The Interactions Between Soil–Biosphere–Atmosphere Land Surface Model with a Multi-Energy Balance (ISBA-MEB) Option in Surfexv8

Home , Biosphere, Biosphere model, Hydrology

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ doi:10.5194/gmd-10-843-2017 © Author(s) 2017. CC Attribution 3.0 License.

The interactions between soil–biosphere–atmosphere land surface model with a multi-energy balance (ISBA-MEB) option in SURFEXv8 – Part 1: Model description

Aaron Boone1, Patrick Samuelsson2, Stefan Gollvik2, Adrien Napoly1, Lionel Jarlan3, Eric Brun1, and Bertrand Decharme1 1CNRM UMR 3589, Météo-France/CNRS, Toulouse, France 2Rossby Centre, SMHI, 601 76 Norrköping, Sweden 3CESBIO – UMR 5126 UPS, CNRS, CNES, IRD, Toulouse, France

Correspondence to: Aaron Boone ([email protected])

Received: 14 October 2016 – Discussion started: 27 October 2016 Revised: 23 January 2017 – Accepted: 27 January 2017 – Published: 21 February 2017

Abstract. Land surface models (LSMs) are pushing towards pack model, a variable-layer soil scheme, an explicit litter improved realism owing to an increasing number of obser- layer, a bulk vegetation scheme, and the atmosphere. It also vations at the local scale, constantly improving satellite data includes a feature that permits a coupling transition of the sets and the associated methodologies to best exploit such snowpack from the canopy air to the free atmosphere. It data, improved computing resources, and in response to the shares many of the routines and physics parameterizations user community. As a part of the trend in LSM develop- with the standard version of ISBA. This paper is the ﬁrst of ment, there have been ongoing efforts to improve the rep- two parts; in part one, the ISBA-MEB model equations, nu- resentation of the land surface processes in the interactions merical schemes, and theoretical background are presented. between the soil–biosphere–atmosphere (ISBA) LSM within In part two (Napoly et al., 2016), which is a separate com- the EXternalized SURFace (SURFEX) model platform. The panion paper, a local scale evaluation of the new scheme is force–restore approach in ISBA has been replaced in recent presented along with a detailed description of the new forest years by multi-layer explicit physically based options for litter scheme. sub-surface heat transfer, soil hydrological processes, and the composite snowpack. The representation of vegetation processes in SURFEX has also become much more sophisticated in recent years, including photosynthesis and respiration and 1 Introduction biochemical processes. It became clear that the conceptual limits of the composite soil–vegetation scheme within ISBA Land surface models (LSMs) are based upon fundamental had been reached and there was a need to explicitly separate mathematical laws and physics applied within a theoretical the canopy vegetation from the soil surface. In response to framework. Certain processes are modeled explicitly while this issue, a collaboration began in 2008 between the high- others use more conceptual approaches. They are designed resolution limited area model (HIRLAM) consortium and to work across a large range of spatial scales, so that unre- Météo-France with the intention to develop an explicit rep- solved scale-dependent processes represented as a function resentation of the vegetation in ISBA under the SURFEX of some grid-averaged state variable using empirical or statis- platform. A new parameterization has been developed called tical relationships. LSMs were originally implemented in nu- the ISBA multi-energy balance (MEB) in order to address merical weather prediction (NWP) and global climate mod- these issues. ISBA-MEB consists in a fully implicit numer- els (GCMs) in order to provide interactive lower boundary ical coupling between a multi-layer physically based snow- conditions for the atmospheric radiation and turbulence parameterization schemes over continental land surfaces. In the

Published by Copernicus Publications on behalf of the European Geosciences Union. 844 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 past 2 decades, LSMs have evolved considerably to include tion de Researche Petite Echelle Grande Echelle (ARPEGE- more biogeochemical and biogeophysical processes in order climat; Voldoire et al., 2013) and by HIRLAM countries to meet the growing demands of both the research and the within the ALADIN–HIRLAM system as HARMONIE– user communities (Pitman, 2003; van den Hurk et al., 2011). AROME and HARMONIE–ALARO Climate configurations A growing number of state-of-the-art LSMs, which are used (Lind et al., 2016). in coupled atmospheric models for operational numerical weather prediction (Ek et al., 2003; Boussetta et al., 2013), 1.1 Rationale for improved vegetation processes climate modeling (Oleson et al., 2010; Zhang et al., 2015), or both (Best et al., 2011; Masson et al., 2013), represent Currently, many LSMs are pushing towards improved re- most or all of the following processes: photosynthesis and alism owing to an increasing number of observations at the associated carbon fluxes, multi-layer soil water and heat the local scale, constantly improving satellite data sets and transfer, vegetation phenology and dynamics (biomass evo- the associated methodologies to best exploit such data, lution, net primary production), sub-grid lateral water trans- improved computing resources, and in response to the fer, river routing, atmosphere–lake exchanges, snowpack dy- user community via climate services (and seasonal fore- namics, and near-surface urban meteorology. Some LSMs casts, drought indexes, etc. . . ). In the SURFEX context, the also include processes describing the nitrogen cycle (Castillo force–restore approach has been replaced in recent years et al., 2012), groundwater exchanges (Vergnes et al., 2014), by multi-layer explicit physically based options for sub- aerosol surface emissions (Cakmur et al., 2004), isotopes surface heat transfer (Boone et al., 2000; Decharme et al., (Braud et al., 2005), and the representation of human im- 2016), soil hydrological processes (Boone et al., 2000; pacts on the hydrological cycle in terms of irrigation (de Ros- Decharme et al., 2011, 2016), and the composite snow- nay et al., 2003) and ground water extraction (Pokhrel et al., pack (Boone and Etchevers, 2001; Decharme et al., 2016). 2015), to name a few. These new schemes have recently been implemented in As a part of the trend in LSM development, there have the operational distributed hydro-meteorological hindcast been ongoing efforts to improve the representation of the system SAFRAN–ISBA–MODCOU (Habets et al., 2008), land surface processes in the Interactions between the soil– Meso-NH, and ARPEGE-climat and ALADIN–HIRLAM biosphere–atmosphere (ISBA) LSM within the EXternalized HARMONIE–AROME and HARMONIE–ALARO Climate SURFace (SURFEX; Masson et al.,2013) model platform. configurations. The representation of vegetation processes in The original two-layer ISBA force–restore model (Noilhan SURFEX has also become much more sophisticated in re- and Planton, 1989) consists in a single bulk soil layer (gen- cent years, including photosynthesis and respiration (Calvet erally having a thickness on the order of 50 cm to sev- et al., 1998), carbon allocation to biomass pools (Calvet and eral meters) coupled to a superficially thin surface compos- Soussana, 2001; Gibelin et al., 2006), and soil carbon cycling ite soil–vegetation–snow layer. Thus, the model simulates (Joetzjer et al., 2015). However, for a number of reasons it fast processes that occur at sub-diurnal timescales, which has also become clear that we have reached the conceptual are pertinent to short-term numerical weather prediction, limits of using of a composite soil–vegetation scheme within and it provides a longer-term water storage reservoir, which ISBA and there is a need to explicitly separate the canopy provides a source for transpiration, a time filter for water vegetation from the soil surface: reaching a hydro-graphic network, and a certain degree of soil moisture memory in the ground amenable to longer- – in order to distinguish the soil, snow, and vegetation term forecasts and climate modeling. Additional modifica- surface temperatures since they can have very differ- tions were made to this scheme over the last decade to in- ent amplitudes and phases in terms of the diurnal cy- clude soil freezing (Boone et al., 2000; Giard and Bazile, cle, and therefore accounting for this distinction facili- 2000), which improved hydrological processes (Mahfouf and tates (at least conceptually) incorporating remote sens- Noilhan, 1996; Boone et al., 1999; Decharme and Douville, ing data, such as satellite-based thermal infrared tem- 2006). This scheme was based on the pioneering work of peratures (e.g., Anderson et al., 1997), into such mod- Deardorff(1977) and it has proven its value for coupled els; land–atmosphere research and applications since its incep- tion. For example, it is currently used for research within – as it has become evident that the only way to simu- the mesoscale non-hydrostatic research model (Meso-NH) late the snowpack beneath forests in a robust and a (Lafore et al., 1998). It is also used within the operational physically consistent manner (i.e., reducing the depen- high-resolution short-term numerical weather prediction at dence of forest snow cover on highly empirical and Météo-France within the limited area model AROME (Seity poorly constrained snow fractional cover parameteriza- et al., 2011) and by HIRLAM countries within the ALADIN– tions) and including certain key processes (i.e., canopy HIRLAM system as the HARMONIE–AROME model con- interception and unloading of snow) is to include a for- figuration (Bengtsson et al., 2017). Finally, it is used for cli- est canopy above or buried by the ground-based snow- mate research within the global climate model (GCM) Ac- pack (e.g., Rutter et al., 2009);

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 845

– for accurately modeling canopy radiative transfer, tional in 2010. In parallel, the dynamic vegetation model within or below canopy turbulent fluxes and soil heat LJP-GUESS was coupled to RCA3 as RCA–GUESS (Smith fluxes; et al., 2011), making it possible to simulate complex biogeophysical feedback mechanisms in climate scenarios. Since – to make a more consistent photosynthesis and carbon al- then RCA–GUESS has been applied over Europe (Wram- location model (including explicit carbon stores for the neby et al., 2010), Africa (Wu et al., 2016), and the Arc- vegetation, litter, and soil in a consistent manner); tic (Zhang et al., 2014). The basic principles developed by – to allow the explicit treatment of a ground litter layer, SMHI have been the foundation since the explicit represen- which has a significant impact on ground heat fluxes and tation of the vegetation was introduced in ISBA and SUR- soil temperatures (and freezing) and, by extension, the FEX, but now in a more general and consistent way. Im- turbulent heat fluxes. plementation of canopy turbulence scheme, longwave radiation transmission function, and snow interception formu- In response to this issue, a collaboration began in 2008 lations in MEB largely follows the implementation used in between the high-resolution limited area model (HIRLAM) RCA3 (Samuelsson et al., 2006, 2011). In addition, we have consortium and Météo-France with the intention to develop taken this opportunity to incorporate several new features an explicit representation of the vegetation in ISBA under the into ISBA-MEB compared to the original SMHI scheme: SURFEX platform. A new parameterization has been developed called the ISBA multi-energy balance (MEB) in order – a snow fraction that can gradually bury the vegetation to account for all of the above issues. vertically thereby transitioning the turbulence coupling MEB is based on the classic two-source model for snow- from the canopy air space directly to the atmosphere free conditions, which considers explicit energy budgets (for (using a fully implicit numerical scheme); computing fluxes) for the soil and the vegetation, and it has – the use of the detailed solar radiation transfer scheme been extended to a three-source model in order to include that is a multi-layer model that considers two spectral an explicit representation of snowpack processes and their bands, direct and diffuse flux components, and the con- interactions with the ground and the vegetation. The vegeta- cept of sunlit and shaded leaves, which was primarily tion canopy is represented using the big-leaf method, which developed to improve the modeling of photosynthesis lumps the entire vegetation canopy into a single effective leaf within ISBA (Carrer et al., 2013); for computing energy budgets and the associated fluxes of heat, moisture, and momentum. One of the first examples of – a more detailed treatment of canopy snow interception a two-source model designed for atmospheric model studies and unloading processes and a coupling with the ISBA is Deardorff(1978), and further refinements to the vegetation physically based multi-layer snow scheme; canopy processes were added in the years that followed leading to fairly sophisticated schemes, which are similar to those – a reformulation of the turbulent exchange coefficients used today (e.g., Sellers et al., 1986). The two-source big-leaf within the canopy air space for stable conditions, such approach has been used extensively within coupled regional as over a snowpack; and global scale land–atmosphere models (Xue et al., 1991; Sellers et al., 1996; Dickinson et al., 1998; Lawrence et al., – a fully implicit Jacobean matrix for the longwave fluxes 2011; Samuelsson et al., 2011). In addition, more recently from multiple surfaces (snow, below-canopy snow-free multi-layer vegetation schemes have also been developed for ground surface, vegetation canopy); application in GCMs (Bonan et al., 2014; Ryder et al., 2016). – all of the energy budgets are numerically implicitly cou- ISBA-MEB has been developed taking the same strat- pled with each other and with the atmosphere using the egy that has been used historically for ISBA: inclusion coupling method adapted from Best et al.(2004), which of the key first-order processes while maintaining a sys- was first proposed by Polcher et al.(1998); tem that has minimal input data requirements and computational cost while being consistent with other aspects of – an explicit forest litter layer model (which also acts ISBA (with the ultimate goal of being used in coupled op- as the below-canopy surface energy budget when litter erational numerical weather forecast and climate models, covers the soil). and spatially distributed monitoring and hydrological modeling systems). In 2008, one of the HIRLAM partners, the This paper is the first of two parts: in part one, the ISBA- Swedish Meteorological and Hydrological Institute (SMHI), MEB model equations, numerical schemes, and theoretical had already developed and applied an explicit representa- background are presented. In part two, a local-scale evalu- tion of the vegetation in the Rossby Centre Regional Cli- ation of the new scheme is presented along with a detailed mate Model (RCA3) used at SMHI (Samuelsson et al., 2006, description of the new forest litter scheme (Napoly et al., 2011). This representation was introduced into the opera- 2016). An overview of the model is given in the next section, tional NWP HIRLAMv7.3 system, which became opera- followed by conclusions. www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 846 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8

2 Model description

SURFEX uses the tile approach for the surface, and separate physics modules are used to compute surface–atmosphere exchange for oceans or seas, lakes, urbanized areas, and the natural land surface (Masson et al., 2013). The ISBA LSM is used for the latter tile, and the land surface is further split into upwards of 12 or 19 patches (refer to Table1), which represent the various land cover and plant functional types. Currently, forests make up eight patches for the 19-class option, and three for the 12-class option. The ISBA-MEB (re- ferred to hereafter simply as MEB) option can be activated for any number of the forest patches. By default, MEB is coupled to the multi-layer soil (ISBA-DF: explicit DiFfu- sion equation for heat and Richard’s equation for soil water flow; Boone et al.,2000; Decharme et al., 2011) and snow (ISBA-ES: multi-layer Explicit Snow processes with 12 layers by default; Boone and Etchevers, 2001, Decharme et al., 2016) schemes. These schemes have been recently updated (Decharme et al., 2016) to include improved physics and in- creased layering (14 soil layers by default). MEB can also be coupled to the simple three-layer soil force–restore (3-L) option (Boone et al., 1999) in order to be compatible with certain applications, which have historically used 3-L, but by Figure 1. A schematic representation of the turbulent aerodynamic default, it is coupled with ISBA-DF since the objective is to resistance, Ra, pathways for ISBA-MEB. The prognostic tempera- move towards a less conceptual LSM. ture, liquid water, and liquid water equivalent variables are shown. A schematic diagram illustrating the various resistance The canopy air diagnostic variables are enclosed by the red-dashed pathways corresponding to the turbulent fluxes for the three circle. The ground-based snowpack is indicated using turquoise, the fully (implicitly) coupled surface energy budgets is shown vegetation canopy is shaded green, and ground layers are colored in Fig.1. The water budget prognostic variables are also dark brown at the surface, fading to white with depth. Atmospheric indicated. Note that the subscripts, which are used to rep- variables (lowest atmospheric model or observed reference level) are indicated using the a subscript. The ground snow fraction, p , resent the different prognostic and diagnostic variables and ng and canopy-snow-cover fraction, p , are indicated. the aerodynamic resistance pathways, are summarized in Ta- nα ble2. The canopy bulk vegetation layer is represented using green, the canopy-intercepted snow and ground-based snowpack are shaded using turquoise, and the ground layers are indicated using dark brown at the surface, which fade to white The surface energy budgets are formulated in terms of with increasing depth. prognostic equations governing the evolutions of the bulk −1 There are six aerodynamic resistance, Ra (s ), pathways vegetation canopy, Tv, the snow-free ground surface (soil or defined as being between (i) the non-snow-buried vegeta- litter), Tg, and the ground-based snowpack, Tn (K). The prog- tion canopy and the canopy air, Ra vg−c, (ii) the non-snow- nostic hydrological variables consist of the liquid soil water buried ground surface (soil or litter) and the canopy air, content, Wg, equivalent water content of ice, Wgf, snow wa- Ra g−c, (iii) the snow surface and the canopy air, Ra n−c, ter equivalent (SWE), Wn, vegetation canopy-intercepted liq- −2 (iv) the ground-based snow-covered part of the canopy and uid water, Wr, and intercepted snow, Wrn (kg m ). The di- the canopy air, Ra vn−c, (v) the canopy air with the overly- agnosed canopy air variables, which are determined implic- ing atmosphere, Ra c−a), and (vi) the ground-based snow sur- itly during the simultaneous solution of the energy budgets, face (directly) with the overlying atmosphere, Ra n−a. Pre- are enclosed within the red-dashed circle and represent the −1 vious papers describing ISBA (Noilhan and Planton, 1989; canopy air specific humidity, qc (kg kg ), air temperature Mahfouf and Noilhan, 1991) expressed heat fluxes using a Tc, and wind speed Vc. The ground surface specific humidity dimensionless heat and mass exchange coefficient, CH; how- is represented by qg. The surface snow cover fraction area is ever, for the new MEB option, it is more convenient to ex- represented by png while the fraction of the canopy buried by −1 press the different fluxes using resistances (s m ), which are the ground-based snowpack is defined as pαn. The snowpack related to the exchange coefficient as Ra = 1/(Va CH), where has Nn layers, while the number of soil layers is defined as Va represents the wind speed at the atmospheric forcing level Ng where k is the vertical index (increasing from 1 at the sur- (indicated by using the subscript a) in m s−1. face downward). The ground and snowpack uppermost layer

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 847

Table 1. Description of the patches for the natural land surface sub-grid tile. The values for the 19-class option are shown in the leftmost three columns, and those for the 12-class option are shown in the rightmost three columns (the name and description are only given if they differ from the 19-class values). MEB can currently be activated for the forest classes: 4–6 (for both the 12- and 19-class options), and 13–17.

Index Name Description Index Name Description 1 NO Bare soil 1 2 ROCK Rock 2 3 SNOW Permanent snow or ice 3 4 TEBD Temperate broad leaf 4 TREE Broad leaf 5 BONE Boreal evergreen needle leaf 5 CONI Evergreen needle leaf 6 TRBE Tropical evergreen broad leaf 6 EVER Evergreen broad leaf 7 C3 C3 crops 7 8 C4 C4 crops 8 9 IRR Irrigated crops 9 10 GRAS Temperate grassland 10 11 TROG Tropical grassland 11 12 PARK Bog, park, garden 12 13 TRBD Tropical broad leaf 14 TEBE Temperate evergreen broad leaf 15 TENE Temperate evergreen needle leaf 16 BOBD Boreal broad leaf 17 BOND Boreal needle leaf 18 BOGR Boreal grassland 19 SHRB Shrubs

temperatures correspond to those used for the surface energy where ahv = 0.2 and the effective canopy base height is set to budget (i.e., k = 1). zhv,min = 2 (m) for forests. The foliage distribution should be reconsidered in further development since literature suggests, 2.1 Snow fractions e.g., Massman(1982), that the foliage is not symmetrically distributed in the crown but skewed upward. Snow is known to have a significant impact on heat conduction fluxes, owing to its relatively high insulating properties. 2.2 Energy budget In addition, it can significantly reduce turbulent transfer owing to reduced surface roughness, and it has a relatively large The coupled energy budget equations for a three-source surface albedo thereby impacting the surface net radiation model can be expressed for a single bulk canopy, a ground- budget. Thus, the parameterization of its areal coverage turns based snowpack, and a underlying ground surface as out to be a critical aspect of LSM modeling of snowpack– atmosphere interactions and sub-surface soil and hydrologi- ∂Tv Cv =Rn v − Hv − LEv + Lf 8v, (4) cal processes. The fractional ground coverage by the snow- ∂t ∂Tg,1 pack is defined as C =1 − p R − H − LE g,1 ∂t ng n g g g p = W /W 0 ≤ p ≤ 1, (1) ng n n,crit ng + + png Ggn τn,Nn SWnet ,n = −2 where currently the default value is Wn,crit 1 (kg m ). − Gg,1 + Lf 8g,1, (5) Note that this is considerably lower than the previous value of ∂Tn,1 10 kg m−2 used in ISBA (Douville et al., 1995), but this value C =R − H − LE − τ SW + ξ n,1 ∂t n n n n n,1 net ,n n,1 has been shown to improve the ground soil temperatures, us- − + ing an explicit snow scheme within ISBA (Brun et al., 2013). Gn,1 Lf 8n,1, (6) The fraction of the vegetation canopy, which is buried by where T , is the uppermost ground (surface soil or litter ground-based snow, is defined as g 1 layer) temperature, Tn,1 is the surface snow temperature, and pnα = Dn − zhv,b / zhv − zhv,b (0 ≤ pnα ≤ 1), (2) Tv is the bulk canopy temperature (K). Note that the subscript 1 indicates the uppermost layer or the base of the layer where D is the total ground-based snowpack depth (m) and n (for fluxes) for the soil and snowpack. All of the following z represents the base of the vegetation canopy (m) (see hvb flux terms are expressed in W m−2. The sensible heat fluxes Fig.2), which is currently defined as are defined between the canopy air space and the vegetation zhvb = ahv zhv − zhv,min (zhvb ≥ 0), (3) Hv, the snow-free ground Hg, and the ground-based snow- www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 848 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8

Table 2. Subscripts used to represent the prognostic and diagnostic variables. In addition, the symbols used to represent the aerodynamic resistance pathways (between the two elements separated by the dash) are also shown (refer also to Fig.1). These symbols are used throughout the text.

Subscript Name Description v Vegetation Bulk canopy layer g Ground Temperature or liquid water (for Ng layers) gf Ground Frozen water (for Ng layers) a Atmosphere At the lowest atmospheric or forcing level c Canopy air space Diagnosed variables n Ground-based snowpack For Nn layers ng Ground-based snowpack Fractional ground snow coverage α n Ground-based snowpack Fractional vegetation snow coverage r Interception reservoir Intercepted rain and snow meltwater rn Interception reservoir Intercepted snow and frozen meltwater or rain vg-c Aerodynamic resistance Non-snow-buried vegetation canopy and canopy air g-c Aerodynamic resistance Non-snow-buried ground surface and canopy air n-c Aerodynamic resistance Snow surface and canopy air vn-c Aerodynamic resistance Ground-based snow-covered canopy and canopy air c-a Aerodynamic resistance Canopy air with overlying atmosphere n-a Aerodynamic resistance Ground-based snow surface and overlying atmosphere

pack Hn. In an analogous fashion to the sensible heat flux, uppermost snowpack layer are represented by 8v, 8g,1, and the latent heat fluxes are defined for the vegetation canopy 8n,1, respectively, and Lf represents the latent heat of fusion −1 Ev, the snow-free ground Eg, and the ground-based snow- (J kg ). The computation of 8g,1 uses the Gibbs free-energy pack En. The net radiation fluxes are defined for the vege- method (Decharme et al., 2016), 8n,1 is based on available tation canopy, ground, and snowpack as Rn v, Rn g, and Rn n, liquid for freezing or cold content for freezing (Boone and respectively. Note that part of the incoming shortwave radia- Etchevers, 2001), and 8v is described herein (see Eq. 83). tion is transmitted through the uppermost snow layer, and this Note that all of the phase change terms are computed as ad- energy loss is expressed as τn,1 SWnet ,n, where τ is the di- justments to the surface temperatures (after the fluxes have mensionless transmission coefficient. The conduction fluxes been computed); therefore, only the energy storage terms are between the uppermost ground layer and the underlying soil modified directly by phase changes for each model time step. and the analogue for the snowpack are defined as Gg,1 and The surface ground, snow, and vegetation effective heat −2 −1 Gn,1, respectively. The conduction flux between the base of capacities, Cg,1, Cv, and Cn,1 (J m K ) are defined, re- the snowpack and the ground surface is defined as Ggn. The spectively, as last term on the right-hand side (RHS) of Eq. (6), ξn,1, represents the effective heating or cooling of a snowpack layer Cg,1 = 1zg,1 cg,1 (7) caused by exchanges in enthalpy between the surface and Cv = Cvb + Ci Wr,n + Cw Wr, (8) sub-surface model layers when the vertical grid is reset (the Cn,1 = Dn,1 cn,1, (9) snow model grid-layer thicknesses vary in time). The ground-based snow fraction is defined as png. Note where Ci and Cw are the specific heat capacities for 3 −1 −1 that certain terms of Eq. (5) are multiplied by png to make solid (2.106 × 10 J kg K ) and liquid water (4.218 × them patch relative (or grid box relative in the case of single- 103 J kg−1 K−1), respectively. The uppermost ground-layer patch mode) since the snow can potentially cover only part of thickness is 1zg,1 (m), and the corresponding heat capac- −3 −1 the patch. Within the snow module itself, the notion of png is ity of this layer is defined as cg 1 (J m K ). The upper- not used (the computations are snow relative). But note that most soil layer ranges between 0.01 and 0.03 m for most when simultaneously solving the coupled equations Eqs. (4)– applications so that the interactions between surface fluxes (6), Eq. (6) must be multiplied by png since again, snow only and fast temperature changes in the surface soil layer can be covers a fraction of the area: further details are given in Ap- represented. There are two options for modeling the ther- pendicesG andI. The formulation for png is described in mal properties of the uppermost ground layer. First, they Sect. 2.1. can be defined using the default ISBA configuration for a The phase change terms (freezing less melting: expressed soil layer with parameters based on soil texture properties, in kg m−2 s−1) for the snow water equivalent intercepted by which can also incorporate the thermal effects of soil or- the vegetation canopy, the uppermost ground layer, and the ganics (Decharme et al., 2016). The second option, which is the default when using MEB, is to model the uppermost

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 849

Figure 2. A schematic sketch illustrating the role of pnα, the fraction of the vegetation canopy, which is buried by ground-based snow. In panel (a), the snow is well below the canopy base, zhvb, resulting in pnα = 0, and the snow has no direct energy exchange with the atmosphere. In panel (b), the canopy is partly buried by snow (0 < pnα < 1) and the snow has energy exchanges with both the canopy air and the atmosphere. In panel (c), the canopy is fully buried by snow (pnα = 1) and the snow has energy exchange only with the atmosphere, whereas the soil and canopy only exchange with the canopy air space (png < 1). Finally, in panel (d), both png = 1 and pnα = 1 so that the only exchanges are between the snow and the atmosphere. ground layer as forest litter. The ground surface in forest etation heat capacity value is limited at 1 × 104 (J m−2 K−1) regions is generally covered by a litter layer consisting of in order to model, in a rather simple fashion, the thermal in- dead leaves and or needles, branches, fruit, and other organic ertia of stems, branches, trunks, etc. The contributions from material. Some LSMs have introduced parameterizations for intercepted snow and rain are incorporated, where Wr,n and −2 litter (Gonzalez-Sosa et al., 1999; Ogée and Brunet, 2002; Wr (kg m ) represent the equivalent liquid water content of Wilson et al., 2012), but the approach can be very differ- intercepted canopy snow and liquid water, respectively. ent from one case to another depending on their complex- The uppermost snow-layer thickness is Dn,1 (m), and the ity. The main goal of this parameterization within MEB is to corresponding heat capacity is represented by cn,1 (Boone account for the generally accepted first-order energetic and and Etchevers, 2001). Note that Dn,1 is limited to values no hydrological effects of litter; this layer is generally accepted larger than several centimeters in order to model a reason- to have a strong insulating effect owing to its particular ther- able thermal inertia (i.e., in order to represent the diurnal cy- mal properties (leading to a relatively low thermal diffusiv- cle) in a fashion analogous to the soil. For more details, see ity), it causes a significant reduction of ground evaporation Decharme et al.(2016). (capillary rise into this layer is negligible), and it constitutes The numerical solution of the surface energy budget, sub- an interception reservoir for liquid water, which can also lose surface soil and snow temperatures, and the implicit numeri- water by evaporation. See Napoly et al.(2016) for a detailed cal coupling with the atmosphere is described in AppendixI. description of this scheme and its impact on the surface energy budget. 2.3 Turbulent fluxes The canopy is characterized by low heat capacity, which means that its temperature responds fast to changes in In this section, the turbulent heat and water vapor fluxes in fluxes. Thus, to realistically simulate diurnal variations in Eqs. (4)–(6) are described. 2 m temperature this effect must be accounted for. Sellers 2.3.1 Sensible heat fluxes et al.(1986) defined the value as being the heat capacity −2 2 −2 of 0.2 kg m of water per unit leaf area index (m m ). The MEB sensible heat fluxes are defined as This results in values on the order of 1 × 104 J m−2 K−1 for (Tv − Tc) forest canopies in general. For local-scale simulations, Cvb Hv =ρa , (10) can be defined based on observational data. In spatially dis- Ra v−c tributed simulations (or when observational data is insuffi- Tg − Tc Hg =ρa , (11) cient), Cvb = 0.2/CV where the vegetation thermal inertia Ra g−c CV is defined as a function of vegetation class by the SUR- (Tn − Tc) (Tn − Ta) FEX default physiographic database ECOCLIMAP (Faroux Hn =ρa (1 − pnα) + pnα , (12) Ra n−c Ra n−a et al., 2013). Note that CV has been determined for the com- (Tc − Ta) posite soil–vegetation scheme, and the factor 0.2 is used to Hc =ρa , (13) reduce this value to be more representative of vegetation and Ra c−a on the order of the value discussed by Sellers et al.(1986). (Tc − Ta) (Tn − Ta) H =ρa 1 − pnα png + pnα png , (14) Numerical tests have shown that using this value, the canopy Ra c−a Ra n−a heat storage is on the order of 10 W m−2 at mid-day for a typ- where ρ represents the lowest atmospheric layer average air ical mid-latitude summer day for a forest. The minimum veg- a density (kg m−3). The sensible heat fluxes appear in the sur- www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 850 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 face energy budget equations (Eqs.4–6). The sensible heat for Tc and using Eq. (15) to determine Tc (see AppendixA flux from the ground-based snowpack (Eq. 12) is partitioned for details). by the fraction of the vegetation, which is buried by the ground-based snowpack pnα, between an exchange between 2.3.2 Water vapor fluxes the canopy air space, and the overlying atmosphere (Eq.2). The heat flux between the overlaying atmosphere and the The MEB water vapor fluxes are expressed as canopy air space is represented by Hc, and it is equivalent (qsat v − qc) Ev =ρa hsv , (17) to the sum of the fluxes between the different energy budgets Ra v−c and the canopy air space. The total flux exchange between the qg − qc overlying atmosphere and the surface (as seen by the atmo- Eg =ρa , (18) sphere) is defined by H. It is comprised of two components: Ra g−c the heat exchange between the overlying atmosphere and the (qsati n − qc) (qsati n − qa) En =ρa hsn (1 − pnα) + pnα , canopy air space and the part of the ground-based snowpack Ra n−c Ra n−a that is burying the vegetation. This method has been devel- (19) oped to model the covering of low vegetation canopies by a (qc − qa) Ec =ρa , (20) ground-based snowpack. Finally, the final fluxes for the given Ra c−a patch are aggregated using png and pnα: the full expressions (qc − qa) E =ρa 1 − pnα png are given in Appendix C1. R − −1 a c a The thermodynamic variable (T : J kg ) is linearly related (qsati n − qa) to temperature as +pnα png hsn . (21) Ra n−a Tx = Bx + Ax Tx, (15) The vapor flux between the canopy air and the overlying atmosphere is represented by Ec, and the total vapor flux ex- where x corresponds to one of the three surface temperatures changed with the overlying atmosphere is defined as E. The (Tg, Tv, or Tn), canopy air temperature, Tc, or the overlying specific humidity (kg kg−1) of the overlying atmosphere is atmospheric temperature, T . The definitions of A and B a x x represented by qa, whereas qsat and qsati represent the spe- depend on the atmospheric variable in the turbulent diffu- cific humidity at saturation over liquid water and ice, respec- sion scheme and are usually defined to cast T in the form tively. For the surface specific humidities at saturation, the of dry static energy, or potential temperature and are deter- convention qsat x = qsat (Tx) is used. The same holds true for mined by the atmospheric model in coupled mode (see Ap- saturation over ice so that qsati n = qsati (Tn). The canopy air pendixA). The total canopy aerodynamic resistance is com- specific humidity qc is diagnosed assuming that Ec is bal- prised of snow buried, Ra vn−c, and non-snow buried, Ra vg−c, anced by the vapor fluxes between the canopy air and each resistances from of the three surfaces considered (the methodology for diag- " #−1 nosing the canopy air thermal properties is described in Ap- (1 − pnα) png 1 − png pendixI, Sect. I3). The effective ground specific humidity is Ra v−c = + . (16) Ra vn−c Ra vg−c defined as q = h q + + h q , The separation of the resistances is done to mainly account g sg sat g (1 a) c (22) for differences in the roughness length between the buried where the humidity factors are defined as and non-covered parts of the vegetation canopy; therefore, Lv Ls the primary effect of snow cover is to increase the resis- hsg =δg hug 1 − pgf + δgf hugf pgf , (23) tance relative to a snow-free surface assuming the same tem- L L perature gradient owing to a lower surface roughness, and Lv Ls ha =δg 1 − pgf + δgf pgf . (24) thus Ra vn−c ≥ Ra vg−c. The formulation also provides a con- L L tinuous transition to the case of vanishing canopy turbulent The latent heats of fusion and vaporization are defined as fluxes as the canopy becomes entirely buried (as p → 1). nα L and L (J kg−1), respectively. The fraction of the surface In this case, the energy budget equations collapse into a sim- s v layer that is frozen, p , is simply defined as the ratio of the ple coupling between the snow surface and the overlying at- gf liquid water equivalent ice content to the total water content. mosphere, and the ground energy budget simply consists in The average latent heat L is essentially a normalization factor heat conduction between the ground surface and the snow- that ranges between L and L as a function of snow cover pack base. The formulations of the resistances between the s v and surface soil ice (see AppendixB). The soil coefficient δ different surfaces and the canopy airspace and the overlying g in Eqs. (23)–(24) is defined as atmosphere are described in detail in Sect. 2.6. The canopy air temperature, which is needed by different physics rou- Ra g−c δg = δgcor, (25) tines, is diagnosed by combining Eqs. (10)–(14) and solving Ra g−c + Rg

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 851 Ra v−c where the soil resistance Rg is defined by Eq. (67). Note that + 1 − png . (28b) the composite version of ISBA did not include an explicit Ra vg−c soil resistance term, and therefore this also represents a new The Halstead coefficients in Eq. (28a) are defined as addition to the model. This term was found to further improve results for bare-soil evaporation within MEB, and its Ra vg−c inclusion is consistent with other similar multi-source mod- hvg = (1 − δ) + δ , (29a) R + R els (e.g., Xue et al., 1991). See Sect. 2.6 for further details. a vg−c s The delta function δ is a numerical correction term that is Ra vn−c gcor ,hvn = (1 − δ) + δ. (29b) required owing to the linearization of qsat g and is unity unless Ra vn−c + Rsn both hug qsat g < qc and qsat g > qc, in which case it is set to zero. The surface ground humidity factor is defined using the The stomatal resistance Rs can be computed using either the standard ISBA formulation from Noilhan and Planton(1989) Jarvis method (Jarvis, 1976) described by Noilhan and Plan- as ton(1989) or a more physically based method that includes a representation of photosynthesis (Calvet et al., 1998). The " !# 1 wg,1 stomatal resistance for the partially snow-buried portion de- hug = 1 − cos ∗ π 0 ≤ hug ≤ 1 . (26) fined as 2 wfc,1 Rsn =Rs/ 1 − min pnα, 1 − Rs/Rs,max In the case of condensation (qsat g < qa), hug = 1 (see Mah- fouf and Noilhan, 1991, for details). The effective field ca- Rsn ≤ Rs,max (30) ∗ pacity wfc,1 is computed relative to the liquid water content of the uppermost soil layer (it is adjusted in the presence of so that the effect of coverage by the snowpack is to increase soil ice compared to the default field capacity). The analo- the canopy resistance. Note that when the canopy is not par- gous form holds for the humidity factor over the frozen part tially or fully buried by ground-based snowpack (pnα = 0) ∗ and does not contain any intercepted snow (p = 0), the of the surface soil layer, hugf, with wg,1 and wfc,1 replaced by nv ∗ 3 −3 leading coefficient for the canopy evapotranspiration simpli- wgf,1 and w (m m ) in Eq. (26), respectively (Boone fcf,1 fies to the Halstead coefficient from the composite version of et al., 2000). Note that it would be more accurate to use qsati ISBA (Mahfouf and Noilhan, 1991) in place of qsat for the sublimation of the canopy-intercepted snow and the soil ice in Eqs. (17)–(18), respectively, but this Ra vg−c complicates the linearization and this has been neglected for hsv = (1 − δ) + δ Ra vg−c + Rs now. The snow factor is defined as hsn = Ls/L. This factor = = can be modified so that En includes both sublimation and (pnα 0 and pnv 0). (31) evaporation (Boone and Etchevers, 2001), but the impact of including a liquid water flux has been found to be negligible; The fraction of the vegetation covered by water is δ and is thus, for simplicity only sublimation is accounted for cur- described in Sect. 2.8.2. rently. The evapotranspiration from the vegetation canopy, Ev, is The leading coefficient for the canopy evapotranspiration comprised of three components: is defined as Ev = Etr + Er + Ern, (32) hsv = (1 − pnv)hsvg (Lv/L) + pnv hsvn (Ls/L), (27) where the transpiration, evaporation from the canopy liquid where pnv is an evaporative efficiency factor that is used to water interception store, and sublimation from the canopy partition the canopy interception storage mass flux between snow interception store are represented by Etr, Er, and Ern, evaporation of liquid water and sublimation (see Eq. 79). respectively. The expressions for these fluxes are given in When part of the vegetation canopy is buried (i.e., pnα > 0), AppendixC. a different roughness is felt by the canopy air space so that a 2.4 Radiative fluxes new resistance is computed over the pnα-covered part of the canopy as is done for sensible heat flux. This is accounted for The R terms in Eqs. (4)–(6) represent the surface net radia- by defining n tion terms (longwave and shortwave components) Ra v−c hsvg =png (1 − pnα) hvn Rn x = SWnet,x + LWnet,x, (33) Ra vn−c Ra v−c where x = n, g, or v. The total net radiation of the surface is + 1 − png hvg, (28a) Ra vg−c R =R + R + R Ra v−c n n n n g n v hsvn =png (1 − pnα) = ↓ − ↑ + ↓ − ↑ Ra vn−c SW SW LW LW , (34) www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 852 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 where the total down-welling solar (shortwave) and atmo- The effective canopy albedo, αv, represents the combined −2 spheric (longwave) radiative fluxes (W m ) at the top of canopy vegetation, αv, and intercepted snow albedos. Cur- the canopy or snow surface (in the case snow is burying rently, however, we assume that αv = αv, which is based the vegetation) are represented by SW ↓ and LW ↓, respec- on recommendations by Pomeroy and Dion(1996). They tively. The total upwelling (towards the atmosphere) short- showed that multiple reflections and scattering of light from wave and longwave radiative fluxes SW ↑ and LW ↑, respec- patches of intercepted snow together with a high probabil- tively, are simply defined as the downward components less ity of reflected light reaching the underside of an overlying the total surface net radiative fluxes (summed over the three branch implied that trees actually act like light traps. Thus, surfaces). The effective total surface albedo and surface ra- they concluded that intercepted snow had no significant influ- diative temperature (and emissivity) can then be diagnosed ence on the shortwave albedo or the net radiative exchange (see the Sect. 2.4.2) for coupling with the host atmospheric of boreal conifer canopies. model. The τn is defined as the solar radiation transmission at In addition to baseline albedo values required by the ra- the base of a snowpack layer, so for a sufficiently thin snow- diative transfer model for each spectral band, the model re- pack, solar energy penetrating the snow to the underlying quires the direct and diffusive downwelling solar compo- ground surface is expressed as τn,Nn SWnet n, where Nn rep- nents. The diffuse fraction can be provided by observations resents the number of modeled snowpack layers (for a deep (offline mode) or a host atmospheric model. For the case snowpack, this term becomes negligible). when no diffuse information is provided to the surface model, the diffuse fraction is computed using the method proposed 2.4.1 Shortwave radiative fluxes by Erbs et al.(1982).

The total land surface shortwave energy budget can be shown 2.4.2 Longwave radiative fluxes to satisfy The longwave radiation scheme is based on a representa- SW ↓= SWnet g + SWnet v + SWnet n + SW ↑, (35) tion of the vegetation canopy as a plane-parallel surface. The model considers one reflection with three reflecting surfaces where SWnet g, SWnet v, and SWnet n represent the net short- (ground, ground-based snowpack, and the vegetation canopy; wave terms for the ground, vegetation canopy, and the a schematic is shown in AppendixE). The total land surface ground-based snowpack. The effective surface albedo (which longwave energy budget can be shown to satisfy may be required by the atmospheric radiation scheme or for comparison with satellite-based data) is diagnosed as LW ↓= LWnet g + LWnet v + LWnet n + LW ↑, (38) where LW , LW , and LW represent the net long- α = SW ↑ /SW ↓ . (36) net g net v net n s wave terms for the ground, vegetation canopy, and the The multi-level transmission computations for direct and ground-based snowpack. The effective surface radiative tem- diffuse radiation are from Carrer et al.(2013). The dis- perature (which may be required by the atmospheric radia- tinction between the visible (VIS) and near-infrared (NIR) tion scheme or for comparison with satellite-based data) is radiation components is important in terms of interactions diagnosed as with the vegetation canopy. Here, we take into account two 1/4 LW ↑ −LW ↓ (1 − s) spectral bands for the soil and the vegetation, where visible Trad = , (39) σ wavelengths range from approximately 0.3 to 0.7 ×10−6 m, s and NIR wavelengths range from approximately 0.7 to where σ is the Stefan–Boltzmann constant, and s represents 1.4 ×10−6 m. The spectral values for the soil and the veg- the effective surface emissivity. In Eq. (39), there are two that etation are provided by ECOCLIMAP (Faroux et al., 2013) are known (LW fluxes) and two that are unknown (Trad and as a function of vegetation type and climate. s). Here we opt to pre-define s in a manner that is consistent The effective all-wavelength ground (below-canopy) with the various surface contributions as albedo is defined as s = png sn + 1 − png sg. (40) αgn = png αn + 1 − png αg, (37) The canopy-absorption-weighted effective snow and ground emissivities are defined, respectively, as where αg represents the ground albedo. The ground-based snow albedo, αn, is prognostic and de- sn =σ n LW v + (1 − σ n LW) n, (41) pends on the snow grain size. It currently includes up to three sg =σ g LW v + 1 − σ g LW g, (42) spectral bands (Decharme et al., 2016); however, when coupled to MEB, only the two aforementioned spectral bands are where v, g, and n represent the emissivities of the vegeta- currently considered for consistency with the vegetation and tion, snow-free ground, and the ground-based snowpack, re- soil. spectively. The ground and vegetation emissivities are given

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 853 by ECOCLIMAP are vary primarily as a function of vege- Decharme et al., 2011). The heat capacities and thermal con- tation class for spatially distributed simulations, or they can ductivities λg for the ground depend on the soil texture, or- be prescribed for local scale studies. The snow emissivity is ganic content (Decharme et al., 2016), and potentially on the currently defined as n = 0.99. The effect of longwave ab- thermal properties of the forest litter in the uppermost layer sorption through the non-snow-buried part of the vegetation (Napoly et al., 2016); all of the aforementioned properties canopy is included as depend on the water content. The snow thermal property parameterization is described in Decharme et al.(2016). σ n LW = 1 − png − pnα 1 − png σLW + png 2.6 Aerodynamic resistances +pnα 1 − png σf LW, (43) σ g LW = 1 − png (1 − pnα) σLW + png (1 − pnα)σf LW, (44) The resistances between the surface and the overlying atmosphere, R − and R − , are based on Louis(1979) modi- where the canopy absorption is defined as a n a a c a fied by Mascart et al.(1995) to account for different roughness length values for heat and momentum as in ISBA: the σLW = 1 − exp(−τLW LAI) = 1 − χv (45) full expressions are given in Noilhan and Mahfouf(1996). and τ represents a longwave radiation transmission fac- LW 2.6.1 Aerodynamic resistance between the bulk tor that can be species (or land classification) dependent, χ v vegetation layer and the canopy air is defined as a vegetation view factor, and LAI represents the 2 −2 leaf area index (m m ). The absorption over the understory The aerodynamic resistance between the vegetation canopy snow-covered fraction of the grid box is modeled quite sim- and the surrounding airspace can be defined as ply from Eq. (45) ∗ −1 Ra vg−c = gav + gav . (50) σf LW = 1 − exp −τLW LAI(1 − pnα) = 1 − exp[−τLW LAIn] (46) The parameterization of the bulk canopy aerodynamic conductance gav between the canopy and the canopy air is based so that transmission is unity (no absorption or reflection by on Choudhury and Monteith(1988). It is defined as the canopy: σ LW = σf LW = 0) when pnα = 1 (i.e., when the canopy has been buried by snow); LAI is used to repre- 2LAIa u 1/2 n = av hv [ − − 0 ] gav 0 1 exp( φv/2) , (51) sent the LAI, which has been reduced owing to burial by φv lw the snowpack. From Eqs. (40)–(44), it can be seen that when there is no snowpack (i.e., png = 0 and pnα = 0), then the ef- where uhv represents the wind speed at the top of the canopy − fective surface emissivity is simply an absorption-weighted (m s 1),and lw represents the leaf width (m: see Table3). soil–vegetation value defined as s = σLW v + (1 − σLW) g. The remaining parameters and their values are defined in Ta- See AppendixE for the derivation of the net longwave radi- ble3. The conductance accounting for the free convection ation terms in Eq. (38). correction from Sellers et al.(1986) is expressed as " # 2.5 Heat conduction fluxes LAIT − T 1/4 g∗ = v c (T ≥ T ). (52) av 890 lw v c The sub-surface snow and ground heat conduction fluxes are modeled using Fourier’s law (G = λ∂T /∂z). The heat con- Note that this correction is only used for unstable conditions. duction fluxes in Eqs. (5)–(6) are written in discrete form as The effect of snow burying the vegetation impacts the aerodynamic resistance of the canopy is simply modeled by mod- 2T − T g,1 g,2 ifying the LAI using Gg,1= = 3g,1 Tg,1 − Tg,2 , 1zg,1/λg,1 + 1zg,2/λg,2 (47) LAIn = LAI(1 − pn α). (53) 2 Tn,1 − Tn,2 Gn,1= = 3n,1 Tn,1 − Tn,2 , (48) The LAI is then used in Eq. (50) to compute R , and D /λ + D /λ n a vn−c n,1 n,1 n,2 n,2 −1 → this resistance is limited to 5000 s m as LAIn 0. 2 Tn,N − Tg,1 G = n = 3 T − T , (49) gn + g,n n,Nn g,1 Dn,Nn /λn,Nn 1zg,1/λg,1 2.6.2 Aerodynamic resistance between the ground and the canopy air where Ggn represents the snow–ground inter-facial heat flux which defines the snow scheme lower boundary condition. The resistance between the ground and the canopy air space All of the internal heat conduction fluxes (k = 2,N − 1) use is defined as the same form as in Eq. (48) for the snow (Boone and Etchev- ers, 2001) and Eq. (47) for the soil (Boone et al., 2000; Rag−c = Rag n/ψH , (54) www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 854 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8

Table 3. Surface vegetation canopy turbulence parameters that are constant.

Symbol Deﬁnition Unit Value Reference Comment −1/2 aav Canopy conductance scale factor m s 0.01 Choudhury and Monteith(1988) Eq. (26) 0 φv Attenuation coeff. for wind – 3 Choudhury and Monteith(1988) p. 386 lw Leaf width m 0.02 φv Attenuation coeff. for mom. – 2 Choudhury and Monteith(1988) p. 386 z0g Roughness of soil surface m 0.007 χL Ross–Goudriaan leaf angle dist. – 0.12 Monteith(1975) p. 26 −1 ul Typical local wind speed m s 1 Sellers et al.(1996) Eq. (B7) υ Kinematic viscos. of air m2 s−1 0.15 × 10−4

where Rag n is the default resistance value for neutral con- The friction velocity at the top of the vegetation canopy is ditions. The stability correction term ψH depends on the defined as canopy structural parameters, wind speed, and temperature k uhv gradient between the surface and the canopy air. The aerody- u∗hv = , (61) ln (zhv − d)/z0v namic resistance is also based on Choudhury and Monteith (1988). It is assumed that the eddy diffusivity K (m2 s−1) in where the wind speed at the top of the canopy is the vegetation layer follows an exponential profile: uhv = fhv Va (62) z and Va represents the wind speed at the reference height K (z) = K (zhv) exp φv 1 − , (55) zhv za above the canopy. The canopy height is defined based on vegetation class and climate within ECOCLIMAP as a where zhv represents the canopy height. Integrating the recip- primary parameter. It can also be defined using an external rocal of the diffusivity defined in Eq. (55) from z0g to d +z0v dataset, such as from a satellite-derived product (as a func- yields tion of space and time). The vegetation roughness length for momentum is then computed as a secondary parameter zhv z0g as a function of the vegetation canopy height. The factor Rag n = exp φv 1 − φv K (zhv) zhv fhv (≤ 1) is a stability-dependent adjustment factor (see Ap- pendixD). d + z0v − exp φv 1 − . (56) The dimensionless height scaling factor is defined as zhv (zhv − d) φz = (φz ≤ 1). (63) The diffusivity at the canopy top is defined as zr The reference height is defined as z = z −d for simulations K (z ) = k u (z − d). (57) r a hv ∗hv hv where the reference height is sufficiently above the top of the vegetation canopy. This is usually the case for local scale The von Karman constant k has a value of 0.4. The displace- studies using observation data. When MEB is coupled to an ment height is defined as Choudhury and Monteith(1988) atmospheric model, however, the lowest model level can be h 1/4i below the canopy height; therefore, for coupled model simu- d = 1.1zhv ln 1 + (cd LAI) , (58) lations zr = max(za, zhv − d + zmin) where zmin = 2 (m). Finally, the stability correction factor from Eq. (54) is de- where the leaf drag coefficient cd,is defined from Sellers et al. fined as (1996) 1/2 ψH = (1 − ahv Ri) (Ri ≤ 0), (64a) 2 1 1.6 1 R c = 1.328 + 0.45 (1 − χ ) , (59) = + i (f − ) d 1/2 L 1/2 1 z0 1 Re π 1 + b Ri(1 + c Ri) Ri,crit Ri > 0 and Ri ≤ Ri,crit , (64b) where χL represents the Ross–Goudriaan leaf angle distribu- f tion function, which has been estimated according to Mon- = z0 R > R , 1/2 i i,crit (64c) teith(1975) (see Table3), and Re is the Reynolds number 1 + b Ri(1 + c Ri) defined as where the Richardson number is defined as u lw −g zhv (Ts − Tc) l R = . Re = . (60) i 2 (65) υ Ts uhv

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 855

Note that strictly speaking, the temperature factor in the de- nominator should be defined as (Ts + Tc)/2, but this has only a minor impact for our purposes. The critical Richardson number, Ri,crit, is set to 0.2. This parameter has been defined assuming that some turbulent exchange is likely always present (even if intermittent), but it is recognized that even- tually a more robust approach should be developed for very stable surface layers (Galperin et al., 2007). The expression for unstable conditions (Eq. 64a) is from Sellers et al.(1996) where the structural parameter is defined as ahv = 9. It is generally accepted that there is a need to improve the parameterization of the exchange coefficient for extremely stable conditions typically encountered over snow (Niu and Yang, 2004; Andreadis et al., 2009). Since the goal here is not to develop a new parameterization, we simply modify the expression for stable conditions by using the standard function Figure 3. Stability correction term is shown using the Sellers for- from ISBA. The standard ISBA stability correction for sta- mulation for Ri ≤ 0 while the function for stable conditions adapted = = ble conditions is given by Eq. (64c), where b 15 and c 5 from ISBA (Ri > 0) for two ratios of z0g/z0gh. The ground surface (Noilhan and Mahfouf, 1996). The factor that takes into ac- roughness length is defined in Table3. count differing roughness lengths for heat and momentum is defined as currently these values are used, in part, since the litter for- ln zhv/z0g fz0 = , (66) mulation is the default configuration for MEB for forests as ln zhv/z0gh it generally gives better surface fluxes (Napoly et al., 2016). where z is the ground roughness length for scalars. The 0gh 2.7 Water budget weighting function (i.e., ratio of Ri to Ri,crit) in Eq. (64b) is = used in order to avoid a discontinuity at Ri 0 (the rough- The governing equations for (water) mass for the bulk = ness length factor effect vanishes at Ri 0) in Eq. (64c). An canopy, and surface snow and ground layers are written as example of Eq. 64c is shown in Fig.3 using the z0g from Ta- ble3, and for z0gh/z0g of 0.1 and 1.0. Finally, the resistance ∂Wr = Prv + max(0, −Etr) − Er − Drv − 8v, (68) between the ground-based snowpack Ra n−c and the canopy ∂t air use the same expressions as for the aerodynamic resis- ∂W r n = I − U − E + 8 (69) tance between the ground and the canopy air outlined herein, ∂t n n rn v but with the surface properties of the snowpack (namely the ∂W p n,1 = P − I + U + p roughness length and snow surface temperature). ng ∂t s n n ng − + − − + + 2.6.3 Ground resistance Pr Prv Drv Fnl,1 En 8n,1 ξnl,1 , (70) ∂wg,1 ρ 1z = P − P + D − E 1 − p The soil resistance term is defined based on Sellers et al. w g,1 ∂t r rv rv g ng (1992) as + − − − png Fnl,Nn R0 Fg,1 8g,1, (71) R = exp a − b w /w . (67) ∂wgf,1 g Rg Rg g sat ρ 1z = 8 − E 1 − p , (72) w g,1 ∂t g,1 gf ng The coefficients are aRg = 8.206 and bRg = 4.255, and the vertically averaged volumetric water content and saturated where Wr and Wr n represent the vegetation canopy wa- volumetric water content are given by wg and wsat, respec- ter stores (intercepted water) and the intercepted snow and −2 tively. The averaging is done from one to several upper lay- frozen water (all in kg m ), respectively. Wn,1 represents the ers. Indeed, the inclusion of an explicit ground surface energy snow liquid water equivalent (SWE) for the uppermost snow budget makes it more conceptually straightforward to include layer of the multi-layer scheme. The soil liquid water content a ground resistance compared to the original composite soil– and water content equivalent of frozen water are defined as 3 −3 vegetation surface. The ground resistance is often used as a wg and wgf, respectively (m m ). surrogate for an additional resistance arising due to a forest The interception reservoir Wr is modeled as single-layer litter layer, therefore the soil resistance is set to zero when bucket, with losses represented by evaporation Er, and the litter-layer option is activated. Finally, the coefficients canopy drip Drv of liquid water that exceeds a maximum aRg and bRg were determined from a case study for a spe- holding capacity (see Sect. 2.8.2 for details). Sources include cific location, and could possibly be location dependent. But condensation (negative Er and Etr) and Prv, which repre- www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 856 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 sents the intercepted precipitation. The positive part of Etr as is extracted from the sub-surface soil layers as a function of ∗ soil moisture and a prescribed vertical root zone distribution In,v,0 = Wr n − Wr n 1 − exp −kn,v Ps 1t , (73) (Decharme et al., 2016). This equation is the same as that where W ∗ is the maximum snow load allowed, P the used in ISBA, except for the addition of the phase change r n s frozen precipitation rate, and k a proportionality factor. term, 8 (kg m−2 s−1). This term has been introduced ow- n,v v k is a function of W ∗ and the maximum plan area of ing to the introduction of an explicit canopy snow intercep- n,v r n the snow–leaf contact area per unit area of ground Cn,vp: tion reservoir Wr n; the canopy snow and liquid water reser- voirs can exchange mass via this term which is modeled as Cn,vp melt less freezing. The remaining rainfall (P − P ) is parti- kn,v = . (74) r rv W ∗ tioned between the snow-free and snow-covered ground sur- r n face, where Pr represents the total grid cell rainfall rate. The For a closed canopy, Cn,vp would be equal to one, but for canopy snow interception is more complex, and represents a partly open canopy it is described by the relationship certain baseline processes such as snow interception In and Cn,vc unloading Un; see Sect. 2.8.1 for details. Cn,vp = , (75) The soil water and snow liquid water vertical fluxes at 1 − Cc uhv zhv/(wn Jn) the base of the surface ground and snow are represented, re- where Cn,vc is the canopy coverage per unit area of ground spectively, by Fg,1 using Darcy’s Law and by Fnl,1 using a which can be expressed as 1 − χv where χv is the sky-view tipping-bucket scheme (kg m−2 s−1). The liquid water flux factor (see Eq. 45), and uhv represents the mean horizontal at the base of the snowpack F is directed downward into nl,Nn wind speed at the canopy top (Eq. 62), which corresponds the soil and consists in the liquid water in excess of the low- to the height zhv (m). The characteristic vertical snow-flake est model liquid water-holding capacity. A description of the −1 velocity, wn, is set to 0.8 m s (Isymov, 1971). Jn is set to snow and soil schemes are given in (Boone and Etchevers, 103 m, which is assumed to represent the typical size of the 2001) and (Decharme et al., 2011), respectively. R0 is the mean forested down wind distance. surface runoff. It accounts for sub-grid heterogeneity of pre- For calm conditions and completely vertically falling cipitation, soil moisture, and for when potential infiltration snowflakes, Cn,vp = Cc. For any existing wind, snow could exceeds a maximum rate (Decharme and Douville, 2006). be intercepted by the surrounding trees so that high wind The soil liquid water equivalent ice content can have some speed increases interception efficiency. Generally for open losses owing to sublimation in the uppermost soil layer Egf boreal conifer canopies, Cn,vc < Cn,vp < 1. Under normal but it mainly evolves owing to phase changes from soil water wind speed conditions (i.e., wind speeds larger than 1 m s−1), freeze–thaw 8g. The remaining symbols in Eqs. (68)–(69) Cn,vc (and Cn,vp) values are usually close to unity. are defined and described in Sect. 2.8.2 and 2.8.1. ∗ The maximum allowed canopy snow load, Wr n , is a function of the maximum snow load per unit branch area, Sn,v 2.8 Precipitation interception (kg m−2), and the leaf area index:

W ∗ = S LAI (76) 2.8.1 Canopy snow interception r n n,v

where Sn,v is defined as The intercepted snow mass budget is described by Eq. (69), 46 while the energy budget is included as a part of the bulk Sn,v = Sn,v 0.27 + . (77) canopy prognostic equation (Eq.4). The positive mass con- ρn,v tributions acting to increase intercepted snow on canopy are Based on measurements, Schmidt and Gluns(1991) esti- snowfall interception I , water on canopy that freezes 8 < n v mated average values for S of 6.6 for pine and 5.9 kg m−2 0, and sublimation of water vapor to ice E < 0. Unload- n,v rn for spruce trees. Because the average value for this param- ing U , sublimation E > 0, and snowmelt 8 > 0, are the n rn v eter only varies by about 10 % across these two fairly com- sinks. All of the terms are in kg m−2 s−1. It is assumed that mon tree species, and ECOCLIMAP does not currently make intercepted rain and snow can co-exist on the canopy. The a clear distinction between these two forest classes, we cur- intercepted snow is assumed to have the same temperature as rently use 6.3 as the default value for all forest classes. ρ is the canopy T ; thus, there is no advective heat exchange with n,v v the canopy snow density (kg m−3) defined by the relationship the atmosphere that simplifies the equations. For simplicity, when intercepted water on the canopy freezes, it is assumed ρn,v = 67.92 + 51.25exp (Tc − Tf)/2.59 (Tc ≤ Tc max), (78) to become part of the intercepted snow. The parameterization of interception efficiency is based where Tc is the canopy air temperature and Tc max is the tem- upon Hedstrom and Pomeroy(1998). It determines how perature corresponding to the maximum snow density. As- much snow is intercepted during the time step and is defined suming a maximum snow density of 750 kg m−3 and solving

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 857

Eq. (78) for canopy temperature yields Tc max = 279.854 K. change timescale is τ8 (s). If it is assumed that the available −2 This gives values of Sn,v in the range 4–6 kg m . heating during the time step for phase change is proportional The water vapor flux between the intercepted canopy snow to canopy biomass via the LAI then Eq. (82) can be written and the canopy air Ern (Eq. C6), includes the evaporative ef- (for both melt and refreezing) as ficiency pnv. This effect was first described by Nakai et al. (1999). In the ISBA-MEB parameterization, the formulation 8v = Snv k8v (Tf − Tv). (83) is slightly modified so that it approaches zero when there is no intercepted snow load: Note that if energy is available for melting, the phase change rate is limited by the amount of intercepted snow, and like- 0.3 0.89Snv wise freezing is limited by the amount of intercepted liquid pnv = , (79) 1 + exp[−4.7(Snv − 0.45)] water. The melting of intercepted snow within the canopy can be quite complex, thus currently the simple approach in where Snv is the ratio of snow-covered area on the canopy to Eq. (83) adopted herein. The phase change coefficient was −6 −2 −1 −1 the total canopy area tuned to a value of k8v = 5.56 × 10 kg m s K for the SNOWMIP2 experiments with the RCA-LSM. Currently, Wr n Snv = ∗ (0 ≤ Snv ≤ 1). (80) this value is the default for ISBA-MEB. Wr n A numerical test is performed to determine if the canopy 2.8.2 Canopy rain interception snow becomes less than zero within one time step due to The rain intercepted by the vegetation is available for poten- sublimation. If this is true, then the required mass is removed tial evaporation, which means that it has a strong influence from the underlying snowpack so that the intercepted snow on the fluxes of heat and consequently also on the surface becomes exactly zero during the time step to ensure a high temperature. The rate of change of intercepted water on veg- degree of mass conservation. Note that this adjustment is etation canopy is described by Eq. (68). The rate that water generally negligible. is intercepted by the overstory (which is not buried by the The intercepted snow unloading, due to processes such as ground-based snow) is defined as wind and branch bending, has to be estimated. Hedstrom and Pomeroy(1998) suggested an experimentally verified expo- P = P (1 − χ ) 1 − p p , (84) nential decay in load over time t, which is used in the param- rv r v ng αn eterization: where χv is a view factor indicating how much of the precipitation that should fall directly to the ground (see Eq. 45). Un,v = In,v,0 exp(−UnLt) = In,v,0 cnL, (81) The overstory canopy drip rate Drv is defined simply as the −1 value of water in the reservoir which exceeds the maximum where UnL is an unloading rate coefficient (s ) and cnL the dimensionless unloading coefficient. Hedstrom and Pomeroy holding capacity: (1998) found that cnL = 0.678 was a good approximation Drv = max 0,Wrv − Wrv,max /1t, (85) that, with a time step of 15 min, gives UnL = −4.498 × 10−6 s−1. A tuned value for the RCA-LSM from the Snow where the maximum liquid water-holding capacity is defined Model Intercomparison Project phase 2 (SnowMIP2) exper- −6 −1 simply as iments (Rutter et al., 2009) is UnL = −3.4254 × 10 s , which has been adopted for MEB for now. All unloaded snow W = c LAI. (86) is assumed to fall to the ground where it is added to the snow rv,max wrv storage on forest ground. Further, corrections to compensate Generally speaking, cwrv = 0.2 (Dickinson, 1984), al- for changes in the original LSM due to this new parameter- though it can be modified slightly for certain vegetation ization have been made for heat capacity, latent heat of va- cover. Note that Eq. (68) is first evaluated with Drv = 0, and porization, evapotranspiration, snow storages, and fluxes of then the canopy drip is computed as a residual. Thus, the fi- latent heat. nal water amount is corrected by removing the canopy drip Finally, canopy snow will partly melt if the temperature or throughfall. This water can then become a liquid water rises above the melting point and become intercepted water, source for the soil and the ground-based snowpack. where the intercepted (liquid and frozen) water phase change The fraction of the vegetation covered with water is de- is simply proportional to the temperature: fined as ∗ Ci Wr n Ci Snv Wr n 2/3 8v = (Tf − Tv) = (Tf − Tv), (82) Wr Lf τ8 Lf τ8 δv = (1 − ωrv) Wr,max where 8v < 0 signifies melting. Tf represents the melting ω W + rv r . (87) point temperature (273.15 K) and the characteristic phase (1 + arv LAI)Wr,max − arv Wr www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 858 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8

Delire et al.(1997) used the first term on the RHS of Eq. (87) feature that permits a coupling transition of the snowpack for relatively low vegetation (Deardorff, 1978) and the sec- from the canopy air to the free atmosphere as a function of ond term for tall vegetation (Manzi and Planton, 1994). Cur- snow depth and canopy height using a fully implicit numer- rently in ISBA, a weighting function is used which intro- ical scheme. MEB has been developed in order to meet the duces the vegetation height dependence using the roughness criteria associated with computational efficiency, high cod- length as a proxy from ing standards (especially in terms of modularity), conservation (of mass, energy, and momentum), numerical stability ωrv = 2z0v − 1 (0 ≤ ωrv ≤ 1), (88) for large (time step) scale applications, and state-of-the-art representation of the key land surface processes required for where the current value for the dimensionless coefficient is current hydrological and meteorological modeling research arv = 2. and operational applications at Météo-France and within the international community as a part of the HIRLAM consor- 2.8.3 Halstead coefficient tium. This includes regional scale real-time hindcast hydrometeorological modeling, coupling within both research and In the case of wet vegetation, the total plant evapotranspira- operational non-hydrostatic models, regional climate mod- tion is partitioned between the evaporation of intercepted wa- els, and a global climate model, not to mention being used ter, and transpiration via stomata by the Halstead coefficient. for ongoing offline land surface reanalysis projects and fun- In MEB, two such coefficients are used for the non-snow- damental research applications. buried and buried parts of the vegetation canopy, h and h vg vn The simple composite soil–vegetation surface energy bud- (Eqs. 29a and 29b, respectively). In MEB, the general form get approach of ISBA has proven its ability to provide solid of the Halstead coefficient, as defined in Noilhan and Planton scientific results and realistic boundary conditions for hy- (1989), is modified by introducing the factor k to take into v drological and meteorological models since its creation over account the fact that saturated vegetation can transpire, i.e., 2 decades ago. However, owing to the ever increasing de- when δ = 1 (Bringfelt et al., 2001). Thus, for MEB we de- v mands of the user community, it was decided to improve fine δ = k δ . The intercepted water forms full spheres just v v the representation of the vegetation processes as a priority. touching the vegetation surface when k = 0, which allows v The key motivation of the MEB development was to move for full transpiration from the whole leaf surface. In contrast, away from the composite scheme in order to address cer- k = 1 would represent a situation where a water film covers v tain known issues (such as excessive bare-soil evaporation the vegetation completely and no transpiration is allowed. To in forested areas, the neglect of canopy snow interception adhere to the interception model as described above, where processes), to improve consistency in terms of the represen- the intercepted water exists as droplets, we set the value of tation of the carbon cycle (by modeling explicit vegetation k to 0.25. Note that in the case of condensation, i.e., E < 0, v energy and carbon exchanges), to add new key explicit pro- h = 1. v cesses (forest litter, the gradual covering of vegetation by Without a limitation of h and h , the evaporative de- vg vn ground-based snow cover), and to open the door to potential mand could exceed the available intercepted water during a improvements in land data assimilation (by representing dis- time step, especially for the canopy vegetation which experi- tinct surface temperatures for soil and vegetation). Finally, ences a relatively low aerodynamic resistance. To avoid such note that while some LSMs intended for GCMs now use a situation, a maximum value of the Halstead coefficient is multiple-vegetation layers, a single bulk vegetation layer is imposed by calculating a maximum value of the δ . See Ap- v currently used in MEB since it has been considered as a rea- pendixF for details. sonable first increase in complexity level from the composite soil–vegetation scheme. However, MEB has been designed 3 Conclusions such that the addition of more canopy layers could be added if deemed necessary in the future. This paper presents the description of a new multi-energy This is part one of two companion papers describing the balance (MEB) scheme for representing tall vegetation in the model formulation of ISBA-MEB. Part two describes the ISBA land surface model component of the SURFEX land– model evaluation at the local scale for several contrasting atmosphere coupling and driving platform. This effort is part well-instrumented sites in France, and for over 42 sites en- of the ongoing effort within the international scientific com- compassing a wide range of climate conditions for several munity to continually improve the representation of land sur- different forest classes over multiple annual cycles (Napoly face processes for hydrological and meteorological research et al., 2016). This two-part series of papers will be followed and applications. by a series of papers in upcoming years that will present the MEB consists in a fully implicit numerical coupling be- evaluation and analysis of ISBA-MEB with a specific focus tween a multi-layer physically based snowpack model, a (coupling with snow processes, regional to global scale hy- variable-layer soil scheme, an explicit litter layer, a bulk drology, and finally fully coupled runs in a climate model). vegetation scheme, and the atmosphere. It also includes a

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 859

4 Code availability

The MEB code is a part of the ISBA LSM and is available as open source via the surface modeling platform called SURFEX, which can be downloaded at http://www. cnrm-game-meteo.fr/surfex/. SURFEX is updated at a relatively low frequency (every 3 to 6 months) and the devel- opments presented in this paper are available starting with SURFEX version 8.0. If more frequent updates are needed, or if what is required is not in Open-SURFEX (DrHOOK, FA/LFI formats, GAUSSIAN grid), you are invited to follow the procedure to get a SVN account and to access real-time modiﬁcations of the code (see the instructions at the previous link).

www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 860 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8

Appendix A: Thermodynamic coupling variable Appendix C: Turbulent ﬂux expressions

If potential temperature is used as the thermodynamic vari- The turbulent fluxes of heat and water vapor can be further able in the coupled model diffusion scheme, then the thermo- decomposed into different components, which are required dynamic variable T (J kg−1; see Eqs. 10–14) coefficients are for computing different diagnostics and coupling with the defined as water budgets. They are presented herein.

Bx =0 (x = v,g,n,c,a), (A1) C1 Sensible heat flux Ax =Cp/5s (x = v,g,n,c), (A2) It is convenient to split H into two components since one A =C /5 , (A3) n a p a governs the coupling between the canopy air space and where 5 is the non-dimensional Exner function and Cp is the snow surface, while the other modulates the exchanges the heat capacity of dry air (J kg−1 K−1). If the atmospheric with the overlying atmosphere (as the canopy layer becomes variable being diffused is dry static energy then buried). The ground-based snowpack heat flux, Hn (Eq. 12), can Bx =0 (x = v,g,n,c), (A4) be split into a part that modulates the heat exchange with Ba =g za, (A5) the canopy air space, Hn−c and the other part which controls the exchanges directly with the overlying atmosphere, Hn−a, Ax =Cp (x = v,g,n,c,a), (A6) defined as where za is the height (m) of the simulated or observed over- (Tn − Tc) lying atmospheric temperature, Ta and g is the gravitational Hn−c =ρa , (C1) constant. The choice of the atmospheric thermodynamic vari- Ra n−c able is transparent to ISBA-MEB (it is made within the (Tn − Ta) Hn−a =ρa . (C2) surface–atmosphere coupler). The default (in offline mode Ra n−a and in inline mode with certain atmospheric models) is us- T is diagnosed by imposing conservation of the heat fluxes ing Eqs. (A1)–(A3). Note that the method can be extended to c between the surface and the canopy air (as described in Ap- use the actual air heat capacity (including water vapor) if a pendixI). Using the definition in Eq. (C2), the total sensible linearization of the heat capacity is used. heat flux exchange with the atmosphere (Eq. 14) can also be written in more compact form as Appendix B: Latent heat normalization factor H = ρa 1 − png pnα Hc + png pnα Hn−a . (C3) The L is a normalization factor (Lv ≤ L ≤ Ls), which could be determined in a number of ways. This coefficient ensures C2 Water vapor flux conservation of mass between the different surfaces and the The various water vapor flux terms must be broken into dif- atmosphere. ferent components for use within the different water balance One possible method is to diagnose it by inverting the equations for the vegetation, soil, and snowpack. Using the equation for LE (multiplying Eq. 20 by L thereby elimi- c definitions in Eqs. (27)–(29b), the components of the canopy nating it from the RHS of this equation, and then solving evapotranspiration E can be expressed as for L), but the resulting equation is difficult to apply since v the terms can be either positive or negative, and division by a small number is possible. Here, a more smooth (in time) L E = ρ v (q − q ) function is proposed, which accounts for each of the surfaces tr a L sat v c weighted by its respective fraction: png (1 − pnα) 1 − png + (1 − pnv)(1 − δ), aLs Ls + aLv Lv R + R R + R L = , (B1) a vn−c sn a vg−c s aLs + aLv (C4) L where E = ρ v (q − q ) r a L sat v c = − + − − − aLv σf (1 pnv) 1 png 1 pgf 1 pngpnα , (B2) png (1 − pnα) 1 − png + (1 − p ) δ , (C5) aL = σf pnv + 1 − png pgf + png 1 − pngpnα nv s Ra vn−c Ra vg−c + pngpnα. (B3) Ls Ern = ρa (qsat v − qc) In the limit as the snow totally buries the canopy vegetation, L L → L . In contrast, for snow and surface ice-free condi- p (1 − p ) 1 − p s ng nα + ng = pnv. (C6) tions, L Lv. Ra vn−c Ra vg−c

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 861

The complex resistances (bracketed terms in Eqs. C4–C6) arise owing to the inclusion of the effects of burying the snow canopy by the ground-based snowpack. If the ground-based snowpack is not sufficiently deep to bury any of the canopy (pnα = 0), then the bracketed term in Eq. (C4) simplifies to 1/ Ra vg−c + Rs (note that Ra vg−c = Ra v−c when pnα = 0 from Eq. 16), and likewise the bracketed terms in Eqs. (C5)– (C6) simplify to 1/Ra vg−c. Finally, the partitioning between the vapor fluxes from intercepted snow and the snow-free canopy reservoir and transpiration is done using pnv, which represents the fraction of the snow interception reservoir that is filled (see Eq. 79). Using the definitions of qg from Eq. (22) together with those for the humidity factors, hsg and ha (Eqs. 23 and 24, respectively) and the soil coefficient, δg (Eq. 25), the bare- Figure E1. Simple schematic for longwave radiation transfer for soil evaporation Eg components can be expressed as one reflection and up to three emitting surfaces (in addition to the down-welling atmospheric flux). Hollow arrows indicate fluxes af- Lv δgcor ter one reflection. Egl= ρa hug qsat g − qc 1 − pgf , (C7) L Ra g + Rg L δgfcor E = ρ s h q − q p , (C8) where the Richardson number R is defined in Eq. (65). The gf a ugf sat g c + gf i L Ra g Rgf coefficients are defined as where Eg = Egl + Egf. The delta function, δgfcor, is a nu- k merical correction term, which is required owing to the lin- Cv,N =ln 1 + φz exp √ − 1 , (D2) C q h q < q DN earization of sat g and is unity unless both ugf sat g c and q > q , in which case it is set to zero. Note that the ground k k sat g c Cv,S = − φz √ − √ , (D3) resistances, Rg and Rgf, are set to zero if the forest litter op- CDN CD tion is active (the default for forests). k k Cv,U = − ln 1 + φz exp √ − √ − 1 , (D4) The ground-based snowpack sublimation, En (Eq. 19), can CDN CD be partitioned into a vapor exchange with the canopy air space, En−c and the overlying atmosphere, En−a, as where the drag coefficient CD and the drag coefficient for neutral conditions CDN are computed between the canopy Ls qsati n − qc En−c = ρa , (C9) air space and the free atmosphere above using the standard L Ra n−c ISBA surface-layer transfer functions (Noilhan and Mahfouf, Ls qsati n − qa 1996). En−a = ρa . (C10) L Ra n−a The corresponding latent heat fluxes can be determined by Appendix E: Longwave radiative flux expressions simply multiplying Eqs. (C4)–(C8) by L. Finally, using the definition in Eq. (C10), the total vapor exchange with the at- The complete expression for the vegetation canopy net long- mosphere (Eq. 21) can also be written in more compact form wave radiation with an infinite number of reflections can as be expressed as a series expansion (e.g., Braud, 2000) as a function of the temperatures of the emitting surfaces (Tv, E = ρa 1 − png pnα Ec + png pnα En−a . (C11) Tg,1, Tn,1), their respective emissivities (v, g and n) and the canopy longwave absorption function, σLW (Eq. 45). The MEB expressions are derived by explicitly expanding the se- Appendix D: Canopy-top wind stability factor ries and assuming one reflection from each emitting source, which is a good approximation since emissivities are gener- The expressions for the stability factor fhv (Eq. 62), which is ally close to unity (fluxes from a single reflection are propor- used to compute the wind at the top of the vegetation canopy tional to 1 − x where x represents g, v, or n, and is close uhv, are taken from Samuelsson et al.(2006, 2011). They are to unity for most natural surfaces). defined as Snow is considered to be intercepted by the vegetation p canopy and to accumulate on the ground below. The cor- f =C + C C /k (R > 0), (D1a) hv v,N v,S D i responding schematic of the radiative transfer is shown in p = Cv,N + Cv,U CD /k (Ri ≤ 0), (D1b) Fig. E1. The canopy-intercepted snow is treated using a www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 862 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 composite approach so that the canopy temperature Tv rep- defined as resents the effective temperature of the canopy-intercepted 0 = − 0 + 0 snow composite. The canopy emissivity is therefore simply σLW 1 png σLW png σf LW. (E4) defined as The factor, σf LW, over the understory snow-covered fraction v = (1 − pnv)v + pnv n. (E1) of the grid box is modeled quite simply from Eq. (46). The net longwave radiation for the understory, snowpack, and In order to facilitate the use of a distinct multi-layer snow- vegetation canopy are therefore defined, respectively, as process scheme, we split the fluxes between those interacting = + + + − − − with the snowpack and the snow-free ground. The expres- LWnet g Cg Fg Jg Jn Dg Gg Ig, (E5a) sions for the snow-free surface are LWnet n =Cn + Fn + Kn + Kg − Dn − Gn − In, (E5b) = + + + + + + LWnet v Ag Dg Gg Ig An Dn Gn Ag = LW ↓ 1 − png , (E2a) + In − Bg − Cg − Eg − Hg − 2Fg Bg = Ag σLW (1 − v), (E2b) − Jg − Lg − Kg − Bn − Cn − En C = A (1 − σ ), (E2c) g g LW − H − 2F − J − L − K , (E5c) n n n n n Dg = Cg 1 − g , (E2d) 0 where the upwelling longwave radiation is computed from Eg = Dg 1 − σLW , (E2e) 0 4 ↑= ↓ − − − Fg = σLW σ v Tv 1 − png , (E2f) LW LW LWnet g LWnet n LWnet v. (E6) Gg = Fg 1 − g , (E2g) The inclusion of the snow-buried canopy fraction in 0 Hg = Gg 1 − σLW , (E2h) Eqs. (E2m) and (E3m) causes all of the vegetation transmission and below canopy fluxes to vanish as p and p → 0 I = σ T 4 1 − p , (E2i) ng nα g g g ng so that the only longwave radiative exchanges occur between 0 0 the atmosphere and the snowpack in this limit. Jg = Ig σLW (1 − v) 1 − png , (E2j) 0 0 Kg = Ig σLW (1 − v) png, (E2k) E1 Net longwave radiation flux derivatives L = I 1 − σ 0 , (E2l) g g LW The first-order derivatives of the net longwave radiation 0 = − png png (1 pnα), (E2m) terms are needed in order to solve the system of linearized surface energy budget equations (Eqs. I1–I3). The Taylor se- and the equations for the snow-covered understory fraction ries expansion (neglecting higher-order terms) is expressed are as

An = LW ↓ png, (E3a) Nseb + X ∂Lnet i + LW =LWnet i + T − Tj Bn = An σf LW (1 − v), (E3b) net i ∂T j j=1 j Cn = An (1 − σf LW), (E3c) (i = 1,Nseb), (E7) Dn = Cn (1 − n), (E3d) 0 where Nseb represents the number of surface energy budgets, En = Dn 1 − σLW , (E3e) and i and j represent the indexes for each energy budget. The = 4 Fn σ f LW σ v Tv png, (E3f) superscript + represents the variable at time t +1t, while by Gn = Fn (1 − n), (E3g) default, no superscript represents the value at time t. Equa- 0 tion (E7) therefore results in a N × N Jacobian matrix Hn = Gn 1 − σ , (E3h) seb seb LW × 4 (3 3 for MEB). The matrix coefﬁcients are expressed as In = σ n Tn png, (E3i) ∂LW ∂G ∂H ∂F ∂G ∂H 0 00 net v = g − g − g + n − n Jn = In σLW (1 − v) 1 − png , (E3j) 2 ∂Tv ∂Tv ∂Tv ∂Tv ∂Tv ∂Tv K = I σ 0 (1 − ) p00 , (E3k) ∂F n n LW v ng − 2 n , (E8a) 0 ∂Tv Ln = In 1 − σLW , (E3l) 00 ∂LWnet v ∂Ig ∂Jg ∂Kg ∂Lg png = png + pnα 1 − png , (E3m) = − − − , (E8b) ∂Tg ∂Tg ∂Tg ∂Tg ∂Tg where the different terms are indicated in Fig. E1. In MEB, ∂LWnet v ∂In ∂Jn ∂Kn ∂Ln = − − − , (E8c) the ground-based snowpack depth can increase to the point ∂Tn ∂Tn ∂Tn ∂Tn ∂Tn that it buries the canopy; thus, for both the snow-covered and ∂LWnet g ∂Fg ∂Gg snow-free understory fractions a modiﬁed snow fraction is = − , (E8d) ∂Tv ∂Tv ∂Tv

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 863

∂LW ∂J ∂I (1 − χv) 1 − pngpαn Pr + (Wrv/1t) (L/Lv) net g g g . = − , (E8e) n o ∂Tg ∂Tg ∂Tg ρa (1 − pnv)kv png (1 − pαn)/Ravn−c + 1 − png /Ravg−c (qsat v − qc) ∂LWnet g ∂J = n , (E8f) Equation (F2) is an approximation since all of the variables ∂Tn ∂Tn on the RHS use conditions from the start of the time step; ∂LW ∂F ∂G net n = n − n , (E8g) however, this method has proven to greatly reduce the risk ∂Tv ∂Tv ∂Tv for occasional numerical artifacts (jumps) and the associated ∂LWnet n ∂Kg need for mass corrections (if net losses in mass exceed the = , (E8h) ∂Tg ∂Tg updated test value for interception storage). ∂LW ∂J ∂I net n = n − n . (E8i) ∂Tn ∂Tn ∂Tn Appendix G: Energy and mass conservation Using Eq. (E5) to evaluate the derivatives we have G1 Energy conservation ∂LWnet v 4 = Gg − Hg − 2Fg + Gn − Hn − 2Fn , (E9a) ∂Tv Tv The soil and snowpack prognostic temperature equations can ∂LWnet v 4 be written in flux form for k = 1,Ng soil layers and k = 1,Nn = Ig − Jg − Kg − Lg , (E9b) ∂Tg Tg snow layers as ∂LW 4 net v = (I − J − K − L ), (E9c) ∂Tg,k n n n n Cg,k = Gg,k−1 − Gg,k + Lf 8g,k, (G1) ∂Tn Tn ∂t ∂LW 4 net g = − ∂Tn,k Fg Gg , (E9d) Cn,k = Gn,k−1 − Gn,k + Lf 8n,k + ξn,k−1 ∂Tv Tv ∂t ∂LWnet g 4 − ξn,k + SWnet ,n τn,k−1 − τn,k . (G2) = Jg − Ig , (E9e) ∂Tg Tg The total energy balance of the vegetation canopy–soil– ∂LWnet g 4 = Jn, (E9f) snowpack system is conserved at each time step 1t and can ∂Tn Tn be obtained by summing the discrete time forms of Eqs. (4), ∂LWnet n 4 (G1), and (G2) for the vegetation and all soil and snow lay- = (Fn − Gn), (E9g) ∂Tv Tv ers, respectively, yielding ∂LWnet n 4 = Kg, (E9h) Ng N ∂Tg Tg P Pn Cv1Tv + Cg,k 1Tg,k + png Cn,k 1Tn,k = ∂LWnet n 4 k=1 k=1 = (Jn − In), (E9i) ∂Tn Tn − + + + + 1t 1 png Gg,0 png Ggn τn,Nn SWnet ,n Gn,0 , and therefore from a coding perspective, the computation of Ng the derivatives is trivial (using already computed quantities). P + Rn v − Hv − LEv + Lf 8v + 8g,k k=1 N ! Appendix F: Halstead coefficient maximum Pn +png 8n,k , k=1 A maximum Halstead coefficient is imposed by estimating (G3) which value of δv that is needed to just evaporate any existing intercepted water Wrv given the conditions at the beginning where 1Tx = Tx(t + 1t) − Tx(t). Note that Eq. (G2) must of the time step. Assuming that phase changes are small, and first be multiplied by png in order to make it patch or grid neglecting canopy drip and any condensation from transpira- cell relative when it is combined with the soil and vegetation, the time-differenced prognostic equation for intercepted tion budget equations. The surface boundary conditions for water on canopy vegetation (Eq. 68) can be approximated as Eqs. (4) and (6) are, respectively, + Wrv − Wrv = (1 − χ )(1 − p p )P − E . (F1) Gg,0 = Rn g − Hg − LEg, (G4) 1t v ng αn r r Gn,0 = Rn n − Hn − LEn, (G5) Assuming that all existing water evaporates in one time step + τn,0 = 1, (G6) (i.e., Wrv = 0), and substituting the full expression for Er = (Eq. C5) into Eq. (F1), the maximum value of δv can be de- ξn,0 0. (G7) termined as Equation (G6) signifies that the net shortwave radiation at the surface enters the snowpack, and Eq. (G7) represents the fact δv,max = (F2) that energy changes owing to the time-evolving snow grid www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 864 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 can only arise in the surface layer owing to exchanges with where Eq. (G11) has been multiplied by png to make it patch the sub-surface layer. Snowfall is assumed to have the same or grid box relative (as was done for energy conservation in temperature as the snowpack; thus, a corresponding cool- Sect. G1). R0 can simply be a diagnostic or coupled with a ing/heating term does not appear in Eq. (G5), although the river routing scheme (Habets et al., 2008; Decharme et al., corresponding mass increase must appear in the snow water 2012; Getirana et al., 2015). The soil water lower boundary budget equation (see Sect. 2.7). condition Fg,Ngw represents the base flow or drainage leaving The lower boundary conditions for Eqs. (G1) and (G2) are, the lowest hydrological layer, which can then be transferred respectively, as input to a river routing scheme (see references above) or to a ground water scheme. In such instances, it can be neg- = Gg,Ng 0, (G8) ative if an option to permit a ground water inflow is acti- = vated (Vergnes et al., 2014). The soil liquid water and equiva- ξn,Nn 0. (G9) lent frozen water equivalent volumetric water content extend The appearance of the same discrete form for 8 in both down to layer Ng w, where Ng w ≤ Ng. Note that the verti- the energy and mass budget equations ensures enthalpy con- cal soil water transfer or evolution is not computed below servation. Owing to Eqs. (G7) and (G9), the total effective zg k = Ngw , whereas heat transfer can be. In order to com- heating of the snowpack owing to grid adjustments is pute the thermal properties for deep soil temperature (thermal conductivity and heat capacity for example), soil moisture D ZNn estimates are needed: values from the soil are extrapolated ξn dDn = 0, (G10) downward assuming hydrostatic equilibrium A detailed description of the soil model is given by Decharme et al.(2011) 0 and Decharme et al.(2013). where DNn represents the total snow depth. Thus, this term Note that Eq. (G11) is snow relative; therefore, this equa- only represents a contribution from contiguous snow layers, tion must be multiplied by the ground-based snow fraction not from a source external to the snowpack. The energy stor- png to be grid box relative for coupling with the soil and age of the snow–soil–vegetation system is balanced by the vegetation water storage terms. The lower boundary condi- net surface radiative and turbulent fluxes and internal phase tion for liquid water flow Fnl,Nn is defined as the liquid wa- changes (solid and liquid phases of water substance). ter exceeding the lowest maximum snow-layer liquid water- holding capacity. ξnl represents the internal mass changes of G2 Mass conservation a snowpack layer when the vertical grid is reset. When integrated over the entire snowpack depth, this term vanishes The soil and snowpack prognostic mass equations can be (analogous to Eq. (G10) for the snowpack temperature equa- written in flux form for k = 2,Ng w soil layers and k = 1,Nn tion). See Boone and Etchevers(2001) and Decharme et al. snow layers as (2016) for details on the snow model processes. The equations describing flooding are not described in de- ∂Wn,k = F − − F − 8 tail here as this parameterization is independent of MEB, and ∂t nl,k 1 nl,k n,k it is described in detail by Decharme et al.(2012). The cou- + ξ − ξ k = ,N , nl,k nl,k−1 ( 2 n) (G11) pling of MEB with the interactive flooding scheme will be ∂wg,k the subject of a future paper. ρ 1z = F − − F − 8 w g,1 ∂t g,k 1 g,k g,k − F2,k max(0,Etr) k = 2,Ng w , (G12) ∂wgf,k Appendix H: Implicit numerical coupling with the ρ 1z = 8 k = 2,N . (G13) w g,1 ∂t g,k g w atmosphere The total grid box water budget at each time step is ob- The land–atmosphere coupling is accomplished through the tained by summing the budget equations for the surface lay- atmospheric model vertical diffusion (heat, mass, momen- ers (Eqs. 68–72) together with those for the sub-surface lay- tum, chemical species, aerosols, etc.) and radiative schemes. ers (Eqs. G11–G13) to have Owing to the potential for relatively large diffusivity, especially in the lower atmosphere near the surface, fairly strict Nn Ngw time step constraints must be applied. In this section, a fully + + X + X + 1Wr 1Wr n png 1Wn, k ρw 1zg, k wg k wgf k implicit time scheme (with an option for explicit coupling) k=1 k=1 h is described. There are two reasons for using this approach; = + − − − − − 1t Pr Ps R0 Fg,Ngw 1 png Eg Ev (i) an implicit coupling is more numerically stable not only for time steps typical of GCM applications but also for some Ng Nn X X i NWP models, and (ii) the methodology permits code modu- − png En − 8v − 8g,k − png 8n,k , (G14) k=1 k=1 larity in that the land surface model routines can be indepen-

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 865

∂LW dent of the atmospheric model code and they can be called + − + net v + − Tv Tv Tg,1 Tg,1 using a standard interface, which is the philosophy of SUR- ∂Tg,1 ∂LW FEX (Masson et al., 2013). The coupling follows the method- + net v + − + + Tn,1 Tn,1 SWnet v LWnet v ology first proposed by Polcher et al.(1998), which was fur- ∂Tn,1 ther generalized by Best et al.(2004). + + + ϕv Av T − Ac T The atmospheric turbulence scheme is generally expressed v c ∂q as a second-order diffusion equation in the vertical (which is sat v + + + hsv ϕv L qsat v + Tv − Tv − qc , (I1) assumed herein) and it is discretized using the backward dif- ∂Tv ference time scheme. Note that a semi-implicit scheme, such T + − T g,1 g,1 ∂LWnet g as the Crank–Nicolson (Crank and Nicolson, 1947), could Cg,1 = also be used within this framework. Thus, the equations can 1t ∂Tv ∂LW be cast as a tri-diagonal matrix. Assuming a fixed for zero + − + net g + − Tv Tv Tg,1 Tg,1 (the general case) upper boundary condition at the top of the ∂Tg,1 atmosphere, the diffusion equations for the generic variable ∂LW + net g + − + + φ can be cast as a linear function of the variable in the layer Tn,1 Tn,1 SWnet g LWnet g ∂Tn,1 below (Richtmeyer and Morton, 1967) as + ϕ A T + − A T + + = + + = − g g g c c φk Bφ,k Aφ,k φ + (k 1,Na 1), (H1) k 1 ∂qsat g + + where Na represents the number of atmospheric model lay- + ϕg L hsg qsat g + Tg − Tg − ha qc ers, k = 1 represents the uppermost layer with k increasing ∂Tg with decreasing height above the surface, and the superscript ∗ + 1 − p + p 3 , T − T , + indicates the value of φ at time t + 1t (at the end of the ng ng g n n,Nn g,1 time step). The coefficients Aφ,k and Bφ,k are computed in a − + − + downward sweep within the turbulence scheme and thus con- 3g,1 Tg,1 Tg,2 , (I2) sist in atmospheric prognostic variables, diffusivity, heat ca- + T − Tn,1 pacities, and additional source terms from layer k and above n,1 ∂LWnet n + png Cn,1 = Tv − Tv evaluated at time level t (Polcher et al., 1998). As shown by 1t ∂Tv Best et al.(2004), the equation for the lowest atmospheric ∂LW + net n + − model layer can be expressed using a flux lower boundary Tg,1 Tg,1 ∂Tg,1 condition as ∂LWnet n + + + + T − T + SW + LW φ = B + A F , (H2) n,1 n,1 net n net n Na φ,Na φ,Na φ,Na+1 ∂Tn,1 + + + + (1 − pnα) ϕn−c An Tn − Ac Tc where Fφ,N +1 is the implicit surface flux from one or mul- a + + tiple surface energy budgets. Technically, only the Bφ,Na + pnα ϕn−a Bn − Ba + An Tn − Aa Ta and Aφ,N coefficients are needed by the LSM in order to a ∂qsati n + + + compute the updated land surface fluxes and temperatures, + (1 − pnα)ϕn−c Ls qsati n + Tn − Tc − qc ∂Tn which are fully implicitly coupled with the atmosphere. Once F + has been computed by the LSM, it can be returned ∂qsati n + + + φ,Na+1 + pnα ϕn−a Ls qsati n + Tn − Ta − qa to the atmospheric turbulence scheme, which can then solve ∂Tn + for φ from k = N to k = 1 (i.e., the upward sweep). For k a − + − + explicit land–atmosphere coupling or offline land-only ap- 3g,1 Tn,1 Tn,2 png. (I3) plications, the coupling coefficients can be set to Aφ,N = 0 a Note that Eq. (I3) has been multiplied by p since the snow- and Bφ,N = φN in the driving code. ng a a pack must be made patch relative when solving the coupled + equations. The qsat x and longwave radiation terms have been Appendix I: Numerical solution of the surface energy linearized with respect to Tx (the longwave radiation deriva- budgets tives are given by Eq. E9). The superscript + corresponds to the values of variables at time t + 1t, while the absence I1 Discretization of surface energy budgets of a superscript indicates variables evaluated at time t. Note that we have defined ϕ = ρ /R (kg m−2 s−1) for simplic- The surface energy budget equations (Eqs.4–6) are in- x a a x ity. The thermodynamic variable, T , in the sensible heat flux tegrated in time using the implicit backward difference x terms have been expressed as a function of T using Eq. (15). scheme. They can be written in discretized form as x Several of the Bx terms have canceled out in the sensible heat + Tv − Tv ∂LWnet v flux terms in Eqs. (I1)–(I3) since they are defined such that Cv = B = B = B = B . Note that compared to Eqs. (4)–(6), the 1t ∂Tv c v g n www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 866 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8

= − phase change terms (8x) do not appear in Eqs. (I1)–(I3). This AeTa ATa ϕc−a Ac 1 png pαn /C, (I7b) is because they are evaluated as an adjustment after the en- n h B = B − B + A 1 − p p ϕ (B − B )+ ergy budget and the fluxes have been computed. eTa Ta a Ta ng αn c−a c a In Eq. (I2), T ∗ represents a test temperature for the low- io n,Nn p p ϕ − (B − B ) /C, (I7c) est snowpack layer. It is first computed using an implicit cal- ng αn n a c a = culation of the combined snow–soil layers to get a first esti- CeTa ATa png pαn ϕn−a Ac/C. (I7d) mate of the snow–ground heat conduction inter-facial flux when simultaneously solving the surface energy budgets. In analogous fashion to determining the air temperature, The final snow temperature in this layer, T + , is computed the specific humidity of the lowest atmospheric model vari- n,Nn afterwards within the snow scheme; any difference between able at time t + 1t is defined from Eq. (H2) as the resulting conduction flux and the test flux in Eq. (I2) is + + added to the soil as a correction at the end of the time step qa = Bq,a + Aq,a E , (I8) in order to conserve energy. In practice, this correction is generally small, especially since the snow fraction goes to where again the subscript q, a represents the values of the unity very rapidly (i.e., for a fairly thin snowpack when us- coefficients A and B for the lowest atmospheric model layer (k = Na). Substitution of Eq. (21) for E in Eq. (I8) and solving MEB; see Eq.1). Thus, in this general case, the difference + between the test flux and the final flux arise only owing to up- ing for Ta yields dates to snow properties within the snow scheme during the q+ = B + A q+ + C q+ , (I9) time step. Since T ∗ is computed using an implicit solution a eq,a eq,a c eq,a sati n n,Nn method for the entire soil–snow continuum, it is also quite where the coefficients are defined as numerically stable. The use of a test flux permits a modular coupling between the snow scheme and the soil–vegetation C = 1 + Aq,a 1 − png pαn ϕc−a + ϕn−a hsn pαn png , parts of ISBA-MEB. (I10a) In order to solve Eqs. (I1)–(I3) for the three unknown sur- + + + Aeq,a = Aq,a ϕc−a 1 − png pαn /C, (I10b) face energy budget temperatures, Tv , Tg,1, and Tn,1, equations for the six additional unknown surface energy budget Beq,a = Bq,a/C, (I10c) temperatures, T +, T +, q+, q+, T + , and T + , must be de- a c a c g,2 n,2 Ceq,a = Aq,a ϕn−a hsn pαn png/C. (I10d) fined. They can be expressed as linear equations in terms of + + + Tv , Tg,1, and Tn,1, and their derivations are presented in the I3 Canopy air temperature and specific humidity remaining sections of this Appendix. + + In order to close the energy budgets, Tc and qc must be I2 Atmospheric temperature and specific humidity determined. Assuming conservation of the heat flux between the differ- The first step in solving the surface energy budget is to elim- ent surfaces and the canopy air space, we have inate the lowest atmospheric energy and water vapor variables from the snow surface energy budget equation. They + + 1 − pngpnα Hc = png (1 − pnα) Hn−c will also be used to diagnose the final flux exchanges be- + − + + + tween the canopy air space and overlying atmosphere. 1 png Hg Hv , (I11) From Eq. (H2), the thermodynamic variable of the lowest which can be expanded as atmospheric model variable at time t + 1t is defined as T + = B + A H +. (I4) ϕc−a 1 − png pαn × Na T ,Na T ,Na B + A T + − B − A T + = Note that using Eq. (15), we can rewrite Eq. (I4) in terms of c c c a a a h + + air temperature as Ac ϕg Tg − Tc 1 − png + = + + + + Ta BTa ATa H , (I5) + ϕv Tv − Tc = − = + + i where BTa BT ,Na Ba /Aa, ATa AT ,Na /Aa, and Ta is ϕn−c Tn − Tc png (1 − pαn) . (I12) shorthand for T (k = Na). Substitution of Eq. (14) for H in + Eq. (I5) and solving for Ta yields Note that the above conservation equation does not include + = + + + + the part of the snow sensible heat flux, which is in direct Ta BeTa AeTa Tc CeTa Tn , (I6) contact with the atmosphere (Hn−a), since it was already ac- + where counted for in the expression for Ta via Eq. (I5). Eliminating n o T + using Eq. I6 and solving for T + yields = + − + a c C Aa 1 ATa ϕc−a 1 png pαn png pαn ϕn−a , + = + + + + + + (I7a) Tc aTc bTc Tv cTc Tg dTc Tn (I13)

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 867 with the coefficients I4 Sub-surface temperatures C =ϕc−a 1 − png pαn Ac − Aa AeT a + The sub-surface conduction heat fluxes (Eqs. 47–49) can be expressed in compact form as Ac ϕv + ϕg 1 − png + ϕn−c png (1 − pαn) , (I14a) h i + + + a = ϕ − 1 − p p B − B + A B /C, (I14b) = − Tc c a ng αn a c a eT a Gx,k 3x,k Tx,k Tx,k+1 , (I19) = bTc Ac ϕv/C, (I14c) where 3x,k represents the ratio of the inter-facial thermal = − cTc Ac ϕg 1 png /C, (I14d) conductivity to the thickness between the mid-points of con- = − tiguous layers (k and k + 1). Using the methodology de- dTc Ac ϕn−c png (1 pαn) scribed in AppendixH for the atmospheric diffusion scheme, +A C ϕ 1 − p p /C. (I14e) a eT a c−a ng αn the soil and snow heat diffusion equation (both using the In an analogous fashion for canopy air temperature deter- form of Eq. G1) can be defined in an analogous fashion as mination, assuming conservation of the vapor flux between T + = B + A T + k = 2,N , (I20) the different surfaces and the canopy air space, g,k g,k g,k g,k−1 g

+ + where the coefficients B and A are determined during 1 − p p E = p (1 − p ) E g,k g,k ng nα c ng nα n−c the upward sweep (first step of the tri-diagonal solution) from + + + 1 − png Eg + Ev , (I15) the base of the soil to the sub-surface soil and snow layers as described by Richtmeyer and Morton(1967). The resulting which can be expanded using the definitions of the evapora- coefficients for the soil are defined as tive fluxes Ex from Eqs. (17)–(I15) together with the defini- + tions of qg from Eq. (22) and qa from Eq. (I9) as C = Cg k/1t + 3g k−1 + 3g k 1 − Ag k+1 , (I21a) B = C /1t T gk + 3 B + ϕc−a 1 − png pαn × g i g k g k g k 1 + − − − + = /C 2 ≤ k ≤ Ng − 1 , (I21b) qc 1 Aeq,a Beq,a Ceq,a qsati n = h + + + + Ag k 3g k−1/C. (I21c) ϕg hsg qsat g − ha qc 1 − png + ϕv hsv qsat v − qc i The same form holds for the snow layers. The upward sweep + − + − ϕn−c hsn qsati n qc png (1 pαn) . (I16) is performed before the evaluation of the energy budget; thus, + + Eq. (I20) is used to eliminate Tg,2 and Tn,2 from Eqs. (I2) and Owing to the linearization of the qsat x, terms about Tx, + (I3), respectively. To do this, the sub-surface implicit fluxes Eq. (I16) can be solved for qc as a function of the surface in Eqs. (5) and (6) can be expressed, respectively, as energy budget temperatures as h i + = + − + + = + + + + + + Gg,1 3g,1 Tg,1 1 Ag,2 Bg,2 , (I22a) qc aqc bqc Tv cqc Tg dqc Tn , (I17) h i G+ =3 T + 1 − A + B . (I22b) where the coefficients are defined as n,1 n,1 n,1 n,2 n,2 C =ϕc−a 1 − png pnα 1 − Aeq,a + ϕg hN 1 − png I5 Surface stresses + + − ϕv hsv ϕn−c hsn png (1 pnα), (I18a) Using the same surface–atmosphere coupling methodology n ∂q = − + − sat v as for temperature and specific humidity, the u wind compo- aqc 1 png pnα ϕc−a Beq,a ϕv hsv qsat v Tv ∂Tv nent in the lowest atmospheric model layer can be expressed as ∂qsat g + ϕg hsg qsat g − Tg 1 − png ∂T + + g u = B + A τ . (I23) a u a u a x ∂qsati n + ϕn−c hsn qsati n − Tn (I18b) ∂Tn The surface u component momentum exchange with the at- o mosphere is expressed as png (1 − pnα) /C, (I18c) + + ∂q τx = −ua 1 − png pnα ϕDc−a + png pnαϕDn−a , (I24) b =h ϕ sat v /C, (I18d) qc sv v ∂T v where it includes stresses from the snow-buried and non- ∂q = sat g − snow-buried portions of the surface consistent with the fluxes cqc hsg ϕg 1 png /C, (I18e) ∂Tg of heat and water vapor. For simplicity, we have defined ∂q = sati n − dqc hsn ϕn−c png (1 pnα)/C. (I18f) ϕ = ρ V C (I25) ∂Tn Dx a a Dx www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 868 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8

+ and CD is the surface drag coefficient, which is defined fol- (Eq. I22a)and Tn,2 (Eq. I22b) can now be substituted + lowing Noilhan and Mahfouf(1996). Eliminating τx from into the energy budget equations (Eqs. I1–I3), which + + + Eq. (I24) using Eq. (I25) gives can then be readily solved for Tv , Tg,1, and Tn,1. B 4. Within the land surface model, perform back substitu- u+ = u a , (I26) a + tion (using T + as the upper boundary condition) to ob- 1 Au a ϕDc g,1 tain T + for soil layers k = 2,N using Eq. (I20). where for convenience we have defined the average drag co- g,k g efficient as 5. Within the land surface model, call the explicit snow- process scheme to update the snow scheme tempera- = − + + ϕDc 1 png pnα ϕDc−a png pnαϕDn−a. (I27) ture, Tn,k, and the snow mass variables for snow layers + + k = 2,Nn. The implicit snow surface fluxes, Rn,n, Hn The net u-momentum flux from the surface to the canopy air + and En , are used as the upper boundary condition along space is expressed as + with the implicit soil temperature, Tg,1, to compute the Bu a ϕD updated lower snowpack boundary condition (i.e., the τ + = − c . (I28) x + snow–soil inter-facial flux, G ). 1 Au a ϕDc gn + Finally, the scalar friction velocity can be computed from 6. Within the land surface model, compute Va (see + + + Sect. I5). Diagnose Ta , Tc+, qa and qc (again, using ϕ V + 1/2 the equations mentioned in step 3) in order to compute u∗ = Dc a , (I29) ρa the updated (implicit) fluxes. The updated evapotranspiration (Eqs. C4–C8) and snowmelt water mass fluxes + + where Va is the updated wind speed (computed from ua and are used within the hydrology schemes to update the + + + va ). Note that va and τy are computed in the same manner, different water storage variables for the soil and vegeta- but using Bv a from the atmosphere (note that Av a = Au a). tion canopy (Eqs. 68–72).

I6 Summary: final solution of the implicitly coupled 7. Within the atmospheric model, perform back substitu- + + + + equations tion (using H , E , τx and τy as the lower boundary conditions: Eq. H2) to obtain updated profiles (or The fully implicit solution of the surface and atmospheric turbulent tendencies, depending on the setup of the at- variables proceeds for each model time step as follows: mospheric model) of Tk, qk, uk and vk for atmospheric layers k = 1,Na. Finally, the updated upwelling short- 1. Within the atmospheric model, perform the downward wave, SW ↑, and implicit longwave flux, LW↑+ (or sweep of the tri-diagonal matrix within the turbulent equivalently, the effective emissivity and implicit long- diffusion scheme of the atmospheric model to obtain + wave radiative temperature, Trad) are returned to the at- the Aφ,k and Bφ,k coefficients for each diffused vari- mospheric model as lower boundary conditions for the able (φ = T , q, u, and v) for each layer of the atmo- respective radiative schemes. sphere (k = 1,Na). Update Aa and Ba, then pass these values along with the aforementioned coupling coeffi- Alternately, in offline mode, Aφ,a = 0 and Bφ,a = φa in the cients at the lowest atmospheric model layer (i.e., AT,a, driving routine in step 1, and the solution procedure ends at BT,a, Aq,a, Bq,a, Au,a, Bu,a, and Bv,a) to the land surface step 6. Finally, if multiple patches and/or tiles are being used + model. These coefficients are then used to eliminate Ta within the grid call of interest, the corresponding fractional- + and qa from the implicit surface energy budget equa- area-weighted fluxes are passed to the atmospheric model in tions (Eqs. I1–I3). step 7. 2. Within the land surface model, perform the upward sweep of the tri-diagonal matrix within the soil and snow layers to determine the An,k, Bn,k, Ag,k, and Bg,k, coefficients for the soil and snow layers (from soil-layer Ng to layer 2, and again from soil-layer Ng to layer 2 of the snow scheme). Note that coefficients for layer 1 of the snow and soil schemes are not needed since they correspond to the linearized surface energy budgets (next step). + 3. Within the land surface model, the expressions for Ta + + + + (Eq. I6), qa (Eq. I9), Tc (Eq. I13), qc (Eq. I17), Tg,2

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 869

Acknowledgements. This work was initiated within the interna- Boone, A., Masson, V., Meyers, T., and Noilhan, J.: The influence of tional HIRLAM consortium as part of the ongoing collective effort the inclusion of soil freezing on simulations by a soil-vegetation- to improve the SURFEX platform for research and operational atmosphere transfer scheme, J. Appl. Meteor., 9, 1544–1569, hydrological and meteorological applications. We wish to make a 2000. posthumous acknowledgement of the contribution to this work by Boussetta, S., Balsamo, G., Beljaars, A., Agusti-Panareda, A., Cal- Joël Noilhan, who was one of the original supporters of this project vet, J.-C., Jacobs, C., van den Hurk, B., Viterbo, P., Lafont, S., and helped initiate this endeavor; his scientific vision was essential Dutra, E., Jarlan, L., Balzarolo, M., Papale, D., and van der Werf, at the early stages of this work. We wish to thank other contributors G.: Natural land carbon dioxide exchanges in the ECMWF Inte- to this development in terms of discussions and evaluation, such as grated Forecasting System: Implementation and offline valida- G. Boulet, E. Martin, J.-C. Calvet, P. Le Moigne, C. Canac, and G. tion, J. Geophys. Res., 18, 5923–5946, doi:10.1002/jgrd.50488, Aouad. The technical support of S. Faroux of the SURFEX team 2013. is also greatly appreciated. We also wish to thank E. Lebas for Braud, I.: SiSPAT User’s Manual, Model Documentation, Septem- preparing the MEB schematic. Part of this work was supported by ber 2000 3.0, LTHE, LTHE, BP 53, 38041 Grenoble Cédex 9, a grant from Météo-France. France, 2000. Braud, I., Bariac, T., Gaudeta, J. P., and Vauclin, M.: SiSPAT- Edited by: S. Valcke Isotope, a coupled heat, water and stable isotope (HDO and 18 Reviewed by: two anonymous referees H2 O) transport model for bare soil. Part I. Model description and first verifications, J. Hydrol., 309, 277–300, 2005. Bringfelt, B., Räisänen, J., Gollvik, S., Lindström, G., Graham, L. P., and Ullerstig, A.: The land surface treatment for the Rossby Centre Regional Atmosphere Climate Model – version 2, Re- References ports of Meteorology and Climatology 98, SMHI, SE-601 76 Norrköping, Sweden, 2001. Anderson, M. C., Norman, J. M., Diak, G. R., Kustas, W. P., and Brun, E., Vionnet, V., Decharme, B., Peings, Y., Valette, R., Boone, Mecikalski, J. R.: A two-source time-integrated model for esti- A., Karbou, F., and Morin, S.: Simulation of northern Eurasian mating surface fluxes using thermal infrared remote sensing, Re- local snow depth, mass and density using a detailed snowpack mote Sens. Environ., 60, 195–216, 1997. model and meteorological reanalyses, J. Hydrometeor., 14, 203– Andreadis, K. M., Storck, P., and Lettenmaier, D. P.: Modeling snow 219, 2013. accumulation and ablation processes in forested environments, Cakmur, R. V., Miller, R. L., and Torres, O.: Incorporating the Water Resour. Res., 45, w05429, doi:10.1029/2008WR007042, effect of small-scale circulations upon dust emission in an at- 2009. mospheric general circulation model, J. Geophys. Res., 109, Bengtsson, L., Andrae, U., Aspelien, T., Batrak, Y., de Rooy, D07201, doi:10.1029/2003JD004067, 2004. W., Gleeson, E., Hansen-Sass, B., Hortal, M., Ivarsson, K.-I., Calvet, J. C. and Soussana, J.-F.: Modelling CO2-enrichment ef- Lenderink, G., Niemelä, S., Nielsen, K. P., Onvlee, J., Rontu, fects using an interactive vegetation SVAT scheme, Agr. Forest L., Samulesson, P., Subias, A., Tijm, S., Toll, V., Yang, X., Meteorol., 108, 129–152, 2001. and Køltzow, M. Ø.: The HARMONIE-AROME model config- Calvet, J.-C., Noilhan, J., Roujean, J.-L., Bessemoulin, P., Ca- uration in the ALADIN-HIRLAM NWP system, Mon. Weather belguenne, M., Olioso, A., and Wigneron, J.-P.: An interactive Rev., doi:10.1175/MWR-D-16-0417.1, in press, 2017. vegetation SVAT model tested against data from six contrasting Best, M. J., Beljaars, A., Polcher, J., and Viterbo, P.: A proposed sites, Agr. Forest Meteorol., 92, 73–95, 1998. structure for coupling tiled surfaces with the planetary boundary Carrer, D., Roujean, J.-L., Lafont, S., Calvet, J.-C., Boone, A., layer, J. Hydrometeor., 5, 1271–1278, 2004. Decharme, B., Delire, C., and Gastellu-Etchegorry, J.-P.: A Best, M. J., Pryor, M., Clark, D. B., Rooney, G. G., Essery, R. L. canopy radiative transfer scheme with explicit FAPAR for the in- H., Ménard, C. B., Edwards, J. M., Hendry, M. A., Porson, A., teractive vegetation model ISBA-A-gs: Impact on carbon fluxes, Gedney, N., Mercado, L. M., Sitch, S., Blyth, E., Boucher, O., J. Geophys. Res., 188, 888–903, 2013. Cox, P. M., Grimmond, C. S. B., and Harding, R. J.: The Joint Castillo, G., Levis, C. K. S., and Thornton, P.: Evaluation of the UK Land Environment Simulator (JULES), model description – New CNDV Option of the Community Land Model: Effects of Part 1: Energy and water fluxes, Geosci. Model Dev., 4, 677–699, Dynamic Vegetation and Interactive Nitrogen on CLM4 Means doi:10.5194/gmd-4-677-2011, 2011. and Variability, J. Climate, 25, 3702–3714, 2012. Bonan, G. B., Williams, M., Fisher, R. A., and Oleson, K. W.: Choudhury, B. J. and Monteith, J. L.: A four-layer model for the Modeling stomatal conductance in the earth system: linking heat budget of homogeneous land surfaces, Q. J. Roy. Meteor. leaf water-use efficiency and water transport along the soil– Soc., 114, 373–398, 1988. plant–atmosphere continuum, Geosci. Model Dev., 7, 2193– Crank, J. and Nicolson, P.: A practical method for numerical eval- 2222, doi:10.5194/gmd-7-2193-2014, 2014. uation of solutions of partial differential equations of the heat Boone, A. and Etchevers, P.: An intercomparison of three snow conduction type, Proc. Camb. Philol. Soc., 43, 50–67, 1947. schemes of varying complexity coupled to the same land-surface Deardorff, J. W.: A parameterization of ground-surface moisture model: Local scale evaluation at an Alpine site, J. Hydrometeor., content for use in atmosphere prediction models, J. Appl. Me- 2, 374–394, 2001. teor., 16, 1182–1185, 1977. Boone, A., Calvet, J.-C., and Noilhan, J.: Inclusion of a Third Soil Layer in a Land-Surface Scheme using the Force-Restore method, J. Appl. Meteor., 38, 1611–1630, 1999. www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 870 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8

Deardorff, J. W.: Efficient prediction of ground surface temperature Getirana, A. C. V., Boone, A., and Peugeot, C.: Evaluating and moisture, with inclusion of a layer of vegetation, J. Geophys. LSM-based water budgets over a West African basin assisted Res., 83, 1889–1903, 1978. with a river routing scheme, J. Hydrometeor., 15, 2331–2346, Decharme, B. and Douville, H.: Introduction of a sub-grid hydrol- doi:10.1175/JHM-D-14-0012.1, 2015. ogy in the ISBA land surface model, Clim. Dynam., 26, 65–78, Giard, D. and Bazile, E.: Implementation of a new assimilation 2006. scheme for soil and surface variables in a global NWP model, Decharme, B., Boone, A., Delire, C., and Noilhan, J.: Local eval- Mon. Weather Rev., 128, 997–1015, 2000. uation of the ISBA soil multilayer diffusion scheme using four Gibelin, A.-L., Calvet, J. C., Roujean, J.-L., Jarlan, L., and pedotransfer functions, J. Geophys. Res., 116, 20126–20155, Los, S. O.: Ability of the land surface model ISBA-A-gs doi:10.1029/2011JD016002, 2011. to simulate leaf area index at the global scale: Compari- Decharme, B., Alkama, R., Papa, F., and Faroux, S.: Global offline son with satellites products, J. Geophys. Res., 111, d18102, evaluation of the ISBA-TRIP flood model, Clim. Dynam., 38, doi:10.1029/2005JD006691, 2006. 1389–1412, doi:10.1007/s00382-011-1054-9, 2012. Gonzalez-Sosa, E., Braud, I., Thony, J.-L., Vauclin, M., Besse- Decharme, B., Martin, E., and Faroux, S.: Reconciling soil thermal moulin, P., and Calvet, J.-C.: Modelling heat and water ex- and hydrological lower boundary conditions in land surface mod- changes of fallow land covered with plant-residue mulch, Agr. els, J. Geophys. Res., 118, 7819–7834, doi:10.1002/jgrd.50631., Forest Meteorol., 97, 151–169, 1999. 2013. Habets, F., Boone, A., Champeaux, J., Etchevers, P., Leblois, E., Decharme, B., Brun, E., Boone, A., Delire, C., Le Moigne, P., Ledoux, E., Moigne, P. L., Martin, E., Morel, S., Segui, Q., and Morin, S.: Impacts of snow and organic soils parameteri- Rousset-Regimbeau, F., and Viennot, P.: The SAFRAN-ISBA- zation on northern Eurasian soil temperature profiles simulated MODCOU hydrometeorological model applied over France, J. by the ISBA land surface model, The Cryosphere, 10, 853–877, Geophys. Res., 113, D06113, doi:10.1029/2007JD008548, 2008. doi:10.5194/tc-10-853-2016, 2016. Hedstrom, N. R. and Pomeroy, J. W.: Measurements and modelling Delire, C., Calvet, J.-C., Noilhan, J., Wright, I., Manzi, A., and of snow interception in the boreal forest, Hydrol. Process., 12, Nobre, C.: Physical properties of Amazonian soils: A model- 1611–1625, 1998. ing study using the Anglo-Brazilian Amazonian Climate Ob- Isymov, N.: An approach to the prediction of snow loads, Tech. rep., servation Study data, J. Geophys. Res., 102, 30119–30133, Faulty of Engineering Science, The Univ. of Western Ontario, doi:10.1029/97JD01836, 1997. London, 442 pp., 1971. de Rosnay, P., Polcher, J., Laval, K., and Sabre, M.: Integrated Jarvis, P. G.: The interpretation of variations in leaf water potential parameterization of irrigation in the land surface model OR- and stomatal conductance found in canopies in the field, Philos. CHIDEE. Validation over the Indian Peninsula, Geophys. Res. T. R. Soc. Lond., 273, 593–610, 1976. Lett., 30, 1986, doi:10.1029/2003GL018024, 2003. Joetzjer, E., Delire, C., Douville, H., Ciais, P., Decharme, B., Car- Dickinson, R. E.: Modelling evapotranspiration for three- rer, D., Verbeeck, H., De Weirdt, M., and Bonal, D.: Improving dimensional global models, in: Climate Processes and Climate the ISBACC land surface model simulation of water and carbon Sensitivity, Geophys. Monogr., 29, Maurice Ewing, edited by: fluxes and stocks over the Amazon forest, Geosci. Model Dev., Hansen, J. E. and Takahashi, T., 1984. 8, 1709–1727, doi:10.5194/gmd-8-1709-2015, 2015. Dickinson, R. E., Shaikh, M., Bryant, R., and Graumlich, L.: Inter- Lafore, J. P., Stein, J., Asencio, N., Bougeault, P., Ducrocq, V., active canopies for a climate model, J. Climate, 11, 2823–2836, Duron, J., Fischer, C., Héreil, P., Mascart, P., Masson, V., Pinty, J. 1998. P., Redelsperger, J. L., Richard, E., and Vilà-Guerau de Arellano, Douville, H., Royer, J.-F., and Mahfouf, J.-F.: A new snow parame- J.: The Meso-NH Atmospheric Simulation System. Part I: adi- terization for the Météo-France climate model, Part I : Validation abatic formulation and control simulations, Ann. Geophys., 16, in stand-alone experiments, Clim. Dynam., 12, 21–35, 1995. 90–109, doi:10.1007/s00585-997-0090-6, 1998. Ek, M., Mitchell, K. E., Lin, Y., Rogers, E., Grunmann, P., Lawrence, D. M., Oleson, K. W., Flanner, M. G., Thornton, P. E., Koren, V., Gayno, G., and Tarpley, J. D.: Implementation Swenson, S. C., Lawrence, P. J., Zeng, X., Yang, Z.-L., Levis, of Noah land-surface model advances in the NCEP opera- S., Sakaguchi, K., Bonan, G. B., and Slater, A. G.: Parameteri- tional mesoscale Eta model, J. Geophys. Res., 108, 8851, zation Improvements and Functional and Structural Advances in doi:10.1029/2002JD003296, 2003. Version 4 of the Community Land Model, J. Adv. Model. Earth Erbs, D. G., Klein, S. A., and Duffie, J. A.: Estimation of the diffuse Sys., 3, M03001, doi:10.1029/2011MS00045, 2011. radiation fraction for hourly, daily and monthly average global Lind, P., Lindstedt, D., Kjellström, E., and Jones, C.: Spatial and radiation, Sol. Energy, 28, 293–304, 1982. Temporal Characteristics of Summer Precipitation over Central Faroux, S., Kaptué Tchuenté, A. T., Roujean, J.-L., Masson, V., Europe in a Suite of High-Resolution Climate Models, J. Cli- Martin, E., and Le Moigne, P.: ECOCLIMAP-II/Europe: a mate, 29, 3501–3518, 2016. twofold database of ecosystems and surface parameters at 1 km Louis, J.-F.: A parametric model of vertical eddy fluxes in the atmo- resolution based on satellite information for use in land surface, sphere, Bound.-Lay. Meteorol., 17, 187–202, 1979. meteorological and climate models, Geosci. Model Dev., 6, 563– Mahfouf, J.-F. and Noilhan, J.: Comparative study of various formu- 582, doi:10.5194/gmd-6-563-2013, 2013. lations of evaporation from bare soil using in situ data., J. Appl. Galperin, B., Sukoriansky, S., and Anderson, P. S.: On the critical Meteorol., 9, 351–362, 1991. Richardson number in stably stratified turbulence, Atmos. Sci. Mahfouf, J.-F. and Noilhan, J.: Inclusion of gravitational drainage Lett., 8, 65–69, doi:10.1002/asl.153, 2007. in a land surface scheme based on the force-restore method, J. Appl. Meteor., 35, 987–992, 1996.

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/ A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8 871

Manzi, A. O. and Planton, S.: Implementation of the ISBA parame- Polcher, J., McAvaney, B., Viterbo, P., Gaertner, M.-A., Hahamann, terization scheme for land surface processes in a GCM-an annual A., Mahfouf, J.-F., Noilhan, J., Phillips, T., Pitman, A., Schlosser, cycle experiment, J. Hydrol., 155, 353–387, 1994. C., Schulz, J.-P., Timbal, B., Verseghy, D., and Xue, Y.: A pro- Mascart, P., Noilhan, J., and Giordani, H.: A modified parameteri- posal for a general interface between land-surface schemes and zation of flux-profile relationships in the surface layer using dif- general circulation models, Global Planet. Change, 19, 263–278, ferent roughness length values for heat and momentum, Bound.- 1998. Lay. Meteorol., 72, 331–344, 1995. Pomeroy, J. W. and Dion, K.: Winter radiation extinction and re- Massman, W.: Foliage distribution in old-growth coniferous tree flection in a boreal pine canopy: measurements and modelling, canopies, Can. J. Forest Res., 12, 10–17, 1982. Hydrol. Process., 10, 1591–1608, 1996. Masson, V., Le Moigne, P., Martin, E., Faroux, S., Alias, A., Richtmeyer, R. and Morton, K.: Difference method for initial values Alkama, R., Belamari, S., Barbu, A., Boone, A., Bouyssel, F., problems, Interscience Publishers, 2nd Edn., 1967. Brousseau, P., Brun, E., Calvet, J.-C., Carrer, D., Decharme, B., Rutter, N., Essery, R., Pomeroy, J., Altimir, N., Andreadis, K., Delire, C., Donier, S., Essaouini, K., Gibelin, A.-L., Giordani, H., Baker, I., Barr, A., Bartlett, P., Boone, A., Deng, H., Douville, H., Habets, F., Jidane, M., Kerdraon, G., Kourzeneva, E., Lafaysse, Dutra, E., Elder, K., Ellis, C., Feng, X., Gelfan, A., Goodbody, M., Lafont, S., Lebeaupin Brossier, C., Lemonsu, A., Mahfouf, A., Gusev, Y., Gustafsson, D., Hellström, R., Hirabayashi, Y., Hi- J.-F., Marguinaud, P., Mokhtari, M., Morin, S., Pigeon, G., Sal- rota, T., Jonas, T., Koren, V., Kuragina, A., Lettenmaier, D., Li, gado, R., Seity, Y., Taillefer, F., Tanguy, G., Tulet, P., Vincendon, W.-P., Luce, C., Martin, E., Nasonova, O., Pumpanen, J., Pyles, B., Vionnet, V., and Voldoire, A.: The SURFEXv7.2 land and R. D., Samuelsson, P., Sandells, M., Schädler, G., Shmakin, ocean surface platform for coupled or offline simulation of earth A., Smirnova, T. G., Stähli, M., Stöckli, R., Strasser, U., Su, surface variables and fluxes, Geosci. Model Dev., 6, 929–960, H., Suzuki, K., Takata, K., Tanaka, K., Thompson, E., Vesala, doi:10.5194/gmd-6-929-2013, 2013. T., Viterbo, P., Wiltshire, A., Xia, K., Xue, Y., and Yamazaki, Monteith, J. L. (Ed.): Vegetation and the atmosphere, vol. 1, Aca- T.: Evaluation of forest snow processes models (SnowMIP2), J. demic Press, 1975. Geophys. Res., 114, doi:10.1029/2008JD011063, 2009. Nakai, Y., Sakamoto, T., Terajima, T., Kitamura, K., and Shirai, T.: Ryder, J., Polcher, J., Peylin, P., Ottlé, C., Chen, Y., van Gorsel, The effect of canopy-snow on the energy balance above a conif- E., Haverd, V., McGrath, M. J., Naudts, K., Otto, J., Valade, erous forest, Hydrol. Process., 13, 2371–2382, 1999. A., and Luyssaert, S.: A multi-layer land surface energy budget Napoly, A., Boone, A., Samuelsson, P., Gollvik, S., Martin, E., Se- model for implicit coupling with global atmospheric simulations, ferian, R., Carrer, D., Decharme, B., and Jarlan, L.: The Interac- Geosci. Model Dev., 9, 223–245, doi:10.5194/gmd-9-223-2016, tions between Soil-Biosphere-Atmosphere (ISBA) land surface 2016. model Multi-Energy Balance (MEB) option in SURFEX – Part Samuelsson, P., Gollvik, S., and Ullerstig, A.: The land-surface 2: Model evaluation for local scale forest sites, Geosci. Model scheme of the Rossby Centre regional atmospheric climate Dev. Discuss., doi:10.5194/gmd-2016-270, in review, 2016. model (RCA3)., Report in Meteorology 122, SMHI, SE-60176 Niu, G.-Y. and Yang, Z.-L.: Effects of vegetation canopy processes Norrköping, Sweden, 2006. on snow surface energy and mass balances, J. Geophys. Res., Samuelsson, P., Jones, C., Willén, U., Ullerstig, A., Gollvik, 109, d23111, doi:10.1029/2004JD004884, 2004. S., Hansson, U., Jansson, C., Kjellström, E., Nikulin, G., Noilhan, J. and Mahfouf, J.-F.: The ISBA land surface parameteri- and Wyser, K.: The Rossby Centre Regional Climate Model sation scheme, Global Planet. Change, 13, 145–159, 1996. RCA3: Model description and performance, Tellus A, 63, 1–3, Noilhan, J. and Planton, S.: A simple parameterization of land sur- doi:10.1111/j.1600-0870.2010.00478.x, 2011. face processes for meteorological models, Mon. Weather Rev., Schmidt, R. A. and Gluns, D. R.: Snowfall interception on branches 117, 536–549, 1989. of three conifer species, Can. J. Forest Res., 21, 1262–1269, Ogée, J. and Brunet, Y.: A forest floor model for heat and moisture 1991. including a litter layer, J. Hydrol., 255, 212–233, 2002. Seity, Y., Brousseau, P., Malardel, S., Hello, G., Bénard, P., Bouttier, Oleson, K. W., Lawrence, D. M., Bonan, G. B., Flanner, M. G., F., Lac, C., and Masson, V.: The AROME-France Convective- Kluzek, E., Lawrence, P. J., Levis, S., Swenson, S. C., Scale Operational Model, Mon. Weather Rev., 131, 976–991, P. E. Thornton, A. D., A., Decker, M., Dickinson, R., Feddema, 2011. J., C. L. Heald, F. H., Lamarque, J. F., Mahowald, N., Niu, G. Y., Sellers, P. J., Mintz, Y., Sud, Y. C., and Dalcher, A.: A Simple Bio- Qian, T., Randerson, J., Running, S., Sakaguchi, K., A. Slater, sphere Model (SiB) for use within General Ciculation Models, J. R. S., Wang, A., Yang, Z. L., and Zeng, X.: Technical Description Atmos. Sci., 43, 505–531, 1986. of version 4.0 of the Community Land Model (CLM), NCAR Sellers, P. J., Heiser, M. D., and Hall, F. G.: Relations between sur- Technical Note TN-478+STR, NCAR, NCAR, P.O. Box 3000, face conductance and spectral vegetation indices at intermediate Boulder, CO, USA, 80307-3000, 2010. (100 m2 to 15 km2) length scales, J. Geophys. Res., 97, 19033– Pitman, A. J.: The evolution of, and revolution in, land surface 19059, doi:10.1029/92JD01096, 1992. schemes designed for climate models, Int. J. Clim., 23, 479–510, Sellers, P. J., Randall, D. A., Collatz, G. J., Berry, J. A., Field, 2003. C. B., Dazlich, D. A., Zhang, C., Collelo, G. D., and Bounoua, L.: Pokhrel, Y. N., Koirala, S., Yeh, P. J.-F., Hanasaki, N., Longuev- A revised land surface parameterization (SiB2) for atmospheric ergne, S. K., and Oki, T.: Incorporation of groundwater pumping GCMs. Part I: Model formulation, J. Climate, 9, 676–705, 1996. in a global land surface model with the representation of human Smith, B., Samuelsson, P., Wramneby, A., and Rummukainen, M.: impacts, Water Resour. Res., 51, 78–96, 2015. A model of the coupled dynamics of climate, vegetation and terrestrial ecosystem biogeochemistry for regional applications,

www.geosci-model-dev.net/10/843/2017/ Geosci. Model Dev., 10, 843–872, 2017 872 A. Boone et al.: The interactions between ISBA-MEB in SURFEXv8

Tellus A, 63, 87–106, doi:10.1111/j.1600-0870.2010.00477.x, Wramneby, A., Smith, B., and Samuelsson, P.: Hot spots of 2011. vegetation-climate feedbacks under future greenhouse forc- van den Hurk, B., Best, M., Dirmeyer, P., Pitman, A., Polcher, J., ing in Europe, J. Geophys. Res.-Atmos., 115, D21119, and Santanello, J.: Acceleration of Land Surface Model Develop- doi:10.1029/2010JD014307, 2010. ment over a Decade of Glass, B. Am. Meteorol. Soc., 92, 1591– Wu, M., Schurgers, G., Rummukainen, M., Smith, B., Samuelsson, 1608, 2011. P., Jansson, C., Siltberg, J., and May, W.: Vegetation–climate Vergnes, J.-P., Decharme, B., and Habets, F.: Introduction of feedbacks modulate rainfall patterns in Africa under future cli- groundwater capillary rises using subgrid spatial variability of mate change, Earth Syst. Dynam., 7, 627–647, doi:10.5194/esd- topography into the ISBA land surface model, J. Geophys. Res., 7-627-2016, 2016. 119, 11065–11086, doi:10.1002/2014JD021573, 2014. Xue, Y., Sellers, P. J., Kinter, J. L., and Shukla, J.: A simpliﬁed Voldoire, A., Sanchez-Gomez, E., y Mélia, D. S., B. Decharme, Biosphere Model for Global Climate Studies, J. Climate, 4, 345– C. C., Sénési, S., Valcke, S., Beau, I., Alias, A., Chevallier, M., 364, 1991. Déqué, M., Deshayes, J., Douville, H., E. Fernandez, G. M., Zhang, W., Jansson, C., Miller, P. A., Smith, B., and Samuelsson, Maisonnave, E., Moine, M. P., Planton, S., Saint-Martin, D. P.: Biogeophysical feedbacks enhance the Arctic terrestrial car- S. S., Tyteca, S., Alkama, R., Belamari, S., A. Braun, L. C., bon sink in regional Earth system dynamics, Biogeosciences, 11, and Chauvin, F.: The CNRM-CM5.1 global climate model: de- 5503–5519, doi:10.5194/bg-11-5503-2014, 2014. scription and basic evaluation, Clim. Dynam., 40, 2091–2121, Zhang, Z., Xue, Y., MacDonald, G., Cox, P. M., and Collatz, G. J.: doi:10.1007/s00382-011-1259-y, 2013. Investigation of North American vegetation variability under Wilson, T., Meyers, T., Kochendorfer, J., Anderson, M., and Heuer, recent climate – A study using the SSiB4/TRIFFID biophys- M.: The effect of soil surface litter residue on energy and carbon ical/dynamic vegetation model, J. Geophys. Res., 120, 1300– ﬂuxes in a deciduous forest, Agr. Forest Meteorol., 161, 134– 1321, doi:10.1002/2014JD021963, 2015. 147, 2012.

Geosci. Model Dev., 10, 843–872, 2017 www.geosci-model-dev.net/10/843/2017/