ALBERT

Description: Subgrid-scale (SGS) velocity variations result in gridscale sea surface flux enhancements that must be parameterized in weather and climate models. Traditional parameterizations are deterministic in that they assign a unique value of the SGS velocity flux enhancement to any given configuration of the resolved state. In this study, we assess the statistics of SGS velocity flux enhancement over a range of averaging scales (as a proxy for varying model resolution) through systematic coarse-graining of a convection-permitting atmospheric model simulation over the Indian Ocean and west Pacific warm pool. Conditioning the statistics of the SGS velocity flux enhancement on 1) the fluxes associated with the resolved winds and 2) the precipitation rate, we find that the lack of a separation between “resolved” and “unresolved” scales results in a distribution of flux enhancements for each configuration of the resolved state. That is, the SGS velocity flux enhancement should be represented stochastically rather than deterministically. The spatial and temporal statistics of the SGS velocity flux enhancement are investigated by using basic descriptive statistics and through a fit to an anisotropic space–time covariance structure. Potential spatial inhomogeneities of the statistics of the SGS velocity flux enhancement are investigated through regional analysis, although because of the relatively short duration of the simulation (9 days) distinguishing true inhomogeneity from sampling variability is difficult. Perspectives for the implementation of such a stochastic parameterization in weather and climate models are discussed.

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: 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 MCMC 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: 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 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. 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 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 apply 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. We reconstruct 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 which account for uncertainties. Our reconstruction performs well in cross-validation experiments and shows a reasonable degree of spatial smoothing.

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: 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.