A Gaussian process emulator for simulating ice sheet-climate interactions on a multi-million year timescale: CLISEMv1.0

On multi-million year timescales, fully coupled ice sheet – climate simulations are hampered by computational limitations, even at coarser resolutions and when considering asynchronous coupling schemes. In this study, a novel coupling method CLISEMv1.0 (CLimate-Ice Sheet EMulator version 1.0) is presented where a Gaussian process emulator is applied to the climate model HadSM3 coupled to the ice sheet model AISMPALEO. The temperature and precipitation fields from HadSM3 are emulated to feed the mass balance model from AISMPALEO. The sensitivity of the evolution of the ice sheet over time is tested to the number of predefined ice sheet geometries the emulator is calibrated on, to the formulation of the ice sheet parameter (being either ice sheet volume, either ice sheet area, or both) and to the coupling time. Sensitivity experiments are conducted to explore the uncertainty introduced by the emulator. Additionally, different lapse rate adjustments are used between the relatively coarse climate model and the much finer ice sheet model topography. It is shown that the ice sheet evolution over a million-year timescale is strongly sensitive to the definition of the ice sheet parameter and to the number of predefined ice sheet geometries. With the new coupling procedure, we provide a computationally efficient framework for simulating ice sheet-climate interactions on a multi-million year timescale that allows for a large number of sensitivity tests.

Probabilistic, high-resolution tsunami predictions in North Cascadia by exploiting sequential design for efficient emulation

The potential of a full-margin rupture along the Cascadia subduction zone poses a significant threat over a populous region of North America. Traditional probabilistic tsunami hazard assessments produce hazard maps based on simulated prediction of tsunami waves either under limited ranges of scenarios or at low resolution, due to cost. We use the GPU-accelerated tsunami simulator VOLNA-OP2 with a detailed representation of topographic and bathymetric features. We replace the simulator by a Gaussian Process emulator at each output location to overcome the large computational burden. The emulators are statistical approximations of the simulator behaviour. We train the emulators on a set of input-output pairs and use them to generate approximate output values over a six-dimensional scenario parameter space, e.g., uplift/subsidence ratio, maximum uplift, that represent the seabed deformation. We implement an advanced sequential design algorithm for the optimal selection of only sixty simulations. This approach allows for a first emulation-accelerated computation of probabilistic tsunami hazard in the region of the city of Victoria, British Columbia. The low cost of emulation provides for additional flexibility in the shape of the deformation, which we illustrate here, considering two families, buried rupture and splay-faulting, of 2,000 potential scenarios.

Expectation-Maximization Algorithm for the Calibration of Complex Simulator Using a Gaussian Process Emulator

The approximated non-linear least squares (ALS) tunes or calibrates the computer model by minimizing the squared error between the computer output and real observations by using an emulator such as a Gaussian process (GP) model. A potential defect of the ALS method is that the emulator is constructed once and it is no longer re-built. An iterative method is proposed in this study to address this difficulty. In the proposed method, the tuning parameters of the simulation model are calculated by the conditional expectation (E-step), whereas the GP parameters are updated by the maximum likelihood estimation (M-step). These EM-steps are alternately repeated until convergence by using both computer and experimental data. For comparative purposes, another iterative method (the max-min algorithm) and a likelihood-based method are considered. Five toy models are tested for a comparative analysis of these methods. According to the toy model study, both the variance and bias of the estimates obtained from the proposed EM algorithm are smaller than those from the existing calibration methods. Finally, the application to a nuclear fusion simulator is demonstrated.

Correcting a bias in a climate model with an augmented emulator

A key challenge in developing flagship climate model configurations is the process of setting uncertain input parameters at values that lead to credible climate simulations. Setting these parameters traditionally relies heavily on insights from those involved in parameterisation of the underlying climate processes. Given the many degrees of freedom and computational expense involved in evaluating such a selection, this can be imperfect leaving open questions about whether any subsequent simulated biases result from mis-set parameters or wider structural model errors (such as missing or partially parameterised processes). Here, we present a complementary approach to identifying plausible climate model parameters, with a method of bias correcting subcomponents of a climate model using a Gaussian process emulator that allows credible values of model input parameters to be found even in the presence of a significant model bias. A previous study (McNeall et al., 2016) found that a climate model had to be run using land surface input parameter values from very different, almost non-overlapping, parts of parameter space to satisfactorily simulate the Amazon and other forests respectively. As the forest fraction of modelled non-Amazon forests was broadly correct at the default parameter settings and the Amazon too low, that study suggested that the problem most likely lay in the model's treatment of non-plant processes in the Amazon region. This might be due to modelling errors such as missing deep rooting in the Amazon in the land surface component of the climate model, to a warm–dry bias in the Amazon climate of the model or a combination of both. In this study, we bias correct the climate of the Amazon in the climate model from McNeall et al. (2016) using an “augmented” Gaussian process emulator, where temperature and precipitation, variables usually regarded as model outputs, are treated as model inputs alongside land surface input parameters. A sensitivity analysis finds that the forest fraction is nearly as sensitive to climate variables as it is to changes in its land surface parameter values. Bias correcting the climate in the Amazon region using the emulator corrects the forest fraction to tolerable levels in the Amazon at many candidates for land surface input parameter values, including the default ones, and increases the valid input space shared with the other forests. We need not invoke a structural model error in the land surface model, beyond having too dry and hot a climate in the Amazon region. The augmented emulator allows bias correction of an ensemble of climate model runs and reduces the risk of choosing poor parameter values because of an error in a subcomponent of the model. We discuss the potential of the augmented emulator to act as a translational layer between model subcomponents, simplifying the process of model tuning when there are compensating errors and helping model developers discover and prioritise model errors to target.

A Gaussian process emulator for simulating ice sheet-climate interactions on a multi-million year timescale

<p>Fully coupled state-of-the-art Atmosphere-Ocean General Circulation Models are the best tool to investigate feedbacks between the different components of the climate system on a decadal to centennial timescale. On millennial to multi-millennial timescales, Earth System Models of Intermediate Complexity are used to explore the feedbacks in the climate system between the ice sheets, the atmosphere and the ocean. Those fully coupled models, even at coarser resolution, are computationally very expensive and other techniques have been proposed to simulate ice sheet-climate interactions on a million-year timescale. The asynchronous coupling technique proposes to run a climate model for a few decades and subsequently an ice sheet model for a few millennia. Another, more efficient method is the use of a matrix look-up table where climate model runs are performed for end-members and intermediate climatic states are linearly interpolated.</p><p>In this study, a novel coupling approach is presented where a Gaussian Process emulator applied to the climate model HadSM3 is coupled to the ice sheet model AISMPALEO. We have tested the sensitivity of the formulation of the ice sheet parameter and of the coupling time to the evolution of the ice sheet over time. Additionally, we used different lapse rate adjustments between the relatively coarse climate model and the much finer ice sheet model topography. It is shown that the ice sheet evolution over a million year timescale is strongly sensitive to the choice of the coupling time and to the implementation of the lapse rate adjustment. With the new coupling procedure, we provide a more realistic and computationally efficient framework for ice sheet-climate interactions on a multi-million year timescale.</p><p> </p>