Geosci. Model Dev., 12, 4309–4346, 2019 https://doi.org/10.5194/gmd-12-4309-2019 © Author(s) 2019. This work is distributed under the Creative Commons Attribution 4.0 License.

The , , and biogeochemistry of functionally diverse, vertically and horizontally heterogeneous : the Demography model, version 2.2 – Part 1: Model description

Marcos Longo1,2,3, Ryan G. Knox4,5, David M. Medvigy6, Naomi M. Levine7, Michael C. Dietze8, Yeonjoo Kim9, Abigail L. S. Swann10, Ke Zhang11, Christine R. Rollinson12, Rafael L. Bras13, Steven C. Wofsy1, and Paul R. Moorcroft1 1Harvard University, Cambridge, MA, USA 2Embrapa Agricultural Informatics, Campinas, SP, Brazil 3Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA 4Massachusetts Institute of Technology, Cambridge, MA, USA 5Lawrence Berkeley National Laboratory, Berkeley, CA, USA 6University of Notre Dame, Notre Dame, IN, USA 7University of Southern California, Los Angeles, CA, USA 8Boston University, Boston, MA, USA 9Department of Civil and Environmental Engineering, Yonsei University, Seoul, Korea 10University of Washington, Seattle, WA, USA 11Hohai University, Nanjing, Jiangsu, China 12The Morton Arboretum, Lisle, IL, USA 13Georgia Institute of Technology, Atlanta, GA, USA

Correspondence: Marcos Longo ([email protected])

Received: 14 February 2019 – Discussion started: 27 March 2019 Revised: 12 August 2019 – Accepted: 23 August 2019 – Published: 14 October 2019

Abstract. Earth system models (ESMs) have been devel- lent conservation of these quantities in long-term simulation oped to represent the role of terrestrial ecosystems on the (< 0.1 % error over 50 years). We also show examples of ED- , water, and cycles. However, many ESMs still 2.2 simulation results at single sites and across tropical South lack representation of within-ecosystem heterogeneity and America. These results demonstrate the model’s ability to diversity. In this paper, we present the Ecosystem Demog- characterize the variability of ecosystem structure, compo- raphy model version 2.2 (ED-2.2). In ED-2.2, the biophys- sition, and functioning both at stand and continental scales. ical and physiological processes account for the horizontal A detailed model evaluation was conducted and is presented and vertical heterogeneity of the ecosystem: the energy, wa- in a companion paper (Longo et al., 2019a). Finally, we high- ter, and carbon cycles are solved separately for a series of light some of the ongoing model developments designed to vegetation cohorts (groups of individual plants of similar improve the model’s accuracy and performance and to in- size and plant functional type) distributed across a series of clude processes hitherto not represented in the model. spatially implicit patches (representing collections of micro- environments that have a similar disturbance history). We de- fine the equations that describe the energy, water, and car- bon cycles in terms of total energy, water, and carbon, which simplifies the differential equations and guarantees excel-

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1 Introduction composition, structure, and functioning. DGVMs, when run coupled to atmospheric models, would then feedback onto The dynamics of the terrestrial play an integral climate. The subsequent generation of terrestrial biosphere- role in the Earth’s carbon, water, and energy cycles (Betts based DGVMs (i.e., DGVMs incorporating couple carbon, and Silva Dias, 2010; Santanello Jr et al., 2018; Le Quéré water, and energy fluxes) such as the Lund–Potsdam–Jena et al., 2018), and consequently, how the Earth’s climate sys- (LPJ) model (Sitch et al., 2003), Community Land Model’s tem is expected to change over the coming decades due to Dynamic Global Vegetation Model (CLM-DGVM) (Levis the increasing levels of atmospheric carbon dioxide arising et al., 2004), and Top-down Representation of Interactive Fo- from anthropogenic activities (IPCC, 2014; Le Quéré et al., liage and Flora Including Dynamics Joint UK Land Envi- 2018). Models for the dynamics of the terrestrial biosphere ronment Simulator (TRIFFID/JULES) (Hughes et al., 2004; and its bidirectional interaction with the atmosphere have Clark et al., 2011; Mangeon et al., 2016) have included ad- evolved considerably over the past decades (Levis, 2010; ditional mechanisms such as disturbance through fires and Fisher et al., 2014, 2018). As described by Sellers et al. multiple types of mortality. (1997), the first generation of land surface models (LSMs) Analyses have shown that most terrestrial biosphere mod- was limited to provide boundary conditions to atmospheric els are capable of reproducing the current distribution of models; they only solved a simplified energy and water bud- global biomes (e.g., Sitch et al., 2003; Blyth et al., 2011) get, and accounted for the effects of surface on frictional and their carbon stocks and fluxes (Piao et al., 2013). How- effects on near-surface winds (e.g., Manabe et al., 1965; ever, they diverge markedly in their predictions of how ter- Somerville et al., 1974). These models, however, did not restrial ecosystems will respond to future account for the active role of vegetation. The second gen- (Friedlingstein et al., 2014). In fully coupled Earth system eration of LSMs considered the active role of vegetation model simulations, some of these differing predictions arise and represented the spectral properties of the canopy, the from divergent predictions about the direction and magni- changes in roughness of vegetated surfaces, and the biophys- tude of regional climate change. However, offline analyses, ical controls on evaporation and transpiration (Sellers et al., in which the models are forced with prescribed climatolog- 1997); examples of these models include National Center ical forcing, have shown that there is also substantial dis- for Atmospheric Research Biosphere-Atmosphere Transfer agreement between the models about how terrestrial ecosys- Scheme (NCAR/BATS) (Dickinson et al., 1986) and Simple tems will respond to any shift in climate (e.g., Sitch et al., Biosphere model (SiB) (Sellers et al., 1986). The increas- 2008; Zhang et al., 2015). In addition, the transitions be- ing recognition of the role of vegetation in mediating the tween biome types, for example, the transition that occurs exchanges of carbon, water, and energy between the land between closed-canopy tropical forests and grass- and shrub- and the atmosphere led to the third generation of LSMs, dominated savannahs in South America, are generally far which incorporated explicit representations of plant photo- more abrupt in typical DGVM results than in observations synthesis and resulting dynamics of terrestrial carbon uptake, (Good et al., 2011; Levine et al., 2016). turnover, and release within terrestrial ecosystems (Sellers One important limitation of most DGVMs is that they do et al., 1997); examples of such models included LSM (Bo- not represent within-ecosystem diversity and heterogeneity. nan, 1995) and SiB2 (Sellers et al., 1996). While the fluxes of The representation of plant functional diversity within ter- carbon, water, and energy predicted by these models would restrial biosphere models is normally coarse, with broadly change in response to changes in their climate forcing, the defined PFTs defined from a combination of morphological biophysical and biogeochemical properties of the ecosystem and leaf physiological attributes (Purves and Pacala, 2008). within each climatological grid cell were prescribed and thus In addition, there is limited variation in the resource con- did not change over time. ditions (light, water, and nutrient levels) experienced by in- Subsequently, building upon previous work (Prentice dividual plants within the climatological grid cells of tradi- et al., 1992; Neilson, 1995; Haxeltine and Prentice, 1996), tional DGVMs. Some models, such as CLM (Oleson et al., Foley et al.(1996) adopted an approach to calculate the pro- 2013), have options to represent a multi-layer plant canopy ductivity of a series of plant functional types (PFTs), based (e.g., two canopy layers allowing for Sun and shade leaves), on a leaf-level model of photosynthesis. The abundance of and/or differences in rooting depth between PFTs; however, each PFT within each grid cell was dynamic, with the abun- resource conditions are assumed to be horizontally homo- dance changes being determined by the relative productivity geneous, meaning that there is no horizontal spatial varia- of the PFTs. This allowed the fast-timescale exchanges of tion in resource conditions experienced by individual plants. carbon, water, and energy within the plant canopy to be ex- The lack of significant variability in resource conditions lim- plicitly linked with the long-term dynamics of the ecosystem. its the range of environmental niches within the climatolog- This approach followed the concept of dynamic global veg- ical grid cells of terrestrial biosphere and makes the coex- etation model (DGVM), originally coined by Prentice et al. istence between PFTs difficult. Consequently, models often (1989) to describe this kind of terrestrial biosphere model in predict ecosystems comprised of single homogeneous vege- which changes in climate could drive changes in ecosystem tation types (Moorcroft, 2003, 2006).

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Field- and laboratory-based studies conducted over the because individual trees are represented in the model, the past 30 years indicate that plant functional diversity sig- results can be directly compared with field measurements. nificantly affects ecosystem functioning (Loreau and Hec- Gap models have various degrees of complexity, with some tor, 2001; Tilman et al., 2014, and references therein), and models being able to represent the interactions between cli- variations in trait expression are strongly driven by dis- mate variability and gross primary productivity (Friend et al., turbances and local heterogeneity of abiotic factors such 1997; Sato et al., 2007), as well as the impact of climate as soil characteristics (Bruelheide et al., 2018; Both et al., change in the ecosystem carbon balance (Fischer et al., 2016, 2019). In many cases, biodiversity increases ecosystem pro- and references therein). However, because the birth and death ductivity and ecosystem stability (e.g., Tilman and Down- of individuals within a plant canopy are stochastic processes, ing, 1994; Naeem and Li, 1997; Cardinale et al., 2007; multiple realizations of given model formulation are required García-Palacios et al., 2018), and biodiversity has also been to determine the long-term, large-scale dynamics of these shown to contribute to enhanced ecosystem functionality models, which limits their applicability over large regions in highly stressed environments (e.g., Jucker and Coomes, or global scales and has precluded their use in Earth system 2012). Other studies have also established correlations be- modeling studies. tween tropical forest diversity and carbon storage and pri- The need to represent heterogeneity in vegetation struc- mary productivity (Cavanaugh et al., 2014; Poorter et al., ture and composition in terrestrial biosphere models, without 2015; Liang et al., 2016; Huang et al., 2018). the computational burden of simulating every tree at regional In addition to the absence of within-ecosystem diversity and global scales, led to the development of cohort-based in conventional terrestrial biosphere models, plants of each models (Hurtt et al., 1998; Moorcroft et al., 2001; Fisher PFT are also assumed to be homogeneous in size, while, et al., 2018). In the cohort-based approach, individual trees in contrast, most terrestrial ecosystems, particularly forests are grouped according to their size (e.g., height or diameter at and woodlands, exhibit marked size structure of individuals breast height); functional groups, which can be defined along within plant canopies (Hutchings, 1997). This size-related trait axes (e.g., Reich et al., 1997; Wright et al., 2004; For- heterogeneity is important because plant size strongly affects tunel et al., 2012); and micro-environment conditions (e.g., the amount of light, water, and nutrients individual plants whether plants are living in a gap, recently burned frag- within the canopy can access, which, in turn, affects their per- ment, or in a patch of old-growth forest). Over the past two formance, dynamics, and responses to climatological stress. decades, several cohort-based models have emerged, includ- It also allows representation of the dynamics of pervasive ing the Ecosystem Demography model (ED; Moorcroft et al., human-driven degradation of forest ecosystems (Lewis et al., 2001; Hurtt et al., 2002; Albani et al., 2006; Medvigy et al., 2015; Haddad et al., 2015), which affects carbon stocks and 2009); the Lund–Potsdam–Jena General Ecosystem Simula- forest structure and composition, which cannot be easily rep- tor (LPJ-GUESS; Smith et al., 2001; Ahlström et al., 2012; resented in highly aggregated models (Longo and Keller, Lindeskog et al., 2013); the Land Model version 3 with per- 2019). fect plasticity approximation (LM3-PPA; Weng et al., 2015); An alternative approach to simulating the dynamics of and the Functionally-Assembled Terrestrial Ecosystem Sim- terrestrial ecosystems has been individual-based vegetation ulator (FATES; Fisher et al., 2015; Huang et al., 2019). Simi- models (Friend et al., 1997; Bugmann, 2001; Sato et al., lar to gap models, these models represent functional diversity 2007; Fischer et al., 2016; Maréchaux and Chave, 2017). and heterogeneity of micro-environments, and consequently Also known as forest gap models, due to the importance the ecosystem’s structure, diversity, and functioning emerge of canopy gaps for the dynamics of closed canopy forests, from the interactions between plants with different strate- these models simulate the birth, growth, and death of individ- gies under different resource availability, albeit at a lesser ex- ual plants, thereby incorporating diversity and heterogene- tent than individual-based models (Fisher et al., 2018). ity of the plant canopy mechanistically. In forest gap mod- The Ecosystem Demography model (ED; Moorcroft et al., els, the ecosystem properties such as total carbon stocks, and 2001) is a cohort-based model. Through this approach, it ad- net ecosystem productivity are emergent properties resulting dresses the need to incorporate heterogeneity into models from competition of limiting resources and the differential of the long-term, large-scale response of terrestrial ecosys- ability of plants to survive and be productive under a vari- tems to changes in climate and other environmental forcings ety of micro-environments (e.g., gaps or the understory of a within a deterministic modeling framework. The size- and densely populated patch of old-growth forest). age-structured partial differential equations that describe the This approach has two main advantages. First, gap mod- plant community are derived from individual-level proper- els represent the dynamic changes in the ecosystem structure ties but are properly scaled to account for the spatially local- caused by disturbances such as tree fall, selective logging, ized of interactions within plant canopies. The model and fires. These disturbances create new micro-environments was later extended by Hurtt et al.(2002) and Albani et al. that are significantly different from old-growth vegetation ar- (2006) to incorporate multiple forms of disturbance includ- eas and allow plants with different life strategies (for exam- ing land clearing, land abandonment, and forest harvesting. ple, shade-intolerants) to coexist in the landscape. Second, An important difference between ED and most DGVMs is www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4312 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2 that in ED, PFTs are defined not simply based on their bio- links the individual’s ability to access resources such as light geographic ranges but also represent diversity in plant life- and water and accumulate carbon under a variety of micro- history strategies within any given ecosystem. These differ- environments, which ultimately drives the long-term dynam- ent PFTs represent a suite of physiological, morphological, ics of growth, reproduction, and survivorship. and life-history traits that mechanistically represent the ways different kinds of plants utilize resources (Fisher et al., 2010). The original ED model formulation was an offline ecosys- 2 Model overview tem model describing the coupled carbon and water fluxes of 2.1 The representation of ecosystem heterogeneity in a heterogeneous tropical forest ecosystem (Moorcroft et al., ED-2.2 2001). Subsequently, Medvigy et al.(2009) applied a similar approach to develop the Ecosystem Demography model ver- In ED-2.2 the terrestrial ecosystem within a given region sion 2 (ED-2) that describes coupled carbon, water, and en- of interest is represented through a hierarchy of structures ergy fluxes of the land surface. Since then, the ED-2 model to capture the physical and biological heterogeneity in the has been continuously developed to improve several aspects ecosystem’s properties (Fig.1). of the model (see Supplement Sect. S1 for further informa- Physical heterogeneity. The domain of interest (grid) is ge- tion): (1) the conservation and thermodynamic representation ographically divided into polygons. Within each polygon, the of energy, water, and carbon cycles of the ecosystems; (2) the time-varying meteorological forcing above the plant canopy representation of several components of the energy, water, is assumed to be spatially uniform. For example, a single and carbon cycles, including the canopy radiative transfer, polygon may be used to simulate the dynamics of an ecosys- aerodynamic conductances and eddy fluxes, and leaf physi- tem in the neighborhood of an eddy flux tower, or alterna- ology (photosynthesis); (3) the structure of the code, includ- tively, a polygon may represent the lower boundary condition ing efficient data storage, code parallelization, and version within one horizontal grid cell in an atmospheric model. Each control and code availability. ED-2 has been used in many polygon is subdivided into one or more sites that are designed studies including offline simulations (e.g., Medvigy et al., to represent landscape-scale variation in other abiotic prop- 2009; Antonarakis et al., 2011; Kim et al., 2012; Zhang et al., erties, such as soil texture, soil depth, elevation, slope, as- 2015; Castanho et al., 2016; Levine et al., 2016) and sim- pect, and topographic moisture index. Each site is defined as ulations running interactively with a regional atmospheric a fractional area within the polygon and represents all regions model (e.g., Knox et al., 2015; Swann et al., 2015). within the polygon that share similar time-invariant physical In this paper, we describe in detail the biophysical, phys- (abiotic) properties. Both polygons and sites are defined at iological, ecological, and biogeochemical formulation of the the beginning of the simulation and are fixed in time, and no most recent version of the ED-2 model (ED-2.2), focusing in geographic information exists below the level of the polygon. particular on the model’s formulation of the fast timescale Biotic heterogeneity. Within each site, horizontal, dynamics of the heterogeneous plant canopy that occur at disturbance-related heterogeneity in the ecosystem at any subdaily timescales. While many parameterizations and sub- given time t is characterized through a series of patches that models in ED-2.2 are based on approaches that are also used are defined by the time elapsed since last disturbance (i.e., in other DGVMs, their implementation in ED-2.2 has some age, a) and the type of disturbance that generated them. critical differences from other ecosystem models and also Like sites, patches are not physically contiguous: each patch previous versions of ED. (1) In ED-2.2, the fundamental bud- represents the collection of canopy gap-sized (∼ 10m) areas get equations use energy and total mass as the main prog- within the site that have a similar disturbance history, defined nostic variables; because we use equations that directly track in terms of the type of disturbance experienced (represented the time changes of the properties we seek to conserve, we by subscript q, q ∈ 1,2,...,NQ; a list of indices is available can assess the model conservation of such properties with in Table1) and time since the disturbance event occurred. fewer assumptions. (2) In ED-2.2, all thermodynamic prop- The disturbance types accounted for in ED-2.2, and the erties are scalable with mass, and the model is constructed possible transitions between different disturbance types, are such that when individual biomass changes, due to growth shown in Fig. S1. The collection of gaps within each given and turnover, the thermodynamic properties are also updated site belonging to a polygon follows a probability distribution to reflect changes in heat and water holding capacity. (3) The function α, which can be also thought of as the relative area water and energy budget equations for vegetation are solved within a site, that satisfies at the individual cohort level and the corresponding equa- tions for environments shared by plants such as soils and N  ∞  XQ Z canopy air space are solved for each micro-environment in  αq (a,t)da = 1. (1) the landscape, and thus ecosystem-scale fluxes are emergent q=1 0 properties of the plant community. This approach allows the model to represent both the horizontal and vertical hetero- Similarly, the plant community population is characterized geneity of environments of the plant communities. It also by the number of plants per unit area (hereafter number

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probability distribution of patches within each site in the size-and-age structured model are defined as (dependencies omitted in the equations for clarity)

∂nf q ∂nf q  = − −∇C · gf nf q −mf nf q , (2) ∂t ∂a | {z }| {z } | {z } | {z } Mortality Change rate Aging Growth

NQ ∂αq ∂αq X  − = − λq0q αq , (3) ∂t ∂a 0 |{z} |{z} q =1 Change rate Aging| {z } Disturbance

where mf is mortality rate, which may depend on the PFT, size, and the individual carbon balance; gf is the vector of the net growth rates for each carbon pool, which also may depend on the PFT, size, and carbon balance; ∇C· is the di- vergence operator for the size vector; and λq0q is the transi- tion matrix from gaps generated by previous disturbance q0 affected by new disturbance of type q, which may depend on environmental conditions. Boundary conditions are shown in Sect. S2. Equations (2) and (3) cannot be solved analytically ex- cept for the most trivial cases; therefore, the age distribu- tion is discretized into patches (subscript u, u ∈ 1,2,...,NP ; Table1) of similar age and same disturbance type, and the population size structure living in any given patch u is dis- cretized into cohorts (subscript k, k ∈ 1,2,...,NT; Table1) of similar size and same PFT (Fig.1). Unlike polygons and sites, patches and cohorts are dynamic levels: changes in dis- tribution (fractional area) of patches are driven by aging and disturbance rates, whereas changes in the distribution of co- horts in each patch are driven by growth, mortality, and re- cruitment (Fig. S2). The environment perceived by each plant (e.g., incident light, temperature, vapor pressure deficit) varies across large Figure 1. Schematic representation of the multiple hierarchical lev- els in ED-2.2, organized by increasing level of detail from top to scales as a consequence of changes in climate (macro- bottom. Static levels (grid, polygons, and sites) are assigned during environment) but also varies at small scales (within the land- the model initialization and remain constant throughout the simula- scape; micro-environment) because of the horizontal and ver- tion. Dynamic levels (patches and cohorts) may change during the tical position of each individual relative to other individ- simulation according to the dynamics of the ecosystem. uals in the plant community (e.g., Bazzaz, 1979) and the position of the local community in landscapes with com- plex terrains. Both macro- and micro-environmental con- density, n) and is further classified according to their PFT, ditions drive the net primary productivity of each individ- represented by subscript f (f ∈ 1,2,...,NF; Table1) and ual, and ultimately determine growth, mortality, and recruit- the type of gap (q). The number density distribution de- ment rates for each individual. Likewise, they can also af- pends on the individuals’ biomass characteristics (size, C), fect the disturbance rates: for example, during drought con- the age since last disturbance (a), and the time (t), and is ditions (macro-environment), open canopy patches (micro- expressed as nf q (C,a,t). Size is defined as a vector C = environment) may experience faster ground desiccation and −1 ; ; ; ; −1 nf q (Cl Cr Cσ Ch Cn) (units: kgC plant ) corresponding consequently increase local fire risk. To account for the to biomass of leaves, fine roots, sapwood, heartwood, and variability in micro-environments within the landscape and non-structural storage (starch and sugars), respectively. within local plant communities, in ED-2.2 the energy, wa- Following Moorcroft et al.(2001), Albani et al.(2006), ter, and carbon dioxide cycles are solved separately for each and Medvigy and Moorcroft(2012), the partial differential patch, and within each patch, fluxes and storage associated equations that describe the dynamics of plant density and with individual plants are solved for each cohort. www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4314 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2

Table 1. List of subscripts associated with ED-2.2’s hierarchical levels for any variable X. NT is the total number of cohorts, NG is the total number of soil (ground) layers, NS is the total number of temporary surface water/snowpack layers, and NC is the total number of canopy air space layers, currently only used to obtain properties related to canopy conductance. The complete list of subscripts is available in Table S1.

Subscript Description

Xc Canopy air space (single layer) { } Xcj Canopy air space, layer j (j ∈ 1,2,...,NC ) Xej Necromass pools: e1, metabolic litter (fast); e2, structural debris (intermediate); e3, humified/dissolved (slow) Xf Plant functional type ∈ { } Xgj Soil (ground), layer j (j 1,2,...,NG ) Xq Disturbance type { } Xsj Temporary surface water/snowpack, layer j (j ∈ 1,2,...,NS ) { } Xtk Cohort k (k ∈ 1,2,...,NT ) Xu Patch u (u ∈ {1,2,...,NP}) { } Xyk Property y of cohort k (k ∈ 1,2,...,NT ). Possible values of y: branch wood (b), structural (heartwood) (h), leaves (l), non-structural carbon storage (starch, sugars) (n), roots (r), total living tissues (α), branch boundary layer (β), carbon balance (1), leaf boundary layer (λ), reproductive tissues (%), sapwood (σ)

The ED-2.2 model represents processes that have inher- ary conditions and are integrated independently of each other ently different timescales; therefore, the model also has a hi- but write the results to a unified output file using collective erarchy of time steps, in order to attain maximum compu- input/output functions from HDF5. In the case of simula- tational efficiency (Table2). Processes associated with the tions dynamically coupled with an atmospheric model such short-term dynamics are presented in this paper. A sum- as BRAMS, polygons are defined to match each atmospheric mary of the phenological processes and those associated with grid cell. longer-term dynamics is presented in Sects. S3 and S4 (see Memory allocation. The code uses dynamic allocation of also Moorcroft et al., 2001; Albani et al., 2006; Medvigy variables and extensive use of pointers to efficiently reduce et al., 2009). the amount of data transferred between routines. To reduce the output file size, polygon-, site-, patch-, and cohort-level 2.2 Software requirements and model architecture variables are always written as long vectors, and auxiliary in- dex vectors are used to map variables from higher hierarchi- Software requirements. The ED-2.2 source code is mainly cal levels to lower hierarchical levels (for example, to which written in Fortran 90, with a few file management rou- patch a cohort-level variable belongs). tines written in C. Most input and output files use the Hi- erarchical Data Format 5 (HDF5) format and libraries (The 2.3 Model inputs HDF Group, 2016). In addition, the Message Passing Inter- face (MPI) is highly recommended for regional simulations Every ED-2.2 simulation requires an initial state for forest and is required for simulations coupled with the Brazilian structure and composition (initial state), a description of soil Improvements on Regional Atmospheric Modeling System characteristics (edaphic conditions), and a time-varying list (BRAMS) atmospheric model (Knox et al., 2015; Swann of meteorological drivers (atmospheric conditions). et al., 2015; Freitas et al., 2017). The source code can be Initial state. To initialize a plant community from inven- also compiled with shared memory processing (SMP) li- tory data, one must have either the diameter at breast height braries, which enable parallel processing of of every individual or the stem density of different diam- and biophysics steps at the patch level and thus allow shorter eter size classes, along with plant functional type identifi- simulation time. cation and location; in addition, necromass from the litter Code design and parallel structure. ED-2.2 has been de- layer, woody debris, and soil organic carbon are needed. Al- signed to be run in three different configurations: (1) as a ternatively, initial conditions can be obtained from airborne stand-alone land surface model over a small list of specified lidar measurements (Antonarakis et al., 2011, 2014) or a pre- locations (sites); (2) as a stand-alone land surface model dis- scribed near-bare-ground condition may be used for long- tributed over a regional grid; (3) coupled with an atmospheric term spin up simulations. Previous simulations can be used model distributed over a regional grid (e.g., ED-BRAMS; as initial conditions as well. Knox et al., 2015; Swann et al., 2015). For regional stand- Edaphic conditions. The user must also provide soil char- alone grids, the model partitions the grid into spatially con- acteristics such as total soil depth, total number of soil lay- tiguous tiles of polygons, which access the initial and bound- ers, the thickness of each layer, as well as soil texture, color,

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Table 2. Time steps associated with processes resolved by ED-2.2. The thermodynamic substep is dynamic and it depends on the error evaluation of the integrator, but it cannot be longer than the biophysics step, which is defined by the user. Other steps are fixed as of ED-2.2. Processes marked with an asterisk are presented in the main paper. Other processes are described in Sects. S3 and S4.

Time step Timescale Processes Thermodynamics Energy and water fluxes∗ ∗ (1tThermo) 1s–1tBio Eddy fluxes (including CO2 flux) Most thermodynamic state functions∗ ∗ Meteorological and CO2 forcing Biophysics Radiation model∗ ∗ (1tBio) 2–15min Photosynthesis model Respiration fluxes (autotrophic and heterotrophic)∗ ∗ Evaluation of energy, water, and CO2 budgets Maintenance of active tissues Update of the storage pool Phenology 1d Leaf phenology (1tPhen) Plant carbon balance Integration of mortality rate due to cold Soil litter pools Growth of structural tissues Cohort dynamics Mortality rate (1tCD) 1month Reproduction – cohort creation Integration of fire disturbance rate Cohort fusion, fission, and extinction Patch dynamics 1year Annual disturbance rates and patch creation (1tPD) Patch fusion and termination and the bottom soil boundary condition (bedrock, reduced must be provided at comparable temporal and spatial resolu- drainage, free drainage, or permanent water table). This flex- tion to other meteorological drivers; otherwise, it is possible ibility allows the user to easily adjust the soil characteristics to provide spatially homogeneous, time-variant CO2, or according to their regions of interest. Soil texture can be read constant CO2, although this may increase uncertainties in from standard data sets (e.g., Global Soil Data Task, 2000; the model predictions (e.g., Wang et al., 2007). Alternatively, Hengl et al., 2017) or provided directly by the user. Soil lay- the meteorological forcing (including CO2) may be provided ers, soil color, and bottom boundary condition must be pro- directly by BRAMS (Knox et al., 2015; Swann et al., 2015). vided directly by the user as of ED-2.2. In addition, simula- Plant functional types. The user must specify which PFTs tions with multiple sites per polygon also need to provide the are allowed to occur in any given simulation. ED-2.2 has fractional areas of each site and the mean soil texture class, a list of default PFTs, with parameters described in Ta- soil depth, slope, aspect, elevation, and topographic moisture bles S5–S6. Alternatively, the user can modify the parame- index of each site. ters of existing PFTs or define new PFTs through an exten- Atmospheric conditions. Meteorological conditions sible markup language (XML) file, which is read during the needed to drive ED-2.2 include temperature, specific humid- model initialization. ity, CO2 molar fraction, pressure of the air above the canopy, precipitation rate, incoming solar (shortwave) irradiance (radiation flux), and incoming thermal (longwave) irradiance 3 Overview of enthalpy, water, and carbon dioxide (Table3) at a reference height that is at least a few meters cycles above the canopy. Subdaily measurements (0.5–6 h) are highly recommended so the model can properly simulate Here, we present the fundamental equations that describe the the diurnal cycle and interdiurnal variability. Meteorolog- biogeophysical and biogeochemical cycles. Because the en- ical drivers can be either at a single location (e.g., eddy vironmental conditions are a function of the local plant com- covariance towers) or gridded meteorological drivers such munity and resources are shared by the individuals, these cy- as reanalyses (e.g., Dee et al., 2011; Gelaro et al., 2017) or cles must be described at the patch level, and the response bias-corrected products based on reanalysis (e.g., Sheffield of the plant community can be aggregated to the polygon et al., 2006; Weedon et al., 2014). Whenever available, CO2 level once the cycles are resolved for each patch. In ED-2.2, www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4316 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2

Table 3. Atmospheric boundary conditions driving the ED-2.2 model. Variable names and subscripts follow a standard notation throughout the paper (Tables S1 and S2). Flux variables between two thermodynamic systems are defined by a dot and two indices separated by a comma, and they are positive when the net flux goes from the thermodynamic system represented by the first index to the one represented by the second index.

Variable Description Units −1 ux Zonal wind speed ms −1 uy Meridional wind speed ms pa Free-air pressure Pa Ta Free-air temperature K −1 wa Free-air specific humidity kgW kg −1 ca Free-air CO2 mixing ratio molC mol za Height of the reference point above canopy m ˙ −2 −1 W∞,a Precipitation mass rate kgW m s ˙ ⇓ −2 QTIR(∞,a) Downward thermal infrared irradiance Wm ˙ −2 QPAR(∞,a) Downward photosynthetically active irradiance, direct Wm ˙ ⇓ −2 QPAR(∞,a) Downward photosynthetically active irradiance, diffuse Wm ˙ −2 QNIR(∞,a) Downward near-infrared irradiance, direct Wm ˙ ⇓ −2 QNIR(∞,a) Downward near-infrared irradiance, diffuse Wm

−2 patches do not exchange enthalpy, water, and carbon dioxide ible fluids for total water mass W (kgW m ): with other patches; thus, patches are treated as independent dH systems. Throughout this section, we will only refer to the = Q˙ + H˙ patch and cohort levels, and indices associated with patches, dt |{z} |{z} |{z} Net heat flux Enthalpy flux due sites, and polygons will be omitted for clarity. Change in enthalpy to mass flux dp + V , (4) 3.1 Definition of the thermodynamic state dt | {z } Pressure change Each patch is defined by a thermodynamic envelope (Fig.2), comprised of multiple thermodynamic systems: each soil dW = W˙ , (5) layer (total number of layers NG), each temporary surface dt |{z} water or snow layer (total number of layers N ), leaves, and |{z} Net water mass flux S Change in water mass branch wood portion of each cohort (total number of cohorts NT), and the canopy air space. For simplicity, roots are as- where V is the volume of the thermodynamic system and p sumed to be in thermal equilibrium with the soil layers and is the ambient pressure. The components on the right-hand have negligible heat capacity compared to the soil layers. Al- side of Eqs. (4) and (5) depend on the thermodynamic sys- though patches do not exchange heat and mass with other tem and will be presented in detail in the following sections. patches, they are allowed to exchange heat and mass with Net heat fluxes (Q˙ ) represent changes in enthalpy that are not the free air (i.e., the atmosphere above and outside of the associated with mass exchange (radiative and sensible heat air space control volume we deem as within canopy) and fluxes), whereas the remaining enthalpy fluxes (H˙ ) corre- lose water and associated energy through surface and subsur- spond to changes in heat capacity due to addition or removal face runoff. We also assume that intensive variables such as of mass from each thermodynamic system. pressure and temperature are uniform within each thermody- The merit of solving the changes in enthalpy over inter- namic system. Note that free air is not considered a thermo- nal energy is that changes in enthalpy are equivalent to the dynamic system in ED-2 because the thermodynamic state is net energy flux when pressure is constant (Eq.4). Pressure is determined directly from the boundary conditions and thus commonly included in atmospheric measurements, making it external to the model. easy to track changes in enthalpy not related to energy fluxes. The fundamental equations that describe the system ther- In reality, the only thermodynamic system where the dis- modynamics are the first law of thermodynamics in terms of tinction between internal energy and enthalpy matters is the enthalpy H (Jm−2), and the mass continuity for incompress- canopy air space. Work associated with thermal expansion

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Table 4. List of state variables solved in ED-2.2. Unless otherwise noted, the reference equation is the ordinary differential equation that defines the rate of change of the thermodynamic state. The list of fluxes that describe the thermodynamic state is presented in Table5. For a complete list of subscripts and variables used in this paper, refer to Tables S1–S2.

State variable Description Units Reference equation −1 cc CO2 mixing ratio – canopy air space molC mol (23) −1 hc Specific enthalpy – canopy air space Jkg (18) −3 a Hgj Volumetric enthalpy – soil layer j Jm (4) −2 Hsj Enthalpy – temporary surface water layer j Jm (4) −2 Htk Enthalpy – cohort k Jm (4) b pc Atmospheric pressure – canopy air space Pa (S81) −1 wc Specific humidity – canopy air space kgW kg (19) −2 Wsj Water mass – temporary surface water layer j kgW m (5) −2 Wtk Intercepted/dew/frost water mass – cohort k kgW m (5) c zc Depth (specific volume) – canopy air space m (17) 3 −3 a ϑgj Volumetric soil moisture – soil layer j mW m (5)

a Budget fluxes are in units of area, and the state variable is updated following the conversion described in Sect. 3.2.1. b Canopy air space pressure is not solved using ordinary differential equations but based on the atmospheric pressure from the meteorological forcing. c Canopy air space depth is determined from vegetation characteristics, not from an ordinary differential equation. of solids and liquids is several orders of magnitude smaller Kutta integrator with dynamic time steps to maintain the er- than heat (Dufour and van Mieghem, 1975), and changes ror within prescribed tolerance. For all fluxes and variables, in pressure contribute significantly less to enthalpy because we follow the subscript notation described in Table S1, and the specific volumes of solids and liquids are comparatively denote flux variables with a dot and two indices separated small. Likewise, enthalpy fluxes that do not involve gas phase by a comma, denoting the systems impacted by the flux. For (e.g., canopy dripping and runoff) are nearly indistinguish- any variable X that has flux between a system m and a sys- ˙ able from internal energy flux, whereas differences between tem n, we assume that Xm,n > 0 when the net flux goes from ˙ ˙ enthalpy and internal energy fluxes are significant when gas system m to system n, and that Xm,n = −Xn,m. Arrows in phase is involved (e.g., transpiration and eddy flux). For sim- Fig.2 indicate the directions allowed in ED-2.2. The list of plicity, from this point on, we will use the term “enthalpy” fluxes solved in ED-2.2 is provided in Table5, and a com- whenever internal energy is indistinguishable from enthalpy. plete list of variables is provided in Table S2. In addition, the The complete list of state variables in ED-2.2 is shown in Ta- values of global constants and global parameters are listed ble4. in Tables S3 and S4, respectively, and the default parameters Variations in enthalpy are more important than their ac- specific for each tropical plant functional type are presented tual values, but they must be consistently defined relative to in Tables S5–S6. a pre-determined and known thermodynamic state, at which we define enthalpy to be zero. For any material other than 3.2.1 Soil water, enthalpy is defined as zero when the material temper- ature is 0K; for water, enthalpy is defined as zero when water In ED-2.2, the soil characteristics (number of soil layers, is at 0K and completely frozen. The general definitions of en- thickness of each soil layer and total soil depth, soil tex- thalpy and internal energy states used in all thermodynamic ture, soil color) are defined by the user, and assumed con- systems in ED-2.2 are described in Sect. S5. In ED-2.2, en- stant throughout the simulation. Within each patch, each soil thalpy is used as the prognostic variable because these are di- layer (comprised by soil matrix and soil water in each layer) rectly and linearly related to the governing ordinary differen- is considered a separate thermodynamic system, with the tial equation (Eq.4). Temperature is diagnostically obtained main size dimension being the layer thickness 1zgj , with based on the heat capacity of each thermodynamic system, j = 1 being the deepest soil layer, and j = NG being the top- and the heat capacities of different thermodynamic systems most soil layer. Typically, the top layer thickness is set to 1z = 0.02m, which is a compromise between computa- are defined in Sect. S6. gNG tional efficiency and ability to represent the stronger gradi- 3.2 Heat (Q˙ ), water (W˙ ), and enthalpy (H˙ ) fluxes ents near the surface, and layers with increasing thickness

(1zgj ) are added for the entire rooting zone. The enthalpy and water cycles for each patch in ED-2.2 are The thermodynamic state is defined in terms of the soil −3 summarized in Fig.2, and these cycles are solved every ther- volume: the bulk specific enthalpy Hgj (Jm ) and volu- 3 −3 modynamic substep (1tThermo), using a fourth-order Runge– metric soil water content ϑgj (mW m ), which can be re- www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4318 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2

Table 5. List of energy, water, and carbon dioxide fluxes that define the thermodynamic state in ED-2.2, along with sections and equations that ˙ define them. Fluxes are denoted by a dotted letter, and two subscripts separated with a comma: Xm,n. Positive fluxes go from thermodynamic system m to thermodynamic system n; negative fluxes go in the opposite direction. Acronyms in the description column: canopy air space (CAS); temporary surface water (TSW). The complete list of subscripts and variables used in this paper is available in Tables S1–S2, and the list of state variables is shown in Table4.

Variable Description Section Equation Units ˙ Ca,c CO2 flux from turbulent mixing 4.4(55) ˙ Cej ,c Heterotrophic respiration flux ( pool ej ) 4.8(102) ˙ a Cl ,c Net leaf (cohort k)–CAS CO2 flux 4.6(93) −2 −1 ˙ k kgCm s Cnk,c Storage turnover (cohort k) respiration flux 4.7(100) ˙ Crk,c Fine-root (cohort k) metabolic respiration flux 4.7(99) ˙ C1k,c Growth and maintenance (cohort k) respiration flux 4.7(101) ˙ Qa,gNG Net absorbed irradiance (topmost soil layer) 4.3.2(52) ˙ Qa,sj Net absorbed irradiance (TSW layer j) 4.3.2(51) ˙ Qa,tk Net absorbed irradiance (cohort k) 4.3.1(49) ˙ QgNG,c Ground–CAS net sensible heat flux 4.5.2(68) −2 ˙ Wm Qgj−1,gj Net sensible heat flux between two soil layers 4.1(26) ˙ QsNS,c TSW–CAS net sensible heat flux 4.5.2(66) ˙ Qsj−1,sj Net sensible heat flux between two TSW layers 4.1(27) ˙ Qtk,c Cohort k–CAS net sensible heat flux 4.5.1(60) ˙ Ha,c Enthalpy flux from turbulent mixing at the top of CAS 4.4(54) ˙ Ha,sNS Enthalpy flux to the top TSW layer associated with throughfall precipitation 4.2(42) ˙ Ha,tk Enthalpy flux associated with rainfall interception by cohort k 4.2(41) ˙ b HgNG,c Enthalpy flux associated with ground–CAS evaporation 4.5.3(75) ˙ Hgj−1,gj Enthalpy flux associated with water percolation between two soil layers 4.1(35) H˙ Enthalpy flux associated with soil water extraction from soil layer j by cohort k 4.6(97) gj ,lk − ˙ Wm 2 Hg1,g0 Enthalpy flux associated with subsurface runoff from the bottom soil layer 4.1(29) ˙ Hlk,c Enthalpy flux associated with transpiration by cohort k 4.6(98) ˙ b HsNS,c Enthalpy flux associated with TSW–CAS evaporation 4.5.3(75) ˙ HsNS,o Enthalpy flux associated with surface runoff from the top TSW layer 4.1(34) ˙ Hsj−1,sj Enthalpy flux associated with water percolation between two TSW layers 4.1(35) ˙ b Htk,c Enthalpy flux associated with evaporation of intercepted water (cohort k) 4.5.3(75) ˙ Htk,sNS Enthalpy flux associated with canopy dripping from cohort k to the top TSW layer 4.2(44) ˙ Wa,c Water flux from turbulent mixing at the top of CAS 4.4(53) ˙ Wa,sNS Precipitation throughfall flux to the top TSW layer 4.2(37) ˙ Wa,tk Water flux from rainfall interception (cohort k) 4.2(36) ˙ b WgNG,c Ground–CAS evaporation flux 4.5.2(69) ˙ Wgj−1,gj Water percolation flux between two soil layers 4.1(28) W˙ Water flux associated with soil water extraction by plants 4.6(96) gj ,lk −2 −1 ˙ kgW m s Wg1,g0 Water flux associated with subsurface runoff from the bottom soil layer 4.1(33) ˙ Wl ,c Transpiration flux (cohort k) 4.6(94) ˙ k Wsj−1,sj Water percolation flux between two TSW layers 4.1(30)–(31) ˙ WsNS,o Surface runoff water flux from the top TSW layer 4.1(34) ˙ b WsNS,c TSW–CAS evaporation flux 4.5.2(67) ˙ b Wtk,c Evaporation flux from intercepted water (cohort k) 4.5.1(61) ˙ Wtk,sNS Canopy dripping flux from cohort k to the top TSW layer 4.2(43) a Net flux between leaf respiration (positive) and gross primary productivity (negative). b When negative, this flux corresponds to dew or frost formation.

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Figure 2. Schematic of the fluxes that are solved in ED-2.2 for a single patch (thermodynamic envelope). In this example, the patch has NT cohorts, NG soil layers, and NS = 1 temporary surface water. Both NG and the maximum NS are specified by the user; NT is dynamically defined by ED-2.2. Letters near the arrows are the subscripts associated with fluxes, although the flux variables have been omitted here for clarity. Solid red arrows represent heat flux with no exchange of mass, and dashed yellow arrows represent exchange of mass and associated enthalpy. Arrows that point to a single direction represent fluxes that can only go in one (non-negative) direction, and arrows pointing to both directions represent fluxes that can be positive, negative, or zero.

= = lated to Eqs. (4)–(5) by defining Hgj Hgj 1zgj and Wgj ρ` · ϑg · 1zg , where ρ` is the density of liquid water (Ta- j j W˙ = W˙ − W˙ − δ W˙ ble S3). Soil net fluxes for any layer j are defined as gj gj−1,gj gj ,gj+1 gj gNG gNG ,c |{z} | {z } | {z } ˙ ˙ ˙ ˙ Net water flux Water percolation Ground evaporation Qg = Qg − ,g − Qg ,g + + δg g Qa,g between consecutive layers (Sect. 4.5.2 and 4.5.3) j j 1 j j j 1 j NG NG ( . . ) |{z} | {z } | {z } Sect 4 1 Net heat flux Net sensible heat flux Absorbed irradiance N between consecutive layers (Sect. 4.3.2) T − X ˙ (Sect. 4.1) Wgj ,lk , = − δ Q˙ , (6) k 1 gj gNG gNG ,c | {z } | {z } water uptake Ground–CAS sensible heat by cohorts (Sect. 4.5.2 and 4.5.3) (Sect. 4.6) (8)

where δ is the Kronecker delta for comparing two ˙ ˙ ˙ ˙ gj gj0 Hg = Hg − ,g − Hg ,g + − δg g Hg ,c j j 1 j j j 1 j NG NG soil layers g and gj 0 (1 if g = gj 0 ; 0 otherwise), CAS |{z} | {z } | {z } j j Net enthalpy flux Water percolation Ground evaporation is the canopy air space, and subscript o denotes the loss due to water flux between consecutive layers (Sect. 4.5.2 and 4.5.3) through runoff. References in parentheses underneath the (Sect. 4.1) terms correspond to the sections in which each term is NT presented in detail. In the equations above, we assume − X ˙ Hgj ,lk , ˙ Qg0,g1 to be zero (bottom boundary condition in thermal k=1 ˙ = − ˙ ˙ = − ˙ | {z } equilibrium) and (Hg1,g0 Hg0,g1 ; Wg1,g0 Wg0,g1 ) to Water uptake be subsurface runoff fluxes (see Sect. 4.1). In addition, by cohorts ˙ ˙ ˙ (Sect. 4.6) (Q ; H ; W ) are equivalent to gNG ,gNG+1 gNG ,gNG+1 gNG ,gNG+1 (7) (Q˙ ; H˙ ; W˙ ), which are the fluxes between gNG ,s1 gNG ,s1 gNG ,s1 www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4320 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2

the topmost soil layer and the bottommost temporary surface where δsj sj0 is the Kronecker delta for comparing two TSW water layer (see also Sect. 3.2.2). layers sj and sj 0 (1 if sj = sj 0 ; 0 otherwise), CAS is the canopy air space, and subscript o denotes loss from the ther- 3.2.2 Temporary surface water (TSW) modynamic envelope through runoff. Terms are described in detail in the sections shown underneath each term. Sim- Temporary surface water (TSW) exists whenever water falls ˙ ilarly to the soil fluxes (Sect. 3.2.1), we assume that (Qs0,s1 ; to the ground, or dew or frost develops on the ground. The H˙ ; W˙ ) is equivalent to (Q˙ ; H˙ ; W˙ ), s0,s1 s0,s1 gNG ,s1 gNG ,s1 gNG ,s1 layer will be maintained only when the amount of water that the fluxes between the topmost soil layer and the bottommost reaches the ground exceeds the water holding capacity of the TSW layer. When solving Eqs. (9)–(11) for layer sN , we as- top soil layer (a function of the soil porosity), or when pre- ˙ ˙ ˙ S sume the terms Qs ,s , Hs ,s and Ws ,s to be all zero, cipitation falls as snow. The maximum number of temporary j j+1 j j+1 j j+1 as layer NS + 1 does not exist. N max surface water layers S is defined by the user, but the ac- In the case of liquid TSW, the layer thickness of the single tual number of layers NS and the thickness of each layer de- = −1 layer is defined as 1zs1 ρ` Ws1 , where ρ` is the density pends on the total mass and the water phase, following Walko of liquid water (Table S3). In the case of snowpack develop- et al.(2000). When the layer is in liquid phase, only one layer ment, the snow density and the layer thickness of the TSW = (NS 1) is maintained. If a snowpack develops, the tempo- are solved as described in Sect. S7. The thickness of each rary surface water can be divided into several layers (sub- layer of snow (1z ) is defined using the same algorithm as = sj script j, with j 1 being the bottommost TSW layer, and LEAF-2 (Walko et al., 2000) and is described in Sect. S7. j = NS being the topmost TSW layer). Net TSW fluxes are defined as ˙ = ˙ − ˙ + ˙ Qsj Qsj−1,sj Qsj ,sj+1 Qa,sj 3.2.3 Vegetation |{z} | {z } | {z } Net heat flux Net sensible heat flux Absorbed irradiance between consecutive layers (Sect. 4.3.2) (Sect. 4.1) In ED-2.2, vegetation is solved as an independent thermo- − δ Q˙ , (9) dynamic system only if the cohort is sufficiently large. The sj sNS sNS ,c | {z } minimum size is an adjustable parameter and the typical min- Ground–CAS sensible heat (Sect. 4.5.2 and 4.5.3) imum heat capacity solved by ED-2.2 is on the order of −2 −1 2 −2 10 Jm K and total area index of 0.005 mleaf+wood m . ˙ ˙ ˙ ˙ Cohorts smaller than this are excluded from all energy and H = Hs , − H ,s + δ s Ha,s sj j−1 sj sj j+1 sj NS NS calculations and assumed to be in thermal equi- |{z} | {z } | {z } Net enthalpy flux Water percolation Throughfall librium with canopy air space. The net fluxes of heat, en- due to water flux between consecutive layers precipitation thalpy, and water for each cohort k that can be resolved are (Sect. 4.1) (Sect. 4.2) N ! XT + δ H˙ − δ H˙ − δ H˙ , sj sNS tk,sNS sj sNS sNS ,o sj sNS sNS ,c k=1 | {z } | {z } Q˙ = Q˙ − Q˙ , (12) | {z } Surface runoff Surface water tk a,tk tk,c Canopy dripping Sect.(4.1) evaporation |{z} | {z } | {z } from cohorts (Sect. 4.5.2 and 4.5.3) Net heat flux Cohort’s net Cohort–CAS Sect.(4.2) absorbed irradiance sensible heat (Sect. 4.3.1) (Sect. 4.5.1) (10)

W˙ = W˙ − W˙ + δ W˙ sj sj−1,sj sj ,sj+1 sj sNS a,sNS |{z} | {z } | {z } Net water flux Water percolation Throughfall between consecutive layers precipitation N ! (Sect. 4.1) (Sect. 4.2) G ˙ = ˙ − ˙ + X ˙ Htk Ha,tk Htk,sN Hgj ,lk NT ! S X ˙ ˙ |{z} |{z} | {z } j=1 + δ s Wt ,s − δ s Ws ,o Net enthalpy flux Rainfall Canopy dripping sj NS k NS sj NS NS | {z } due to water flux interception (Sect. 4.2) k=1 | {z } (Sect. 4.2) Soil moisture | {z } Surface runoff uptake (transpiration) Canopy dripping (Sect. 4.1) (Sect. 4.6) from cohorts − ˙ − ˙ (Sect. 4.2) Hlk,c Htk,c , − δ W˙ , (11) |{z} |{z} sj sNS sNS ,c Transpiration Evaporation of | {z } (Sect. 4.6) intercepted water Surface water (Sect. 4.5.3) evaporation (Sect. 4.5.2 and 4.5.3) (13)

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space budget:   dhc 1 ˙ ˙ dpc = Qc + Hc + zc , (18) dt ρc zc dt N ! XG dw 1 W˙ = W˙ − W˙ + W˙ c = ˙ tk a,tk tk,sNS gj ,lk Wc, (19) |{z} | {z } | {z } j=1 dt ρc zc Water flux Rainfall Canopy dripping interception | {z } (Sect. 4.2) Soil moisture where (Sect. 4.2) uptake (transpiration) (Sect. 4.6) N ! XT − W˙ − W˙ . Q˙ = Q˙ + Q˙ lk,c tk,c c tk,c sNS ,c | {z } | {z } |{z} k=1 | {z } Transpiration Evaporation of Net heat flux | {z } Surface water–CAS (Sect. 4.6) intercepted water Cohort–CAS sensible heat (Sect. 4.5.3) sensible heat (Sect. 4.5.2 and 4.5.3) (Sect. 4.5.1 and 4.5.3) (14) + Q˙ , (20) gNG ,c | {z } Ground–CAS sensible heat Each term is described in detail in the sections shown under- (Sect. 4.5.2 and 4.5.3) neath each term on the right-hand side of Eqs. (12)–(14).

NT ! ˙ = ˙ + X ˙ 3.2.4 Canopy air space (CAS) Hc Ha,c Htk,c |{z} |{z} k=1 Net enthalpy flux Enthalpy flux from | {z } turbulent mixing(Sect. 4.4) Evaporation of The canopy air space is a gas; therefore, extensive properties intercepted water akin to the other thermodynamic systems are not intuitive (Sect. 4.5.1 and 4.5.3) N ! because total mass and total volume cannot be directly com- XT + H˙ + H˙ + H˙ , pared to observations. Therefore, all prognostic and diagnos- lk,c sNS ,c gNG ,c tic variables are solved in the intensive form. Total enthalpy k=1 | {z } | {z } | {z } Surface water Ground evaporation Hc and total water mass Wc of the canopy air space can be Transpiration evaporation (Sect. 4.5.2 and 4.5.3) (Sect. 4.6) (Sect. 4.5.2 and 4.5.3) written in terms of air density ρc and the equivalent depth of (21) the canopy air space zc as

NT ! Hc = ρc zc hc, (15) X W˙ = W˙ + W˙ = c a,c tk,c Wc ρc zc wc, (16) |{z} |{z} k=1 Net water flux Water flux from NT(canopy) ! ( . ) | {z } P turbulent mixing Sect. 4 4 Evaporation of k=1 ntk BAtk ztk = intercepted water zc max 5.0, N , (17) P T(canopy) (Sect. 4.5.1 and 4.5.3) k=1 ntk BAtk N ! XT + W˙ + W˙ + W˙ . lk,c sNS ,c gNG ,c k=1 | {z } | {z } where BA (cm2) and z (m) are the basal area and the | {z } Surface water Ground evaporation tk tk Transpiration evaporation (Sect. 4.5.2 and 4.5.3) height of cohort k, respectively; and NT(canopy) is the num- (Sect. 4.6) (Sect. 4.5.2 and 4.5.3) ber of cohorts that are in the canopy, and we assume that (22) cohorts are ordered from tallest to shortest. In the event that the canopy is open, NT(canopy) is the total number of cohorts, Unlike in the other thermodynamic systems (soil, tempo- and a minimum value of 5m is imposed when vegetation is rary surface water, and vegetation), the net enthalpy flux of absent or too short to prevent numerical instabilities. Because the canopy air space is not exclusively due to associated wa- the equivalent canopy depth depends only on the cohort size, ter flux: the eddy flux between the free air and the canopy air ˙ zc is updated at the cohort dynamics step (1tCD, Table2). If space (Ha,c) includes both water transport and flux associ- we substitute Eqs. (15) and (16) into Eqs. (4) and (5), respec- ated with mixing of air with different temperatures, and thus tively, and assume that changes in density over short time enthalpy, between canopy air space and free air. steps are much smaller than changes in enthalpy or humidity, In addition, we must also track the CAS pressure pc. In and then we obtain the following equations for the canopy air ED-2.2, CAS pressure is not solved through a differential www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4322 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2 equation; instead, pc is updated whenever the meteorologi- respiration with long-term dynamics that depend on carbon cal forcing is updated, using the ideal gas law and hydrostatic balance such as such as carbon allocation to growth and re- equilibrium following the method described in Sect. S8. The production, and mortality (long-term dynamics described in rate of change of canopy air pressure is then applied in Sect. S3). The accumulated carbon balance is defined by the Eq. (18). Likewise, CAS density (ρc) is updated at the end of following equation: each thermodynamic step to ensure that the CAS conforms dC to the ideal gas law. 1k = − ˙ − ˙ − ˙ Clk,c Crk,c Cnk,c dt |{z} |{z} | {z } 3.3 Carbon dioxide cycle | {z } Net leaf–CAS flux Fine-root Storage turnover Change in (respiration–GPP) respiration respiration carbon balance (Sect. 4.6) (Sect. 4.7) In ED-2.2, the carbon dioxide cycle is a subset of the full (Sect. 4.7) − ˙ − ˙ − ˙ , which is shown in Fig.3. The canopy air space C1k,c Ctk,e1 Ctk,e2 | {z } | {z } | {z } is the only thermodynamic system with CO2 storage that is Growth and maintenance Turnover of Turnover of solved by ED-2.2; nonetheless, we assume that the contribu- respiration non-lignified litter lignified litter (Sect. 4.7) (Sects. 4, S4) (Sects. 4, S4), tion of CO2 to density and heat capacity of the canopy air (25) space is negligible; hence, only the molar CO2 mixing ratio c (mol mol−1) is traced. c C where C˙ and C˙ are the individual carbon losses The change in CO storage in the canopy air space is de- tk,e1 tk,e2 2 caused by leaf shedding and turnover of living tissues that be- termined by the following differential equation: ˙ ˙ come part of the litter (Ctk,e1 ) and structural debris (Ctk,e2 ). dc M 1 The transfer of carbon from plants to the soil carbon pools c = d ˙ Cc, (23) and between the soil carbon pools does not directly im- dt MC ρc zc pact the carbon dioxide budget but contributes to the long- term ecosystem carbon stock distribution and carbon bal- NT NT ance. These components have been discussed in previous ED ˙ = ˙ + X ˙ + X ˙ Cc Ca,c Clk,c Crk,c and ED-2 publications (Moorcroft et al., 2001; Albani et al., |{z} |{z} k=1 k=1 2006; Medvigy, 2006; Medvigy et al., 2009) and are summa- Net carbon flux Carbon flux from | {z } | {z } turbulent mixing Net leaf–CAS flux Fine-root rized in Sect. S4. (Sect. 4.4) (respiration–GPP) respiration (Sect. 4.6) (Sect. 4.7) NT NT 3 4 Submodels and parameterizations of terms of the + X ˙ + X ˙ + X ˙ Cnk,c C1k,c Cej ,c , general equations k=1 k=1 j=1 | {z } | {z } | {z } Storage turnover Growth and maintenance Heterotrophic 4.1 submodel and ground energy exchange respiration respiration respiration (Sect. 4.7) (Sect. 4.7) (Sect. 4.8) The ground model encompasses heat, enthalpy, and water (24) fluxes between adjacent layers of soil and temporary surface water, as well as losses of water and enthalpy due to surface where M and M are the molar masses of dry air and d C runoff and drainage. Fluxes between adjacent layers are pos- carbon, respectively, used to convert mass to molar fraction itive when they are upwards, and runoff and drainage fluxes (1 mol = 1 mol ). The terms on the right-hand side of C CO2 are positive or zero. Eq. (24) are described in detail in the sections displayed un- Sensible heat flux between two adjacent soil or temporary derneath each term. The net leaf–CAS flux (C˙ ) for any lk,c surface water layers j − 1 and j is determined from thermal cohort k is positive when leaf respiration exceeds photo- conductivity ϒ and temperature gradient (Bonan, 2008), synthetic assimilation. The heterotrophic respiration is based Q with an additional term for temporary surface water to scale on a simplified implementation of the CENTURY model the flux when the temporary surface water covers only a frac- (Bolker et al., 1998) that combines the decomposition rates tion f of the ground: from three soil carbon pools, defined by their characteristic TSW lifetime: fast (metabolic litter and microbial; e1), intermedi- ∂T  ˙ = − g ate (structural debris; e ), and slow (humified and passive soil Qgj− ,g ϒQ , (26) 2 1 j gj−1,gj ∂z gj− ,g carbon; e3). Note that the soil carbon pools are not directly 1 j   related to the soil layers used to describe the thermodynamic ˙ ∂Ts Qs − ,s = −fTSW ϒQ , (27) state (Sect. 3.2.1). j 1 j sj−1,sj ∂z sj−1,sj In addition to canopy air space, we also define a virtual co- hort pool of carbon corresponding to the accumulated carbon where the operator h i is the log-linear interpolation − balance (C1k ). The accumulated carbon balance links short- from the midpoint height of layers j 1 and j to the term carbon cycle components such as photosynthesis and height at the interface. The bottom boundary condition of

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Figure 3. Schematic of the patch-level carbon cycle solved in ED-2.2 for a patch containing NT cohorts. Like Fig.2, letters near the arrows are the subscripts associated with fluxes. Fluxes shown in solid yellow lines are part of the CO2 cycle discussed in this paper, and dashed red lines are part of the carbon cycle but do not directly affect the CO2 flux; these fluxes are summarized in Sects. S3 and S4.

  ∂T ≡ Eq. (26) is ∂z 0. The interface between the top the bottom boundary depends on the type of drainage and g0,g1 ˙ is determined using a slight modification of Eq. (28). Let soil layer and the first temporary surface water (QgN ,s1 )  G ð be an angle-like parameter that controls the drainage be- is found by applying Eq. (27) with T ;ϒ ;1z = s0 Qs0 s0 neath the deepest soil layer. Because we assume zero gradi-   ent in soil matric potential between the deepest soil layer and T ;ϒ ;1z . Soil thermal conductivity depends gNG QgN gNG ˙ G the boundary condition, the subsurface drainage flux (Wg1,g0 ) on soil moisture and texture properties, and the parameter- becomes ization is described in Sect. S9. Both the fraction of ground covered by the temporary surface water and the thermal con- ductivity of the temporary surface water are described in ˙ ˙ Wg ,g = −Wg ,g = ρ` ϒ9 sinð. (29) Sect. S10. 1 0 0 1 g1 Soil moisture exchange between layers occurs only if wa- ter is in liquid phase. The water flux between soil layers Special cases of Eq. (29) are the zero-flow conditions (ð = 0) g − and g ,j ∈ {2,3,...,N } is determined from Darcy’s j 1 j G = π law (Bonan, 2008): and free drainage (ð 2 ). For the temporary surface water, water flux between lay-   ˙ ∂9 dzg ers through percolation is calculated similarly to LEAF-2 Wg , = −ρ`hϒ9 i + , (28) j−1 gj gj−1,gj ∂z dz (Walko et al., 2000). Liquid water in excess of 10 % is in gj−1,g j principle free to percolate to the layer below, although the where 9 is the soil matric potential and ϒ9 is the hy- maximum percolation of the first surface water layer is lim- draulic conductivity, both defined after Brooks and Corey ited by the amount of pore space available at the top ground (1964), with an additional correction term applied to hy- layer: draulic conductivity to reduce conductivity in the event that the soil is partially or completely frozen (Sect. S9). The bot- tom boundary condition for soil matric potential gradient is 1   ˙ = − ˙ = ∂9 ≡ Ws1,gN WgN ,s1 ∂z 0. G G 1tThermo g0,g1 dzg   ` − 0.1  The term in Eq. (28) is the flux due to gravity, and it is sj   dz max 0,min Ws ,ρ` ϑPo − ϑg 1zg , 1 for all layers except the bottom boundary condition, which 1 0.9 NG NG depends on the subsurface drainage. Subsurface drainage at (30) www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4324 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2

of each cohort (8tk ):

1 ˙ ˙ 8tk ˙ = − ˙ = Wa,t = (1 − O) W∞,a , (36) Wsj ,sj−1 Wsj−1,sj k PNT 0 8 1tThermo k =1 tk0  −  ˙ ˙ `sj 0.1 W = O W∞ , (37) a,sNS ,a max 0,Wsj , for j > 1. (31) 0.9 NT = Y −  O 1 Xtk , (38) Surface runoff of liquid water is simulated using a simple k=1 extinction function, applied only at the topmost temporary where 8 = 3 +  is the total plant area index, 3 and surface water layer: tk tk tk tk tk being the leaf and wood area indices, both defined from PFT-dependent allometric relations (Sect. S18); Xt is the  1t  k ˙ = − Thermo crown area index of each cohort, also defined in Sect. S18. WsN ,o `sN WsN exp , (32) S S S tRunoff Throughfall precipitation is always placed on the topmost temporary surface water layer. In the event that no temporary where tRunoff is a user-defined e-folding decay time, usually surface water layer exists, a new layer is created, although it on the order of a few minutes to a few hours (Table S4). may be extinct in the event that all water is able to percolate In addition to the water fluxes due to subsurface drainage, down to the top soil layer. surface runoff, and the transport of water between layers, Precipitation is a mass flux, but it also has an associ- ˙ we must account for the associated enthalpy fluxes. Enthalpy ated enthalpy flux (H∞,a) that must be partitioned and in- fluxes due to subsurface drainage and surface runoff are de- corporated into the cohorts and temporary surface water. fined based on the water flux and the temperature of the lay- Similar to the water exchange between soil layers, the en- ers where water is lost by applying the definition of enthalpy thalpy flux associated with rainfall uses the definition of en- (Sect. S5): thalpy (Sect. S5). Because precipitation temperature is sel- dom available in meteorological drivers (towers or gridded meteorological forcing data sets), we assume that precipita- H˙ = W˙ q T − T , (33) g1,g0 g1,g0 ` g1 `0 tion temperature is closely associated with the free-air tem-   ˙ = ˙ − perature (T ), and we use T to determine whether the pre- HsN ,o WsN ,o q` TsN T`0 , (34) a a S S S cipitation falls as rain, snow, or a mix of both. Importantly, the use of free-air temperature partly accounts for the thermal where q` is the specific heat of liquid water (Table S3), and difference between precipitation temperature and the temper- T is defined in Eq. (S53). The enthalpy flux between two `0 ature of intercepted surfaces. Rain is only allowed when Ta is adjacent layers is solved similarly, but it must account for the above the water triple point (T3 = 273.16K); in this case, the sign of the flux in order to determine the water temperature rain temperature is always assumed to be at Ta. Pure snow of the donor layer: occurs when the free-air temperature is below T3, and like- wise snow temperature is assumed to be Ta. When free-air  W˙ q T − T , if W˙ < 0 temperature is only slightly above T3, a mix of rain and snow H˙ = xj−1,xj ` xj `0 xj−1,xj , (35) xj−1,xj ˙ −  ˙ ≥ T Wxj−1,xj q` Txj−1 T`0 , if Wxj−1,xj 0 occurs, with the rain temperature assumed to be a and snow temperature assumed to be T3: where the subscript xj represents either soil (gj ) or tempo- ˙ ˙   H∞,a = W∞,a (1 − `a) qi min(T3,Ta) + `a q` (Ta − T`0) , (39) rary surface water (sj ).

where (qi;q`) are the specific heats of ice and liquid, respec- 4.2 Precipitation and vegetation dripping tively, and T`0 is temperature at which supercooled water would have enthalpy equal to zero (Eq. S53). The fraction In ED-2.2, precipitating water from rain and snow increases of precipitation that falls as rain `a is based on the Jin et al. the water storage of the thermodynamic systems, as rainfall (1999) parameterization, slightly modified to make the func- can be intercepted by the canopy or reach the ground. This tion continuous: influx of water also affects the enthalpy storage due to the  1.0, if Ta > 275.66K enthalpy associated with precipitation, although no heat ex-  0.4 + 1.2(Ta − T3 − 2.0), if 275.16K < Ta ≤ 275.66K change is directly associated with precipitation. `a = . (40) 0.2 (T − T ), if T < T ≤ 275.16K  a 3 3 a To determine the partitioning of total incoming precipita- 0.0, if T ≤ T ˙ ˙ a 3 tion (W∞,a) into interception by each cohort (Wa,t ) and di- ˙ k rect interception by the ground (throughfall, Wa,s ), we use The enthalpy flux associated with precipitation is then NS ˙ the fraction of open canopy (O) and the total plant area index partitioned into canopy interception (Ha,tk ) and throughfall

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(H˙ ) using the same scaling factor as in Eqs. (36) and given by a,sNS (37): dQ˙ 8 mk = − ˙ ˙ ˙ tk µk Qmk , (45) Ha,t = (1 − O) H∞,a , (41) k PNT d8e | {z } k0= 8tk0 | {z } 1 Downward direct Interception H˙ = O H˙∞ . (42) profile a,sNS ,a Leaves and branches can accumulate only a finite amount ⇓ of water on their surfaces, proportional to their total area. dQ˙ mk = − ˙ ⇓ + − ˙ ⇓ When incoming precipitation rates are too high (or more µk Qmk (1 βmk) ςmk Qmk rarely when dew or frost formation is excessive), any water d8e | {z } | {z } | {z } Forward scattering amount that exceeds the holding capacity is lost to the ground Downward diffuse Interception profile (downward diffuse) as canopy dripping. Similarly to incoming precipitation, the ⇑ µ excess water lost through dripping also has an associated en- + ˙ + k −  ˙ + − ˙  βik ςmk Qmk ςmk 1 βmk Qmk (1 ςmk) Qmk, thalpy that must be taken into account, although dripping has | {z } µk | {z } Backscattering | {z } Emission no associated heat flux. The canopy dripping fluxes of wa- (upward diffuse) Forward scattering ter (W˙ ) and the associated enthalpy (H˙ ) are defined (downward direct) tk,sNS tk,sNS such that the leaves and branches lose the excess water within (46) one time step:

˙ 1  Wt ,s = − max 0,Wt −w ˆ max 8t , (43) k NS 1t k k ˙ ⇑ Thermo dQ ⇑ ⇑ ˙ ˙    −µ mk = − Q˙ + (1 − β ) ς Q˙ Ht ,s = Wt ,s 1 − `t qiTt + `t Tt − T`0 , (44) k mk mk mk mk k NS k NS k k k k d8e |{z} | {z } | {z } Interception Forward scattering where `tk is the liquid fraction of surface water on top of Upward diffuse (upward diffuse) profile cohort k and wˆ max is the cohort holding capacity, which is an adjustable parameter (Table S4) but is typically of the order ⇓ µ + β ς Q˙ + k ς β Q˙ + (1 − ς ) Q˙  , of 0.05 − 0.40kg m−2 (Wohlfahrt et al., 2006). mk mk mk mk mk mk mk mk W Leaf+Wood | {z } µk | {z } Backscattering | {z } Emission 4.3 Radiation model (downward diffuse) Backscattering (downward direct) The radiation budget is solved using a multi-layer version of (47) the two-stream model (Sellers, 1985; Liou, 2002; Medvigy, where index k ∈ {1,2,...,N } corresponds to each cohort k 2006) applied to three broad spectral bands: photosynthet- T or its lower interface (Fig.4); interface N + 1 is immedi- ically active radiation (PAR, wavelengths between 0.4 and T ately above the tallest cohort; Q˙ is the downward direct 0.7 µm), near-infrared radiation (NIR, wavelengths between mk ˙ ⇓ ˙ ⇑ 0.7 and 3.0 µm) and thermal infrared radiation (TIR, wave- irradiance incident at interface k;(Qmk and Qmk) are the lengths between 3.0 and 15 µm). downward and upward (hemispheric) diffuse irradiance inci- dent at interface k; ςmk is the scattering coefficient, and thus − 4.3.1 Canopy radiation profile (1 ςmk) is the absorptivity; βmk and βmk are the backscat- tered fraction of scattered direct and diffuse irradiance, re- For each spectral band m, the canopy radiation scheme as- spectively; 8e is the effective cumulative plant area index, sumes that each cohort corresponds to one layer of vegeta- assumed zero at the top of each layer, and increasing down- tion within the canopy, and within each layer the optical and wards (8ek is the total for layer k); µk and µk are the inverse thermal properties are assumed constant. For all bands, the of the optical depth per unit of effective plant area index for top boundary condition for each band is provided by the me- ˙  direct and diffuse radiation, respectively; and Qmk is the ir- teorological forcing (Table3). In the cases of PAR ( m = 1) radiance emitted by a black body at the same temperature as and NIR (m = 2), the downward irradiance is comprised of the cohort (Ttk ). a beam (direct) and isotropic (diffuse) components, whereas Equations (45)–(47) simplify for each spectral band. First, TIR irradiance (m = 3) is assumed to be all diffuse. Direct ˙ ≡ = Qmk 0 for the TIR (m 3) band, because we assume that irradiance that is intercepted by the cohorts can be either all incoming TIR irradiance is diffuse. Likewise, the black- backscattered or forward-scattered as diffuse radiation, and ˙  = = = body emission Qmk 0 for the PAR (m 1) and NIR (m direct radiation reflected by the ground is assumed to be en- 2) bands, because thermal emission is negligible at these tirely diffuse. wavelengths. The black-body emission for the TIR band is Following Sellers(1985), the extinction of downward di- defined as rect irradiance and the two-stream model for hemispheric dif- m = , , Q˙  = σ T 4, fuse irradiance for each of the spectral bands ( 1 2 3) is m=3 k SB tk (48) www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4326 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2

Figure 4. Schematic of the radiation module for a patch with NT cohorts, showing the grid arrangement of the irradiance profiles relative  ˙ ˙ ⇓ ˙ ⇑  to the cohort positions. Index k corresponds to each cohort, or, in the case of Qmk,Qmk,Qmk , the interface beneath each cohort; m  ˙ ˙ ⇓  corresponds to each spectral band; Qm(∞,a),Qm(∞,a) are the incoming direct and diffuse irradiance (Table3); Z is the Sun’s zenith  ˙ ˙ ⇓ ˙ ⇑  angle; Qmk,Qmk,Qmk are the downward direct, downward diffuse, and upward diffuse irradiance (Eqs. 45–47); 8ek is the effective plant area index (Eq. S100); (ςmk;βmk) are the scattering coefficients and the backscattering fraction for diffuse irradiance (Eqs. S101, S102);   ; ˙  ςmk βmk are the scattering coefficients and the backscattering fraction for direct irradiance (Eqs. S104–S105); Qmk is the black-body irradiance (Eq. 48); and Q˙ is the net absorbed irradiance (Eq. 49). a,tk

˙ where σSB is the Stefan–Boltzmann constant (Table S3). Qa,tk : Note that for emission of TIR radiation (Eqs. 45–47), we as- sume that emissivity is the same as absorptivity (Kirchhoff’s 3 h    ˙ = X ˙ − ˙ + ˙ ⇓ − ˙ ⇓ law; Liou, 2002) and hence the (1 − ς) term. Qa,tk Qm(k+1) Qmk Qm(k+1) Qmk = The effective plant area index 8ek is the total area (leaves m 1 and branches) that is corrected to account for that leaves  ˙ ⇑ ˙ ⇑ i + Q − Q + . (49) are not uniformly distributed in the layer. It is defined as mk m(k 1) 8ek = k + fClump 3k, where fClump is the PFT-dependent k k This term is then used in the enthalpy budget of each cohort clumping index (Chen and Black, 1992, default values in Ta- (Eqs.4 and 12). bles S5–S6), 3tk is the leaf area index, and tk is the wood area index. 8 is assumed zero at the top of each layer, in- e 4.3.2 Ground radiation creasing downwards. The optical properties of the leaf layers – optical depth The ground radiation submodel determines the irradiance and scattering parameters for direct and diffuse radiation emitted by the ground surface and the profile of irradiance for each of the three spectral bands – are assumed con- through the temporary surface water layers and top soil layer. stant within each layer. These properties are determined from Note that the ground radiation and the canopy radiation PFT-dependent characteristics such as mean orientation fac- model are interdependent: the incoming radiation at the top tor, spectral-band-dependent reflectivity, transmissivity, and ground layer is determined from the canopy radiation model, emissivity (Sect. S11). Because the properties are constant and the ground scattering coefficient (ς ; see Sect. S11) is within each layer, it is possible to analytically solve the full m0 needed for the canopy radiation bottom boundary condition profile of both direct and diffuse radiation using the solver (Sect. S12). However, since the scattering coefficient does described in Sect. S12. ⇓ ⇑ not depend on the total incoming radiation, the irradiance Once the profiles of Q˙ , Q˙ and Q˙ are determined, mk mk mk profile can be solved for a standardized amount of incom- we obtain the irradiance that is absorbed by each cohort ing radiation, and once the downward radiation at the bottom of the canopy has been calculated, the absorbed irradiance for each layer can be scaled appropriately.

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˙  Black-body emission from the ground (Qm0) is calculated has been widely used by biosphere–atmosphere models rep- as an area-weighted average of the emissivities of exposed resenting a variety of biomes (e.g., Walko et al., 2000; Best soil and temporary surface water: et al., 2011; Oleson et al., 2013), although this is often an ex- trapolation of the theory that was not originally developed for ˙  = ∈ Qm0 0 if m (1,2), heterogeneous vegetation or tall vegetation (Foken, 2006). h   4   4 i In order to obtain the fluxes, we assume that the eddy dif- (1 − fTSW) 1 − ς3g σSB Tg + fTSW (1 − ς3s ) σSB Ts NG NS fusivity of buoyancy is the same as the diffusivity of enthalpy,   −1 (1 − fTSW) 1 − ς3g + fTSW (1 − ς3s ) if m = 3 water vapor, and CO2. This assumption allows us to define a (50) single canopy conductance Gc for the three variables, follow- ing the algorithm described in Sects. S13 and S14.1. We then where (1 − ς3g) and (1 − ς3s), are, respectively, the thermal- obtain the following equations for fluxes between canopy air infrared emissivities of the top soil layer and the temporary space and the free atmosphere: surface water (Table S4), and fTSW is the fraction of ground ˙ covered by temporary surface water. In ED-2.2, the soil and Wa,c = ρc Gc (wa − wc), (53) snow scattering coefficients for the TIR band are assumed ˙  Ha,c = ρc Gc eha − hc , (54) constant (Table S4), following Walko et al.(2000). ˙ MC Once the irradiance profile for the canopy is determined Ca,c = ρc Gc (ca − cc), (55) from Eqs. (45) to (47), the irradiance absorbed by each tem- Md porary surface water layer (j ∈ {1,2,...,NS}) is calculated where eha is the equivalent enthalpy of air at reference height by integrating the transmissivity profile for each layer, start- za when the air is adiabatically moved to the top of the ing from the top layer: canopy air space, using the definition of potential tempera- ture: ˙ = Qa,sj        1zs  ha = h Ta,wa , from Eq. (S50), (56) P2 ˙ ⇓ ˙ NS e e  = fTSW Q + Q 1 − exp −  m 1 m1 m1 µs R    M q   ⇓  pc d pd  + − ˙ − 4 = Ta = θa , (57)  fTSW (1 ς3s) Qm= k= σSBTs ,if j NS e  3 1 NS p0  ( " N ! P S 1z P2  ˙ ⇓ ˙  j0=j+1 sj , = fTSW Q + Q exp − where p0 is the reference pressure, R is the universal gas  m 1 m1 m1 µs  constant, qpd is the specific heat of dry air at constant pres-  N !#)  P S 1z  j0=j sj0 sure, and Md is the molar mass of dry air (Table S3).  −exp − , otherwise  µs Sensible heat flux between the free atmosphere and canopy air space (Q˙ ) can be derived from the definition of en- (51) a,c thalpy and enthalpy flux (Eqs. S50 and 54), although it is where µ is the inverse of the optical depth of temporary sur- not directly applied to the energy balance in the canopy air s ˙ face water. space (Ha,c is used instead): The irradiance absorbed by the ground is a combination ˙   of irradiance of exposed soil and irradiance that is transmit- Ha,c = ρc Gc (1 − wa) qpd Tea + wa qpv Tea − Tv0  ted through all temporary surface water layers and the net −(1 − wc) qpd Tc − wc qpv (Tc − Tv0) absorption of longwave radiation: = −  − − ρc Gc qpa Tea qpc Tc ρc Gc (wa wc) qpv Tv0, (58) ˙ | {z } Q = ˙ a,gNG Qa,c    PNS  2 0 1z X  j =1 sj0 1 − fTSW + fTSW exp−  µ ˙ = ˙ + ˙ m=1  s Qa,c Ha,c Wa,c qpv Tv0. (59)  o ˙ ⇓ + ˙ + − −  4.5 Heat and water exchange between surfaces and Qm1 Qm1 (1 fTSW) 1 ς3g canopy air space  ⇓  Q˙ − σ T 4 . m=3 k=1 SB gN (52) G 4.5.1 Leaves and branches 4.4 Surface layer model ˙ ˙ Fluxes of sensible heat (Qtk,c) and water vapor (Wtk,c) be- The surface layer model determines the fluxes of enthalpy, tween the leaf surface and wood surface and the canopy air water, and carbon dioxide between the canopy air space and space follow the same principle of conductance and gradi- the free air above. It is based on the Monin–Obukhov similar- ent that define the eddy fluxes between the free atmosphere ity theory (Monin and Obukhov, 1954; Foken, 2006), which and canopy air space (Eqs. 53, 54). Throughout this section, www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4328 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2 we use subscripts λk and βk to denote leaf and wood bound- the same for soil and temporary surface water: ary layers of cohort k, respectively; the different subscripts   are needed to differentiate fluxes coming from the leaves’ in- Q˙ = f G ρ q T − T , (66) sNS ,c TSW Sfc c pc sNS c tercellular space (e.g., transpiration; see also Sect. 4.6). Let   G (ms−1) and G (ms−1) be the conductances of heat W˙ = f G ρ w − w , (67) Qλk Wλk sNS ,c TSW Sfc c sNS c and water between the leaf boundary layer of cohort k and the ˙   Qg ,c = (1 − fTSW) GSfc ρc qp Tg − Tc , (68) canopy air space, and GQβk and GWβk be the wood bound- NG c NG ary layer counterparts. The surface sensible heat and surface ˙   Wg ,c = (1 − fTSW) GSfc ρc wg − wc . (69) water vapor fluxes are NG NG Specific humidity for temporary surface water is com-   = puted exactly as leaves and branches, wsN wSat TsN ,pc ˙ = ˙ + ˙ = ˙ + ˙ S S Qtk,c Qλk,c Qβk,c 23k qλk,c π k qβk,c, (60) (Sect. S15). For soils, the specific humidity also accounts for ˙ = ˙ + ˙ = ˙ + ˙ Wtk,c Wλk,c Wβk,c 3k wλk,c k wβk,c, (61) the soil moisture and the sign of the flux, using a method   similar to Avissar and Mahrer(1988): q˙ = G ρ q T Sfc − T , (62) λk,c Qλk c pc lk c  !  Sfc  Mw g 9g q˙ = G ρ q T − T , (63)  NG  βk,c Qβk c pc bk c  s exp w (T ,p ) + 1 − s w ,  g Sat gNG c g c  RTgN  Sfc   G w˙ λ ,c = GWλ ρc w − wc , (64) w = if w (T ,p ) > w , k k lk gNG Sat gNG c c  w (T ,p ),  Sfc   Sat gNG c w˙ β ,c = GWβ ρ w − w , (65)  k k c bk c  if w (T ,p ) ≤ w Sat gNG c c (70)

˙ ; ˙ ; ˙ ; ˙ where (qλk,c qβk,c wλk,c wβk,c) are the leaf surface and branch surface heat and water fluxes by unit of leaf and      min ϑg ,ϑFc − ϑRe branch area, respectively; the factors 2 and π in Eq. (60) 1  NG  sg = 1.0 − cosπ  , (71) mean that sensible heat is exchanged on both sides of the 2  ϑFc − ϑRe  leaves and on the longitudinal area of the branches, which are assumed cylindrical. Intercepted water and dew and frost for- where g is the gravity acceleration, Mw is the water mo- mation is allowed only on one side of the leaves, and an area lar mass, and R is the universal gas constant (Table S3); equivalent to a one-sided flat plate for branches, and there- T , ϑ , and 9 are the temperature, soil moisture, gNG gNG gNG fore only the leaf and wood area indices are used in Eq. (61). and soil matric potential of the topmost soil layer, respec- Canopy air space temperature, specific humidity, density, and tively; and ϑFc and ϑRe are the soil moisture at field capacity specific heat, leaf temperature, and wood temperature are de- and the residual soil moisture, respectively. The exponential termined diagnostically. We also assume surface temperature term in Eq. (70) corresponds to the soil pore relative humid- of leaves and branches to be the same as their internal tem- ity derived from the Kelvin equation (Philip, 1957), and sg Sfc ≡ Sfc ≡ peratures (i.e., Tl Tlk and Tb Tbk ). Specific humidity is the soil wetness function, which takes a similar functional k  k  at the leaf surface wSfc = w T Sfc,p and branch surface form as the relative humidity term from Noilhan and Planton lk Sat lk c   (1989) and the β term from Lee and Pielke(1992). The total wSfc = w T Sfc,p are assumed to be the saturation spe- βk Sat bk c resistance between the surface and the canopy air space is a cific humidity wSat (Sect. S15). combination of the resistance if the surface was bare, plus the Heat conductance for leaves and branches is based on the resistance due to the vegetation, as described in Sect. S14.3. convective heat transfer, as described in Sect. S14.2. Fur- ther description of the theory can be found in Monteith and 4.5.3 Enthalpy flux due to evaporation and Unsworth(2008, Sect. 10.1). condensation Dew and frost are formed when water in the canopy air space 4.5.2 Temporary surface water and soil condenses or freezes on any surface (leaves, branches, or ground); likewise, water that evaporates and ice that subli- mates from these surfaces immediately become part of the Sensible heat and water fluxes between the temporary sur- canopy air space. In terms of energy transfer, two processes face water and soil and the canopy air space are calculated occur, the phase change and the mass exchange, and both similarly to leaves and branches. Surface conductance GSfc must be accounted for the enthalpy flux. Phase change de- is assumed to be the same for both heat and water, and also pends on the specific latent heat of vaporization (llv) and

Geosci. Model Dev., 12, 4309–4346, 2019 www.geosci-model-dev.net/12/4309/2019/ M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2 4329 sublimation (liv), which are linear functions of temperature, heat flux and water flux from leaf surface water must over- based on Eqs. (S48) and (S49): come the boundary layer resistance only (Fig.5). When soil moisture is not a limiting factor, the fluxes of CO and water  2 llv(T ) = llv3 + qpv − q` (T − T3), (72) can be written as = + −  − liv(T ) liv3 qpv qi (T T3), (73) ˙ = ˆ −  = ˆ −  Ak GCλk cc cλk GClk cλk clk where llv3 and liv3 are the specific latent heats of vaporiza- Gˆ Gˆ = Cλk Clk −  T q cc clk , (76) tion and sublimation at the water triple point ( 3), pv is the ˆ + ˆ GCλk GClk specific heat of water vapor at constant pressure, and qi and q` are the specific heats of ice and liquid water, respectively ˙ = ˆ −  = ˆ −  (Table S3). The temperature for phase change must be the Ek GWλk wc wλk GWlk wλk wlk surface temperature because this is where the phase change Gˆ Gˆ = Wλk Wlk w − w , (77) occurs. In the most generic case, if a surface x at temperature ˆ ˆ c lk GWλ + GWl Tx has a liquid water fraction `x, the total enthalpy flux be- k k ˙ tween the surface and canopy air space Hx,c associated with where the water flux W is x,c =  wlk wSat Ttk ,pc (Sect. S15), (78)   and ˙ = ˙  − + −  Hx,c Wx,c (1 `x) qi Tx `x q` (Tx Tl0) ρ G ˆ = c Xλk | {z } GXλk , (79) Enthalpy flux due to mass exchange Md  and  +[(1 − ` ) l (T ) + ` l (T )] . (74) ρ G x iv x x lv x ˆ = c Xlk | {z } GXlk , (80) Enthalpy flux due to phase change  Md −1 By using the definitions from Eq. (S54), Eq. (74) can be fur- where GXλk and GXlk (units ms ) are the leaf boundary ther simplified to layer and stomatal conductances for element X (either wa- ter W or carbon C), respectively; cλ and wλ are the CO2 ˙ ˙   ˙ k k Hx,c = Wx,c qpv (Tx − Tv0) = Wx,c h(Tx,wx = 1), (75) mixing ratio and the specific humidity of the leaf boundary | {z } Eq. (S50) layer, respectively; clk and wlk are the CO2 and specific hu- midity of the leaf intercellular space, respectively; Md is the which is consistent with the exchange of pure water vapor molar mass of dry air; and ρc is the air density. As stated in and enthalpy between the thermodynamic systems. Equa- Eq. (78), we assume the leaf intercellular space to be at wa- tion (75) is used to determine H˙ , H˙ , and H˙ ,k ∈ gNG ,c sNS ,c tk,c ter vapor saturation. The leaf boundary layer conductances {1,2,...,NT }. are obtained following the algorithm shown in Sect. S14.2. The net CO2 assimilation flux and stomatal conductances are 4.6 Leaf described below. From Farquhar et al.(1980), the net CO assimilation flux In ED-2.2, leaf physiology is modeled following Farquhar 2 is defined as et al.(1980) and Collatz et al.(1991) for C 3 plants; Collatz 1 et al.(1992) for C 4 plants; and the Leuning(1995) model ˙ = ˙ − ˙ − ˙ Ak VCk VOk Rk . (81) for stomatal conductance. This submodel ultimately deter- |{z} 2 |{z} ˙ Carboxylation | {z } Leaf respiration mines the net leaf-level CO2 uptake rate of each cohort k (Ak, Oxygenation −2 −1 () molC mLeaf s ), controlled exclusively by the leaf environ- ment, and the corresponding water loss through transpiration Oxygenation releases 0.5 molCO2 for every molO2 , hence the ˙ −2 −1 half multiplier, and it is related to carboxylation by means of (Ek, molW mLeaf s ). The exchange of water and CO2 between the leaf intercel- the CO2 compensation point 0k (Lambers et al., 2008): lular space and the canopy air space is mediated by the stom- 20 ˙ = k ˙ ata and the leaf boundary layer, which imposes an additional VOk VCk , (82) c resistance to fluxes of these substances. For simplicity, we as- lk sume that the leaf boundary layer air has low storage capac- where clk is the CO2 mixing ratio in the leaf intercellular ity, and thus the fluxes of any substance (water or CO2) enter- space. The CO2 compensation point is determined after Col- ing and exiting the boundary layer must be the same. Fluxes latz et al.(1991, 1992): of water and carbon between the leaf intercellular space and ( o⊕ , in case cohort k is a C3 plant the canopy air space must overcome both the stomatal re- 0k = 2$ , (83) sistance and the boundary layer resistance, whereas sensible 0, in case cohort k is a C4 plant www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4330 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2

Figure 5. Schematic of fluxes between a leaf and the surrounding canopy air space for a hypostomatous plant during the photo period, as represented in ED-2.2. Conductances are represented by the resistances between the different environments (G−1). Leaf-level sensible heat ˙ ˙ flux (qλk,c; Eq. 60) and leaf-level vapor flux between intercepted water and canopy air space (wλk,c; Eq. 61) are also shown for comparison. Cohort index k is omitted from the figure for clarity.

= +  where o⊕ is the reference O2 mixing ratio (Table S3), and where KMEk KCk 1 o⊕/KOk is the effective Michaelis $ represents the ratio between the rates of carboxylase to constant, and KCk and KOk are the Michaelis constants for oxygenase and is a function of temperature. The general form carboxylation and oxygenation, respectively. Both KCk and of the function T describing the metabolic dependence upon KOk are dependent on temperature, following Eq. (84) (de- temperature for any variable x (including $ ) is fault parameters in Table S4), whereas V˙ max follows a mod- Ck ified temperature-dependent function to account for the fast T −T15 = × 10 decline of both productivity and respiration at low and high T (T ,x) x15 Q10 , (84) x temperatures (Sellers et al., 1996; Moorcroft et al., 2001): where x15 is the value of variable x at temperature T15 = ◦ T 0 (T ,x) 288.15 K (15 C), and Q10x is the parameter which describes temperature dependence (Table S4). T(T ,x) =       , Because C4 plants have a mechanism to concentrate 1 + exp −fCold (T − TCold) 1 + exp +fHot (T − THot) CO2 near the CO2-fixing enzyme RuBisCO (ribulose-1,5- (86) biphosphate carboxylase oxygenase), photorespiration is nearly nonexistent in C4 plants (Lambers et al., 2008) and where fCold, fHot, TCold, and THot are PFT-dependent phe- hence the assumption that 0k is zero. For C4 plants, the car- nomenological parameters to reduce the function value at boxylation rate under ribulose-1,5-biphosphate (RuBP) sat- low and high temperatures (Tables S5–S6). urated conditions becomes the maximum capacity of Ru- The original expression for the initial slope of the carboxy- max ˙ InSl BisCO to perform the carboxylase function (V˙ = V˙ ). lation rate under near-zero CO2 (VC ) for C4 plants by Col- Ck Ck k For C3, this rate is unattainable even under RuBP-saturated latz et al.(1992) has been modified later (e.g., Foley et al., 1996) to explicitly include V˙ max; this is the same expression conditions because carboxylation and oxygenation are mu- Ck tually inhibitive reactions (Lambers et al., 2008). Therefore, used in ED-2.2: ˙ ˙ RuBP the maximum attainable carboxylation (VC = V ) is ex- ˙ InSl ˙ max k Ck V = kPEP V cl , (87) pressed by a modified Michaelis–Menten kinetics equation: Ck Ck k c where kPEP represents the initial slope of the response curve ( ˙ max lk RuBP VC c +K , if cohort k is a C3 plant to increasing CO2; the default value in ED-2.2 (Table S4) is V˙ = k lk MEk , (85) Ck V˙ max, if cohort k is a C plant the same value used by Foley et al.(1996). Ck 4

Geosci. Model Dev., 12, 4309–4346, 2019 www.geosci-model-dev.net/12/4309/2019/ M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2 4331

From the total photosynthetically active irradiance ab- Troughton(1971), stomatal conductance of CO 2 is estimated ˙ sorbed by the cohort QPAR:a,tk (Eq. 49), we define the photon by the ratio fGl between the diffusivities of water and CO2 ˙PAR −2 −1 flux that is absorbed by the leaf (qk ,molmLeaf s ): in the air (Table S4): ˆ = ˆ f GWlk fGl GClk . (92) PAR 1 Clumpk ˙ q˙ = Q :a,t , (88) k Ein PAR k Variables w , V˙ max, R˙ , $ , K , K , 0 , and K 8ek lk Ck k k Ok Ck k MEk are functions of leaf temperature and canopy air space pres- where Ein is the average photon-specific energy in the PAR sure and thus can be determined directly. In contrast, nine band (0.4–0.7 µm; Table S3). Even though a high fraction variables are unknown for each limitation case, namely the ? of the absorbed irradiance is used to transport electrons k RuBP-saturated (Eq. 85), CO2-limited (Eq. 87), and light- needed by the light reactions of photosynthesis (Lambers limited (Eq. 89) variables, as well as for the case when the et al., 2008), only a fraction of the irradiance absorbed by ˙ ˙ ˙ ˙ stomata are closed (Eq. 91 for when Ak ≤ 0): Ek, Ak, VC , the leaf is absorbed by the chlorophyll; in addition, the num- ˙ ˆ ˆ k VO , cl , cλ , wλ , GWl , and GCl . These are determined nu- ber electrons needed by each carboxylation and oxygenation k k k k k k ˙ merically for each limiting case, and the value of Ak is taken reaction poses an additional restriction to the total carboxyla- ˙ to be the limiting case that yields the lowest Ak, following tion rate. The product of these three factors is combined into the algorithm described in Sect. S16. a single scaling factor for total absorbed PAR, the quantum The stomatal conductance model by Leuning(1995) yield (k), which is a PFT-dependent property in ED-2.2 (Ta- (Eq. 91) is regulated by leaf vapor pressure deficit. However, bles S5–S6). The maximum carboxylation rate under light Eqs. (76) and (77) do not account for soil moisture limita- limitation V˙ PAR is Ck tion of photosynthesis. To represent this effect, we define a c soil-moisture-dependent scaling factor (f ; Sect. S17) to  PAR lk Wlk k q˙ ,  k cl +2 0k reduce productivity and transpiration as soil available wa-  k ˙ PAR if cohort k is a C3 plant ter decreases. Because stomatal conductance cannot be zero, VC = . (89) k  q˙PAR, f  k k the scaling factor Wlk interpolates between the fully closed  ˙∅; ˙ ∅ if cohort k is a C4 plant case (Ak Ek ) and the solution without soil moisture limi- ˙ ; ˙ ˙ tation (Ak Ek), yielding to the actual fluxes of CO2 (Clk,c, Carboxylation may also be limited by the export rate of −2 −1 ˙ −2 −1 kg m s ) and water (Wl ,c, kg m s ): starch and sucrose that is synthesized by triose , C k W h i especially when CO concentration and irradiance are simul- ˙ = − −  ˙∅ + ˙ 2 Clk,c þk MC 3k 1 fWlk Ak fWlk Ak , (93) taneously high, at low temperatures, or O2 concentration is h i ˙ = −  ˙ ∅ + ˙ low (von Caemmerer, 2000; Lombardozzi et al., 2018). This Wlk,c þk Mw 3k 1 fWlk Ek fWlk Ek , (94) limitation is not included in ED-2.2. ˙ where þk is 1 if the PFT is hypostomatous or 2 if the PFT The leaf respiration term Rk comprises all leaf respiration terms that are not dependent on photosynthesis, and is pri- is amphistomatous or needleleaf (Tables S5–S6). Alterna- marily constituted of mitochondrial respiration; it is currently tively, Xu et al.(2016) implemented a process-based plant represented as a function of the maximum carboxylation rate, hydraulics scheme that solves the soil–stem–leaf water flow following Foley et al.(1996): in ED-2.2; details of this implementation are available in the above-mentioned paper. R˙ = f V˙ max, (90) For simplicity, we assume that the water content in the leaf k R Ck intercellular space and the plant vascular system is constant; where fR is a PFT-dependent parameter (Tables S5–S6). therefore, the amount of water lost by the intercellular space A plant’s stomatal conductance is a result of a trade-off through transpiration always matches the amount of water between the amount of carbon that leaves uptake and the absorbed by roots. Plants may extract water from all layers amount of water that they lose. Leuning(1995) proposed to which they have access, and the amount of water extracted a semi-empirical stomatal conductance expression for water from each layer is proportional to the available water in the based on these trade-offs: layer relative to the total available water (W ? ): gj  ˙ ˆ ∅ + Mk Ak ˙ N GWl  w −w  , if Ak > 0 G  k  lk λk X ˆ = cλ −0k 1+ ˙ = ˙ GWlk k 1wk , (91) Wgj ,lk Wlk,c, (95)  ˆ ∅ ˙ ≤ j=j0k GWl , if Ak 0 k ? − ? Wg Wg + W˙ = W˙ j j 1 , (96) where Gˆ ∅ is the residual conductance when stomata are gj ,lk lk,c ? Wlk W gj0 closed, Mk is the slope of the stomatal conductance function, where W ? is defined following Sect. S17 and W ? ≡ 0. and 1wk is an empirical coefficient controlling conductance gj g(NG+1) under severe leaf-level water deficit; Gˆ ∅ , M , and 1w are The net water flux in the leaf intercellular space due to tran- Wlk k k PFT-dependent parameters (Tables S5–S6). From Cowan and spiration is assumed to be zero; however, the associated net www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4332 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2 energy flux is not: water enters the leaf intercellular space as bon pool ej ;j ∈ (1,2,3), we determine the maximum car- liquid water at the soil temperature, reaches thermal equilib- bon loss based on the characteristic decay rate, which corre- rium with leaves, and is lost to the canopy air space as water sponds to the typical half-life for metabolic and microbial lit- vapor at the leaf temperature. Therefore, the enthalpy flux ter (fast, e1), structural litter (intermediate, e2), and humified ˙ between the soil layers and the cohort (Hgj ,lk ) is calculated and passive soil carbon (slow, e3), determined from Bolker in a similar manner to Eq. (35), whereas the enthalpy flux et al.(1998): between the leaf intercellular space and the canopy air space  0  ˙ ˙ =  0 (Hlk,c) is solved in a similar manner to Eq. (75): Cej ,c Cej fhej Bej ET T g20 Eϑ ϑ20 , (102)   ˙ = ˙ − Hgj ,lk Wgj ,lk q` Tgj T`0 , (97) where fhe is the fraction of decay that is lost through respi- ration (Table S4), and by definition f must always be 1 H˙ = W˙ q T − T . (98) he3 lk,c lk,c pv tk v0 (slow soil carbon can only be lost through heterotrophic res-

4.7 Non-leaf autotrophic respiration piration); Bej is the decay rates at optimal conditions of soil

carbon ej , based on Bolker et al.(1998) (Table S4); T g20 and Respiration from fine roots is defined using a phenomeno- 0 ϑ are the average temperature and relative soil moisture of logical function of temperature that has the same functional 20 the top 0.2m of soil; the relative soil moisture for each layer form as leaf respiration (Moorcroft et al., 2001). Because is defined as roots are allowed in multiple layers, and in ED-2.2 roots have − a uniform distribution of mass throughout the profile, the to- 0 ϑgj ϑRe ˙ −2 −1 ϑ = ; (103) tal respiration (Cr ,c: kg m s ) is the integral of the con- gj k C ϑPo − ϑRe tribution from each soil layer, weighted by the layer thick- 0 ness: 0 and ET (T g20 ) and Eϑ (ϑ20) are functions that reduces the de- h   i PNG 0 composition rate due to temperature or soil moisture under j=j T Tgj ,rrk 1zgj ˙ = 0k non-optimal conditions: Crk,c Crk , (99) PNG 1z j=j0k gj ET (T g ) = −1 20 where rrk (s ) is the PFT-dependent factor that describes 1 the relative metabolic activity of fine roots at the reference n h h io , 1 + exp −fˆ T − T  1 + exp +fˆ T − T  temperature (15 ◦C) (Tables S5–S6), and T 0 is the same Cold g20 gCold Hot g20 gHot temperature-dependent function from Eq. (86); default pa- (104) rameters are listed in Tables S5–S6. Plants have two additional respiration terms: a phe- nomenological term that represents the long-term turnover 0 ˙ Eϑ0 (ϑ ) = rate of the accumulated storage pool (Cnk,c), assumed con- 20 stant (Medvigy et al., 2009), and a term related to the losses 1 n h  0 ion h  0 io , associated with the assimilated carbon for growth and main- + − ˆ − 0 + + ˆ − 0 1 exp fDry ϑ20 ϑDry 1 exp fWet ϑ20 ϑWet tenance of the living tissues (C˙ ; Amthor, 1984). The lat- 1k,c (105) ter term is a function of the plant metabolic rate, which has strong daily variability and hence is a function of the daily ˆ ˆ ˆ 0 where (fCold;TgCold ), (fHot;TgHot ), (fDry;ϑDry), and carbon balance: ˆ 0 (fWet;ϑWet) are phenomenological parameters to de- ˙ = Cnk,c τnk Cnk , (100) crease decomposition rates at low and high temperatures, ˙ = and dry and saturated soils, respectively (Table S4). The C1k,c τ1k C1k , (101) decay fraction from fast and structural soil carbon that is not where (τnk ,τ1k ) are the PFT-dependent decay rates asso- lost through heterotrophic respiration is transported to the ciated with storage turnover and consumption for growth, slow soil carbon (Sect. S4). −2 respectively (Tables S5–S6); and C1k (kgC m ) is the to- tal accumulated carbon from the previous day as defined in Eq. (25). The transport from non-structural storage and the 5 Results accumulated carbon for maintenance, growth, and storage is summarized in Sect. S3. 5.1 Conservation of energy, water, and carbon dioxide

4.8 Heterotrophic respiration The ED-2.2 simulations show a high degree of conservation of the total energy, water, and carbon (Fig.6). In the ex- Heterotrophic respiration comes from the decomposition of ample simulation for one patch at Paracou, French Guiana carbon in the three soil/litter carbon pools. For each car- (GYF), a tropical forest site, the accumulated deviation from

Geosci. Model Dev., 12, 4309–4346, 2019 www.geosci-model-dev.net/12/4309/2019/ M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2 4333 perfect closure (residual) of the energy budget over 50 years estation along the southern and eastern edges of the biome (2 629 800 time steps) was 0.1 % of the total enthalpy stor- (Fig.7). Similarly, the abundance of different plant func- age – sum of enthalpy stored at the canopy air space, co- tional groups shows great variability across the region, with horts, temporary surface water and soil layers, (Fig.6a) and dominance of grasses and early successional tropical trees in 0.002 % of the accumulated losses through eddy flux, the deforested regions and in drier areas in the Brazilian Cerrado, largest cumulative flux of enthalpy. Results for the water bud- whereas late-successional tropical trees dominate the tropical get were even better, with maximum accumulated residuals forests, albeit with lower dominance in parts of central Ama- of 0.04 % of the total water stored in the ED-2.2 thermody- zonia (Fig. S4). namic systems, or 0.0006 % of the total water input by pre- The variability of forest structural and functional composi- cipitation (Fig.6b), and the accumulated residual of carbon tion observed in regional simulations emerges from both the was 0.008 % of the total carbon storage or 0.017 % the to- competition among cohorts in the local micro-environment tal accumulated loss through eddy flux. The average abso- and the environmental controls on the disturbance regime. In lute residual errors by time step, relative to the total storage, Fig.8, we present the impact of different disturbance regimes ranged from 3.6×10−11 (carbon) to 3.8×10−10 (energy) and modulating the predicted ecosystem structure and composi- were thus orders of magnitude less than the truncation error tion for two sites: Paracou (GYF), a tropical forest region in of single-precision numbers (1.2 × 10−7) and the model tol- French Guiana, and Brasília (BSB), a woody savanna site erance for each time step (1.2 × 10−5). in central Brazil. Both sites were simulated for 500 years The conservation of energy and water of ED-2.2 also rep- using a 40-year meteorological forcing developed from lo- resents a substantial improvement from previous versions cal meteorological observations, following the methodology of the model. We carried out additional decade-long simu- described in Longo et al.(2018); we allowed fires to occur lations with ED-2.2 and two former versions of the model but for simplicity we did not prescribe land use change. Af- (ED-2.0.12 and ED-2.1) and the most similar configuration ter 500 years of simulation, the structure at the two sites is possible among versions, and found that cumulative resid- completely different, with large, late-successional trees dom- ual of enthalpy relative to eddy flux loss decreased from inating the canopy at GYF (Fig.8a) and open areas with 15.2 % (ED-2.0.12) or 5.7 % (ED-2.1) to 6.1 % × 10−5 % shorter, mostly early successional trees dominating the land- (ED-2.2) (Fig. S3a–c). Similarly, the cumulative violation of scape at BSB (Fig.8b). For GYF, the structural and func- perfect water budget closure, relative to total precipitation in- tional composition is achieved only after 200 years of simu- put, decreased from 3.4 % (ED-2.0.12) or 1.1 % (ED-2.1) to lation, whereas in BSB a dynamic steady state caused by the 1.2 % × 10−4 % (ED-2.2) (Fig. S3d–f). strong fire regime is achieved in about 100 years (Fig. S5). At both sites, early successional trees dominate the canopy 5.2 Simulated ecosystem heterogeneity at recently disturbed areas (Fig.8c, d) with late-successional (GYF) or mid-successional trees (BSB) increasing in size Because ED-2.2 accounts for the vertical distribution of the only at the older patches (> 30 years, Fig.8c, d), and the vari- plant community and the local heterogeneity of ecosystems, ation of basal area as a function of age since last disturbance it is possible to describe the structural variability of ecosys- show great similarity at both sites (Fig.8e). However, the dis- tems using continuous metrics. To illustrate this, we show the turbance regimes are markedly different: at GYF, fires never results of a 600-year simulation (1400–2002) carried out for occurred and disturbance was driven exclusively by tree fall tropical South America, starting from near-bare-ground con- (prescribed at 1.11%year−1), whereas fires substantially in- ditions and driven by the Princeton Global Meteorological crease the disturbance rates at BSB (average fire return inter- Forcing (Sheffield et al., 2006, 1969–2008), and with active val of 19.3 years). Consequently, old-growth patches (older fires (Sect. S3.4). For the last 100 years, we also prescribed than 100 years) are nonexistent at BSB and abundant at GYF land use changes derived from Hurtt et al.(2006) and Soares- (Fig.8f). In addition, the high disturbance regime at BSB Filho et al.(2006). The distribution of basal area binned by meant that large trees and late-successional trees (slow grow- diameter at breast height (DBH) classes shows high vari- ers) failed to establish but succeeded and maintained a stable ability across the domain and even within biome bound- population at GYF (Fig. S5). aries (Fig.7). For example, larger trees (DBH ≥ 50cm) are The impacts of simulating structurally and functionally di- nearly absent outside the Amazon biome, with the exception verse ecosystems are also observed in the fluxes of energy, of more humid regions such as the Atlantic forest along the water, carbon, and momentum. For example, in Fig.9, we Brazilian coast, western Colombia, and Panama (Fig.7d,e). show the monthly average fluxes from the last 40 years of In contrast, in seasonally dry areas such as the Brazilian simulation at GYF, along with the interannual variability of Cerrado, intermediate-sized trees (10 ≤ DBH < 50cm) con- the fluxes aggregated to the polygon level (hereafter poly- tribute the most to the basal area (e.g., areas near the Brasília gon variability; error bars) and the interannual variability (BSB) site; Fig.7b, c). Even within the Amazon ecoregion, of the fluxes accounting for the patch probability (hereafter basal area shows variability in the contribution of trees with patch variability; colors in the background). The polygon- different sizes, including the areas outside the arc of defor- level variability can be thought as the variability attributable www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4334 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2

Figure 6. Examples of (a) enthalpy, (b) water, and (c) carbon conservation assessment in ED-2.2, for a single-patch simulation at GYF for 50 years. Terms are presented as the cumulative contribution to the change storage. Total storage is the combination of canopy air space, cohorts, and temporary surface water and soil layers in the cases of enthalpy and water, and canopy air space, cohorts, seed bank, and soil carbon pools in the case of carbon. Positive (negative) values mean accumulation (loss) by the combined storage pool over the time. Pressure change accounts for changes in enthalpy when pressure from the meteorological forcing is updated, and density change accounts for changes in mass to ensure the ideal gas law. CAS change and vegetation heat capacity (Veg Hcap) change reflect the addition/subtraction of carbon, water, and enthalpy due to the vegetation dynamics modifying the canopy air space depth and the total heat capacity of the vegetation due to biomass accumulation or loss. Storage change is the net gain or loss of total storage, and the residual corresponds to the deviation from the perfect closure. Note that we present the y axis in cube root scale to improve visualization of the smallest terms.

Figure 7. Simulated distribution of size-dependent basal area across tropical South America, aggregated for the following diameter at breast height (DBH) bins: (a) 0–10 cm; (b) 10–30 cm; (c) 30–50cm; (d) 50–80 cm; (e) ≥ 80cm. Maps were obtained from the final state of a 6000-year simulation (1400–2002), initialized with near-bare-ground conditions, active fires, and prescribed land use changes between 1900 and 2002. Points indicate the location of the example sites (Fig.8): ( ) Paracou (GYF), a tropical forest site; ( ) Brasília (BSB), a woody savanna site. White contour is the domain of the Amazon biome, and grey contours are the political borders.

Geosci. Model Dev., 12, 4309–4346, 2019 www.geosci-model-dev.net/12/4309/2019/ M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2 4335

Figure 8. Examples of size, age, and functional structure simulated by ED-2.2, after 500 years of simulation using local meteorological forcing and active fires. (a, b) Individual realization of simulated stands for sites (a) Paracou (GYF, tropical forest); (b) Brasília (BSB, woody savanna). The number of individuals shown is proportional to the simulated stem density, the distribution in local communities is proportional to the patch area, the crown size and stem height are proportional to the cohort size, and the crown color indicates the functional group. (c, d) Distribution of cohorts as a function of size (DBH and height) and age since last disturbance (patch age) for sites (c) GYF and (d) BSB. Crown sizes are proportional to the logarithm of the stem density within each patch. (e, f) Patch-specific properties as a function of age since last disturbance (patch age) for sites GYF and BSB after 500 years of simulation: (e) basal area and (f) probability density function of patch age (fractional patch area). See Fig.7 for the location of both example sites. exclusively to climate variability, whereas the patch variabil- mary productivity, the relevance of patch variability was even ity also incorporates the impact of the structural heterogene- higher, with the polygon-to-patch variability ratio ranging ity in the variability. Most highly aggregated (“big-leaf”) from 3.7 % during the dry season to 17 % during the wet sea- models characterize the polygon-level variability but not the son (Fig.9d). Importantly, the broader range of fluxes across patch variability. However, in all cases, the patch variabil- patches in the site can be entirely attributed to structural and ity greatly exceeded the polygon variability, indicating that functional diversity, because all patches were driven by the structural variability is as important as the interannual vari- same meteorological forcing. ability in complex ecosystems. In the case of sensible heat, the polygon variable was between 39 % and 64 % of the patch variability (Fig.9a). The polygon-to-patch variability ratio was similar for both friction velocity (19 %–39 %) and wa- ter fluxes (17 %–44 %) (Fig.9b, c). In the case of gross pri- www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4336 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2

Figure 9. Monthly averages and variability of fluxes attributable to meteorological conditions and plant community heterogeneity combined with interannual variability. Results are shown for GYF, a tropical forest site, for (a) sensible heat flux; (b) friction velocity (momentum flux); (c) water vapor flux; and (d) gross primary productivity. The variability was calculated for the last 40 years of a 500-year simulation starting from near-bare ground. Points correspond to the 40-year monthly averages for the entire polygon, line bars correspond to the 2.5 %–97.5 % quantile of monthly averages aggregated at the polygon level (polygon interannual variability), and background colors represent the 40-year probability density function of monthly means for each simulated patch, and scaled by the area of each patch (patch interannual variability). Density function colors outside the 2.5 %–97.5 % quantile interval are not shown. Note that the density function scale is logarithmic. See Fig.7 for the location of the example site.

6 Discussion model (Fig.6), which is significantly less than the error ac- cepted in each time step (1 %). 6.1 Conservation of biophysical and biogeochemical The model’s excellent conservation of these three key properties properties is possible because the ordinary differential equa- tions are written directly in terms of the variables that As demonstrated in Sect. 5.1, it is possible to represent the we sought to conserve, thus reducing the effects of non- long-term, large-scale dynamics of heterogeneous and func- linearities. A key feature that facilitates the model’s high tionally diverse plant canopy, while still accurately conserv- level of is the use of enthalpy as the ing the fluxes of carbon, water, and energy fluxes that oc- primary energy-related state variable within the model. This cur in the ecosystem. ED-2.2 exhibits excellent conservation contrasts with most terrestrial biosphere models, which use of energy, water, and carbon dioxide even in multi-decadal temperature as their energy state variable (e.g., Best et al., scales. After 50 years of simulation, the accumulated resid- 2011; Oleson et al., 2013). By using enthalpy, the model uals from perfect closure never exceeded 0.1 % of the total can seamlessly incorporate energy storage changes caused energy, water, and carbon stored in the pools resolved by the

Geosci. Model Dev., 12, 4309–4346, 2019 www.geosci-model-dev.net/12/4309/2019/ M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2 4337 by rapid changes in water content and consequently heat ca- framework allows users to easily modify the traits and trade- pacity. It also reduces errors near phase changes (freezing offs of existing PFTs, or include new functional groups; pre- or melting), when changes in energy may not correspond to vious studies using ED-2.2 have leveraged this feature of the changes in temperature. Nonetheless, the residual errors in code to define PFTs according to the research question both ED-2.2 are larger than the error of each time step after inte- in the tropics (e.g., Xu et al., 2016; Trugman et al., 2018; grating the model over multiple decades (Fig.6), which sug- Feng et al., 2018) and in the extratropics (e.g., Raczka et al., gests that the errors may have a systematic component that 2018; Bogan et al., 2019). deserves further investigation. The main contribution to the Previous analysis by Levine et al.(2016) has shown that remaining residual errors in carbon, water, and energy fluxes the dynamic, fine-scale heterogeneity and functional diver- comes from the linearization of the prognostic equations due sity of the plant canopy in ED-2.2 is essential for captur- to changes in density in the canopy air space (Eqs. 18–19; ing macro-scale patterns in tropical forest properties. Specifi- 23). The magnitude of these residuals would likely be fur- cally, Levine et al.(2016) found that ED-2.1 was able to char- ther reduced by using the bulk enthalpy, water content, and acterize the smoother observed transition in tropical forest carbon dioxide content in the canopy air space as the state biomass across a dry-season length gradient in the Amazon, variables instead of the specific enthalpy, specific humidity, whereas a highly aggregated (big-leaf-like) version of ED- and CO2 mixing ratio. 2.1 predicted abrupt shifts in biomass, which is commonly Unlike most existing terrestrial biosphere models (but see observed in many dynamic global vegetation models (e.g., SiB2, e.g., Baker et al., 2003; Vidale and Stöckli, 2005), in Good et al., 2011). Results from two related studies have ED-2.2, we explicitly include the dynamic storage of energy, shown that the incorporation of subgrid-scale heterogeneity water, and carbon dioxide in the canopy air space. Canopy and diversity within ED-2 also improves its ability to cor- air space storage is particularly important in tall, dense trop- rectly capture the responses of terrestrial ecosystems to envi- ical forests; accounting for this storage term, as well as the ronmental perturbation. First, in an assessment of the ability energy storage of vegetation, allows a more realistic repre- of four terrestrial biosphere models to capture the impact of sentation of the fluxes between the ecosystem and the air rainfall changes on biomass in Amazon forests (Powell et al., above (see also Haverd et al., 2007). In addition, the sepa- 2013), ED-2.1 was the only model that captured the tim- ration of the ecosystem fluxes in the model into eddy fluxes ing and average magnitude of aboveground biomass loss that and change in canopy air space storage allows a thorough was observed in two experimental drought treatments, while evaluation of the model’s ability to represent both the total all three big-leaf model formulations predicted minimal im- exchange and the ventilation of water, energy, and carbon in pacts of the drought experiment. Second, a recent analysis by and out of the ecosystem with eddy covariance towers, as Longo et al.(2018) on the impact of recurrent droughts in the shown in the companion paper (Longo et al., 2019a). Amazon found that drought-induced carbon losses in ED-2.2 arose mostly from the death of canopy trees, a characteristic 6.2 Heterogeneity of ecosystems that is consistent with field and remote-sensing observations of drought impacts in the region (Phillips et al., 2010; Yang It has been long advocated that terrestrial biosphere models et al., 2018). must incorporate demographic processes and ecosystem het- Importantly, since its inception, the ED model accounts for erogeneity to improve their predictive ability in a changing the disturbance-driven horizontal heterogeneity of ecosys- world (Moorcroft, 2006; Purves and Pacala, 2008; Evans, tems (Moorcroft et al., 2001). As demonstrated in Moor- 2012; Fisher et al., 2018). In ED-2.2, we aggregate individ- croft et al.(2001), the continuous development of tree- uals and forest communities according to similar character- fall gaps is fundamental to explaining the long-term tra- istics (Fig.1). For example, individuals are only aggregated jectory of biomass accumulation in tropical forests; for ex- into cohorts if they are of similar size, same functional group, ample, by representing both recently disturbed and old- and live in comparable micro-environments. Likewise, local growth fragments of forests, it is possible to simulate micro- plant communities are aggregated only if their disturbance environments where either shade-intolerant plants thrive history and their vertical structure are similar. The level of or slow-growing, shade-tolerant individuals dominate the aggregation of ED-2.2 still allows mechanistic representation canopy (Fig.8a, c). Moreover, ED-2.2 can also represent of ecological processes such as how individuals’ access to dynamic and diverse disturbance regimes, which ultimately and competition for resources vary depending on their size, mediate the regional variation of ecosystem properties. For adaptation, and presence of other individuals. This approach example, tropical forests and woody savannas may share allows representing a broad range of structure and compo- similarities in local communities with similar age since dis- sition of ecosystems (Figs.7, S4), as opposed to simplified turbance (Fig.8e); however, because fire disturbances fre- biome classification. In this paper, we presented the func- quently affect large areas in the savannas, fragments of old- tional diversity using only the default tropical PFTs, which growth vegetation are nearly absent in these regions (Fig.8f), describe the functional diversity along a single functional which creates an environment dominated mostly by smaller trait axis of broadleaf tropical trees. However, the ED-2.2 trees (Fig. S5c). www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4338 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2

Furthermore, the heterogeneity of ecosystems in ED-2.2 The ED-2.2 model framework is designed to simulate is integrated across all timescales, because we solve the bio- functionally diverse ecosystems, but trait values within each physical and biogeochemical cycles for each cohort and each functional group are fixed. To account for the observed plas- patch separately (Figs.2–3). While solving the cycles at sub- ticity in many leaf traits, a new parameterization of leaf trait grid scale adds complexity, it also improves the characteriza- variation as function of the light level, based on the param- tion of heterogeneity of available water and energy for plants eterization by Lloyd et al.(2010) and Xu et al.(2017) is of different sizes, even within the same polygon: for example, being implemented. In addition, the ED-2.2 model has also the light profile and soil water availability are not only de- been recently updated to represent the light competition and termined by meteorological conditions but also by the num- parasite–host relationships between lianas and trees (di Por- ber of individuals, their height and rooting depth, and their cia e Brugnera et al., 2019), and it is currently being ex- traits and trade-offs that determine their ability to extract soil tended to incorporate plant functional types from different moisture or assimilate carbon. As a result, the variability in biogeographic regions, such as temperate semi-arid shrub- ecosystem functioning represented by ED-2.2 is significantly lands (Pandit et al., 2018), as well as boreal ecosystems, increased relative to the variability that a highly aggregated building on previous works using ED-1 (Ise et al., 2008). model based on the average ecosystem structure would be Anthropogenic forest degradation is pervasive throughout able to capture (Fig.9). the tropics (Lewis et al., 2015). To improve the model’s abil- ity to represent damage and recovery from degradation, we are implementing a selective logging module that represents 6.3 Current and future developments the direct impact of felling of marketable tree stems, and accounts the damage associated with skid trails, roads, and In this paper, we focused on describing the biophysical and decks, which are modulated by logging intensity and log- biogeochemical core of the ED-2.2 model, and appraising its ging techniques (Pereira Jr. et al., 2002; Feldpausch et al., ability to represent both short-term (intra-annual and inter- 2005). In addition, the original fire model has been recently annual) and long-term (decades to century) processes. How- improved to account for size- and bark-thickness-dependent ever, the ED-2.2 community is continuously developing and survivorship (Trugman et al., 2018), and is being developed improving the model. In this section, we summarize some of to account for natural and anthropogenic drivers of ignition, the recent and ongoing model developments being built on fire intensity, fire spread, and fire duration, building on exist- top of the ED-2.2 dynamic core. ing process-based fire models (Thonicke et al., 2010; Le Page Terrestrial biosphere models still show significant uncer- et al., 2015). tainties in representing photosynthesis due to missing pro- The complexity and sophistication of ED-2.2 also creates cesses and inconsistencies in parameter estimations (Rogers important scientific challenges. For example, the multiple et al., 2017). We are currently implementing the carboxyla- processes for functionally diverse ecosystems represented by tion limitation by the maximum electron transport rate and the model also require a large number of parameters, with by the triose phosphate utilization (von Caemmerer, 2000; some of them being highly uncertain given the scarcity of Lombardozzi et al., 2018), and constrained by observations data. To explore the effect of parameter uncertainty on model (Norby et al., 2017), and and limitation results and leverage the growing number of observations, the have been recently incorporated (Medvigy et al., 2019). In ED-2.2 model has been fully integrated with the Predictive addition, the model has also been recently updated to mech- Ecosystem Analyzer (LeBauer et al., 2013; Dietze et al., anistically represent plant hydraulics, and initial results in- 2014), a hierarchical Bayesian-based framework that con- dicate a significant improvement of the model’s predictions strains model parameters based on available data and quanti- of water use efficiency and water stress in tropical forests in fies the uncertainties on model predictions due to parameter Central America (Xu et al., 2016). Also, to better represent uncertainty. the dynamics of soil carbon in ED-2.2, we are implementing Importantly, the need to incorporate terrestrial ecosystem and optimizing a more detailed version of the CENTURY heterogeneity in Earth system models has been long advo- decomposition model (Bolker et al., 1998). cated (e.g., Moorcroft, 2006; Purves et al., 2008; Evans, To improve the representation of surface and soil water dy- 2012), but only recently have global models been incorporat- namics, the model has been coupled with a hydrological rou- ing ecological mechanisms that allow representing function- tine model that accounts for lateral flux of water as a func- ally diverse and heterogeneous biomes at global scale with- tion of terrain characteristics and simulates river discharge out relying on artificial climate envelopes. Two examples (Pereira et al., 2017; Arias et al., 2018). Moreover, an inte- are the Geophysical Fluid Dynamics Laboratory (GFDL) grated approach of hydraulic routing based on TOPMODEL Land Model version 3 with perfect plasticity approximation (Walko et al., 2000; Beven and Freer, 2001), which allows (Weng et al., 2015, LM3-PPA;) and the Functionally Assem- exchange of water and internal energy exchange between dif- bled Terrestrial Ecosystem Simulation (FATES; Fisher et al., ferent sites as a function of topographic characteristics, is be- 2015), which incorporated the patch and cohort structure ing implemented in ED-2.2.

Geosci. Model Dev., 12, 4309–4346, 2019 www.geosci-model-dev.net/12/4309/2019/ M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2 4339 of ED-2.2 into the Community Land Model (CLM; Oleson Supplement. The supplement related to this article is available on- et al., 2013) framework. line at: https://doi.org/10.5194/gmd-12-4309-2019-supplement.

Author contributions. ML, RGK, DMM, MCD, YK, RLB, SCW, and PRM designed the ED-2.2 model. ML, RGK, DMM, NML, MCD, YK, ALSS, KZ, CR, and PRM developed the model. ML, 7 Conclusions RGK, NML, and ALSS carried out the ED-2.2 simulations. ML, RGK, DMM, NML, MCD, YK, ALSS, and PRM wrote the paper. ED-2.2 represents a significant advance in how to integrate a variety of processes ranging across multiple timescales in heterogeneous landscapes: it retains all the detailed rep- Competing interests. The authors declare that they have no conflict resentation of the long-term dynamics of functionally di- of interest. verse, spatially heterogeneous landscapes and long-term dy- namics from the original ED (Moorcroft et al., 2001; Hurtt et al., 2002; Albani et al., 2006) but also Acknowledgements. The research was partially carried out at the Jet Propulsion Laboratory, California Institute of Technology, un- solves for the associated energy, water, and CO fluxes of 2 der a contract with the National Aeronautics and Space Admin- plants living in horizontally and vertically stratified micro- istration. We thank the reviewers Ian Baker and Stefan Olin, as environments within the plant canopy, which was initially well as Miriam Johnston, Luciana Alves, John Kim, and Shawn implemented by Medvigy et al.(2009) (ED-2) by adapting Serbin for suggestions that improved the manuscript, and Alexan- the big-leaf land surface model LEAF-3 (Walko et al., 2000) der Antonarakis, Fabio Berzaghi, Carl Davidson, Istem Fer, Miriam to the cohort-based structure of ED-2. Johnston, Geraldine Klarenberg, Robert Kooper, Félicien Meunier, The results presented in the model description demon- Manfredo di Porcia e Brugnera, Afshin Pourmokhtarian, Thomas strated that ED-2.2 has a high degree of conservation of Powell, Daniel Scott, Shawn Serbin, Alexey Shiklomanov, Anna carbon, energy, and water, even over multi-decadal scales Trugman, Toni Viskari, and Xiangtao Xu for contributing to the (Fig.6). Importantly, the current formulation of the model code development. The model simulations were carried out at the allows representation of functional and structural diversity Odyssey cluster, supported by the FAS Division of Science, Re- search Computing Group at Harvard University. Marcos Longo was both at local and regional scales (Figs.7–8; S4–S5), and the supported the NASA Postdoctoral Program, administered by Uni- effect of the heterogeneity on energy, water, carbon, and mo- versities Space Research Association under contract with NASA. mentum fluxes (Fig.9). In the companion paper, we use data Abigail L. S. Swann was supported as a Giorgio Ruffolo Fellow from eddy covariance towers, forest inventory, bottom-up es- in the Science Program at Harvard University, for timates of carbon cycles, and remote-sensing products to as- which support from Italy’s Ministry for Environment, Land and Sea sess the strengths and limitations of the current model imple- is gratefully acknowledged. mentation (Longo et al., 2019a). This paper focused on the major updates to the energy, water, and carbon cycle within the ED-2.2 framework; the Financial support. This research has been supported by the Con- model continues to be actively developed. Some of the fur- selho Nacional de Desenvolvimento Científico e Tecnológico (grant ther developments include implementing more mechanisms no. 200686/2005-4), the NASA Earth and Space Science Fel- that influence photosynthesis and water cycle, such as plant lowship (grant no. NNX08AU95H), the National Science Foun- hydraulics; additional nutrient cycles; expanding the repre- dation, Office of International Science and Engineering (grant no. OISE-0730305), the National Science Foundation (grant no. sentation of plant functional diversity, including trait plastic- ATM-0449793), the National Aeronautics and Space Administra- ity and lianas; and expanding the types of natural and anthro- tion (grant no. NNG06GD63G), and the Fundação de Amparo à pogenic disturbances. ED-2.2 is a collaborative, open-source Pesquisa do Estado de São Paulo (grant no. 2015/07227-6). model that is readily available from its repository, and the sci- entific community is encouraged to use the model and con- tribute with new model developments. Review statement. This paper was edited by Christoph Müller and reviewed by Ian Baker and Stefan Olin.

Code availability. The ED-2.2 software and further developments are publicly available. The most up-to-date source code, post- processing R scripts, and an open discussion forum are available on References the GitHub repository (The ED-2 Model Development Team, 2014). The code described in this paper, along with a wiki-based techni- Ahlström, A., Schurgers, G., Arneth, A., and Smith, B.: Robust- cal manual, is stored as a permanent release at https://github.com/ ness and uncertainty in terrestrial ecosystem carbon response mpaiao/ED2/releases/tag/rev-86 (last access: 25 September 2019) to CMIP5 climate change projections, Environ. Res. Lett., 7, and permanently stored at Longo et al.(2019b). 044008, https://doi.org/10.1088/1748-9326/7/4/044008, 2012. www.geosci-model-dev.net/12/4309/2019/ Geosci. Model Dev., 12, 4309–4346, 2019 4340 M. Longo et al.: Biophysical and biogeochemical cycles in ED-2.2

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