# Advances in Permafrost Representation: Biophysical Processes in Earth System Models and the Role of Offline Models

Heidrun Matthes, Adrien Damseaux, Sebastian Westermann, Christian Beer, Aaron Boone, Eleanor Burke, Bertrand Decharme, Hélène Genet, Elchin Jafarov, Moritz Langer, et al.

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## To cite this version:

Heidrun Matthes, Adrien Damseaux, Sebastian Westermann, Christian Beer, Aaron Boone, et al. "Advances in Permafrost Representation: Biophysical Processes in Earth System Models and the Role of Offline Models. Permafrost and Periglacial Processes, 2025, 10.1002/ppp.2269". hal-04974654

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REVIEW ARTICLE

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# Advances in Permafrost Representation: Biophysical Processes in Earth System Models and the Role of Offline Models

Heidrun Matthes¹ | Adrien Damseaux¹,² | Sebastian Westermann³ | Christian Beer⁴ | Aaron Boone⁵ | Eleanor Burke⁶ |
Bertrand Decharme⁵ | Hélène Genet⁷ | Elchin Jafarov⁸ | Moritz Langer¹,⁹ | Frans-Jan Parmentier³ | Philipp Porada⁴ |
Anna Gagne-Landmann¹⁰ | Deborah Huntzinger¹⁰ | Brendan M. Rogers⁸ | Christina Schädel⁸ | Tobias Stacke¹¹ | Jon Wells¹⁰ |
William R. Wieder¹²

¹Climate Sciences, Alfred Wegener Institute Helmholtz Center for Polar and Marine Research, Potsdam, Germany | ²Atmospheric Environmental Research, Karlsruher Institut für Technologie, Garmisch-Partenkirchen, Germany | ³Department of Geosciences, University of Oslo, Oslo, Norway | ⁴Department of Earth System Sciences, Universität Hamburg, Hamburg, Germany | ⁵Centre National de Recherches Météorologiques, Météo-France, CNRS, Université de Toulouse, Toulouse, France | ⁶Met Office Hadley Centre, Exeter, UK | ⁷Institute of Arctic Biology, University of Alaska Fairbanks, Fairbanks, Alaska, USA | ⁸Woodwell Climate Research Center, Falmouth, Massachusetts, USA | ⁹Faculty of Science, Earth and Climate, Vrije Universiteit Amsterdam, Amsterdam, Netherlands | ¹⁰School of Earth and Sustainability, Northern Arizona University, Flagstaff, Arizona, USA | ¹¹Climate Dynamics, Max-Planck-Institut für Meteorologie Hamburg, Hamburg, Germany | ¹²Climate and Global Dynamics, National Center for Atmospheric Research, Boulder, Colorado, USA

**Correspondence:** Heidrun Matthes (heidrun.matthes@awi.de)

**Received:** 16 April 2024 | **Revised:** 6 January 2025 | **Accepted:** 16 January 2025

**Funding:** H.M. was supported by the European Union's Horizon 2020 Program SOCIETAL CHALLENGES (grant agreement no. 869471). T.S. was funded by the European Research Council under the European Union's Horizon 2020 research and innovation program as part of the Q-Arctic project (Grant agreement No. 951288).

**Keywords:** Earth system modeling | permafrost modeling | soil biogeophysical dynamics

## ABSTRACT

Permafrost is undergoing rapid changes due to climate warming, potentially exposing a vast reservoir of carbon to be released to the atmosphere, causing a positive feedback cycle. Despite the importance of this feedback, its specifics remain poorly constrained, because representing permafrost dynamics still poses a significant challenge for Earth System Models (ESMs). This review assesses the current state of permafrost representation in land surface models (LSMs) used in ESMs and offline permafrost models, highlighting both the progress made and the remaining gaps.

We identify several key physical processes crucial for permafrost dynamics, including soil thermal regimes, freeze–thaw cycles, and soil hydrology, which are underrepresented in many models. While some LSMs have advanced significantly in incorporating these processes, others lack fundamental elements such as latent heat of freeze–thaw, deep soil columns, and Arctic vegetation dynamics. Offline permafrost models provide valuable insights, offering detailed process testing and aiding the prioritization of improvements in coupled LSMs.

Our analysis reveals that while significant progress has been made in incorporating permafrost-related processes into coupled LSMs, many small-scale processes crucial for permafrost dynamics remain underrepresented. This is particularly important for capturing the complex interactions between physical and biogeochemical processes required to model permafrost carbon dynamics. We recommend leveraging advancements from offline permafrost models and progressively integrating them into LSMs, while recognizing the computational and technical challenges that may arise in coupled simulations. We highlight the

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importance of enhancing the representation of physical processes, including through improvements in model resolution and complexity, as this is a fundamental precursor to accurately incorporate biogeochemical processes and capture the permafrost carbon feedback.

# 1 | Introduction

Around 11% of the exposed land globally is underlain by permafrost, mostly in areas that face rapid changes in climate due to Arctic Amplification [1, 2]. In the last decade, permafrost temperatures have warmed almost everywhere in the circum-Arctic [3], driving substantial changes in hydrology, landscapes, biogeochemical cycles [4, 5], ecosystems and biodiversity [6], infrastructure [7–9], and general sustainability of living on permafrost [10, 11]. Arctic and subarctic soils harbor a vast reservoir of carbon, estimated to be roughly twice the amount present in Earth’s atmosphere [12–15]. Presently, the majority of this carbon is locked within the permafrost. However, the ongoing effects of global warming are gradually rendering this organic matter susceptible to decomposition. As a consequence, the release of CO₂ and CH₄ emissions exacerbates temperature rises, amplifying the significance of the permafrost carbon feedback as a crucial yet uncertain terrestrial climate factor [16, 17].

The need to understand permafrost distribution as well as permafrost responses to climate change has led to a long tradition of applying numerical models to simulate permafrost extent and active layer depth (ALT). Riseborough et al. [18] supplied an overview over the application and development of spatial permafrost models, mostly stand-alone models on a regional scale, using meteorological conditions such as climate projections for the future as upper boundary conditions. They emphasized the need to incorporate the developments within these models into Global Circulation Models (GCMs). Koven, Riley and Stern [19] provide an overview of the permafrost representation in the Coupled Model Intercomparison Project Phase 5 (CMIP5) ([20]) GCMs and their trajectories for permafrost under climate change, concluding that many models fail to agree with “fundamental aspects of the observed soil thermal regime at high latitudes”.

Since CMIP5, there has been an increasing awareness of the importance of the permafrost carbon feedback in the climate system. Specifically, synthesis and model investigations have suggested that the impact of permafrost thaw on greenhouse gas emissions may impact climate at the global scale (e.g., [5, 16, 17, 21]). Therefore, representing the feedback between permafrost carbon emissions and the climate system [4, 5, 22] and the interaction between permafrost and hydrology [23–25] is crucial.

Land surface representation in Earth system models (ESMs), in general, has advanced significantly over the past decades, from simple schemes producing lower boundary conditions for the atmosphere to complex land surface models (LSMs) [26]. Process representation has evolved from the basic surface energy fluxes to explicit consideration of dynamic vegetation, carbon cycling, crops, or urban areas and, very recently, even considering lateral interaction between grid cells and between landscape units [27].

In concurrence with these model improvements, various gaps have been identified that need to be addressed to make LSMs in ESMs more reliable in representing permafrost processes and their impacts and feedback on the global climate system.

The Intergovernmental Panel on Climate Change (IPCC) states that for the next assessment report, in relation to biogeochemical feedback and permafrost, we need an improved “understanding and representation in Earth system models of changes in land carbon storage and associated carbon-climate feedbacks including: better treatment of the CO₂ fertilization, nutrient-limitations, soil organic matter (SOM) stabilization and turnover; land-use change; large-scale and fine-scale permafrost carbon; plant growth, mortality, and competition dynamics; plant hydraulics; and disturbance processes.” [28]. Blyth et al. [26] state that for permafrost representation in land surface modeling, the current challenges are (1) regional pedotransfer functions, (2) soil properties changing over time, (3) topography changes over time, and (4) representations of subgrid heterogeneity (e.g., soil tiling to explicitly model peat soils, variations in maximum infiltration, soil textures, and irrigation). Schädel et al. [22] emphasize that “Earth system models must include permafrost carbon processes,” identifying process representations required to model permafrost carbon dynamics. They emphasize existing poor representation of lateral fluxes, snow distribution and insulation, wetland and lake distribution, and subgrid-scale heterogeneity in LSMs.

Despite the strong consensus on the important impacts of permafrost on the global climate system under climate change projections, not all models in the Coupled Model Intercomparison Project Phase 6 (CMIP6) ([29])—the latest CMIP, which informed the 6th IPCC assessment report [30]—utilize land surface schemes appropriately set up to represent permafrost dynamics. A number of studies have used the CMIP6 models to assess their capabilities in representing permafrost dynamics. Burke, Zhang, and Krinner [31] provided an extensive analysis of 18 CMIP6 models in their ability to capture present-day permafrost-related variables in terms of permafrost extent, mean annual near-surface temperature, and ALT. Two-thirds of the models analyzed accurately simulated permafrost extent within 15% of the observed range, compared to four-fifths of the models assessed in Chadburn et al. [32] for CMIP5. However, the multimodel ensemble mean from CMIP6 exhibits a smaller bias than the multimodel CMIP5 mean. Less than half of the analyzed CMIP6 models simulated ALT within the observed range, with a slight improvement over the CMIP5 models, but ALT representation of the multimodel ensemble mean between CMIP5 and CMIP6 remained the same.

Andresen et al. [23] compared eight LSMs participating in the Permafrost Carbon Network Model Intercomparison Project (PCN-MIP) ([4]) with respect to soil hydrology in the Arctic. Even though these LSMs were often used in more advanced
setups than for coupled simulations within ESMs, the study
found that while most models captured the long-term timing of
surface runoff from the major river basins in the northern per-
mafrost region, the magnitude was underestimated. The IPCC
itself states that from the 11 models analyzed for carbon–con-
centration and carbon–climate feedbacks within the 1pctCO2
simulations from the Coupled Climate-Carbon Cycle Model
Intercomparison Project (C⁴MIP) framework [33], only two rep-
resented permafrost carbon [28].

These previous studies focus on identifying and discussing the
strengths and deficiencies of the models with respect to perma-
frost dynamics, mostly without explicitly discussing process rep-
resentation in the models. Our review starts with presenting the
physical processes that are considered important for represent-
ing permafrost dynamics in LSMs in terms of soil physics, snow-
soil interactions, and snow-vegetation-soil interactions, since
thermal and hydrological dynamics govern permafrost thaw
and are required precursors for subsequent release of green-
house gases. We leave an extensive discussion of biogeochemical
processes to Gagné-Landmann et al. [34], which focuses on bio-
geochemical and biogeophysical permafrost related process rep-
resentation in models with respect to permafrost carbon. This
description of relevant processes is followed by describing exist-
ing implementations and parameterizations of these processes
in the global LSMs used in ESMs from the CMIP6 ScenarioMIP
contributions. Finally, we assess the ongoing progress in LSM
developments towards integrating processes considered im-
portant for representing permafrost dynamics, including future
directions in this field that are informed by advancement of
standalone permafrost models, that is, those models that are not
interactively coupled to an atmosphere. We aim to identify possi-
ble synergies and assess if the developments in stand-alone mod-
els could be used to stimulate advancements in LSMs in ESMs.

## 2 | Key Biophysical Processes for Permafrost Modeling in LSMs

The representation of permafrost dynamics depends on the soil
processes and soil-snow-vegetation interactions considered in
a given model. Commonly considered soil processes are vert-
tical transport of heat and water in multilayer soil columns of
often several meters in depth, including important processes for
permafrost like latent heat exchange from freezing and melt-
ing ground ice, and organic matter content in the soil column.
Models focused on hydrology often also consider lateral heat
transport associated with lateral water flow. The exchange of
water and heat with the atmosphere at the top of the soil is con-
sidered via surface characteristics and processes representing
snow, vegetation, surface water, and meteorology.

2.1 | Soil Heat Conductivity

Due to its strong influence on soil thermodynamics, soil thermal
conductivity is considered one of the most important physical
parameters in land modeling studies [24, 35-37]. Incorporating
the dependency of soil thermal conductivity on the presence of
liquid water and ice is especially important in permafrost soils
[38], which also points to the importance of representing soil

water content correctly. Gao and Coon [39] show that neglect-
ing the redistribution of water in partially frozen, unsaturated
soils caused by increased matric suction (cryosuction) in model
experiments with the Advanced Terrestrial Simulator (ATS v1.2)
resulted in 10%-30% errors in thaw depth and 10%-30% errors in
1 m soil temperature. A detailed description of the soil thermal
conductivity schemes for mineral soils used in the LSMs partici-
pating in CMIP6 can be found in Dai et al. [35] and He et al. [36].
He et al. [36] conclude from their comparisons with measure-
ments of frozen soil thermal conductivity that there are clear
differences in performance between the different schemes ana-
lyzed and that no scheme performs particularly well, suggesting
that new approaches developed specifically for frozen soils may
be needed [40]. In addition, two key requirements related to the
structure of the model soil columns have been identified from
previous studies. First, Lawrence et al. [41] emphasized the need
for high vertical resolution within the top 3 m of the soil column
to improve the representation of freezing and thawing front dy-
namics and ALT. Secondly, Alexeev et al. [42] demonstrated that
the soil column should extend to a minimum depth of 30 m to
properly resolve the seasonal cycle in temperature. A geother-
mal steady heat flow at depths greater than 40 m as the lower
boundary condition was found acceptable to simulate long-term
permafrost changes [43].

Inclusion of an upper organic layer is important and improves
estimates of ALT and keeps permafrost cooler in models [44, 45].
Soil organic matter (SOM) exhibits distinct hydraulic and ther-
mal properties when compared to mineral soils, augmenting
available water capacity [46] and influencing soil porosity and
saturated hydraulic conductivity [47-49]. These differences re-
sult in significantly reduced soil thermal conductivity, while
concurrently elevating soil heat capacity in comparison to min-
eral soils, ultimately manifesting as lower temperatures during
the summer months. This phenomenon has been studied over
Arctic permafrost regions [48, 50-54]. At the same time, SOM
increases soil field capacity and therefore soil water content
after rainfall or snowmelt, and both thermal conductivity and
heat capacity increase under wet conditions. This leads to an el-
evated heat conduction in particular in spring.

2.2 | Snow

Snow exerts a strong control over the surface energy balance
that influences the soil thermal regime [55]. Snow thermal
conductivity plays a pivotal role in determining the rate of
heat transfer to the underlying soil, which is arguably the most
crucial model parameter within snow physics [24] and one of
the largest sources of uncertainty in LSMs with respect to soil
temperature simulation [56]. The use of too simplistic a snow
scheme can lead to an incorrect assessment of permafrost ex-
tent, and even affect the biogeochemistry [57]. Commonly,
LSMs parameterize snow thermal conductivity as a function
of simulated snow density or snow temperature [58]. However,
the representation of snow density profiles common to tun-
dra environments (shallow snow pack, high-density wind-slab
top layer, and low-density hoar frost-dominated lowest layer)
is challenging even for sophisticated snow models [54, 59],
which introduces large uncertainties into the determination
of snow thermal conductivity from snow densities. These
dynamics also play out seasonally. For example, an increasing
depth of snow with low density in autumn counteracts the in-
creasing heat loss into the atmosphere, which is one important
factor for the pronounced zero curtain period in autumn. By
comparison, snow dynamics are reversed in spring, where a
longer snow cover cools permafrost. In addition, snow depth
variability due to extreme temperature events in autumn can
substantially reduce the insulation strength of snow, hence
cooling the soil [60]. Finally, accurately simulating snow ther-
mal properties under climate change scenarios becomes even
more challenging. Projected increases in rain-on-snow events
[61, 62] may have substantial consequences on soil thermal
dynamics during winter, resulting from rain water infiltration
through the snow layer [63].

2.3 | Vegetation

Beyond soils and snow, vegetation exerts control over the sur-
face energy balance [64]. For permafrost ecosystems, the com-
position and thickness of mosses strongly reduce soil heat flux
in summer [65] and may substantially decrease average soil
temperature due to insulation of the surface layer in the sum-
mer months [66, 67] while heat conductivity can be increased
by wet mosses and lichens [60]. Certain lichen species have
a high albedo [64] and may lead to surface cooling in open
canopy ecosystems [68], while shrub canopies can influence
local microclimate by shading the ground in summer [69].
Tall vegetation also captures more snow in winter [70], and
ecosystems with tall shrubs and trees have warmer soil tem-
peratures than those with short-statured tundra vegetation
[71]. This suggests that the ongoing greening and shrubifica-
tion of the Arctic may lead to a thickening of the active layer
(e.g., [72, 73]). Simultaneously, taller vegetation like shrubs,
which do not get buried by snow completely, change the land
surface-atmosphere energy exchange. They may lead to lower
albedo in spring and autumn [74, 75]. Shrubs buried in snow
are typically taken to have a warming effect on permafrost by
decreasing the overall conductivity of the snowpack [76, 77],
but recent results suggest that low shrubs can actually cool
the ground in winter by providing a thermal bridge through
the snowpack [78]. Representing a shrub vegetation type is es-
sential for LSMs to be able to capture these dynamics, as well
as an adequate representation of vegetation buried in snow. In
boreal forests, Abe et al. [79] suggest from a modeling study
that changes in LAI lead to changes in canopy interception of
snow, affecting the snow-albedo feedback. An accurate simu-
lation of vegetation-permafrost interactions is, therefore, not
only necessary to model the exchange of carbon with the at-
mosphere but also to project the present and future physical
state of permafrost.

## 2.4 | Wetlands

Wetlands, with their organic-rich soils and water-saturated
conditions, play a crucial role in shaping permafrost dynamics.
These environments act as insulators to the underlying perma-
frost, slowing the rate of thawing. However, changes in wetland
water balance due to climate warming can lead to the forma-
tion or disappearance of permafrost beneath these areas. The

hydrology of permafrost wetlands is complex and sensitive to
climate change, as the presence of ice affects water movement
and can lead to the formation of unique landforms such as po-
lygonal tundra, as well as wetland-associated dry permafrost
landforms such as palsas and peat plateaus. Open water bodies,
including lakes, ponds, and rivers, also significantly influence
permafrost conditions. These water bodies store heat and freeze
slowly due to latent heat effects, leading to the development of
taliks—unfrozen ground in permafrost areas—beneath them.
This process accelerates permafrost thawing and complicates
the thermal stability of permafrost. Moreover, open water bodies
alter groundwater flow paths and dynamics, influencing surface
water thermal regimes and stream temperatures, which are cru-
cial for understanding the broader impacts of permafrost thaw
on Arctic ecosystems. Incorporating wetlands and open water
bodies into permafrost models is essential for realistic simula-
tions of permafrost dynamics under current and future climate
scenarios. Detailed data on water body distribution, size, and
seasonal dynamics are necessary for accurate representation
within models.

2.5 | Nongradual Thaw Processes

In addition to the gradual thaw of permafrost driven by a warming climate, abrupt thaw plays an important role for permafrost thaw-related CO₂ emissions [80]. Abrupt thaw is associated with disturbances on often small spatial scales, related to processes like permafrost-fire interactions, belowground combustion and melt of excess ground ice, subsequent subsidence, and thermokarst formation in ice-rich permafrost, as well as changes in snow cover and hydrology [81]. Moreover, nongradual disturbance processes, which largely control the rate of permafrost degradation, take place at spatial scales of a few to hundreds of meters (e.g., [82]). Among these disturbance processes, wildfires are included in some LSMs that have the capability to employ dynamic vegetation [83]; however, fires only affect vegetation, and there is no direct permafrost-fire interaction, while other listed forms of disturbance remain poorly represented [22]. In addition, in order to realistically represent the effects of disturbances like fire on vegetation structure and dynamics and associated effects on permafrost, different trajectories of plant functional type (PFT) developments are required where patches (or cohorts) are defined based on the time since a disturbance [84], a capacity only few LSMs have.

2.6 | Factors Beyond Process Representation

Besides process representation, horizontal resolution is an im-
portant feature for capturing the very high landscape heteroge-
neity of permafrost areas. Even ESMs using sophisticated LSMs
in their framework are still relatively coarse in their horizontal
resolution, with the median resolution of atmosphere and land
in CMIP6 being ~140 km (ranging from 75 to 250 km, [30]).
Many models attempt to address this problem by using tiling
approaches to represent landscape heterogeneity, allowing for
grid cell fractions of different vegetation types (primary and
secondary natural vegetation, crops, etc.), lakes, glaciers, wet-
lands, and recently, hillslope categories [85]. However, these ap-
proaches cannot overcome the lack of high-resolution input data
for critical drivers of soil thermal regimes (e.g., soil texture map, ice content, and organic layer thickness). Furthermore, model results are dependent on parameter choices in their process representations (e.g., [86, 87]), suggesting that careful attention to parameter choices is critical to improving model accuracy and reliability.

Collectively, these challenges related to soils, snow, vegetation, disturbance, and horizontal resolution underscore the challenges of adequately simulating physical permafrost dynamics in models that are used for climate change projections.

# 3 | Where Do the LSMs of the CMIP6 ESMs Stand?

In our following analysis, we focus on models that have a maximum soil depth exceeding 3 m (center depth of the lowest soil layer; see comment on soil column requirements above) and accessible documentation of the representation of soil physics. We give an overview of the important physical processes in permafrost representation discussed in the previous section for the models we consider and how their approaches have been discussed in the literature. Note that contribution to CMIP6 has been an ongoing effort, many contributions occurred after the deadline for inclusion in the IPCC AR6, and many models have provided simulations with updated coupled ESMs since. This study did not track the submission dates of models to the CMIP6 archive; rather, we describe the state of model development of the current list of CMIP6 contributions to both CMIP and ScenarioMIP ([88], accessed 12 January 2024), which might yield different assessments of models compared to other studies. We restrict our analysis to the most up-to-date versions of LSMs used in the CMIP6 ESM simulations. We acknowledge the capability of LSMs to be run with different levels of complexity, for example, in the employment of deep soil columns, dynamic vegetation, and terrestrial carbon cycling. We describe the setup that was actually used in CMIP6 ScenarioMIP, in the knowledge that these settings are not necessarily employed in all model intercomparison projects and do not necessarily reflect the full capability of the LSMs with regard to processes relevant for permafrost dynamics.

Within CMIP6, 49 institutions submitted simulations from 133 models (including different model versions), 64 of which contributed to ScenarioMIP, which is focused on future projections of the Earth system under different shared socioeconomic pathways (see Table S1; [88]). These models employ 18 different LSMs (where we counted different development versions of the same LSM as one LSM for simplicity), among which we identified eight models that do not fulfill the criteria: CABLE (too shallow, center depth of lowest layer 2.9 m), BCC-AVIM2 (too shallow, 2.9 m), CLASS/CTEM (too shallow, 2.3 m), HTESSEL and HTESSEL/LPJ-GUESS (too shallow when used in the coupled setting within the EC-Earth framework, 1.95 m), GISS LSM (too shallow, 2.7 m), JULES (too shallow, 2 m), HAL 1.0 (inadequate documentation), NOAH-MP (too shallow in its standard configuration, 2 m), and INMLND1 (inadequate documentation). The ESM MCM-UA-1-0 gives the “standard Manabe bucket hydrology scheme” as a sole description of its land component and was also excluded

from further analysis. Table 1 provides an overview of these LSMs and the CMIP6 models they are used in.

Figure 1 provides an overview of the column structure of the LSMs analyzed in our study, demonstrating the different approaches with a group of models with relatively shallow columns (ISBA, GFDL-LM4, MATSIRO, and JSBACH) and a group with deep soil columns considered most suitable for long-term climate simulations (CLM5, CoLM, ELM, and ORCHIDEE), whereas Table 2 summarizes the differences in soil physics among those models, focusing on column depth and discretization, heat capacity and soil thermal conductivity, and inclusion of organic matter.

## 3.1 | Soil Heat Conduction

Models discussed here represent heat transport in soil with the 1D heat flow equation, including latent heat as a sink or source (with the exception of JSBACH and MATSIRO6.0), and none of the models incorporate lateral heat flow. The key differences lie in how they estimate soil heat capacity and soil thermal conductivity. Most models use a soil heat capacity scheme derived from de Vries [109] or altered after this scheme. Only GFDL-LM4 adopts a fixed soil heat capacity dependent on soil type, which may adversely impact soil temperature representation. Soil thermal conductivity parameterization schemes are employed globally, for desert, rainforest, or permafrost soils alike. While models account for freezing of the soil when calculating soil thermal conductivity, a comprehensive comparison by He et al. [36] demonstrated that all of the analyzed 39 approaches to calculate soil thermal conductivity in frozen soils performed inadequately, which suggests that new parameterizations are needed.

SOM is considered in most models, following different schemes, for example, a linear weighted combination of organic soil properties with standard mineral soil properties as suggested by Lawrence and Slater [47], sometimes with added complexity. ISBA incorporates a pedotransfer function linking soil water retention at various pressure levels to the fiber content of organic soils [48]. ISBA calculates soil thermal conductivities as geometric averages of organic and mineral soils. JSBACH does not explicitly represent SOM, alternatively representing a moss and/or lichen layer at the surface, which possesses dynamic moisture contents and thermal properties, thus serving as a physical representation of the surface organic layer [32, 66]. MATSIRO6.0 adopts a similar approach by incorporating a top organic layer [112]. There is no extensive comparison of the performance of these different schemes, but the summer offset calculated by Burke, Zhang, and Krinner [31] suggests that they are widely different in their effects.

The majority of models solve water mass transfer by using Darcy's law and soil moisture dynamics by using the Richards equations in a multilayered representation of the soil column. There are two commonly used models to calculate the relationship between volumetric water content and soil hydraulic conductivity, as well as soil matric potential: one by Brooks and Corey [116] and the other by Van Genuchten [117]. Note again that these schemes are employed globally and were not specifically developed for permafrost soils.
<table><caption>**TABLE 1** | CMIP6 models and their respective LSMs. LSMs discussed further are marked in bold.</caption><thead><tr><th>Land surface models (previous versions)</th><th>Earth system model(s)</th><th>Reference paper (LSM)</th></tr></thead><tbody><tr><td>CTSM/CLM5 (CLM4.5, CLM4)</td><td>CESM2, CESM2-FV22, CESM2-WACCM, CIESM, CMCC-CM2-SR5, CMCC-ESM 2, FGOALS-g3, FIO-ESM-2-0, KIOST-ESM, NorESM2-LM, NorESM2-MM, SAM0-UNICON, TaiESM1</td><td>Lawrence et al. [41]</td></tr><tr><td>ISBA/SURFEX 8.0c</td><td>CNRM-CM6-1, CNRM-ESM 2-1</td><td>Decharme et al. [89]</td></tr><tr><td>ELMv1.1 (v1.0)</td><td>E3SM-1-0, E3SM-1-1, E3SM-1-1-ECA, E3SM-2-0</td><td>Golaz et al. [90]</td></tr><tr><td>GFDL-LM4.1 (LM4)</td><td>GFDL-CM4, GFDL-ESM 4</td><td>Zhao et al. [91], Shevliakova et al. [92]</td></tr><tr><td>ORCHIDEE-MICT v8.4.1</td><td>IPSL-CM6A</td><td>Guimberteau et al. [93]</td></tr><tr><td>JSBACH3.20 (v3.1)</td><td>MPI-ESM 1-2, AWI-CM-1-1, AWI-ESM-1, NESM3</td><td>Reick et al. [94]</td></tr><tr><td>MATSIRO6.0</td><td>MIROC6</td><td>Yokohata et al. [95]</td></tr><tr><td>CoLM</td><td>CAMS-CSM1-0, CAS-ESM 2.0</td><td>Dai et al. [96], Li et al. [97]</td></tr><tr><td>CLASS3.6/CTEM1.2</td><td>CanESM5</td><td>Swart et al. [98]</td></tr><tr><td>JULES-ES-1.0</td><td>UKESM-1-LL</td><td>Mathison et al. [99]</td></tr><tr><td>JULES-HadGEM3-GL7.1</td><td>HadGEM3-GC31-MM, HadGEM3-GC31-LL, KACE-1-0-G</td><td>Wiltshire et al. [100]</td></tr><tr><td>ICON-Land</td><td>ICON-ESM</td><td>Schneck et al. [101]</td></tr><tr><td>NOAH-MP</td><td>IITM-ESM</td><td>He et al. [102]</td></tr></tbody></table>

(Continues)

<table><caption>**TABLE 1** | (Continued)</caption><thead><tr><th>Land surface models (previous versions)</th><th>Earth system model(s)</th><th>Reference paper (LSM)</th></tr></thead><tbody><tr><td>CABLE2.5 (2.4)</td><td>ACCESS-CM2, ACCESS-ESM 1-5</td><td>Haverd et al. [103]</td></tr><tr><td>BCC-AVIM2 (AVIM1)</td><td>BCC-CSM2-MR</td><td>Wu et al. [104]</td></tr><tr><td>HTESSEL/ LPJ-GUESS</td><td>EC-Earth3-CC, EC-Earth-Veg</td><td>Smith et al. [105]</td></tr><tr><td>GISS LSM</td><td>GISS-E2-1-G, GISS-E2-2-G, GISS-E3-G</td><td>Kelley et al. [106]</td></tr><tr><td>HAL 1.0</td><td>MRI-ESM 2-0</td><td>Yukimoto et al. [107]</td></tr><tr><td>INM-LND1</td><td>INM-CM4-8, INM-CM5-0</td><td>Volodin et al. [108]</td></tr></tbody></table>

## 3.2 | Snow

Snow cover significantly impacts the thermal regime of the soil, but its insulating properties are highly variable and insufficiently detailed in ESMs [59, 118]. All LSMs discussed here employ multilayer snow, with some models allowing for a dynamic number of snow layers. An overview of the snow representation within the LSMs can be found in Table S2. Four models parameterize fresh snow density depending on variables like wind speed and temperature. Three models employ fixed snow densities, while the other schemes allow dynamic snow densities, considering processes like compaction due to overburden pressure, destructive metamorphism, and melt metamorphism. Constructive metamorphism [58], related to temperature gradients and the formation of depth hoar, is not included in any of the snow models studied here or in most state-of-the-art snowpack models [119]. Studies show that neglecting the role of depth hoar in providing thermal insulation properties to Arctic snow packs can have significant consequences for soil temperature [118–120], leading to distinct negative biases in winter time soil temperatures. The association of snow density to snow thermal conductivity is fixed for three of the models, while different schemes are used elsewhere (see Table S2). While many models consider the effects of percolating and refreezing melt water, other meteorological events like rain on snow are not well represented, even though they have been shown to impact permafrost temperatures [62].

## 3.3 | Vegetation

All models except GFDL-LM4.1 adopt a dynamical global vegetation model (DGVM) approach—as opposed to individual-based statistical and demographic—that relies on PFTs to represent different plant characteristics, where “dynamical” indicates that leaf area index is a prognostic variable. This approach uses
fractional PFT coverage, which allows for a mixture of PFTs within a single grid point, which is critical for capturing vegetation heterogeneity. In contrast, GFDL-LM4.1 uses a cohort-based approach in its vegetation model, representing ecosystem demography and allowing explicit representation of light competition between PFTs as well as disturbance. Actual vegetation dynamics in terms of changes of PFT distributions with time are included in JSBACH, CoLM, and GFDL-LM4.1. Table S3 presents the variations in PFT utilized by each model for grid points designated as vegetated. Regarding PFTs associated with arctic vegetation used by the models, only five LSMs employ similar Arctic-based PFTs: CLM5, CoLM, ISBA, ELMv0, and JSBACH account for Arctic vegetation through C3 grass and boreal forest PFTs. JSBACH uses a “tundra” PFT, which bears similarities to C3 grass but with a reduced maximum rate of carboxylation in leaves [32]. However, the tundra biome is much more diverse than C3 grass alone, containing a wide variety of shrubs, sedges, mosses, and lichens. Recent work by Sulman et al. [121] and Curasi et al. [122] emphasizes that the addition of new PFTs to represent northern vegetation enhances the ability of LSMs in

simulating the carbon cycle over the Arctic region. Rogers et al. [123] point out that implementing trait values observed from Arctic plants is crucial to an accurate representation of photosynthesis in Arctic PFTs implemented in models. Snow vegetation interaction discussed in relevance for permafrost mainly focuses on changes in snow thermal conductivity considering different vegetation buried in snow as well as different snowpack properties associated with vegetation (boreal forest and shrubs) [124]. To be able to consider these processes, LSMs need to represent shrubs as PFTs (see Table S3) as well as employ dynamic snow thermal conductivity schemes (see Table S2). From the models containing both capabilities, only SURFEX employing CROCUS has the capability to consider shrub-snow interactions by modifying snow compaction depending on the vegetation type [125].

## 3.4 | Wetlands

While the representation of wetlands in LSMs differs considerably among models, most models employ dynamic wetland

<figure><img src="image_3.png" /><figcaption>**FIGURE 1** | Overview of column structures in LSMs of CMIP6 models fulfilling the selection criteria. [Colour figure can be viewed at wileyonlinelibrary.com]</figcaption></figure>
<table><caption>TABLE 2 | Soil physical characteristics of land surface models.</caption><thead><tr><th>LSM</th><th>Max no layers (max depth)</th><th>Latent heat included</th><th>Soil heat capacity scheme</th><th>Soil thermal conductivity scheme</th><th>Organic carbon included</th><th>Soil hydrology parametrization</th></tr></thead><tbody><tr><td>CLM5</td><td>20 soil + 5 bedrock layers (50 m)</td><td>Yes</td><td>de Vries [109]</td><td>Lawrence and Slater [47]</td><td>Yes</td><td>Richards equations (BC model)</td></tr><tr><td>SURFEX</td><td>14 soil layers (12 m)</td><td>Yes</td><td>de Vries [109]</td><td>Peters-Lidard et al. [110]</td><td>Yes</td><td>Mixed form of Richards equation (BC or VG model)</td></tr><tr><td>ELMv0</td><td>15 soil layers (42.1 m)</td><td>Yes</td><td>de Vries [109]</td><td>Lawrence and Slater [47]</td><td>Yes</td><td>Richards equations (BC model)</td></tr><tr><td>GFDL-LM4.1</td><td>20 soil layers (10 m)</td><td>Yes</td><td>Fixed, depending on soil type</td><td>Fixed depending on soil type</td><td>Yes</td><td>Continuous vertical representation of soil water including water table depth</td></tr><tr><td>ORCHIDEE</td><td>32 soil layers (87 m) — soil hydrology only in 11 layers (2 m)</td><td>No</td><td>de Vries [109]</td><td>Wang, Cheruy, and Dufresne [111]</td><td>Yes</td><td>Richards equations (VG model)</td></tr><tr><td>MATSIRO6.0</td><td>6 soil layers (14 m)</td><td>No</td><td>Saito [112]</td><td>Sass, Lachenbruch, and Munroe [113]</td><td>Yes</td><td>Richards equations (BC model)</td></tr><tr><td>CoLM</td><td>15 soil layers (44 m)</td><td>Yes</td><td>de Vries [109]</td><td>Farouki [114]</td><td>Yes</td><td>Richards equations (BC model)</td></tr><tr><td>JSBACH</td><td>5 (7) soil layers (10 m (30.1 m))</td><td>No</td><td>de Vries [109]</td><td>Johansen [115]</td><td>Yes</td><td>Richards equations (VG model)</td></tr></tbody></table>
schemes. Wetland extent is determined using water table depth or saturated soil in combination with soil properties (CLM5, Lawrence et al. [41]) or subgrid-scale orography parameters (ORCHIDEE, Ringeval et al. [126]). MATSIRO employs predetermined wetland areas for the high latitudes [127], SURFEX also uses a fixed wetland map that is represented as a landcover type [128], and wetlands in CoLM are also based on a fixed wetland map. GFDL LM4.1 and JSBACH3.2 have no explicit wetland representation. The wetland schemes in all models do not represent ice wedges or other forms of excess ice or talik formation associated with open water bodies.

## 4 | What Processes/Parameterizations Are LSMs Coupled to ESMs Working on?

Various LSMs discussed above have worked on improvements in the representation of physical processes that impact permafrost since their CMIP6 simulations were completed. The following section summarizes model developments regarding processes relevant to permafrost dynamics. To assess these developments, we conducted a literature review focused on publications that referred to model versions that extended the CMIP6 contributions of the coupled ESMs. We acknowledge that this section can only give an overview of potential model developments going towards the next phase of ESM simulations for CMIP7, since not all of the LSM developments might be incorporated into the coupled frameworks of their parent ESMs. Furthermore, the conclusions drawn from offline simulations of LSMs in terms of model performance for specific process representations are in their direct implications restricted to these offline simulations. Implementing the same changes in coupled ESM simulations might yield different performance results, for example, because of the LSM's sensitivity to meteorological forcing (see, for example, Hardouin et al. [129]).

The Community Land Model 6 (CLM6) has integrated a subgrid-scale hillslope hydrology scheme [73], improved their snow albedo model [130], and included means to change the parameterization used for snow thermal conductivity (following findings in [119]). New surface datasets will provide updates to soil properties, including organic matter contents that are used in global simulations. Ongoing parameter calibration activities are aimed at increasing vegetation survival in permafrost regions, relative to previous versions of the model [131].

CLASS/CTEM already contains representation of latent heat of freeze and thaw and organic matter in the soil column, one snow layer considering snow densification by compaction and refreezing, dynamical vegetation, and a dynamical wetland representation based on soil water content and subgrid-scale orography (Swart et al. [98], Verseghy [132], Verseghy [133], Arora, Melton, and Plummer [134]). CLASSIC1.0 [135] is the successor of CLASS/CTEM and has implemented a wide array of improvements concerning permafrost processes [136], for example, a much deeper soil column (61.4m), a more complex snow aging, shrubs [137], and nitrogen cycling [138]. Furthermore, CLASSIC1.0 has been expanded to contain PFTs representative of the Canadian Arctic [122] and is indicated to improve the simulation of permafrost carbon dynamics by replacing its bulk soil

carbon pool with an explicit tracking of soil carbon per soil layer ([135]).

ICON-ESM V1.0 [139], which comprises a part of the JSBACH model (JSBACH v 4.3, [101]) now called ICON-LAND, was represented only in the historical simulations in CMIP6 and, therefore, not discussed above. It includes moisture phase transitions, the representation of supercooled water, and an improved snow scheme [140]. Updates to the computation of soil thermal properties were made considering the amount of water, ice, and organic content within the soil. The current ICON release (2024.07) contains further enhancements to the soil hydrology scheme, including vertical variations in organic matter content that dynamically affect thermal and hydrological soil properties. The presence of ice modulates the vertical soil water transport, and the root zone is confined to the depth of the active layer, leading to a more plausible representation of plant water stress in the boreal regions.

Advancements in ORCHIDEE now enable the incorporation of processes related to the generation, movement, and emission of dissolved organic carbon (DOC) from permafrost soils in high-latitude regions to inland waters and the ocean [141]. A representation of hillslope hydrology [142] has been implemented, albeit in a version where permafrost was turned off. The peatland representation [143] was extended to allow the computation of methane emissions from northern peatlands, tested in single-site simulations [144].

For GFDL-LM4.1, a new snow scheme has been developed [145], which has a dynamical vertical snow structure, accounting for the temporal development of snow grain size and shape. This new scheme has impacts on bulk snow properties such as depth, thermal conductivity, and optical characteristics. Comparisons with previous versions of the GFDL snow model reveal the improved scheme enhances predictions of seasonal snow water equivalent and soil temperature beneath the snowpack.

LPJ-GUESS has recently been extended to contain a standard 3m, nine-layer soil column in its setup within the EC-Earth model [146]. The representation of soil physical processes was also modified in general, and soil heat transport is now calculated by solving the heat diffusion equation, while soil water transport is solved by applying Richards' equation. LPJ-GUESS can now also be run with a multilayer snow model [57].

JULES has been enabled to represent subgrid-scale microtopography highly prevalent in the permafrost landscapes through a tiling approach [147]. There is also work towards enabling soil heterogeneity at the subgrid-scale level [148]. Offline versions of JULES have been run with deeper soil layers, a representation of organic soil properties, and an additional thermal column at the base of the soil profile to represent bedrock [149]. An interactive nitrogen cycle has been included, showing the impact of thawing permafrost fertilizing the vegetation [150].

CoLM includes carbon-nitrogen interactions, supercooled liquid water in the soil column, and a multilayer soil organic carbon (OC) scheme for cryoturbation and bioturbation allowing soil carbon generated at the top of the soil column to propagate downwards [151].
# 5 | Where Do the Offline Models Stand and What Are Potential Synergies in Developments?

Offline permafrost models are not part of a coupled Earth System modeling framework. They are generally forced by near-surface meteorological variables, for example, air temperature, precipitation, and relative humidity, which can be obtained from measurements, historical climate datasets, or atmospheric model projections. These forcing data are static and not influenced by the state of the land surface. While this may introduce inconsistencies, offline models offer distinct advantages in many applications.

Offline permafrost models are free of the operational burdens of a comprehensive ESM which offers developers more freedom and allows for rapid innovation cycles. A simpler regional or local application reduces restrictions on horizontal resolution. Forcing models with observed meteorological data, as opposed to the modeled climate in a coupled ESM, removes potential biases in the atmospheric model and interactive feedback between components of the coupled systems that may accentuate these biases. The same development cycles can be employed in LSMs that are components of ESMs, when the models are used in an “offline” configuration outside of the coupled ESM.

There are a large number of offline permafrost models, developed with different purposes in mind. Equilibrium models are widely used to determine permafrost maps, for example, CryoGrid1 for Scandinavia [152] or GÍPL1 for Alaska [153]. For assessments of climate change on permafrost extent and active layer development, spatial numerical models solving the surface energy balance like CryoGrid3 (e. g., [154]), GÍPL2 (e. g., [155]), the CoupModel (e. g., [156]), or GEOtop2.0 (e. g., [157]) have been applied. Cold-region hydrological models with a focus on permafrost-associated hydrological changes have been used equally widely, including WASIM [158], TopoFlow [159], SUTRA-ICE [160], permaFoam [161], PFLOTRAN-Ice [162], and Amanzi-ATS [163, 164]; see Bui, Lu, and Nie [165] for an overview. Some of these models (PFLOTRAN, SUTRA, and ATS) are high-fidelity models that were developed to study small watershed-type regions. On the large grid cells commonly used in ESMs, their representation of hydrological processes would largely be on the subgrid-scale level. To run these models on larger regions (Alaska, Norway, etc.) would be impractical and impossible due to massive computational demand.

The flexibility of offline models facilitates fast development cycles and allows for the exploration of new parameterizations and enhanced model components. An example is the subsurface grid structure and maximum depth which is generally fixed in coupled models due to computational constraints, while it can be selected completely free in most offline models (e.g., [166]). As a result, ground thermal properties can be calibrated for different ecosystems and upscaled using local or regional landcover maps and data assimilation from site-level field observations [167]. Similar to some LSMs in coupled frameworks, offline models can also represent the physical properties of multiple organic horizons and represent the dynamic of organic layer thickness resulting from litterfall and decomposition, disturbances such as wildfire, or vegetation succession. Thus, these models can directly represent the impact of the organic layer composition

and dynamic on permafrost vulnerability to thaw in response to wildfire or climate warming [168–170]. In the past years, successful algorithms first demonstrated in offline models have found their way into land-surface schemes of ESMs. An example is a representation of excess ice melt in complex microtopography, in particular polygonal tundra and peat plateaus. Developed first in the offline permafrost model CryoGrid [171], the algorithm was adapted and implemented for offline NOAH-MP simulations [172] and offline JULES simulations [147], potentially being included in their parent ESMs (IITM-ESM for NOAH-MP and HadGEM, KACE, and UKESM for JULES).

Offline models also offer the advantage that, while they inherently solve conservation equations for mass, carbon, and energy, they are not constrained by the strict coupling requirements of ESMs. This flexibility allows for easier experimentation and development, as any conservation issues that arise do not disrupt the functioning of the broader modeling system, unlike in fully coupled ESMs where violations of conservation can cause the entire system to fail. This freedom allows for more detailed examination of small-scale processes and their impact on permafrost dynamics (e.g. [173]), but it also limits the possibilities of integrating developments into ESM frameworks.

On spatial scales of meters to hundreds of meters, offline permafrost models enable spatially distributed modeling of key landscape-scale processes, for example, related to ground ice and the water cycle [174]. In particular, models like Amanzi-ATS and CryoGrid3 have variable vertical structuring that allows explicit representation of ground ice dynamics, melt ponds, subsidence, and microtopography as well as water flow [166, 174]. By considering the heterogeneity and microtopography of the terrain at a meter or even submeter lateral resolution, dedicated offline models can simulate the spatial variation in properties and processes affecting the ground thermal regime, both in natural settings (e.g., [175, 176]) and around infrastructure elements [152]. This capability is crucial for accurately representing the complexity of permafrost regions, where variations in soil properties, ground ice, vegetation cover, and microtopography significantly influence permafrost dynamics (e.g. [45, 177]). This allows the representation of effects like differential subsidence caused by the melting of excess ground ice leading to significant drying on decadal timescales [174], which LSMs in ESMs cannot capture. High-resolution simulations with offline permafrost models can also be directly compared to laboratory experiments, site-scale observations, or catchment-scale observations, to analyze model performance and parameter uncertainties [174, 178]. Bui, Lu, and Nie [165] provide a review on offline hydrological models for the Arctic permafrost region, discussing the applicability on different spatial scales (e.g., small-scale catchments versus large-scale catchments) as well as cryohydrological process representation. They find that different models have strengths on different scales, stating that “GEOtop, SUTRA-ICE, and PFLOTRAN-ICE are found to be suitable for small-scale catchments, whereas ATS and CryoGrid3 are potentially suitable for large-scale catchments.”

Offline permafrost models also have fewer constraints on runtime compared to their coupled counterparts. In global-scale Earth system and even regional circulation models, computational resources are distributed among various components,
constraining the spatial extent of the simulations to global or large regions and limiting the spatiotemporal resolution at which simulations are conducted. In contrast, offline models can concentrate computational resources on specific regions of interest. This not only enables higher resolution simulations of permafrost dynamics (e.g., [179]) but also simulations of permafrost dynamics on centennial to millennial timescales, allowing for the representation of the legacy effect of past climate on current and future permafrost distribution (e.g., [180–182]).

In particular, offline models can also be forced by a simple temperature boundary condition for spatially explicit simulations of permafrost mapping using near-surface air or surface temperature. Regional air temperature data sets at kilometer-scale resolutions have been used to generate permafrost maps with offline models (e.g., [155, 183, 184]), while globally available satellite-derived land surface temperatures were ingested in an empirical offline model to produce a northern hemisphere permafrost map at 1-km scale [185]. In summary, the flexibility of offline models broadens our toolbox for permafrost investigations and enhances our understanding of complex interactions between permafrost and the Earth system.

# 6 | Discussion: Advancements and Challenges in Permafrost Representation Within ESMs

A number of challenges in land surface modeling in general (e.g., [26, 27]) as well as in the representation of permafrost-related processes in Earth system modeling [22, 186] have been identified and discussed in the past years, suggesting development priorities for improving model projections of Earth's climate as well as giving recommendations on how to tackle open questions. The vast majority of models assessed in this study (57 out of 64) employ sophisticated, well-documented LSMs that can potentially address these challenges. Among these models, we identified two different approaches to implementing advancements in LSMs into ESMs: 41 out of the 64 models listed in Table S1 employ LSMs that are also developed outside their ESMs as stand-alone models, often by modeling groups associated with the same modeling center as the ESM. A second method used for the integration of LSMs into ESMs is to utilize an externally developed, complex LSM, which is used by 16 models.

ESMs from the first group benefit from developments of their LSMs outside of the coupled ESM framework, for example, in applications like ISIMIP [187]. Many of these LSMs have made headway towards the recommendations for better representation of permafrost-related processes since their CMIP6 ScenarioMIP simulations were completed. In concurrence, a number of these LSMs can be run with varying levels of complexity, where the application of a more complex setting than what was used for CMIP6 would already allow them to address some of the recommendations and requirements made with respect to permafrost-relevant processes. For example, SURFEX can be run with the sophisticated snow model CROCUS [59] which has improved capabilities of representing the interaction between Arctic vegetation and snow [118]. NOAH-MP, LPJ-GUESS, JSBACH, JULES, CLASSIC, and CLM5 can be run with varying numbers of soil layers covering requirements like high resolution in the

upper soil column as well as sufficiently deep overall soil columns. CLM and ELM can be run with the ecosystem dynamics model FATES in an offline configuration [188] instead of the standard DGVM big leaf scheme. Adjusting the level of complexity of the LSMs employed in coupled ESM simulations can improve the capacity for permafrost representation in coupled ESMs; however, technical and computational constraints often limit the complexity of LSMs applied in coupled ESM simulations. Additionally, within ESMs, the computing infrastructure is often not set up to handle lateral exchange between grid cells, a logistical challenge that offline permafrost models developed as hydrological models have addressed already, but limited to small regional extents like watersheds. Integrating lateral transport into LSMs that are applied to large domains is limited by computational constraints.

The group of models utilizing externally developed, complex LSMs can also directly benefit from the developments in their employed LSM regarding permafrost processes or from employing more complex setups of the LSMs they incorporate than they did within the CMIP6 ScenarioMIP framework. However, ESMs using externally developed LSMs may not have the same depth of understanding of the model as groups that develop their LSMs in-house. This could potentially limit their ability to fully leverage new scientific advances or functionalities. Nonetheless, external LSMs are often accompanied by extensive documentation, user support, and ongoing collaborations with development teams, which help mitigate these limitations and enable meaningful integration of advanced processes into the ESMs. For example, among the 17 models in this group, 11 models use some version of CLM, either the most recent version within the CMIP6 framework (CLM5, in NorESM), older versions (CLM4.0 or CLM4.5 in CMCC-CM2-SR5, CMCC-ESM 2, FGOALS-f3-L, FIO-ESM-2-0, KIOST-ESM, SAM0-UNICON, and TaiESM1), or modified versions of CLM4.5 (CIESM and FGOALS-g3). While updating model versions in a coupled framework poses a multitude of technical challenges and does not always directly yield improvements of the coupled simulations (like the improvement of process representation in general; see e.g., [189, 190]), the capability of the models using older versions of CLM to represent permafrost dynamics could be improved by incorporating the most recent CLM developments. Similar to the ESMs with a direct involvement in “their” LSM development, ESMs could improve their permafrost process representation by including a higher level of complexity in the LSM. For example, as apparent from Table S1, various ESMs using development versions of CLM employ the “BGC mode,” which allows for terrestrial carbon cycling, but most do not, even though this capability existed already in CLM4 [191].

The remaining group of 7 ESMs employs land surface schemes not well documented and often less complex. These models may have other development priorities, potentially in combination with limited resources, or difficulty acquiring expertise in land surface modeling. However, even among that group of ESMs, several modeling groups have made significant progress in representing permafrost-related processes in comparison to CMIP5 (HAL and INM-LND1).

Overall, the advancements made in offline versions of LSMs and offline permafrost models provide valuable insights that can be
incorporated into coupled ESMs to enhance their permafrost representation. However, the implementation is often challenging due to the complex interactions between all components of ESMs, where the improved physical representation of specific processes does not always yield overall improvements in the coupled simulations (e.g., [190]).

# 7 | Conclusion: Advancing Permafrost Representation in ESMs

In conclusion, while considerable strides have been made in incorporating permafrost dynamics into coupled ESMs, a number of challenges persist. One notable achievement since CMIP5 is the improved understanding of large-scale processes governing permafrost behavior and gradual thaw processes associated with climate change through deeper and better structured soil columns. Yet, fine-scale processes crucial for the accurate representation of permafrost remain inadequately addressed. Here, the challenges arise from the complexity of interactions between thermal and hydrological processes and the high heterogeneity of permafrost landscapes, particularly in remote permafrost regions where data availability is limited and the still often coarse resolution of LSMs in ESMs.

Improving model resolution and complexity, especially through the incorporation of subgrid-scale processes, emerges as a critical pathway towards capturing the heterogeneity of permafrost landscapes. Increasing the spatial resolution to account for microtopography and vegetation patterns, alongside the incorporation of more complex soil columns and lateral processes such as subsurface hydrology, holds the potential for refining permafrost representation. However, this endeavor is hindered by challenges associated with computational costs and the need for better datasets for model initialization and validation at finer scales.

Emphasizing the importance of correct representation of biogeochemical processes as a precursor to accurate biogeochemical process representation underscores the need for continued research and collaboration. Despite existing shortcomings, particularly concerning abrupt thaw processes, current models possess capabilities that can be leveraged for further advancements. Offline permafrost models are important tools to test the influence of the processes driving permafrost dynamics (e.g., lateral flows, dynamic organic layers, and disturbances) and provide information on prioritizing permafrost-related developments in ESMs.

## Data Availability Statement

The authors have nothing to report.

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## Supporting Information

Additional supporting information can be found online in the Supporting Information section.