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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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Cliffs present a unique flora that has been little studied until now mainly because of the inherent difficulties to access this unique environment, as shown in Fig. 2. The techniques currently used to access plants on steep slopes and cliffs (e.g., abseiling, helicopter) are generally dangerous, costly and time consuming. Using a small aerial manipulator to sample plants on the cliffs can represent many advantages, including safety and portability, as well as the capability of reaching otherwise inaccessible locations easily, quickly and at low cost.Figure 2Examples of the cliff habitats of some critically endangered species on the Kauaʻi Island along with the count of known individuals as of February 2022.Full size imageHowever, several technical challenges make it difficult to develop suitable aerial manipulators for this task. Indeed, the sampling of plants on cliffs necessarily leads to significant collision risks, as well as contact forces and moments during sampling that can destabilize the drone. The samples collected would also need to be accessed from the side of the aerial platform22. Any weight (e.g., sampling tool, collected samples) located horizontally away from the center of mass of the drone creates large additional demands on the propulsion system of most drones. To collect specific plant parts in windy conditions (e.g., scion, flowers, seeds, etc.), precise and fast motion is required even in degraded Global Navigation Satellite System (GNSS) coverage near the cliffs. The great diversity of plant species and morphology found on cliffs, as well as the variety of targeted sections of plant, also represent a major design challenge. Finally, to maximize the adoption of this tool, it is also desirable that scientists with minimal training could use this platform. The next sections describe how these challenges were addressed through the development of the Mamba.Suspended sampling platformThere are a multitude of configurations that could have been explored to sample plants on cliffs. Some drones have manipulators rigidly attached to their structure20,23. However, these manipulators tend to have a limited reach to keep the center of mass within the propeller footprint and to minimize the inertia of the system. This could result in a high collision risk with the propellers in the uneven terrain found on cliffs. The contact forces created during the sampling operation also generate destabilizing moments through manipulators rigidly attached to the drone. To address these challenges, concepts involving a compliant manipulator operated from specialized drones were also explored10. Alternatively, some aerial manipulators were also passively suspended under the drone through a long rod21,24. This keeps the drone above potential obstacles within the environment, significantly reducing the operator’s mental demand and stress while also reducing the disturbances transmitted to the drone to a downward force aligned with the rod and yaw torque. To maintain these advantages while providing better precision, some projects have developed cable suspended platforms equipped with thrusters25,26. As these platforms do not have to counter gravity, the thrusters can be positioned to fight external disturbances more efficiently (e.g., wind, contact forces, drone movements). Existing systems however only stabilize the suspended platform close to its equilibrium point.The chosen concept for the Mamba, illustrated at Fig. 3, consists of a suspended platform that can stabilize itself far from its natural equilibrium to provide a large workspace. The lifting drone in this system stays safely away and above from steep cliff faces, while supporting the platform and providing rough positioning in space through better GNSS coverage. The platform is suspended 10 m below the lifting drone using four attachment points to prevent pitch and roll motions. The cable also acts as a low pass filter, isolating the platform from the fast drone movements required to fight wind disturbances. The suspended platform design can then focus on fast and precise positioning, while also being tolerant to contacts during sampling. To do so, four pairs of bidirectional actuators are used to control the motion in the plane of the pendulum (i.e., x and y translation, as well as yaw). Two pairs of actuators are installed in the x-direction to provide sufficient force to reach plants as far as 4 m from the equilibrium position. This corresponds to roughly 3.3 m from the tip of the lifting drone’s propellers.Figure 3(a) General concept of the Mamba and lifting drone during transit and sampling on cliffs. (b) Side view of the Mamba showing the components and cable installations. (c) Top view showing the antagonist thrusters configuration. (d) Close-up of the sampling tool and 2 degrees of freedom (DOF) wrist specifically designed to sample small fragile plants.Full size imageSince the Mamba is self-powered and has its own communication system, the lifting drone function is simply to lift the platform and hold it in place. This made it possible to select amongst the many commercially available products to accelerate the development of the Mamba. The DJI M300 was chosen as it comes equipped with a 360° optical obstacle avoidance vision system, an IP45 rating, and a flight time of 20 min with the Mamba attached (3.3 kg). It also advertised a four constellation GNSS receiver for better coverage around buildings, structures, and cliffs.Precise control in windsWinds under 20 km/h represent a gentle breeze on the Beaufort scale. At this level, the wind only moves the leaves, and not the branches, which allows for ideal sampling conditions. According to historical weather data from 2020, daily maximum winds are less than 20 km/h for 40 to 70% of the year, depending on the exact location on Kauaʻi Island (i.e., Lihuʻe International airport, as reported by the National Oceanic and Atmospheric Administration, and the Makaha Ridge Weather Station, as reported in the MesoWest database). This also implies that Kauaʻi experiences stronger winds on certain days which would make precise sampling difficult. Wind conditions are also more challenging near cliff faces, with increased turbulence and vertical airflow along the cliff.To allow operations on most days, while providing precise positioning and fast rejection of wind disturbances, the actuators of the Mamba are oriented in the horizontal plane. This allows the actuator forces to directly affect the motion of the suspended platform. Each actuator of the Mamba consists of a pair of brushless DC motors and 23 cm propellers capable of producing 7 N of force. The motors are installed in opposite directions, are always idling at their minimum rotation speed, and are commanded to only create force in their preferred direction. This antagonistic configuration avoids the low-velocity dead zone of a brushless motor during thrust reversal. This makes it possible to quickly revert the direction of the thrust and nearly triples the bandwidth of the actuators to approximately 2.5 Hz27. This configuration, however, comes at the expense of added mass and components.The Mamba is equipped with a flight controller that includes a control system, and a state estimator. To avoid degraded GNSS coverage issues, the state estimator only uses data from a high accuracy inertial measurement unit (IMU) to estimate the attitude of the platform. This provides the relative position of the platform with respect to the drone and is sufficient for teleoperation. Three separated proportional-derivative controllers are used for each of the DOF controlled by the actuators. This control system also provides attitude-hold assistance (i.e., pitch and roll, which correspond to x and y displacements, as well as yaw). This implies that if the user does not send any commands, the suspended platform maintains its current state.Figure 4 illustrates the stabilization accuracy of the Mamba when moving along a representative trajectory when suspended indoors from a 5.7 m cable (limited by ceiling height). This experiment confirmed that the sampling tool can maintain a position at a horizontal reach of 2.25 m with a precision of about 5 cm for 30 s. As the horizontal reach and precision are limited by the cable angular displacements (e.g., component of weight acting on the pendulum, IMU angular resolution), the resulting workspace when operating with a 10 m long cable would reach a radius of 4 m with a positioning accuracy of about 9 cm. To account for potential external disturbances like wind, the sampling tool was designed with an opening of 15 cm. This creates some margin for the pilot to align the target with the sampling mechanism. Field trials detailed below demonstrated that the Mamba actuators and controller could maintain a sufficiently stable position to sample plants in winds During the sampling phase, wind speed averaged 15.7 km/h with a standard deviation of 6.8 km/h, while wind gusts reached an average of 20.1 km/h with a standard deviation of 6.5 km/h. The maximum average wind speed recorded during sampling was 28 km/h with gusts up to 37 km/h. This represents a lower bound of the system performance, as no failure resulted from the wind conditions experienced during the trials. The a ttached Supplementary Video also demonstrates the stability of the system.Figure 4Representative motion of the sampling tool within its workspace based only on feedback from a high accuracy IMU and recorded using a motion capture system. The natural equilibrium point is at (0,0). The experiment starts with a 90° rotation around the z axis, followed by a forward movement along the x-axis of the Mamba and a lateral movement along its y-axis. The system then maintains this position for 30 s without any user inputs. Produced in MATLAB R2021a.Full size imageTeleoperated sampling of cliffs habitatsPlants growing on Kauaʻi cliffs exhibit a wide morphological variety. For this project, targets ranged from small herbaceous plants such as Euphorbia eleanoriae (plants  More

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