goal of this study is to update a model of salt-bearing permafrost degradation since the Holocene transgression in the Laptev Sea shelf. Uncertainties in the presented model lie in specifying the soil properties such as the thermal parametersCf and λf, the volumetric porosity η, and the salt content σ. The values of λf and Cf used in this work are typical of ground materials with small porosity value η. We note that the values of λf and Cf are associated with silt/sandy silt (in the first layer) or sand/gravel (in the second layer) sediments found in the Laptev Sea at depths of 400 meters [Kim et al., 1999]. The volumetric unfrozen liquid water content θ is typically higher for more finely grained materials [Yershov, 1998], and qualitatively similar results(more significant thawing) can be expected in both considered cases.

[76] In the presented model, we assume a static ground mineralization, excluding salt diffusion, salt fingering and buoyancy-driven flows. We further acknowledge that the omitted phenomena may be important to the sub-sea permafrost modeling [Baker and Osterkamp, 1988; Hutter and Straughan, 1997]. The salt transport is considered in a well-verified 2-D thermo-hydro-chemical model, which was applied to investigate permafrost dynamics for a 115,000 year glacial cycle at a potential repository for spent nuclear fuel at Forsmark, Sweden [Hartikainen et al., 2010]. It was revealed that some salt exclusion and transport occurs. However, sensitivity of the modeled permafrost thickness with respect to inclusion of the salinity transport is low. The difference between the modeled permafrost thicknesses at the end of a 70,000 year cycle was less than 10 meters, while the permafrost thickness was about 250 meters. We note that at the larger depths salt transport can influence the modeled permafrost thickness more significantly, but parametrization of the ground properties and initial salt concentrations are the largest unknowns in such modeling studies.

[77] Pockets of soil with anomalous salinity are possible and would complicate any generalization of seabed soil salinity. In an evaluation of well-logs from oil fields on the North Slope of Alaska,Collett and Bird [1993]showed that the ice-bearing permafrost has numerous vertical discontinuities, marked by horizons in which ice content is greatly diminished or absent. The most prominent horizon lays between 50 and 250 meters below the ground surface and is laterally continuous over an area of at least 1000 km2. According to the well-logs, the ground temperature within this horizon is −8°C, and thus the pore water salinity was calculated to be at least 130 g/L. These brines are thought to be formed below the freezing front as it advances downward during glacial cycles, and finally trapped above a low-permeability, clay-rich sedimentary sequence.

[78] We hypothesize that additional locations of open taliks may coincide with the active faults - the boundary between horsts and grabens - associated with abnormally high geothermal heat flux and also with pre-Holocene channels of large rivers such as the Lena and Yana Rivers. This consideration is out of the scope of the presented modeling study; the interested reader is referred toRomanovskii et al. [2005] and Delisle [1998], where some modeling attempts were accomplished.

[79] We assume that the modeled permafrost is homogeneous ground material. However, several physical processes such as anomalies in geothermal heat flux [Romanovskii et al., 2005], intrapermafrost groundwater heating [Glotov, 1994], water pathways due to liquid water within frozen ground material [Biggar et al., 1998], permafrost breaks due to tectonic movement [Cramer and Franke, 2005], and endogenous seismicity resulted from hydrate decay and sediment settlement [Osterkamp and Harrison, 1985] can cause temporal and permanent sub-sea permafrost destabilization. Each of these processes may contribute to formation of frozen and thawed ground material layers, possibly even taliks, in the sub-sea permafrost.

[80] We emphasize that because of the spatial resolution, temporal discretization, and scope of the considered physical processes, the presented numerical model cannot resolve the impact of the most recent warming trend in the benthic temperatures [Dmitrenko et al., 2011] on the modeled present-day distribution of sub-sea permafrost. Nevertheless, we accentuate that the increasing benthic temperatures promote downward thawing of the near-bottom sub-sea permafrost, and degradation of submerged ice complex remnants. The mechanism of the ice complex destabilization and its potential impact on the upward migration of methane is as follows.

[81] During the Pleistocene transgressions, the ice complex that covered the ESAS mostly disintegrated, but parts of it became inundated by the ocean. For example, some ice-rich deposits are found to be covered by several meters of ocean sediments within ESAS [Soloviev et al., 1987; Rachold et al., 2007]. An interested reader is referred to Nicolsky and Shakhova [2010]for a description of near-bottom observations bySoloviev et al. [1987] in the Dmitry Laptev straits. According to Overduin et al. [2007b], an approximately 10-meter-thick ice complex is also found at the depth of 50–60 meters below the ground surface of nearshore zone of the Laptev Sea. Recall that a layering of marine and continental sediments was also found in the Canadian Beaufort Shelf byBlasco et al. [1990] and Blasco [1995]. Thus, the ground material beneath the ESAS ocean bottom actually has a complicated structure consisting of salt-contaminated sediments, both frozen and thawed, layered with ice complexes.

[82] We suggest that near-bottom ice-rich (NBIR) layers, because of their terrestrial origin, are not contaminated by salt, and thus may have a near 0°C temperature point depression,Tp. This implies that NBIR layers can be surrounded by thawed saline sediments as long as temperature of the neighboring ground is below Tp. Since these layers can have a low gas permeability and can laterally extent to significant distances, they potentially constitute a natural membrane that impedes migration of the methane to the ocean bottom. If during the warming trend, the benthic temperature increases above the value of Tp, the NBIR layers can be severely destabilized or even destroyed [Nicolsky and Shakhova, 2010].

[83] Since the increasing benthic temperature trend is more pronounced in shallow regions [Semiletov et al., 2005; Dmitrenko et al., 2011], destabilization of the already weakened NBIR layers under the submerged thaw lakes [Nicolsky and Shakhova, 2010] might result in breaking a last physical barrier for the methane to be released to the ocean bottom. We emphasize that modeling of the methane trapped under the buried ice complex remnants is beyond the scope of the current work and is rather a topic for the future research projects. Finally, we mention that the above-mentioned theory underscores the need to improve existing models by implementing sub-algorithms that account for detailed structures within the soil column and include the afore-mentioned mechanical processes affecting the permafrost distribution.

8. Conclusions

[84] We numerically model sub-sea permafrost dynamics in the Laptev Sea Region for the last several glacial cycles. Numerical results in the reference case for the “I”-sub-cells (outside the inundated thermokarst depressions) show that the permafrost thickness varies across the Laptev Sea shelf. The thickness is greatest within horsts (≈900 meter), but much less within the ULR and BSNRB grabens (≈400 m). In horsts, the liquid pore water fraction is ≈20% while in grabens it is higher and may reach 50%, as shown inFigure 10 (middle).

[85] At the same time, for the “L”-sub-cells (beneath the submerged thermokarsts lakes), the liquid pore water fraction is ≈70%, higher than for the “I”-sub-cells in grabens, and much higher than within the horsts, as shown inFigure 10 (bottom). Open taliks cannot develop in the reference case, as shown in Figure 10. The permeability of gases through such partially thawed permafrost is beyond the scope of this article and needs to be studied.

[86] The sensitivity study reveals that beneath the submerged thermokarsts lakes, in Cases D or F, related respectively either to a less porous ground material or to the elevated geothermal heat flux 70 ⋅ 10−3 Wm−2 (within the range of variability for the undisturbed blocks), open taliks can develop. Through such taliks, escape of gases is likely and is recommended for future consideration.

[87] The presented model also demonstrated that in areas affected by warm benthic water, the permafrost can significantly degradate from the top-down and form a strata of thawed sediments lying on top of the frozen material, as observed by Grigoriev who found ice-rich sediments 86 meters below the bottom in locations with a positive sea bottom temperature.

Appendix A:: Numerical Implementation

A1. Disintegration of the Ice Complex

[88] Although, formation of the ice complex (IC) is a rather complicated phenomenon [e.g., Soloviev, 1959; Romanovskii, 1993] its thermal insulation effect on the entire column of the permafrost is negligible due to nearly absent thermokarst development in Sartanian stadial. Therefore, we can assume a rather simple linear growth model of the IC layer on top of the shelf, and suppose that tS = −20,000 years the IC layer reached the thickness of s0 = 30 meters, quantitatively matching the 10–40 meter IC thickness currently observed along the Laptev Sea shoreline.

[89] Given the present-day bathymetryb(x) according to Jakobsson et al. [2008], we assume that the transgression proceeded over the topography, the elevation of which at point x is given

display math

Here, s = s(x, t) stands for the IC thickness that depends on the time t. Since most of the IC on the present shelf has disappeared, one has to reconstruct dynamics of the IC disintegration from the Sartanian thermal minimum s(x, tS) = s0 to present s(x, 0) = 0.

[90] A difficulty lies in prescribing evolution of the IC thickness s(x, t) that needs to take into account terrain lowering rates, parametrized by tectonic structures, as well as the coastal abrasion processes. The former are modeled by prescribing two rate functions, rg and rh, for grabens Ωg and horsts Ωh, respectively. The latter is simulated by an application of the level set method [Sethian, 1999; Osher and Fedkiw, 2002], in which the coastline is assumed to move in its normal direction inland with some speed Va, depending on time. The terrain lowering rates for grabens rg and for horsts rh are found such that the modeled coastline qualitatively match the coastline in Gavrilov et al. [2006] at certain moments of time. The found parametrizations for the terrain lowering functions are plotted in Figure A1. Since the KU is a massive relatively flat uplift, the thermokarst and thermal abrasion were two important processes in lowering its terrain, therefore its terrain lowering function rKU is assumed to be twice as fast as for the regular horst, see Figure A1. We note that modeling the permafrost dynamics within the KU is not considered a primary focus of the present research.

Figure A1.

Terrain lowering functions.

[91] We simulate the IC disintegration by a consecutive application the terrain lowering and coastal abrasion steps superimposed with an inundation scheme as described by the following algorithm:

[92] 1. Step 0: At the time step i = 0, set time ti = tS, and s(x, t0) = s0.

[93] 2. Step 1: Find the current positions of the sea level wi = w(ti).

[94] 3. Step 2: Find a dry part of the shelf Ωdry(ti) = {x : h(xti) > wi}.

[95] 4. Step 3: Apply a level set method to simulate the thermal abrasion of the coastline ∂Ωdry(ti) during the current time step titi+1 and thus obtain a temporal configuration Ωdry(ti+1/2) that accounts for the thermal abrasion effects. Dependence of the coastal abrasion velocity with time is discussed in Section 4.3.

[96] 5. Step 4: Find a part of the ice complex on top of the horst by

display math

and then define its compliment

display math

that is associated with grabens and parts of the already flooded horsts.

[97] 6. Step 5: Apply a terrain lowering corrections and derive a new configuration of the IC:

display math

[98] 7. Step 6: Set t = ti + Δt and go back to Step 1.

[99] Modeled dynamics of the ice complex disintegration are shown in Figure 7 that closely resembles the figures in Gavrilov et al. [2006]. The well-known islands of Vasilevsky and Semenovsky were located on horsts and were completely eroded approximately 200 years ago [Romanovskii et al., 2004].

A2. 1-D Non-linear Heat Equation

[100] We model permafrost dynamics on the Laptev Shelf by computing the ground temperature on a grid of points inline imagespaced uniformly in longitudinal and latitudinal directions, with a resolution of 6 arc-minutes. At each point, we assume that there are no water migration or heat sources in the ground material, and thus we simulate the ground temperatureT[°C] by a 1-D heat equation with phase change [Carslaw and Jaeger, 1959]:

display math

Here, z ∈ [0, l] is depth below the ground/seafloor at the point inline image, and t ∈ [t0, 0] is the time from some moment in the past to present. Following Tipenko et al. [1999], we start our simulations at t0 = 360,000 years ago in the middle of the glacial cycle, when the shelf was frozen. The lower boundary z = l is assumed to be almost twice below the maximum estimated permafrost thickness during the glacial cycles, or at l = 2500 meters.

[101] The quantities C = C(T, z) [Jm−3 K−1] and λ = λ(T, z) [Wm−1 K−1] represents the volumetric heat capacity and thermal conductivity of soil, respectively; L [Jm−3] is the volumetric latent heat of fusion of water, and θ is the liquid pore water fraction. The thawed and completely frozen ground correspond to θ = 1 and θ = 0, respectively. The quantity θ = θ(T) depends on the temperature T, soil texture and salinity. For coarsely grained soils, the quantity θcan be parameterized based on sodium chloride - water binary phase diagram [Hivon and Sego, 1990, 1995].

[102] The thermal properties of each layer are parameterized according to de Vries [1963] and Sass et al. [1971] while assuming that the material is fully saturated. Hence, the thermal conductivity λ of the soil and its volumetric heat capacity C can be expressed according to Nicolsky et al. [2009] as

display math

where λf and Cf are the thermal properties of completely frozen ground material, and subscripts w and i mark the properties of water and ice, respectively.

[103] The heat equation is supplemented by initial temperature distribution T(z, t0) = T0(z) that is equal to a steady state temperature T0(z) = Tg0 + γz, where inline image is the geothermal gradient at inline image and Tg0 is the ground surface temperature at t = t0. To specify the boundary conditions at the ground surface z = 0 and at the depth l, we exploit the Dirichlet and Neumann boundary conditions, i.e., inline image, inline image, respectively.

[104] When the point inline image is dry, the temperature Tu is specified by the paleotemperature reconstruction Tg(t). Otherwise, when submerged, the temperature Tu is given by the benthic temperature Tb(xi, d). From the mathematical point of view

display math

where d = w(t) − h(xi, t) is the ocean depth when the point inline image is flooded. Note that the benthic temperature Tb depends on the coordinate xi in order to simulate a warming effect of the Lena River outflow.

Acknowledgments

[105] We would like to thank H.-W. Hubberten, Yu. Shur, G. Delisle, J. Stroh, G. Panteleev, V. Alexeev, C. Burn, and others for all their valuable advice, critique and reassurances along the way. We are thankful to reviewers and the editor for valuable suggestions making the manuscript easier to read and understand. This research was funded by the U.S. National Science Foundation (ARC-1023281, ARC-0909546); the NOAA OAR Climate Program Office (NA08OAR4600758); by the Russian Foundation for Basic Research (11-05-00781, 11-05-12021, 11-05-12027, 11-05-12028, 11-05-12032), and by the State of Alaska.

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