The Cryosphere, 10, 1721–1737, 2016www.the-cryosphere.net/10/1721/2016/doi:10.5194/tc-10-1721-2016© Author(s) 2016. CC Attribution 3.0 License.

Evaluation of air–soil temperature relationships simulated by landsurface models during winter across the permafrost regionWenli Wang1, Annette Rinke1,2, John C. Moore1, Duoying Ji1, Xuefeng Cui3, Shushi Peng4,17,18, David M. Lawrence5,A. David McGuire6, Eleanor J. Burke7, Xiaodong Chen21, Bertrand Decharme9, Charles Koven10,Andrew MacDougall11, Kazuyuki Saito12,15, Wenxin Zhang13,19, Ramdane Alkama9,16, Theodore J. Bohn8,Philippe Ciais18, Christine Delire9, Isabelle Gouttevin4, Tomohiro Hajima12, Gerhard Krinner4,17,Dennis P. Lettenmaier8, Paul A. Miller13, Benjamin Smith13, Tetsuo Sueyoshi14, and Artem B. Sherstiukov20

1College of Global Change and Earth System Science, Beijing Normal University, Beijing, China2Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research (AWI), Potsdam, Germany3School of System Science, Beijing Normal University, Beijing, China4The Laboratory of Glaciology, French National Center for Scientific Research, Grenoble, France5National Center for Atmospheric Research, Boulder, USA6US Geological Survey, Alaska Cooperative Fish and Wildlife Research Unit, University of Alaska Fairbanks,Fairbanks, AK, USA7Met Office Hadley Centre, Exeter, UK8School of Earth and Space Exploration, Arizona State University, Tempe, AZ, USA9Groupe d’étude de l’Atmosphère Météorologique, Unité mixte de recherche CNRS/Meteo-France, Toulouse cedex, France10Lawrence Berkeley National Laboratory, Berkeley, CA, USA11School of Earth and Ocean Sciences, University of Victoria, Victoria, BC, Canada12Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan13Department of Physical Geography and Ecosystem Science, Lund University, Lund, Sweden14National Institute of Polar Research, Tachikawa, Japan15University of Alaska Fairbanks, Fairbanks, AK, USA16L’Institute for Environment and Sustainability (IES), Ispra, Italy17Université Grenoble Alpes, LGGE, Grenoble, France18Climate and Environment Sciences Laboratory, the French Alternative Energies and Atomic Energy Commission, FrenchNational Center for Scientific Research, University of Versailles Saint-Quentin-en-Yvelines, Saclay, France19Center for Permafrost (CENPERM), Department of Geosciences and Natural Resource Management, University ofCopenhagen, Copenhagen, Denmark20All-Russian Research Institute of Hydrometeorological Information – World Data Centre, Obninsk, Russia21Department of Civil and Environmental Engineering, University of Washington, Seattle, WA, USA

Correspondence to: Duoying Ji (duoyingji@bnu.edu.cn)

Received: 4 February 2016 – Published in The Cryosphere Discuss.: 11 March 2016Revised: 20 July 2016 – Accepted: 21 July 2016 – Published: 11 August 2016

Published by Copernicus Publications on behalf of the European Geosciences Union.

1722 W. Wang et al.: Evaluation of air–soil temperature relationships

Abstract. A realistic simulation of snow cover and its ther-mal properties are important for accurate modelling of per-mafrost. We analyse simulated relationships between air andnear-surface (20 cm) soil temperatures in the Northern Hemi-sphere permafrost region during winter, with a particular fo-cus on snow insulation effects in nine land surface models,and compare them with observations from 268 Russian sta-tions. There are large cross-model differences in the simu-lated differences between near-surface soil and air tempera-tures (1T ; 3 to 14 ◦C), in the sensitivity of soil-to-air tem-perature (0.13 to 0.96 ◦C ◦C−1), and in the relationship be-tween 1T and snow depth. The observed relationship be-tween 1T and snow depth can be used as a metric to evalu-ate the effects of each model’s representation of snow insu-lation, hence guide improvements to the model’s conceptualstructure and process parameterisations. Models with betterperformance apply multilayer snow schemes and considercomplex snow processes. Some models show poor perfor-mance in representing snow insulation due to underestima-tion of snow depth and/or overestimation of snow conduc-tivity. Generally, models identified as most acceptable withrespect to snow insulation simulate reasonable areas of near-surface permafrost (13.19 to 15.77 million km2). However,there is not a simple relationship between the sophisticationof the snow insulation in the acceptable models and the sim-ulated area of Northern Hemisphere near-surface permafrost,because several other factors, such as soil depth used in themodels, the treatment of soil organic matter content, hy-drology and vegetation cover, also affect the simulated per-mafrost distribution.

1 Introduction

Present-day permafrost simulations by global climate mod-els are limited and future projections contain high, model-induced uncertainty (e.g. Slater and Lawrence, 2013; Kovenet al., 2013). Most of the model biases and cross-model dif-ferences in simulating permafrost area are due to inaccurateatmospheric simulation, e.g. of air temperature and precipi-tation, deficient simulation of snow and soil temperature andthe coupling between atmosphere and land surface. In winter,the snow insulation effect is a key process for air–soil tem-perature coupling. Its strength depends on the snow depth,areal coverage, snow density and conductivity (see overviewby Zhang, 2005). Many individual model studies have shownthe strong impact of snow parameterisations on soil temper-ature simulations (e.g. Langer et al., 2013; Dutra et al., 2012;Gouttevin et al., 2012; Essery et al., 2013; Wang et al., 2013;Jafarov et al., 2014). Most importantly, these studies showedthat the consideration of wet snow metamorphism and snowcompaction, improved snow thermal conductivity and multi-layer snow schemes can improve the simulation of snow dy-namics and soil temperature. Parameterisations that take into

account snow compaction (e.g. related to overburden pres-sure, thermal metamorphism and liquid water) work betterthan simpler schemes such as an exponential increase of den-sity with time (Dutra et al., 2010). The influence of snowthermal conductivity on soil temperature has been demon-strated by many model studies (e.g. Bartlett et al., 2006; Sahaet al., 2006; Vavrus, 2007; Nicolsky et al., 2007; Dankers etal., 2011; Gouttevin et al., 2012). Winter soil temperature canchange by up to 20 K simply by varying the snow thermalconductivity by 0.1–0.5 W m−1 K−1 (Cook et al., 2008). Thesnow insulation effect also plays an important role for theArctic soil temperature response to climate change and there-fore for future near-surface permafrost thawing and soil car-bon vulnerability (e.g. Schuur et al., 2008). Shallower snowcan reduce soil warming while shorter snow season can en-hance soil warming (Lawrence and Slater, 2010). The modelskill in atmosphere–soil coupling with the concomitant snowcover in the Arctic is an important factor in the assessmentof limitations and uncertainty of carbon mobility estimates(Schaefer et al., 2011).

The Snow Models intercomparison project (SnowMIP;Essery et al., 2009) and the Project for Intercomparisonof Land Surface Parameterization Schemes (PILPS) Phase2e (Slater et al., 2001) examined the snow simulations ofan ensemble of land surface schemes for the midlatitudes.However, until now there has been no attempt to evaluatethe air–soil temperature relationship in the Northern Hemi-sphere permafrost region and the detailed role of snow depththerein across an ensemble of models. In such an investi-gation, a first suitable approach is the evaluation of stand-alone (offline) land surface models (LSMs). The retrospec-tive (1960–2009) simulations from the model integrationgroup of the Permafrost Carbon Network (PCN; http://www.permafrostcarbon.org) provide an opportunity to evaluate anensemble of nine state-of-the-art LSMs. Here, the LSMs arerun with observation-based atmospheric forcing, meaningthat snow depth is not influenced by biases in the atmosphericforcing in a coupled model set-up. The evaluation of the of-fline modelled air temperature–snow depth–near-surface soiltemperature relationship in winter is therefore important forrevealing a model’s skill in representing the effects of snowinsulation.

Most of the LSMs participating in PCN are the land sur-face modules of Earth system models (ESMs) participat-ing in the Coupled Model Intercomparison Project (CMIP5;http://cmip-pcmdi.llnl.gov/cmip5/) although in some casesdifferent versions were used for PCN and CMIP5 simula-tions. Thus, the results we present can guide the correspond-ing evaluation of these ESMs, though analysis of coupledmodel results requires consideration of couplings betweenmodel components and is necessarily more complex.

The scope of the present study is to analyse the extent towhich the ensemble of PCN models can reproduce the ob-served relationship between air and near-surface soil temper-atures in the Northern Hemisphere permafrost region during

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W. Wang et al.: Evaluation of air–soil temperature relationships 1723

winter, with a particular focus on the snow insulation effect.For the latter we analyse the impact of snow depth on the dif-ference between near-surface soil and air temperatures. Ourrelated key questions are the following: how well do the mod-els represent the observed spatial pattern of the air–soil tem-perature difference in winter and how it is controlled by snowdepth? What is the range of the simulated air–soil tempera-ture relationship across the model ensemble? To the greatestextent possible, we try to relate the performance of the mod-els to their snow schemes. With this aim in mind, a simulta-neous analysis of simulated air and near-surface soil temper-atures and snow depth is presented and compared with thosefrom a novel data set of Russian station observations. Weused this data set because it has been compiled within PCN,and it is hard to find other station data sets which provide si-multaneous observations of both air and soil temperatures aswell as snow depth over a long period.

In Sect. 2, we describe the model simulations, the stationobservations used for evaluation and the analysis methods.In Sect. 3, we present a detailed analysis of near-surfaceair temperature–snow depth–soil temperature relationshipsin winter. In Sect. 4, we discuss the roles of atmospheric forc-ing and model processes. In Sect. 5, we investigate the rela-tionship between simulated snow insulation and permafrostarea. We summarise our findings and present conclusions inSect. 6.

2 Data and analysis

2.1 Models

We use data from nine LSMs participating in the PCN,including CLM4.5, CoLM, ISBA, JULES, LPJ-GUESS,MIROC-ESM, ORCHIDEE, UVic and UW-VIC. For de-tailed information about the models and simulations we referto Rawlins et al. (2015), Peng et al. (2015) and McGuire etal. (2016). The total soil depth for soil thermal calculationsranges from 3 m (divided into 8 layers) in LPJ-GUESS to250 m (divided into 14 layers) in UVic. The physical proper-ties of the soil differ among the models as well, and four ofthem (CLM4.5, ISBA, UVic, UW-VIC) include organic hori-zons. Three models (ISBA, LPJ-GUESS, UW-VIC) do notarchive soil subgrid results and provide only area-weightedground temperature (i.e. averaged over wetlands and vege-tated areas, and in some cases lake fractions).

Table 1 lists relevant snow model details. One model(UVic) uses an implicit snow scheme which replaces theupper soil column with snow-like properties, i.e. the near-surface soil layer takes the temperature of the air–snow in-terface. The other models use separate snow layers on topof the ground, either a single bucket (LPJ-GUESS, UW-VIC) or multilayer snow schemes (CLM4.5, CoLM, ISBA,JULES, MIROC-ESM, ORCHIDEE). Snow insulation is ex-plicitly considered in all models: increasing snow depth in-

creases the insulation effect. Most models consider the ef-fect of varying snow density on insulation (Table 1). Thisis parameterised by a snow conductivity–density relation-ship. Some of the models (LPJ-GUESS, MIROC-ESM, OR-CHIDEE, UVic) use a fixed snow density, consider only drysnow and no compaction effects, while others represent liq-uid water in snow and different processes for snow densifi-cation such as mechanical compaction and thermal and de-structive metamorphism (Table 1).

The simulations were generally run for the period 1960–2009, although some simulations were stopped a few yearsearlier. Each model team was free to choose appropriate driv-ing data sets for weather and climate, atmospheric CO2, ni-trogen deposition, disturbance, land cover, soil texture, etc.However, the climate forcing data (surface pressure, surfaceincident longwave and shortwave radiation, near-surface airtemperature, wind and specific humidity, rain and snowfallrates) are from gridded observational data sets (e.g. CRUN-CEP, WATC; Table S1 in the Supplement). The exceptionis MIROC-ESM, which was run as a fully coupled model,forced by its own simulated climate. Mean annual air tem-perature simulated by MIROC-ESM for the permafrost re-gion was within the range (−7.2 to 2.2 ◦C) of the other forc-ing data sets used in this study and the trend in near-surfaceair temperature (+0.03 ◦C yr−1) was the same for all forc-ing data sets. However, MIROC-ESM had both the highestannual precipitation (range 433 to 686 mm) and the highesttrend in annual precipitation (range −2.1 to +0.8 mm yr−1)

among the forcing data sets.The spatial domain of interest is the Northern Hemi-

sphere permafrost land regions. Our analysis is based on the0.5◦× 0.5◦-resolution gridded driving and modelled data forwinter (DJF) 1980–2000.

2.2 Observations

A quality-checked data set of monthly near-surface air tem-perature, 20 cm soil temperatures and snow depth from Rus-sian meteorological stations have been provided by the All-Russian Research Institute of Hydrometeorological Informa-tion – World Data Centre (RIHMI-WDC; http://meteo.ru/).Of the stations, 579 report snow depth and 268 provide si-multaneous data on all three variables. Ground surface tem-perature data are not available. A detailed description of dataset preparation is provided in Sherstiukov (2012a). Observ-ing conditions at the Russian stations in all meteorologicalelements correspond with WMO standards. The observationspresented have been included in other data sets, such as theGlobal Summary of the Day (GSOD) data set, HadSRUT4etc., and are widely used in climate research (e.g. Anisi-mov and Sherstiukov, 2016; Decharme et al., 2016; Parket al., 2014; Brun et al., 2013; Pavlov and Malkova, 2009;PaiMazumder et al., 2008). The soil temperature data setwas run through four independent methods of quality con-trol (Sherstiukov, 2012b). However, some soil temperature

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1724 W. Wang et al.: Evaluation of air–soil temperature relationships

Table 1. PCN snow model details.

Model reference Snow Snow Water Liquid water Snow density3 Snow thermalfor snow scheme scheme1 layers phases treatment2 conductivity4

CLM4.5 ML Dynamic Liquid, Bucket-type depends on quadraticSwenson and Lawrence (2012) (max. 5) ice prognostic in snow depth; equation on ρOleson et al. (2013) each layer compaction3a, b, c

CoLM ML Dynamic Liquid, Bucket-type depends on quadraticDai et al. (2003) (max. 5) ice prognostic in snow depth; equation on ρJi et al. (2014) each layer compaction3a, b, c

ISBA ML Static Liquid, ice, Diagnosed from compaction3a, b quadratic equation onBoone and Etchevers (2001) (3) vapour snow temperature, ρ, contribution due

mass, density to vapour transfer

JULES ML Dynamic Liquid, ice, Bucket-type prognostic compaction 3a power equationBest et al. (2011) (max. 3) vapour in each layer on ρ

LPJ-GUESS Wania et al. (2009) BL Static Ice Not fixed fixedGerten et al. (2004) (1) represented 362 kg m−3 0.196 W m−1 K−1

MIROC-ESM ML Dynamic Ice Not fixed fixedTakata et al. (2003) (max. 3) represented 300 kg m−3 0.3 W m−1 K−1

ORCHIDEE ML Dynamic Ice Not fixed fixedGouttevin et al. (2012) (max. 7) represented 330 kg m−3 0.25 W m−1 K−1

for tundra,0.042 W m−1 K−1

for taiga

UVic I Static Ice Not fixed bulkMeissner et al. (2003) (1) represented 330 kg m−3 conductivityAvis (2012)

UW-VIC BL Dynamic Liquid, ice, Constant liquid compaction 3a, b fixedAndreadis et al. (2009) (max. 2) vapour water holding capacity 0.7 Wm−1 K−1

1 ML: Multilayer, BL: Bulk-layer, I: Implicit; according to Slater et al. (2001). 2 Not represented means dry snow. 3 Processes for densification of the snow: (a) mechanical compaction (dueto the weight of the overburden), (b) thermal metamorphosis (via the melting–refreezing process), (c) destructive metamorphism (crystal breakdown due to wind, thermodynamic stress);Anderson (1976), Jordan (1991), Kojima (1967). 4 quadratic equation on ρ according to Jordan (1991), Anderson (1976); contribution due to vapour transfer according to Sun et al. (1999).

observations could be disturbed by grass cutting during thewarm season and the removal of organic materials, mainlyat agricultural sites, which may affect the trend in the warmseason (Park et al., 2014), but this does not affect our resultson the air–upper soil temperature relationship in winter.

Precipitation station data have been compiled from theGSOD data set produced by the National Climatic Data Cen-ter (NCDC; http://www.ncdc.noaa.gov) for all of the stationsthat are included in the RIHMI-WDC data set. In additionto the station’s ground snow depth observations we use grid-ded snow water equivalent (SWE) data from the GlobSnow-2product (http://www.globsnow.info/swe/), which have beenproduced using a combination of passive microwave ra-diometer and ground-based weather station data (Takalaet al., 2011). Orographic complexity, vegetation cover andsnow state (e.g. wet snow) affect the accuracy of this product.When compared with ground measurements in Eurasia, theGlobSnow product shows root mean square error (RMSE)values of 30 to 40 mm for SWE values below 150 mm,with retrieval uncertainty increases when SWE is above thisthreshold (e.g. Takala et al., 2011; Muskett, 2012; Klehemet

et al., 2013). In order to be compared with station data, snowdepth was then calculated from SWE using a snow densityof 250 kg m−3, which is a median observed value in win-ter. Zhong et al. (2014) report snow density values of 180–250 kg m−3 for tundra/taiga and 156–193 kg m−3 for alpinesnow classes. Woo et al. (1983) report snow density values of250–400 kg m−3 for various terrain types. Choice of densitydoes not materially affect the results.

All these data have been compiled for winter (DJF) andthe same time period of 1980–2000. This period was cho-sen because soil temperature data are sparse before 1980 andthe JULES simulation stopped in the year 2000. Compari-son of the simulations with the station data was done usinga weighted bilinear interpolation from the four surroundingmodel grid points onto the station locations.

2.3 Analysis methods

Our analysis is focused on the common winter (DJF) con-dition, although snow can begin in November or even ear-lier and end at the beginning of May, but we checked thata different winter definition (NDJFMA) does not qualita-

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W. Wang et al.: Evaluation of air–soil temperature relationships 1725

tively change any of the intervariable relationships found.The focus in our study is on the evaluation of the simulatedair–soil temperature relationships, modulated by snow depth.For this, we analyse the winter mean as well as the inter-annual variability (expressed as the standard deviation) offour key variables: near-surface air temperature (Tair), near-surface soil temperature (soil temperature at 20 cm depth;Tsoil), snow depth (dsnow) and the difference between Tsoiland Tair. This difference1T (1T = Tsoil−Tair) is called theair–soil temperature difference. By limiting our analysis towinter only, we are able to attribute the cross-model andmodel-to-observation differences in 1T primarily to snowinsulation effects. In winter, the effects of other factors (e.g.soil moisture, texture) on 1T are much smaller than that ofsnow. Ground surface temperatures were not recorded in theRussian data set, but 20 cm soil depth temperatures were.To test how sensitive results are using 20 cm depth tem-peratures instead of ground surface temperatures, we alsoanalysed model-simulated temperature differences betweenground surface and Tair, and found no qualitative differences,hence justifying the use of 20 cm observations.

We use the Pearson product–moment correlation coeffi-cient and its significance (von Storch and Zwiers, 1999) toinvestigate the covariability between 1T and dsnow as wellas between Tsoil and its two forcing factors (Tair and dsnow).Before we compute the correlations, we detrended the databy removing a least squares regression line. The calculatedcorrelation maps (i.e. spatial distributions of correlation co-efficients) based on model and observation data, allow com-parison of the spatial patterns of these relationships.

To further examine the functional behaviour between thekey variables, we present relation diagrams between pairs ofvariables (e.g. variation of 1T with change of dsnow). Toevaluate the performance of the individual LSMs we cal-culate the RMSE between the observed and modelled re-lationships. We illustrate the dependence of 1T vs. dsnowand Tsoil vs. dsnow relations for three Tair ranges. To distin-guish dry snow pack regimes from those where sporadic meltmay occur even in winter, we split Tair into three regimes:the coldest conditions (Tair ≤−25 ◦C, representing 24 %of observations), the intermediate temperature conditions(−25 ◦C < Tair ≤−15 ◦C, representing 42 % of the observa-tions), and the warmest conditions (−15 ◦C < Tair ≤−5 ◦C,representing 34 % of observations). Hence it is an indirectseparation of temperature-gradient metamorphosis regimesand density-gradient metamorphosis snow pack regimes. Ad-ditionally, we present conditional probability density func-tions (PDFs) of 1T for different snow depth and air temper-ature regimes and compare the simulated PDFs with thoseobtained from station observations.

Figure 1. Variation of 1T (◦C), the difference between soil tem-perature at 20 cm depth and air temperature with snow depth (cm)for winter 1980–2000. The dots represent the medians of 5 cm snowdepth bins and the upper and lower bars indicate the 25th and 75thpercentiles, calculated from all Russian station grid points (n= 268)and 21 individual winters. The numbers in each model panel indi-cate the RMSE between the observed and modelled relationship.Colours represent different air temperature regimes.

3 Results

3.1 Relationship between air–soil temperaturedifference and snow depth

The relationship between air–soil temperature difference(1T ) and snow depth (dsnow) in winter (Fig. 1) shows anincrease of 1T with increasing dsnow in the Russian sta-tion observations. The data exhibit a linear relation between1T and dsnow at relatively shallow snow depths with a trendtowards asymptotic behaviour at thicker snow, which is inagreement with earlier findings (Zhang, 2005; Ge and Gong,2010; Morse et al., 2011). There is also significant scatter inthe observation-based relationship indicated by the interquar-tile range in 1T of 1.5–8.5 ◦C at specific snow depth and airtemperature regimes, likely resulting from complicating fac-tors such as snow pack density and moisture content variabil-ity over the winter, as well as observational errors.

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1726 W. Wang et al.: Evaluation of air–soil temperature relationships

Figure 2. Conditional probability density functions (PDFs) of 1T (◦C), the difference between soil temperature at 20 cm depth and airtemperature for (a) different snow depth classes and (b) air temperature regimes for winter 1980–2000.

All models reproduce the observed relationship, i.e. in-creasing 1T with increasing dsnow. However, Fig. 1 alsoshows a wide cross-model spread in the simulated relation-ships and shows that some of the models are not consis-tent with the behaviour in the observations. Only three mod-els (CLM4.5, CoLM, JULES) reproduce the observed 1Tvs. dsnow relationship reasonably well using a benchmark ofRMSE < 5 ◦C for all temperature regimes. In particular LPJ-GUESS, ORCHIDEE, UVic, UW-VIC, MIROC-ESM showlarge RMSE for cold air conditions. ISBA stands out overall,with a RMSE of 7–18 ◦C in all temperature ranges. We con-clude that these models do not adequately represent the fea-tures of the observed 1T vs. dsnow relationship. The scatterin the modelled relationships, indicated by the interquartilerange, is of the same order as in the observations, except forISBA and MIROC-ESM, which produce noticeably smallervariations.

Figure 2a views the 1T vs. dsnow relationship in a com-plementary form using the PDFs of 1T for different snowdepth regimes. This analysis allows for a detailed evaluationof the snow-regime-dependent 1T separation by quantify-

ing and comparing the modal value and width of the differentconditional PDFs. Since the Russian snow depths are clearlynon-normal in distribution (Fig. S1 in the Supplement, witha median dsnow of 30 cm), we divide the data into “shal-low” (dsnow ≤ 20 cm) and “thick” (dsnow ≥ 45 cm) regimes toseparate two snow depth regimes. The modal value of thestation-based 1T PDF is 5 ◦C for shallow snow and 14 ◦Cfor thick snow; that is, thick snow is a better insulator thanthin snow. Based on the 1T PDFs, five models (CoLM,CLM4.5, JULES, ORCHIDEE, MIROC-ESM) successfullyseparate the 1T regimes under different snow depth condi-tions. Their simulated 1T PDFs have a smaller modal valuefor thin snow than for thick snow, like in the observations.The other models clearly fail in separating the 1T PDFs forthe two different snow depth regimes. However, even for thefive successful models, both the shapes and the modal valuesof the simulated PDFs differ from the observed PDF.

Both Figs. 1 and 2b further indicate that 1T is related toTair conditions. This is expected due to the effects of Tair onsnow pack properties, particularly its density and moisturecontent that affect the thermal conductivity of the snow. For

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Figure 3. Spatial maps of the correlation coefficients between snow depth and 1T , the difference between soil temperature at 20 cm depthand air temperature for winter 1980–2000. Regions with greater than 95 % significance are hashed.

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1728 W. Wang et al.: Evaluation of air–soil temperature relationships

example, the density of fresh fallen snow tends to be muchlower under cold Tair than warm (Anderson, 1976), leading toincreased insulation (larger 1T ). Snow densification is alsoa function of Tair; for example, depth hoar metamorphosisof the snow pack, which produces more insulation (looselypacked depth-hoar crystals have very low thermal conduc-tivity), is promoted by strong thermal gradients in the snowpack and is typical of continental climates (e.g. Zhang et al.,1996). Therefore, we can expect that the same thickness ofsnow in colder climates will provide greater insulation thanit would in warmer climates.

Our analysis of observations (Figs. 1 and 2b) confirms(i) a larger 1T for colder Tair than for warmer Tair (for agiven snow depth), (ii) a greater sensitivity of1T to changesin dsnow in colder Tair (Fig. 1) and (iii) a larger modalvalue of the 1T PDF for colder Tair than for warmer Tair(21 ◦C for Tair ≤−25 ◦C and 9 ◦C for−15 ◦C < Tair ≤−5 ◦C;Fig. 2b). These effects are consistent with colder climateshaving lower density snow packs, and the differences are inline with measurements of snow density variability (Zhong etal., 2014). Additionally, both the interquartile range in Fig. 1and the width of the PDFs in Fig. 2b become larger as Taircool. This may be related to the formation of depth hoar,which is a very good insulator and its varying presence inthe snow pack decouples 1T from dsnow. Cold, thin snowpacks tend to contain much more low-density depth hoarthan warmer snow packs (e.g. Zhang et al., 1996; Singh etal., 2011). Continental regions have large annual temperaturecycles, with greater interannual variability and thinner snowpacks than maritime ones. This variability leads to greaterscatter and greater sensitivity of the 1T vs. dsnow relation-ship in the cold winter regions. An additional cause of scat-ter is that the density of fresh-fallen snow decreases withthe decrease of temperature. Accordingly, in the cold Tairregime (Tair ≤−25 ◦C) we find a larger 1T in early winter(November–December), when the snow pack is composed ofthinner lower-density fresh snow (and depth hoar), than latewinter (January–February; Fig. S2). Under warm conditions(−15 ◦C < Tair ≤−5 ◦C) such a separation is not observed.

If we evaluate the models with respect to this observed im-pact of Tair on the1T vs. dsnow relationship, we demonstratethat some models (CLM4.5, CoLM, JULES) are better ableto replicate the effect than others (LPJ-GUESS, MIROC-ESM, ORCHIDEE, UW-VIC; Fig. 1). The latter do not fullyreplicate the larger 1T under cold Tair conditions. CLM4.5,CoLM and JULES capture a larger 1T for colder Tair fora given dsnow in agreement with the observations. However,for shallow snow, JULES simulates an increase of 1T withincreasing dsnow for all temperature ranges that is twice aslarge as observations. Two models (ISBA, UVic) clearly failin this evaluation. Poor model performance in reflecting Tairinfluence on the 1T vs. dsnow also manifests itself in regimeseparation of the PDFs (Fig. 2b). Some models do not sepa-rate the1T regimes under different Tair conditions well or atall (ISBA, LPJ-GUESS, MIROC-ESM, UVic), while others

Table 2. Sensitivity of near-surface soil temperature (Tsoil) to airtemperature (Tair) in winter (DJF) calculated by the slopes of thelinear regression between Tsoil (◦C) and Tair (◦C) for differentregimes of snow depth (dsnow), using data from all Russian stationgrid points and 21 individual winter 1980–2000. All relationshipsare statistically significant at p ≤ 0.01.

Snow depth regimes

Shallow Thickdsnow ≤ 20 cm dsnow ≥ 45 cm

Tsoil vs. Tair R2 Tsoil vs. Tair R2

(◦C ◦C−1) (◦C ◦C−1)

Observation 0.62 0.79 0.21 0.41CLM4.5 0.69 0.89 0.33 0.56CoLM 0.49 0.73 0.13 0.44ISBA 0.93 0.98 0.93 0.94JULES 0.68 0.77 0.19 0.46LPJ-GUESS 0.73 0.89 0.52 0.75MIROC-ESM 0.78 0.98 0.49 0.67ORCHIDEE 0.86 0.83 0.56 0.64UVic 0.96 0.97 0.81 0.68UW-VIC 0.54 0.74 0.76 0.65

cannot capture the observed cold temperature regime features(i.e. too broad PDFs and shifts towards smaller modal values;ORCHIDEE, UW-VIC). The three models with reasonableintervariable relations (CLM4.5, CoLM, JULES) also cap-ture the regime separation in the PDFs. These three models,as well as LPJ-GUESS and ORCHIDEE, also represent theobserved greater insulation of early winter snow packs undercold conditions (Fig. S2).

The maps of the 1T vs. dsnow correlations in winter(Fig. 3) demonstrate a pronounced spatial variability in the1T vs. dsnow relationship. The highest positive correlationoccurs in the region of eastern Siberia and the Siberian High-lands. In other regions, namely Scandinavia, the westernRussian Arctic, West Siberian Plain and Central SiberianPlateau, the correlation is much weaker and often not sta-tistically significant. These regions have snow (Sect. 4.1.2)influenced by North Atlantic cyclonic activity which bringsrelatively warm moist air and heavy precipitation in winter(and a positive correlation between dsnow and Tair), leadingto relatively small mean 1T .

Some models (CLM4.5, CoLM, ORCHIDEE, UW-VIC)show a reasonable spatial pattern of correlation coefficient(r ≥ 0.4) compared to those of the observations, while theothers do not (Fig. 3). Obvious outliers are the LPJ-GUESSand UVic models, which do not reproduce the observed pat-tern of correlation. UVic calculates a reverse spatial patterncomparing to that of the observations (e.g. significant posi-tive correlation in West Siberian Plain and Central SiberianHighlands). LPJ-GUESS produces very few statistically sig-nificant correlations.

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W. Wang et al.: Evaluation of air–soil temperature relationships 1729

Figure 4. Variation of soil temperature at 20 cm depth (◦C) withair temperature (◦C) for winter 1980–2000. The dots represent themedians of 5 ◦C air temperature bins and the upper and lower barsindicate the 25th and 75th percentiles, calculated from all Russianstation grid points (n= 268) and 21 individual winters. The num-bers in each model panel indicate the RMSE between the observedand modelled relationship. Colours represent different snow depthregimes.

3.2 Variability of soil temperature with airtemperature and snow depth

Next we assess whether or not the models can correctly re-produce the interannual near-surface soil temperature (Tsoil)

variability in relation to snow depth (dsnow) and near-surfaceair temperature (Tair) variability. Previous studies have notedthat the strength of the relationship between Tsoil and Tair ismodulated by dsnow and the snow insulation effect increasesonly up to a limiting depth beyond which extra snow makeslittle difference to soil temperatures (Smith and Riseborough,2002; Sokratov and Barry, 2002; Zhang, 2005; Lawrence andSlater, 2010). Zhang (2005) reported that the limiting snowdepth is approximately 40 cm.

To inspect the difference in insulation capacity for shallowand thick snow, we investigate the Tsoil vs. Tair relationshipunder shallow (dsnow ≤ 20 cm) and thick (dsnow ≥ 45 cm)snow conditions. Our Russian observation analysis (Fig. 4,

Figure 5. Variation of soil temperature at 20 cm depth (◦C; y axis)with snow depth (cm) for winter 1980–2000. The dots represent themedians of 5 cm snow depth bins and the upper and lower bars indi-cate the 25th and 75th percentiles, calculated from all Russian sta-tion grid points (n= 268) and 21 individual winters. The numbersin each model panel indicate the RMSE between the observed andmodelled relationship. Colours represent different air temperatureregimes.

Table 2) indicate a regression slope between Tsoil and Tair(0.62 ◦C ◦C−1, R2

= 0.8) that is 3 times higher under shal-low snow pack than thicker snow conditions (0.21 ◦C ◦C−1,R2= 0.4). This is consistent with observations that the mean

freezing n-factor (the ratio of freezing degree days at theground surface to air freezing degree days) is high at siteswhere the snow cover is thin or absent and low at siteswhere the snow cover is thick (e.g. for Yukon in Canada;Karunaratne and Burn, 2003).

Figure 4 clearly shows that some models (CoLM, CLM45,JULES) can capture this difference well. Their regressionslopes for thick and thin snow are well separated and inagreement with those from the observed relationship (Ta-ble 2). The RMSE of their modelled Tsoil vs. Tair relation-ships from observations is smaller than 4 ◦C. These mod-els better reproduce the observed 1T vs. dsnow relationship.Other models (LPJ-GUESS, MIROC-ESM, ORCHIDEE) donot reproduce the much greater regression slope betweenTsoil and Tair for shallow snow than for thick snow as the

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1730 W. Wang et al.: Evaluation of air–soil temperature relationships

observations show. They also produce a regression slope forthick snow which is more than twice as large as for the ob-servations. Two models (ISBA, UVic) do not show any sen-sitivity in the Tsoil vs. Tair relation to snow conditions (Fig.4,Table 2). Another measure quantitatively confirms the samemodels behaviour: the observed average dsnow in the shallowsnow regime is 13.7 cm and that for the thick snow regimeis 58.5 cm, so we would expect, if near-surface Tair and con-ductivities were equal in both snow depth classes, that a ra-tio between the slopes for shallow and thick snow would be4.3. CLM4.5, CoLM and JULES reproduce this observedvariation in the Tsoil vs. Tair relation better than others (Ta-ble 2). JULES and CoLM indicate a change of a factor of4, while CLM4.5 indicates a change of factor of 2. Othermodels (LPJ-GUESS, MIROC-ESM, ORCHIDEE) underes-timate the increase of the regression slope for decreasingsnow depth; they simulate only a factor change of about 1.5.The two models with unrealistic 1T vs. dsnow relationships(ISBA, UVic) also fail in this evaluation of their Tsoil vs. Tairrelationship. They simulate a too-strong sensitivity of Tsoilto Tair (regression slopes larger than 0.9 ◦C ◦C−1, R2 > 0.7;Table 2) that is almost completely independent of the snowdepth regimes, particularly in ISBA, which is not consistentwith observations. These models’ spatial correlation patternsbetween Tsoil and Tair also differ greatly from the observa-tions and the other models (Fig. S3) and show very high pos-itive correlation (r > 0.8) in most regions, as may be expectedfrom the large regression slope shown in Fig. 4. The RMSEof their modelled Tsoil vs. Tair relationships from observa-tions reaches ca. 10 ◦C .

The Tsoil vs. dsnow relationship (Fig. 5) displays the varia-tion of Tsoil with changing snow depth and emphasises the re-duced sensitivity of Tsoil to snow depth under thick snow con-ditions. With increasing dsnow, Tsoil asymptotically convergestowards a value of around 0 ◦C. Overall, the Russian obser-vations indicate that snow depth above about 80–90 cm hasvery little additional insulation effect on Tsoil. Most modelsshow consistent results with regard to this aspect, althoughthe interquartile range of Tsoil for specific snow depths isquite large in some models (ISBA, ORCHIDEE, UVic, UW-VIC; Fig. 5). The figure further points to the air temperaturedependency of the relation. On average, for a given dsnow,a colder Tsoil is observed for colder near-surface air temper-atures, compared with warmer air temperatures. Most mod-els can replicate this effect of air temperature on the Tsoilvs. dsnow relationship, though with differing accuracy. TheRMSE between the observed and modelled relationships canreach ca. 10 ◦C or more (in ISBA, UVic, UW-VIC), particu-larly under cold conditions.

The spatial patterns of the correlation coefficients betweenTsoil and Tair (Fig. S3) and between Tsoil and dsnow (Fig. S4)show a relatively large cross-model scatter in many regions.Obvious outliers in the Tsoil vs. Tair correlation maps areISBA and UVic, which strongly overestimate the correlation(r > 0.9) over most of the Arctic. This indicates an underes-

timated snow insulation effect and confirms the weak insu-lation in both models, which we already discussed based ontheir underestimated 1T (Fig. 1) and weak correlation be-tween 1T and dsnow (Fig. 3). Other models (LPJ-GUESS,ORCHIDEE, UW-VIC) also overestimate the correlation insome regions (e.g. western Russian Arctic, r > 0.7). Most ofthe simulated maps of Tsoil vs. dsnow correlation agree withthe observations on a strong positive correlation in easternSiberia. This is a region of relatively shallow snow (10–40 cm; Fig. 6) and there Tsoil is very sensitive to variationsin snow depth (e.g. Romanovsky et al., 2007). Comparingboth simulated correlation maps, it is obvious that in this re-gion, Tsoil correlates more strongly with dsnow than with Tair,in agreement with the Russian data and earlier studies (Ro-manovsky et al., 2007; Sherstyukov, 2009).

4 Roles of atmospheric forcing and model processes

The cross-model differences in the snow insulation effect,presented by the air temperature–snow depth–soil temper-ature relationships described above, are partially due tothe differences in the atmospheric forcing data and alsodue to differences in the snow and soil physics used inthe LSMs. However, because the climate forcing data setsutilised with each model are observation-based (except forMIROC-ESM), obvious outliers in individual model perfor-mance likely indicate poor or deficient physical descriptionsof the air–snow–soil relations in that specific LSM.

4.1 Atmospheric forcing and snow depth

4.1.1 Air temperature and precipitation

Both near-surface air temperature (Tair) and precipitation aregiven by the climate forcing data sets (Table S1) for allmodels, except for MIROC-ESM, which simulates both. Thecross-model differences in forcing Tair are relatively smalland the simulated spatial patterns of temperature are verysimilar (Fig. S5). All forcing data sets are somewhat colderthan Russian station data in their grid cells. The biases ofwinter mean Tair range from −0.8 to −4.7 ◦C (Table S2), re-flecting biases in the climate forcing data used by the models.In contrast, MIROC-ESM has a positive (mean) Tair bias of+2.7 ◦C.

The large-scale patterns of precipitation are similar acrossthe models, but regional differences can be large (Fig. S6).The individual differences in winter precipitation range from−0.2 to +0.5 mm day−1 (Table S2) relative to the aver-age of the Russian station data. Unfortunately, snowfall wasarchived in only a few models; however large-scale spatialpatterns are similar across these models (Fig. S7).

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W. Wang et al.: Evaluation of air–soil temperature relationships 1731

Figure 6. Spatial maps of snow depth (cm) for winter 1980–2000.

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Table 3. Russian station location averaged error statistics for snow depth (cm) and temperature difference between 20 cm soil and airtemperature (1T ; ◦C) for winter 1980–2000. For each variable, the maximum available number of observations (n) is used. MeanSt,GS andSTDSt,GS are the observed mean and interannual variability (standard deviation), while STD is the standard deviations of each model. Biasis the mean error “simulation minus observation” and RMSE is the root mean square error. The statistics for snow depth are given based onboth station observation (St) and GlobSnow (GS) data.

Snow depth (n= 579) 1T (n= 268)

meanSt= 26.4 cm, meanGS

= 23.4 cm meanSt= 11.9 ◦C

STDSt= 9.0 cm, STDGS

= 6.5 cm STDSt= 2.3 ◦C

biasSt RMSESt biasGS RMSEGS STD biasSt RMSESt STD

CLM4.5 11.5 18.1 14.3 18.1 5.8 2.3 4.1 2.2CoLM 15.6 21.4 17.8 22.1 9.8 2.7 3.7 2.4ISBA 13.0 18.8 15.7 19.8 9.5 −8.4 9.1 0.9JULES −4.1 14.1 −1.3 12.8 7.7 −0.8 4.2 3.2LPJ-GUESS −5.3 17.3 −2.5 16.0 5.0 −0.7 3.7 1.7MIROC-ESM −0.4 17.9 1.9 14.0 6.3 −4.9 6.7 2.0ORCHIDEE −8.7 16.5 −5.3 15.3 6.9 −5.2 6.0 1.9UVic −3.7 18.9 −0.5 16.8 9.4 −5.1 6.5 1.4UW-VIC 12.5 19.8 15.0 20.0 10.4 −1.3 4.8 2.1

4.1.2 Snow depth

The broad-scale spatial snow depth (dsnow) patterns are sim-ilar across the models and show general agreement with theobserved patterns (Fig. 6). The well-pronounced areas ofmaximum winter dsnow (50–100 cm) are in Scandinavia, theUrals, the West Siberian Plain, Central Siberian Highlands,the Far East, Alaska, Labrador Peninsula and Isle of New-foundland. However, large regional cross-model variability isobvious. Some models (JULES, LPJ-GUESS, ORCHIDEE,UVic) underestimate dsnow, while others (CLM4.5, CoLM,ISBA, UW-VIC) overestimate it (Fig. 6; Table 3). The modelbiases are quite similar with respect to station observationsand GlobSnow data. It should be noted that the models donot account for snowdrift. However, redistribution of snowdue to wind is an important aspect, which makes comparisonbetween in situ measured and modelled snow depths difficult(e.g. Vionnet et al., 2013; Sturm and Stuefer, 2013; Gisnas etal., 2014).

Precipitation/snowfall cross-model differences cannot bethe primary explanation for these dsnow differences sincesome models (JULES, MIROC-ESM, ORCHIDEE) havepositive bias in precipitation (> 0.2 mm day−1, Table S2)but simulate much lower dsnow compared to other models(Figs. 6, S6, S7, Table 3). Cross-model differences in theinterannual variability of winter precipitation do not trans-late simply to corresponding differences in the interannualdsnow variability (not shown). For example, UVic calculatesthe (unrealistically) largest interannual dsnow variability inthe boreal European permafrost region, which is not reflectedin the precipitation variability. These results indicate that thesimulated snow depth is a function of both the prescribed

winter precipitation and the model’s snow energy and waterbalance.

4.2 Model processes

We have shown that the cross-model spread in the represen-tation of snow insulation effects (Sects. 3.1, 3.2) cannot pre-dominantly be explained by differences in the forcing data(Sect. 4.1), but to a large extent is due to the representationof snow processes in the models. By considering the relation-ship plots (Figs. 1, 4 and 5) and conditional PDFs (Fig. 2),we were able to categorise the models in terms of their snowinsulation performance. In this section we discuss the influ-ence of the different snow parameterisations in the models.

Models with better performance (CLM4.5, CoLM,JULES) apply multilayer snow schemes. This allows themto simulate more realistic (stronger) insulation because theyconsider the snowpack’s vertical structure and variability.They calculate the energy and mass balance in each snowlayer, are able to capture nonlinear profiles of snow tem-perature and can also account for thermal insulation withinthe snowpack such as when the upper layer thermally insu-lates the lower layers (e.g. Dutra et al., 2012). These modelsalso incorporate storage and refreezing of liquid water withinthe snow and parameterise wet-snow metamorphism, snowcompaction and snow thermal conductivity (Table 1), whichhave been found to be among the most important processesfor good snow depth and surface soil temperature simulation(e.g. Wang et al., 2013).

An underestimated snow depth directly leads to insulationthat is too weak in JULES, LPJ-GUESS, ORCHIDEE andUVic (Fig. 6, Table 3). However only in ORCHIDEE andUVic does this lead to a significant underestimation of 1T

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W. Wang et al.: Evaluation of air–soil temperature relationships 1733

(Table 3, Fig. S8), indicating bias compensation in the twoother models. Thus, compensating error effects occur due tosnow density and conductivity (Fig. S9, Table 1), which im-pact snow thermal insulation.

Our analysis showed that two models (ISBA, UVic) haveTsoil vs. Tair correlation that are too high, indicating that theydo not represent the modulation of the Tsoil vs. Tair relation-ship by snow depth (Fig. 4). This is consistent with their un-derestimation of 1T (Figs. 1, 2, S8, Table 3). In UVic, thesnowpack is treated not as a separate layer but as an extensionof the top soil layer and a combined surface-to-soil thermalconductivity is calculated (Table 1). Such a scheme largelynegates or reduces the insulating capacity of snow (Slater etal., 2001). Koven et al. (2013) noted that such a scheme sim-ulates very little warming of soil and sometimes even cool-ing. The slightly underestimated snow depth (Table 3, Fig. 6)contributes (but not as the primary factor) to reduced snowinsulation, as reported for UVic (Avis, 2012).

ISBA strongly underestimates 1T , while strongly over-estimating dsnow, compared with the observations (Table 3,Fig. 6). However, ISBA uses the same atmospheric forcingdata as JULES (accordingly the air temperature and pre-cipitation are quite similar; Table S2). Also, the model’ssnow density (150–250 kg m−3) is similar to other models(CLM45, CoLM, JULES; Fig. S9) and in agreement withZhong et al. (2014), who report snow density values of 180–250 kg m−3 for tundra/taiga and 156–193 kg m−3 for alpinesnow classes in winter. This apparent contradiction comesfrom the parameterisation of snow cover fraction within eachgrid cell (SCF). The version of ISBA used here calculates aunique superficial soil temperature whether or not the soilis covered by snow and all the energy and radiative fluxesare area-weighted by SCF (Eqs. 7 and 20 in Douville et al.,1995). In order to get reasonable albedos in snow-coveredforests, as is necessary when ISBA is coupled to the CNRM-CM climate model, the parameterisation gives very low SCFin the boreal forest (between 0.2 and 0.5). Hence, snow in-sulates only 20 to 50 % of the grid cell, despite fairly highsnow depths. The heat fluxes from the snow-covered frac-tion are averaged with the fluxes from the snow-free surface,strongly concealing the actual insulating effect of snow andunderestimating it over the grid cell. Using the detailed snowmodel Crocus (Brun et al., 1992; Vionnet et al., 2012) with aSCF equal to 100 % leads to an almost perfect simulation ofnear-surface soil temperature over northern Eurasia (Brun etal., 2013). A similar experiment with ISBA and a SCF equalto 100 % (Decharme et al., 2016) leads to good performancesshowing that the low 1T in ISBA, despite high snow depthin the present study, is mostly due to this subgrid snow frac-tion. Decharme et al. (2016) still showed that the ISBA re-sults are further improved by updating the snow albedo andsnow densification parameterisation.

Interestingly, the ORCHIDEE performance in simulatingsnow depth and 1T is similar to UVic (underestimation ofdsnow and 1T ; Table 3). However, ORCHIDEE can better

Table 4. Permafrost area, defined as maximum seasonal active layerthickness < 3 m in 1960 (Mc Guire et al., 2016). The IPA map es-timate is 16 million km2 (Brown et al., 1997; Slater and Lawrence,2013).

Land surface Snow insulation PermafrostModel skill area (106 km2)

CLM4.5 High 15.77CoLM High 7.62ISBA Low 20.86JULES High 13.19LPJ-GUESS Medium 17.41MIROC-ESM Medium 13.02ORCHIDEE Medium 20.01UVic Low 16.47UW-VIC Medium 17.56

represent the observed Tsoil vs. Tair relationship and its mod-ulation due to the snow pack. ORCHIDEE employs, simi-larly to UVic, a fixed snow density and thermal conductivity.However, in contrast to UVic, ORCHIDEE applies a multi-layer scheme and simulates heat diffusion in the snowpack inup to seven discrete layers (Table 1; Koven et al., 2009). Thishelps to resolve the snow thermal gradients between the topand the base of the snow cover and might explain how someof the snow insulation effects are reasonably represented inORCHIDEE, despite the simpler treatment of temperaturediffusion.

5 Permafrost area

Snow cover plays an important role in modulating thevariations of soil thermodynamics, hence near-surface per-mafrost extent (e.g. Park et al., 2015). Here we evaluatewhether there is a simple relationship between the simu-lated Northern Hemisphere permafrost area and the sophis-tication and ability of the snow insulation component inthe LSM to match the observed snow packs. The simulatednear-surface permafrost area varies greatly across the ninemodels in the hindcast simulation (1960–2009; Table 4).Some of the better-performing snow insulation effect mod-els (CLM4.5, JULES) simulate a near-surface permafrostarea of 13.19 to 15.77 million km2, which is comparablewith the IPA map estimate (16.2 million km2; Brown et al.,1997; Slater and Lawrence, 2013). CoLM and ORCHIDEE,identified as reasonable models with respect to snow insu-lation, simulate much lower (7.62 million km2) and higher(20.01 million km2) areas respectively. The main deficiencyof CoLM is its too-shallow soil depth (3.4 m) comparedwith CLM4.5 (45.1 m), despite having very similar snowmodules (Table 1). However, ISBA, one of the two modelsthat showed rather limited skill in representing snow insula-tion effects, also significantly overestimate permafrost area

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1734 W. Wang et al.: Evaluation of air–soil temperature relationships

(20.86 million km2). This is inconsistent with previous stud-ies (e.g. Vavrus, 2007; Koven et al., 2013), which concludedthat the first-order control on modelled near-surface per-mafrost distribution is the representation of the air-to-surfacesoil temperature difference. Table 4 shows that the situa-tion is more complex and that snow insulation simulation isnot the dominant factor in a good permafrost extent simula-tion. When the land surface models with poor snow modelsare eliminated, the remaining models’ simulated permafrostarea show little or no relationship with the performance ofthe snow insulation component, because several other fac-tors such as differences in the treatment of soil organic mat-ter, soil hydrology, surface energy calculations, model soildepth and vegetation also provide important controls on thesimulated permafrost distribution (e.g. Marchenko and Et-zelmüller, 2013).

6 Summary and conclusions

The aim of this work was to evaluate how state-of-the-artLSMs capture the observed relationship between winter near-surface soil and air temperatures (Tsoil, Tair) and their mod-ulation by snow depth (dsnow) and climate regime. We pre-sented some benchmarks to evaluate model performance.The presented relation diagrams of Tsoil and the differencebetween Tsoil and Tair regarding snow depth allow for a muchbetter assessment, used to reveal structural issues of the mod-els, than a direct point-by-point comparison with station ob-servations. The results are based on the comparison of LSMswith a comprehensive Russian station data set.

We see large differences across the models in their meanair–soil temperature difference (1T ) of 3 to 14 ◦C, in thesensitivity of near-surface soil temperature to air tempera-ture (Tsoil vs. Tair; 0.49 to 0.96 ◦C ◦C−1 for shallow snow,0.13 to 0.93 ◦C ◦C−1 for thick snow) and in the increaseof 1T with increasing snow depth (modal value of 1TPDF: 0 to 10 ◦C for shallow snow, 5 to 21 ◦C for thicksnow). Most of the nine models compare to the observa-tions reasonably well (observations:1T = 12 ◦C, modal1Tvalues of 5 ◦C for shallow snow and of 14 ◦C for thicksnow, Tsoil vs. Tair = 0.62 ◦C ◦C−1 for shallow snow, Tsoilvs. Tair = 0.21 ◦C ◦C−1 for thick snow). Several models alsocapture the modulation by air temperature condition (largerincrease in 1T with increasing dsnow under colder condi-tions) and display the control of snow depth on Tsoil (weakerTsoil vs. Tair relationship under thicker snow). However,while they generally capture these observed relationships,their strength can differ in the individual models. Two mod-els (ISBA, UVic) show the largest deficits in snow insulationeffects and cannot separate the1T regimes neither for differ-ent snow depths nor for different air temperature conditions.

This study uses the ensemble of models to documentmodel performance with respect to the Tsoil vs. Tair relation-ship, and to identify those with better performance, rather

than to quantify the best model. We were able to attributeperformance strength/weakness to snow model features andcomplexity. Models with better performance apply multi-layer snow schemes and consider complex snow processes(e.g. storage and refreezing of liquid water within the snow,wet snow metamorphism, snow compaction). Those mod-els which show limited skill in snow insulation representa-tion (underestimated 1T , very weak dependency of 1T ondsnow, almost unity ratio of Tsoil vs. Tair) have some deficien-cies or oversimplification in the simulation of heat transferin snow and soil layer, particularly in the representation ofsnow depth and density (conductivity). We also emphasisethat compensation of errors in snow depth and conductiv-ity can occur. For example, an excessive correlation betweenTsoil and Tair can be attributed to excessively high thermalconductivity even when the snow depth is correctly (or over-) simulated. This finding underscores the need for detailedmodel evaluations using multiple independent performancemetrics to ensure that the models get the right functionalityfor the right reason. It should be noted that the treatment ofground properties, particularly soil organic matter and soilmoisture/ice content, also affect the simulated winter groundtemperatures. The specific evaluation of these individual pro-cesses is more robustly investigated with experiments con-ducted for individual models (e.g. recently, Wang et al., 2013;Gubler et al., 2013; Decharme et al., 2016).

Snow and its insulation effects are critical for accuratelysimulating soil temperature and permafrost at high latitudes.The simulated near-surface permafrost area varies greatlyacross the nine models (from 7.62 to 20.86 million km2).However, it is hard to find a clear relationship betweenthe performance of the snow insulation in the models andthe simulated area of permafrost, because several other fac-tors (e.g. related to soil depth and properties and vegetationcover) also control the simulated permafrost distribution.

7 Data availability

The data will be made available through the National Snowand Ice Data Center (NSIDC; http://nsidc.org); the contactperson is Kevin Schaefer (kevin.schaefer@nsidc.org).

The Supplement related to this article is available onlineat doi:10.5194/tc-10-1721-2016-supplement.

Author contributions. Annette Rinke developed the idea that leadto this paper, Wenli Wang and Annette Rinke carried out research,John C. Moore contributed ideas, Annette Rinke, John C. Moore,Wenli Wang, and Duoying Ji wrote the paper and all authors dis-cussed the results and commented on the paper at all stages.

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W. Wang et al.: Evaluation of air–soil temperature relationships 1735

Acknowledgements. This study was supported by the PermafrostCarbon Vulnerability Research Coordination Network, whichis funded by the US National Science Foundation (NSF).Any use of trade, firm, or product names is for descriptivepurposes only and does not imply endorsement by the USGovernment. Eleanor J. Burke was supported by the JointUK DECC/Defra Met Office Hadley Centre Climate Program(GA01101). Eleanor J. Burke, Shushi Peng, Philippe Ciais andGerhard Krinner were supported by the European Union SeventhFramework Program (FP7/2007-2013) under grant agreementno. 282700. Theodore J. Bohn was supported by grant 1216037from the NSF Science, Engineering and Education for Sustainabil-ity (SEES) Post-Doctoral Fellowship program. Bertrand Decharme,Ramdane Alkama and Christine Delire were supported by theFrench Agence Nationale de la Recherche under agreementANR-10-CEPL-012-03. This research was sponsored by theintegrated approaches and impacts, China Global Change Program(973 Project), National Basic Research Program of China Grant2015CB953602 and the National Natural Science Foundation ofChina Grant 40905047. We also thank the editor and reviewers fortheir comments which improved the manuscript.

Edited by: J. BoikeReviewed by: two anonymous referees

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