# Boosted Regression Trees Machine Learning Method Improves the brGDGT-Based Climate Reconstruction in Drylands

Lucas Dugerdil, Sébastien Joannin, Odile Peyron, Amy Cromartie, Mary Robles, Yanwu Duan, Xiaozhong Huang, Fahu Chen, Guillemette Ménot

► To cite this version:

Lucas Dugerdil, Sébastien Joannin, Odile Peyron, Amy Cromartie, Mary Robles, et al.. Boosted Regression Trees Machine Learning Method Improves the brGDGT-Based Climate Reconstruction in Drylands. Paleoceanography and Paleoclimatology, 2025, 40 (10), 10.1029/2025PA005214. hal-05331801

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Distributed under a Creative Commons Attribution 4.0 International License
# Paleoceanography and Paleoclimatology®

## RESEARCH ARTICLE

10.1029/2025PA005214

**Key Points:**

* Machine Learning methods reduce confounding effects and error in Branched glycerol dialkyl glycerol tetraether climate calibrations

* Boosted Regression Trees yields better results than Random Forest for both modern and past climate reconstructions

* Machine Learning methods permit accurately predict both temperature (annual or seasonal) and moisture

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

L. Dugerdil,  
lucas.dugerdil@ens-lyon.fr

**Citation:**

Dugerdil, L., Joannin, S., Peyron, O., Cromartie, A., Robles, M., Duan, Y., et al. (2025). Boosted regression trees machine learning method improves the brGDGT-based climate reconstruction in drylands. *Paleoceanography and Paleoclimatology, 40*, e2025PA005214. https://doi.org/10.1029/2025PA005214

Received 9 MAY 2025
Accepted 6 OCT 2025

**Author Contributions:**

**Conceptualization:** Lucas Dugerdil, Sébastien Joannin, Odile Peyron, Guillemette Ménot

**Data curation:** Lucas Dugerdil, Amy Cromartie, Mary Robles, Yanwu Duan, Xiaozhong Huang, Fahu Chen

**Formal analysis:** Lucas Dugerdil, Amy Cromartie

**Funding acquisition:** Sébastien Joannin

**Investigation:** Lucas Dugerdil, Sébastien Joannin, Odile Peyron, Amy Cromartie, Guillemette Ménot

**Methodology:** Lucas Dugerdil, Amy Cromartie

© 2025. The Author(s). This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

<figure><img src="image_2.png" /></figure>

## Boosted Regression Trees Machine Learning Method Improves the brGDGT-Based Climate Reconstruction in Drylands

Lucas Dugerdil¹,² ID, Sébastien Joannin¹ ID, Odile Peyron¹ ID, Amy Cromartie¹,³ ID, Mary Robles¹,⁴ ID, Yanwu Duan⁵ ID, Xiaozhong Huang⁶,⁷ ID, Fahu Chen⁵,⁶,⁸ ID, and Guillemette Ménot² ID

¹University Montpellier, CNRS, IRD, EPHE, UMR 5554 ISEM, Montpellier, France, ²ENS de Lyon, Université Lyon 1, CNRS, UMR 5276 LGL-TPE, Lyon, France, ³Université Côte d'Azur, CNRS, CEPAM, UMR 7264, Nice, France, ⁴Aix-Marseille University, CNRS, IRD, INRAE, CEREGE, Aix-en-Provence, France, ⁵Alpine Paleoecology and Human Adaptation Group, State Key Laboratory of Tibetan Plateau Earth System, Resources and Environment (TPESRE), Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing, China, ⁶Key Laboratory of Western China's Environmental Systems (Ministry of Education), College of Earth and Environmental Sciences, Lanzhou University, Lanzhou, China, ⁷Yunnan Key Laboratory of Plateau Geographical Processes and Environmental Changes, Faculty of Geography, Yunnan Normal University, Kunming, China, ⁸College of Resources and Environment, University of Chinese Academy of Sciences, Beijing, China

## Abstract
Branched glycerol dialkyl glycerol tetraethers (brGDGTs), bacterial membrane lipids, are widely used as temperature proxies. Although these proxies are effective for reconstructing past temperatures, brGDGT-based methods encounter limitation in extreme climate gradients and confounding factors such as salinity and aridity, conditions particularly prevalent in drylands. In Arid Central Asia (ACA), the commonly used linear brGDGT calibration exhibits significant biases, resulting in substantial errors in temperature reconstructions. This study compares two machine learning regression methods, Random Forest (RF) and Boosted Regression Trees (BRT), with traditional linear calibrations, using 761 surface samples from the ACA surface database. It also evaluates an unsupervised machine learning approach based on cluster and weighted combined calibrations. The analyses focuses on the robustness of BRT and RF methods, their effectiveness to reduce biases specific to drylands, and their performance in reconstructing Holocene climate, especially temperature and aridity. The results demonstrate that (a) machine learning methods reduce biases caused by confounding factors in drylands and improve temperature accuracy compared to linear models; (b) among the tested approaches, BRT outperforms RF in climate reconstructions; (c) machine learning enables independent and reliable predictions of both temperature and moisture; and (d) cluster-based calibrations provide additional improvements in specific archive contexts. This new machine learning-based framework increases the reliability of brGDGT-derived climate reconstructions in drylands. Nonetheless, challenges persist due to past environmental fluctuations affecting the study context. Further expansion of surface data sets across a wider range of climates and archive types is essential to strengthen machine learning training and improve model precision.

## Plain Language Summary
Branched glycerol dialkyl glycerol tetraethers (brGDGTs) are lipid molecules produced by bacteria in their cell walls. These biomarkers are preserved in the environment, such as in actual soil or in past sediment. Different brGDGT distributions are observable under different climate and environmental conditions, such as the temperature and the pH. That is why brGDGT distribution is reliably used to reconstruct climate conditions in the past using reliable calibration. However, in drylands such as Arid Central Asia, other factors such as the aridity and the salinity may mitigate the brGDGT reliability. Here, we try to test two machine learning (a study field in artificial intelligence) methods: the Random Forest (RF) and the Boosted Regression Trees (BRT). RF and BRT are both based on regression trees to systematically partition data, but they differ in the training phase. We have shown that, using these biomarkers, machine learning outperforms traditional linear models, and BRT outperforms RF to accurately reconstruct past climate. Moreover, it appears that both temperature and aridity changes may be reconstructed, improving our understanding of past climate conditions in Arid Central Asia.
**Project administration:**

Sébastien Joannin, Odile Peyron,
Fahu Chen, Guillemette Ménot

**Resources:** Mary Robles, Yanwu Duan,
Xiaozhong Huang, Fahu Chen

**Software:** Lucas Dugerdil

**Supervision:** Sébastien Joannin,
Odile Peyron, Guillemette Ménot

**Validation:** Guillemette Ménot

**Visualization:** Lucas Dugerdil

**Writing – original draft:** Lucas Dugerdil

**Writing – review & editing:**

Sébastien Joannin, Odile Peyron,
Amy Cromartie, Mary Robles,
Yanwu Duan, Xiaozhong Huang,
Fahu Chen, Guillemette Ménot

# 1. Introduction

The unpredictable impacts of future anthropogenic climate change on environmental systems, hydrology, and human societies underscore the importance of past temperature reconstructions to better understand the interactions between climate variability and the coupled climate-human-vegetation system (Tierney et al., 2020). This is particularly relevant in drylands like Arid Central Asian (ACA) area, where climate reconstructions are essential for evaluating past and future environmental dynamics. Branched glycerol dialkyl glycerol tetraethers (brGDGTs), lipid molecules derived from bacterial membranes, have become widely used as temperature proxies in continental archives (Rao, Guo, et al., 2020; d’Oliveira et al., 2023). Commonly, 15 distinguishable compounds are measured in brGDGT studies. However, the source organisms responsible for brGDGT production remain partially documented. Yet, only two strains of *Acidobacterium* have been identified as brGDGT producers (Y. Chen et al., 2022), while molecular dynamic simulations favor the physiological plasticity hypothesis (B. D. A. Naafs et al., 2021). Despite uncertainties surrounding their origin, laboratory studies (Martínez-Sosa et al., 2020), simulations (B. D. A. Naafs et al., 2021), and surface sample analyses (De Jonge et al., 2014) have shown that the number of methyl groups on brGDGTs is linearly related to air temperature (Weijers et al., 2007). In addition to temperature, the analysis of brGDGT also provides past pH variations (Guo et al., 2021), salinity changes (H. Wang et al., 2021) and tracking of specific source variations over time (Martin et al., 2019; Zhu et al., 2021). The application of brGDGT-based reconstruction has been extensively globalized (Raberg et al., 2022), and partially used in drylands (Dang, Yang, et al., 2016; Rao, Guo, et al., 2020). BrGDGTs also benefit from excellent preservation through various sample types, including peat bogs (B. Naafs et al., 2017; d’Oliveira et al., 2023), riverine sediments (De Jonge et al., 2015), surface soil samples (C. Chen et al., 2021; Guo et al., 2021; Yang et al., 2014), and lake sediments (H. Wang et al., 2021). In lacustrine sediments, brGDGTs are particularly valuable due to their stability across a wide range of physicochemical conditions, from acidic (Dang, Xue, et al., 2016) to alkaline lakes (Dang, Xue, et al., 2016; Yang et al., 2014), and from freshwater (Dugerdil, Ménot, et al., 2021; Robles et al., 2022) to saline lakes (H. Wang et al., 2021). However, the error in temperature reconstruction remains a major issue, even when using local calibrations (Dang et al., 2018; Yang et al., 2014) or regionally adjusted global models (C. Chen et al., 2021).

Numerous confounding factors (i.e., secondary environmental factors that impact the brGDGT-temperature relationship) were identified worldwide and can partially explain the error in temperature reconstructions. For instance, the seasonality biases the Mean Annual Air Temperature (MAAT) prediction since brGDGT distribution is more associated with warmer periods, that is, the period of higher bacterial production or of not-frozen soil or lake water, by recording a warmer offset than the current MAAT (Deng et al., 2016). To prevent this bias, the mean air temperature of Months Above Freezing (MAF) is commonly used instead of MAAT (Dearing Crampton-Flood et al., 2020). Precipitation via soil water content (Yang et al., 2014) or vegetation via its impact on soil organic matter content and pH (Pérez-Angel et al., 2020) are also ubiquitous biasing factors. Particularly, in arid environments such as the ACA, the aridity is also enhancing brGDGT-temperature biases (Guo et al., 2021). Aridity is mainly inferred by the Aridity Index (AI) defined as the ratio between Mean Annual Precipitation and soil evapotranspiration (Zomer et al., 2022). It was shown that precipitation below 500 mm.yr⁻¹ (which is the case for the main part of the ACA) drastically changes the brGDGT distribution in soil samples (Dang, Yang, et al., 2016). Under semi-to hyper-arid conditions, the bacterial community may change in soil (Guo et al., 2021). Drylands also have a particular soil composition: on arid sandy soil (such as *barkhans*) higher oxygen content could be responsible for this community change (Pei et al., 2021). This shift of soil biocenosis is likely responsible for a brGDGT isomerization variation, enhancing the 6- over the 5-methylated brGDGTs (Duan et al., 2020). Lakes and compact soils (such as *solonchaks*) also suffer from salinity influences, which also lead to high 6- and 7-methyl compounds (H. Wang et al., 2021; Kou et al., 2022). All of these confounding factors specific to drylands mitigate the brGDGT temperature calibrations. In global calibrations, there is an ongoing debate about whether to include or exclude these samples to reduce uncertainty (B. Naafs et al., 2017; Dearing Crampton-Flood et al., 2020). But for past temperature reconstruction in drylands, the brGDGT signal may not be sufficient to disentangle the aridity, alkalinity, and salinity effects on primary temperature controls, except if efforts are carried out to provide specific calibration for confounding factor groups (e.g., specific calibration for fresh/saline or acidic/alkaline samples; C. Chen et al., 2021; Dugerdil, Peyron, Ménot, et al., 2025; Dugerdil, Peyron, Violle, et al., 2025; Dugerdil et al., 2025a, 2025b). One other avenue is to develop new mathematical approaches to improve brGDGT response to climate within particular conditions (Tian et al., 2024; Zhu et al., 2025).
Several palaeoclimate proxies, such as pollen, have followed a development trajectory similar to that of brGDGT-based reconstructions (Telford & Birks, 2005; d'Oliveira et al., 2023). In both cases, a key challenge was the indirect link between proxy (i.e., pollen or brGDGT) and climate, as vegetation and bacterial communities mediate this relationship. Initially, proxies like pollen were used to infer past climate qualitatively, based on ecological indicators (Whittaker et al., 1973). Quantitative reconstructions followed, first correlating pollen abundances or ratios with climate gradients (Birks, 2019), then progressing to more complex approaches including Multiple linear Regressions (MR) and transfer functions (Chevalier et al., 2020). Machine learning approaches, such as BRT, have emerged more recently as powerful tools for pollen-based climate reconstructions by capturing nonlinear and multivariate pollen-climate relationships (Salonen et al., 2014, 2019). Early brGDGT-based reconstructions relied on linear models using indices reflecting the number of methylations (MBT'_{5Me} and internal cyclizations (CBT'), or MR (De Jonge et al., 2014). These brGDGT MR calibrations are similar to earlier pollen-based methods. As with pollen, more advanced statistical techniques, including Bayesian models, have recently been introduced to reduce brGDGT-based temperature errors (Dearing Crampton-Flood et al., 2020; Martínez-Sosa et al., 2021). For these calibrations, improvements have included source-weighted or site-specific calibrations, and adjustments for ecological variability (Liang et al., 2024; Martin et al., 2019; B. Zhao et al., 2021). Clustering the whole calibration data set, is also an enhanced approach by reducing variability within sub-calibration data sets (O'Beirne et al., 2023). While each approach addresses specific issues, machine learning offers a more holistic solution by integrating multiple sources of variability (O'Beirne et al., 2023; Véquaud et al., 2022). Recent developments have demonstrated the effectiveness of machine learning algorithms - such as Gaussian process emulators, Random Forests (RF), and Bayesian deep learning - in improving calibration accuracy by reducing the Root Mean Square Error (RMSE) and minimizing biases linked to pH and aridity (Häggi et al., 2023; Tian et al., 2024; Zhu et al., 2025). In particularly complex regions like the ACA area, combining machine learning regression with cluster-based classification shows strong potential for improving brGDGT-based climate reconstructions across lake, peat, and loess-paleosol archives.

Our study aims to develop a new calibration for drylands by testing the different machine learning approaches and their benefits concerning the brGDGT reliability in this particular context. This study is based on the Arid Central Asian surface Data Base (ACADB) compiled in Dugerdil et al. (2025a, 2025b), which gathers fractional abundances of brGDGTs from 761 surface samples. The linear relationship between the brGDGT distributions and temperature is largely mitigated primarily by salinity and aridity, and secondly by alkalinity and winter precipitation (Dugerdil, Peyron, Ménot, et al., 2025; Dugerdil, Peyron, Violle, et al., 2025; Dugerdil et al., 2025a, 2025b). Using the ACADB, two machine learning regression methods, the RF and the BRT, have been tested and compared to the linear brGDGT-based calibration approach. RF has already been tested on brGDGTs (O'Beirne et al., 2023; Véquaud et al., 2022) and BRT on pollen (Salonen et al., 2014, 2019). As RF already gave promising results on brGDGT calibrations and BRT on pollen calibrations, we compare, here and for the first time, both methods on brGDGTs. Both approaches were tested on three different calibration data sets: the whole ACADB and two sub-datasets determined by unsupervised machine learning using the Fuzzy C-means method in order to track two different brGDGT responses to climate within the ACA. Then, these new calibration data sets and approaches were applied on three key brGDGT Holocene sequences from the Caucasus (western ACA), Altai mountains (central ACA), and Qaidam basin (eastern ACA). Finally, the results were compared to pollen-based climate reconstructions from the same areas. Our study addresses the following research questions.

1. Does the machine learning approach outperform the linear methods (e.g., MBT'_{5Me}, MR and Bayesian calibration)?

2. Which approach, between BRT and Random Forest produces the more robust brGDGT-based past climate reconstructions?

3. Can we use brGDGT to independently reconstruct both temperature and moisture in the past drylands?

4. Is the machine learning approach sufficient to disentangle the biases induced by confounding factors (e.g., aridity, salinity and bacterial community changes) in arid environments?

Recently, the reduction of the calibration uncertainties was led by taking into account the different brGDGT distribution among different sample types (i.e., soil and lacustrine samples); the majority of calibration studies have focused on filtered data sets: only for soil, peat, or lacustrine environments (J. Chen et al., 2017; Dearing Crampton-Flood et al., 2020; Zhu et al., 2025). However, in the present study, we apply machine learning on the full available brGDGT samples (i.e., both soil and lacustrine samples) for several reasons. First, tracking the
<figure><img src="image_3.png" /><figcaption>**Figure 1.** The methodological workflow followed in this study is illustrated from the initial step (input data on the left-hand side) to the final outcomes, which are the multi-proxy climate reconstructions based on both Branched glycerol dialkyl glycerol tetraether and pollen-derived past archives. Each column of boxes corresponds to a specific methodological step. The red boxes represent climate parameters, the gray boxes indicate the surface data set, and the yellow boxes denote the past proxies. The blue and orange items represent the two fuzzy C-means clusters (K1 and K2). Orange arrows highlight the main statistical procedures used in this study. Bullet links show the information that has been processed, while arrows represent the data themselves. Workflow abbreviations: ACA, Arid Central Asia; ACADB, ACA Data Base; AI, Aridity Index; MAAT, Mean Annual Air Temperature; MAF, mean air temperature of Months Above Freezing; MPCOQ, Mean Precipitation of Coldest Quarter; BRT, Boosted Regression Trees; RF, Random Forest and MR, Multiple linear Regression.</figcaption></figure>

source of brGDGTs in palaeoenvironmental archives remains difficult despite numerous efforts (Martin et al., 2019; Martínez-Sosa et al., 2023; Zhu et al., 2021). Then, the sample type-specific calibration is difficult to select on past archives. Moreover, brGDGT sourcing may change over time (Cromartie et al., 2025), and mixed input from in situ and watershed brGDGT production is common and hard to disentangle (Tian et al., 2024; Zhu et al., 2021). It is particularly true in arid environments, as wetlands - from which the brGDGT archives are retrieved - are mostly seasonally changing wetlands, from winter lakes to summer temporary ponds (Dugerdil, Ménot, et al., 2021) or wetlands from endorheic basins (Yapiyev et al., 2017). The pronounced frequencies and impacts of drought also affect wetland water tables and erosion influx in ACA (Zou et al., 2020). In this particular context, brGDGT calibration requires a specific methodological workflow. We also estimate that machine learning may track the nonlinear response from brGDGT to climate, sample type, and confounding factors, due to the nonlinear and multivariate adaptability of approaches based on regression trees (Salonen, Seppä, et al., 2012). Tian et al. (2024) applied a machine learning approach on the full database without sample type distinction, unlike Véquaud et al. (2022), Zhu et al. (2025) and O’Beirne et al. (2023). Finally, our methodological workflow applied on both soil and lacustrine samples (fully described in Figure 1) is enforced by the fact that, in the ACADB, the primary grouping factor on brGDGT variance is salinity and aridity before sample type (Dugerdil, Peyron, Ménot, et al., 2025; Dugerdil, Peyron, Violle, et al., 2025; Dugerdil et al., 2025a, 2025b). pH and salinity are often reported to be important confounding factors (Kou et al., 2022; H. Wang et al., 2021), however, the present study focuses only on the prediction of climate parameters, excluding soil and lake physico-chemical properties.

## 2. Materials and Methods

### 2.1. Study Area

#### 2.1.1. Geographical and Climatic Context

Arid Central Asia (ACA), a region defined by F. Chen et al. (2008), covers a vast area characterized by low precipitation (Figure 2a) and by aridity ranging from semi-to hyper-arid areas (Figure 2b). Elevations range from
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Map of the Arid Central Asian Data Base Branched glycerol dialkyl glycerol tetraether (brGDGT) surface samples on, (a) Mean Annual Precipitation (MAP), (b) Aridity Index (AI) and Mean Annual Air Temperature (c, MAAT). The orange dots indicate the location of the three brGDGT past sequences used in our study: NRX peatland from the Altai range (Rao, Guo, et al., 2020), the XRD loess-paleosol sequence from the Qaidam Basin (W. Sun et al., 2019) and the Vanevan peatland from the Armenian Lesser Caucasus (Robles et al., 2022). Pollen is also available in Vanevan and in two other pollen past sequences: Lake Kanas, located in Altai (Huang et al., 2018) and Lake Hurleg in the Qaidam Basin (Y. Zhao et al., 2007). The elevation map is derived from the SRTM Digital Elevation Model (version 4.1; Jarvis et al., 2008), the AI is sourced from CGIAR (Trabucco & Zomer, 2018), and the MAP and MAAT were extracted from worldclim2.1 (Fick & Hijmans, 2017).</figcaption></figure>

−28 to 4,038 m a.s.l., with an average of 1,600 m. This region encompasses eastward the Caucasus (including the Great and Lesser Caucasus and the Talish Mountains) and southward the Alpine-Himalayan orogenic belt extending through Iran, Afghanistan, and northern India. The central part of ACA, centered around the Touran Basin, encompasses Middle Asia (i.e., Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, and Uzbekistan) and is marked by deserts like Kyzylkum and Karakum, with significant mountain ranges surrounding it, such as the Pamir-Alai Range. The eastern part of ACA is shaped by plateaus formed during the Indo-Asian collision, such as the Tibetan and Mongolian Plateaus, with deserts such as the Taklamakan and the Gobi Deserts. The northern part of ACA is distinct, encompassing the Siberian Basin and the Altai-Sayan Mountains, characterized by different precipitation patterns and vegetation.

The extreme aridity in the region is influenced by multiple factors, including latitude and orographic effects, which explain the unique climate and vegetation patterns found in ACA. MAP is relatively uniform across the
region, averaging low values of approximately 400 ± 140 mm, yr⁻¹. However, seasonal precipitation patterns vary markedly: the western part of ACA is dominated by Mean Precipitation on the Coldest Quarter (MPCOQ) with 65% of the rainfall within the winter, while the eastern regions (such as the Central Asian plateaus and southern Siberia) are dominated by summer precipitation, accounting for up to 87% of the annual total (S. Chen et al., 2024). The climate systems controlling ACA's aridity are complex, with interactions between the Westerly winds, Siberian Highs, and the East Asian Summer Monsoon. These systems influence the region's precipitation patterns, with the south-west experiencing summer-wet conditions and the north-east winter-wet conditions (Figure S1A in Supporting Information S1).

For temperature, MAAT range from -4 to 12°C with significant disparities (Figure 2c). The ACADB covers both warm/mild environments (MAAT > 10°C) in the western ACA (Caucasus, Middle Asia) and colder, continental climates (MAAT < 3°C) in Central Asia (southern Siberia, Mongolian and Qinghai Plateaus). The Touran Basin and the Iran-Afghan area are the warmest, while the Tibetan and Mongolian Plateaus, as well as the Baikal Basin in southern Siberia, are the coldest (Figure 2c). The MAF exhibits greater variability, with warmer periods in Tajikistan and Uzbekistan (13 ± 2.5°C) and cooler conditions in China (7.5 ± 2.7°C), reflecting higher seasonality in Central Asia (Figure S1B in Supporting Information S1). The ACA spatial heterogeneity impacting the MAF-precipitation relationship (i.e., synchronous high precipitation and warm temperature in the west and asynchronous in the east), may mitigate the applicability of brGDGT-based MAF reconstructions.

### 2.1.2. Surface Database Compilation

The Arid Central Asian surface brGDGT Data Base (ACADB, Figure 1, stage 1) includes 22 samples from Armenia (Cromartie et al., 2025), 48 samples from Azerbaijan (Dugerdil et al., 2025a, 2025b), 358 samples from China (Dang et al., 2018; Duan et al., 2020; Dugerdil, Peyron, Ménot, et al., 2025; Dugerdil, Peyron, Violle, et al., 2025; Dugerdil et al., 2025a, 2025b; Guo et al., 2021; Kou et al., 2022; H. Wang et al., 2020; Zang et al., 2018), 48 samples from Iran (Duan et al., 2022), 31 samples from Mongolia (Dugerdil, Joannin, et al., 2021), 20 samples from Russia (De Jonge et al., 2015; Dugerdil, Joannin, et al., 2021; H. Wang et al., 2021), 65 samples from Tajikistan (C. Chen et al., 2021; Dugerdil et al., 2025a, 2025b) and 54 samples from Uzbekistan (Dugerdil et al., 2025a, 2025b; Dugerdil, Peyron, Ménot, et al., 2025; Dugerdil, Peyron, Violle, et al., 2025). We finally append 52 samples from ACA (lacustrines samples from Kazakhstan, Mongolia, and Russia; H. Wang et al., 2021) and 63 samples from global soil databases (B. Naafs et al., 2017; Dearing Crampton-Flood et al., 2020). Most of these samples were already compiled and cleaned by Raberg et al. (2021). The final data set size is 761 samples, of which 560 are soil samples and 201 are lacustrine samples. As only 50% of the data set reports 7-methyl isomer measurements, we removed them from the data set and recalculated the fractional abundances of the 15 remaining compounds. To avoid division by zero, we add 0.00001 to all brGDGT fractional abundances following Zhu et al. (2025). The ACADB data set is publicly available on PANGAEA following Dugerdil et al. (2025a, 2025b).

When temperature and precipitation were available from published studies, these values were selected (Figure 1, stage 2). For missing information, climate parameters were inferred using extrapolated data from GIS databases. Climate data were extracted for each surface sample using GIS R packages *rgdal* (version 1.6-7; Bivand et al., 2015) and *raster* (version 3.6-30; Hijmans et al., 2015), incorporating information from *world-clim2.1* (Fick & Hijmans, 2017) and the extrapolated AI from the *CGIAR* database (version 2; Trabucco & Zomer, 2018). Specifically, the extracted parameters included AI, MAAT, MAF, and MPCOQ. MAF was calculated in R as the mean of monthly temperatures exceeding 0°C for each grid cell. These four climate parameters were selected because they have been shown to be the primary factors explaining both the multivariate climatic space of ACA and brGDGT variability (Dugerdil, Peyron, Ménot, et al., 2025; Dugerdil, Peyron, Violle, et al., 2025; Dugerdil et al., 2025a, 2025b). All data processing and statistical operations in this study were performed with the R language (version 4.2; R Core Team, 2020).

## 2.2. Machine Learning

### 2.2.1. Unsupervised Machine Learning

Using sub-datasets permits establishing more precise calibrations in the past due to the greater similarity between training and predicting data sets (O'Beirne et al., 2023). Similar ecological clusters are used for pollen-inferred BRT reconstructions using biome scores (Robles et al., 2022). Unsupervised machine learning clustering was
performed on surface samples in order to produce these different calibration subsampled data sets (Figure 1, stage 3) following the methodological workflow presented in Martínez-Sosa et al. (2023).

First, the Hopkins H-statistic was used to assess the inherent clustering tendency within the ACADB following Hopkins and Skellam (1954) and O'Beirne et al. (2023). H estimates the probability that a data set originates from a uniform (random) distribution, providing a measure of cluster tendency and the appropriateness of applying clustering algorithms. H is given between zero and one, with values close to zero indicating uniformly distributed data, 0.5 indicating random distribution, and one a well-clustered distribution of the data. Then, Partitioning Around Medoids method was performed to determine the number of relevant clusters, using the cluster package (version 2.1.8; Maechler, 2019). This method is a clustering algorithm that groups data by selecting actual data points as cluster centers, aiming to minimize the dissimilarity between each point and its assigned center. The silhouette analysis, via the get_clust_tendency() function from factoextra package (version 1.0.7; Kassambara & Mundt, 2020) was graphically used to determine this best number of clusters. Afterward, a Fuzzy C-Means Clustering inferred from the e1071 package (version 1.7–16; Meyer et al., 2020) produced these clusters. From the 761 surface samples, we obtained the two clusters, K1 ($n_{K1} = 324$) and K2 ($n_{K2} = 437$), using Fuzzy C-Means Clustering. To address cluster imbalance in the classification, the Synthetic Minority Oversampling Technique (SMOTE) was applied to upsample the smaller cluster, resulting in 437 samples per cluster (Cromartie et al., 2025). This was achieved using the SMOTE() function from the smotefamily package (version 1.4.0; Siriseriwan, 2019).

Finally, we conducted a Multivariate Analysis of Variance (MANOVA) using the manova() function to identify the primary bioclimate parameters driving the variance within the two clusters. Subsequently, univariate ANOVA results for each climate parameter were obtained using the summary.aov() function. Both functions are part of the stats package in the base R software (version 4.4.2; R Core Team, 2020). The calibration resulting from the K1 and K2 sub-datasets was finally compared to the full ACADB data set.

### 2.2.2. Supervised Machine Learning: Classification

To determine the most appropriate cluster calibration (K1 or K2) for each past brGDGT sample (Figure 1, stage 4, lower panel), we employed a methodology similar to that of O'Beirne et al. (2023). A supervised classification model was trained on the 761 samples plus 113 SMOTE synthetic samples, the 15 brGDGT compounds, and the two fuzzy C-means clusters, with 500 decision trees applied using the randomForest() function from the randomForest package (version 4.7–1.1; Liaw, 2018). Then, clusters were predicted from past brGDGT records, and the probability of each cluster was estimated. If the probability of cluster K1 exceeded 0.5, the past sample was assigned to cluster K1; otherwise, it was assigned to cluster K2. We choose Random Forest for classification, as this algorithm has already demonstrated its robustness in the brGDGT classification context (Cromartie et al., 2025; O'Beirne et al., 2023).

### 2.2.3. Supervised Machine Learning: Regression

To reconstruct climate parameters, two supervised machine learning regression methods were compared: Random Forest (RF, Breiman, 2001) and the Boosted Regression Trees (BRT; Salonen et al., 2014; Salonen et al., 2019), on both clusters K1 and K2, and on the global ACADB (Figure 1, stage 4, upper panel). RF and BRT methods are already commonly used to reconstruct climate parameters from past proxies, such as pollen and chironomids (Salonen et al., 2014, 2019; d'Oliveira et al., 2023). While the RF approach were applied to brGDGT fractional abundances to infer biomarker sources (e.g., BIGMaC; Martínez-Sosa et al., 2023) or climate parameters (e.g., FROG; Véquaud et al., 2022), we present here the first brGDGT-based climate reconstructions using BRT. Both methods are based on constructing and aggregating multiple regression trees to improve predictive performance. Each tree is generated from a set of brGDGT samples selected by bootstrapping (Chevalier et al., 2020). The main difference between RF and BRT lies in the tree selection process: in RF, trees are chosen randomly, whereas in BRT, brGDGT samples that are under-represented in tree *n* are less likely to be selected for tree *n*+1. An extensive presentation of the BRT approach in the palaeoclimate context is given in Salonen, Seppä, et al. (2012).

The RF was performed using the randomForest package (version 4.7–1.1; Liaw, 2018), with 500 trees. The BRT was performed with the gbm() function from the gbm package (version 2.2.2; B. Greenwell et al., 2019). The question of the hyper-parameter selection (learning rate, maximum number of trees, interaction depth,
e.g., complexity of each tree, and minimal number of observations per node) can be addressed by trying a range of values and testing the effect on the model performance (Elith et al., 2008). However, over-parametrization of the BRT hyper-parameter may enhance model overfitting (i.e., fitting well only the training data but not the testing data). In this context, we used nested cross-validation to tune the hyper-parameter values. It is a model evaluation technique that involves two loops: an inner loop for hyper-parameter tuning and an outer loop for assessing model performance. It helps prevent overfitting and provides an unbiased estimate of model accuracy (Varma & Simon, 2006). In the present study, the hyper-parameter effect on model performance was performed with the train() function from caret package (version 6.0-94; Kuhn et al., 2020). The calculation time was optimized using parallelization. Then, for each model, the error for each climate parameter is expected to follow a Gaussian distribution. We finally retuned the number of trees using the gbm.perf() function from the gbm package. The selected settings (Table S1 in Supporting Information S1) broadly follow the recommendations of Salonen, Seppä, et al. (2012) and Salonen et al. (2014). For RF, the parameters were tuned following Véquaud et al. (2022).

## 2.3. Statistical Analysis

### 2.3.1. Weighted Combined Models

For each past sequence, we reconstruct the four past climate parameters (AI, MAAT, MAF, and MPCOQ) with RF using the predict() function, and with BRT using the predict.gbm() from the R base and gbm packages. The same random seed was used in order to allow result replicability. Both models were trained from the three calibration data sets (ACADB and the two sub-datasets K1 and K2). Then, for each RF- and BRT-based climate parameter, a weighted combined model was inferred using the K1 and K2 clustering probability estimate determined in Section 2.2.2, to weight the mixed model (Equation 1). These models are named BRT-combined and RF-combined later in the study. If the brGDGT distribution in past sequences is shifting from a cluster to another, this weighted combined model is supposed to fit better the different brGDGT-climate response from the two clusters.

$$CP_{i,j} = \hat{P}_{K1,j} \times \text{BRT}(CP_{i,j})_{K1,j} + \hat{P}_{K2,j} \times \text{BRT}(CP_{i,j})_{K2,j} \quad (1)$$

with CP_i the climate parameter i reconstructed for each sample j by combining the BRT model from cluster K1 weighted by $\hat{P}_{K1,j}$, the probability estimate for clusters K1 and K2, respectively. Finally, the ACADB-based and the weighted combined models are compared.

### 2.3.2. Assessment of the Model Training

The evaluation of the performance of the machine learning training phase is mandatory to select the most efficient reconstructions (Figure 1, stage 5). Coefficient of determination ($R^2$) and RMSE are commonly used to assess the strength and reliability of the proxy-climate calibrations (De Jonge et al., 2014; Martínez-Sosa et al., 2020; Raberg et al., 2021). For machine learning, different ways permit obtaining $R^2$ and RMSE. (a) The self-statistics give model performance by comparing the predicted to observed values on the same training and testing data set (i.e., the full data set). It is a biased and over-optimistic method. (b) Machine learning uses an internal cross-validation process during the step of the regression tree selection. For RF, the internal cross-validation is based on bootstrapping (i.e., the process of data resampling with replacement) through the out-of-bag error estimate, based on 63.2% of the data used in each tree's training set and 36.8% of the data used for the testing set. For BRT, internal cross-validation is produced based on ten k-fold cross-validations (i.e., 90% of the data for training and 10% for the testing set, 10 times without replacement) to tune the model without overfitting by selecting the best number of trees (Hijmans et al., 2017). (c) Although it is assumed that no external cross-validation process is necessary to access the RF and BRT overfitting (Breiman, 2001), we tested an a priori ten k-fold cross-validation process. (d) A nested cross-validation was also tested during the tuning step. Here, we tested these four performance estimations only on the MAAT prediction based on the ACADB calibration data set. The method combining best accuracy and lower time-consumption was, then, extrapolated to models (Table S2 in Supporting Information S1).

The relative importance of brGDGTs compounds in each BRT and RF model may also help to determine the reliability of the model (Elith et al., 2008). This could be evaluated using the permutation importance method (Breiman, 2001). The relative importances were finally scaled from 0 to 100 for comparison between models. To
disentangle the particular effect of each brGDGT compounds on their global importance, the use of partial dependence plots to graphically interpret machine learning output was introduced by Friedman (2001), first for BRT, but it is worthy for all regression trees methods. Basically, this plot highlights the variations in the average predicted value (ŷ) as a specified feature varies over its marginal distribution (Goldstein et al., 2015). The ŷ is calculated for given values of each brGDGT compound, while averaging out the influence of all other compounds. The plot permits to visualize how the predicted climate parameter changes as the values of one compound vary, holding all other compounds constant (Elith et al., 2008). Two-ways partial dependence plots allow to cross the interaction between two brGDGT compounds as heat-maps. Friedman H-statistic permits to quantify the interaction strength between the compounds. It measures how much the effect of one feature depends on another, beyond their individual effects. Here, we used the pdp package (version 0.8.2; B. M. Greenwell, 2017) to produce these plots and statistics.

Then, the spatial autocorrelation of the reconstructed climate parameter was tested for each calibration data set. The calculation of Moran's I (with its p-value) based on the model residuals was undertaken for each method, with the aim of indicating how much the model is incorrectly enhanced by autocorrelation (Telford & Birks, 2005). This was achieved by using the Moran.I() function from the ape package (version 5.8; Paradis et al., 2004). Moran's I values close to -1 indicate perfectly dispersed data, values close to zero indicate random dispersion, and values close to one indicate perfectly autocorrelated data. This statistical value was already used for pollen calibration studies in order to remove spatially autocorrelated calibration data sets (Dugerdil, Peyron, Ménot, et al., 2025). The normal distribution of the residual was also tested using skewness, kurtosis and Shapiro test. Finally, Wilcoxon signed-rank tests were applied to paired BRT and RF R², RMSE, and Moran's I values to assess whether one method significantly outperformed the other under the null hypothesis of no difference.

## 2.4. Palaeoclimate Applications

### 2.4.1. Holocene Records

In order to test the applicability of the machine learning calibration to past reconstructions (Figure 1, stage 6), we selected three open-access available brGDGT Holocene sequences: the Vanevan peat from the Armenian Plateau (Robles et al., 2022), located in the Caucasus (western ACA), the NRX sequence from the Narenxia peatland (Rao, Guo, et al., 2020), located in the Altai Range (center of ACA), and the Xiangride loess-paleosol sequence (XRD; W. Sun et al., 2019) from the Qaidam Basin (eastern part of ACA). The multi-proxy approach is among the most robust methods for assessing the reliability of past climate reconstructions (Dugerdil, Ménot, et al., 2021; Martin et al., 2019): that is why we select for each of these three brGDGT-based climate reconstructions an associated pollen-based reconstruction. Vanevan pollen sequence was retrieved from the same core used for brGDGT study (Robles et al., 2022), but this was not the case for NRX and XRD. The pollen sequence from Lake Kanas, located in Altai (Huang et al., 2018) is only 17 km distant from the NRX brGDGT sequence; Lake Hurleg (Y. Zhao et al., 2007) is about 208 km distant from the XRD section, also within the Qaidam Basin. Both pollen sequences are freely available on https://www.neotomadb.org/. From the raw pollen data, we reconstructed the same climate parameters as the brGDGT-based reconstructions using the BRT method (Salonen et al., 2014). A calibration data set of pollen surface samples from the ACA was used to train the BRT. This data set compiles pollen surface samples within the ACA area (Dugerdil, Peyron, Violle, et al., 2025) after removing aquatic pollen and human impact indicators.

### 2.4.2. brGDGT Indices and Linear Calibrations

As demonstrated in De Jonge et al. (2014), the Roman numerals correspond to the various GDGT structures. The 6-methyl brGDGTs are denoted by an apostrophe after the Roman numerals. To compare machine learning with linear brGDGT-based reconstructions, several calibrations were tested here. The first one is a global soil calibration following De Jonge et al. (2014) with $n = 222$, $R^2 = 0.66$ and RMSE = 4.8°C (Equation 2).

$$MAAT_{DJ}(^{\circ}\text{C}) = -8.57 + 31.45 \times \text{MBT}'_{5\text{Me}} \quad (2)$$

in which MBT'_{5Me is defined by:
$$MBT'_{5Me} = \frac{[Ia] + [Ib] + [Ic]}{[Ia] + [Ib] + [Ic] + [IIa] + [IIb] + [IIc] + [IIIa]} \quad (3)$$

A local calibration based on soil surface samples from Tajikistan were also tested (C. Chen et al., 2021) with $n = 28$, $R^2 = 0.52$ and RMSE = 2.3°C (Equation 4). Equation 4 is based on Equation 2 with a local correction to reduce the offset of the global calibration and better reproduce the Tajikistan current temperatures.

$$MAAT_{Tjk} (^{\circ}\text{C}) = -1.1 + 19.2 \times MBT'_{5Me} \quad (4)$$

From De Jonge et al. (2014), we also applied a multiple linear regression with $n = 222$, $R^2 = 0.68$ and RMSE = 4.6°C (Equation 5). This calibration links MAAT with the fractional abundances of major brGDGTs.

$$MAAT_{mr} (^{\circ}\text{C}) = 7.17 + 17.1 \times [Ia] + 25.9 \times [Ib] + 34.4 \times [Ic] - 28.6 \times [IIa] \quad (5)$$

For the MAF which is tough to reduce seasonal bias in brGDGT production, we applied the linear model developed with a Bayesian approach in Martínez-Sosa et al. (2021) following Equation 6, and two multiple quadratic regressions from Raberg et al. (2021) presented in Equations 7 and 8, with $n = 182$, $R^2 = 0.90$ and 0.91, and RMSE = 2.1 and 1.97°C, respectively. Equation 7 is based on the fractional abundances of each compound over the sum of the compounds with same number of internal cyclization and same methylation position ($FA_{Meth}$), while Equation 8 is based on the fractional abundances of each compound over the sum of the 15 compounds ($FA_{Full}$).

$$MAF_{Bay} (^{\circ}\text{C}) = \frac{MBT'_{5Me} - 0.075}{0.03} \quad (6)$$

$$\begin{aligned} MAF_{Meth.} (^{\circ}\text{C}) = & 92.9 + 63.84 \times [Ib]_{m}^{2} - 130.51 \times [Ib]_{m} - 28.77 \times [IIa]_{m}^{2} - 72.28 \times [IIb]_{m}^{2} \\ & - 5.88 \times [IIc]_{m}^{2} + 20.89 \times [IIIa]_{m}^{2} - 40.54 \times [IIIa]_{m} - 80.47 \times [IIIb]_{m} \end{aligned} \quad (7)$$

$$\begin{aligned} MAF_{Full} (^{\circ}\text{C}) = & -8.06 + 37.52 \times [Ia] - 266.83 \times [Ib]^{2} + 133.42 \times [Ib] \\ & +100.85 \times [IIa']^{2} + 58.15 \times [IIIa']^{2} + 12.79 \times [IIIa] \end{aligned} \quad (8)$$

For the NRX sequence, no MAAT reconstruction is given, only the $MBT'_{5Me}$ index (Equation 3) is used to infer brGDGT-based climate variations (Rao, Guo, et al., 2020). In XRD, the MR soil sample calibrations (Equation 5) is used (W. Sun et al., 2019). In Vanevan, the sediment shifts around 5,000 years cal. BP from a lake to a soil dominant sourcing. Robles et al. (2022) chose to apply Equation 9 ($n = 177$, $R^2 = 0.76$, RMSE = 4.1°C; B. Naafs et al., 2017) on the upper part of the core and Equation 10 on the lower part ($n = 100$, $R^2 = 0.73$, RMSE = 4.3°C; Q. Sun et al., 2011).

$$MAAT_{Naafs} (^{\circ}\text{C}) = -14.50 + 39.09 \times MBT'_{5Me} \quad (9)$$

$$MAAT_{Sun} (^{\circ}\text{C}) = -3.949 + 5.593 \times \text{CBT} + 38.213 \times \text{MBT} \quad (10)$$

in which CBT and MBT are defined by:

$$MBT = \left( \frac{[Ia] + [Ib] + [Ic]}{[Ia] + [Ib] + [Ic] + [IIa] + [IIb] + [IIc] + [IIIa] + [IIIb] + [IIIc]} \right) \quad (11)$$

and

$$\text{CBT} = -\log_{10} \left( \frac{[Ib] + [IIb]}{[Ia] + [IIa]} \right) \quad (12)$$
The Isomer Ratio IR showing the relative proportion of 5- over 6-methyl was presented in De Jonge et al. (2014) following (Equation 13). This ratio is commonly used to monitor alkaline conditions (De Jonge et al., 2014) or bacterial community changes (Liang et al., 2024), similarly to the Community Index (CI) (Equation 14) from De Jonge et al. (2019).

$$IR = \frac{[IIa'] + [IIIa']}{[IIa] + [IIIa] + [IIa'] + [IIIa']}, \quad (13)$$

$$CI = \frac{[Ia]}{[Ia] + [IIa] + [IIIa]}, \quad (14)$$

### 2.4.3. Past Reconstruction Selection

Statistical analyses and tests were used to choose the most relevant model for each past brGDGT sequence. To select the best model between BRT and RF, the performance of the models was evaluated using $R^2$, RMSE and Moran's I. To select the primary and secondary climate parameters, a correlation matrix was used based on corrplot (version 0.92; Wei et al., 2017). To select between the ACADB and weighted combined models, we used the randomTF() function from the palaeoSIG package (version 2.1–3; Telford & Birks, 2011) to statistically evaluate which training model best fits the past brGDGT sequences. The full BRT calibration workflow is easily applicable from GitHub (https://github.com/LucasDugerdil/ACADB_brGDGT_calibrations/) for any past brGDGT sequence. The version 1.0.2 is available on Zenodo (Dugerdil, 2025b).

## 3. Results

### 3.1. Surface Sample Clusters

#### 3.1.1. Cluster Statistical Significance

The Hopkins H-statistic for the ACADB surface samples (based on 15 brGDGT compounds) is 0.9, indicating a strong clustering tendency and the potential to form distinct groups within the data set. Using the Partitioning Around Medoids method, the highest average silhouette width (0.32) is achieved with two clusters. Beyond two clusters, silhouette values decrease (ranging from 0.22 to 0.25; Figure S2 in Supporting Information S1), supporting the conclusion that two clusters best represent the structure of the ACADB data set.

#### 3.1.2. Climate Signal Within Clusters

The Fuzzy C-Means Clustering analysis identified two clusters, labeled K1 ($n_{K1} = 324$) and K2 ($n_{K2} = 437$), which are well centered on the second loading with only a few outliers, primarily along the first loading axis in the multivariate space (Figure 3a). The distribution of sample types within the two clusters is relatively balanced, with 20% of K1 and 35% of K2 samples classified as lacustrine samples. Examining the climatic differences between K1 and K2 (Figure 3b) reveals the most significant variation in AI, with an ANOVA F-statistic of 46.9 and a p-value < 0.001. Next come MAAT ($F = 45.7***$), MPCOQ (20.6***), and MAF (2.3***). Notably, the variance in MAF is similar between K1 and K2, while MPCOQ, AI, and MAAT clearly differentiate the two clusters. For MPCOQ, the K1 and K2 average values are similar, but an important number of sites present high MPCOQ values. The spatial distribution of the clusters further highlights these differences (Figure 3c): both clusters are found throughout the ACA, but with distinct spatial patterns. In the Caucasus, K1 is mainly located in the lowlands (the Ararat steppes in Armenia and the Kura-Araxes Basins in Azerbaijan), while K2 is located at higher elevation in the Lesser and Great Caucasus. In Central Asia, K1 is concentrated in the southern part of the Kyzylkum, Karakum, and Sudunkli warm deserts, as well as in the piedmont steppes, while K2 is found in the northern Kyzylkum, the Kazakh steppes, and the Pamir-Alai Mountains. In Central Asia and southern Siberia, a clear north-west/south-east gradient separates K1 in warmer, drier conditions (Tibetan Plateau, Qaidam Basin, Gobi Desert, and Inner Mongolian steppes) from K2 in cooler, wetter conditions (Tian Shan, Altai, Arkhangai, Khentii mountains, Baikal Basin, and Manchurian steppes). Based on these climatic and spatial differences, we have renamed K1 as K-warm/arid and K2 as K-cold/wet.
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Characteristics of the two sub-datasets obtained by Fuzzy C-mean clustering with (a) the multivariate C-means partitioning results, (b) box plots of four key climate parameters (Aridity Index, AI; Mean Annual Air Temperature, MAAT; Mean Precipitation of Cold Quarter, MPCOQ; and mean air temperature of Months Above Freezing, MAF) and the *F*-statistics for their ANOVA (*** indicates a *p*-value < 0.001), (c) the sample location within the Arid Central Asian area, (d) the Branched glycerol dialkyl glycerol tetraether distribution of fractional abundances for the 5- and 6-methyl compounds, (e) Isomer Ratio versus MBT'_{5Me} and (f) MBT'_{5Me} versus MAAT scatter plots. The two groups are labeled *K-cold/wet* (n_{K1} = 324, royal blue colored) and *K-warm/arid* (n_{K2} = 437, colored in dark orange).</figcaption></figure>
### 3.1.3. brGDGT Distribution Within Clusters

The distribution of fractional abundances between clusters is mainly different for major brGDGT compounds (Figure 3d). For *K-cold/wet*, the dominant compounds are IIa' (≈ 19%), Ia (≈ 18%), IIa (≈ 17%), IIIa' (≈ 10%) and IIIa (≈ 9%); while for *K-warm/arid*, the dominant compounds are IIa' (mean value ≈ 30%), IIIa' (≈ 28%), Ia (≈ 10%), Iib' (≈ 7%) and IIIa (≈ 6%). These different patterns result in a higher representation of the tetramethylated compounds in the *K-cold/wet*, and a dominance of the penta- and hexamethylated compounds for the *K-warm/arid* cluster (Figure S3 in Supporting Information S1). Compounds with low abundance (IIib, IIib', IIic, IIic', IIc, IIc', and Ic) are similar for the *K-cold/wet* and the *K-warm/arid*, while IIa and Ia are higher in *K-cold/wet*, and IIIa' and IIa' are higher in *K-warm/arid*. IIIa, Ib, IIb, and IIb' are similar among the two clusters. The 5-methyls are favored in the *K-cold/wet*, and the 6-methyls are favored in the *K-warm/arid*. This result reveals a clear separation of the IR with *K-cold/wet* between 0.5 and 1, and *K-warm/arid* between 0 and 0.75 (Figure 3e). IR and $MBT'_{5Me}$ are more correlated for *K-warm/arid* ($R^2$ = 0.55) than *K-cold/wet* ($R^2$ = 0.19). Similarly, the relationship between the CI and the IR is higher for the *K-warm/arid* than for the *K-cold/wet* cluster (Figure S4 in Supporting Information S1). The CI and the $MBT'_{5Me}$ themselves are not enough to distinguish the two clusters. About the brGDGT-temperature response, the relationship between $MBT'_{5Me}$ and MAAT is better for the *K-warm/arid* cluster ($R^2$ = 0.35) than for the *K-cold/wet* cluster ($R^2$ of 0.11, Figure 3f).

## 3.2. Machine Learning Regressions

### 3.2.1. Calibration Results

The different ways to assess the model performance were tested on the MAAT reconstructions from ACADB on RF and BRT (Table S2 in Supporting Information S1). The self-statistics are biased and over-optimistic ($R^2$ of 0.95 and 0.97, for RF and BRT, respectively), while the internal cross-validation process (out-of-bag errors for RF and k-fold cross-validation for BRT) is more reliable, with lower $R^2$ and higher RMSE values. The external k-fold and nested cross-validations give similar $R^2$ and RMSE values to the internal ones (external and nested have both $R^2$ of 0.58 for RF, and 0.64 and 0.62 for BRT; internal $R^2$ of 0.58 and 0.63, respectively). As external cross-validation statistics are less time-consuming to obtain and as realistic as the nested ones, we kept them as performance estimators later in this study.

The statistical results of the BRT and RF calibrations for the three different calibration data sets are given in Table 1. For each climate parameter, the best statistical results are highlighted in bold. First, the statistical results are always better for the BRT than for the RF, with higher $R^2$, lower RMSE in most of the cases and Moran's *I* closer to zero. For instance, for MAAT predicted with the ACADB calibration, BRT obtains $R^2$ of 0.64, RMSE of 3.99, and Moran's *I* of 0.30*, while RF obtains $R^2$ of 0.58, RMSE of 4.25, and Moran's *I* of 0.47*. This means that the cross-validation results are weaker for RF with higher error and higher spatial autocorrelation. All statistical results indicate a superior performance for BRT than RF, except for the AI with have slightly lower RMSE for RF than BRT. Results of the Wilcoxon signed-rank tests indicate that Moran's *I* and $R^2$ values of BRT models are significantly higher than those of RF models (*p* < 0.001). No significant difference was found in RMSE (*p* = 0.43). Therefore, BRT obtains better correlation between observed and predicted values, with a lower bias due to spatial autocorrelation than RF. The reconstructed error is, however, broadly similar between the two methods.

Focusing on the BRT results, for the climate parameter reconstructions, statistical strength is higher for temperatures (particularly MAAT with $R^2$ of 0.72 for *K-warm/arid*, 0.64 for ACADB, and 0.34 for *K-cold/wet*) than moisture parameters (for AI, $R^2$ = 0.35, 0.41, and 0.39, while for MPCOQ, $R^2$ = 0.52, 0.46, and 0.23, depending on the calibration data set). Generally, the spatial autocorrelation is higher for the *K-cold/wet* with an average Moran's *I* of 0.35 than the ACADB with an average Moran's *I* of 0.33. The *K-warm/arid* has the lower spatial autocorrelation, with an average value of 0.31. Generally, for all the models and calibration data sets, the higher the determination coefficient, the lower the RMSE, despite a few exceptions (e.g., BRT predictions for AI and MPCOQ).
<caption>**Table 1**</caption>

Statistical Results of the BRT and RF Calibrations for the Four Climate Parameters (AI, MAAT, MAF, and MPCOQ) Based on 15 brGDGT Compounds (i.e., All 5- and 6-Methyls)

<table><thead><tr><th rowspan="2">Climate<sup>a</sup></th><th rowspan="2">Data set</th><th colspan="3">BRT</th><th colspan="3">RF</th></tr><tr><th>R<sup>2</sup></th><th>RMSE</th><th>Moran's I<sup>b</sup></th><th>R<sup>2</sup></th><th>RMSE</th><th>Moran's I<sup>b</sup></th></tr></thead><tbody><tr><td rowspan="3">AI</td><td>ACADB</td><td><strong>0.41</strong><sup>c</sup></td><td><strong>1,330</strong></td><td><strong>0.3</strong>*</td><td>0.40</td><td>1,340</td><td>0.38</td></tr><tr><td>K-cold/wet</td><td>0.39</td><td>1,480</td><td>0.33</td><td>0.37</td><td>1,460</td><td>0.38</td></tr><tr><td>K-warm/arid</td><td>0.35</td><td>1,250</td><td>0.33</td><td>0.34</td><td>1,240</td><td>0.38</td></tr><tr><td rowspan="3">MAAT</td><td>ACADB</td><td>0.64</td><td>3.99</td><td>0.30</td><td>0.58</td><td>4.25</td><td>0.47</td></tr><tr><td>K-cold/wet</td><td>0.34</td><td>4.47</td><td>0.39</td><td>0.32</td><td>4.48</td><td>0.50</td></tr><tr><td>K-warm/arid</td><td><strong>0.72</strong></td><td><strong>3.78</strong></td><td><strong>0.25</strong>*</td><td>0.65</td><td>4.15</td><td>0.44</td></tr><tr><td rowspan="3">MAF</td><td>ACADB</td><td>0.63</td><td>2.48</td><td>0.25</td><td>0.59</td><td>2.61</td><td>0.39</td></tr><tr><td>K-cold/wet</td><td>0.42</td><td>2.62</td><td>0.26</td><td>0.42</td><td>2.61</td><td>0.38</td></tr><tr><td>K-warm/arid</td><td><strong>0.71</strong></td><td><strong>2.43</strong></td><td><strong>0.24</strong>*</td><td>0.66</td><td>2.64</td><td>0.41</td></tr><tr><td rowspan="3">MPCOQ</td><td>ACADB</td><td>0.46</td><td>44.3</td><td>0.48</td><td>0.38</td><td>47.2</td><td>0.64</td></tr><tr><td>K-cold/wet</td><td>0.23</td><td>43.8</td><td>0.44</td><td>0.16</td><td>44.6</td><td>0.60</td></tr><tr><td>K-warm/arid</td><td><strong>0.52</strong></td><td><strong>46.1</strong></td><td><strong>0.43</strong>*</td><td>0.43</td><td>49.5</td><td>0.64</td></tr></tbody></table>

Note. The global ACADB and the two clustered groups (*K-cold/wet* and *K-warm/arid*) are tested by cross-validation, yielding the determination coefficient, Root Mean Square Error, and the Moran's *I* with its *p*-values to determine the residual spatial autocorrelation. <sup>a</sup>The bioclimate parameters are the Aridity Index (AI), the Mean Annual Air Temperature (MAAT), the mean air temperature of Months Above Freezing (MAF), and the Mean Precipitation of Cold Quarter (MPCOQ). Data were extracted from *worldclim2.1* (Fick & Hijmans, 2017) and *CGIAR* (Trabucco & Zomer, 2018). <sup>b</sup>The * displays the Moran's *I* with *p*-values < 0.001. <sup>c</sup>For each climate parameter, the best statistical results are highlighted in bold.

### 3.2.2. brGDGT Importances in Machine Learning Regressions

The brGDGT relative importances to each model are displayed in Figure 4 for BRT (a) and RF (b) and for each climate parameter. For all panels, brGDGT compounds were sorted by average relative importance for the two methods and three calibration data sets (i.e., by order of importance, IIIa, Ia, Ib, IIa', IIa, IIc', IIIc, IIc, IIIb...). First, it appears that a similar rank of importance is found between BRT and RF, but the BRT is more settled on a few dominant compounds, while RF has a more balanced importance among all compounds. For RF, all the compounds have an average importance between 6% and 8%, instead of a few compounds over 8% and the majority below 7% for the BRT (Figure 4c). This means that RF gives balanced importance to all compounds, while BRT gives more importance to a smaller set of predictor. It also shows the specific way of BRT to select regression trees, based on the enhanced likelihood of tree *n+1* to keep important feature from tree *n*.

The brGDGT importance to each machine learning model also depends on the predicted climate parameter: for MPCOQ and AI, compounds without internal cyclization are dominant (IIIa, IIa, Ia, and IIa'), followed by compounds with one (mainly Ib and IIIb'), and two cyclizations (IIc, IIc', and IIIc). Similar trends are observable for temperature parameters, with slightly more importance given to tetramethylated compounds (Ia and Ib), than for moisture parameters. Important variations are also observable among the calibration data set. For instance, the BRT-based MAAT prediction is dominated by Ib and IIIb for the *K-cold/wet*, Ia and IIIc for the *K-warm/arid*, and IIc' and IIIb for the ACADB (Figure S5 in Supporting Information S1). Broadly, the order of relative importance is similar between the ACADB and the *K-warm/arid* cluster, with particular emphasis carried on the IIc', IIIc, and Ia, while these compounds are less important in *K-cold/wet*.

Behind the importance, some particular effect of the compounds may explain their relative importance in the model (Elith et al., 2008). To access that point, the partial dependence plots show how the brGDGT variation influence the model (Figure 8). Here, for the MAAT, it appears that rising tetramethylated compounds gives rising predicted MAAT. It is particularly true for Ib and Ic. Same rising trend is observable for the IIa', IIc' and IIIb', mainly for the *K-warm/arid*, while IIa, IIb, and IIb' yield decreasing MAAT for increasing fractional abundances. The partial dependences of the model to the compounds is generally nonlinear, with particular effect of steep brGDGT fraction abundance variations on their relative importance within the model. It is particularly the case for Ib, IIIb and IIb which handle high relative importances in temperature BRT model (Figure 4a), due to
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Relative importance of each Branched glycerol dialkyl glycerol tetraether (brGDGT) (%) in (a) the Boosted Regression Trees and (b) Random Forest models, according to the permutation importance method (Breiman, 2001). The brGDGT compounds were sorted by average relative importance for both methods and the three calibration data sets. The gray lines correspond to 0%, 5%, 10%, 15%, and 20% of relative importances. Panel C displays the average importance of brGDGT compounds (with the 95% confidence interval) across the three data sets and the four climate parameters.</figcaption></figure>
threshold values in their partial dependences. Some minor compounds have also strong importance due to this threshold effect around zero value (e.g., IIIc, IIc, and IIIb). In Figure 8, panels a2 and b2, the Friedman H-statistic shows the level of overall interaction affecting each compound. For the *K-cold/wet* cluster, Ic, IIa, and IIIc have particular interaction (with *H* above 0.15), while for the *K-warm/arid*, the IIa', IIa, Ia and Ib have strong interaction. Broadly, the higher *H* is also associated to a higher relative importance in the model. Finally, some particular interaction between compounds are displayed in heat-map in panels a3 and b3. Here, we can see how the relation between temperature and the interplay between two compounds is varying.

### 3.2.3. Climate Calibration Test on Surface Data Sets

To detail the calibration performances, the residuals were obtained by external cross-validation (i.e., k-fold cross-validation) on each sample from the different data sets (i.e., 761 samples for the ACADB, 324 for the *K-cold/wet* and 437 for the *K-warm/arid*), and compared to their observed values. The predicted versus observed values and the residuals are displayed for the MAF in Figure S6 in Supporting Information S1 and for MAAT in Figure 5. For the MAAT, the *K-warm-arid* calibration (a3 and b3) gives the best determination coefficient ($R^2$ = 0.72 for BRT and $R^2$ = 0.65 for RF), followed by the ACADB (a1, $R^2$ = 0.64 for BRT, and b1, $R^2$ = 0.58 for RF) and *K-cold/wet* (a2, $R^2$ = 0.34 for BRT, and b3, $R^2$ = 0.32 for RF). Similar trends occur for the MAF, showing slightly better cross-validation performances for the BRT than the RF (Figure S6 in Supporting Information S1). Both MAAT and MAF residuals from machine learning models, show a normal distribution with important kurtosis (values above 4), showing the capacity of machine learning models to accurately fit extreme temperatures (Table S3 in Supporting Information S1). Moreover, the residual distribution against the predicted temperatures (left marginal subplots) evidence no particular deviation of the residuals at extreme temperatures.

Among machine learning models, the residuals are smaller for BRT than RF (this observation explains the RMSE differences between the two methods in Table 1). The range is similar (values between -15 and 13°C for both models trained on the ACADB, Figures 5a1 and b1 and Table S3 in Supporting Information S1). However, the median value is closer to zero for BRT than RF. Especially for the RF, numerous sites display a residual superior to three for MAAT above 10°C and below 0°C. It results in a higher skewness value for RF than BRT (0.26 vs. 0.22).

Regarding the two cluster calibrations, the major difference between the performance is discernible: for the *K-cold/wet* (Figures 5a2 and 5b2), MAAT between -5 and 5°C are accurately predicted, but MAAT upper to 5°C are predicted between 0 and 10, leading to a cooler bias for mild and warm sites. This is consistent with the selection of a particular brGDGT response within this cluster for cold samples prediction. On the opposite, for *K-cold/wet* (Figures 5a3 and 5b3), the residuals are homogenous along the temperature gradient without over-biased prediction for colder sites. It results in better statistics (average, median residuals and skewness about zero). In any cases, these shifts are more pronounced with the RF method than the BRT.

Then, the same approach is tested on brGDGT linear calibrations (i.e., $MBT'_{5Me}$- and MR-based MAAT reconstructions, panel C). The determination coefficients are lower and the calibration errors are higher than machine learning models with $R^2$ = 0.27, RMSE = 6.8°C for $MBT'_{5Me}$-based calibrations from global soil data (De Jonge et al., 2014), $R^2$ = 0.23 and RMSE = 7.3°C for MR calibration from the same data set (De Jonge et al., 2014), and $R^2$ = 0.27 and RMSE = 8.9°C for MR calibration from Tajikistan soils (C. Chen et al., 2021). These high RMSEs are mainly explain by an important residual deviation for cold samples which are predicted warmer (with minimum residuals of about -23 to -20°C for the three calibrations). The difficulties to predict temperature extremes are also observable through the skewness and kurtosis values (closer to zero for the linear calibrations than the machine learning ones), driven by the rareness of predicted extreme temperatures. The residual distribution versus predicted MAAT (right margin subplots in Figures 5c1-5c3), show important residual deviation, mainly for the $MBT'_{5Me}$-based global and MR Tajikistan calibrations, with higher residuals for warmer predicted MAAT.

### 3.2.4. Climate Parameter Selection

At the ACADB scale, AI, MAAT, MAF, and MPCOQ were the sufficient and necessary climate parameters to explain the ACA climate gradient (Dugerdil, Peyron, Ménot, et al., 2025; Dugerdil, Peyron, Violle, et al., 2025; Dugerdil et al., 2025a, 2025b). However, in order to accurately reconstruct past climate parameters from brGDGT
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Observed versus predicted Mean Annual Air Temperature (MAAT) for Boosted Regression Trees (BRT) (a), Random Forest (RF) (b), and linear calibration reconstructions (c). For a1 and b1, the machine learning methods were trained on ACADB, for panels (a2 and b2) on *K-cold/wet* and for panels (a3 and b3) on *K-warm/arid* clusters. The RF and BRT predicted values come from 10 k-fold cross-validation. The linear calibrations are (c1) a global soil-based calibration $MBT'_{5Me}$ (De Jonge et al., 2014), (c2) a multiple linear regression applied on global soils (De Jonge et al., 2014), and (c3) Tajikistan soil multiple linear regression (C. Chen et al., 2021). The residuals between observed and predicted MAAT are displayed at the bottom and right of each panel. The hexagonal bin shows the sample density from gray (only one sample) to dark red (more than 100 samples within the bin). The gray dashed line is the 1:1 reference line, and the blue one shows the regression between observed and predicted MAAT.</figcaption></figure>

past records, it is necessary to verify that the primary and secondary climate parameters are not covariant. To test
the independence between them, linear regressions between them were tested at the three calibration data sets
scale (i.e., for the whole ACADB and for the *K-cold/wet* and *K-warm/arid* clusters, Figure 6). Mainly, the
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Correlation matrix between the four determinant climate parameters in Arid Central Asia, owing to determine the independence between the primary climate parameters and any secondary ones (Salonen et al., 2019). Correlation matrixes were performed on the full data set (a), the sites from the *K-cold/wet* cluster (b) and the sites from the *K-warm/arid* cluster (c). The temperature parameters are the Mean Annual Air Temperature (MAAT) and the mean air temperature of Months Above Freezing (MAF), the moisture parameters are the Mean Precipitation of Cold Quarter (MPCOQ) and the Aridity Index (AI).</figcaption></figure>

statistical results for BRT (Table 1) have shown that the regression was higher for temperature (broadly similar results for MAAT and MAF) than for moisture. For the moisture conditions, MPCOQ and AI are broadly independent for all three data sets ($r \in [0.25; 0.34]$), but the MPCOQ-MAAT correlation is stronger than the AI-MAAT one ($r = 0.57$ vs. $r = -0.27$ for the ACADB, Figure 6a). Both AI and MPCOQ could be reasonability reconstructed, with a slight preference for AI. For temperature, however, MAAT and MAF are not independent (especially for *K-warm/arid* with $r = 0.88$ and ACADB with $r = 0.81$, Figures 6a and 6c). A clear choice between MAAT and MAF must be made as the primary reconstructed climate parameter in the past in each brGDGT archive.

## 3.3. Past Climate Reconstruction

### 3.3.1. Cluster Prediction and Weighted Combined Model in Past Records

The RF classification gives a very reliable estimate, with a confusion matrix reaching an estimated rate of 97.5% for the 874 samples (761 real samples and 113 synthetic samples from SMOTE). For the 437 *K-cold/wet* samples, 425 are well estimated for only 12 false negatives, while for *K-warm/arid*, the method estimates 427 true classes for 10 false negatives. Applied to the past sequences, the clusters are very consistent over time. The two peatland sequences, NRX and Vanevan, are fully composed of *K-cold/wet* (Figures 7a1 and 7b1), while the loess-paleosol sequence of XRD is fully identified as *K-warm/arid* except for one sample dating around 5,600 cal yr BP (Figure 7c1). For all three sequences, the classification generally relies on high probability estimates: for NRX, the probability estimation of the *K-cold/wet* cluster is always above 75% and even above 95% for the last 3,000 years. For Vanevan, only the five oldest samples have a *K-warm/arid* probability estimation above 10%. The oldest part of XRD (i.e., before 4,000 cal yr BP) is more mixed with a *K-cold/wet* cluster probability between 0% and 45%. Therefore, the weighted combined models for NRX and Vanevan are mainly driven by the *K-cold/wet* cluster, while in XRD, it is driven by the *K-warm/arid* cluster.

### 3.3.2. Machine Learning Application in Past Records

In Figure 7, panels a2, b2, and c2, the reconstructions for the BRT model based on ACADB, *K-cold/wet*, and *K-warm/arid* calibration data sets, are shown. For NRX and Vanevan, ACADB, *K-cold/wet*, and the weighted combined model give similar trends, except for slightly higher variability in the reconstructed MAAT for the ACADB calibration. In NRX, the *K-warm/arid* gives opposite reconstruction than the other models with three warmer periods (8,500–7,500, 6,000–5,000 and 2,000–500 cal yr BP), while ACADB, *K-cold/wet* and the weighted combined model produce a warm period between 4,000 and 2,500 cal yr BP. For Vanevan, the *K-warm/arid* provides a broadly similar trend with the other calibration, except between 5,000 and 3,000 cal yr BP. It also produces an important MAAT average offset along the time with warmer reconstruction up to 5°C from 7,500 to 5,000 and from 3,000 to 1,500 cal yr BP. For XRD, the three calibrations are very similar, especially during the
<figure><img src="image_9.png" /><figcaption>Figure 7.</figcaption></figure>
6,000–5,000 cal yr BP period, when the cluster probability is more balanced between the two clusters. During the 7,000–6,000, 5,000–4,000 and 2,000–1,000 cal yr BP periods, the *K-cold/wet* calibration shows lower variability and does not record colder phases.

### 3.3.3. Machine Learning Versus Linear Reconstructions in Past Records

The lower panels of Figure 7 (i.e., a3, b3, and c3) allow comparing the weighted combined model results with the linear calibrations applied to the same sequence. For ease of reading, only the MAAT is displayed here; however, the same process was applied to each climate parameter (Figures S7 and S8 in Supporting Information S1). Mainly, in NRX, the weighted combined model is similar to the $MBT'_{5Me}$ calibration before 4,200 cal yr BP and similar to both $MBT'_{5Me}$ and MR global soil calibrations afterward. In Vanevan, the weighted combined model is similar to the soil calibrations from B. Naafs et al. (2017) and De Jonge et al. (2014), with slightly higher variability. The offset of actual temperature is lower than the MBT/CBT lake and $MBT'_{5Me}$ soil calibrations, but higher than the MR calibration from De Jonge et al. (2014). In XRD, all the calibrations record a Holocene warming trend. The temperature variations are low with the MR calibration, high with the $MBT'_{5Me}$ one and intermediate for the weighted combined model.

### 3.3.4. Relevant Calibration and Climate Parameter Selection

To assess the pollen-based transfer function reliability, the *randomTF()* integrative analysis was developed to track the similarity between the surface calibration data set, the prediction method used, and its result on the past sequence (Telford & Birks, 2011; J. Chen et al., 2017). Since the shape of the data is similar between pollen and brGDGT (i.e., both in fractional abundances), the *randomTF()* can be applied to brGDGT-based BRT machine learning calibrations for all three past brGDGT sequences (Table 2). The brGDGT surface and past data match better for MAF (≈ 0.30), followed by AI (average value of 0.28), MPCOQ (≈ 0.20), and MAAT (≈ 0.19). These results permit to select moisture factor among AI and MPCOQ, and a temperature factor among MAAT and MAF as primary and secondary climate parameters. The MAAT and MAF reconstructions for XRD, and the MPCOQ, AI and MAF reconstructions for Vanevan passed the significance test (i.e., a *randomTF()* value higher than the *p*-value obtained by comparison between the reconstructed parameter and a random variable). Therefore, we choose to reconstruct the MAF and AI for NRX and Vanevan wetlands, and the MAAT and MPCOQ for the loess-paleosol sequence from XRD. In XRD, the ACADB calibration were used, as well as, the AI prediction from NRX, while the MAF in NRX and the AI and MAF from Vanevan were inferred with the weighted combined model. Although, the *randomTF()* invites us to select the MPCOQ instead of the AI in Vanevan, the lower model performances of the *K-cold/wet* cluster (which is dominant in the weighted combined model for Vanevan) for MPCOQ than for AI (Table 1), drives this choice.

## 4. Discussion

This study aims to develop a new machine learning calibration for the ACA, owing to reduce the numerous confounding factors specific to drylands, which dramatically complicate the brGDGT-based palaeothermometer (e.g., aridity, salinity, alkalinity; Duan et al., 2020; Duan et al., 2022; Kou et al., 2022; H. Wang et al., 2021), leading to important errors in temperature reconstruction (Duan et al., 2022; Yang et al., 2014). Integrative statistical approaches were applied (a) to test the best-performing models and parameters and (b) to ease the selection of the most reliable reconstructions in the past. This present study is the continuity of recent efforts carried out to improve palaeoclimate reconstruction calibrations using machine learning (Chevalier et al., 2020;

**Figure 7.** Example of a BRT-weighted combined model based on the clustering probability estimates for two Branched glycerol dialkyl glycerol tetraether past sequences: (a) NRX peatland from the Altai Range (Rao, Guo, et al., 2020), (b) Vanevan peatland from Armenia (Robles et al., 2022) and (c) XRD loess-paleosol sequence from the Qaidam Basin (W. Sun et al., 2019). Only the Mean Annual Air Temperature (MAAT) is displayed on this figure. A blue dot is assigned when the sample is associated with the *K-cold/wet* cluster, while an orange dot shown the *K-warm/arid* association. For each core, the first panel (a1, b1, and c1) presents the probability estimate for each sample to be associated with the *K-warm/arid* (orange area) or *K-cold/wet* (blue area). Then (a2, b2, and c2), the reconstructed MAAT from the Boosted Regression Trees is inferred from the full ACADB (gray line), the *K-cold/wet* (blue line), the *K-warm/arid* (orange line), and the weighted combined model (dark red line). Finally, the last panel (a3, b3, and c3) compares the weighted combined models to the most relevant linear calibration in the literature (De Jonge et al., 2014; B. Naafs et al., 2017; Q. Sun et al., 2011). Actual MAAT is presented with horizontal dashed lines.
<caption>**Table 2**</caption>

Statistical Results for the Significance Test Performed With randomTF(), Designed to Assess the Reliability of the BRT Climate Reconstruction Based on Various Calibration Sets (ACADB and the Dominant Cluster for the Weighted Combined Models), Were Compared to a Transfer Function Trained on Randomly Selected Calibration Sets, Using 999 Permutations

<table><thead><tr><th rowspan="2">Archive name</th><th rowspan="2">Database</th><th rowspan="2">Model</th><th colspan="2">Temperature</th><th colspan="2">Moisture</th><th rowspan="2">Threshold<sup>a</sup></th><th rowspan="2">PCA<sub>1</sub><sup>b</sup><br>(Var. %)</th></tr><tr><th>MAAT</th><th>MAF</th><th>AI</th><th>MPCOQ</th></tr></thead><tbody><tr><td rowspan="2">NRX</td><td>ACADB</td><td>BRT</td><td>0.01</td><td>0.24</td><td>0.41</td><td>0.02</td><td>0.46</td><td>0.84</td></tr><tr><td>ACADB-combined</td><td>BRT</td><td>0.11</td><td>0.24</td><td>0.30</td><td>0.07</td><td>0.45</td><td>0.84</td></tr><tr><td rowspan="2">Vanevan</td><td>ACADB</td><td>BRT</td><td>0.07</td><td>0.21</td><td><strong>0.36</strong>*</td><td><strong>0.43</strong>*</td><td>0.35</td><td>0.64</td></tr><tr><td>ACADB-combined</td><td>BRT</td><td>0.16</td><td>0.33*</td><td><strong>0.37</strong>*</td><td><strong>0.47</strong>**</td><td>0.34</td><td>0.64</td></tr><tr><td rowspan="2">XRD</td><td>ACADB</td><td>BRT</td><td><strong>0.52</strong>*</td><td><strong>0.44</strong>*</td><td>0.15</td><td>0.17</td><td>0.31</td><td>0.81</td></tr><tr><td>ACADB-combined</td><td>BRT</td><td>0.26</td><td>0.32*</td><td>0.08</td><td>0.03</td><td>0.34</td><td>0.81</td></tr></tbody></table>

*Note.* All three archives (NRX, XRD, and Vanevan) are tested. For each climate parameter, the best statistical results are highlighted in bold. <sup>a</sup>This threshold represents the 95% interval values from the 999 permutations of randomly generated transfer functions, that is, climate reconstructions with a proportion of variance exceeding that of 95% of the randomly generated transfer functions (J.Chen et al., 2017). <sup>b</sup>This percentage of variance (denoted as PCA₁) theoretically corresponds to the maximum explainable variance in past brGDGT data.

Dugerdil, Joannin, et al., 2021; O'Beirne et al., 2023; d'Oliveira et al., 2023; Salonen et al., 2019; Véquaud et al., 2022).

## 4.1. Improve brGDGT-Inferred Climate Reconstruction: The Machine Learning Solution

### 4.1.1. Machine Learning Approaches Reduce the Error in Temperature Reconstructions

When considering the ACADB, the residuals for global soil MBT'_{5Me}-based calibration are large (from -24 to 14°C, Figure 5c1), however, the dispersion is well centered on the 1:1 line, with no specific bias on extreme MAATs. On the contrary, for both MR calibrations (Figures 5c2 and 5c3), the residuals from observed MAAT below 0°C and above 10°C range from -25 to -10°C and from 0 to 10; for observed MAAT between 0 and 10°C, residuals range from -10 to 5. These calibrations are therefore more suitable for warm sites and lead to important warmer MAAT predictions for cold and cool sites (C. Chen et al., 2021). While higher errors at cold sites are common in brGDGT calibrations (De Jonge et al., 2014), the magnitude observed in ACA is unusually large. To minimize this bias, the use of MAF rather than MAAT is increasingly recommended (Martínez-Sosa et al., 2021; Raberg et al., 2021). However, the MAF residual analysis for linear, Bayesian and quadratic calibrations produce similar range of bias in colder sites (Figure S6 and Table S3 in Supporting Information S1). Although local calibrations are often recommended as a potential solution (Dang et al., 2018), no significative improvement from the Tajikistan MR is shown in ACA. Temperature errors on extreme values are highlighted when local calibration is applied in a different study area (Dugerdil, Joannin, et al., 2021).

brGDGT-based climate reconstructions from ACA remain largely unreliable, despite efforts to apply a range of calibration approaches (including Bayesian models, MBT'_{5Me}-based regressions, MR, and quadratic MR) along with the use of MAF to mitigate seasonal bias in bacterial production and the comparison of global versus regional calibrations. In this context, performance metrics from the various machine learning models demonstrate a substantial improvement in both reliability (R²) and accuracy (RMSE) of past climate reconstructions in ACA (Figure 5; Table 1). Although these scores remain lower than those achieved by global calibrations (Dearing Crampton-Flood et al., 2020; Raberg et al., 2021), they show a better fit when applied specifically to drylands. These mixed results likely stem from both the regional calibration effect, mainly due to the narrower climate range, which amplifies brGDGT variability relative to climate controls (Dugerdil, Joannin, et al., 2021); and the stronger influence of confounding factors in drylands (Duan et al., 2022; Kou et al., 2022). Nevertheless, both machine learning approaches yield significantly more robust calibrations in ACA, primarily because they capture the multivariate structure of regression trees and the nonlinear behavior of brGDGTs across the extremes of the climate gradient (Salonen et al., 2019). These advantages are particularly pronounced for BRT models (Schonlau, 2005).
4.1.2. Toward the Comprehension of the Particular Bacterial Communities in Drylands

Although cross-validation results indicate that machine learning calibrations consistently outperform linear
models in predictive performance (Figure 5), notable differences in performance persist across calibration data
sets. Surprisingly, among them, the *K-warm/arid*-based calibrations perform better than both the full ACADB
data set and the *K-cold/wet* sub-dataset (Table 1). The *K-warm/arid* and ACADB data sets yield similar *R*² and
RMSE values; however, performance drops markedly for the *K-cold/wet* data set. For example, temperature
reconstructions using BRT yielded *R*² values of 0.72, 0.64, and 0.34, and RMSE values of 3.8, 4.0, and 4.5 for the
*K-warm/arid*, ACADB, and *K-cold/wet* data sets, respectively. Similarly, the temperature–MBT<sup>1</sup><sub>5Me</sub> regression
performs better for the *K-warm/arid* data set (*R*² = 0.35) than for the *K-cold/wet* data set (*R*² = 0.11, Figure 3f).
These results are unexpected, as the brGDGT distribution of the *K-cold/wet* cluster (Figure 3d) closely resembles
that of the global brGDGT database, characterized by high abundances of tetramethylated compounds and
balanced 5- and 6-methyl isomers in hexa-, and pentamethylated compounds (De Jonge et al., 2014). In contrast,
the *K-warm/arid* cluster exhibits lower tetra- and a clear dominance of 6-methyl over 5-methyl brGDGTs, a
pattern typical of drylands (C. Chen et al., 2021). This suggests that the two clusters may reflect distinct bacterial
communities.

This assumption is supported by Guo et al. (2021), who demonstrated that the relationship between temperature and the degree of methylation differs between 5- and 6-methyl brGDGTs in arid environments. The observed dominance of Actinobacteria and Verrucomicrobia in arid-alkaline soils, each with distinct 5- and 6-methyl signatures, may explain the different calibration robustness between the *K-warm/arid* and *K-cold/wet* clusters in capturing climate signals. The Community Index proposed by De Jonge et al. (2019) to track bacterial community changes in brGDGT assemblages is insufficient alone to distinguish the divergent temperature responses (Figure S4 in Supporting Information S1). However, when combined with the Isomer Ratio, it becomes a more powerful indicator of differing methylation responses to soil temperature variations, as recently demonstrated by Liang et al. (2024). Finally, clustering approaches based on Random Forest classification offer a robust framework to determine the dominant bacterial community type in past brGDGT records (Figure 7). This assumption related to different brGDGT response to climate associated to diverse bacterial communities may also be supported by the difference brGDGT importance in machine learning models for the *K-warm/arid* and the *K-cold/wet* clusters (Figure 4).

The BRT model for MAAT is mainly driven by Ia, IIIC, IIc', Ib, IIb, and IIa. Among these, Ia and IIa are the predominant compounds in ACA (Dugerdil, Peyron, Ménot, et al., 2025; Dugerdil, Peyron, Violle, et al., 2025; Dugerdil et al., 2025a, 2025b) and also play a key role in influencing the MBT'_{5Me}-temperature relationship (De Jonge et al., 2014). These compounds are also involved in MR calibrations for drylands (Dugerdil, Joannin, et al., 2021; H. Wang et al., 2016; Yang et al., 2014). Similarly, for moisture calibration (i.e., AI and MPCOQ), and especially for the *K-cold/wet* (i.e., the cluster closest to global humidity and soil condition, Figure 3); IIIa, IIa, IIa', Ib, and Ia are included in the BRT model. These compounds are usually involved in the cyclization ratios such as the CBT', CBT_{5Me} and CBT_{6Me} (De Jonge et al., 2014; Yang et al., 2015), which are generally associated with pH and then, with precipitation (Duan et al., 2022). They are also directly involved in MR calibrations for precipitation in northern Iranian soils (Duan et al., 2022). However, some compounds with low abundance are important in the machine learning models, but not commonly used in brGDGT studies (e.g., IIIC and IIc' in Figure 8). It is important to remember that BRT and RF are not based on linear response from brGDGTs to climate parameters, then, particular nonlinear response and multivariate interactions may explain the BRT and RF performances, rather than comparison with previous linear correlations (Elith et al., 2008).

4.1.3. Unpacking the Machine Learning Black Box: Insights Into brGDGT Interactions

To go further in the understanding on brGDGT importance on the machine learning models, the particular effect
of each compound on the model were explored. Mainly, three questions remains: (a) how to interpret the strong
importance of unexpected compounds (mainly the IIIc and IIIB), (b) why the machine learning models monitored
the brGDGT-response differently between the *K-cold/wet* and *K-warm/arid* subsets, and (c) how these two
questions may help us to understand the particular brGDGT-climate relationship in ACA? First, the BRT models
highlight a strong influence of IIIc and IIIB on the prediction of each climate parameter (Figure 4), with IIIc being
especially important in the ACADB and *K-warm/arid* data sets, and IIIB in the ACADB and *K-cold/wet* cluster,
particularly for temperature. However, both compounds are minor components in the ACADB data set
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Presentation of the different Branched glycerol dialkyl glycerol tetraethers (brGDGTs) effect on the temperature prediction based on Boosted Regression Trees method for the two different sub-datasets: (a) *K-cold/wet* and (b) *K-warm/arid*. In the upper panels (a1) and (b1), the partial dependence plots for all brGDGT compounds are displayed with compounds importance highlighted from red to gray by decreasing importance. In lower panels (a2) and (b2), the two-ways partial dependence plots for IIa versus Ic and IIa versus Ia are given. The red to gray color scale in panels (a1 and b1) refers to the decreasing compound importance from the results of Figure 4. The partial dependence plots show the change in average predicted variable (ŷ), here the Mean Annual Air Temperature (MAAT), over the marginal distribution of each compounds. On the two-ways plot, the ŷ is given in yellow for warmer predicted MAAT and blue for colder one.</figcaption></figure>

(Figure 3d) and in the global brGDGT distribution (De Jonge et al., 2014). At the global scale, neither IIIc nor IIb shows a strong linear relationship with climate parameters (Raberg et al., 2022), and both have been excluded from the revised MBT index commonly used as a temperature proxy (Equation 3). Notably, IIIc is also omitted from the Bayesian calibration of Martínez-Sosa et al. (2021). Second, the importance of IIIc and IIb appears to be dataset-dependent, with substantial variability across the three data sets. For example, IIb ranks second in importance in both the *K-cold/wet* and ACADB data sets, but drops to 12th in the *K-warm/arid* cluster. Additionally, the two clusters exhibit contrasting patterns in the relative importance of tetramethylated compounds and 5-, 6-methyl isomers: in *K-cold/wet*, Ib and IIa are more influential than Ia and IIa', whereas the reverse is observed in *K-warm/arid*.
To assess these points, we evaluated the influence of each brGDGT compound on the average predicted MAAT using BRT models trained separately on the *K-cold/wet* and *K-warm/arid* clusters (Figure 8). The partial dependence plots show that the response of IIIb within the *K-cold/wet* cluster is nonlinear, displaying a threshold-like pattern akin to a presence/absence effect in the surface samples. The samples without IIIb are more likely warm (higher ŷ in Figure 8a1). The same behavior is visible for the IIc within the *K-warm/arid* cluster. These threshold effects help explaining why both compounds exhibit high importance in the models despite their low overall abundance. They also account for the distinct climatic responses observed between the two clusters. In contrast, dominant compounds such as the tetramethylated brGDGTs display a classical positive relationship with warmer temperatures, as previously captured in the MBT<sub>5Me</sub>-based linear calibration (De Jonge et al., 2014). Besides, in BRT models, the tetramethylated compounds also exhibit nonlinear responses, especially for the Ib, which shows a pseudo-threshold about 10% of abundance. It is also noteworthy that a saturation effect appears at high fractional abundances (at 5% for the Ic, 20% for the Ia, 55% for the IIa' in *K-warm/arid*, Figure 8b1).

About the differences between the two clusters, the Ia is more important in the *K-warm/arid* than in the *K-cold/wet* cluster (Figure 4), likely due to a steeper partial dependence within the BRT model. The IIa' is also more important in the *K-warm/arid* model, with steeper rising and a saturation effect at higher fractional abundance. Finally, the interaction between the compounds is also taken into account by the machine learning models (Figures 8a2 and 8b2). For example, warmer predicted temperature is found in the *K-cold/wet* for Ib above 10% and IIa between 5% and 20%, while for *K-warm/arid*, it is the case for Ib between 7% and 9% and IIa between 0% and 5%. The difference appears on the interaction between Ia and IIa. The interaction between IIa and tetramethylated compounds is higher and more complex within the *K-warm/arid* cluster due to the drop in temperature for IIa between 10% and 15%, while for *K-cold/wet*, the IIa is continuously leading to decreasing temperature after IIa above 10%.

The nonlinear effects of brGDGT compounds in machine learning models, along with the complex interactions between compounds, underscore the difficulty of tracking membrane responses in dryland environments. These findings suggest that the specific conditions of ACA may promote distinctive brGDGT assemblages rather than a simple linear relationship with methylation degree. While membrane fluidity can be modeled based on methylation under controlled temperature variations, the interplay of multiple confounding factors in ACA likely leads to more complex membrane compositions (B. D. A. Naafs et al., 2021). The differing interaction effects observed between the two clusters further support the hypothesis of shifts in bacterial community composition in ACA (Guo et al., 2021). This is especially compelling given that both clusters share similar brGDGT signatures across soil and lacustrine samples, ruling out differences in source environment. Although the two clusters span significantly different climate ranges (ANOVA; Figure 3b), there remains substantial overlap, reinforcing the idea that distinct bacterial communities may respond differently to similar climatic conditions. In this context, machine learning not only yields more accurate and lower-error climate reconstructions but also offers valuable insight into the nonlinear and interactive responses of brGDGTs to environmental variables (Hornung & Boulesteix, 2022).

## 4.2. Methodological Perspectives

### 4.2.1. Boosted Regression Trees Versus Random Forest

This study demonstrates that BRT models exhibit better statistical performances compared to RF models (Table 1). It is particularly true for the $R^2$ and Moran's *I*, as indicated by the Wilcoxon signed-rank tests. RF results show higher spatial autocorrelation for their residuals, which mitigates their $R^2$ and RMSE reliability (Telford & Birks, 2005). The outperformance of BRT could be partly explained by the increased importance assigned to dominant brGDGT compounds in BRT, while the brGDGT importance to RF is more evenly distributed (Figure 4c). A similar balanced distribution of major and minor compounds was noted in the RF regression application within FROG (Véquaud et al., 2022). Moreover, the limited dominant brGDGT compounds that contribute to BRT exhibit a stronger association and specificity to climate parameters compared to RF.

BRT also outperforms RF in past climate reconstructions based on other proxies. The pollen-based BRT predictions for temperature and precipitation have shown greater statistical robustness compared to those derived from RF (Robles et al., 2022; d'Oliveira et al., 2023). This is also the case when training BRT and RF from modern chironomids or diatoms (Salonen et al., 2016, 2019). This applies broadly across the tested study area;
however, the outperformance behavior is notably more pronounced in ACA (Table 1). The regression curve for each brGDGT machine learning model, representing the observed versus reconstructed values, is flatter than the 1:1 line (blue segment on Figure 5). It indicates that cold samples are forecasted to be warmer than they are, while warm samples are forecasted to be cooler than they are. It is especially the case for RF, whose residuals on extreme values are higher. This makes sense given the extreme aridity and seasonality ranges of ACA, as BRT seems to be particularly effective for climate extremes by minimizing the maximum bias at the extremes of the climate gradient (Figure S6 in Supporting Information S1 and Salonen et al., 2019). In conclusion, our analysis indicates that for brGDGT data sets, BRT demonstrates greater efficiency than RF in predicting temperature and aridity in ACA. However, it is essential to note that this conclusion holds particularly true in extreme climates and for extensive data sets (i.e., more than 100 samples; Salonen et al., 2019).

### 4.2.2. Climate Parameter Selection

**BRT provides both temperature and moisture reliable reconstructions.** The nonlinear behavior of machine learning calibrations generally allows us to reconstruct both primary and secondary climate parameters (Salonen et al., 2019). Similarly, in ACA, the results show that it is generally possible to use brGDGT distribution to infer two past climate parameters: temperature (i.e., MAAT or MAF) and moisture (i.e., MPCOQ or AI, Table 1, Figure 6). In most cases, AI is more associated with brGDGT regression than MPCOQ (Dugerdil, Peyron, Ménot, et al., 2025; Dugerdil, Peyron, Violle, et al., 2025; Dugerdil et al., 2025a, 2025b). Nonetheless, temperature is not consistently the dominant controlling factor when compared to moisture (Duan et al., 2020; Dugerdil, Joannin, et al., 2021; Guo et al., 2021), despite worldwide surface calibration results demonstrating superior performance for temperature relative to precipitation (Häggi et al., 2023; Lin et al., 2024). Given the collinearity of temperature parameters (MAAT and MAF) and moisture parameters (AI and MPCOQ), a selection among these variables is essential.

**Temperature.** The two studied temperature parameters (i.e., MAAT and MAF) are not independent in surface data sets, even within the two sub-sampled clusters (Figure 6). When reconstructing past temperatures, it is necessary to select between MAAT and MAF. The choice of the primary temperature parameter for machine learning-based climate reconstruction appears to be site-dependent. The surface calibration results are broadly similar for MAAT and MAF at the ACADB scale (similar range of $R^2$, RMSE, and Moran's *I* in Table 1). However, the fit with past data appears to be better for MAF (better *randomTF*() result for MAF in the NRX and Vanevan, Table 2) or for MAAT (e.g., for XRD). The observed differences may be attributed to the site characteristics, including winter temperature, altitude and slope, continentality, and archive type (Deng et al., 2016; Lei et al., 2016). MAAT is the most frequently utilized climate parameter in multi-proxy studies (Dugerdil, Ménot, et al., 2021; d'Oliveira et al., 2023), facilitating comparison among various proxies.

MAF is favored over MAAT depending on the altitude or latitude of the considered record (Dearing Crampton-Flood et al., 2020; Martínez-Sosa et al., 2021), as it is less influenced by the seasonal bias affecting brGDGT production (De Jonge et al., 2014). This consideration depends on the climate context of the study. Seasonality is reduced in tropical areas (Häggi et al., 2023; Pérez-Angel et al., 2020). Conversely, seasonality is pronounced in Arctic contexts (Raberg et al., 2024), in continental areas (Lei et al., 2016), and at high elevations (Deng et al., 2016). The impact of seasonality on brGDGT-based temperature calibration may be biased toward summer temperatures (Dang et al., 2018; Raberg et al., 2024). The effect is also significant in soil-based calibrations (Deng et al., 2016). However, several studies do not record this over-warming of reconstructed temperatures, despite the significance of seasonality in the study area (Lei et al., 2016).

In ACA, seasonality is strong, with different patterns observable along an east-west gradient (Tan et al., 2024). Then, in the ACADB, issues related to continentality and soil samples would enhance the seasonality bias on brGDGT calibrations, thereby favoring the MAF selection over the MAAT. While this holds true for NRX and Vanevan reconstructions, it does not apply to XRD. Even if the seasonality is significant in the Qaidam Basin (W. Sun et al., 2019), our results indicate that MAAT demonstrates greater statistical significance than MAF in XRD. It has been shown that the distribution of brGDGTs does not necessarily correlate with monthly temperature fluctuations (Cao et al., 2018), attributed to low turnover in brGDGT production and deposition in soil samples (Weijers et al., 2011). Additionally, XRD is a loess-paleosol sequence, which may be less affected by seasonality bias compared to lacustrine archives. Moreover, loess-paleosol sequences globally reflect land surface temperature rather than air temperature, which is influenced more by vegetation cover than by seasonality (Lu et al., 2019).
*Moisture.* In drylands, the moisture effect is the primary controlling factor on brGDGT distribution (Lin et al., 2024). In the ACADB, moisture is inferred through both MPCOQ and AI. The surface calibration process yields comparable statistical results for both climate parameters (R², RMSE, and Moran's I, Table 1). However, the correlation between past and surface data (i.e., *randomTF*()) results is generally stronger for AI. Consistent with other studies in drylands that suggest that brGDGT-based precipitation calibrations (Duan et al., 2022; Dugerdil, Joannin, et al., 2021), the AI, which incorporates the influence of soil moisture via potential evapo-transpiration (Trabucco & Zomer, 2018), may yield greater accuracy. The influence of soil water content on the brGDGT methylation process is well documented (Dang, Yang, et al., 2016). Moreover, aridity is primarily attributed to soil water content, with precipitation serving as a secondary factor (W. Sun et al., 2019; C. Chen et al., 2021). Additionally, AI has already been employed as a possible reconstructed climate parameter in drylands (Guo et al., 2021). For precipitation, MPCOQ was tested instead of annual or summer average values, as it was previously identified as the most representative variable to capture both the climatic space and the multivariate brGDGT-climate space in ACA (Dugerdil, Peyron, Ménot, et al., 2025; Dugerdil, Peyron, Violle, et al., 2025; Dugerdil et al., 2025a, 2025b). While this choice is statistically valid at the scale of the entire ACA, it does not hold for its western regions, where monsoonal influence leads to peak precipitation during summer (S. Chen et al., 2024; Tian et al., 2024). In such areas, using summer precipitation rather than MPCOQ may better reflect seasonal precipitation patterns and potentially highlight summer rainfall over the AI as a more relevant secondary climatic factor.

In summary, MAAT calibrations exhibit statistical similarities to MAF for surface calibration but diverge when applied to past archives. Therefore, it is essential to choose the most appropriate climate parameter based on (a) the predominant sample type of the archive (i.e., MAF for lakes and peatlands, MAAT for loess sequences); (b) the climate conditions of the study site (i.e., MAF when seasonality is significant, MAAT otherwise); and (c) the outcomes of the *randomTF()* test. In terms of moisture, the optimal reconstructed climate parameter is the AI in the past.

### 4.2.3. Clustering Performances

The unsupervised classification approach yields highly accurate results, as evidenced by the pronounced grouping behavior of both primary climate parameters (Figure 3b), and predominant brGDGT compounds (Figure 3d) within the *K-warm/arid* and *K-cold/wet* clusters. This method confirms its reliability (Martínez-Sosa et al., 2023). The RF cluster prediction models for unknown samples yield reliable outputs, evidenced by a confusion matrix reaching an estimated rate of 97.5%. This finding aligns with predictions made in Cromartie et al. (2025), thereby affirming the efficiency of RF in cluster prediction from GDGT data (O’Beirne et al., 2023). In the ACADB, similarly to their study, the predictions primarily rely on the predominant brGDGT compounds in the classification, such as high abundances of IIIa’ and IIa’ for *K-warm/arid* (Figure 3d), which are also significant in XRD (W. Sun et al., 2019), and the high abundances of Ia and IIa in *K-cold/wet* as well as in NRX and Vanevan peat sequences. The collection of soil and lacustrine samples in ACADB enhances the reliability of cluster classification by accounting for potential fluctuations in brGDGT sources over time (Cromartie et al., 2025; Robles et al., 2022). O’Beirne et al. (2023) points out that RF prediction is constrained by its inability to extrapolate beyond the values present in the training data sets. However, this limitation is not significant for classification purposes, as the brGDGT distribution range in the training data set exceeds that observed in past archives.

This cluster-based calibration method has demonstrated promising results in past archives by enabling the association of past samples with modern clusters, thereby simplifying the selection of training data sets, a complex yet essential task (d’Oliveira et al., 2023). Due to the inability to extrapolate reconstructed values beyond the training data range (O’Beirne et al., 2023), employing cluster-specific calibration reduces the range of reconstructed values (Figure 7). This observed positive effect is similar to the necessity for local calibrations (C. Chen et al., 2021; H. Wang et al., 2016), given that the brGDGT reconstruction typically overestimates the temperature variation throughout the Holocene in comparison to other proxies (d’Oliveira et al., 2023).

### 4.2.4. Cluster-Based Weighted Combined Models Efficiency

Surprisingly, in our study, the weighted combined models do not dramatically outperform models trained on the full ACADB (half of the times, the weighted combined model is preferred to the full model through *randomTF()*, Table 2). This could be due to the selection of our three testing archives which are poorly mixed in terms of clusters
*K-cold/wet* and *K-warm/arid*, but also because the low calibration performances of cluster *K-cold/wet* mitigate the weighted combined models mainly based on this cluster (Table 1). While Cromartie et al. (2025) demonstrate that employing probability estimates improves the machine learning brGDGT source prediction compared to the grouping method (e.g., Martínez-Sosa et al., 2023), in our study, the application of probability estimates to construct a mixed weighted model is more constrained. The weighted combined model is primarily analogous to one of the cluster-derived models (Figures 7a2, 7b2, and 7c2). The cluster probability estimates exhibit poor mixing, with the dominant cluster frequently influenced by values exceeding 80%, except on the oldest part of sequences. Consequently, the weighted combined model closely resembles the dominant cluster. The weighted combined models for NRX and Vanevan approximate the *K-cold/wet* model, whereas the weighted combined model for XRD aligns more closely with the *K-warm/arid* model. The weighted combined approach could be evaluated using (a) A more mixed system to assess its efficiency (Martin et al., 2019; Zhu et al., 2021), or (b) A model that integrates more than two clusters (O’Beirne et al., 2023).

In any case, weighted combined models, especially trained on a wide-range data set covering several sample types (soil and lacustrine samples), and the wider range of possible climate parameter values within the ACA, permit to filter the likely brGDGT variability in the past fitting the best in the calibration set. A similar approach is proposed by Tian et al. (2024), which used both strength of the Modern Analog Technique (MAT) and the Weighted Average-Partial Least Squares (WAPLS) regression. In their study, the MAT is used to select an optimal calibration data set for each past brGDGT sample. It is similar to our weighted combined model, as the calibration data set for the past sample *i* is based on the k-nearest neighbors for *i* in the global modern database, performed with the MAT instead of the Fuzzy C-mean clustering (Figure 1). Then, the prediction is based on a transfer function, here the WAPLS, instead of BRT or RF, in this present study. For pollen-based climate reconstructions, it has already been shown that BRT can outperform WAPLS, particularly when the data set is sufficiently large, even if the local climate range is not completely covered by the calibration data set (Salonen, Ilvonen, et al., 2012; d’Oliveira et al., 2023; Dugerdil, Peyron, Ménot, et al., 2025). However, weighted combined models provide more reliable predictions than linear calibration across a wide range of palaeoclimate archives (i.e., peatlands, loess-paleosol sequences and lakes; Tian et al., 2024), even though the testing regions are less complex for brGDGT studies than the ACA (Lin et al., 2024).

## 4.3. Accuracy Improvement of Past Climate Reconstructions by BRT Application

### 4.3.1. NRX Peatland

On the NRX record, two calibrations by De Jonge et al. (2014), and the weighted combined-BRT model are compared (Figure 7a). The weighted combined model is more similar to the actual MAAT value than the global soil calibrations. Before 2,000 cal yr BP, the weighted combined model has similar trends than the $MR_{global}$ (with a different offset), but after this period, the BRT gives a trend closer to the $MBT'_{5Me}$-based MAAT calibrations. Especially, the trends diverge significantly between 3,000 and 2,000 cal yr BP with a cooling record in the BRT-weighted combined and the $MBT'_{5Me}$-based models, while the $MR_{global}$ shows a warming trend during this period. Between 7,500 and 6,500 cal yr BP, only the weighted combined reports a warm period.

The MAF BRT-weighted combined calibration is chosen based on the *randomTF()* test (Table 2), as the primary temperature parameter (Figure S8 in Supporting Information S1). This calibration indicates a warming trend during the mid-to late Holocene, consistent with its original publication (Rao, Guo, et al., 2020), and our pollen-based MAF reconstruction from Kanas. The mid-Holocene is characterized by cooler temperatures, resulting in significant vegetation changes, including a lower treeline and the expansion of steppe-forest in the lowlands (Huang et al., 2018). Although contrasting trends may be discussed (D. Zhang & Feng, 2018), the differential climate trends at low- and high-elevation sites require further investigation (Rao, Guo, et al., 2020). Moreover, given that the BRT-weighted combined models for MAAT and MAF exhibit opposite trends between 4,000 and 2,000 cal yr BP, it is necessary to address the potential influence of seasonality on both pollen and brGDGTs.

### 4.3.2. Vanevan Peatland

In the Vanevan record, the lake calibration based on MBT/CBT from Q. Sun et al. (2011) and two $MBT'_{5Me}$-based soil calibrations (De Jonge et al., 2014; B. Naafs et al., 2017) are compared with the BRT-weighted combined
model, as these calibrations were employed in the original study (Robles et al., 2022). The BRT-weighted combined model more closely resembles soil calibrations, exhibiting intermediate values between the MBT'_{5Me}-based models proposed by B. Naafs et al. (2017) and De Jonge et al. (2014). Notably, after 5,000 cal yr BP, the reconstruction of MBT'_{5Me}-based from B. Naafs et al. (2017) closely resembles the BRT-weighted combined model. On the complete sequence, the BRT-weighted combined models provide a more stable MAAT, especially from 10,000–5,000 cal yr BP. Machine learning provides a reconstructed MAAT from the top of the peat that closely aligns with the actual MAAT, similarly to the findings of De Jonge et al. (2014). In contrast, the trend presented by the calibration from B. Naafs et al. (2017) is slightly cooler, while the lake calibration indicates a significantly warmer residual, exceeding 10°C. However, Cromartie et al. (2025) demonstrate that the 5,000 to 3,000 cal yr BP phase is experiencing significant sediment changes, likely attributable to local variations related to Lake Sevan. Furthermore, Robles et al. (2022) indicated that at approximately 4,800 cal BP, a transition occurred from clay lacustrine sediment to organic peat, signifying a distinct change in depositional conditions. The interval from 4,800 to 3,000 cal yr BP is marked by significantly low water levels and the emergence of a fern-dominated local vegetation (Robles et al., 2022), factors that may have impacted the brGDGT signal. RF attempts on this core do not adequately account for sedimentary changes, resulting in inaccurate temperature reconstructions (Cromartie et al., 2025). In accordance with the recommendations of Robles et al. (2022) concerning significant human impact and Cromartie et al. (2025) regarding sedimentary alterations, our efforts have not succeeded in fully eliminating temperature biases in the intricate Vanevan record. Even if the weighted combined model which fits well the Vanevan brGDGT distribution though the *K-cold/wet* sub-dataset, the training data set appears to be deficient in samples that exhibit comparable environmental influences and mixed influx.

### 4.3.3. XRD Loess-Paleosol Sequence

In the XRD record, all calibrations indicate a Holocene warming trend (Figure 7c). However, variations are observed in the MAAT range, the deviation from current MAAT, and the magnitude of millennial fluctuations, particularly during the periods of 5,000–3,000 cal yr BP and from 1,500 to today. The calibration based on MBT'_{5Me} presents an excessively broad range of MAAT, particularly highlighting a significant warming trend from 1,500 cal yr BP to the present. The global soil MR exhibits stability with diminished variability; notably, this calibration does not indicate a distinct warming trend from 7,000 to 4,200 cal yr BP. The MBT'_{5Me}-based calibration presents results comparable to those of the BRT-weighted combined, characterized by reduced variations (especially on the last millennium) and a perfect offset with surface MAAT. Although the sharp transition around 1,500 cal yr BP from cold to warmer conditions (reaching up to 10°C) appears more gradual than suggested by the MBT'_{5Me}-based calibration, the weighted combined model fails to produce a reliable MAAT reconstruction.

In the original study, W. Sun et al. (2019) use the MAAT_{mr} calibration derived from global soils (De Jonge et al., 2014), as they regard this calibration as the most appropriate for the XRD section. This calibration gives a slightly cooling trend, almost steady, from 6,000 to 1,800 cal yr BP, followed by a warming trend for the remainder of the period. Reconstructions from all other calibrations indicate a warming trend from 7,000 to 3,800 cal yr BP, consistent with the BRT application. Over the past 1,800 cal yr BP, all calibrations are consistent, and the BRT application provides a more accurate temperature range with a reduced offset relative to current air temperature. However, brGDGT-based climate reconstructions from loess-paleosol sequences must be approached with caution, as the assumption of synchronous brGDGT and sediment deposition is not always easily validated in this context due to the differential GDGT distribution observed in actual soil profiles (Hägg et al., 2023; Yang et al., 2019). Additionally, diachronic GDGT synthesis linked to plant roots may compromise the reliability of loess-paleosol archives (Huguet et al., 2012).

The moisture reconstructions presented in Figure S7 in Supporting Information S1 present AI and MPCOQ trends reconstructed using the BRT-ACADB calibration. In XRD, a wet event occurs at 4,200 cal yr BP, followed by a prolonged aridification trend during the mid-late Holocene transition, consistent with the Siberian–Mongolian calibration used for the same sequence in Dugerdil, Ménot, et al. (2021). Comparable observations are noted in the speleothems $\delta^{18}$O from the Chinese loess plateau (H. Zhang et al., 2019), particularly in the Huangye and Xianglong caves. XRD may exhibit a stronger monsoon influence at this period. A similar precipitation trend is noted in the Lake Qinghai geochemical and pollen multi-proxy analyses (Ji et al., 2005). Precipitation reconstructions from Hurleg pollen record are also consistent with the brGDGT-based reconstructions from XRD (Y. Zhao et al., 2007).
<figure><img src="image_11.png" /></figure>

**Figure 9.** Presentation of the palaeoclimate reconstructions based on pollen and Branched glycerol dialkyl glycerol tetraether (brGDGT) sequences from Arid Central Asia. From upper panel to the lower, the (a, b) Vanevan peat (pollen and brGDGT from the same Armenian peatland; Robles et al., 2022), two Altai Range sites (c) Kanas pollen (Huang et al., 2018) and (d) NRX brGDGTs (Rao, Guo, et al., 2020) and two Qaidam Basin sequences with (e) Hurleg pollen (Y. Zhao et al., 2007) and (f) XRD brGDGT section (W. Sun et al., 2019). For pollen-based Boosted Regression Trees (BRT) climate reconstructions, the ACADB pollen data set was used for the calibration (Dugerdil, Peyron, Violle, et al., 2025). For the brGDGT-based BRT, the ACADB model and the weighted combined model were trained following the methodological framework summarized in Figure 1. Only the most reliable reconstructions for temperature (a) and moisture (b) is displayed here, that is, the AI and Months Above Freezing (°C) BRT-weighted combined for NRX and Vanevan peatlands, and the MPCOQ (in mm.yr⁻¹) and MAAT (°C) BRT-ACADB for the XRD loess-paleosol sequence.

#### 4.3.4. Holocene Multi-Proxy Reconstructions in ACA

The Holocene climate in ACA, as indicated by limited environmental records, exhibits notable fluctuations, with drier early Holocene conditions than present, followed by a wetter phase in the mid-Holocene, and then a gradual aridification during the late Holocene (W. Sun et al., 2019; Rao, Guo, et al., 2020; Lin et al., 2024). The aridification likely corresponded to a decrease in westerly winds, with significant implications for vegetation and human societies in drylands (Y. Zhao et al., 2007; Huang et al., 2018; Robles et al., 2022). Can similar observations be made based on NRX, Vanevan, and XRD records? The synthesis of the most relevant BRT model, climate parameters (AI or MPCOQ, MAAT or MAF, depending on archives), and calibration (using optimal results from the *randomTF()* function) for the three brGDGT archives are presented alongside the pollen-based BRT reconstruction for the same climate parameters in Figure 9.

*Holocene temperature variations.* Temperature reconstructions (Figure 9a) indicate that both proxies are largely consistent, particularly regarding multi-millennial trends: in Armenia, there is a cooling period from 9,000 to
7,000 cal yr BP, followed by a warming until approximately 4,200 cal yr BP, and then a subsequent cooling, consistent with a warmer mid-Holocene (Herzschuh et al., 2023; Joannin et al., 2014). The significant difference between pollen- and brGDGT-based reconstructed temperatures presented in the original publication is diminished with our methodology, although the mid-Holocene thermal optimum remains lower compared to global Holocene studies (S. Chen et al., 2024), aligning more closely with Asian mid-latitude reconstructions (Herzschuh et al., 2023). Vanevan pollen samples from the last few centuries (2,300–800 cal yr BP) were excluded from the BRT-based reconstruction due to significant human influence on pollen assemblages leading to unexpected warming trend (Robles et al., 2022). In contrast, the brGDGT BRT reconstruction during this period indicates a continuous and slight cooling in MAF. The two MAF reconstructions from Altai present the lowest level of consistency among the three study areas. However, a slight cooling is noted in Altai between 8,200 and 4,500 cal yr BP, succeeded by a gradual and nearly continuous warming trend, in both pollen- and brGDGT-based reconstructions, although the climate trends are not perfectly synchronous. This temperature trend is in lines with δ¹⁸O measurements from several archives from Altai, likely due to the interplay between decreasing summer solar insolation, replaced by higher winter insolation along the Holocene (Rao, Shi, et al., 2020). In Qaidam, the trends of pollen and brGDGT are well aligned, indicating three warm phases occurring between 6,500 and 5,500, 4,200–3,000, and 1,200 to 500 cal yr BP. However, the MAAT range for brGDGTs is notably higher than that of pollen, with MAAT ranges of 5°C and 9°C. Besides, our new calibration efforts reduce this unlikely temperature range compared to previous calibrations (Dugerdil, Joannin, et al., 2021).

*Holocene aridity variations.* Regarding aridity (Figure 9b), arid conditions are observable across all cores and both proxies prior to 8,200 cal yr BP. Subsequently, from 8,200 to 4,200 cal yr BP, an increase in moisture is observed in the three sequences. Diverging trends occur during the two last millennia with continuous humidification in Armenia and Qaidam; whereas an aridification is recorded in the Altai. This trend is consistent with lake levels and diatom assemblages (Rudaya et al., 2008). Slightly wetter conditions compared to the Armenian and Altai reconstructions are evident in the Qaidam prior to 8,200 cal yr BP, likely attributable to variations in monsoon influence in the region (Ji et al., 2005; Y. Zhao et al., 2007). Between 2,000 and 1,000 cal yr BP, brGDGT and pollen-based models exhibit opposing trends in the Altai and Qaidam regions, subsequently aligning once more after 1,000 cal yr BP. It is not clear if this opposition is due to proxy differences or age-depth model variability among archives. Increasing human impact occurring at this period, may also explain this mismatch (Huang et al., 2018; Rudaya et al., 2008). In Vanevan, comparable aridification is noted for both proxies from 4,200 cal yr BP to the present. All these considerations are in lines with global aridity variations over the Holocene in continental Asia (F. Chen et al., 2008; S. Chen et al., 2024).

The observations validated the applicability of brGDGTs as a reliable moisture proxy in past records, as demonstrated by Guo et al. (2021) and Lin et al. (2024). This study enhances our comprehension of moisture evolution in ACA throughout the Holocene (F. Chen et al., 2008), indicating predominantly arid phases during the 4.2 and 8.2 events (S. Wang et al., 2013), along with a trend of increasing precipitation following 8,200 cal yr BP in summer precipitation regions (Tan et al., 2024), including the Caucasus (Joannin et al., 2014).

## 5. Conclusions

In drylands, confounding factors exert a strong influence on the response of brGDGTs to environmental parameters, thereby constraining the accuracy of brGDGT-based climate reconstructions (Guo et al., 2021; Lin et al., 2024). This study employs a surface data set from Arid Central Asia (n = 761) to train machine learning regressions, specifically Random Forest (RF) and BRT, for various clusters identified through unsupervised classification. The research presents a novel method aimed at minimizing errors in brGDGT-based climate reconstructions in drylands. Primarily, it was shown that.

1. Machine learning methods effectively mitigate the influence of confounding factors and bacterial community shifts on brGDGT-based calibrations due to their nonlinear behavior and training on data sets that encompass a broad environmental range. This method also decreases the temperature error relative to linear approaches, particularly at the extremes of the climate gradients.

2. BRT provides more reliable statistical outcomes than RF for climate reconstructions, both at the surface calibration scale and in past archive applications.

3. The brGDGT-based machine learning approach enables the independent prediction of the two main climate factors influencing brGDGT distributions. The choice between MAAT and MAF, or AI and MPCOQ, depends
on the archive type (lake, peat, or loess) and the strength of seasonality. The use of the randomTF() statistical test can help in identifying the most appropriate primary and secondary climate parameters.

4. Cluster-based calibrations enhance reconstructions for archives within specific contexts, as a reduced training data set limits the range of predicted values in past records. Nonetheless, if weighted combined models do not significantly improve the reconstruction of the three evaluated brGDGT archives, it is necessary to assess their performance on archives affected by substantial mixed brGDGT source effects. Cluster-based machine learning can also enhance our understanding of specific brGDGT assemblages in ACA, which are likely related to specific bacterial communities.

The application of machine learning in past records is constrained by the specificity of past brGDGT archive settings, which must identify a range of analogous contexts within the surface training data set. This observation necessitates ongoing efforts to understand the actual behavior of brGDGTs in various environmental contexts. We provide a user-friendly BRT calibration in *R*, following instructions given on the GitHub link: https://github.com/LucasDugerdil/ACADB_brGDGTCalibrations with the first release available and citation from Zenodo (Dugerdil, 2025a).

## Acronyms

<table><tr><td>ACA</td><td>Arid Central Asia</td></tr><tr><td>ACADB</td><td>Arid Central Asia Data Base</td></tr><tr><td>AI</td><td>Aridity Index</td></tr><tr><td>brGDGT</td><td>Branched Glycerol Dialkyl Glycerol Tetraethers</td></tr><tr><td>BRT</td><td>Booted Regression Tree</td></tr><tr><td>IR</td><td>Isomer Ratio</td></tr><tr><td>MAAT</td><td>Mean Annual Air Temperature</td></tr><tr><td>MAF</td><td>mean air temperature of Months Above Freezing</td></tr><tr><td>MAP</td><td>Mean Annual Precipitation</td></tr><tr><td>MBT</td><td>Methylations Branched glycerol dialkyl glycerol Tetraethers</td></tr><tr><td>MPCOQ</td><td>Mean Precipitation of Coldest Quarter</td></tr><tr><td>MR</td><td>Multiple linear Regression</td></tr><tr><td>NRX</td><td>Narenxia peatland</td></tr><tr><td>RMSE</td><td>Root Mean Square Error</td></tr><tr><td>SMOTE</td><td>Synthetic Minority Oversampling Technique</td></tr><tr><td>XRD</td><td>Xiangride loess-paleosol sequence</td></tr></table>

## Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

## Data Availability Statement

The ACADB data set is publicly available on PANGAEA following Dugerdil et al. (2025b). Two *R* scripts are associated with this publication: (a) The ready-to-apply script is available on the following GitHub repository: https://github.com/LucasDugerdil/ACADB_brGDGTCalibrations/ with a first release on Zenodo from Dugerdil (2025a). Here, the different BRT calibrations for MAAT, MAF and AI based on the ACADB, the *K-cold/wet*, the *K-warm/arid*, and the weighted combined models are applied to the XRD loess-paleosol sequence. To be used, it only needs to shape the brGDGT past archive in the same shape as the XRD brGDGT matrix. Then,
Acknowledgments

This research was funded, in whole or in part, by (ANR, Grant ANR-22-CE27-0018). A CC-BY public copyright license has been applied by the authors to the present document and will be applied to all subsequent versions up to the Author Accepted Manuscript arising from this submission, in accordance with the grant's open access conditions. The ENS de Lyon financed the PhD scholarship of L. Dugerdil. Some parts of the manuscript were reformulated with the assistance of a generative AI to improve clarity and readability. We are grateful to *La Tendresse* and *Le BIB* for their precious support. This is an ISEM contribution ISEM 2025-230. We also gratefully acknowledge the thoughtful comments of the two anonymous reviewers and the editor, whose efforts significantly improved the manuscript.

(b) the full script to train the machine learning algorithms and their applications on NRX, Vanevan, and XRD sequences is available on the following GitHub repository: https://github.com/LucasDugerdil/ACADB_brGDGT_full/ and the release 1.0.2 is available on Zenodo (Dugerdil, 2025b).

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