Earth system models (ESMs) use bottom boundaries for their land surface model (LSM) components which are shallower than the depth reached by surface temperature changes in the centennial timescale associated with recent climate change. Shallow bottom boundaries reflect energy to the surface, which along with the lack of geothermal heat flux in current land surface models, alter the surface energy balance and therefore affect some feedback processes between the ground surface and the atmosphere, such as permafrost and soil carbon stability. To evaluate these impacts, we modified the subsurface model in the Community Land Model version 4.5 (CLM4.5) by setting a non-zero crustal heat flux bottom boundary condition uniformly across the model and by increasing the depth of the lower boundary from 42.1 to 342.1 m. The modified and original land models were run during the period 1901–2005 under the historical forcing and between 2005 and 2300 under forcings for two future scenarios of moderate (Representative Concentration Pathway 4.5; RCP4.5) and high (RCP8.5) emissions. Increasing the thickness of the subsurface by 300 m increases the heat stored in the subsurface by 72 ZJ (1 ZJ = 10
In the current context of anthropogenic climate change, there is a need to forecast future impacts of climate change as reliably as possible. Climate change projections are based on simulations from ensembles of Earth system models (ESMs), numerical models of oceans, atmosphere, land, ice and biosphere subsystems coupled together
Thermal diffusion in the subsurface allows the land system to act like a heat reservoir, contributing to the thermal inertia of Earth's climate. However, this contribution is relatively small as the capacity of the oceans to absorb energy is orders of magnitude above that of the continents
Several works
Most of the current land models use a zero heat flux as thermal boundary condition at their base, as the geothermal gradient is small (
Soils in permafrost regions act as a long-term carbon sink that stores an estimated 1100–1500 GtC of organic carbon, twice the carbon content of the pre-industrial atmosphere
The generation of ESMs used in the fifth phase of the Climate Model Intercomparison Project (CMIP5) shows large disagreement in the simulation of present-day permafrost extent. The response of permafrost area to the increase of global temperatures shows a wide range of sensitivities across the different CMIP5 LSMs (0.75–
It is possible to use analytical methods to estimate the effect that the bottom boundary depth and basal heat flux condition have on the thermal profile of the ground
The Earth's continental lithosphere (
The general solution for any surface temperature perturbation
Future scenarios
Numerical models, however, cannot simulate the subsurface as a semi-infinite solid, also known as a half-space model, but instead limit the subsurface to a given depth that varies between models. Many land models include only the upper 3–4 m of the subsurface, which they consider as soil, to model the most basic hydrological processes such as infiltration and runoff in a first-order approximation. Other models further extend the subsurface to include the bedrock below, the deepest currently being CLM4.5 with a total depth of 42.1 m. We can simplify these models by considering conduction only and modeling the land subsurface as a solid bounded by two parallel planes (the surface and the lower boundary). Assuming a lower boundary condition of no heat flux (as most current models do) and a linearly increasing temperature increasing linearly with time
Using Eqs. (
Departure from the initial temperature profile due to constant rate of surface temperature increase of 0.01 K yr
We calculated the temperature anomalies for the half-space model and the layers of thickness at 42.1 and 342.1 m, after 100 and 400 years. After 100 years, the temperature anomaly for the thinnest (42.1 m) model has departed from that of the half-space model (Fig.
Heat absorbed by the land column per unit of area (
The maximum time before the shallow bottom boundary affects the thermal behavior of the model is better appreciated in terms of heat absorption by the subsurface. The heat stored in the subsurface can be calculated from the temperature change in Eq. (
The heat absorbed per unit of area for the 42.1 m model is slightly smaller than that of the half-space model after 100 years and less than half after 400 years, while for the 342.1 m model no difference can be observed (Fig.
The heat Eq. (
In the conductive regime described by Eq. (
The propagation into the subsurface of an harmonic temperature signal such as the annual air temperature cycle is characterized by exponential amplitude attenuation,
The Community Earth System Model version 1.2 (CESM1.2) is a coupled ESM, consisting of components representing the atmosphere, land, ocean, sea ice and land ice. Individual components can be run separately, taking the necessary inputs from prescribed datasets. Because running the coupled model is computationally expensive, we have run only the CLM4.5 LSM
Carbon and nitrogen cycles are included in CLM4.5 through the biogeochemistry (BGC) module, which includes a methane module
The subsurface is discretized in 15 horizontal layers with exponentially increasing node depths:
The total thickness of the model is 42.1 m. The upper 10 layers, to a depth of 3.8 m, are soil layers where biogeochemistry and hydraulic processes take place. The lower five layers are the bedrock, where the only process is thermal diffusion. The soil in each land column has a vertically uniform clay/sand/silt composition and a vertically variable carbon density which determines its hydraulic properties and, along with its time-varying water content, its thermal properties. Bedrock layers, assumed to be made of saturated granite (without pores or interstices that could absorb water), are uniform both horizontally and vertically. The thermal properties for bedrock in CLM4.5 are a thermal conductivity
As the horizontal dimensions of the grid are much larger than the thickness of the subsurface, horizontal heat conduction is considered negligible and thermal diffusion is considered only in the vertical direction as described in Eq. (
The hydrology model in CLM4.5 parameterizes interception, throughfall, canopy drip, snow accumulation and melt, water transfer between snow layers, infiltration, evaporation, surface runoff, subsurface drainage, redistribution within the soil column and groundwater discharge and recharge. The vertical movement of water in the soil is determined by hydrological properties of the soil layers, which can be altered by their ice content as this reduces the effective porosity of the soil. The model also includes an artificial aquifer with a capacity of 5 m below the soil column, from which discharge is calculated. This aquifer is treated as a virtual layer, because it does not interact with the bedrock and it does not simulate any physical process, except for acting as a storage of water percolated from the soil and draining water to the river transport model.
The parametrization of snow in CLM4.5 follows the approaches of
CLM version 4 includes a representation of the carbon and nitrogen cycles (CLM4CN) largely based on the ecosystem process model Biome-BGC (Biome BioGeochemical Cycles)
In CLM4.5
Schema of the carbon flux in CLM4.5-BGC. Figure redrawn from
As the flowchart in Fig.
The methane model (Fig.
We made two main modifications to the LSM. First, we increased the thickness of the bedrock and the depth of the lower boundary. Second, we assumed uniform and constant heat flux as bottom boundary condition. Increasing the thickness of the LSM is necessary to reduce the effect of the lower boundary on the temperature profile. The non-zero heat flux adds the geothermal gradient to the temperature profiles of the subsurface, which is needed to determine the lower limit of permafrost in the land column.
We increased the thickness
The bottom boundary condition of the LSM is changed to a worldwide uniform value of heat flux. While the continental heat flux is spatially variable, we lack heat flux measurements in wide areas of the world such as South America, Asia, Africa and the Northern Hemisphere permafrost regions. We use several values of heat flux (0, 20, 40, 60 and 80 mW m
We define a subsurface layer as permafrost if it remains 2 consecutive years below 0
Near-surface permafrost is commonly defined as the permafrost present within the upper 3 m of the soil
Because natural soils can reach deeper than the 3.8 m used in CLM4.5, we aim at gaining some insight on how bottom heat flux and model thickness affect permafrost deeper than 3.8 m. However, it is outside the scope of this study to introduce a realistic soil thickness in CLM4.5. For this reason, we will also study the permafrost present between the surface and a depth of 42.1 m, the thickness of the CLM4.5 subsurface, which we define as intermediate-depth permafrost.
While near-surface permafrost and intermediate-depth permafrost define permafrost within a depth range, to study the maximum depth of the top of the permafrost, we use the concept of active layer thickness (ALT). In environments containing permafrost, the active layer is the upper layer of soil that thaws during summer. The ALT is the maximum depth at which annual temperature variations at the surface are able to thaw the soil, which coincides with the upper limit of permafrost. ALT provides information on permafrost complementary to its areal extent, as variations in the thermal regime of the subsurface can displace the upper limit of permafrost in the soil, and therefore ALT, but be too small to completely thaw the permafrost within the soil.
Region of study (blue), which corresponds to the extent of near-surface permafrost in the Northern Hemisphere in the year 1901, for the original CLM4.5 model.
We are interested in how the modifications to the bottom boundary produce changes in the carbon pools of the permafrost region and how the areal extent of the permafrost region evolves in time. To avoid ambiguities, we define the region of study as the region of the Northern Hemisphere where near-surface permafrost is present at the initial time of the simulations in 1901 CE (Fig.
We follow the standard spinup procedure
Increasing the depth
Each version of the LSM is run offline between 1901 and 2300 CE, taking prescribed atmospheric variables from external sources as input to force the model. These simulations include two phases depending on the input used, (1) between 1901 and 2005, from reanalysis of historical data, and (2) between 2006 and 2300, from the IPCC climate projection under two warming scenarios
The first phase is a historical 20th century simulation between 1901 and 2005. The forcing data are taken from the CRUNCEP dataset
The second phase continues the first phase between 2006 and 2300, forces the LSM with the atmospheric output from a simulation for a specific trajectory of greenhouse gas concentration. These trajectories, called Representative Concentration Pathways (RCPs), are based on scenarios of future human emissions and provide a basis to the climate research community for modeling experiments in the long and short terms
We use two scenarios, RCP4.5 and RCP8.5, for our simulations after 2005. RCP4.5 is an mitigation scenario of anthropogenic emissions where radiative forcing reaches 4.5 W m
Mean SAT over land relative to the 20th century mean, from the CRUNCEP dataset (black) and the RCP4.5 (red) and RCP8.5 (blue) scenarios. Data are taken from
Forcing datasets of monthly averages are provided by the Earth System Grid
Heat stored in the subsurface since 1901 CE for the years 2000, 2100, 2200 and 2300 CE for the RCP4.5 and RCP8.5 scenarios.
Heat stored in the subsurface as function of time for models of subsurface thickness
The results summarized in Table
Heat stored in the subsurface as function of subsurface thickness for the years 2000 (black), 2100 (blue), 2200 (red) and 2300 (green).
At a given time, the heat absorbed by the subsurface increases with the depth of the bottom boundary
Heat stored in the upper 42.1 m as function of time for models of subsurface thickness
Deepening the bottom boundary below 42.1 m also affects the storage of heat within the layers above (Fig.
Heat stored in the soil (upper
Most of the subsurface is considered as bedrock, where the only heat transport process is thermal diffusion. The region of most interest is the soil (upper
The quantitative differences in Table
In a purely conductive thermal regime of the subsurface, the value of the heat flux used as bottom boundary condition does not affect heat diffusion. This is not the case for the soil, because in CLM4.5 the thermal properties of the soil depend on temperature through the water/ice content. However, because of the shallowness of the soil, the geothermal gradient does not raise soil temperature sufficiently to affect heat propagation. Therefore, while the heat content of the subsurface increases with the lower boundary heat flux, it does not affect its time evolution (see Figs. S3 and S4).
For the 42.1 m of the subsurface, the bottom heat flux increases the heat content by
This increase of soil heat content due to the bottom heat flux does not translate into a uniform increase of soil temperature across individual cells, because soil composition and thermal properties vary. Each 20 mW m
Northern Hemisphere intermediate-depth (0–42.1 m) permafrost area as function of time. Model versions with bottom boundary depth
Given the increasing SAT anomalies used to force the model (Fig.
In our simulations, the area with intermediate-depth permafrost in the Northern Hemisphere (Fig.
For both scenarios, the decrease of intermediate-depth permafrost area becomes smaller as we increase the depth of the bottom boundary (Figs.
Areal extent of intermediate-depth permafrost at 1901, 2000 and 2300 CE for the RCP4.5 and RCP8.5 scenarios.
The addition of a non-zero heat flux boundary condition at the LSM's bottom boundary has a small effect on intermediate-depth permafrost area (Table
Northern Hemisphere near-surface permafrost area as function of time. Model versions with bottom boundary depth at 3.8 m (magenta), 42.1 m (black), 92.1 m (blue), 192.1 m (red) and 342.1 m (green).
The near-surface permafrost (within the upper 3.8 m) area in the Northern Hemisphere is much less affected by the thickness of the model than the intermediate-depth permafrost (Fig.
Areal extent of near-surface permafrost at 1901, 2000 and 2300 CE for the RCP4.5 and RCP8.5 scenarios.
The effect of the bottom heat flux
Active layer thickness for the unmodified model (top row) and differences to the original model at each time frame for the modified model with 80 mW m
The initial state of the subsurface in 1901 is identical for model versions with different subsurface thickness, provided they use the same bottom heat flux. The temperature of the upper subsurface increases at a slower rate for a deeper bottom boundary; thus, the ALT increases at a slower rate for model versions with deeper subsurface. At the end of the simulations in 2300, the ALT is in some areas larger for the original model (42.1 m) than for the model with thickness increased to 342.1 m and smaller than for the model with thickness of 3.8 m for both scenarios (Fig.
The bottom heat flux increases temperature proportionally to the flux and the depth. Therefore, bottom heat flux does not alter ALT if permafrost is shallow. Where ALT is large, the higher temperature due to the bottom heat flux is enough to induce thawing and lower the upper limit of permafrost (Fig.
Evolution of soil carbon pool in the Northern Hemisphere permafrost region, compared to the size for the original model at 1901 CE. Models with varying bottom boundary depth.
Evolution of soil carbon pool in the Northern Hemisphere permafrost region, compared to the size for the original model at 1901 CE. Models with varying basal heat flux.
Distribution of soil carbon for the original model (top row) and differences to the original model at each time frame for the modified model with 80 mW m
The size of the soil carbon pool increases during the first
Increasing the bottom heat flux
Because the changes in soil carbon due to the modification of model thickness and bottom heat flux are very small relative to the size of the pool, we have calculated the difference in soil carbon between the original model and the modified models with increased thickness
Models with different bottom heat flux
Mean initial size (1901–1910) of the soil carbon pool in the Northern Hemisphere permafrost region, in function of bottom heat flux.
Because the local differences on the soil carbon pool due to the bottom heat flux have different signs, the effect on the whole region is proportionally much smaller and also produces the absence of a consistent trend in the initial size of the soil carbon pool (Fig.
Distribution of vegetation carbon for the original model (top row) and differences to the original model at each time frame for the modified model with 80 mW m
The vegetation carbon in the Northern Hemisphere is also affected by the depth of the bottom boundary. Because rising temperatures allow plants to colonize higher latitudes, the vegetation increases for both RCP scenarios, reaching a stable level between 2100 and 2300. Increasing
While the models with different depth of the bottom boundary
The bottom heat flux also has a small effect in the evolution of vegetation carbon in the Northern Hemisphere for both RCP scenarios. The average vegetation carbon between 2100 and 2300 for the model with 80 mW m
Mean initial size (1901–1910) of the vegetation carbon pool in the Northern Hemisphere permafrost region, in function of bottom heat flux.
The bottom heat flux changes the initial stable size of the vegetation carbon pool in individual cells, which results in a positive change over the North Hemisphere permafrost region (Fig.
Distribution of methane yearly production for the original model (top row) and differences to the original model at each time frame for the modified model with 80 mW m
Methane is produced by methanogenic microbes in the anaerobic fraction of soil. Therefore, it concentrates in areas where the water table rises high enough to reach the carbon-rich soil near the surface, or in inundated areas. The production of methane in natural wetlands is mainly located in the tropical areas, responsible for 64 %–88 % of the global wetland production
In our CLM4.5-BGC simulations, most of the methane production is concentrated in the Northern Hemisphere cold regions, including not only the permafrost region but the areas of seasonal soil freezing as well (Fig.
In the Northern Hemisphere, there are significant differences in the production of methane due to the bottom heat flux and the depth of the bottom boundary. In a few areas, the difference in methane production can be as high as 50 %–80 % with respect to the original model. However, as the sign of these differences can be either positive or negative, the net effect over methane production is small.
The net effect of the subsurface thickness and the bottom heat flux on the global methane production is much smaller than for the localized areas displayed in Fig.
In this paper, we have examined the effects of two simplifications made by most ESMs: not taking the geothermal gradient into account and using an excessively thin subsurface. This paper follows previous estimations
Our results show that deepening the bottom boundary by 300 m increases the heat stored in the subsurface by 72 and 201 ZJ at the end of the simulations at 2300 CE, which corresponds, respectively, to 260 % and 217 % of the heat stored by the original model for the RCP4.5 and RCP8.5 scenarios, respectively. Heat absorption within the soil (upper 3.8 m) is reduced by 1 %–3 % depending on the scenario and the length of the simulation. On the other hand, moving the bottom boundary from 42.1 to 3.8 m increases the heat absorbed by the soil between 1901 and 2000 by 20 %, while the heat absorbed by 2300 only increases by 8 % (RCP4.5) and 3.4 % (RCP8.5), because the heat reflected at the bottom boundary has had time to return to the surface and affect soil temperature. Increasing the bottom heat flux by 20 mW m
Permafrost is affected by the depth of the bottom boundary, in a degree that depends on the depth to which we consider permafrost, in the same manner as the heat absorption by the subsurface. Permafrost near the surface is only slightly affected, but for intermediate-depth permafrost the thickness of the model has a more significant effect. Increasing the thickness of the subsurface from 42.1 to 342.1 m reduces the area loss of intermediate-depth permafrost by a factor of 3 in the RCP4.5 scenario and by a factor of 5.5 in the RCP8.5 scenario (Fig.
Increasing the depth of the bottom boundary leads to less vegetation and more soil carbon in the Northern Hemisphere permafrost region at the end of the simulations, compared to the thinner models. This is to be expected, as the increasing the depth of the subsurface leads to reduced permafrost loss, which opens less area to vegetation and exposes less soil carbon to microbial activity. These effects are small, as the stable vegetation level reached between 2100 and 2300 in the thickest model is only reduced by 0.8 %–1.2 % compared to the original model, while soil carbon is reduced by 1.3 %–3.6 %. On the other hand, a subsurface of 3.8 m overestimates the soil carbon lost by 2300 considerably, by as much as 35 % in the RCP4.5 scenario, although this is reduced to 4.4 % in the RCP8.5 scenario, where the loss of soil carbon is greater.
A higher basal heat flux has a regionally variable effect across the Northern Hemisphere, increasing soil carbon and vegetation where near-surface permafrost is present but decreasing both outside of the permafrost region. The loss of soil carbon in the permafrost region is 4 %–22 % smaller with 80 mW m
In CLM4.5, subsurface biogeochemistry only takes place within the soil, in the upper 3.8 m. For this reason, the small effect of the bottom boundary depth on near-surface permafrost translates into a small effect on the soil carbon and vegetation pools and the methane production. While the same could be expected from the basal heat flux, it has a variable effect across the Northern Hemisphere, especially in the areas where seasonal freezing of the soil occurs, but no soil permafrost is present.
The Community Land Model is based on many simplifying and often erroneous assumptions (uniform soil
thickness, uniform granitic composition of the bedrock, no heat flow, etc.). While CLM4.5 uses a uniform soil thickness value of 3.8 m, natural soil thickness varies notably, with an estimated global mean of
The purpose of the present study is not to build an exact model of the subsurface and calculate its response
to climate forcing. It would be pointless because the subsurface has not been surveyed with sufficient resolution
to construct such a model. The crustal heat flux is not uniform in the continents but its long wavelength variations
across stable continental regions are not very large (
A thicker soil in some areas implies that the effect of the basal heat flux and the bottom boundary depth are bigger than our estimations, made for a soil depth of 3.8 m. While soil carbon pools in the permafrost region concentrate within the upper 3 m, additional reserves exist below 3 m which contain
The methane production in CLM4.5-BGC is dependent on the hydrology model used in CLM4.5, which keeps the water table too low in the tropical regions of the Earth where most (64 %–88 %) wetland methane is produced
The local variability of the results across the Northern Hemisphere permafrost region is difficult to interpret. Increasing the thickness of the subsurface or the crustal heat flux reduces the size of the carbon pools and the production of methane in some areas, but it increases it in others. There is a possible explanation for the local differences in the production of methane: the increase in ALT allows more methane to be produced if there is still a frozen soil layer beneath, because it restricts the seepage of water and allows the active layer to be inundated; however, if the entire soil thaws, the water can percolate to the aquifer and less methane is produced. This might also explain the local differences in the size of the carbon pool, as the differences in the production of methane accumulate over time. The local differences in vegetation carbon are more difficult to interpret, but the dominant trend is that warmer soil (because of a larger crustal heat flux or a thinner subsurface) results in more vegetation carbon in the coldest areas of the permafrost region and less vegetation carbon in the periphery. A tentative explanation is that, while a warmer soil favors the colonization of plants, it may result in less available water in areas where additional heat thaws the soil completely and allows water to percolate to the aquifer and slightly reduce the growth of the vegetation.
The depth of the bottom boundary has a considerable effect on the heat absorbed by the subsurface. We have shown that, in a simulation spanning 400 years, the LSM requires a thickness of at least 200 m to correctly estimate the temperature profile. The thickness
We have determined that each successive increase of ground thickness provides diminishing returns for subsurface heat storage and permafrost and soil carbon stability. Therefore, it is to be expected that the improvement from increasing the thickness of the model from 42.1 to 342.1 m is much smaller than that from increasing it from 3.8 to 42.1 m. This was already investigated by several studies with CLM3, where the thickness of the subsurface was increased from 3.5 m to more than 30 m, which improved the estimates of the permafrost significantly during the 20th century (
Any LSM, before a simulation starts, must be initialized with appropriate initial conditions, i.e., an initial state of the model that is close to the real profile at the time. An appropriate initial condition for the temperature of the subsurface is the steady state determined by the surface temperatures at the start of the simulation. This state can be reached during the length of the spinup from arbitrary initial temperatures if the depth of the bottom boundary is much shallower than the depth determined by the relation
The temperature differences due to insufficient depth of the bottom boundary and lack of basal heat flux are considerable throughout the subsurface. However, they are of little importance for the global heat budget, as the heat absorbed by the continents is less than even the uncertainty on the heat absorbed by the oceans
The area loss of intermediate-depth permafrost (below 42.1 m) in the 1901–2300 period is largely overestimated (3–6 times larger for the RCP4.5 and RCP8.5 scenarios, respectively) for a subsurface of 42.1 m than a subsurface of 342.1 m. Therefore, the inclusion of deep carbon deposits in LSMs will require the use of an appropriate subsurface thickness (
To correctly determine near-surface permafrost in LSMs, the subsurface requires a minimum thickness of 40 m, which avoids bottom boundary effects on the propagation of the seasonal temperature cycle. We suggest the use of a subsurface thickness of 200 m in 400-year simulations (100 m for 100 years) and the use of the crustal heat flux, in order to avoid errors on the order of 1 %–4 %. These changes will be most relevant in centennial simulations of LSMs that include deep carbon deposits.
The modified CLM4.5 software, as well as the instructions for its use in a functional CLM4.5 installation, are available in the Zenodo repository under the DOI
The supplement related to this article is available online at:
IHdM coded the software modifications to the model, conducted the simulations and wrote the main body of the paper. HB and JCM provided continuous feedback, made substantial contributions to the writing of this paper and oversaw the editorial developments. HB, JCM and AHMD provided the theoretical background leading to this project. All authors contributed to suggestions towards the direction of this study and contributed to the interpretations of the results.
The authors declare that they have no conflict of interest.
This work was supported by a Discovery grant from the Natural Sciences and Engineering Research Council of Canada (NSERC DG 140576948) and by the Canada Research Chair Program (CRC 230687) to Hugo Beltrami.
Computational facilities were provided by the Atlantic Computational Excellence Network (ACEnet-Compute Canada) with support from the Canadian Foundation for Innovation. H. Beltrami holds a Canada Research Chair in Climate Dynamics. Ignacio Hermoso was funded by graduate fellowships from a NSERC-CREATE Training Program in Climate Sciences based at St. Francis Xavier University and by additional support from the faculty of sciences at UQAM. Andrew H. MacDougall acknowledges support from the NSERC Discovery grant program.
This research has been supported by the Natural Sciences and Engineering Research Council of Canada (grant no. NSERC DG 140576948) and the Canada Research Chairs (grant no. CRC 230687).
This paper was edited by Didier Roche and reviewed by David Lawrence and two anonymous referees.