Evaluating Soil Biogeochemistry Parameterizations in Earth System Models with Observations

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Global Biogeochemical Cycles

RESEARCH ARTICLE Evaluating soil biogeochemistry parameterizations 10.1002/2013GB004665 in Earth system models with observations Key Points: William R. Wieder1, Jennifer Boehnert1, and Gordon B. Bonan1 • SOC estimates from ESMs show wide variation and are exceptionally low 1National Center for Atmospheric Research, Boulder, Colorado, USA in CLM4cn • After modifications DAYCENT parameterizations provide more realistic SOC pools Abstract Soils contain large reservoirs of terrestrial carbon (C), yet soil C dynamics simulated in Earth • SOC responses to warming suggest systems models show little agreement with each other or with observational data sets. This uncertainty further evaluation of models underscores the need to develop a framework to more thoroughly evaluate model parameterizations, are warranted structures, and projections. Toward this end we used an analytical solution to calculate approximate equilibrium soil C pools for the Community Land Model version 4 (CLM4cn) and Daily Century (DAYCENT) soil Supporting Information: biogeochemistry models. Neither model generated sufficient soil C pools when forced with litterfall inputs • Readme • Text S1 from CLM4cn; however, global totals and spatial correlations of soil C pools for both models improved when • Text S2 calculated with litterfall inputs derived from observational data. DAYCENT required additional modifications • Text S3 to simulate soil C pools in deeper soils (0–100 cm). Our best simulations produced global soil C pools totaling 746 and 978 Pg C for CLM4cn and DAYCENT parameterizations, respectively, compared to observational Correspondence to: W. R. Wieder, estimates of 1259 Pg C. In spite of their differences in complexity and equilibrium soil C pools, predictions of soil [email protected] C losses with warming temperatures through 2100 were strikingly similar for both models. Ultimately, CLM4cn and DAYCENT come from the same class of models that represent the turnover of soil C as a first-order decay Citation: process. While this approach may have utility in calculating steady state soil C pools, the applicability of this Wieder, W. R., J. Boehnert, and G. B. model configuration in transient simulations remains poorly evaluated. Bonan (2014), Evaluating soil biogeochemistry parameterizations in Earth system models with observations, Global Biogeochem. Cycles, 28, 211–222, 1. Introduction doi:10.1002/2013GB004665. Soils contain the largest terrestrial pool of carbon (C) globally [Jobbágy and Jackson, 2000; Tarnocai et al., Received 28 MAY 2013 2009], yet the response of soil C pools to environmental change remains uncertain. Driven by heterotrophic Accepted 26 JAN 2014 respiration of organic C substrates, turnover of soil organic carbon (SOC) pools is sensitive to changes in Accepted article online 3 FEB 2014 temperature, moisture, and plant productivity [Davidson and Janssens, 2006; Davidson et al., 2012; Falloon Published online 13 MAR 2014 et al., 2011]. The degree to which soils globally may serve as a source or a sink for C in the future remains an open question. This uncertainty around the response of SOC pools to environmental change remains a significant challenge for Earth system models (ESMs) [Jones et al., 2003] that are used to investigate carbon- climate feedback and make climate predictions through the 21st century and beyond. Predictions of SOC response to environmental change depend on accurately simulating extant SOC pools and also simulating the processes governing SOC stabilization and turnover in a highly heterogeneous soil environment. Thus, simulating soil biogeochemical processes at the global scale requires reasonable approximations of climate and productivity, and in some cases additional information on the soil physical and chemical environment. Given this complexity, it is not surprising that ESMs vary widely in their predictions of SOC pools and generally show poor spatial correlation with observations [Todd-Brown et al., 2013]. The Community Land Model version 4 (CLM4cn), the terrestrial component of the Community Earth System Model version 1.0 (CESM), simulates notably small SOC pools globally and has low SOC densities at high latitudes [Thornton et al., 2007; Todd-Brown et al., 2013]; soil carbon from a CLM4cn twentieth century control simulation [Lawrence et al., 2011] totals 502 Pg C globally, providing motivation for the work presented here. Small SOC pools in CLM4cn may result from input biases, such as climate or productivity, or from structural errors in simulations of the processes that regulate C turnover in soils. Global productivity in CLM4cn is high [Beer et al., 2010]; however, regionally dry soils in the arctic result in low productivity, which may account for some of CLM4cn’s low SOC pools [Lawrence et al., 2011]. Unrealistically, small SOC pools in CLM4cn may also result from rapid SOC turnover inherent in its soil biogeochemistry parameterization. Compared to observations from the Long-term Intersite Decomposition Experiment (LIDET) leaf and root litter decomposes too rapidly in CLM4cn simulations [Bonan et al., 2013]. In contrast, litter decomposition in Daily Century (DAYCENT) (and its predecessor CENTURY), a well-tested ecosystem model [Kelly et al., 1997; Parton et al., 1987, 1993, 1994], better

matched LIDET observations [Bonan et al., 2013]. Since litter decomposition serves as the precursor to SOC formation, this suggests DAYCENT biogeochemistry may more accurately represent soil biogeochemical processes. Despite its widespread use in soil biogeochemical models, the DAYCENT soil biogeochemistry parameterization has not yet been tested at the global scale [see Schimel et al., 1994]. We continue efforts initiated with the LIDET study [Bonan et al., 2013] to evaluate soil biogeochemical models with observations at the global scale, here focusing on equilibrium SOC pools generated by CLM4cn and DAYCENT soil biogeochemical models. We focus our analysis on these two models; however, all of the ESMs used to make global climate projections employ soil biogeochemistry models with analogous structures— simulating the turnover of SOC in n soil C pools via ﬁrst-order kinetics [Todd-Brown et al., 2013]. Thus, the general approach outlined here is widely applicable to a diversity of models. Using an analytical solution to ﬁnd equilibrium SOC pools [Xia et al., 2012], we test how well each model replicates global SOC observations and identify input parameters important for global SOC simulations. We additionally evaluate the importance of different model structures when simulating potential effects of soil warming on SOC over the 21st century.

2. Methods Soil biogeochemical models are slow to spin-up to an equilibrium state [Thornton and Rosenbloom, 2005]; yet at their core soil biogeochemistry models are relatively simple—simulating the exponential decay of litterfall inputs and SOC pools with decay rates in n pools modulated by environmental scalars (e.g., soil temperature and moisture). To facilitate model analyses, we used an analytical solution to calculate equilibrium soil C pools for CLM4cn and DAYCENT. Both models were forced with prescribed litterfall input, soil temperature, and soil moisture. Simulations used the CLM grid, approximately 1° horizontal resolution. Model results were compared to soil carbon observations. 2.1. Analytical Solution We used an analytical solution to calculate equilibrium soil C pools modiﬁed from Xia et al. [2012, 2013]. The Xia et al. [2012, 2013] framework calculates steady state ecosystem carbon pools (vegetation, coarse woody debris, litter, and soil organic matter) from gross primary production. Our modiﬁed approach calculates coarse woody debris, litter, and soil pools from litterfall.

Generally, these models are described where the carbon balance for pool i is the sum of the litter input ui to pool i and all the ﬂows to pool i from all n pools minus the carbon turnover: n dx ÀÁ i ¼ u þ ∑ 1 r f ξ k x ξ k x (1) dt i ij ij j j j i i i j ¼ 1 j ≠ i

Here ki is the base fractional loss for pool i, ξi is an environmental scalar that modifies the turnover rate, and ξikixi is the carbon turnover from pool i. Similarly, ξjkjxj is the turnover from donor pool j, and fij is fraction that transfers from donor pool j to receiver pool i. The fraction 1 rij is the microbial growth efficiency, or the fraction of the carbon turnover that is assimilated into microbial biomass; the fraction rij of the flow to the receiver pool is lost as respiration. Equation (1) can be written in matrix notation, with dX ¼ BU þ AξKX (2) dt

T T where, X =[x1,x2, …,xn] is a n × 1 column vector of n carbon pools; U =[u1,u2, …,um] is a m × 1 column vector of litter fluxes for m types of litter; B is a n × m litter flux partitioning matrix in which bij is the partitioning of litter flux j to pool i; A is an n × n carbon transfer matrix in which ajj = 1 for pool j and aij =(1 rij)fij is the fraction of carbon loss from pool j entering pool i (for j ≠ i); ξ is a n × n diagonal matrix in which ξjj is the environmental scalar for pool j and all other elements are zero (ξij = 0 for j ≠ i); and K is a n × n diagonal matrix in which kjj is the base fractional loss for pool j and all other elements are zero (kij = 0 for j ≠ i). At steady state, dX/dt = 0 and the steady state equilibrium pools (Xss) are

1 Xss ¼ðÞAξK BU (3)

The coefﬁcients in equation (3) can vary over time with environmental conditions. However, time-mean values B, A, and ξ approximate the steady state solution for a given U [Xia et al., 2012].

2.2. Model Descriptions Soil biogeochemistry in CLM4cn represents organic matter decomposition as a converging cascade that uses three litter pools, four soil organic matter pools, and one course woody debris (CWD) pool [Bonan et al., 2013; Thornton and Rosenbloom, 2005]. Fine litter inputs (leaves and fine roots) are partitioned into labile, cellulose, and lignin litter pools, 25%, 50%, and 25%, respectively—invariant among plant functional types (PFTs). These litter pools have base turnover times ranging from hours to months. Coarse woody debrisisphysicallyfragmented and enters cellulose and lignin litter pools (76% and 24%, respectively). Litter pools flow into corresponding SOC pools (four total) that have base turnover times ranging from weeks to decades. Bases turnover rates of all pools are modified by soil temperature and moisture scalars. Text S1 of the supporting information gives the matrices B, K, ξ,andA. These are time invariant, except for ξ, which uses time-mean values. DAYCENT has a different structure and explicitly simulates surface and belowground processes, which includes four surface C pools, five belowground C pools, and three CWD pools [Parton et al., 1987, 1993, 1994]. Surface and belowground pools have different base turnover rates that are generally slower than the pools in CLM4cn [Bonan et al., 2013]. Leaf and fine root litter is partitioned into metabolic and structural litter pools based on litter chemical quality, calculated by lignin and nitrogen (N) concentration. Woody debris enters one of three CWD litter pools (fine branches, coarse roots, and large wood) that have decreasing rates of decomposition. Decomposing metabolic litter enters the active SOC pool, whereas structural and CWD litter enters active and slow SOC pools with partitioning based on lignin content. DAYCENT allows for two-way transfer between active and slow SOC pools, mixing of slow SOC from surface to belowground pools and includes a belowground passive SOC pool that has a base turnover rate > 300 years. Base turnover rates in DAYCENT are modified by soil temperature and moisture scalars, soil pH, litter lignin content, soil texture, soil oxygen availability, and land use practices (i.e., cultivation). Soil texture also modifies respiration losses and C transfers between belowground SOC pools. In the present work we do not use soil oxygen or cultivation features available in DAYCENT, nor do we have leaching losses active in our simulations. Text S1 gives the matrices B, K, ξ, and A. These are time invariant, except for ξ, which uses time-mean values. In both soil biogeochemistry models, base turnover rates are modified by temperature and soil moisture scalars. Together these scalars are commonly referred to as the climate decomposition index (CDI). Unless noted

otherwise, we used CDI as calculated in CLM4cn, which calculates a temperature scalar using a Q10 temperature function (Q10 = 1.5, base temperature 25°C) and soil moisture scalar that increases monotonically with increasing soil water potential [Andrén and Paustian, 1987]. We calculated an annual average CDI for the environmental scalar matrix ξ (see section 2.3 for details). DAYCENT has additional environmental scalars that depend on soil pH, lignin fraction, and texture. Text S1 gives a full description of the environmental scalar matrix ξ.

2.3. Input Data Sets We used observations of global SOC, soil texture, and pH from the Harmonized World Soil Database (HWSD) [Food Agriculture Organization, 2012] to evaluate and constrain the models. Soil characteristics in the HWSD represent data from real soil profiles at various stages of pedogenic development, land use, land use history, and disturbance history. We recognize that soils are dynamic, heterogeneous environments and HWSD observations are not necessarily derived from soil pedons at “equilibrium” with present-day climate, vegetation, and management practices. Yet our aim with this analysis is to evaluate if soil biogeochemistry models simulate soil C pools that broadly resemble observations from the real world. The HWSD represents the most exhaustive, comprehensive, and contemporary database of soil characteristics that is available for global analyses and is a powerful resource for evaluating soil biogeochemistry models used in ESMs. Soil properties in the HWSD are available for surface soil horizons (0–30 cm) and deeper soil profiles (30–100 cm). The horizontal resolution for HWSD is30arcsec(approximately1km).Weregridded the HWSD from its native resolution to the CLM grid, which has approximately a 1° horizontal resolution. Using Environmental Systems Research Institute ArcGIS 10.0, we performed a zonal statistics on the HWSD in order to obtain the most common HWSD soil mapping unit identifier (MU_GLOBAL) for each HWSD grid cell. We calculated the SOC by multiplying the soil organic C (%) by bulk density (kilogram per cubic meter) and soil depth for each soil mapping unit. We regridded the SOC pools from the 30 arc sec HWSD grid to the 1° CLM grid cell using an area-weighted,

mass-conserving algorithm. This area-weighting approach better represents the spatial heterogeneity of SOC pools within the larger CLM grid cell. For other soil physiochemical variables (i.e., sand, clay, and pH, needed for DAYCENT) calculating area-weighted averages would generate an anomalous soil type that may not actually exist within the larger grid cell; therefore, the spatially dominant mapping units for each CLM grid cell were used as model inputs. For comparison, we also used the dominant mapping unit to estimate SOC pools in each CLM grid cell. Although global soil C totals are similar between the two approaches, the distribution of SOC estimates produced using area weighting better matched observations from the original HWSD database (Text S2). Therefore, we focused subsequent analyses on HWSD observations of SOC estimates generated with the area-weighted approach. We forced CLM4cn and DAYCENT soil biogeochemical models with environmental variables and litter fluxes from a twentieth century CLM4cn simulation driven by historical meteorology [Lawrence et al., 2011]. Using soil temperature and soil moisture integrated over the top 21 cm, we calculated monthly temperature and soil moisture scalars from a decade long CLM4cn simulation. These monthly scalars were averaged to compute an annual CDI value for each grid cell. We used two sources of litter inputs in our analyses, one model based and one observationally based. Our model-based inputs were mean annual litterfall from a decade long CLM4cn simulation; however these modeled data have known biases. For example, in high-latitude systems productivity in CLM4cn is notably low [Lawrence et al., 2011], while in tropical forests CLM4cn strongly favors wood production over fine litterfall (W. Wieder and P. Taylor, unpublished data, 2013). Therefore, we also generated observationally based global estimates of leaf, fine root, and coarse woody debris (CWD) litter inputs. We used the global biogeography of plant functional types (PFTs) in CLM combined with biome estimates of litterfall based on observational data [Matthews, 1997] to obtain gridded estimates of annual litterfall (Text S3). To our knowledge, the data presented by Matthews [1997] represent the best observationally derived estimate of litterfall estimate across biomes; the analysis uses over 1100 measurements of litter fluxes and includes multiple direct and indirect estimates of aboveground, belowground, CWD litter inputs. Matthews [1997] uses a regression model to calculate total litter production as the difference between total soil respiration and root respiration. We estimate fine root litter inputs as the difference between total litter production, and Matthews [1997] observed estimates of aboveground litter production. In DAYCENT simulations CWD inputs from both data sets were split equally between the fine branch, coarse root, and large wood CWD litter pools. CLM4cn holds litter lignin constant (25%) and defines PFT specific litter N concentrations (mainly 0.71–0.83% N). The lignin rich, N poor litter generated by CLM4cn is of lower quality than observations from the TRY database [Brovkin et al., 2012]. Thus, to produce more realistic estimates of litterfall chemistry we generated independent estimates of PFT specific leaf litter chemistry (lignin and N) using results from Brovkin et al. [2012] mapped onto the CLM distribution of PFTs (Text S3).

2.4. Model Evaluation and Sensitivity Analyses To confirm the validity of the analytical solution, we compared SOC pools calculated from our analytical solution forced with CLM4cn litterfall and environmental scalars to the SOC from a twentieth century CLM4cn control simulation using sample cross correlation. We also compared SOC pools from our analytical solutions to observed SOC pools from the HWSD using sample cross correlation and area weighted root-mean-square error (RMSE). Thus, model configurations that improved spatial correlation and reduced RMSE provide a better match to observations from the HWSD. We also calculated the zonal statistics (i.e., mean SOC densities at each latitude band) for observations and model output to facilitate the visualization of latitudinal trends in our results. The depth of SOC pools simulated by CLM4cn is never specified; therefore we calculated spatial statistics with observed SOC pools from surface and the full soil profile (0–30 cm and 0–100 cm, respectively). In its base configuration DAYCENT explicitly simulates surface soils (0–20 cm) [Metherell et al., 1993]; accordingly, we compared model results with HWSD observations from 0 to 30 cm. To simulate deeper soil profiles in DAYCENT Metherell et al. [1993] recommend decreasing base turnover rates of belowground active and slow SOC pools and increasing the transfer of SOC into the passive SOC pool (Text S1). Results from simulations with these modifications were evaluated with HWSD observations from the full soil profile (0–100 cm). We

evaluated the inﬂuence of increasing belowground SOC residence times on simulated rates of root litter decomposition compared to observations from the LIDET )

-2 study, replicating methods from [Bonan et al., 2013]. We additionally evaluated CLM4cn and DAYCENT by calculating the litter inputs needed to create equilibrium SOC pools that matched the HWSD observations. To calculate necessary litter inputs we used a reduced complexity model modiﬁed from Analytical solution (g C m Todd-Brown et al. [2013]. This approach has the advantage of collapsing model complexity into simple terms that can be 0 5000 10000 15000 20000 evaluated individually. Equilibrium SOC

0 2000 4000 6000 8000 10000 12000 14000 pools (Xss) are a function of litterfall inputs Numerical spin-up (g C m-2) (U) divided by decomposition rates (k) modiﬁed by CDI [k(CDI)]. Since we forced Figure 1. Scatter plot for grid cell soil C estimates for CLM4cn using the models with the same U and CDI, analytical steady-state approximation versus results from a numerical differences in X were caused by model spin-up. The analytical solution was calculated using mean annual lit- ss terfall and environmental scalars calculated from a decade of monthly variation in k. For each model, we values from a CLM4cn simulation. The dashed line represents a 1:1 line, approximated k with a simple linear (p < 0.0001, r = 0.97). regression using litter inputs and CDI to predict equilibrium SOC pools. Given these rate differences, and assuming CDI values were “true,” we asked what litter inputs would be necessary (Û)

to calculate SOC pools that match the HWSD observation (Xobs): ðÞX b CDI U^ ¼ obs (4) m where b and m are the intercept and slope, respectively, from linear regressions. This exercise assumes that CDI scalars adequately represent environmental effects on C turnover in soils globally and that globally gridded estimates of SOC match reality. The HWSD estimates of global SOC pools used here fall on the low end, but within the range of other less detailed surveys of global soil C pools [Amundson, 2001; Batjes, 1996; Jobbágy and Jackson, 2000; Post et al., 1982]. We compared these results to observationally derived estimates from plot-scale measurements [Matthews, 1997], (section 2.3), as well as upscaled gross primary product (GPP) estimates from Fluxnet sites [Beer et al., 2010] that were regridded to the CLM grid. To use Fluxnet GPP estimates as an independent approximation of litterfall inputs we assumed that net primary productivity (NPP) is 50% of GPP and that all terrestrial ecosystems are at steady state, so that litterfall equals NPP. Finally, differences in model structure may produce different projections of SOC dynamics. Ultimately, these soil biogeochemistry routines are part of larger Earth system models that are used to make global climate predictions. Given their different structures, we wanted to explore how SOC pools simulated by CLM4cn and DAYCENT may change in a warming world. Climate change will modify soil temperature, hydrology, and C inputs; however, the magnitude and timing of this response remain highly uncertain [Arora et al., 2013; Friedlingstein et al., 2006]. Thus, we constrain our analysis here to model response to projected changes in temperature alone. To do this, we took one CESM ensemble member from archived Coupled Model Intercomparison Project Phase 5 (CMIP5) experiments [Gent et al., 2011], publicly available online at http://www.earthsystemgrid.org. We used our analytical solution with Matthews [1997] derived litter inputs to calculate equilibrium SOC pools for the end of the twentieth century. Using these equilibrium pools, we ran two sets of simulations at daily time steps from 2005 to 2100. Control simulations were forced with twentieth century CDI. Transient simulations were forced with a temperature scalar based on soil temperature from Representative Concentration Pathways 8.5 (RCP 8.5)—the highest CMIP5 representative concentration pathway that increases radiative forcing by 8.5 W m 2 in 2100. We used this extreme future scenario to highlight potential differences of predictions generated by different modeling approaches. Soil C losses for each soil biogeochemistry model were calculated as the difference between control and transient

Table 1. Global SOC Pools From Observations (HWSD) and Different Models Calculated With the Analytical Approacha CLM4cn Litterfall Observed Litterfall

Model Global SOC (Pg C) r RMSE (kg C/m2) Global SOC (Pg C) r RMSE (kg C/m2)

CLM4cn spin-up 502 0.43 8.1 - - - CLM4cn 551 0.42 8.0 746 0.61 6.7 DAYCENTb 421 0.42 4.0 552 0.60 3.5 Deep DAYCENT 749 0.41 7.9 978 0.61 6.5

aDepth modifications for DAYCENT slow down base turnover rates for belowground SOC pools and increase partitioning into the passive pool. Litterfall inputs came from CLM4cn model runs or from observationally derived data set based on Matthews [1997]. Spatial correlation coefficients (r) and area-weighted RMSE are calculated for different model configurations and compared to the HWSD observations (0–100 cm), unless otherwise noted. bSpatial statistics calculated with HWSD (0–30 cm).

simulations, thus allowing us to quantify potential losses of soil C from different model conﬁgurations from changes in soil temperature alone.

3. Results 3.1. Equilibrium SOC Pools Soil C pools approximated for CLM4cn with our analytical solution were in good agreement with results from a control simulation that used a traditional numerical spin-up (Figure 1). Global SOC calculated with the analytical solution for CLM4cn was larger than that from the numerical spin-up (Table 1, 551 Pg C and 502 Pg C, respectively; 1 Pg = 1015 g). This discrepancy may reﬂect, in part, our exclusion of carbon-nitrogen interactions in the equilibrium solution (see Text S1). However, the difference between the analytical and numerical spin-up solutions (49 Pg C or 10%) is much smaller than the error compared with the HWSD global SOC (1259 Pg C, CLM4cn bias 757 Pg C). Global SOC for DAYCENT biogeochemistry forced with the same model-derived litterfall and CDI values was similarly low (421 Pg C). The modiﬁed DAYCENT (adjusting turnover rates and transfer to the passive SOC pool by

a) b)

c) d)

g C m-2

Figure 2. Global SOC pools from observations compared to simulations, including spatial correlation coefﬁcients (r) between observed and modeled SOC pools: (a) observations (0–100 cm) based on the Harmonized World Soils Database (1259 Pg C), (b) a spun-up version of CLM4cn (502 Pg C, r = 0.43), (c) analytical solution for CLM4cn forced with observationally derived litter inputs (746 Pg C, r = 0.61), and (d) analytical solution for DAYCENT modiﬁed to simulate deeper soil C pools and forced with observationally derived litter inputs (978 Pg C, r =0.61).

40% to represent deeper SOC pools, Text S3) minimizedRMSEwithobservationsforthefull soil profile (0–100 cm) (W. Wieder, unpublished data, 2013) and resulted in larger equilibrium SOC pools (749 Pg C). Collectively, CLM4cn and DAYCENT results using model-derived litter fluxes are biased low and have low spatial correlation with HWSD observations (Table 1). Global SOC pools from the HWSD (0–100 cm depth) are 1259 Pg C (Figure 2a); approximately 52% (661 Pg C) of the global SOC lies in surface soils (0–30 cm). Global litter inputs obtained from the CLM4cn twentieth century control simulation [Lawrence et al., 2011] totaled 43.1 Pg C yr 1; of this approximately 32%, 46%, and 23% was SOC (g C m-2) delivered as leaf litterfall, fine root litter, and CWD, respectively. Global litter inputs Figure 3. Zonal mean of soil C density (gram of carbon per square estimated from observations [Matthews, 1997] meter) calculated for each latitude band for HWSD observations mapped to the CLM PFT biogeography totaled (black line, regridded to the CLM grid), CLM4cn (red line), and 1 deep DAYCENT (blue line). The gray shaded area shows mean ± 1 45.0 Pg C yr ; of this approximately 38%, 52%, standard deviation of observations. Model results were calculated and 10% was delivered as leaf litterfall, fine using the analytical solution forced with observationally derived root litter, and CWD, respectively. Estimates of litter inputs (as in Figures 2c and 2d). global totals show good agreement with Moderate Resolution Imaging Spectroradiometer- derived estimates of NPP (44.3 Pg C yr 1;[Cleveland et al., 2013]) and more recent simple regression models (46 Pg Cyr 1)[Del Grosso et al., 2008]. Estimates of belowground litter inputs used here are higher than estimates from Del Grosso and others (2008), highlighting uncertainty in quantifying belowground productivity across ecosystems. Using the observationally based estimate of litterfall inputs, CLM4cn soil biogeochemistry produced larger global SOC (746 Pg C and 42 Pg C of CWD), and longer mean SOC turnover time (42.5 years, compared with 27.0 years obtained using model litterfall). These results have higher spatial correlation to HWSD observations and significantly reduced RMSE (Figure 2c and Table 1). DAYCENT SOC pools forced with observed litter inputs totaled 552 Pg C (with 773 Pg C in CWD pools), with a mean SOC turnover time of 28.5 years. Although smaller than CLM4cn SOC pools forced with the same litter inputs, the DAYCENT solution has a lower RMSE with SOC observations for the surface soils (0–30 cm; Table 1). The modified DAYCENT resulted in the lowest RMSE and 978 Pg of SOC globally with a turnover time of 50.6 years (Table 1, Figures 2d, and 3). To distinguish between these models we will refer to base DAYCENT as the model in its unaltered state (that only simulates surface soils), and deep DAYCENT as the model modified for deeper soil profiles (0–100 cm). The base DAYCENT parameterizations better replicate the LIDET 10 year litterbag observations compared with CLM4cn [Bonan et al., 2013]. Increasing belowground turnover times and allocation to the passive pool in deep DAYCENT had no effect on rates of Table 2. Root-Mean-Square Error (RMSE) Between Simulated and leaf litter decomposition simulations, and Observed Carbon Mass Remaining for Three Types of Root Litter fi a these modi cations reduced the RMSE Decomposed Over 10 Years at 20 Sites associated with root litter decomposition in Biome n Base DAYCENT Deep DAYCENT all biomes (Table 2). Tundra 56 21.0 18.8 3.2. Model Sensitivity Analyses Boreal forest 57 16.4 14.0 Conifer forest 124 13.8 11.6 We found a strong linear relationship Deciduous forest 74 13.2 10.8 between equilibrium SOC pools and the Tropical forest 67 11.7 11.3 ratio of inputs to CDI (P < 0.0001; R2 =1.0 Humid grassland 54 11.9 10.5 and0.77forCLM4cnanddeepDAYCENT, a Observations and simulations are as in Bonan et al. [2013], but respectively). Using equation (4) and fi additionally with DAYCENT modi ed to represent deep soils. results from these regressions, we

estimate that to match HWSD observations global litter fluxes would have to total 83.2 and 66.8 Pg C yr 1 for CLM4cn and deep DAYCENT, respectively (Figure 4). Both estimates have good spatial agreement with estimates of gross primary productivity (GPP; r = 0.65) [from Beer et al., 2010], although DAYCENT estimates fall more within the range of estimates of GPP [Beer et al., 2010; Jung et al., 2011; Welp et al., 2011], assuming that NPP is half of GPP and that at steady state litterfall should equal NPP. This is not to say either approach is estimating terrestrial productivity correctly or that they are getting terrestrial productivity right for the right reasons, but the similarity of the findings is noteworthy. Litter Fluxes (g C m-2 y-1) We ran each model configuration forced with Figure 4. Zonal mean of global litterfall estimates and net primary soil temperature from RCP 8.5 for the period productivity (gram of carbon per square meter per year) at each lati- 2005–2100. By the end of this simulation global tude band. The grey line shows litterfall derived from observations SOC pools decreased 54.5, 44.2, and 54.0 Pg C across biomes [Matthews 1997] and mapped onto CLM PFTs (global sum = 45.0 Pg C yr 1). The black line shows data upscaled from from CLM4cn, base DAYCENT, and deep Fluxnet sites [Beer et al., 2010] and regridded to the CLM grid (global DAYCENT configurations, respectively sum = 57.7 Pg C yr 1). The red line shows litter inputs needed to (Figure 5). This represents a 7% C loss from match HWSD observations of global SOC pools using CLM4cn soil initial SOC pools in both CLM4cn and base 1 biogeochemistry (global sum = 82.3 Pg C yr ).Thebluelineshows DAYCENT models, and a 5% loss from initial litter inputs needed to match HWSD SOC pools using deep DAYCENT soil biogeochemistry, modified to simulate deep SOC pools (global SOC pools using deep DAYCENT. In the RCP 8.5 total = 66.8 Pg C yr 1). forcing data set mean global air temperature over land increased 4.7°C for the last decade of the 21st century, relative to the last decade of the twentieth century. Thus, our respective soil biogeochemistry model configurations predict a net C loss from SOC pools of 11.6, 9.4, and 11.5 Pg C °C 1 from rising temperatures alone, without concurrent changes in litterfall or soil moisture.

4. Discussion Earth system models (ESMs) have widely divergent simulations of SOC pools, and deviations in model output from observations may arise from errors or biases in forcing data sets, model parameterizations, or model structures [Todd-Brown et al., 2013]. The analytical solution forced with prescribed litterfall input, soil temperature, and soil moisture provides a convenient framework to broadly explore differences between model configurations and to evaluate soil biogeochemistry models in global simulations. The analyses reported here highlight likely sources of errors, with examples focusing on input data sets, model parameterizations, and model structure. We found that both CLM4cn and DAYCENT soil biogeochemistry models could not simulate reasonable SOC pools without significant modifications to input data and/or model configuration (Table 1, Figures 2, and 3). Earth system model simulations with CLM4cn have low global SOC [Todd-Brown et al., 2013]. This may arise, in part, because CLM4cn has high rates of litter decomposition compared with long-term (10 year) LIDET observations [Bonan et al., 2013]. In contrast, DAYCENT better matches the litter decomposition observations, and we expected DAYCENT would provide similar improvements with SOC observations. Our results, however, demonstrate that good agreement with a decade of litter decomposition data do not necessarily result in the formationofmorereasonableSOCpools.Whenforced with the same inputs, SOC pools generated with DAYCENT soil biogeochemistry were consistently smaller than those simulated withCLM4cn(Table1).This discrepancy may be attributable to the depth of soil each model aimed to represent. While this in unclear in CLM4cn, in its base state DAYCENT is only meant to simulate the top 20 cm of soil [Metherell et al., 1993]. Thus,

adjusting rates of belowground C cycling and pool allocation in DAYCENT improves modeled results at 100 cm depth (Table 1, Figures 2, and 3). This modification concurrently reduced the RMSE associated with root litter decomposition observations for the LIDET study (Table 2), demonstrating that the deep DAYCENT parameterization shows reasonable agreement with observations at both 10 year and steady- state timescales. Moreover, the litter inputs required to match SOC observations are more realistic for deep DAYCENT than for other model configurations (Figure 4). Altering the spatial distribution of litter inputs, with minor changes to the total litter fluxes, resulted in the greatest improvement in SOC estimates (Table 1). Forced with litterfall from a Figure 5. Absolute change in SOC pools (Petagram of carbon, glob- CLM4cn control simulation, neither model ally) from soil biogeochemistry models forced with depth integrated soil temperatures predicted by CESM for RCP 8.5 using CLM4cn (red simulated adequate SOC pools, especially at solid line), base DAYCENT (dashed light blue line), and deep DAYCENT high latitudes. Reallocating the spatial (solid dark blue line) soil biogeochemistry models. Equilibrium SOC distribution of litter inputs using the best pools were calculated using our analytical approach. Subsequent estimates available from published literature control and transient simulations ran from 2005 to 2100. The change [Matthews, 1997] significantly improved in SOC pools was calculated as the difference between control simulations (using 1985–2005 soil temperatures), and transient agreement with SOC observations (Figures 2 simulations (using soil temperatures predicted by a single ensemble and 3). Much of the improvement comes at member of CESM for RCP 8.5). We used observationally derived litter high latitudes where the observationally inputs and CDI calculated as in CLM4cn. derived litterfall data set results in greater SOC densities. Other regions, however, like the eastern North America and much of the tropics show unwarranted decreases in SOC pools. Some of this discrepancy likely comes from uncertainty in observations. Global approximations of NPP extrapolated from flux tower sites [Beeretal., 2010] show a reasonable resemblance to the litterfall estimates derived from plot- scale measurements [Matthews, 1997]. We found notably strong agreement of litterfall estimates generated from these very different methods at high latitudes, whereas estimates of tropical productivity show greater uncertainty (Figure 4). At the time of publication Matthews [1997] acknowledged the database was not meant to be exhaustive and noted to paucity of data in many biomes. The ESM community would be well served by a more exhaustive, contemporary meta-analysis of plant productivity and litterfall estimates across multiple biomes. The litter fluxes required to simulate reasonable SOC pools at high latitudes with CLM4cn and DAYCENT biogeochemistry models are clearly untenable (Figure 4), suggesting further modifications to model parameterizations and or structures are necessary. In general, soil biogeochemistry models do a poor job simulating organic-rich and permafrost soils [Schimel et al., 1994], largely because the biophysical conditions that preserve SOC in these soils are poorly represented [see Koven et al., 2011, 2013]. Interactions between soil hydrology and soil biogeochemistry clearly impact steady-state SOC pools and their response to climate change; however, the water scalar calculated as part of CDI in this analysis does not adequately account for slow rates of decomposition in water-saturated soils. Nor, however, does CLM adequately account for water-saturated soils in the arctic [Lawrence et al., 2011]. This motivates ongoing efforts to improve the representation of arctic hydrology [Swenson and Lawrence, 2012; Swenson et al., 2012]. Future analyses of soil biogeochemistry models in EMSs should be evaluated on their ability to simulate SOC dynamics in mineral and organic soils, since the response of these diverse soil environments will determine the magnitude of future carbon cycle climate feedbacks. Ultimately, Earth system models are used to make predictions about what the world may look like in the next century under different scenarios. Despite their different complexity, configurations, input requirements, and equilibrium SOC estimates, the soil biogeochemistry models tested here predicted remarkably similar SOC

losses to warming conditions throughout the 21st century (Figure 5). Soil biogeochemistry in CLM4cn, DAYCENT, and other ESMs generally assume exponential decay of SOC pools is determined by the molecular structure of the C pool and modified by environmental scalars [Dungait et al., 2012; Schmidt et al., 2011; Todd- Brown et al., 2012]. Accordingly, most of the variation in SOC pools simulated by different ESMs is generated by differences in litterfall and the temperature sensitivity of soil C cycling, not because of inherent differences in model structure [Todd-Brown et al., 2013]. Thus, although initial pool sizes may vary, at their core these soil C models really are not that different and produce comparable results in transient simulations (i.e., warming). However, emerging understanding of factors influencing the formation of soil organic matter may challenge this assumption and motivate the development of alternative model structures. Representations of coupled biogeochemical cycles in land surface models are in their infancy, and authentic evaluation of their assumptions, structures, and projections are needed [Bonan and Levis, 2010; Thomas et al., 2013]. The analysis here focuses on soil C dynamics; Xia et al. [2012] recommend solving the analytical solution for aC-onlyconfiguration and deriving steady-state N pools from the C:N ratios assigned to particular C pools. Yet this may neglect important differences in carbon-nitrogen dynamics between the model configurations [Bonan et al., 2013]. In CLM4cn, for example, low N availability has the potential to down regulate rates of decomposition, although such conditions rarely exist (W. Wieder and G. Bonan, unpublished data, 2013). DAYCENT allows variable C:N ratios in different soil organic matter pools. This feature prevents low N availability from constraining rates of C flows between pools, but it also complicates derivation of equilibrium N pools with the analytical solution used here. More broadly, neither approach accurately reflects contemporary understanding of soil C and N dynamics. Emerging conceptual theories of soil organic matter dynamics highlight the importance of simulating deep soil profiles, separately representing root inputs, physiochemical stabilization of SOC, and explicitly representing microbial physiology [Conant et al., 2011; Cotrufo et al., 2013; Dungait et al., 2012; Schmidt et al., 2011]. Each of these details may be important for different aims; the challenge then becomes evaluating what complexities of heterogeneous soil environments are critical to simulate. Our work provides a tool to rapidly assess equilibrium SOC pools and begins outlining an approach to evaluate model output at global scales [see also Bonan et al., 2013]. Simple modifications to existing model structures may begin to address the gap between our theoretical understanding of soil biogeochemical processes and their representation in ESMs. For example, deeper soil horizons can be simulated with modifications described here or using more complex model structures that explicitly represent soil horizons [Koven et al., 2011; 2013]. Similarly, explicitly simulating litter and subsurface dynamics should improve soil biogeochemistry models in EMSs. Although this seems intuitive, many ESMs, including CLM4cn, do not distinguish between aboveground and belowground litter inputs or rates of C turnover. Yet empirical work highlights the importance of root inputs to SOC formation [Kramer et al., 2010; Rasse et al., 2005]. By representing aboveground and belowground processes separately DAYCENT soil biogeochemistry better matches observed rates of fine root litter decomposition [Bonan et al., 2013], but only modestly improved equilibrium SOC pools (Table 1). More work must be done to evaluate modeled responses to warming [Frey et al., 2013; Tucker et al., 2013] or perturbations that change belowground C

allocation (e.g., elevated CO2 or N enrichment) [Drake et al., 2011; Iversen et al., 2012; Liu and Greaver, 2010; Phillips et al., 2011]. Incorporating contemporary theoretical understanding that emphasizes the role of soil mineralogy and microbial physiology in governing soil biogeochemical processes poses greater challenges [Schmidtetal., 2011]. DAYCENT uses soil clay content as a proxy for the physical protection of SOC on mineral surfaces and partitioning into the “passive” SOC pool. Accordingly, soil texture has a strong effect on SOC pools [Schimel et al., 1994]. This approach may be sufficient to approximate SOC adsorption onto mineral surfaces [see Torn et al., 1997]; however, it neglects the importance of interactions with mineral surfaces, occlusion within aggregates, and interactions between soil mineralogy and microbial activity that may stabilize SOC [Dungaitetal., 2012; Grandy and Neff, 2008; Six et al., 2006]. Simulating the heterogeneous suite of biological, chemical, and physical characteristics governing microbial accessibility of SOC remains a significant challenge for modeling SOC dynamics at multiple spatial scales. This challenge may be especially acute in trying to simulate microbial processes at global scales. Typical soil biogeochemistry models, like the ones evaluated here, implicitly simulate microbial processes. An emerging body of work suggests that significant improvements to soil biogeochemistry models may be possible by explicitly representing key aspects of microbial physiology that govern C turnover in soils [Cotrufo et al., 2013;

Wieder et al., 2013; Todd-Brown et al., 2012; Treseder et al., 2012]. Given the intense interest in these ideas and the importance of soil biogeochemistry for ESMs, we reiterate that the approach outlined here, and in Bonan et al. [2013], introduces a framework to evaluate model structures, parameterizations, and projections at multiple temporal (e.g., 10 year litter decay, steady-state) and spatial (e.g., site level litterbag, global) scales. If restructured with these theoretical ideas in mind, ESMs may provide some valuable insight into the potential fate of C in a changing world, and provide fertile ground for empirical and modeling communities to advance our understanding of soil processes in a changing world. Model parameterization and evaluation activities should be paired with appropriate observational studies to reﬁne our theoretical understanding of mechanisms responsible for soil organic matter turnover and stabilization across spatial and temporal scales. Yet if one function of ESMs is to predict carbon-climate feedback, these ﬁndings emphasize the need for greater communication and collaboration between modeling and empirical disciplines.

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