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Comparing machine learning-derived global estimates of soil respiration and its 2
components with those from terrestrial ecosystem models 3
Haibo Lu1, 2, Shihua Li1, Minna Ma1, Vladislav Bastrikov3, Xiuzhi Chen1, 2, Philippe 4
Ciais3, Yongjiu Dai1, 2, Akihiko Ito4, Weimin Ju5, Sebastian Lienert6, Danica 5
Lombardozzi7, Xingjie Lu1, 2, Fabienne Maignan3, Mahdi Nakhavali8, Timothy Quine9, 6
Andreas Schindlbacher10, Jun Wang5, 11, Yingping Wang12, 13, David Wårlind14, 7
Wenping Yuan1, 2* 8
Affiliations 10
1Guangdong Province Key Laboratory for Climate Change and Natural Disaster 11
Studies, School of Atmospheric Sciences, Sun Yat-sen University, Zhuhai 519082, 12
Guangdong, China 13
519082, China 15
3Laboratoire des Sciences du Climat et de l’Environnement, LSCE/IPSL, CEA-16
CNRS-UVSQ, Gif Sur Yvette, 91191, France 17
4National Institute for Environmental Studies, Tsukuba, Ibaraki 305-8506, Japan 18
5Jiangsu Provincial Key Laboratory of Geographic Information Science and 19
Technology, International Institute for Earth System Sciences, Nanjing University, 20
210023 Nanjing, China 21
6Climate and Environmental Physics, Physics Institute and Oeschger Centre for 22
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7Climate and Global Dynamics Laboratory, National Center for Atmospheric 24
Research, Boulder, CO, USA 25
8College of Engineering, Mathematics and Physical Sciences, University of Exeter, 26
Exeter, EX4 4QE, UK 27
9Department of Geography, College of Life and Environmental Sciences, University 28
of Exeter, EX4 4RJ Exeter, UK 29
10Department of Forest Ecology, Federal Research and Training Centre for Forests, 30
Natural Hazards and Landscape-BFW, A-1131 Vienna, Austria 31
11Department of Atmospheric and Oceanic Science, University of Maryland, College 32
Park, Maryland 20742, USA 33
12CSIRO, Oceans and Atmosphere, Private Bag 1, Aspendale, Victoria 3195, 34
Australia. 35
13South China Botanical Garden, Chinese Academy of Sciences, Guangzhou 510650, 36
China. 37
14Department of Physical Geography and Ecosystem Science, Lund University, Lund, 38
Sweden 39
Tel: (86)20-84110109 42
Address: Sun Yat-sen University, 135 West Xingang Road, Haizhu District, 43
Guangzhou 510275, China 44
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Abstract 45
The CO2 efflux from soil (soil respiration, SR) is one of the largest fluxes in the global 46
carbon (C) cycle and its response to climate change could strongly influence future atmospheric 47
CO2 concentrations. Still, a large divergence of global SR estimates and its autotrophic (AR) 48
and heterotrophic (HR) components exists among process based terrestrial ecosystem models. 49
Therefore, alternatively derived global benchmark values are warranted for constraining the 50
various ecosystem model output. In this study, we developed models based on the global soil 51
respiration observations database (SRDB, Version 5.0), using the Random Forest (RF) method 52
to generate the global benchmark distribution of total soil respiration and its components. 53
Benchmark values were then compared with the output of ten different global terrestrial 54
ecosystem models. Our observationally-derived global mean annual benchmark rates were 85.5 55
± 40.4 (SD) Pg C yr-1 for SR, 50.3 ± 25.0 (SD) Pg C yr-1 for HR and 35.2 Pg C yr-1 for AR 56
during 1982-2012, respectively. Evaluating against the observations, the RF models showed 57
better performance in both of SR and HR simulations than all investigated terrestrial ecosystem 58
models. Large divergences in simulating SR and its components were observed among the 59
ecosystem models. The estimated global SR and HR by the ecosystem models ranged from 61.4 60
to 91.7 Pg C yr-1 and 39.8 to 61.7 Pg C yr-1, respectively. The most discrepancy lays in the 61
estimation of AR, the difference (12.0 to 42.3 Pg C yr-1) of estimates among the ecosystem 62
models was up to 3.5 times. The contribution of AR to SR highly varied among the ecosystem 63
models ranging from 18% to 48%, which differed with the estimate by RF (41%). This study 64
generated global SR and its components (HR and AR) fluxes, which are useful benchmarks to 65
constrain the performance of terrestrial ecosystem models. 66
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ecosystem models 69
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Introduction 71
As the largest CO2 flux from the terrestrial biosphere to the atmosphere, soil 72
respiration (SR) plays an important role in regulating land C budgets and atmospheric CO2 73
concentrations (Raich & Schlesinger, 1992; Rustad et al., 2000; Davidson & Janssens, 2006). 74
Soil respiration primarily consists of autotrophic respiration (AR) from plant roots and 75
heterotrophic respiration (HR) from decomposition of soil organic carbon by microorganisms 76
(Lambers, 1979; Hanson et al., 2000). Soil respiration rates are highly sensitive to changing 77
environment and disturbances (Davidson & Janssens, 2006; Harmon et al., 2011; Wang et al., 78
2017), and especially global warming is expected to enhance SR on the global scale (Bond-79
Lamberty et al., 2018). Moreover, disturbances induced soil C loss likely accounts for 20% - 80
50% heterotrophic soil respiration flux in forests. Therefore, changes of disturbances in 81
frequency and severity can profoundly impact soil respiration dynamics (Harmon et al., 2011). 82
Due to its large magnitude, even a small change in the global SR can substantially impact 83
atmospheric CO2 concentrations (Zhou et al., 2014). 84
Large uncertainties in simulating global SR and its components (HR and AR) exist 85
among current terrestrial ecosystem models. The simulations of global HR by twenty Earth 86
System Models (ESMs) from CMIP5 varied from 42 to 73 Pg C yr-1, and the maximum 87
estimates by MPI-ESM-MR (~ 73 Pg C yr-1) model was 1.7 times of the lowest estimate of ~ 88
42 Pg C yr-1 simulated by CESM1-BGC (Hashimoto et al., 2015). Such a large divergence 89
implies a low confidence in the estimated C budgets over global scales. Therefore, it is 90
necessary to evaluate models based on well-defined benchmarks to diagnose model strengths 91
and deficiencies. However, there is limited knowledge on model performance with respect to 92
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SR, as well as the HR and AR component fluxes, due to limited benchmark datasets that allow 93
for identification of simulated uncertainties in the magnitude and spatial distribution of soil 94
respiration (Bond-Lamberty, 2018). 95
The changes of SR components (HR and AR) provides information about the different 96
carbon cycling processes in the diverse ecosystem models. HR is the CO2 efflux that derives 97
from microbial decomposition of soil organic matter, which is regulated by C substrate supply 98
and quality, soil and environmental factors (i.e., soil temperature and moisture, clay content and 99
pH), as well as microbial physiology. The AR indicates the CO2 released from the autotrophic 100
metabolism of plant roots, which is more directly from plant photosynthesis, and highly 101
depends on C allocation of plant photosynthate to root (Trumbore, 2006; Brunner et al., 2015). 102
A recent study showed an increasing ratio of HR to SR during the past two decades, which 103
suggests larger increased magnitude of soil C losses due to climate change in many ecosystems 104
(Bond-Lamberty, 2018). Accurate quantification of HR and AR is essential to understanding of 105
C-cycling processes in response to global change (Trumbore & Czimczik, 2008). Therefore, 106
the model evaluations and analyses also require distinguishing the spatial variations of HR and 107
AR to assess if the inter-ecosystem processes of the model have been represented adequately. 108
Usually, the model evaluations only focused on the magnitude of SR (sum of HR and AR), 109
which cannot judge the reliability of HR and AR simulations, and was not able to reveal the 110
inadequate representation of HR and AR in the ecosystem models. 111
The development of global soil respiration observations datasets (SRDB) open the 112
path to the application of machine learning approaches in global simulations of SR and its 113
components (Bond-Lamberty, 2018; Bond-Lamberty & Thomson, 2018). The random forest 114
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(RF) algorithm is widely considered to be one of the best methods to model complex 115
interactions among independent variables (Cutler et al., 2007), which has been deployed in 116
estimating biomass and litterfall production over regional and global scales (Xia et al., 2018; 117
Li et al., 2019). Jian et al. (2018) estimated global SR of 78.8 Pg C yr-1 by the RF approach. 118
Warner et al. (2019) generated global SR at 1-km spatial resolution using RF, based on that, 119
they indirectly predicted global HR by empirical relationships between SR and HR deriving 120
from meta-analyses. However, only a few studies have been conducted to estimate SR and its 121
components (HR and AR) using the RF method. In this study, the latest SRDB (Version 5.0) 122
database (Jian et al., 2020) and related climate data would be used to develop the RF model. 123
The primary objectives of this study were to (1) develop RF models to estimate the global 124
spatial distribution of SR and its components (HR and AR), (2) evaluate the performance of 125
process-based ecosystem models on reproducing SR, HR, and AR against the simulations of 126
the RF model and (3) compare the differences among process-based ecosystem models. 127
128
Global datasets of soil respiration 130
In this study, the field observations of SR and HR were collected from the global soil 131
respiration database (SRDB), Version 5.0, which encompasses all published studies that report 132
the annual SR or HR data measured in the field (not laboratory). The SRDB v5.0 compiled 133
more than 10000 soil respiration records from nearly 2000 publications (Jian et al., 2020). We 134
selected a subset of the SR and HR observations from the SRDB database using the following 135
criteria: () the observed SR and HR were under natural condition, without any experimental 136
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treatments (i.e., experimental warming, precipitation manipulation, nitrogen addition); () for 137
each record, the SR value should be larger than the corresponding HR value if the corresponding 138
HR was reported, to avoid inconsistent data. In total, 3331 annual SR flux records and 840 139
annual HR flux records were selected in this analysis. The observation sites were distributed 140
across various ecosystem types with latitudes ranging from 44.23°S to 69.42°N and longitudes 141
from 150.33°W to 175.77°E (Figure 1). 142
Random forest method 143
The SR and HR models were developed using the ‘quantregForest’ package version 144
1.3-7 (https://cran.r-project.org/web/packages/quantregForest/index.html) in the R software 145
version 3.4.3 (R Core Team, 2017). The ‘quantregForest’ package is similar to the previous 146
‘random Forest’ package (https://cran.rproject.org/web/packages/randomForest/), but can 147
yield the entire distribution of predictions instead of a single mean value of prediction 148
(Meinshausen, 2006). As an efficient machine learning method, the random forest (RF) 149
approach was extensively used for spatial prediction of biogeochemical parameters in 150
geosciences (Xia et al., 2018; Li et al., 2019; Reichstein et al., 2019). The original random 151
forest algorithm was proposed by Breiman (2001). The RF algorithm produces a model 152
composed of many independent regression trees. The independent trees are obtained by 153
randomly selecting from a subgroup of predictors every time a branch of a tree is grown. 154
Based on the given training database, each individual decision tree in random forest outputs 155
the mode of classes or the mean prediction, and the generalization error for RF can converge 156
to a limit with the increase of the decision tree number. 157
The SR and HR models were developed by the RF approach. The initial set of 158
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explanatory variables included: mean annual air temperature (MAT), annual precipitation 159
(Prec), mean annual relative humidity (RH), mean annual leaf area index (LAI), annual 160
photosynthetically active radiation (PAR), soil organic carbon content (SOC, in 0-30 cm soil 161
depth), precipitation during growing season (Prec_GS), mean relative humidity during growing 162
season (RH_GS), mean LAI during growing season (LAI_GS) and PAR during growing season 163
(PAR_GS). In this study, the growing season is composed of all months where the mean 164
monthly air temperature was above 0 °C. The period of the time series of all these variables 165
was from 1982 to 2012. The LAI data were derived from the Global Land Surface Satellite 166
(GLASS) LAI datasets (Xiao et al., 2013) and the SOC data were developed by Shangguan et 167
al. (2014). The meteorological variables were derived from the MERRA (Modern-Era 168
Retrospective analysis for Research and Applications) datasets (Rienecker et al., 2011). 169
A complete combinatorial method was employed to select the optimal set of 170
predictors out of the ten variables. The root mean squared error (RMSE) was used to evaluate 171
the performance of each model based on different predictor combination. In our RF models, 172
five predictors, including MAT, Prec, RH, RH_GS and LAI_GS, were selected to predict SR. 173
The variables combination of MAT, Prec, RH, PAR, RH_GS, LAI_GS, PAR_GS was selected 174
for HR prediction. The best combination of predictors was further used for the RF model 175
establishment and cross-validation. It should be noticed that there was a large discrepancy in 176
the number of the observations within SRDB dataset among various vegetation types. We 177
compared the proportions of the SR and HR observations and the area proportion of various 178
vegetation types (Figure S1a, Table S1). Large divergences were observed between the 179
proportions of the SR and HR observations and the area proportion of the corresponding 180
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ecosystem types. Especially, the proportion of SR and HR observations at the evergreen 181
broadleaf forests and the shrublands were much lower comparing with the proportion of 182
corresponding ecosystem area (Figure S1). The results reflected the scarce observations of SR 183
and HR in evergreen broadleaf forest and shrubland ecosystems which are corresponding to the 184
high and low respiration rate regions, respectively (Figure S1b). Therefore, in order to reduce 185
the model uncertainty induced by observations imbalance among various ecosystem types, the 186
SR and HR observations were binned to five bins according to the ecosystem types (Table S1). 187
The RF models of SR and HR were developed and cross-validated by randomly selecting 188
observations from each vegetation type bin with the different probability. The probability of 189
selection was equal to the area proportion of the corresponding vegetation types to global 190
vegetated land area (Figure S1). As a result, 80% of the observations were selected for model 191
training, leaving 20% for cross-validation. The observations selection procedures and the RF 192
models were run 2000 times for cross-validation and prediction. In addition, as a comparison, 193
we also developed RF models by selecting observations from each vegetation type with equally 194
probability (Figure S2, S3). The established models were implemented to estimate SR and HR 195
at 0.5° × 0.5° resolution over 1982 – 2012. The global AR fluxes were calculated as the 196
difference of SR and HR. The uncertainty of the predicted global SR, HR and AR were 197
expressed in the standard deviation (SD), the median absolute deviation (MAD) and the 198
coefficient of variation (C.V., %). The variable importance and partial dependence analyses of 199
the RF models for SR and HR were conducted (Figure S4, S5, S6). However, it should be 200
cautious the instability of the variable importance ranking, especially when the predictors are 201
highly correlated (Gregorutti et al., 2017). 202
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This study includes ten process-based terrestrial ecosystem models: the Boreal 204
Ecosystem Productivity Simulator (BEPS) (Liu et al., 1997), the coupled Canadian Land 205
Surface Scheme and Canadian Terrestrial Ecosystem Model (CLASS-CTEM) (Melton & Arora, 206
2016), the Community Land Model, version 5.0 (CLM5.0) (Lawrence et al., 2019), the CSIRO 207
Atmosphere and Biosphere Land Exchange (CABLE) (Wang et al., 2010), the Integrated 208
Biosphere Simulator (IBIS) (Foley et al., 1996; Yuan et al., 2014), the Land surface Processes 209
and eXchanges (LPX-Bern) (Lienert & Joos, 2018), the Lund-Postdam-Jena General 210
Ecosystem Simulator (LPJ-GUESS) (Smith et al., 2014; Olin et al., 2015), the ORganizing 211
Carbon and Hydrology In Dynamic EcosystEms (ORCHIDEE) (Krinner et al., 2005), the 212
Vegetation Integrated Simulator for Trace Gases (VISIT) (Ito, 2019), and the Vegetation Global 213
Atmosphere Soil model (VEGAS) (Zeng et al., 2004). 214
The CLASS-CTEM, the CLM5.0, the LPX-Bern, the ORCHIDEE, the VEGAS and 215
the VISIT model were driven with the CRU JRA v2.0 atmospheric forcing dataset 216
(https://catalogue.ceda.ac.uk/uuid/7f785c0e80aa4df2b39d068ce7351bbb). The BEPS, the 217
CABLE, the LPJ-GUESS and the IBIS model were driven by CRUNCEP v7 dataset 218
(https://rda.ucar.edu/datasets/ds314.3/). Both the CRU JRA and the CRUNCEP datasets are 6-219
hourly and gridded reanalysis data which are based on the combination with the Climatic 220
Research Unit (CRU) monthly dataset. The CRU JRA version 2.0 dataset is constructed by 221
combining the CRU monthly data covering from 1901 to 2018 with the Japanese Reanalysis 222
data (JRA) 6-hourly data covering from 1958 to 2018. The CRUNCEP dataset is a 223
combination of the CRU monthly data covering the period 1901 to 2015 and the NCEP 224
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(National Centers for Environmental Prediction) reanalysis 6-hourly data covering the period 225
1948 to 2016. There is high consistence of the two datasets in terms of several major climate 226
variables (i.e., air temperature, precipitation, specific humidity, pressure and the incident 227
shortwave radiation; Figure S7, S8). All models used the Land-use Harmonization (LUH2) 228
land use data (http://gsweb1vh2.umd.edu/LUH2/LUH2_GCB_2019/states.nc). 229
230
Results 231
Global estimates of SR, HR and AR derived from the RF models 232
The RF models were cross-validated against total soil respiration (SR) and 233
heterotrophic soil respiration (HR) observations to test the model performance. SR model and 234
HR model explained 89% and 86% of the variation of observed SR and HR, respectively 235
(Figure 2a, b). Based on the RF models, we generated global distribution of SR and HR from 236
1982 to 2012. On average, total global SR and HR were 85.5 Pg C yr-1 (83.6 to 87.8 Pg C yr-1) 237
and 50.3 Pg C yr-1 (49.2 to 51.1 Pg C yr-1) during this period, respectively. The global 238
uncertainty were 27.3 (MAD) and 40.4 (SD) Pg C yr-1 for SR, and 16.9 (MAD) and 25.0 (SD) 239
Pg C yr-1 for HR. Average global autotrophic soil respiration (AR, the difference between SR 240
and HR) was 35.2 Pg C yr-1 (33.9 to 36.9 Pg C yr-1 during 1982-2012). The global average ratio 241
of AR contribution to SR (AR/SR) was 0.41 across all ecosystem types. 242
Overall, our results showed that the simulated SR, HR and AR were the highest in the 243
tropical moist forest regions and lowest in cold tundra and dry desert regions (Figure 3a, c, e). 244
The simulated ratio of AR contribution to SR pointed toward an exceptionally high contribution 245
of AR at northern hemisphere high latitude regions (Figure 3f, 7d). Generally, the C.V. of 246
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simulated SR and HR were highest in the regions with lower SR and HR predictions (i.e., cold 247
tundra and dry desert regions) (Figure 3b, d). 248
Evaluation and intercomparison of process-based ecosystem models 249
The performance of the RF model and the ten investigated terrestrial ecosystem 250
models were examined against the SR and HR observations from the SRDB database (Figure 251
4). The Pearson’s correlation was employed to evaluate the relationship between the observed 252
and simulated SR and HR values. Both of the correlation coefficient for SR and HR simulated 253
by the RF model were above 0.5 and it was larger than all the other investigated models (Figure 254
4a, b). The root mean squared error (RMSE) was used for quantifying the spatial differences 255
between the simulations and observations of SR and HR. The smaller RMSE indicate the better 256
model performance for reproducing spatial pattern of SR and HR against the observations. The 257
RMSE of SR and HR simulated by RF across the observation sites were 348 g C m-2 yr-1 and 258
240 g C m-2 yr-1, respectively. Comparing with the ten investigated ecosystem models, the 259
RMSE of both SR and HR simulated by RF were the lowest (Figure 4c, d). Overall, among the 260
ten investigated ecosystem models, the VEGAS model performed the best on SR simulation 261
(Figure 4a, c), while the VEGAS and CLM5.0 model performed the best on HR simulation 262
(Figure 4b, d). The performance of the RF models was better than all the ten investigated 263
ecosystem models. 264
Our results showed large differences in the simulations of SR and its components 265
among the investigated terrestrial ecosystem models. For SR simulation, the estimate derived 266
by the CLASS-CTEM model (91.7 Pg C yr-1) was ~ 30 Pg C yr-1 larger than the estimate of 267
61.4 Pg C yr-1, derived from the BEPS model (Figure 5a). The SR simulated by the RF model 268
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was 85.5 Pg C yr-1, which was higher than the average simulated SR of the ten models (76.9 Pg 269
C yr-1). The simulated HR ranged from 39.8 Pg C yr-1 by the ORCHIDEE model to 61.7 Pg C 270
yr-1 by the CLASS-CTEM model. The differences of the HR simulations among the models 271
were up to 1.5 times (Figure 5b). The estimate of HR by the RF model (50.3 Pg C yr-1) almost 272
matched the ensemble mean of the ten ecosystem models (50.4 Pg C yr-1). A large divergence 273
of AR estimates was observed among the ten investigated terrestrial ecosystem models. The 274
highest estimate of 42.3 Pg C yr-1 derived from the CLM5.0 model was 3.5 times of the lowest 275
estimate of 12.0 Pg C yr-1 by the BEPS model (Figure 5c). The ensemble mean of the ecosystem 276
models (26.5 Pg C yr-1) was 8.7 Pg C yr-1 lower than the estimate by RF (35.2 Pg C yr-1). The 277
estimates of global average AR/SR ratio varied from 18% by the LPX-Bern model to 48% by 278
the LPJ-GUESS model (Figure 5d). 279
Ecosystem models reproduced overall similar latitudinal variations of SR and HR 280
(Figure 6). The largest quantitative divergences among individual models were found at the 281
tropical and subtropical regions (Figure 6a, b). The simulated RF values showed similar 282
latitudinal pattern of SR and HR with that derived from ecosystem models, except at the 283
northern high latitudes where the RF simulations were higher than those of all process-based 284
models between 70 and 80° north. AR showed an overall similar latitudinal pattern as SR and 285
HR with increasing trend towards the equator (Figure 6c). While the RF models suggest an 286
increasing AR contribution to SR towards higher latitudes, most ecosystem models suggest a 287
reverse trend towards highest contribution of AR at the mid-latitudes and/or the tropics (Figure 288
6d). 289
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Discussion 291
Simulation of global SR and its components by the RF models 292
In this study, we developed SR and HR models by the Random Forest (RF) method 293
and estimated the global distribution of SR and its components (HR and AR). The model 294
validation against the observations suggested that the RF models can reproduce very well the 295
global patterns of SR and its components (Figure 2). Our estimate of the average global SR was 296
85.5 Pg C yr-1, which was close to a recent estimate of 87.9 Pg C yr-1 by Warner et al. (2019) 297
generated by the RF mothod. However, higher estimates of SR were also reported. Hashimoto 298
et al. (2015) developed a climate-driven empirical model and yielded the mean global SR of 91 299
Pg C yr-1 during 1965-2012, and Zhao et al. (2017) reported a mean annual global SR of 93 Pg 300
C yr-1 using an artificial neural network (ANN) model. Our estimate of global HR (50.3 Pg C 301
yr-1) was also comparable to other estimations. Hashimoto et al. (2015) employed the empiric 302
relationship from a meta-analysis between HR and SR and estimated the mean global HR of 51 303
Pg C yr-1. In a recent study, Warner et al. (2019) provided a global HR of 49.7 Pg C yr-1 based 304
on the empiric ratio between HR and SR. 305
Other lines of evidences also implied that our estimates were reliable. Our RF 306
simulations suggest a HR/SR ratio 0.59. Based on the global soil respiration observations 307
database, Bond-Lamberty et al. (2018) reported that the global HR/SR ranging from 0.54 to 308
0.63 during 1990–2014. Our estimate of global HR/SR ratio therefore is consistent with this 309
result. The highest AR/SR ratios in our RF simulations were observed in boreal tundra and 310
coniferous forest ecosystems in high latitude regions (Figure 3f, 6d). A recent global analysis 311
of carbon allocation showed the larger photosynthate allocate ratio to root in boreal forests than 312
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subtropical and tropical forests (Xia et al., 2019). As the CO2 emission from the autotrophic 313
metabolism of root biomass contributes to AR, and therefore, the larger carbon allocation ratio 314
to root in boreal forests highly increase the ratio of AR to SR. 315
However, the RF outputs in high latitude regions has to be seen with some caution. 316
The C.V. maps of simulated SR and HR showed the highest variation in the regions with lower 317
SR and HR predictions (i.e., cold tundra and dry desert regions) (Figure 3b, d). One of the 318
reasons is that the relatively high C.V. may be caused by the low estimates of SR and HR, which 319
does not necessarily mean a higher prediction error. In other cases, the high C.V. of simulated 320
SR and HR may be due to the divergent prediction distributions across the RF model (Warner 321
et al., 2019) (Figure S9). Moreover, the northern high latitude regions were comparatively 322
poorly represented in our model training dataset, and the observation records within 60°N-90°N 323
regions only account for ~ 8% of the total records of SRDB dataset (Figure 1). Previous study 324
has highlighted that the quantity of the training data had strong influence on the performance 325
of machine learning models (Chen et at., 2014), and therefore sparse distribution of 326
observations in the high latitudes may be the major cause for low reliability of the simulated 327
AR contribution to SR. Hence, more intensive field observations regarding SR, HR and AR 328
should be conducted in the high latitude regions in order to enhance the estimates of SR and its 329
components. In addition, it should be cautious that ecological data are almost always spatial 330
autocorrelated, ignoring the autocorrelation might lead to an overoptimistic performance of 331
model validation and hide model overfitting (Dormann et al., 2007; Roberts et al., 2017; Ploton 332
et al., 2020). Recently, Ploton et al. (2020) founded that ignoring the spatial autocorrelation of 333
data leaded strong disparities in modeling aboveground carbon stocks of tropical forests by 334
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machine learning approaches. 335
Due to the defect of SR and HR measurement methods, few studies directly measured 336
CO2 efflux from decomposing dead wood debris. That resulted in an inevitable bias on the 337
observations of SR and HR in the SRDB dataset. Given that, we assumed that the RF models 338
which based on the SRDB dataset might lead to the underestimation of SR and HR. However, 339
the model bias highly depends on the ratio of decomposition of dead woody pools to soil 340
respiration. Rowland et al. (2013) estimated that the respiration from the coarse wood debris 341
(≥10 cm diameter) is approximately 5% of annual total ecosystem respiration in tropical 342
rainforest. Considering the grassland and the other forest biomes where the productivity and 343
wood density is less than the tropical rainforest, we infer that the contribution of dead wood 344
debris respiration to the total ecosystem respiration is less than 5% at global scale. The further 345
evaluation should be conducted by integrating more observations of decomposition from dead 346
woody pools. 347
Benchmark analysis of process-based ecosystem models against RF estimates 348
Our estimates of soil respiration and its components by RF method provides an 349
opportunity to conduct the benchmark analysis of ecosystem models. All investigated 350
ecosystem models in this study estimated the global SR varying from 61.4 to 91.7 Pg C yr-1 351
(Figure 5), however, their estimates of global terrestrial net C sink are in the reasonable ranges 352
3.8 Pg C yr-1 with a relative low variation (standard deviation of 0.8 Pg C yr-1) during 2008-353
2017 (Le Quéré et al., 2018). In order to match the estimates of terrestrial net C sink within 354
reasonable ranges, the models usually adjust estimates of vegetation gross primary production 355
(GPP) with SR estimates. Therefore, the uncertainties of SR simulations can lead to the bias of 356
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other variables in C cycling (e.g. GPP and NPP). Moreover, there are large differences in the 357
components estimates (i.e., HR and AR) (Figure 5b, c). Especially, the variation of simulated 358
AR from the ten investigated ecosystem models was higher than that of SR and HR (Figure 359
S10). It is a big challenge of current terrestrial ecosystem models that model validation and 360
benchmark for the internal processes are absent, which strongly limits our abilities to accurately 361
quantify the magnitude of C cycle variabilities and to predict future scenarios. In addition, the 362
inadequate performance of internal processes also highly impacts the simulated responses of 363
ecosystem carbon cycle to future climate change. 364
Based on this study and other estimates using machine learning methods and meta-365
analysis independently, the critical variables of global C cycling can be estimated for further 366
model benchmarking analysis (Table 1). The global GPP was reported as ~ 120 Pg C yr-1 (111 367
to 126 Pg C yr-1) by FLUXCOM using machine learning methods (Jung et al., 2017), and the 368
NPP was estimated as 56 ± 14.3 (mean ± SD) Pg C yr-1 by a global meta-analysis (Ito, 2011). 369
Based on the global GPP and NPP estimates, the total ecosystem autotropic respiration (TAR) 370
was calculated as 64 Pg C yr-1. Our results showed the AR (below ground autotrophic 371
respiration) was 35.2 Pg C yr-1. Given that, the aboveground autotrophic respiration (AAR) was 372
28.8 Pg C yr-1. Meanwhile, this study estimated SR as 85.5 Pg C yr-1, and HR as 50.3 Pg C yr-373
1, thus the net ecosystem production (NEP, the residual of NPP and HR), was 5.5 Pg C yr-1. If 374
we take the C emission due to global fire disturbance in account, which was estimated of 2.2 375
Pg C yr-1 during 1997 – 2016 (van der Werf et al., 2017), the global C sink was 3.3 Pg C yr-1, 376
this figure is very close to the estimate of 3.8 ± 0.8 Pg C yr-1 by Global Carbon Project during 377
2008-2017 (Le Quéré et al., 2018). 378
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Intercomparison of process-based ecosystem models 379
Basically, the magnitude of simulated SR and HR was determined by environmental 380
variables (e.g. soil temperature and moisture), respiration substrates and model parameters (e.g., 381
soil organic carbon transit time, temperate sensitivity). Our results showed no significant 382
relationship between simulated soil respiration and SOC, litterfall and root biomass C stocks 383
among the investigated ecosystem models (Figure 7). The results suggested the 384
parameterization exerted more important influence on the soil respiration simulation than SOC, 385
litterfall and root biomass C stocks, although there were extensive differences of simulated C 386
pools among investigated models (Figure 8). Other lines of evidences also support this 387
conclusion that terrestrial ecosystem models have shown substantial differences of soil C transit 388
time (Wang et al., 2019). For example, there is a 4-fold difference in the simulated C transit 389
time among the ESMs from the CMIP5 (Todd-Brown et al., 2013). In addition, the soil and 390
litter C pools is a result of C input and decomposition at long time scale and a proportion of 391
soil organic carbon was chemically and physically protected from decomposition by microbes, 392
which contribute to the recalcitrant carbon pools (Bradford et al., 2016). We further examined 393
the variation of simulated gross primary production (GPP) and net primary production (NPP) 394
and their relationship with the simulated soil respiration and its components among ecosystem 395
models (Figure 9). Significant positive relationship was observed between simulated NPP and 396
HR (Figure 9d). It can attribute to the changes of litterfall production induced by NPP which 397
directly impact the HR. However, there were no significant correlation between AR and GPP 398
(Figure 9e). AR only represents the root respiration, and therefore the ecosystem GPP hardly 399
explains the differences of AR among various models. Our results highlight that detailed 400
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analysis should be conducted to investigate the relationship between AR and the ratio of the 401
photosynthates allocating to belowground components. 402
Moreover, previous studies also highlighted the importance of the Q10 (temperature 403
sensitivity of soil respiration) value in current terrestrial ecosystem models to the divergent of 404
HR simulations (Holland et al., 2000; Todd-Brown et al., 2014). Furthermore, some ESMs 405
employ constant Q10 values whereas highly spatial variability of Q10 has been widely observed 406
in field studies (Anav et al., 2013). Those simplified representations can contribute to the poor 407
model performance on soil respiration simulations (Figure 4, 6). In addition, the global SR, HR, 408
AR and AR/SR of different ecosystem types simulated by the ecosystem models were estimated. 409
The highest C.V. of the simulated SR, HR, AR and AR/SR by the ecosystem models were 410
observed in open shrublands/tundra ecosystems which mainly distributed in the northern high 411
latitude regions (Table S2, S3, S4 and S5). That might attribute to the large divergences in 412
simulating permafrost soil carbon and turnover time among the ecosystem models (Todd-413
Brown et al., 2013). This also suggested that more field observation of soil respiration should 414
be conducted in those regions to constrain the ecosystem models. 415
416
Conclusion 417
The accurate estimation of global soil respiration and its components is crucial to the 418
projection of terrestrial C budgets. In this study, we developed soil respiration models by the 419
RF method based on the global observed soil respiration database. The RF model performed 420
well on simulating the global distribution of soil respiration and its components. The estimates 421
of global average total soil respiration, heterotrophic soil respiration and autotrophic soil 422
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respiration were 85.5, 50.3 and 35.2 Pg C yr-1 during 1982-2012, respectively. Comparing with 423
the observation data, the RF models showed better performance than all the investigated 424
ecosystem models. Moreover, inter-comparison of the ten terrestrial ecosystem models revealed 425
large divergence of model performance on soil respiration simulation. All the models could 426
reproduce the spatial patterns of soil respiration, but substantial differences in magnitude of 427
simulations were shown. Our study provided an extensive and normalized global distribution 428
of soil respiration and its components, which can be used as a benchmark for advancing 429
ecosystem models and their parameterization and validation. 430
431
Acknowledgments 432
This study was supported by the National Key Basic Research Program of China 433
(2018YFA0606104), National Science Fund for Distinguished Young Scholars (41925001) and 434
Fundamental Research Funds for the Central Universities (19lgjc02, 18lgpy09). 435
436
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Figure Captions 599
Figure 1 Distribution of the total soil respiration (SR) and heterotrophic soil respiration (HR) 600
observations. Background colors show the vegetation type derived from the Global Land Cover 601
2000 (GLC-2000; Giri et al. (2005)). 602
Figure 2 Observed and predicted total soil respiration (SR) (a) and heterotrophic soil respiration 603
(HR) (b). The dash line indicates 1:1 line and the solid line is the fitted linear regression to the 604
data. 605
Figure 3 Global distribution of estimated benchmark values for total soil respiration (SR) and 606
the corresponding coefficient of variation (C.V.) (a, b), heterotrophic soil respiration (HR) and 607
its C.V. (c, d), autotrophic soil respiration (AR) (e) and the ratio of AR to SR (f). 608
Figure 4 The RMSE and correlation coefficient of simulated SR (a, c) and HR (b, d) against 609
the observations. The RMSE shows the spatial differences between the simulated and 610
observed SR and HR, a lower RMSE value indicates better performance of the model (a, b). 611
The unit of RMSE is kg C m-2 yr-1. The correlation coefficient indicates the correlation 612
relationship between the estimates by models and the observations (c, d). A correlation 613
coefficient value of a model close to 1 represents good model performance. 614
Figure 5 Simulated average global annual total soil respiration (SR) (a), heterotrophic soil 615
respiration (HR) (b), autotrophic soil respiration (AR) (c) and the average ratio of AR to SR (d) 616
by the benchmark RF model and process-driven ecosystem models during 1982 - 2012. The 617
dash line indicates the ensemble mean of the ten ecosystem models. 618
Figure 6 Latitudinal patterns of total soil respiration (SR) (a), heterotrophic soil respiration 619
(HR) (b), autotrophic soil respiration (AR) (c) and the ratio of AR to SR (d) by the benchmark 620
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RF model and the compared process-driven ecosystem models. The grey shaded area indicates 621
the mean ± MAD of predicted SR and HR by RF. 622
Figure 7 The relationship between the simulated soil respiration and carbon pools derived from 623
the process-based ecosystem models. SR, HR and AR indicate the soil respiration, 624
heterotrophic soil respiration, and autotrophic soil respiration, respectively. Csoil, Clitter and 625
Croot indicate soil organic carbon stock, litterfall carbon stock and root biomass carbon stock, 626
respectively. The black dots in the plots showed the average outputs from each model during 627
1982-2012. The shade areas indicate the 95% confidential intervals. The dash lines indicate no 628
significant relationship. 629
Figure 8 Estimated global soil carbon stock (a), litterfall carbon stock (b), root biomass carbon 630
stock (c), gross primary production (GPP, d) and net primary production (NPP, e) by the diverse 631
ecosystem models. 632
Figure 9 The relationship between the simulated soil respiration and vegetation production 633
derived from the process-based ecosystem models. SR, HR and AR indicate the soil respiration, 634
heterotrophic soil respiration, and autotrophic soil respiration, respectively. GPP and NPP 635
indicate gross primary production and net primary production, respectively. The black dots in 636
the plots showed the average outputs from each model during 1982-2012. The shade areas 637
indicate the 95% confidential intervals. The dash lines indicate no significant relationship. 638
Table 1 Representation of C flux in global carbon cycle. 639
640
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641
Figure 1 Distribution of the total soil respiration (SR) and heterotrophic soil respiration (HR) 642
observations. Background colors show the vegetation type derived from the Global Land Cover 643
2000 (GLC-2000; Giri et al. (2005)). 644
645
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1000
2000
3000
4000
500
1000
1500
-1 )
646
Figure 2 Observed and predicted total soil respiration (SR) (a) and heterotrophic soil respiration 647
(HR) (b). The dash line indicates 1:1 line and the solid line is the fitted linear regression to the 648
data. 649
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650
Figure 3 Global distribution of simulated average total soil respiration (SR) and the 651
corresponding coefficient of variation (C.V.) (a, b), heterotrophic soil respiration (HR) and its 652
C.V. (c, d), autotrophic soil respiration (AR) (e) and the ratio of AR to SR (f) during 1982 - 653
2012. 654
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655
Figure 4 The RMSE and correlation coefficient of simulated SR (a, c) and HR (b, d) against 656
the observations. The RMSE shows the spatial differences between the simulated and 657
observed SR and HR, a lower RMSE value indicates better performance of the model (a, b). 658
The unit of RMSE is kg C m-2 yr-1. The correlation coefficient indicates the correlation 659
relationship between the estimates by models and the observations (c, d). A correlation 660
coefficient value of a model close to 1 represents good model performance. 661
662
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663
Figure 5 Simulated global annual total soil respiration (SR) (a), heterotrophic soil respiration 664
(HR) (b), autotrophic soil respiration (AR) (c) and the average ratio of AR to SR (d) by the 665
benchmark RF model and process-driven ecosystem models during 1982 - 2012. The dash lines 666
indicate the ensemble mean of the ten ecosystem models. 667
668
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-60
-30
0
30
60
90
-90
-60
-30
0
30
60
90
-60
-30
0
30
60
90
(a)
-1 )
-1 )
-1 )
669
Figure 6 Latitudinal patterns of total soil respiration (SR) (a), heterotrophic soil respiration 670
(HR) (b), autotrophic soil respiration (AR) (c) and the ratio of AR to SR (d) by the benchmark 671
RF model and the compared process-driven ecosystem models. The grey shaded area indicates 672
the mean ± MAD of predicted SR and HR by RF. 673
674
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675
Figure 7 The relationship between the simulated soil respiration and carbon pools derived from 676
the process-based ecosystem models. SR, HR and AR indicate the soil respiration, 677
heterotrophic soil respiration, and autotrophic soil respiration, respectively. Csoil, Clitter and 678
Croot indicate soil organic carbon stock, litterfall carbon stock and root biomass carbon stock, 679
respectively. The black dots in the plots showed the average outputs from each model during 680
1982-2012. The shade areas indicate the 95% confidential intervals. The dash lines indicate no 681
significant relationship. 682
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684
Figure 8 Estimated global soil carbon stock (a), litterfall carbon stock (b), root biomass carbon 685
stock (c), gross primary production (GPP, d) and net primary production (NPP, e) by the diverse 686
ecosystem models. 687
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689
Figure 9 The relationship between the simulated soil respiration and vegetation production 690
derived from the process-based ecosystem models. SR, HR and AR indicate the soil respiration, 691
heterotrophic soil respiration, and autotrophic soil respiration, respectively. GPP and NPP 692
indicate gross primary production and net primary production, respectively. The black dots in 693
the plots showed the average outputs from each model during 1982-2012. The shade areas 694
indicate the 95% confidential intervals. The dash lines indicate no significant relationship. 695
696
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Table 1 Representation of C flux in global carbon cycle. 697
C Flux (Pg C yr-1) Reference C Flux (Pg C yr-1) Reference
GPP 120 (111-126) Jung et al.
(2017) TAR=GPP-NPP 64
HR 50.3 This study NEP=NPP-HR 5.5
AR 35.2 This study NBP=NEP-Disturb 3.3
Disturb 2.2 van der Werf
et al. (2017) NBP 3.8 ± 0.8
Le Quéré et
Note: GPP: gross primary productivity; NPP: net primary productivity; HR: heterotrophic soil 698
respiration; AR: autotrophic soil respiration; TAR: total ecosystem autotrophic respiration; 699
AAR: aboveground autotrophic respiration; NEP: net ecosystem productivity; NBP: net 700
biosphere productivity; Disturb: C emission due to global fire disturbance. 701
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