methane emissions from permafrost thaw lakes limited by lake drainage

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© 2011 Macmillan Publishers Limited. All rights reserved. LETTERS PUBLISHED ONLINE: 1 MAY 2011 | DOI: 10.1038/NCLIMATE1101 Methane emissions from permafrost thaw lakes limited by lake drainage J. van Huissteden 1 * , C. Berrittella 1 , F. J. W. Parmentier 1,2 , Y. Mi 1 , T. C. Maximov 3 and A. J. Dolman 1 Thaw lakes in permafrost areas are sources of the strong greenhouse gas methane 1–5 . They develop mostly in sedi- mentary lowlands with permafrost and a high excess ground ice volume, resulting in large areas covered with lakes and drained thaw-lake basins (DTLBs; refs 6,7). Their expansion is enhanced by climate warming, which boosts methane emis- sion and contributes a positive feedback to future climate change 3,4,8 . Modelling of thaw-lake growth is necessary to quantify this feedback. Here, we present a two-dimensional landscape-scale model that includes the entire life cycle of thaw lakes; initiation, expansion, drainage and eventual re-initiation. Application of our model to past and future lake expansion in northern Siberia shows that lake drainage strongly limits lake expansion, even under conditions of continuous permafrost. Our results suggest that methane emissions from thaw lakes in Siberia are an order of magnitude less alarming than pre- viously suggested, although predicted lake expansion will still profoundly affect permafrost ecosystems and infrastructure. Thaw lakes (also known as thermokarst or alas lakes) are widespread in sedimentary basins with permafrost. In particular, lowland areas with fine-grained sediments (for example river plains in northern Siberia) often contain large amounts of excess ice (ice volume exceeding the normal pore volume of the sediment). Thawing of ice-rich permafrost causes subsidence and lake formation 6,7 . Subsequently, anaerobic decomposition of fossil and fresh organic matter from thawing permafrost and local primary production results in emission of the greenhouse gas methane (CH 4 ; refs 1–5). Lake expansion by permafrost degradation is therefore considered as a strong positive feedback to climate warming 4 . During the Last Glacial Termination (LGT), thaw-lake expansion may have significantly contributed to the rise of the atmospheric CH 4 concentration recorded in ice cores 9 . Many existing thaw lakes date from the LGT and early Holocene 9–14 , but their formation and expansion is expected to be enhanced strongly by future climate warming 3,7,15 . Besides their effect on the carbon cycle, thaw lakes also strongly influence permafrost ecosystems, Arctic hydrology and human activities in the Arctic 8,16,17 . Thaw lakes may grow and disappear over relatively short time spans (centuries to millennia) compared with other lakes. The land- scape in many Arctic lowlands is covered with overlapping DTLBs, suggesting that the process of thaw-lake formation and drainage occurred repeatedly; thaw-lake deposits also occur in Pleistocene successions in Europe 18,19 . In the evolution of thaw lakes a wide range of processes is involved: soil and lake water heat exchange, erosion and sediment redistribution, permafrost hydrology and 1 Vrije Universiteit, Faculty of Earth and Life Sciences, Hydrology and Geo-Environmental Sciences, De Boelelaan 1085, 1081HV Amsterdam, The Netherlands, 2 Lund University, Department of Earth and Ecosystem Sciences, Physical Geography and Ecosystem Analysis, Sölvegatan 12, 223 62 Lund, Sweden, 3 Russian Academy of Sciences, Siberian Branch, Institute for Biological Problems of the Cryolithozone, 41 Lenin Ave., 677980 Yakutsk, Russia. *e-mail: [email protected]. Temperature Ground ice 1¬¬Lake initiation 2¬¬Lake expansion 3¬¬Lake drainage 5 4 Precipitation Figure 1 | Schematic of the thaw-lake cycle model. The rate of lake initiation (1) and subsequent expansion (2) is determined by air temperature, precipitation and ground ice content. Lake formation creates thawed permafrost underneath the lake. Subsequent drainage of lakes by river erosion (3) is determined by precipitation. After lake drainage, new ice-rich permafrost may be established (4), after which new lakes may form in the same area (5). drainage basin processes (Supplementary Information S1). Existing models describe parts of the thaw-lake evolution 20–23 . However, the scale at which these models operate is not appropriate for understanding the carbon cycle effects of thaw lakes on a global scale (hundreds of km 2 and more). At this scale, incorporation of detailed physical processes is impractical because of the non-availability of parameters and the excessive computing time required. Our stochastic thaw-lake model (Fig. 1) overcomes these problems and simulates lake formation over regions of the order of hundreds of km 2 , relating lake-area change to climate change. Mean annual precipitation (P ), summer air temperature (T july ) and mean annual air temperature (T ann ) are climatic driving variables in the model (see Methods). We assume a reference climate at which ice-rich permafrost is considered to be geomorphologically stable 17 ; the Last Glacial Maximum (LGM) climate was used for this purpose. A second assumption is that lake change processes relate linearly to deviations from this reference climate (Supplementary Information S1). The rates of the lake formation and expansion depend on the deviations of P and NATURE CLIMATE CHANGE | VOL 1 | MAY 2011 | www.nature.com/natureclimatechange 119

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Page 1: Methane emissions from permafrost thaw lakes limited by lake drainage

© 2011 Macmillan Publishers Limited. All rights reserved.

LETTERSPUBLISHED ONLINE: 1 MAY 2011 | DOI: 10.1038/NCLIMATE1101

Methane emissions from permafrost thaw lakeslimited by lake drainageJ. van Huissteden1*, C. Berrittella1, F. J. W. Parmentier1,2, Y. Mi1, T. C. Maximov3 and A. J. Dolman1

Thaw lakes in permafrost areas are sources of the stronggreenhouse gas methane1–5. They develop mostly in sedi-mentary lowlands with permafrost and a high excess groundice volume, resulting in large areas covered with lakes anddrained thaw-lake basins (DTLBs; refs 6,7). Their expansionis enhanced by climate warming, which boosts methane emis-sion and contributes a positive feedback to future climatechange3,4,8. Modelling of thaw-lake growth is necessary toquantify this feedback. Here, we present a two-dimensionallandscape-scalemodel that includes the entire life cycle of thawlakes; initiation, expansion, drainage and eventual re-initiation.Application of our model to past and future lake expansion innorthern Siberia shows that lake drainage strongly limits lakeexpansion, even under conditions of continuous permafrost.Our results suggest that methane emissions from thaw lakesin Siberia are an order of magnitude less alarming than pre-viously suggested, although predicted lake expansion will stillprofoundly affect permafrost ecosystems and infrastructure.

Thaw lakes (also known as thermokarst or alas lakes) arewidespread in sedimentary basins with permafrost. In particular,lowland areas with fine-grained sediments (for example river plainsin northern Siberia) often contain large amounts of excess ice(ice volume exceeding the normal pore volume of the sediment).Thawing of ice-rich permafrost causes subsidence and lakeformation6,7. Subsequently, anaerobic decomposition of fossil andfresh organic matter from thawing permafrost and local primaryproduction results in emission of the greenhouse gasmethane (CH4;refs 1–5). Lake expansion by permafrost degradation is thereforeconsidered as a strong positive feedback to climate warming4.During the Last Glacial Termination (LGT), thaw-lake expansionmay have significantly contributed to the rise of the atmosphericCH4 concentration recorded in ice cores9. Many existing thaw lakesdate from the LGT and early Holocene9–14, but their formation andexpansion is expected to be enhanced strongly by future climatewarming3,7,15. Besides their effect on the carbon cycle, thaw lakesalso strongly influence permafrost ecosystems, Arctic hydrology andhuman activities in the Arctic8,16,17.

Thaw lakes may grow and disappear over relatively short timespans (centuries tomillennia) compared with other lakes. The land-scape in many Arctic lowlands is covered with overlapping DTLBs,suggesting that the process of thaw-lake formation and drainageoccurred repeatedly; thaw-lake deposits also occur in Pleistocenesuccessions in Europe18,19. In the evolution of thaw lakes a widerange of processes is involved: soil and lake water heat exchange,erosion and sediment redistribution, permafrost hydrology and

1Vrije Universiteit, Faculty of Earth and Life Sciences, Hydrology and Geo-Environmental Sciences, De Boelelaan 1085, 1081HV Amsterdam, TheNetherlands, 2Lund University, Department of Earth and Ecosystem Sciences, Physical Geography and Ecosystem Analysis, Sölvegatan 12, 223 62 Lund,Sweden, 3Russian Academy of Sciences, Siberian Branch, Institute for Biological Problems of the Cryolithozone, 41 Lenin Ave., 677980 Yakutsk, Russia.*e-mail: [email protected].

Temperature

Ground ice

1¬¬Lake initiation

2¬¬Lake expansion

3¬¬Lake drainage

5

4

Precipitation

Figure 1 | Schematic of the thaw-lake cycle model. The rate of lakeinitiation (1) and subsequent expansion (2) is determined by airtemperature, precipitation and ground ice content. Lake formation createsthawed permafrost underneath the lake. Subsequent drainage of lakes byriver erosion (3) is determined by precipitation. After lake drainage, newice-rich permafrost may be established (4), after which new lakes mayform in the same area (5).

drainage basin processes (Supplementary Information S1). Existingmodels describe parts of the thaw-lake evolution20–23. However,the scale at which these models operate is not appropriate forunderstanding the carbon cycle effects of thaw lakes on a global scale(hundreds of km2 andmore). At this scale, incorporation of detailedphysical processes is impractical because of the non-availabilityof parameters and the excessive computing time required. Ourstochastic thaw-lake model (Fig. 1) overcomes these problems andsimulates lake formation over regions of the order of hundreds ofkm2, relating lake-area change to climate change.

Mean annual precipitation (P), summer air temperature(Tjuly) and mean annual air temperature (Tann) are climaticdriving variables in the model (see Methods). We assume areference climate at which ice-rich permafrost is considered tobe geomorphologically stable17; the Last Glacial Maximum (LGM)climate was used for this purpose. A second assumption is that lakechange processes relate linearly to deviations from this referenceclimate (Supplementary Information S1). The rates of the lakeformation and expansion depend on the deviations of P and

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© 2011 Macmillan Publishers Limited. All rights reserved.

LETTERS NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE1101

Tjuly from the reference climate. The lake drainage rate is relatedto P , and refreezing of drained lake basins and re-growth ofground ice depend on Tann. Besides climate, lake initiation andlake expansion rates also depend on the volumetric ice contentof the subsoil. The directional expansion of lakes depending onwind direction is included in the model. The model is two-dimensional, as it assumes a flat terrain underlain by ice-richpermafrost. The subsoil volumetric ice content is prescribed, withsuperposed random variation. The model time step is one year,and the model area of 400 km2 is subdivided into 500 × 500grid cells of 40×40m.

We conducted validation and sensitivity experiments to testthe model and evaluate its implications for methane emissionfrom permafrost thaw (Supplementary Information S5, S6). TheTERRAIN experiment compares model results with a thaw-lake area in northern Siberia: the Indigirka lowlands (refs 24,25; Supplementary Information S3). We simulated thaw-lakeformation with a synthetic climate time series consisting of astep change in Tann, Tjuly and P , followed by a gradual risetowards present-day climate, approximating the LGT andHolocene(Supplementary Information S6, Table S4; Fig. 2). The resultinglake area fraction and lake sizes agree with that of the terrain;differences occur mainly at very small lake sizes and are attributedto uncertainty in the field data. Most of the Indigirka lowlandsarea is occupied by DTLBs, which is also reproduced by themodel. Lake formation occurs sporadically before climate change,picks up rapidly after the climate begins to change (Fig. 2), andreaches a maximum of 21–30% 150–200 years later. Thereafter,the lake area is reduced by drainage of lakes. Subsequently, thelake area tends to oscillate at a lower percentage, approximatingthe present-day lake area. The initial conditions of the terrain alsoaffect the model results (Supplementary Information S6, Fig. S4).However, the average lake area is robust to these perturbations.We conclude that the model correctly simulates the dynamics ofthaw-lake formation.

The oscillations are caused by repeated lake drainage, regrowthof excess ice and renewed lake formation, and may be an intrinsicproperty of thaw-lake evolution. Their amplitude and wavelengthis influenced by the ice regrowth factor Igrow (ICEGROWTH ex-periment), MP and MT (which relate lake initiation rate to precip-itation and summer temperature) and drainage density (Methods,Supplementary Information S6, Fig. S5). The implication of theseoscillations is that localized, smaller expansions of lake area do notnecessarily signify climate change, but simply the presence of areasrich in ground ice in which lakes can be initiated.

The timing of lake formation is crucial for modelling the effectsof future lake expansion. Radiocarbondatings of LGTandHolocenethaw-lake formation9 indicate a peak of lake formation during theLGT, which is reproduced correctly by the model. In detail, thereare small differences in timing (a slower reaction of the model),which relate to both data and model parameters (SupplementaryInformation S6). The TIMING experiment explores adjustmentsin the model to produce a faster response. Increasing the values ofMP and MT results in progressively earlier and more pronouncedpeaking of thaw-lake area (Supplementary Information S6, Fig. S6).However, with a high value of MP and MT the resulting lake-sizedistribution contains an unrealistically high number of very smalllakes. We also simulated the creation of lakes by flooding ofdepressions, by generating lakes with a random size distributionwhen a precipitation threshold is crossed. This produces a lakeformation peak very shortly after the climate change step withoutfurther effects on the final lake distribution. It is probable thatlake initiation at the LGT is caused at least partly by an increasedprecipitation surplus14.

The FUTURE experiment simulates the effect of 100 years offuture climate change using climate model output for the test

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Figure 2 | Simulated thawed area data for the test area. a, Simulated thawlakes for one model run. b, Ice content at the end of the model run. The icecontent shows overlapping DTLBs, characterized by different soil icecontent. c, Average thawed area (blue) and drained area (red) evolutionthrough time, averaged over 10 model runs. The grey lines represent thestandard deviation of the thawed area. d, Climate input data (mean annualair temperature (Supplementary Information S5). e, Size and shape(isoperimetric quotient) distribution of the modelled lakes (lake sizes on alogarithmic scale).

area (model simulations from six climate models, based on theIntergovernmental Panel onClimate Change (IPCC) Special Reporton Emissions Scenarios (SRES) A2 and B1 climate scenarios,Supplementary Information S5 and S6). For the test area, thesimulated climates would still sustain continuous permafrost. Themodel is initialized with randomly generated lakes with a similararea coverage (8%) to that in the test area, to eliminate theeffects of lake configuration. The thawed area increases, mainlyas a result of lake expansion, on average from 8% to 25%± 3%after 70 years. Thereafter, the thawed area decreases as a resultof lake drainage (Fig. 3). After 100 years, approximately half ofthe simulations result in a lower thawed area than the initial lakearea, with percentages as low as 2.2% (A2) or 2.7% (B1). Oneclimate model (NOAAGFDL) predicts relatively low temperaturesand precipitation, and results in a slower growth of thawed area andno decrease. The differences between the A2 and B1 scenarios aremarginal, for B1 the decrease in lake area tends to start slightly later.The modelled initial increase in lake area is lower than estimatesof recent lake expansion rates of 14.7% in 26 years (ref. 3) and12% in 25 years (ref. 15), but slightly higher than a 4.4% lake areaincrease in 19 years (ref. 17). However, remote-sensing estimatesof lake area expansion have a high uncertainty, and depend onresolution and lake level variation. Additional experiments show

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NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE1101 LETTERS

2000 2020 2040 2060 2080 2100Year

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Figure 3 | Ensemble of thaw-lake model runs for climate change expected in the twenty first century. The climate input is derived from six climate modelsfor SRES A2 and B1 climate scenarios from the IPCC fourth assessment report. For every climate model, ten runs of the thaw-lake model have been carriedout. The coloured lines indicate the development of the thawed area; colours indicate climate models: UK Met Office HadCM3 (HADCM3), Max PlanckInstitute for Meteorology ECHAM5 (ECHAM5), NOAA Geophysical Fluid Dynamics Laboratory CM2.1 (NOAA GFDL CM2.1), CSIRO AtmosphericResearch Mk3.5 (CSIRO Mk3.5), National Center for Atmospheric Research CCSM3.0 (NCAR CCSM3.0) and Russian Institute for Numerical MathematicsINMCM3.0 (INMCM3.0). The thick lines represent the average thaw-lake area for each climate model.

that the future lake growth is sensitive to ground ice content andprecipitation. A lower ground ice content and lower precipitationresult in slower lake expansion.

To extrapolate lake area to CH4 emission, we multiply lake-area fractions by emission estimates for Siberian thaw lakes andthe area of permafrost which is vulnerable to lake development,assuming that our test area is representative of these areas(Supplementary Information S7). For the LGT the emissionestimate is based on the first thaw lake peak in the TERRAINexperiment, lasting approximately 370 years. As it is generatedby conversion of relatively dry cold steppe to lake, we assumethat CH4 emission was insignificant before thaw-lake formation.This results in a total emission of 1,368± 44 Tg CH4 from lakeformation, over the 370 years of the peak duration, or 3.73 TgCH4 yr−1 (Supplementary Information S7). Previous estimates ofLGT thaw-lake emission9 gave 13–26 Tg CH4 yr−1; our yearlyemissions are lower because we include the effect of lakedrainage in our model.

Likewise, future emissions resulting from anthropogenic climatechange are based on the FUTURE experiment (HADCM3 climatemodel). In this case we have to subtract the emission of thepresent-day wet tundra25 (F. J. W. Parmentier, manuscriptin preparation) from the lake emission. For the A2 scenariosimulations the resulting emission increase over 100 years for theentire area of thaw-sensitive sediments26 is 1.84±0.04 Tg CH4 yr−1and the maximum emission 3.28 ± 0.49 Tg CH4 yr−1; for B1slightly higher values (1.92 ± 0.4 Tg CH4 yr−1 and 3.32 ±0.52 Tg CH4 yr−1) are obtained, because of the higher lake-area fraction (Supplementary Information S7). Our estimateof CH4 emission from thaw-lake development is considerablyless than the previous estimate of 50–100 Tg CH4 yr−1, whichwas based on the assumption of complete thawing of ice-rich permafrost4.

Our model shows that expansion of thaw lakes is restrictedby lake drainage. Lake drainage causes lake areas to return toterrestrial wetland areas with lower emission rates and possiblyhigher carbon accumulation rates25. Reduction of CH4 emissionis further enhanced when the climate allows re-establishment ofice-rich permafrost, resulting in drier soil conditions by frostheave25 (F. J. W. Parmentier, manuscript in preparation). Thelake expansion would increase the high-latitude lake emission27

of 6.8± 4.9 Tg CH4 yr−1 by 49%. Recent northern wetland CH4

emission estimates28 vary between 23 and 157 Tg yr−1. Usingan estimate of 78 Tg yr−1, thaw-lake expansion would amountto 4% of total northern wetland emission at most. Thereforeother climate-driven changes in high-latitude wetlands, such asvegetation, active-layer and river-discharge changes24,25,28, probablyproduce stronger responses of Arctic CH4 fluxes.

Our model simulations are restricted to continuous permafrost,where rapid lake formation is likely15 and which contains the largestarea of ice-rich permafrost. Lake drainage proves to be a criticalprocess. At present, our model only includes lake drainage resultingfrom lake expansion encroaching on the drainage system. Activeexpansion of the drainage by channel erosion is not included,nor is underground drainage of lakes through taliks (unfrozenportions of the permafrost). Therefore the modelled drainagerate is conservative. Future warming will result in conversion ofcontinuous permafrost areas to discontinuous and permafrost-free areas, where drainage by groundwater flow is likely tobecome more important4. Despite the deliberate omission ofprocess details, our model allows us to bracket future Arctic CH4fluxes from lake expansion more precisely, as lake drainage isincluded explicitly. The model also shows that better quantitativedata on ground ice distribution and thaw-lake initiation andexpansion is crucial to quantify future Arctic lake expansion.The model results in considerably lower estimates of CH4 fluxesfrom thaw-lake expansion. Moreover, it is shown that evenstabilization of anthropogenic greenhouse-gas emissions cannotmitigate the transformation of Arctic permafrost landscapes oncepermafrost destabilization has started. Although the methaneemission appears less alarming than suggested previously, lakeexpansion on the scale predicted by our model will still profoundlyaffect permafrost ecosystems, including wildlife habitats andhuman infrastructure.

MethodsModel description. (See also Supplementary Information S1 and S2). The modeldomain is subdivided into N grid cells. The ice content of the permafrost per gridcell Ii,j,t varies between a minimum and maximum Imin and Imax. The referenceclimate (Supplementary Information S1) is defined bymean annual air temperature(MAAT) Tref,ann, mean July temperature Tref,july and annual precipitation Pref.Climate input consists of a time series of MAAT Tann, July temperature Tjuly andannual precipitation P . The model time step is one year.

The fraction of grid cells fthaw,t where partial thaw (thaw pond formation)is initialized is determined by the summer temperature deviation from the

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LETTERS NATURE CLIMATE CHANGE DOI: 10.1038/NCLIMATE1101

reference climate at time t , Tdiff,t = Tjuly−Tref,july and precipitation deviationPdiff,t = Pt −Pref:

fthaw,t =Tdiff,t ·MT+Pdiff,t ·MP

whereMT andMP are constants. Thaw occurs preferentially in grid cells with a highice content, exceeding a minimum Iminthaw. The fraction of grid cells that exceedIminthaw is fminthaw,t . The actual number of cells Nthaw,t where thaw occurs at a giventime step t is determined by:

fthaw,t < fminthaw,t :Nthaw,t =N ·fthaw,t

fthaw,t ≥ fminthaw,t :Nthaw,t =N ·fminthaw,t

If fthaw,t < fminthaw,t , the cells with highest ice content are selected first. For each gridcell, the thawed fraction at time t is denoted as Li,j,t . When thawing occurs, an areafraction Lnew,i,j,t is converted into thaw ponds. This fraction depends on the icecontent of the grid cell:

Lnew,i,j,t = Lmax ·Ii,j,t

in which Lmax (constant) is the maximum grid cell fraction that can be thawed inone time step. This area fraction is added to Lt :

Li,j,t = Li,j,t−1+Lnew,i,j,t

If Li,j,t exceeds a threshold value Lthresh, the grid cell is considered as beingcompletely thawed:

Li,j,t > Lthresh : Li,j,t = 1.0

Once a grid cell is completely thawed, it is a lake cell and can expand intoadjacent grid cells. Surrounding non-lake cells are affected by extra thaw, dependingon summer temperature, precipitation and ice volume. The maximum amount ofthermal erosion at time t , Lmaxexp,t is related to Tdiff,t and Pdiff,t :

Tdiff,t > a,Pdiff,t > 0 : Lmaxexp,t = b(Tdiff,t −a)+ cPdiff,t

Tdiff,t ≤ a : Lmaxexp,t = 0

where a is a constant threshold value, and b is a constant. The constant a allowslake expansion to occur in summers that are cooler than the reference climate. Theamount of thaw for each lake border grid cell Lexp,i,j,t is determined by Lmaxexp,t andice content Ii,j,t , and added to the thawed fraction. If the thawing threshold Ltresh isexceeded, the cell is marked as completely thawed:

Li,j,t = Lmaxexp,t ·Ii,j,t +Li,j,t−1

Li,j,t > Ltresh : Li,j,t = 1.0

Lake orientation is implemented by weighting the threshold for completethawing Ltresh of adjacent cells according to themean wind direction and orientationwith respect to the lake grid cell:

d = |cos(W +G)| ·Ltresh ·Fw

Ld=(max(d)−d)

Fw+d

Here d is a directional weight, Ld is the thawing threshold for surrounding cells,Wis the dominant wind direction, Fw determines the strength of the wind directioneffect, and G is the direction angle of every adjacent grid cell with respect to thecell under consideration. Fw weights the thawing threshold based on d to decreasethe threshold. The grid restricts the lake orientation to integer multiples of 45◦.Lake shore promontories (cells with less than 3 adjacent non-lake cells) may beeroded preferentially to obtain smoother lake banks. This depends on an uniformlydistributed erosion probability perode.

The drainage system can expand into lakes if a connection between lake andfloodplain cells is established. Connection occurs when the thawed fraction of agrid cell adjacent to a floodplain cell exceeds a threshold value, Ldrain, which can bereduced if Pdiff,t is positive:

Pdiff,t > 0 : Ldrain,t = Ldrain−Mdrain ·Pdiff,t

Pdiff,t ≤ 0 : Ldrain,t = Ldrain

An iterative algorithm expands the drainage system at each time step until alladjacent lake cells and partially thawed cells are linked to the drainage system.

Drained lake cells can refreeze if the mean annual air temperature Tann,t islower than Tfreeze. If Tann,t is cold enough to allow ice wedge growth (Tann,t ≤Tgrow),the amount of ground ice Ii,j,t increases in all non-thawed cells. The rate of growthdepends on the ice content and is fastest at low ice content:

Iadd,i,j,t = (Imax− Ii,j,t ) ·Igrow

This also restricts the amount of ice to the limiting amount Imax. Ice regrowthcauses frost heave, which ultimately causes grid cells to become detached from thedrainage system. This occurs when a limit ice amount Iheave is exceeded.

Received 12 January 2011; accepted 4 April 2011; published online1 May 2011

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AcknowledgementsWe acknowledge G. van der Werf for critically reading a first version of the manuscript.We thank our colleagues at the RAS Institute for Biological Problems of the Cryolithozonein Yakutsk (A. V. Kononov, S. V. Karsanaev) for facilitating fieldwork in the SiberianNorth. This research is financed by Netherlands Organization for Scientific Research(NWO) Grant no. 815.01007 ‘Methane flux from northern wetlands at rapid climatechange during the last glacial’ and NWO/Russian Federal Bureau of Research (RFBR)

Dutch–Russian Scientific Cooperation Grant 047.017.037, and EU FP7 Marie CurieResearch and Training Network GREENCYCLES II.

Author contributionsAll authors contributed to the analysis of model results, proposed modifications to theexperiments and commented on the manuscript. J.v.H. constructed the model andconducted most of the model experiments. C.B. contributed to the text and the systemanalysis preceding the model construction. C.B. and F.J.W.P. collected the field data.A.J.D. contributed to the text. Y.M. did experiments with the future climate scenarios.T.C.M. facilitated fieldwork in the Siberian North and contributed with discussionson scientific results. A.J.D.

Additional informationThe authors declare no competing financial interests. Supplementary informationaccompanies this paper on www.nature.com/natureclimatechange. Reprints andpermissions information is available online at http://www.nature.com/reprints.Correspondence and requests formaterials should be addressed to J.v.H

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