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MaterialsWeinan city is located in the middle reaches of the Yellow River and in the southern part of the Loess Plateau (34°13’–35°52’N, 108°58’–110°35’E) (Fig. 1). It has a temperate semihumid, semiarid climate. The modern MAT observations indicate a value of 13.8 °C, and MAP is 570 mm; these values were obtained from the China meteorological data network, comprising the meteorological data of 2000–2015 (http://data.cma.cn/). Weinan has four distinct seasons, with hot and rainy conditions occurring in the same season. Much of the annual precipitation falls from June to August. The Weinan profile contains 42.8 m of loess–paleosol sequences (LPSs), including five paleosol layers from S0–S4 and five loess layers from L1–L5 and covering five glacial–interglacial cycles. The sampling method involved collecting one sample every 10 cm without interruption. A total of 427 samples were collected from this profile.Modern brGDGTs dataset and MAP datasetPreviously published brGDGTs data from surface soil samples were extracted using an established brGDGT-MAP model. The surface soil samples contain various types of soil and cover nearly all climatic and latitudinal zones. These datasets contain 712 surface soil samples, which all have separated 5-methyl and 6-methyl brGDGTs isomers (Table 1). To reduce the errors in collecting data from different laboratories, the MAP datasets we entered into the brGDGT-MAP model were all published in their previous studies, and we calculated the fractional abundances of each brGDGTs compound for each sample (Table 1), although there were no data regarding changes in soil occurring based on the brGDGTs indices among various laboratories. To eliminate and test the error of the previous MAP dataset, in this study, we also extracted each soil site’s multiyear MAP (1990–2020) through TerraClimate, which is a dataset of high-spatial-resolution monthly climate for global terrestrial surfaces (1/24°, ∼4 km)48. TerraClimate datasets reveal significant advances in the overall mean absolute error and enhance spatial realism compared with coarser resolution gridded datasets. Supplementary Fig. 3 shows that the two MAP datasets have high correlations, with only a few sites exhibiting large deviations. In this study, we entered these two MAP datasets into the DLNN model to obtain the most suitable DLNN-MAP model.Grain-size and magnetic susceptibility measurementsSamples at 10-cm intervals were dried in an oven at 40 °C for 3 days. Then, 0.2 g of each sample was weighed using a clean beaker with an electronic balance. Then, 10 ml of 30% H2O2 and 10 ml 10% HCl were added to remove organic matter and carbonate, respectively. Before the grain-size measurement, 0.05 mol/L (NaPO3)6 was added, and the solutions were placed in an ultrasonic machine for 10 min. The magnetic susceptibility of the samples were measured with an MS-2B Bartington meter. The grain-size was measured using a Mastersizer 2000 produced by Marvern Company in the UK, with an error of less than 1%.ChronologyWe used the ages of LPS control points on the Loess Plateau to obtain the age of each sample in the Weinan profile40. We used the magnetic susceptibility as an indicator of the accumulation rate39 combined with the U–230Th-dated oxygen isotope records from Sanbao caves in central China14. Each sample’s magnetic susceptibility was analyzed at 10-cm intervals (Supplementary Fig. 7). The calculation was as follows:$${T}_{{{{{{rm{m}}}}}}}={T}_{1}+frac{left({sum }_{i=1}^{m}{a}_{i}{s}_{i}right)left({T}_{2}-{T}_{1}right)}{{sum }_{i=1}^{n}{a}_{i}{s}_{i}}$$
(1)
where T1 and T2 indicate the ages of the control points, ai indicates the thickness of the layer, and si indicates the magnetic susceptibility of the layer.GDGTs analysisLipids in a total of 238 LPS samples were extracted, including the 198 samples reported in ref. 49. Forty samples at depths from 34.9 m to 43.7 m were selected every 20 cm intervals from the Weinan profile, and dried in an oven at 40 °C for 3 days. Afterward, the loess and paleosol samples were ground into powder and passed through a 60-mesh sieve. Each sample was weighed and extracted with 80 ml of methanol: dichloromethane (DCM) (1:9, v/v) using accelerated solvent extractors (ASE 100 or 150, Dionex, USA). The temperature and pressure were set at 100 °C and 1400 psi, respectively. Then, the lipid extracts were condensed in a rotary evaporator at 40 °C and separated into apolar and polar fractions on a flash silica gel column (0.7 cm i.d. and 1.5 g activated silica gel) chromatography using n-hexane and methanol as eluents, respectively. All polar components were passed through a 0.45-µm PTFE syringe filter. All apolar and polar compositions were dried under a gentle stream of nitrogen gas.The GDGTs were analyzed by using an Agilent 1200 series liquid chromatography-atmospheric pressure chemical ionization-6460A triple quadrupole mass spectrometry (LC-APCI-MS/MS). Ten microlitres of C46 GTGTs (0.001157 μg/μl) were added to each polar fraction, and the samples were then dissolved in 300 μl of n-hexane: iso-isopropanol (IPA) (98.2:1.8, v/v)). Two silica gel columns in series (150 mm × 2.1 mm, 1.9 μm, Thermo Finnigan; USA) were used for the separation of 5-methyl and 6-methyl brGDGTs, with the column temperature kept at 40 °C. The mass spectrometry settings were as follows: the vaporizer pressure 60 psi, the vaporizer temperature 400 °C, the flow rate of dry gas (N2) 6 l/min, drying gas temperature 200 °C, the capillary voltage 3500 V, the corona current 5 μA (∼3200 V), and a single-ion monitoring mode (SIM) was used50, targeting the protonated molecular ions ([M + H]+) 1304, 1302, 1300, 1298, 1296, 1292, 1050, 1048, 1046, 1036, 1034, 1032, 1020, 1018, and 744.The MATmr proxy was calculated to identify the changes that occurred in the mean annual temperature in the Weinan section over the last 430 ka. The calculation was as follows24,51.$${{MAT}}_{{mr}} =7.17+17.1*[{Ia}]+25.9*[{Ib}]+34.4*[{Ic}]-28.6*[{IIa}],(n=222,,{R}^{2} \ =0.68,; {RM}{SE}=4.6 {deg} {{{rm{C}}}},,P ; < ; 0.01)$$ (2) $${{MAT}}_{{mr}}=5.58+17.91*[{Ia}]-18.77*[{IIa}]$$ (3) $${MAT}({SSM})= 20.9-13.4*[{IIa}+{IIa}^{{prime}}]-17.2*[{IIIa}+{IIIa}^{{prime}}]\ -17.5*[{IIb}+{IIb}^{{prime}}]+11.2*[{Ib}]$$ (4) $${MAAT}=0.81-5.67*{CBT}+31.0*{MBT}^{{prime}}$$ (5) The soil pH was calculated using the following formulas24.$${pH}=7.15+1.59*{CBT}^{{prime}}(n=221,,{R}^{2}=0.85,,{RMSE}=0.52,, P , < ,0.0001)$$ (6) $${{CBT}}^{{prime} }=-{{log }}frac{{Ic}+{II}{a}^{{prime}}+{II}{b}^{{prime}}+{{IIc}}^{{prime} }+{{IIIa}}^{{prime} }+{III}{b}^{{prime} }+{{IIIc}}^{{prime} }}{{Ia}+{Ib}+{Ic}}$$ (7) SWC is well correlated with MBT’ when IR6ME  > 0.5, and these proxies were calculated using the following expressions:$${{MBT}}^{{prime} }=frac{({Ia}+{Ib}+{Ic})}{({Ia}+{Ib}+{Ic}+{IIa}+{{IIa}}^{{prime} }+{IIb}+{{IIb}}^{{prime} }+{IIc}+{{IIc}}^{{prime} }+{IIIa}+{IIIa}^{prime} )}$$
(8)
$${{IR}}_{6{ME}}=frac{sum (C6-{methylated; brGDGTs})}{sum {brGDGTs}}$$
(9)
$${{MBT}^{prime} }_{6{ME}}=frac{({Ia}+{Ib}+{Ic})}{({Ia}+{Ib}+{Ic}+{{IIa}}^{{prime} }+{{IIb}}^{{prime} }+{{IIc}}^{{prime} }+{IIIa}^{prime} )}$$
(10)
where the Roman numerals indicate different brGDGTs structures (Supplementary Fig. 1).Principal component analysis (PCA)CANOCO version 5 software was utilized to reveal the relationships among various environmental factors. The first PCA figure (Fig. 3a) was generated for the environmental factors MAT, MAPc, SWC, and pH. These variables are based on the same dataset (238 LSPs samples from Weinan profile) without any data transformation. The second PCA figure (Fig. 3b) was generated for the environmental factors MAT, MAP (based on 10Be), SWC and pH, which were all in the transition of the glacial–interglacial after 430 ka BP on the CLP. As the two LSPs profile had similar sedimentation rates, we obtained the same chronological control through linear interpolation in those transition periods. All datasets passed the Gaussian distribution test in this study.Cross wavelet analysisCompared with wavelet special analysis, cross wavelet analysis is even more complicated. The wavelet cross-spectrum can be defined as follows:$${CS}left(b,, a right)={m}_{1c}(b,, a){m}_{2c}(b,, a)$$
(11)
where ({m}_{1c}) and ({m}_{2c}) describe the covarying fractions of the overall spectra given by:$${m}_{1}left(b,, a right)={m}_{1c}left(b,, a right)+{m}_{1i}(b,, a)$$
(12)
$${m}_{2}left(b,, a right)={m}_{2c}left(b,, a right)+{m}_{2i}left(b,, a right)$$
(13)
where ({m}_{1i}) and ({m}_{2i}) are independent contributions to the variance.Overall, this is a multipart function that may be decomposed into amplitude and phase:$${CS}left(b,, a right)={{{{{rm{|}}}}}}{CS}left(b,, a right){{{{{rm{|}}}}}}{{exp }}(i;{{arg }}({CS}(b,, a)))$$
(14)
In this study, a and b represent the array of reconstructed MAPc and the Sanbao speleothem δ18O, respectively.Multiple regression linear modelTo compare the precision of the DLNN-MAP model we established, we set up a multiple regression linear model based on all 6-methyl brGDGTs except Ib. The basis of the model is defined as:$$y=a+{b}_{1}{x}_{1}+{b}_{2}{x}_{2}ldots+{b}_{n}{x}_{n}$$
(15)
where y represents MAP, x represents all 6-methyl brGDGTs and Ia and Ic, and a, b1, b2…bn represent the partial regression coefficients. n represents the number of 6-methyl we entered into the model (in this study, n = 8).The multiple correlation coefficient (R) was defined as follows:$$R=sqrt{frac{{sum }_{i=1}^{n}{({hat{y}}_{i}-bar{y})}^{2}}{{sum }_{i=1}^{n}{({y}_{i}-bar{y})}^{2}}}$$
(16)
where ({y}_{i}) represents the actual observed value, ({hat{y}}_{i}) represents the calculation value and (bar{y}) represents the mean value of all observed data.The t statistic is used to test the validity of regression coefficients, and it can be defined as follows:$${t}_{{b}_{j}}=frac{{b}_{j}}{{s}_{{b}_{j}}}$$
(17)
$${s}_{{b}_{j}}=sqrt{{p}_{{jj}}}*s$$
(18)
$$s=sqrt{frac{1}{n-m-1}mathop{sum }limits_{i=1}^{n}{({y}_{i}-{hat{y}}_{i})}^{2}}$$
(19)
$$P={({p}_{{jj}})}^{-1}=mathop{sum }limits_{i=1}^{n}({x}_{{ij}}-{bar{x}}_{j})({x}_{{ik}}-{bar{x}}_{k})$$
(20)
where ({b}_{j}) represents the regression coefficient of ({x}_{j}), n represents the number of samples and m represents the number of variables.The F statistic is used to test the linear relationship of variables and can be defined as follows:$$F=frac{1}{m{s}^{2}}mathop{sum }limits_{i=1}^{n}{({hat{y}}_{i}-bar{y})}^{2}$$
(21)
The variance inflation factor (VIF) is used to measure collinearity between variables and can be defined as follows:$${{VIF}}_{j}=frac{1}{1-{R}_{j}^{2}}$$
(22)
As shown in Supplementary Fig. 5, we found no obvious collinearity between different variables. However, there are fewer contributions in IIc’, IIIa’, IIIb’, and IIIc’ in the multiple regression linear model we established, and the value of t cannot attain the 95% confidence level (Table 2). The results of both the training dataset and extrapolated experimental dataset (Supplementary Fig. 6), although they seem good (R2 = 0.44 and 0.46, respectively), still have a considerable gap compared with the DLNN-MAP model. Especially when MAP  > 1500 mm, the multiple linear model is unable to forecast the real MAP. These results all indicate that the MAP influence on the brGDGTs compounds is not a simple linear relationship; instead, we suggest that there are complex pilot processes between them.Table 2 List of the parameters of the multiple linear modelFull size tableDLNN modelsDLNNs usually contain an input layer, a few hidden layers, and an output layer. A conceptual structure of the DLNN model was established for forecasting MAP values. The first layer accepts input signals that are various combinations of brGDGTs. The relationships among different variables are processed and analyzed in the hidden layers. The final class output is presented in the output layer; in this study, the output is the MAP reconstruction at the study site.The rectified linear unit (ReLU) activation function is applied in each neuron of the hidden layer, which is computationally simpler than the traditionally applied sigmoid function. The function of the ReLU activation function is given as follows:$$fleft(xright)=left{begin{array}{c}x,, x , > , 0 \ 0,, x , le , 0end{array}right.={{{{{rm{max }}}}}}(0,, x)$$
(23)
where x represents an input signal to a neuron and f represents the activation function.Furthermore, the bias between the measured and forecasted output values is reflected by the loss function. The loss function applied herein is the MAE (mean absolute error), which is given as follows:$${MAE}=frac{1}{N}mathop{sum }limits_{i=1}^{n}{{{{{rm{|}}}}}}T-Y{{{{{rm{|}}}}}}$$
(24)
where N is the number of training data points, and T and Y represent the measured output value and the forecasted class value, respectively.To realize the backpropagation framework, the derivative of the ReLU activation function needs to be acquired. According to the definition of the ReLU, the derivative is shown as follows.$$f{^prime} left(xright)=left{begin{array}{c}1,; x , > , 0 \ 0,; x , le , 0end{array}right.$$
(25)
Given a minibatch of m training samples obtained from the training set {x(1), x(2)…, x(m)} and their corresponding targets T(i) (i = 1,2…, m), the gradient used in the backpropagation framework is shown as follows:$$f=frac{1}{m}mathop{sum }limits_{i=1}^{n}frac{partial L}{partial w}$$
(26)
where L is the loss function; w represents the network weights; and n = 1 is the number of output values (MAP).In addition, considering that the adaptive moment estimation algorithm (Adam) was proven to be an effective neural network training method with a fast convergence speed and great classification performance, we applied this algorithm to train the DLNN model for MAP forecasting in this study. Adam has two biased equations, which are shown as follows:$$a={rho }_{1}a+(1-{rho }_{1})g$$
(27)
$$b={rho }_{2}b+(1-{rho }_{2})gtimes g$$
(28)
where ({rho }_{1}=0.9) and ({rho }_{2}=0.999) are exponential decay rates; g is the gradient; and (times) represents an elementwise product operator.After this calculation, the correct biases in the above two moments are given as follows:$${a}_{c}=frac{a}{1-{rho }_{1}^{t}}$$
(29)
$${b}_{c}=frac{b}{1-{rho }_{2}^{t}}$$
(30)
where t represents the current time step.Moreover, the update of the network weights is shown as follows:$${triangle }_{w}=-lambda frac{{a}_{c}}{sqrt{{b}_{c}}+epsilon }$$
(31)
where (lambda=0.001) represents the learning rates and (epsilon={10}^{-8}) is a constant used to ensure numerical stability.Eventually, the DLNN parameters can be updated according to the following formula.$$w ,=, w ,+, {triangle }_{w}$$
(32)
brGDGT-MAP modelsWe entered 9 brGDGTs compounds (all 6-methyl brGDGTs; each compound entered in the model is the percentage of all brGDGTs in the surface soil) into the input layer of the DLNN; these compounds are closely related to soil moisture. Then, we selected 533 surface soil samples as the training dataset and 179 surface soil samples as the validation dataset, both of which satisfied the principle of randomness. We assessed the precision of the model using forecast data R2 and root mean square error (RMSE) values.Through several parameters applied in the DLNN model, we found that the frequency of training and the number of neurons play the most significant roles in the brGDGT-MAP models. In addition, four hidden layers containing the other DLNN parameters allow the model to become more stable (detailed parameters are shown in Supplementary Fig. 7). To test the best frequency of training and the number of neurons in each hidden layer, we set a series of gradients to test the model to find the most suitable combination. As shown in Supplementary Fig. 8, for the frequency of training, we set the minimum and maximum training times to 1000 and 1500, respectively, with 100 times as the interval. We also set the numbers of neurons from 160 to 260 with a 20-neuron interval.Testing the weights of different compounds in the DLNN model and determining whether it was essential to eliminate some compounds that may make the dataset redundant were also required. Based on the model in which the Ib parameter was removed, we also set a series of experiments to test the effects of the different 6-methyl isomers on the predicted MAP values. Then, we made seven attempts to test the forecast effect of the brGDGT-MAP models by removing the Ic, IIa’, IIb’, IIc’, IIIa’, IIIb’, and IIIc’ parameters (Supplementary Fig. 9). Then, we obtained the best brGDGT-MAP model (Supplementary Fig. 10).Comparison of various ANN structuresTo improve the accuracy of our brGDGT-MAP models and the models’ universality, we also tested more complex ANN structures and then compared them with our DLNN models.RNNA recurrent neuron network (RNN) is an artificial neural network in which nodes are directionally connected into loops. The essential feature of RNN is that there are both internal feedback connections and feedforward connections between processing units. The inner structure of RNN is similar to that of the human brain, which can learn to transform a lifetime of sensory input streams into an efficient sequence of motor outputs (Supplementary Fig. 11a). Therefore, the basis of the RNN is defined as follows:$${h}_{t}=fleft(U ,*, {X}_{t}+W ,*, {h}_{t-1}right)$$
(33)
$${o}_{t}={softmax}(V ,{h}_{t})$$
(34)
where Xt represents the input value at time t; ot represents the output value at time t; ht represents the memory value at time t; and U, V, and W are the parameters of this network. For the motivative function, we chose softmax.LSTMLong short-term memory networks (LSTM) are a special type of RNN that can learn long-term dependence and contain three gates (forget gate, input gate and output gate) and one memory cell. The horizontal line above the box is called the cell state, and it acts as a conveyor belt to control the flow of information to the next moment (Supplementary Fig. 11b). Therefore, the basis of LSTM is defined as follows:$${C}_{t}={f}_{t}*{C}_{t-1}+{i}_{t}*{widetilde{C}}_{t}$$
(35)
where ({C}_{t-1}) represents the knowledge state of the model at time t − 1 and ({widetilde{C}}_{t}) represents the newly acquired information after entering new observations. ({f}_{t}) and ({i}_{t}) represent the weight parameters of ({C}_{t-1}) and ({widetilde{C}}_{t}), respectively.$${f}_{t}=sigma ({W}_{f}cdot left[{h}_{t-1},, {x}_{t}right]+{b}_{f})$$
(36)
$${i}_{t}=sigma ({W}_{f}cdot left[{h}_{t-1},, {x}_{t}right]+{b}_{i})$$
(37)
$$kern0.9pc {widetilde{C}}_{t}={{tanh }}({W}_{c}cdot left[{h}_{t-1},, {x}_{t}right]+{b}_{c})$$
(38)
where ({h}_{t-1}) represents the output value at time t − 1 and ({x}_{t}) represents the new input value at time t. ({W}_{f}) represents the motivative function in this study. We used tanh as the motivative function when our model was learning. Each new input may not have a positive impact on the machine, but it may also have a negative impact., ({b}_{f}), ({b}_{i}) and ({b}_{c}) represent the random disturbances (white noise).GRUAs mentioned above, the LSTM is proposed to overcome RNN’s inability to address remote dependence and the gate recurrent unit (GRU), a variant of the LSTM, keeps the effect of the LSTM while making the structure simpler.Compared with the LSTM, the GRU only has two gates (update (zt) and reset (rt) gates). The update gate is used to control the degree to which the state information at the previous moment is brought into the current state. The larger the value of the update gate is, the more state information at the previous moment is brought in. The reset gate is used to control the degree to which the state information at the previous moment is ignored (Supplementary Fig. 11c). Therefore, the basis of the LSTM is defined as follows:$${r}_{t}=sigma ({W}_{r}cdot [{h}_{t-1},, {x}_{t}])$$
(39)
$${z}_{t}=sigma ({W}_{z}cdot [{h}_{t-1},, {x}_{t}])$$
(40)
$${widetilde{h}}_{t}={tanh }({W}_{widetilde{h}}cdot [{{r}_{t}*h}_{t-1},, {x}_{t}])$$
(41)
$${h}_{t}=left(1-{z}_{t}right)*{{r}_{t}*h}_{t-1}+{z}_{t}*{widetilde{h}}_{t}$$
(42)
$${y}_{t}=sigma ({W}_{o}cdot {h}_{t})$$
(43)
where [] represents the connection of two vectors and * represents the multiplication of matrix elements. The xt and yt represent the input and output values at time t, respectively.It can be seen from the above formula that the parameters to be learned are the weight parameters of Wr, Wz, Wh, and Wo. The first three weights are spliced; therefore, they need to be segmented during learning. These can be defined as follows:$${W}_{r}={W}_{{rx}}+{W}_{{rh}}$$
(44)
$${W}_{z}={W}_{{zx}}+{W}_{{zh}}$$
(45)
$${W}_{widetilde{h}}={W}_{widetilde{h}x}+{W}_{widetilde{h}h}$$
(46)
As we can find in the RNN, LSTM, and GRU models we reconstructed (Supplementary Fig. 12), the training datasets all show extraordinarily high R2 values (0.99, 0.99, and 0.99, respectively) and low RMSE values (0.36, 0.23, and 0.16, respectively). However, the validation datasets do not show good prediction ability compared with the DLNN. These results indicate that the two ANN structures are not suitable for MAP prediction based on brGDGTs, although their inner structures are more complex than those of the DLNN. The reason we suggested is that the RNN, LSTM and GRU are more appropriate to the massive amounts of data and the data that have obvious spatiotemporal characteristics. The great prediction precision in the training dataset and the poor performance in the extrapolated datasets indicate that the models based on the RNN, LSTM and GRU have significant overfitting. As a result, compared with other ANN structures, we concluded that our DLNN model is the most suitable one to forecast MAP based on brGDGTs.Environmental indicators of n-alkanes proxiesLong-chain n-alkanes in plant leaf waxes are universal in terrestrial environments and can deliver signals of variations in plant sources and past climate. They are widely distributed in surface soils and Quaternary sediments, especially in LPSs. In this study, due to the insufficient samples in Weinan profile, we only analyzed n-alkanes components for 40 LPS samples, which contain ages between 340 and 430 ka BP.Instrumental measurementsFor the apolar fractions, a total of 40 samples in this study, mainly containing n-alkanes, were all investigated utilizing a Shimadzu 2010 gas chromatograph (GC) equipped with a flame ionization detector (FID) and a DB-5 fused silica capillary column (60 m (times) 0.32 mm (times) 0.25 μm film thickness) with helium as the carrier gas. The temperature of the GC oven was enhanced from 70 to 300 °C at a rate of 3 °C/min. Then, this temperature (300 °C) was maintained for 30 min. Finally, the concentrations of the n-alkane homologs were evaluated by assessing the peak area of the n-alkanes to that of the internal standard (cholane).Long-term paleoclimatic changeThe carbon preference index (CPI) evaluates the relative abundances of odd vs. even-numbered n-alkanes. The CPI increases as the environmental aridity increases. The CPI indicated warm–wet periods and cold-dry periods in paleoclimate and corresponded well with the loess–paleosol cycle52. The average chain length (ACL) value is the weighted average of the different carbon chain lengths. The lower ACL value corresponds to the lower temperature in the research of LPSs. The variations in the ACL value have good coordination with the magnetic susceptibility and particle size. The n-alkane CPI53 and ACL54 are calculated as follows:$${CPI}(1)=frac{({C}_{23}+{C}_{25}+{C}_{27}+{C}_{29}+{C}_{31})+({C}_{25}+{C}_{27}+{C}_{29}+{C}_{31}+{C}_{33})}{2({C}_{24}+{C}_{26}+{C}_{28}+{C}_{30}+{C}_{32})}$$
(47)
$${CPI}left(2right)=frac{1}{2}left(frac{{C}_{25}+{C}_{27}+{C}_{29}+{C}_{31}+{C}_{33}}{{C}_{24}+{C}_{26}+{C}_{28}+{C}_{30}+{C}_{32}}+frac{{C}_{25}+{C}_{27}+{C}_{29}+{C}_{31}+{C}_{33}}{{C}_{26}+{C}_{28}+{C}_{30}+{C}_{32}+{C}_{34}}right)$$
(48)
$${ACL}=frac{{23C}_{23}+{25C}_{25}+{27C}_{27}+{29C}_{29}+31{C}_{31}+{33C}_{33}}{{C}_{23}+{C}_{25}+{C}_{27}+{C}_{29}+{C}_{31}{+C}_{33}}$$
(49)
Figure 13 shows the variations in CPI (Supplementary Fig. 13a) and ACL (Supplementary Fig. 13b) values in the Weinan profile from 340 to 430 ka BP. Compared with the MAP (Supplementary Fig. 13c) and SWC (Fig. 2e) reconstructions based on brGDGTs, we found that they all had a peak at ∼350 ka BP, which indicates relatively high soil moisture at approximately 350 ka BP.MAP reconstruction in the XRD sectionIn this section, we test the brGDGT-MAP model in the Xiangride (XRD) profile, which is located in the margin region of the East Asian monsoon (Fig. 1). With robust chronological control, we reconstructed the rainfall changes in 7000 years BP (Supplementary Fig. 14b). We found that MAP was ∼200 mm in the late Holocene, which approaches multiple modern observations in this region (180 mm). Moreover, we suggest that this region experienced the most humid period in the mid-Holocene, when the rainfall reached 600 mm. Afterward, the precipitation declined from 6000 to 4000 years BP and then increased and reached a peak value at ∼3000 years BP. Then, it had a drought trend until modern times.We discovered that our brGDGT-MAP model could precisely capture rainfall dynamics based on the Weinan profile (Supplementary Fig. 14a) and XRD profile (Supplementary Fig. 14b). Combined with the most acceptable rainfall records in the Holocene (i.e., 10Be (Supplementary Fig. 14c), pollen in Gonghai (Fig. 1 and Supplementary Fig. 14d), and Dongge cave δ18O (Fig. 1 and Supplementary Fig. 14e)), we found the same precipitation peak values in the early Holocene and mid-Holocene. In addition, they all revealed a drought trend throughout the whole Holocene. We suggest that brGDGTs can become a robust proxy to reconstruct precipitation in the Holocene. More

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Historical land use and cover changesExisting databases differed significantly in representing historical LUCC in China (Fig. 1). Generally, datasets agree on the direction of change in cropland area until 1980 in Liu and Tian18, Ramankutty19, Houghton20, and this study (Fig. 1b, c), while the magnitude of change varied greatly. Specifically, the total cropland expansion in China was comparable between our new data set and the LUH2-GCB from 1900 onwards (56 vs 60 Mha, Fig. 1b), but cropland area changes since 1980 diverged considerably (−14 vs 41 Mha, Fig. 1c). The differences were also evident across space and more distinct during the period of 1980 to 2019 (Fig. 2a–d), in which the cropland coverage was mainly declining in our reconstructed data but increasing in LUH2-GCB (Fig. 2b, d). We found that the distinct changes are derived from the abrupt cropland increases in the FAO data reported from China, upon which LUH2-GCB was based (see Supplementary Information 3).Fig. 1: Temporal, net changes of cropland and forest from 1900 (unit: Mha).Panel a–c: cropland; panel d–f: forest; the bar charts indicate the total accumulated areas (b, e) from 1900 and (c, f) from 1980 until the last available year; LUH2-GCB was the latest version of LUH2 data used in Global Carbon Budget assessments projects (LUH2 used in MsTMIP and TRENDY were showed in Supplementary Figs. S7 and S10); Houghton data were derived from Houghton and Nassikas20 and the data in 1900 were interpolated from 1850 and 1950; Liu&Tian and Ramankutty data were derived from the works of Liu and Tian16 and Ramankutty and Foley18; the open circles indicate the changes of cropland and forest areas derived from inventory-based benchmark data; details of the benchmark data for cropland and forest were presented in Yu et al.11 and Supplementary Information 1.2 of this study, respectively; error bars: one standard deviation from the mean.Full size imageFig. 2: Spatial distribution of the fractional coverage changes of cropland and forest in China (unit: %).Panels a–d: cropland; panel e–h: forest; panels a, b, e, and f indicate the results derived from this study; data in panels c, d, g, and h were from LUH2-GCB; panels a, c, e, and g show the changes from 1900 to 1980, whereas panels b, d, f, and h show the changes from 1980 to 2019; negative and positive values indicate coverage reduction and increment, respectively.Full size imageThe problems of cropland area expansion reported to FAO are likely caused by changes in the underlying database, in which the Chinese Agricultural Yearbook (CAY) was used prior to 1996, the China Land and Resources Statistical Yearbook (LRSY) from 1996 to 2007, and the National Land and Resources Bulletin (NLRB) after 2007 (Supplementary Information 3).These three datasets are not consistent with each other because surveying methods were distinct. For example, cropland area in CAY before 1982 used an extrapolation method (i.e. “production-to-acreage” approach) due to limited field survey data11. Specifically, the extrapolation method was widely adopted for convenience and for taxation purposes in the early period, such as in the framework of the first benchmark cropland survey conducted in 1953. Such methods assumed that low-productivity cropland occupied an area of 1/3–1/8 of a predetermined, “standard-productivity” cropland21, which greatly underestimates the acreages of low productivity cropland. Biases accumulated in this method persisted until the satellite era (1980s), while the 1953 surveying data were used as the baseline for CAY to update cropland area on an annual basis.Besides the survey method, policies also contributed to a bias of reported cropland area. To tackle rising food demands, cropland expansion was highly encouraged by the government before the 1980s, implementing an incentive policy to allow new tax-free cropland without reporting to the government for the first 3–5 years22,23. Even after the initial reporting free period, these newly cultivated croplands continued to be unreported due to political incentives to show increasing crop yield to the local authorities23,24.When the first comprehensive and systematic survey (i.e. the second national cropland survey conducted during 1985–1996) was completed, the cropland area was found to be larger than previously reported in CAY11. Similarly, the shift from the use of LRSY to NLRB also introduced a spurious cropland area increment from 2007 to 2010 as small, fragmented croplands were identified by better technologies adopted in NLRB, which had remained undetected previously (Supplementary Fig. S10).Thus, LUH2-GCB has inherited spurious temporal signals of abrupt cropland increment in FAO from the 1980s to 2010 (Fig. 1a and Supplementary Fig. S10). Therefore, if the areas of other land cover types (e.g. forest) are indirectly constrained from cropland area change, cropland area biases were mirrored in the area change of other land use types. This is the case for the LUH2-GCB and for Liu and Tian’s previous land use gridded datasets. Our new database, rebuilt from Yu et al.11, corrected these problems in temporal dynamics by assimilating multiple data sources (Fig. 1a). More specifically, we retrospectively reconstructed information about cropland and forest areas year by year, using tabular data from official agencies (Supplementary Information 1 and Supplementary Data 1). To further reduce the aforementioned biases, we used the most recent and authoritative record of provincial cropland and forest areas available as the benchmark, and then spatialized the cropland and forest distributions using gridded maps as ancillary data (Supplementary Information 1). The area changes were also validated using inventory-based benchmark data (Fig. 1a, d, details were presented in Yu et al.11 and Supplementary Information 1.2).Changes in forest area in China also varied dramatically among databases. Based on Ramankutty and Foley19 and LUH2-GCB, a net forest loss was found from 1900 to the last available year, at 33–108 Mha whereas Liu and Tian18 and Houghton and Nassikas20 reported a net increase of 15 Mha (1900–2005) and 70 Mha (1900–2015) in forest area, respectively (Fig. 1d, e).By assimilating multiple source records, reports, and national surveys, however, our newly reconstructed and intensively validated database (Supplementary Figs. S4, S5, and S8) with corrected biases suggests that the forest area increased by 58 Mha from 1900 to 2019 (Fig. 1e). In particular, our data suggest that there is a surprisingly large underestimation of forest expansion in all other databases (38–102 Mha) after 1980 (Fig. 1f). We performed spatial analyses and show that widespread forest expansion in our reconstructed data was represented as a forest decline in LUH2-GCB during the period 1980–2019 (Fig. 2f, h). These existing biases in the dataset during the last four decades can be simply removed using recently available and spatially explicit forest products (Supplementary Table S2).Bias in forest change might be explained by two reasons. First, gridded datasets inherited and transferred errors from the use of FAO-based cropland dataset in developing global land use databases such as HYDE and thus LUH2-GCB8. Second, the FAO forest area reported is an important reference data used in these databases. The FAO forest area is reported based on a “land use” definition, which underestimated gross “land cover” change signals between reported years (Supplementary Information 1.3). Specifically, the FAO forest area describes lands that have been forested and will continue to be used for forestry (e.g. cut-over area, fired-over area, unestablished afforestation land) (Supplementary Table S5). This approach overestimates forest area by including lands used for reforestation where no forest was yet created. Thus, for example, the FAO statistics reported a 157.2 Mha forest area in 1990 (Supplementary Fig. S7), which is ~30 Mha higher than officially released data.More importantly, newly established forests were underestimated in such an accounting approach. The forest area expansion in China reported in the FAO statistics was 61 Mha from 1990 to 2019, which is 30 Mha lower than the officially released data16. Our reconstructed dataset, in agreement with officially released forest area, uses a “land cover” definition that characterizes the distribution of annually established forests. Therefore, the FAO statistics – a data set with definition specified to describe the area of land use – should be used with caution for constraining the temporal evolution of forest cover distribution in gridded data reconstruction, and the modeling community should be alerted to treat the LUCC data appropriately.Nonetheless, the FAO and the related LUH2 products were the dominant LUCC forcing data used in multiple studies3,25, including various process-model-based intercomparison projects (e.g. MsTMIP, LUMIP, NMIP, TRENDY), annually released Global Carbon Budget reports2,26, and IPCC reports5, implying a potential bias of these assessments for the China region. In contrast, changes in forest area from our database were independently developed (Supplementary Information 1.2), intensively calibrated, and validated using officially released national forest inventories (NFIs, see Supplementary Figs. S4 and S5), which can help to reduce the potential bias of C balance assessment in China. More specifically, the total forest area and PF area in our database were compared with historical NFIs released by the National Forestry and Grassland Administration at provincial level since 1949 (Supplementary Figs. S4 and S5), which supports the reliability of our reconstructed data.Historical carbon stock changesTo illustrate the bias in the C balance of China when using previous LUCC dataset, we performed simulations with the DLEM model for the period 1900–2019 at a resolution of 0.5 × 0.5 degree forced by our new LUCC dataset. We validated the distribution and changes of C stock using published studies and previously reported inventory-based estimations (Supplementary Information 6 and 7). The model could capture well C dynamics in China using inventory-based forest C stock changes at both provincial and national levels as the validation data set (Supplementary Fig. S14).Our results show that the total C stock decreased by 6.9 ± 0.6 Pg from 1900 to 1980 and increased by 8.9 ± 0.8 Pg C from 1980 to 2019 (Fig. 3, derived from experiment S1 in Supplementary Table S10). Such a large C stock increment since the 1980s, which is dominated by vegetation biomass C accumulation, was not captured in the MsTMIP and TRENDY projects driven by different versions of the LUH2 data (Fig. 3). This is attributed to the fast expansion of forest area(s) that was not captured by this land use forcing (Fig. 1).Fig. 3: Temporal changes of carbon storage from 1900 to 2010s in China.Panel a–c indicate vegetation carbon, soil organic carbon, and total ecosystem carbon, respectively. Results derived from experiment designed to have all environmental factors vary historically from 1900 to the 2010s, for model design details of this study see Supplementary Information 8); pink color: MsTMIP (1900–2010); blue color: TRENDY (1900–2019); dark color: this study (1900–2019); the shade areas represent the ranges of 1 standard deviation; unit: Pg C.Full size imageWe found that the large-scale forest expansion in China alone has caused a substantial C accumulation since 1980 (0.21 ± 0.006 Pg C per year, Table 1). In contrast, the forest C sink of the TRENDY models is negligible (−0.02 ± 0.05 Pg C per year, Table 1). A moderate C source (0.10 ± 0.08 Pg C per year, Table 1) was even found in the MsTMIP models, since these models were driven by continuous forest area loss and cropland expansion since the 1980s (Supplementary Fig. S7).Table 1 Comparison of reported carbon fluxes from various biomes in ChinaFull size tableA recent atmospheric inversion-based study reported that China’s land ecosystems were a large CO2 sink of −1.11 ± 0.38 Pg C per year27, which seems to be ecologically implausible and critically sensitive to the assimilation of the CO2 record from one station28. The compilation of previous studies from inventory- and satellite-based estimation, atmospheric inversion, and process-based models suggested that the Chinese C sink was much smaller (−0.18– −0.45 Pg C per year; Table 1). Our model-simulated terrestrial sink (~−0.28 ± 0.06 Pg C per year) was in this range (Table 1).While our simulated C balance in different categories or biomes is close to previous estimations, three major differences are observed (Table 1). First, because the LUCC data used in previous global models suffered from biases as shown above, the national C sink was generally underestimated in these simulations (Table 1). Second, our estimation of the forest sink is around two to three times larger than the previous one during 1949–199829. This was mainly because forest area was underestimated by over 33% (53 Mha) in the previous study29 compared to the national forest inventory (NFI)16. This underestimation may stem from exclusion of economic and bamboo forests. The third major difference is the role of grassland soils in C balance during the period 1980–2000. China’s grassland soils were previously reported as a minor sink of −0.007–−0.022 Pg C per year from the 1980s to the 2000s (Table 1), while our simulations suggest that grassland soils were a C source of 0.062–0.066 Pg C per year. This discrepancy lies in the approaches used and the accounting boundaries between studies (i.e. whether the transitions of grassland were considered), in which LUCC impacts were represented differently. For example, impervious surfaces (part of urbanized area) expanded into ~15 Mha of natural lands in China from 1978 to 201730, which further drove redistribution of cropland into marginal lands with the majority converted from grassland, causing wind erosion, habitat loss, and more water and fertilizer consumption31. Earlier studies using a static grassland map exclude the C stock loss in the land-use transition32. Thus, the distinct roles of grassland soils (i.e. sink vs source) derived from our simulations and earlier studies are not contradictory but are due to differences in accounting boundaries.LUCC impacts on carbon stock changesOur DLEM simulation indicates that LUCC induced a C loss of 5.1 ± 0.7 Pg C from 1900 to 2010s (Fig. 4a), which is substantially lower than that from MsTMIP (13.8 ± 7.7 Pg C, 1900–2010) and TRENDY (9.4 ± 3.3 Pg C, 1900–2019; Fig. 4e, f and Supplementary Fig. S18d, g). From 1980 onward, LUCC increased C storage by 4.3 ± 0.7 Pg C, with the major contribution from vegetation biomass C increment in the southwestern and northeastern regions (Fig. 4d and Supplementary Fig. S19a). Nonetheless, this C increase in biomass was not captured in MsTMIP and TRENDY models (Fig. 4e, f and Supplementary Fig. S19d, g), which simulated that LUCC continued to reduce C stock by 7.5 ± 1.6 and 5.3 ± 2.3 Pg C during the period 1980 to the 2010s, respectively (Fig. 4 and Supplementary Fig. S20).Fig. 4: Spatial distribution of LUCC impacts on ecosystem carbon storage.Panel a–c: LUCC impacts for period of 1900–2019; panel d–f: LUCC impacts for period of 1980–2019 (d–f). Panels a and d are from this study; data in panels b and e are from MsTMIP; data in panels c and f are from TRENDY; negative and positive values indicate sink and source, respectively; green and yellow bar stacked in the insert indicate LUCC impacts on vegetation and soil organic carbon in Pg C; spatial map unit: g C m−2; error bars: one standard deviation from the mean of LUCC impacts on total carbon storage.Full size imageTo confirm that such discrepancy was induced by LUCC data but not the DLEM model, we set up additional DLEM simulations using the LUH2-GCB database (Supplementary Information 8). The simulated C losses induced by LUCC when DLEM was driven with LUH2-GCB were 6.5 ± 0.4 and 11.4 ± 0.6 Pg C during the periods of 1980–2019 and 1900–2019, which are close to MsTMIP and TRENDY simulations. These results confirm that the LUCC forcing database is the major contributor to the difference between our simulations and the MsTMIP and TRENDY projects. An earlier study reported that global LUCC-induced C emissions are substantially underestimated due to underrepresented tree harvesting and land clearing from shifting cultivation33. Our simulation revealed that regional LUCC-induced C emission could also be overestimated in China due to a bias in the LUCC data.There are also disputes over whether the LUCC induced a C sink in China since the 1990s or not (Supplementary Table S8). By using an updated LUCC database, our simulations revealed that LUCC was a strong C sink in China, and that its magnitude was larger than previous estimates since the 1990s (Supplementary Table S8). Our results using an improved LUCC forcing data can facilitate narrowing down the well-known, large uncertainty in LUCC-induced C change at regional scale.Attributions of different factors on C stock changes since 1980By using the DLEM model with factorial simulations (see Supplementary Information 8 for details), we examined the direct and interactive contributions of different drivers to terrestrial C stock change in China for the period 1980–2019, including LUCC, climate, forest management, N deposition, and CO2 fertilization (see Methods, Fig. 5). Note that historical C stock change is not equivalent to the sum of factorial attributions as the baseline conditions differ (see Supplementary Information 8).Fig. 5: Attributions of different environmental factors on carbon stock change in China from 1980 to 2019.Panels a–c indicate attributions of impacts on the changes of vegetation carbon, soil organic carbon, and total ecosystem carbon, respectively; CLM: climate; CO2: rising atmospheric CO2 concentration; Ndep: N deposition; Man: forest management; Nfer: N fertilizer and manure application.Full size imageOverall, 81.9% (6.5 Pg C) of the terrestrial C sink during this period was attributed to direct impacts of all major factors, while the interactive effect contributed 18.1% (1.43 Pg C; Fig. 5c). Among all the factors examined, LUCC was the dominant driver accounting for 50.3% (3.96 Pg C) of the total C increment during the period 1980–2019 (Fig. 5c), which was largely attributed to biomass C accumulation (70.0%; Fig. 5a, c). Tian et al.13 reported that LUCC’s contribution to the sink in China was at 0.05 Pg C yr−1 since the 1980s – an amount that is only about 30% of our simulations. The discrepancy is attributed to the different representation of forest expansion in model simulations, which was 65 Mha from 1980 to 2005 in our database but only ~14 Mha in Tian et al.13. Similarly, the increase in the global land sink during the recent period (1998–2012) was also mainly attributed to LUCC (i.e. decreased tropical forest area loss and increased afforestation in northern temperate regions), instead of CO2 or climate change34.Climate change enhanced biomass C stocks by 1.63 Pg but caused a soil C loss of 0.30 Pg, thus contributing to land sink of 1.41 Pg C (18.0% of the total with all factors) since 1980 (Fig. 5). Other global change factors, such as N fertilizer application, atmospheric N deposition, and rising CO2, had a relatively minor contribution (0.1–9.54%) to the terrestrial C sink. Therefore, conversely to previous studies13,35,36,37, we showed that LUCC was the dominant driver of the recent land C sink in China, and other factors including climate change, rising CO2, and N deposition, contributed much less (0.1–18.0%) to the C stock increment in China (Fig. 5c). Tian et al.13 pointed out that LUCC effects in China should not be ignored and that the CO2 fertilization effect might be overestimated in Piao et al.38.Our simulations confirm these statements, and further show that LUCC was actually the largest contributor to land sink in China since 1980 (Fig. 5). In those studies which did not account for the influence of LUCC separately, the effects of other global change factors may have been overestimated by including LUCC impacts. For example, Chen et al.39 and He et al.37 attributed China’s C sink into different components including climate change, leaf area index (LAI) change, rising CO2, and N deposition. Such partition inevitably masked the separate contribution from LUCC, because LAI changes are closely related to land-cover changes. Thus, the accurate representation of the LUCC should be prioritized in future modeling attribution studies.Carbon stock changes in each land cover type since 1980The contribution of the establishment of young and new forest plantations to C sink has received increasing attention3,40,41,42. Our simulation (experiment S1, see Methods section) revealed that the increase in terrestrial C stock was dominantly contributed by biomass C accumulation (76.3%) (Fig. 5), in which the natural and planted forests accounted for 65% (2.9 Pg C) and 35% (1.6 Pg C) during the last four decades. We examined the LUCC effect (i.e. the largest contributor of C stock increment in Fig. 5) on the C stock of different biomes and confirmed that forest was the major contributor of the net C accumulation in China since 1980, while other biomes, including cropland, grassland, shrubland, and wetland, were relatively stable, varying from −0.3 to 0.3 Pg C during the same period (Fig. 6). A recent study documented that forest expansion was essential for a large C sink in southern China during 2002–2017, where newly-established and existing forests contributed to 32% and 34% of land C sink in the region43. In comparison to the large biomass C increase since 1980 (3.0 Pg C, Fig. 6a), the SOC increase was much lower (0.7 Pg C) during the concurrent period, although SOC changes in each biome varied greatly (–3.4–8.6 Pg C; Fig. 6b) due to area change from land conversions. The biome-level analyses further revealed that the LUCC-induced C stock increment was dominantly contributed from forest and by area expansion, while C storage in grassland and shrubland was reduced by LUCC (Fig. 6).Fig. 6: LUCC-induced carbon storage changes by land cover types based on model simulations during 1980–2019.Panel a–c indicate vegetation carbon, soil organic carbon, and total ecosystem carbon, respectively; the widths of the red blocks indicate the estimation ranges of net changes in model simulations; purple error bars indicate one standard deviation of multiple model runs; negative and positive changes indicate carbon loss and gain, respectively.Full size imageThis study highlights the dominant role of LUCC in determining the terrestrial C sink in China. Because of inaccurate representations of land cover change in China, previous estimates of the terrestrial C sink have been strongly underestimated. In contrast, forest expansion and cropland abandonment have been overestimated in the U.S., resulting in an underestimated C emission since 19807. Hence, we highlighted that the global LUCC database should be further improved, which could potentially narrow down the C imbalance reported in global C budget accounting2. In contrast to the previous studies, we showed that the contributions of factors including rising CO2, N deposition, and climate change to the land C sink in China were much smaller than LUCC over the past four decades (1980-present time). Thus, reforestation projects could represent important climate change mitigation pathways, with co-benefits for biodiversity33. To achieve the ‘C neutrality’ goal as the Chinese government declared, future climate policy should be directed to improve land management, especially forest ecosystems.Implications for future LUCC data improvementsThis study provides a novel reconstruction of recent land use change in China and assesses its implications in quantifying for terrestrial C storage dynamics. The improved dataset more accurately depicts the spatiotemporal dynamics of LUCC in China because the historically contradictory surveying records were identified, which helped to correct the biased temporal signals. Specifically, the improved surveying methods and the socioeconomic factors have greatly shaped the LUCC signals. We advocate that these impacts should be considered in the reconstruction of the national and global LUCC dataset, especially in the areas that have been intensively disturbed by human activities as is the case of China. These endeavours will be worthwhile, as demonstrated by the large impact that these bias corrections have on China’s C dynamic assessments since 1900. Thus, accurate delineation of LUCC forcing should be stressed in global simulations, including C budget accounting, biodiversity assessments, and ecosystem services evaluations. More

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Chocolate, a serious contender for the world’s most beloved food, is made from the seed kernels of the cacao tree (Theobroma cacao). But despite its popularity, Justine Vansynghel at the University of Würzburg in Germany and her colleagues found that nobody had quantified how species living on small-scale cacao farms collectively affect production1.

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doi: https://doi.org/10.1038/d41586-022-02908-0

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