# Subsea Methane Hydrates: Origin and Monitoring the Impacts of Global Warming
## 2 Formation of Subsea Pernafrost and Methane Hydrate Stability Zones
### Results of the Numerical Simulation  
Using the model of heat transfer in bottom sediments with changes in boundary conditions (at the upper boundary) according to the constructed paleogeographical scenario [31], changes in the thickness of the subsea permafrost and MHSZ over the past 200 thousand years (until 1950) were estimated. In numerical calculations for the period 1950-2200, the increase in the average annual temperature of bottom water was considered. An analysis of summer observations [6] collected over the Laptev inner shelf, including the region of our interest, has shown a warming tendency in sea waters with the bottom layer temperature rising by 0.8 \({}^{\circ}\)C from 1984 to 2009 (0.032 \({}^{\circ}\)C/year). Considering further warming over Arctic shelves in the second decade of this century, we used a warming trend of 0.02 \({}^{\circ}\)C/year for all seasons (see Figure 2). Preliminary modeling of the geocryological situation over a long period (200 thousand years) made it possible to establish the general patterns of its changes. The state of the permafrost depends both on the properties of the deposits that make up the geological section (the thermal and physical characteristics, moisture content and salinity) and on the combination of upper and lower boundary conditions and the thermal conductivity of the deposits. Figure 3 shows temperature profiles in the upper 500 m of bottom sediments at different time horizons up to 2200. According to Figure 3, the maximum differences in the state of permafrost occur after the shelf flooding seven thousand years ago and the transition of continental permafrost to a subaqueous state. At the same time, the changes in the sediment temperature in the permafrost are insignificant for the last 5 thousand years. We present the change in the permafrost thickness over the past 20 thousand years, based on the results of numerical experiments in Figure 2. During the period of the last glacial maximum (about 20 thousand years ago) and the subsequent five thousand years, the thickness of frozen deposits reached a maximum of 440 m (Figure 2). The subsequent warming and flooding of the shelf with sea water led to an increase in the temperature of bottom sediment and thawing of the subsea permafrost (Figure 2). The estimates based on the model results show that, at present, the thickness of relict permafrost in the bottom sediments of the considered shelf area is about 300 m; Figures 2 and 3. The evolution of the methane hydrate stability zone corresponds to the dynamics of the P-T conditions, i.e., the permafrost dynamics and sea level change. The maximum changes occurred during the warm period seven-six thousand years ago, which was accompanied  
Figure 3: Evolution of the temperature profiles in the upper 500 m of bottom sediments in the past, present and future. The profiles correspond to 20 thousand years ago (20 kyr), 10 thousand years ago (10 kyr), 5 thousand years ago (5 kyr), and the year 2000 (present) as well as the years 2100 and 2200 (future). Figure 2: The results of numerical simulation based on the heat transfer model. The upper panel shows the paleotemperature scenario for the period 20 thousand years ago–1950 and 1950–2200 (highlighted in pink). At the bottom—the evolution of the permafrost and methane hydrate stability zone over the past 20 thousand years: the lower boundary of the permafrost (PERMB) is the blue line, the upper boundary of the permafrost (PERMT) is the blue line, and the upper boundary of the methane hydrate stability zone (HSZT) is the green line. The area of possible hydrate existence is highlighted in gray. by a sea level rise and flooding of this part of the shelf (Figure 2). The lowering of the MHSZ upper boundary roof shows approximately 60 m (Figure 2). According to the results of numerical experiments presented in Figure 3, the mean annual surface temperature becomes positive (in \({}^{\circ}\)C) after 2050.