Supplementary Information for

Detection and attribution of nitrogen runoff trend for

China’s croplands

Xikang Hou 1,+, Xiaoying Zhan 1,+, Feng Zhou 1,*, Xiaoyuan Yan 2, Baojing Gu 3, Stefan Reis 4,6, Yali Wu 1, Hongbin Liu 5, Shilong Piao 1, Yanhong Tang 1

1. Sino-France Institute of Earth Systems Science, Laboratory for Earth Surface Processes,

College of Urban and Environmental Sciences, Peking University, Beijing, 100871, P.R.

China

2. State Key Laboratory of Soil and Sustainable Agriculture, Institute of Soil Science, Chinese

Academy of Sciences, Nanjing, 210008, P.R. China

3. Department of Land Management, Zhejiang University, Hangzhou 310058, P.R. China 4. Natural Environment Research Council, Centre for Ecology & Hydrology, Bush Estate,

Penicuik EH26 0QB, United Kingdom

5. Institute of Agricultural Resources and Regional Planning, Chinese Academy of Agricultural

Sciences, Beijing 100081, P.R. China

6. University of Exeter Medical School, Knowledge Spa, Truro, TR1 3HD, United Kingdom

+ X.K.H and X.Y.Z contributed equally to this work.* Corresponding author. Phone: +86 10 62756511. Email: zhouf@pku.edu.cn (F. Z.)

Contents of this file

Texts S1 to S3

Tables S1 to S4

Figures S1 to S9

Supporting references

1

Text S1. Model inputs

The calibrated data-driven upscaling model was applied to simulate the spatial patterns of N runoff over Chinese croplands for the period from 1990 to 2012 at a 1 km scale. The forcing dataset was prepared as follows: (i) County-level data of the annual amounts of synthetic fertilizers, manure, and crop residues applied from 1990 to 2012 were obtained for 2884 political units and disaggregated into 1 km gridded maps based on crop type distribution, where sowing areas of wheat, maize, rice, soybean, and the other crops were obtained from ~334 municipal statistical registers. N fertilizer application rate was calculated as the ratio of the annual amounts of N fertilizer application to sowing areas. We further divided the county-scale N fertilizer application rates (Nratecounty,yr) into those for different fertilizer and crop types. The provincial datasets of N fertilizer application percentages by fertilizers and crops(pro,fert,crop,yr) can be found in the Cost and Income of Chinese Farm Produce from 1990 to 2012 provided by the National Development and Reform Commission of China (http://tongji.cnki.net/). Therefore, the N fertilizer application rate for fertilizers and crops in the year yr can be calculated as Nratecounty,fert,crop,yr = Nratecounty,yr

pro,fert,crop,yr; (ii) Municipal-scale irrigation water amounts used for croplands were acquired for the period 1990-2012 in China from Water Resource Bulletin published by local governments. The irrigation rate was then calculated as the municipal-scale irrigation water used for croplands divided by actual irrigation area (ha) and eventually resampled it into 1-km grid cells; (iii) a set of 1 km crop type (upland and paddy field) maps at 5-year intervals for the period 1990 to 2010 extracted from Liu et al. (2014), each of which is assumed to represent the nearest target years for the period 1990-2012. (iv) Annual soil organic matter content (SOM, 0-30 cm) distributions from 1990-2012 were estimated by the Agro-C model (Yu et al., 2012), and then downscaled into 1 km grid cells. Other soil attributes (TN, pH, clay) are sampled from the 1 km Harmonized World Soil Database (HWSD) v1.2 (www.iiasa.ac.at), respectively, which were considered representative of the target years 1990-2012. (iv) Annual mean air temperature and annual precipitation from 1990-2012 were obtained from the 0.1-degree China Meteorological Forcing Dataset (CMFD) v0106 (http://westdc.westgis.ac.cn/), and then downscaled based on 1 km WorldClim v1.4 (Hijmans et al., 2005). The spatial patterns of these forcing dataset can be found Figure S1.

2

Text S2. BRRT methodology

1.1 General Principles

We begin with an introduction of the general principles of BRRT v2. The BRRT v2 is an updated version of Bayesian TREED model developed by Chipman et al. (2002). Taking N2O EF for example, combining the conditional distribution of EF with prior p(T) for model structure, the posterior probability p(T|X,EF) is calculated as

(S1)

up to a norming constant (Gelman et al, 2003) , where EF and X are emission factor and environmental factors, respectively; X={xk}; , i.e., N and xk in Eq. (1). T represents a binary tree. Its terminal nodes and splitting rules correspond to the sub-functions, i.e., Eq. (1) and the sub-domains k lx , respectively. Thus, specification of p(T|X,Y) consists of two basic components.

First is the tree prior , which could be specified independently according to Bayes’ theorem (Gelman et al, 2003). p(T) is determined by specifying two functions for an binary tree T: the probability p(l,T) that terminal node l is to be split and the probability p(|l,T) of assigning splitting rule ={xkSk} to node l if it is split, which are defined as

, (S2a)

where

, (S2b)

3

, (S2c)

and is environmental factors applied for sub-domain division; (<1) and (>0) are hyperparameters; d is the depth of node l; K

and Ml are the number of and observations in terminal node l, respectively.

Second is the marginal likelihood p(EF|X,T), which can be obtained as integral form of regression coefficients l={l,l}:

, (S3a)

Where

, (S3b)

2 ,l l l lN a , (S3c)

2 2 l , (S3d)

0 1 , 1,...,...

nK

kl KK K K

Cp x T k nC C C

, (S3e)

and p(EFlm|xklm,l), p(l|T), and p(xkl|T) are probabilities of EF, regression coefficients, and selection of n of regression variables xk

in terminal l, respectively, in which n is the number of selected xk. EFlm and xklm the EF and regression variable k of the mth observation in the lth terminal node, respectively, where klmx X , m=1,2,…, Ml. All

4

of lEF are assumed to be independent and identically distributed, in

which Tl lx corresponds to Eq. (1). l represent a set of regression

coefficients l and the variance l of EF in terminal l. l is Normal-

distributed, defined as l ={ , bkl, cl} . l is inverse Gaussian-

distributed with mean and shape parameter, in which and are the other two hyperparameters of the BRRT v2. The choice of hyperparameters (<1), (>0), a (=1 or 3), (=3), and (=0.404 or 0.1173) is determined with minimum cost function (Freeman et

al., 2009). The ranges of are determined based on the marginal

responses of EF to xk.

Consequently, progressive multi-restart stochastic search (hereafter PMRS) algorithm (see Sub-section 1.3) is designed for determining the posterior probability of T with minimum cost function. Based on the above prior p(T) and p(l|T), Metropolis-Hastings algorithm could be used to search for a Markov chain sequence of trees (Chib et al., 1995). Starting with an initial tree T0, it simulates iteratively the transitions from Ti to Ti+1 through two steps: (1) generate a candidate value T* by five-mode stochastic search (see Sub-section

S1.2) with probability ; (2) set Ti+1 = T* with acceptance probability:

. (S4)

Else, set Ti+1 = Ti and return to step 1. When i+1>I where I is maximum number of iterations, then stop. Moreover, the transition from Ti to Ti+1 is processed by stochastically choosing among five modes (S1.2): GROW, PRUNE, CHANGE, SWAP, and GREEDY.

Finally, from Markov chain sequence, the optimal tree (Tfinal) is selected based on the criterion of minimum cost function. In our

5

model, cost function that is minimized is Bayesian Information Criterion (BIC, Schwarz, 1978; Jung et al., 2009):

(S5)

where MSE is the mean squared error based on 5-fold cross-

validations; n the number of samples (= ); and K+1 the number of coefficients and intercepts in regression equation l. Certainly, other commonly used tree criteria would be also useful,

such as maximization of marginal likelihood . The associated piecewise functions for all terminal nodes can be expressed as:

, where l lX , l, (6)

and l represents the sub-domain of Xl. It should be noted that regression coefficients l are not determined by multiple linear regression after stochastic search (e.g., Jung et al. (2009)), but PMRS process directly. In BRRT v2, the cost function that is minimized is BIC. Other commonly used cost function would be also acceptable, such as maximization of p(EF|X,T).

1.2 Five modes for stochastic search

The details of PMRS algorithm and the associated five modes are introduced in the following two sub-sections. In contrast to conventional Bayesian tree-based models (Chipman et al., 2002; Liu et al., 2008; Jung et al., 2009), a PMRS algorithm is designed in BRRT v2. This algorithm accelerates traversing the entire optima of trees to identify the optimal tree via a minimum number of model executions.

6

(1) GROW. A terminal node l is randomly selected based on prior

and then split into two new nodes by randomly assigning it a

splitting rule according to p(|l,T). The corresponding

transition kernel q and are deduced as follows:

(S7a)

(S7b)

(S7c)

where or is the probability of choosing GROW

mode; a1 is the number of terminal nodes that can be split; is the

number of internal nodes in with terminal children nodes; is the terminal node that is split for GROW mode and the internal nodes before CHANGE and SWAP; represents the two children nodes of for GROW mode.

(2) PRUNE. A parent of two terminal nodes is randomly selected and turned into a terminal node by collapsing the nodes below it.

The corresponding transition kernel q and are calculated by:

7

(S8a)

(S8b)

(S8c)

where represents the internal node to be pruned of its two children nodes 1.

(3) CHANGE. An internal node is randomly selected and reassigned a new splitting rule according to p(|l,T);

(S9a)

(S9b)

where represents the internal nodes after CHANGE and SWAP; is the number of both the chosen node and all nodes below it.

(4) SWAP. A parent-child pair that are both internal nodes is randomly selected, and the splitting rules are swapped, unless the other child has the same rule, in which case the splitting rule of the parent is swapped with that of both children. Chipman et al. (2002) pointed that this search converged toward regions of higher

posterior probability or marginal likelihood . The

corresponding transition kernel q and are identical to that of CHANGE mode.

8

(5) GREEDY. Previous studies, such as Liu et al. (2008) and Jung et al. (2009), grow deterministic tree by GREEDY algorithm as starting point (e.g., TRIAL), and launch stochastic search for subsequent Markov chain sequence of trees. However, our strategy is to insert GREEDY directly into five-mode stochastic research as one choice of modes. The methodology of GREEDY is same as CART of Breiman et al. (1984), but only one terminal nodes is split or sub-tree of an intermediate node is pruned for each transition from Ti to Ti+1. When implementing GREEDY mode, a terminal node is randomly selected

based on prior and only the terminal node in which the corresponding residual sums of squares (RSS) is minimum among all terminal nodes in T* has chance to be split into two children nodes.

If the fact that RSS within terminal node is larger than that of its two child nodes, that is

, (S10a)

where

, (S10b)

, (S10c)

is satisfied, we set Ti+1 = T*. Where l represents two child nodes in

T* of terminal node l. Else, an intermediate node t (as parent of any sub-tree Tt) is randomly selected and pruned upward into a terminal node when the complexity cost reaches a minimum, where the measure of complexity cost of pruned tree can be found in Breiman

9

et al. (1984). We then also set Ti+1 = T*. Otherwise, and the search returns to generate another candidate value T* with

probability again. The corresponding transition kernel q and

are same as that of GROW or PRUNE modes.

1.3 PMRS algorithm

The basic strategy of the progressive multi-restart stochastic search is to synchronously run a number (j=1,…,Jk) of restart scenarios of Markov chain sequence Tj

0…Tji and progressively eliminate

underperforming trees before executing subsequent running stages, until the optimal tree is identified in final running stages with minimum cost function.

Specifically, Jk denotes the total number of restart scenarios in stage k, and I denotes the user-specified number of iterations in the stochastic search. For restart stage 1, each restart scenario j (where

j Jk, k=1) begins with a single node initial tree T0 and ends in a multi-node tree with a structure obtained through the stochastic search process, where the Metropolis-Hastings algorithm is used to simulate a Markov chain sequence of trees by randomly choosing among the five stochastic operations. Specifically, if the root node is chosen, it is split where probability p(GROW) is 1; if an internal node is chosen, it is randomly reassigned a splitting rule, its splitting rule is swapped, or it is deterministically split or pruned, where p(CHANGE), p(SWAP), or p(GREEDY) is 1/3; if a terminal node is selected, it is randomly split, or pruned, or deterministically split or pruned, where p(GROW), p(PRUNE), or p(GREEDY) is 1/3.

Subsequently, a candidate tree is generated with the acceptance

probability . If , can be accepted as the next value

10

; otherwise, the current value of is retained, such that

.

Restart stage 1 is considered complete when all the J1 initial trees have been run to generate J1 different resultant trees. Upon completion of stage 1, the BIC of all the J1 trees are ranked from

highest to lowest, and the first trees with higher

are used as the initial trees for restart stage 2. The

process continues until the optimal tree structure is obtained in

restart stage K, where .

1.4 Solution procedure

To facilitate the real-world application of the BRRT v2, the source code was written in the VC++ language and comprises the following five steps (ask authors for executable file BRRT v2.exe if interested):

Step #1: Sensitivity analysis of hyperparameters. Explore a range of hyperparameters (<1), (>0), a (=1 or 3), and (=0.404 or 0.1173) and determine their optimal values when BIC is minimum;

Step #2: Setup for stochastic search. Set the initial number of restart J1 and iterations I per comparison stage;

Step #3: Model implementation. Calibrate BRRT v2.exe by X-EF dataset to generate Markov chain sequence and calculate the corresponding BICs;

Step #4: Selection of the Tfinal. Select optimal Tfinal with minimum BIC;

Step #5: Output. Export a set of piecewise functions and the associated sub-domains of Xl.

1.5 Glossary table for the BRRT v2

X, Xl environmental factors matrix

s index of comparison stage

11

EF,EFl emission factor vector l {l, l}

xklm factor k of the mth sample in the lth terminal node

l regression coefficients, defined

as{ , bkl, cl}

EFlm EF of the mth sample in the lth terminal node

l variance of EFl

T binary tree regression coefficients of N

l Index of sub-function or terminal node

initial level of EF

k index of environmental factor

p(EF|X,T) marginal likelihood

m index of sample p(EFlm|xklm,l)

probability of EF

Ml samples in terminal node l

p(|l,T) probability of assigning splitting rule to node l

d depth of node l p(xkl|T) probability of selection of n of regression variables xk in terminal l

1st hyperparameter of tree

transition probability

2nd hyperparameter of tree

BIC Bayesian Information Criterion

a 3rd hyperparameter of tree

MSE mean squared error

4th hyperparameter of tree

l the sub-domain of Xl

5th hyperparameter of tree

RSS residual sums of squares

N nitrogen application rate p(T) tree prior

bkl regression coefficients of p(l|T) parameter prior

12

xk

cl

intercept forp(l,T) probability that

terminal node l is to be split

acceptance probability Tfinal optimal tree

i index of iteration l error

j index of restart

Text S3. Uncertainty estimation

To assist the application of this model in the future, we discuss here four potentially significant sources of uncertainty: N application rates, environmental factors, agricultural management practices, and parameter estimates.

The sum of county-level data (i.e., synthetic fertilizer, manure, and crop residues) from 2,884 political units is slightly different to national level estimates obtained from FAO. Coefficients of variations (CVs) for synthetic fertilizers (including compound fertilizer) and manure were calculated as 4% and 1.3% by Zhou et al. (2014), respectively. N application rates vary within county by fertilizer types, crop types, fractions of livestock excretion return to cropland, and farmers’ customs. However, our ability to account for local variations in fertilizer consumption is limited by the use of county-level average values for each fertilizer type. Thus, the CVs of N application rates have been generally assumed as equally 5%. The uncertainties in relation to environmental factors, including soil properties, land uses for each crop, water input and mean daily air temperature, arise mainly from temporal variations (i.e., soil clay, total nitrogen, pH and land use) and spatial downscaling (i.e. precipitation, temperature, irrigation rate), respectively. Owing to the fact that no independent data for estimating these uncertainties exist, their CVs are also assumed as equaling 5%. Uncertainty in parameters calibrated by BRRT v2 is determined as standard error through linear regression.

Finally, a Monte Carlo ensemble simulation was performed to estimate the uncertainty range of the RTN in the calibrated model. This model was run 10,000 times by randomly varying all of the input data and parameters given by the above mentioned CVs, where uniform and normal distributions were applied for input data

13

and parameters, respectively. The code for uncertainty estimation was set up as illustrated below. Overall of N runoff in 1990-2012 was estimated using the Monte Carlo method to range from 29-42% for upland grain crops and 14-22% for rice paddy fields.

For r=1:10000

mask=all(~isnan(var),3);

for p=1:4300

for q=1:5000

if mask(p,q)==1

f_no=NaN;

for c=1:15

if var(p,q,1)>level(c,1) && var(p,q,1)<=level(c,2) && var(p,q,2)>level(c,3) &&

var(p,q,2)<=level(c,4) && var(p,q,3)>level(c,5) && var(p,q,3)<=level(c,6) &&

var(p,q,4)>level(c,7) && var(p,q,4)<=level(c,8) && var(p,q,5)>level(c,9) &&

var(p,q,5)<=level(c,10) && var(p,q,6)>level(c,11) && var(p,q,6)<=level(c,12) &&

var(p,q,7)>level(c,13) && var(p,q,7)<=level(c,14) && var(p,q,8)>level(c,15) &&

var(p,q,8)<=level(c,16)

f_no=c;

continue;

end

end

if ~isnan(f_no)

R(p,q)=0;

R0(p,q)=0;

for t=2:21

R(p,q)=R(p,q)+(var(p,q,t)+varSD(p,q,t)*randnSD(1,r))*(coef(f_no,t)+SD(f_no,t)*randnSD(1,r));

end

R(p,q)=R(p,q)+coef(f_no,1)+SD(f_no,1)*randnSD(1,r);

for t=3:8

R0(p,q)=R0(p,q)+var(p,q,t)*(coef(f_no,t)+SD(f_no,t)*randnSD(1,r));

end

R0(p,q)=R0(p,q)+coef(f_no,1)+SD(f_no,1)*randnSD(1,r);

RRN(p,q)=R(p,q)-R0(p,q);

end

end

end

14

end

15

Table S1. Correction coefficients (CEs) for different fertilizer and crop types. Fertilizer type CEi(RR) Crop type CEl(RR) CEl(R0)

Urea 1 Wheat 1 1

Compound fertilizers 0.84 Maize 0.52 0.69

Ammonium bicarbonate 0.58 Soybean 0.85 0.83

manure / crop residues 0.32 Vegetables & fruits 1.01 2.87

Cotton 1.04 1.81

Tobacoo 0.08 1.04

The other crops 1.26 1.67

Table S2. Environmental factors for the dataset collected from field experimentsType Name of variable Variable type UnitFertilizer N application rate (Nrate) a Continuous kg N ha1

Crop Crop type b Discrete －Hydroclimatic parameters

Mean air temperature (Temp) c

Water input (P+I) dContinuousContinuous

Cmm

Soil e Soil organic matter content (SOM)Soil nitrogen contentSoil pHSoil clay content (clay)

ContinuousContinuousContinuousContinuous

g kg1

g kg1

－%

a Nrate is defined as the sum of split applications within experiment duration.b Includes paddy field, upland including wheat, maize and the others.c mean air temperature for each observation are calculated as the mean value during the

experiment period.d Water input defined as the sum of precipitation and irrigation rate.e Values for topsoil

16

Table S3. Response functions of upscaling model. Model coefficients are shown as meanSD (standard deviation), with applying domain (l) of fk noted for each response function.

No. Response function Applying domain (l) *

1 RTN=((2.79E-06±0.00)clay(1.60E-07±0.00)P(7.79E-05±0.00)TN)N2rate

+((1.46E-04±0.00)P (2.09E-03±0.00)Temp)Nrate

(7.97±2.96)pH+(60.42±17.50)

f3[0,6.5]∩f4[0,23.2]∩f7=1

2 RTN=(1.01E-06±0.00)SOMN2rate

+(2.88E-05±0.00)PNrate

+(1.51±0.59)

f3(6.5,+]∩f4[0,23.2]∩f7=1

3 RTN=((2.23E-05±0.00)pH(4.67E-06±0.00)Temp) N2rate

+(1.89±0.19)

f4(23.2,35]∩f5[0,20.8]∩f6[0,860]∩f7=1

4 RTN=((2.58E-06±0.00)pH)N2rate

+(7.90E-04±0.00)TempNrate

(0.02±0.00)P(8.18±2.06)TN+(36.38±4.07)

f4(23.2,35]∩f5[0,20.8]∩f6(860,+∞]∩f7=1

5 RTN=((4.06E-07±0.00)P(7.42E-06±0.00)clay))N2rate

+(1.97E-02±0.00)TNNrate

(8.72±1.87)pH+(4.72E-03±0.00)P +(61.28±12.5)

f4(23.2,35]∩f5(20.8,+∞]∩f7=1

6 RTN=((6.89E-05±0.00)P(8.06E-04±0.00)SOM)Nrate

+(8.49±1)

f4(35,+∞]∩f7=1

7 RTN=(0.01±0.00)TNNrate

+(0.02±0.00)W(9.94±1.53)pH+(58.81±9.93)

f1[0,19.275]∩f2[0,1.21]∩f5[0,21.8]∩f7=2

8 RTN= ((1.88E-04±0.00)SOM(4.65E-03±0.00)TN(4.21E-04±0.00))N2rate f1(19.275,+]∩f2[0,1.21]∩f5[0,21.8]∩f7=2

17

+(4.08±0.48)pH+(0.01±0.00)clayNrate(21.64±2.87)

9 RTN=(2.12E-06±0.00)Temp N2rate

+(9.19E-05±0.00)WNrate

(0.02±0.00)W(69.33±23.03)TN+(36.04±7.22)pH(117.92±25.07)

f2[0,1.21]∩f3[0,6.7]∩f4[0,16.9]∩f5(21.8,+∞]∩f7=2

10 RTN= ((9.57E-06±0.00)pH(8.69E-05±0.00)TN) N2rate

(4.65±1.93)TN(7.97±1.5)

f2[0,1.21]∩f3(6.7,+∞]∩f4[0,16.9]∩f5(21.8,+∞]∩f7=2

11 RTN= ((5.05E-05±0.00)W(0.07±0.00)TN +(8.75E-03±0.00)pH)Nrate

+(0.54±0.07)Temp (4.55±1.49)

f2[0,1.21]∩f4(16.9,+∞]∩f5(21.8,+∞]∩f7=2

12 RTN= (6.74E-06±0.00)clay N2rate

+(2.38E-03±0.00)clay Nrate

+(0.39±0.14)SOM(4.07±3.49)

f2(1.21,1.8]∩f3[0,6]∩f7=2

13 RTN=(3.69E-05±0.00)W Nrate

+(6.76±1.58)

f2(1.21,1.68]∩f3(6,+∞]∩f7=2

14 RTN=(4.516±0.836)Temp－(32.88±12.72) f2(1.68,1.8]∩f3(6,+∞]∩f7=215 RTN= (5.03E-06±0.00)SOM N2

rate

+((5.79E-03±0.00)pH +(1.33E-03±0.00)clay)Nrate

+(0.35±0.19)Temp+(0.03±0.00)W(12.57±3.88)

f2(1.8,+∞]∩f7=2

* f1: Temp, f2: TN, f3: pH, f4: SOM, f5: clay, f6: P, f7: crop type (paddy field=1, upland=2)

18

Fig. S1 The correlation between air and soil temperature based on the observations of 100 experimental sites (a) and between soil water content and clay content (b; Wäldchen et al., 2012).

19

Figure S2. Soil attributes and Climate factors of China. (a) Soil total nitrogen content, g/kg; (b) Soil clay content, %; (c) Soil pH; (d) Soil organic carbon content (2012), %; (e) Precipitation (2012), mm; (f) Mean air temperature (2012), K; (g) Nitrogen fertilizer application rate per unit sowing area (2012), 102 kg N ha1 yr1; (h)

20

Irrigation (2012), mm/yr. The maps in 2012 are only shown for example.

21

Figure S3. Spatial patterns (1-km) of the trend of cropland N runoff and administrative divisions (regions and provinces) in China.

Figure S4. Temporal trends of cropland N runoff during 1990-2012. The gray shaded area for this study represents the standard deviation coming from our uncertainty assessment (see Text S2).

22

Fig. S5 Trend of N fertilizer (a) and irrigation (b) application rates in China from 1990 to 2012. County-level data of the annual amounts of synthetic fertilizers, manure, and crop residues applied from 1990 to 2012 are obtained for 2884 political units and disaggregated into 1-km maps based on the above crop type distribution. Municipal-scale sowing areas of wheat, maize, rice, soybean, and the other crops were obtained from ~334 municipal statistical registers. Irrigation rate (I, mmyr-1) was calculated as the municipal-scale irrigation water (m3yr-1) used for croplands divided by actual irrigation area (ha) and then resampled it into 1-km grid cells. Slopes of N fertilizer and irrigation application rates for each grid cell are calculated based on linear regression approach.

Figure S6. Trends in precipitation and irrigation during the period 1990-2012 at the provincial scale. (a) paddy field, (b) upland.

23

a b

Figure S7. Absolute difference of RR due to the change in environmental conditions or agricultural management practices. (a) paddy field, (b) upland. Two types of scenarios are run to separate the impact of changes in environmental conditions or agricultural management practices: a control simulation with the all conditions and practices varied from 1990 to 2012 and an experimental simulation with one of conditions or practices fixed at year 1990. The difference was considered as the response to one of conditions or practices and was averaged in the period 1990-2012.

Figure S8. Effect of SOM to N runoff rate in southern China. Two types of scenarios are run to separate the impact of changes in SOM: a control simulation with the all conditions and practices fixed at year 1990 and an experimental simulation with SOM varying from 1990 to 2012. The difference was considered as the effect of SOM to N runoff rate.

24

Figure S9. Relationship between RR and SOM based on the observations of 63 field sites across China. (a) Paddy field (n=20); (b) upland (n=41). Data source can be found in Supplementary Data S1

25

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