The variability of the SASM was investigated by using an empirical orthogonal function (EOF) decomposition of oxygen isotope data from a network of paleoclimate records and isotope-enabled climate model simulations. The EOF decomposition allows for discrete aspects of monsoon variability to be isolated and displayed as leading modes. A Monte Carlo EOF (MCEOF) was applied to the network of paleorecords, with the Monte Carlo resampling ensuring that uncertainties associated with the age models of the individual paleoclimate records were conserved. This method was originally developed for the analysis of West African lacustrine sediments (Anchukaitis and Tierney, 2013). Since its development, this technique has been applied to a variety of proxy networks, including in South America by Campos et al. (2019) and Novello et al. (2021). For all EOF analyses, the first two modes were considered significant using North's rule (North et al., 1982) and the fact that they aligned with a dynamically and physically plausible interpretation.

The 14 records used in this analysis were derived from raw samples from varied archives of speleothems (n=12), an ice core (n=1), and authigenic calcite in a lake sediment core (n=1). These records were identified as PAR (composed of PAR01 + PAR03), PAL (composed of PAL3 + PAL4), Pumacocha, P00-H1, MV (composed of MV1 + MV3), PIM4, DV2, SBE3 + SMT5, Quelccaya, ALHO6, TM0, Boto (composed of Boto1 + Boto3 + Boto7 + Boto10), JAR (composed of JAR1 + JAR4), and CR1. For each sample, 1000-member ensembles of age models were developed based on a Monte Carlo resampling from a Gaussian distribution of the 1-sigma measurement uncertainty of each age tie point. Each age model ensemble member was linearly interpolated between depth–age points and fit by the depth time series from each proxy sample to establish an ensemble of proxy time series (Deininger et al., 2017; Campos et al., 2019; Novello et al., 2021). In cases where individual samples did not span the entire time period of study, multiple shorter samples were merged to form composite records. Oxygen isotope time series were resampled to annual resolution and truncated to 850–1850 CE, resulting in a 1000-member ensemble of 14 complete records spanning the LM. Each of the 1000 ensemble sets of oxygen isotope records was subsequently decomposed into leading modes of spatial and temporal variability, and the median of the ensemble modes was analyzed in this study (Anchukaitis and Tierney, 2013; Deininger et al., 2017).

The spatial distribution of the proxy archives is shown in Fig. 1, and more detailed information is provided in Table 1. Much of the data used here have been published, with the exception of the MV1 and MV30 samples, which were collected in the Mata Virgem Cave in Brazil (see Azevedo et al., 2019, for site information). Published data were accessed through the National Centers for Environmental Information (NCEI) Paleo Data server (https://www.ncdc.noaa.gov/paleo-search/, last access: 30 January 2022) or through the University of São Paulo Institute of Geosciences. The records used for this analysis have sub-decadal to annual resolution, as determined by the number of isotopic samples available in between U–Th dates that establish record age chronologies. This dating method provides an uncertainty of approximately 1 % at 2-sigma confidence levels, yielding errors on the order of a few years (less than 10 years in the vast majority of samples used in this study). Three records in the network were published with annual resolution (Quelccaya, Pumacocha, ALHO6), determined from visible stratigraphy, and confirmed with radiometric dating where possible (Bird et al., 2011; Thompson et al., 2013; Novello et al., 2016). These records were linearly interpolated to exact calendar years where necessary, with the finalized record duplicated for each ensemble member. For those samples that do not cover the entire LM, composite records were synthesized by merging multiple samples consistent with data in the original publications (indicated in Table 1), and samples with hiatuses were interpolated to ensure a continuous record for analysis.

Samples actively growing upon collection (P00-H1, CR1, SBE3, PIM4) were assigned an age tie point without error to the year of collection at zero depth to anchor the chronology (Anchukaitis and Tierney, 2013). Some age points of the TM0 record were published with multiple samples indicated for a given depth; the employed final dates were calculated as the mean of the samples analyzed. Age models were constructed with strict superposition enforcement. Those age ties with processing errors or dates leading to age reversals were excluded from analysis to ensure superposition of the age chronologies (JAR1, JAR4, MV30). In the Monte Carlo resampling, simulated age tie values that violated superposition were rejected and recalculated. Isotopic measurements excluded from previously published analyses were likewise excluded here (SBE3, PIM4), as were individual data points exceeding 3 standard deviations (MV30). Multiple isotopic measurements from a single depth were averaged to establish one value per depth (PAL3).

Samples that contained hiatuses (SBE3, PIM4) or multiple discontinuous samples (MV1, MV30) had gaps filled after the pre- and post-gap segments underwent ensemble generation. Gap filling proceeded in two steps: (1) a linear interpolation was used to fill gaps in the time series, and (2) the isotopic value for each year of the gap was resampled from a normal distribution centered on the interpolated point from a normal distribution scaled to the average standard deviation of the 30 years before and after the gap. This procedure bridges a gap in the data in order to ensure isotopic time series have common time steps when applying the EOF analysis while also maintaining the intrinsic characteristics of variability present in a given record. As a result of the Monte Carlo age model resampling of the MV1 and MV30 samples, a small number of ensemble members returned samples that overlapped or did not have a gap in data, in which case the samples were merged or taken to be continuous, respectively.

Six of the isotopic records used in this analysis were composited from multiple raw samples (MV, JAR, PAR, SBE3 + SMT5, PAL, Boto). With the exception of the unpublished MV record, this compositing is consistent with the original publications of these records. As in Novello et al. (2021), composite records were formed by merging individual ensemble members using three steps: (1) ensemble members in the period of overlap were fit with a cubic spline function and synchronized to annual resolution, (2) each time series was standardized by its respective mean and standard deviation during the LM, and (3) samples were averaged together to create one time series that was reconstructed by inverting the normalization of the record with the longest coverage during the LM. Finally, records were truncated to 850–1850 CE to cover the LM and linearly interpolated to achieve annual resolution.

Output from two previously published isotope-enabled fully coupled global climate model (GCM) experiments were used to investigate mechanisms associated with climate variability over the LM: (1) the water-isotope-enabled NCAR Community Earth System Model (iCESM; Brady et al., 2019) and (2) the Goddard Institute for Space Studies coupled ocean–atmosphere model (GISS-E2-R; Schmidt et al., 2007, 2014; Colose et al., 2016a, b). In these isotope-enabled simulations, stable oxygen and hydrogen isotopes have been added as tracers of the hydrological cycle, enabling a more direct comparison of model and proxy data and a better understanding of water cycle dynamics. The iCESM was run with 1.9∘×2∘ horizontal resolution and 30 vertical levels. Analyzed simulations were from the isotope-enabled Last Millennium Ensemble project, including full- and single-forcing (volcanic, solar, and orbital) experiments following the CESM Last Millennium Ensemble (iLME, Otto-Bliesner et al., 2016; Brady et al., 2019). The GISS-E2-R model was run at 2∘×2∘ horizontal resolution with 40 vertical levels. We analyzed the simulation from the E4rhLMgTKck experiment (Blake et al., 2018), which contains a full suite of transient external forcings. Both models include forcings selected from the PMIP3 Last Millennium forcing set v1.0 (Schmidt et al., 2011).

The iCESM is known to have a negative isotope bias (Brady et al., 2019), overestimating the strength of the relationship between precipitation and δ18O. This is particularly true at higher rainfall rates, though spatial patterns are consistent with observations, and values are similar to the proxy data (Brady et al., 2019; Stevenson et al., 2019). Isotopes in the GISS-ER2-R are highly correlated with observations but show a weak dependence on changes in temperature and precipitation (Schmidt et al., 2007); the GISS-E2-R reproduces key isotopic features of the South American monsoon (Colose et al., 2016a).

We extracted the leading EOFs from two model-derived data sets that are complementary in their comparison with proxy records of the monsoon domain: one based on spatially continuous data across the full monsoon domain and one using a pseudoproxy experiment (PPE) framework (Smerdon, 2012, 2016). In both cases, the EOFs were based on precipitation-weighted δ18O during DJF, which corresponds to the mature monsoon season when isotopic proxies receive the largest fraction of their total annual precipitation (Fig. 1).

For the spatially continuous EOF approach, data from both the full-forcing ensemble members of the iCESM and GISS-E2-R model and the single-forcing simulations of the iLME using the volcanic, solar, and orbital forcings were used. The ensemble members forced by land use–land cover and greenhouse gas changes do not exhibit significant change in the forcing data sets during the LM and were thus excluded from the analysis.

For the pseudoproxy approach, the iLME full-forcing experiment was used, and a spatial sub-sampling was applied by extracting an ensemble of pseudoproxies from the latitude–longitude grid cells of the climate model simulations corresponding to real-world proxy locations. The use of PPEs as an independent way to evaluate the signal-to-noise ratio statistical profiles of proxy data was based on examples used in past literature (Smerdon et al., 2016; Yun et al., 2021). Randomly generated Gaussian white noise was then added to these sub-sampled time series, effectively scaling the model-simulated isotopic time series to more realistically reflect internal variability of the proxy systems. In our specific experiment, the white noise was used to represent unresolved sub-grid-scale processes (Berner et al., 2017), which constitute the noise inherent to the climate system in both the real world and model simulations. While this representation cannot fully account for the cascading influence of sub-grid-scale processes resulting from external forcings, it does allow the EOF analysis to decompose spatial modes based on a broader representation of multi-frequency (i.e., multi-scale) information as captured by the proxy record. We interpret the PPE as a filter for analyzing the variability of the climate signal in both the models and the network of paleorecords. Following Smerdon (2012), this white noise perturbation was drawn from a Gaussian distribution and added to model-derived pseudoproxy isotopic time series using signal-to-noise ratios (SNRs) of 0.5 and 0.25. Previous PPE studies focused on temperature have found SNR =0.5 to be a realistic estimate (Mann et al., 2007; Smerdon, 2012; Wang et al., 2014). Given the larger variability of precipitation compared to temperature, SNR =0.5 and SNR =0.25 were considered here to be bounding estimates of SNR for hydrological proxies, though further work to understand noise in hydroclimate proxies is important for a more sophisticated hydrological PPE.

Our physical interpretations of the leading MCEOFs are based on modern observations for the DJF season. The upper tropospheric (200 hPa) wind field data are based on ERA5 Reanalysis for the present day (1979–2019; Hersbach et al., 2020). Precipitation station data were extracted from Global Historical Climatology Network (GHCN) (Menne et al., 2012) and supplemented with data obtained from the national weather services of Bolivia, Peru, and Brazil. A time series of seasonal (DJF) precipitation at the site of each proxy record was created based on the median of all stations available within a 2∘ radius. The data period was 1975–2014 for all locations, except for those near the PIM4 site, where 4 years of data are missing (1998, 2002, 2003, 2004). Outgoing longwave radiation (OLR), a commonly employed proxy for tropical convection, was analyzed using the NOAA interpolated OLR data set (Liebmann and Smith, 1996) for the same period as the precipitation data. OLR data for the SACZ region were decomposed using an EOF decomposition and the resulting PC1 correlated in space with the gridded OLR product and precipitation data.

A composite analysis was performed for the MCA (850–1160 CE) and LIA (1489–1850 CE) periods based on both paleoclimatic records and climate model data. The MCA and LIA periods were defined using the Campos et al. (2019) change point analysis, which highlighted major departures in South American hydroclimate. Anomalies were calculated for these periods relative to the LM. Atmospheric circulation and hydroclimate diagnostics of mid-tropospheric vertical velocity (ω500, 500 hPa), precipitation, and precipitation-weighted δ18O of precipitation were analyzed by averaging these variables for the mature monsoon season (DJF) for the three full-forcing ensemble members from the iLME experiment. Proxy composites were calculated during the above time periods from the average of annually interpolated composite records generated for the MCEOF analysis. Statistical significance was calculated using a two-tailed Student t test and evaluated at p≤0.1.

The results of the proxy-based MCEOF analysis are shown in Fig. 2. The magnitude of the MCEOF loadings in the spatial patterns represent the correlation coefficient between the median of the Monte Carlo ensemble of proxy records at those locations and the corresponding principal component (PC) time series for that mode.

The leading mode of isotopic variability explains approximately 24 % of the total variance. This mode is characterized by in-phase isotopic variability across the core monsoon region and is shown in PC1 to vary on centennial timescales. The majority of the proxy records in the region of strong monsoonal convection (the center and western regions of the monsoon domain) vary in phase, while the northeastern and eastern records are negatively correlated with PC1, implying that they vary out of phase (Fig. 2a). The PC time series indicates that records over the southwestern SASM domain exhibited anomalously positive isotopic values during the MCA and anomalously negative values during the LIA, while records to the northeast show opposite isotopic anomalies (Fig. 2a and b).

The second mode explains approximately 12 % of the total variance and exhibits the strongest cluster of loadings in central-eastern Brazil, a region influenced by the SACZ (Fig. 2c). Proxy records that project strongly onto this mode include ALHO6, SBE3 + SMT5, TM0, and DV2, while records over the southern central Andes (Quelccaya and especially Boto) vary out of phase. There is a prolonged negative excursion of PC2 during the core of the LIA (approximately 1550–1750 CE; Fig. 2d). The Boto record, a regional anomaly, loads strongly onto this mode, indicating a strong local response inversely correlated with spatiotemporal dynamics that are primarily dominant in southeastern Brazil.

To further illustrate the application of isotope-enabled climate models for diagnosing past climate dynamics, we analyze spatial anomalies of three diagnostic variables during the MCA and LIA periods relative to the full LM. The centennial-scale departures from the mean state during these periods are observed in both individual records across the monsoon basin and extracted from the network by means of the MCEOF analysis as well as documented in the CESM LM ensemble experiments (Otto-Bliesner et al., 2016). Here we employ model diagnostics from the iLME full-forcing simulation ensemble average (n=3) to examine dynamical changes associated with hydroclimatic perturbations observed during these time periods. During the MCA, upward motion in the mid-troposphere (500 hPa) is reduced over the tropical Andes, Peruvian Amazon, and central Brazil and in the monsoon trough region (South Atlantic Convergence Zone; Fig. 5a). Anomalies during the LIA are roughly opposite, with enhanced vertical motion over the Amazon basin and central Brazil and increased rising motion along the southwestern margin of the South Atlantic Convergence Zone (Fig. 5b). These results support the hypothesis of a weak (strong) SASM during the MCA (LIA) and an adjustment in the downstream isotopic records. The SACZ axis was displaced to the southwest during the LIA rather than experiencing a stationary enhancement of convective activity (Novello et al., 2018).

Isotopic changes during the MCA and LIA are simulated well in iCESM as far as the observed spatial pattern across SA is concerned (Fig. 5c and d), although the amplitude of the anomalies is lower in iCESM compared to the paleorecord (circles overlaid on the model-simulated contours). The anomalies seen in the paleorecord during the MCA and LIA give more insight into the isotopic variability of the SASM during these periods than the model simulations. The MCA was a period of overall positive δ18O anomalies as seen in both the model and paleorecords, especially over the western Amazon, Andes, and downstream monsoon records. The Boto record stands out as a regional anomaly characterized by more negative values during the MCA (Fig. 5c). As discussed above, the isotopic signal at this distal site provides a challenge for the model to capture correctly, highlighting the value of increased observational studies to better understand regional variability in isotopic composition. The LIA period on the other hand shows a clear east–west dipole of δ18O anomalies in both the proxies and model (Fig. 5d), reminiscent of EOF1 and consistent with the large departure in PC1 during this time. Strong isotopic enrichment of heavy isotopes is observed over northeastern Brazil and associated with enhanced subsidence and reduced precipitation. Negative isotopic anomalies over the Andes are associated with enhanced upstream convection and high rainfall rates, while depleted isotopic anomalies in the downstream monsoon region are associated with enhanced local convection (Fig. 5b). Notably, significant precipitation anomalies during the MCA and LIA (Fig. 5e and f) are primarily located in the northern (upstream) monsoon region and are coincident with changes in vertical motion but not local δ18O changes. Instead, the isotopic signals are displaced downstream of the largest changes seen in vertical motion. This supports our interpretation of changes in oxygen isotopes in tropical precipitation being dominantly controlled by processes associated with deep tropical convective activity upstream of the paleorecord archives. While this study does not decompose convective processes at play, satellite observations have identified air mass trajectory history, continental precipitation recycling, and convective intensity as key processes linked to deep convection that influence δ18O of precipitation in the austral summer (Samuels-Crow et al., 2014; Vimeux et al., 2021).