ALBERT

Description: Probabilistic spatial reconstructions of past climate states are valuable to quantitatively study the climate system under different forcing conditions because they combine the information contained in a proxy synthesis into a comprehensible product. Unfortunately, they are subject to a complex uncertainty structure due to complicated proxy–climate relations and sparse data, which makes interpolation between samples difficult. Bayesian hierarchical models feature promising properties to handle these issues, like the possibility to include multiple sources of information and to quantify uncertainties in a statistically rigorous way. We present a Bayesian framework that combines a network of pollen and macrofossil samples with a spatial prior distribution estimated from a multi-model ensemble of climate simulations. The use of climate simulation output aims at a physically reasonable spatial interpolation of proxy data on a regional scale. To transfer the pollen data into (local) climate information, we invert a forward version of the probabilistic indicator taxa model. The Bayesian inference is performed using Markov chain Monte Carlo methods following a Metropolis-within-Gibbs strategy. Different ways to incorporate the climate simulations into the Bayesian framework are compared using identical twin and cross-validation experiments. Then, we reconstruct the mean temperature of the warmest and mean temperature of the coldest month during the mid-Holocene in Europe using a published pollen and macrofossil synthesis in combination with the Paleoclimate Modelling Intercomparison Project Phase III mid-Holocene ensemble. The output of our Bayesian model is a spatially distributed probability distribution that facilitates quantitative analyses that account for uncertainties.

Description: While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter estimation. To overcome the challenges, we introduce a strongly regularized posterior by normalizing the likelihood and by imposing physical constraints through priors of the parameters and states. We investigate joint parameter-state estimation by the regularized posterior in a physically motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate reconstruction. The high-dimensional posterior is sampled by a particle Gibbs sampler that combines a Markov chain Monte Carlo (MCMC) method with an optimal particle filter exploiting the structure of the SEBM. In tests using either Gaussian or uniform priors based on the physical range of parameters, the regularized posteriors overcome the ill-posedness and lead to samples within physical ranges, quantifying the uncertainty in estimation. Due to the ill-posedness and the regularization, the posterior of parameters presents a relatively large uncertainty, and consequently, the maximum of the posterior, which is the minimizer in a variational approach, can have a large variation. In contrast, the posterior of states generally concentrates near the truth, substantially filtering out observation noise and reducing uncertainty in the unconstrained SEBM.

Description: Studying past climate states is important to understand climate changes and climate variability on centennial to orbital timescales, to analyze the reaction of the Earth system to large-scale changes in external forcings, and to identify physical and biogeochemical processes that drive these changes. It improves not just the understanding of the climate system but can also lead to more accurate projections of future climate conditions. As the instrumental record is restricted to approximately the last 150 years, paleoclimatology has to rely on indirect observations of climate variables, so-called proxy data. Examples are isotope compositions in ice cores, pollen counts from lake sediment records, and geochemical indices measured in marine sediment cores. In addition, numerical Earth system models can run simulations with adjusted boundary conditions to test their ability to reproduce past climate states and to study mechanisms which control them. Probabilistic spatial or spatio-temporal reconstructions of past climate states, known as climate field reconstructions, are an important tool to quantitatively study the climate system under different forcing conditions because they combine the information contained in a proxy synthesis in a comprehensible product. Unfortunately, they are subject to a complex uncertainty structure due to complicated proxy-climate relations and sparse data, which makes interpolation between samples difficult. Therefore, advanced statistical methods are required which are robust under sparse and noisy data. In this thesis, Bayesian hierarchical models are developed for spatial and spatio-temporal reconstructions from terrestrial proxy networks. The focus is on pollen and macrofossil records, which provide information on the past vegetation composition and indirectly on past temperature and precipitation distributions. Bayesian hierarchical models feature promising properties for climate field reconstructions like the possibility to include multiple sources of information and to quantify uncertainties in a statistically rigorous way. To interpolate between the proxy samples, this study combines geostatistical and data assimilation methods. While data assimilation techniques facilitate the use of physically consistent estimates of past climate states on regional scales provided by Earth system models, geostatistical methods are required to account for the small number of available state-of-the-art simulations and potentially large biases in the produced climate states. Bayesian inference is performed using Markov chain Monte Carlo methods following a Metropolis-within-Gibbs strategy. The Bayesian frameworks produce spatially or spatio-temporally distributed probability distributions that facilitate quantitative analyses which account for uncertainties. The first application of this study is a reconstruction of European summer and winter temperature during the mid-Holocene using a published pollen and macrofossil synthesis in combination with a multi-model climate simulation ensemble from the Paleoclimate Modelling Intercomparison Project Phase III. To transfer the pollen and macrofossil data into climate information, a forward version of the probabilistic indicator taxa method is applied. Different ways to incorporate the climate simulations in the Bayesian reconstruction framework are compared using identical twin and cross-validation experiments. The spatial reconstruction features dipole structures with warming in Northern Europe and cooling in Southern Europe in concordance with previous results from the literature. The reconstruction performs well in cross-validation experiments and exhibits a reasonable degree of spatial smoothing. In a second application of the spatial reconstruction framework, summer temperature and mean annual precipitation during the Last Glacial Maximum in Siberia are reconstructed. A compilation of local reconstructions from pollen samples, provided by the Polar Terrestrial Environmental Systems Division at the Alfred-Wegener-Institute, is combined with the Last Glacial Maximum multi-model ensemble from the Paleoclimate Modelling Intercomparison Project Phase III. The reconstruction features a strong summer cooling in the mid latitudes but only moderate cooling in high latitudes perhaps due to the impact of lower sea levels. Our findings provide new insights into explanations for the absence of a Siberian ice sheet during the last Glacial. To understand the climate evolution from the Last Glacial Maximum to the mid-Holocene, this study develops a data-driven Bayesian hierarchical model for reconstructing the spatio-temporal temperature evolution during the Last Deglaciation on continental scales. Eurasia is chosen as reconstruction domain because more proxy records are available compared to other continents. The Last Deglaciation features millennial-scale trends with a shift from Glacial to Interglacial climate conditions and additional abrupt climate changes. Therefore, a statistical model is required which can recover temporal and spatial non-stationarities. The Bayesian hierarchical model is tested in a controlled environment using pseudo-proxy experiments with a reference climate simulation. These experiments show that the model is recovering non-linear millennial-scale trends with high accuracy and abrupt climate changes are detected even though the magnitude of events tends to be slightly underestimated. Thus, the Bayesian hierarchical model is well-suited for future applications with new and existing proxy syntheses.

Description: Comparing temporal and spatial vegetation changes between reconstructions or between reconstructions and model simulations requires carefully selecting an appropriate evaluation metric. A common way of comparing reconstructed and simulated vegetation changes involves measuring the agreement between pollen- or model-derived unary vegetation estimates, such as the biome or plant functional type (PFT) with the highest affinity scores. While this approach based on summarising the vegetation signal into unary vegetation estimates performs well in general, it overlooks the details of the underlying vegetation structure. However, this underlying data structure can influence conclusions since minor variations in pollen percentages modify which biome or PFT has the highest affinity score (i.e. modify the unary vegetation estimate). To overcome this limitation, we propose using the Earth mover's distance (EMD) to quantify the mismatch between vegetation distributions such as biome or PFT affinity scores. The EMD circumvents the issue of summarising the data into unary biome or PFT estimates by considering the entire range of biome or PFT affinity scores to calculate a distance between the compared entities. In addition, each type of mismatch can be given a specific weight to account for case-specific ecological distances or, said differently, to account for the fact that reconstructing a temperate forest instead of a boreal forest is ecologically more coherent than reconstructing a temperate forest instead of a desert. We also introduce two EMD-based statistical tests that determine (1) if the similarity of two samples is significantly better than a random association given a particular context and (2) if the pairing between two datasets is better than might be expected by chance. To illustrate the potential and the advantages of the EMD as well as the tests in vegetation comparison studies, we reproduce different case studies based on previously published simulated and reconstructed biome changes for Europe and capitalise on the advantages of the EMD to refine the interpretations of past vegetation changes by highlighting that flickering unary estimates, which give an impression of high vegetation instability, can correspond to gradual vegetation changes with low EMD values between contiguous samples (case study 1). We also reproduce data–model comparisons for five specific time slices to identify those that are statistically more robust than a random agreement while accounting for the underlying vegetation structure of each pollen sample (case study 2). The EMD and the statistical tests are included in the paleotools R package (https://github.com/mchevalier2/paleotools, last access: 3 May 2023).

Description: How fast the Northern Hemisphere (NH) forest biome tracks strongly warming climates is largely unknown. Regional studies reveal lags between decades and millennia. Here we report a conundrum: Deglacial forest expansion in the NH extra-tropics occurs approximately 4000 years earlier in a transient MPI-ESM1.2 simulation than shown by pollen-based biome reconstructions. Shortcomings in the model and the reconstructions could both contribute to this mismatch, leaving the underlying causes unresolved. The simulated vegetation responds within decades to simulated climate changes, which agree with pollen-independent reconstructions. Thus, we can exclude climate biases as main driver for differences. Instead, the mismatch points at a multi-millennial disequilibrium of the NH forest biome to the climate signal. Therefore, the evaluation of time-slice simulations in strongly changing climates with pollen records should be critically reassessed. Our results imply that NH forests may be responding much slower to ongoing climate changes than Earth System Models predict.

Description: During the last deglaciation (∼19–11 ka before present), the global mean temperature increased by 3–8 K. The concurrent hydroclimate and land cover changes are not well constrained. Here, we use a pollen database to quantify global‐scale vegetation changes during this transitional period at orbital (∼104 years) and millennial timescales (∼103 years). We focus on the proportion of tree and shrub pollen, the arboreal pollen (AP) fraction. Temporal similarities over long distances are identified by a paleoclimate network approach. At the orbital scale, we find coherent AP variations in the low and mid‐latitudes which we attribute to the global climate forcing. While AP fractions predominantly increased through the deglaciation, we identify regions where AP fractions decreased. For millennial timescales, we do not observe spatially coherent similarity structures. We compare our results with networks computed from three deglacial climate simulations with the CCSM3, HadCM3, and LOVECLIM models. Networks based on simulated precipitation patterns reproduce the characteristics of the AP network. Sensitivity experiments with statistical emulators indicate that, indeed, precipitation variations explain the diagnosed patterns of vegetation change better than temperature and CO2 variations. Our findings support previous interpretations of deglacial forest evolution in the mid‐latitudes being the result of atmospheric circulation changes. The network analysis identifies differences in the vegetation‐climate‐CO2 relationship simulated by CCSM3 and HadCM3. We conclude that network analyses are a promising tool to benchmark transient climate simulations with dynamical vegetation changes. This may result in stronger constraints of future hydroclimate and land cover changes.

Description: Plain Language Summary: We do not understand changes in rainfall and plant cover since the last ice age as good as temperature changes. Pollen is widely used to study which plants grew under which climate in the past. We check how many tree and shrub pollen, versus how many from herbs and grasses can be found in many locations. This shows how similar plant cover changes were in different regions. We find that plant cover changed similarly across all continents from the last ice age to the current warm period. During this transition, tree and shrub pollen increased while herbs and grasses decreased. However, we identify distinct regions where the change is the other way around. To understand this better, we use data from three climate models. The vegetation components of the climate models calculate how Earth's plant cover changed. By comparing the model results to pollen data, we find that the tree and shrub cover changes since the last ice age are better explained by rainfall than by temperature and carbon dioxide in the low and mid‐latitudes. Comparing the pollen data and model results in this way can help us to understand how well climate models simulate plant cover and rainfall changes.

Description: Key Points: An analysis of arboreal pollen networks shows largely coherent vegetation changes in the low and mid‐latitudes during the last deglaciation. A comparison with climate simulations suggests that hydroclimate changes explain regionally anti‐correlated vegetation variations best. Our work is a promising step toward process‐based benchmarking of vegetation and hydroclimate in transient simulations of the deglaciation.

Description: Deutsche Forschungsgemeinschaft (DFG) http://dx.doi.org/10.13039/501100001659

Description: Bundesministerium für Bildung und Forschung (BMBF) http://dx.doi.org/10.13039/501100002347