Forecasting solar radiation is critical for balancing the electricity grid due to increasing production from solar energy. To this end, we need precise simulation of clouds, which is traditionally done by numerical weather prediction. However, these large-scale (LS) models struggle especially with forecasting stratocumulus clouds because their coarse vertical resolution cannot capture the sharp inversion present at stratocumulus cloud top. To address this issue, we employ large eddy simulation (LES), which operates at high resolution and has demonstrated superior accuracy in simulating stratocumulus clouds. However, LES relies on input data from a LS model, which is imperfect. To reduce the uncertainty caused by the LS data, we integrate a single ensemble Kalman filter step at the start of simulation in the LES model, utilizing local observations. Our results show that this approach is computationally feasible, robust, and reduces prediction error at assimilation by 50%. The improvement diminishes after approximately 1 hour of simulation due to the influence of large-scale forcing. Future work will focus on enhancing the LS inflow through nested simulations with realistic lateral boundary conditions to sustain the improvements in forecasting accuracy.

Probabilistic forecasts are regarded as the highest achievable goal when predicting earthquakes, but limited information on stress, strength, and governing parameters of the seismogenic sources affects their accuracy. Ensemble data-assimilation methods, such as the Ensemble Kalman Filter (EnKF), estimate these variables by combining physics-based models and observations. While the EnKF has demonstrated potential in perfect model experiments using earthquake simulators governed by rate-and-state friction (RSF) laws, challenges arise from the non-Gaussian distribution of state variables during seismic cycle transitions. This study investigates the Adaptive Gaussian Mixture Filter (AGMF) and the Particle Flow Filter (PFF) as alternatives for improved stress and velocity estimation in earthquake sequences compared to Gaussian-based methods like the EnKF. We test the AGMF and the PFF's performance using Lorenz 96 and Burridge–Knopoff 1D models which are, respectively, standard simplified atmospheric and earthquake models. This approach, using widely recognized and commonly used testbed models in their fields, makes the methods and findings accessible to both the data assimilation and seismology communities, while supporting comparisons and collaboration. We test these models in periodic, and aperiodic conditions, and analyze the impact of assuming Gaussian priors on the estimates of the ensemble methods. The PFF demonstrated comparable performance in chaotic scenarios, yielding lower RMSE for the estimates of the Lorenz 96 models and stronger resilience to underdispersion for the Burridge–Knopoff 1D models. This is vital given the limited and sparse historical earthquake data, underscoring the PFF's potential in enhancing earthquake forecasting. These results emphasize the need for careful data assimilation method selection in seismological modeling.

In this comprehensive study, we discuss a novel approach to enhance data assimilation and uncertainty quantification in the field of Geological Carbon Sequestration (GCS). We specifically address the complexities of channelized reservoirs, which pose significant challenges due to non-Gaussian permeability distributions and the intricate non-linear physics of CO2 injection processes. Our innovative method integrates Fourier Neural Operators (FNOs) and Transformer UNet (T-UNet) with advanced data assimilation techniques - the Surrogate-based Hybrid Ensemble Smoother with Multiple Data Assimilation (SH-ESMDA) and the Surrogate-based Hybrid Randomized Maximum Likelihood (SH-RML). These techniques make use of the very efficient computation of gradients that neural networks provide and they not only improves the speed of data processing but also enhances the accuracy of predictions in synthetic data assimilation experiments for GCS applications. A key element of our approach is the use of proxy models alongside high-fidelity simulations, ensuring the consistency and reliability of physical posterior distributions. We utilized Alluvsim for detailed geological modeling and the Delft Advanced Research Terra Simulator (DARTS) for comprehensive fluid flow simulations, providing a comprehensive understanding of reservoir dynamics. A synthetic case study on a channelized reservoir model for CO2 sequestration demonstrates the effectiveness of these methods, with improvements in predicting CO2 plume migration and pressure dynamics within the reservoir. The results of our study show that the integration of FNOs and T-UNet with SH-ESMDA and SH-RML leads to enhanced prediction capabilities, particularly in the challenging context of channelized reservoirs. The SH-ESMDA method proves to be highly efficient in speeding up the data assimilation process without compromising accuracy, while SH-RML demonstrates a more effective history matching compared to standard Ensemble Smoother with Multiple Data Assimilation (ESMDA) techniques, indicating a robust strategy for assimilating complex data. This research not only contributes to the realm of GCS but also presents a novel solution for the integration of artificial intelligence with traditional methodologies that can be applied in various fields where data assimilation and uncertainty quantification are crucial. Our study paves the way for future advancements in this domain, highlighting the potential of AI-driven techniques in enhancing data assimilation and uncertainty quantification for GCS projects.

This study investigates the integration of machine learning (ML) and data assimilation (DA) techniques, focusing on implementing surrogate models for Geological Carbon Storage (GCS) projects while maintaining the high fidelity physical results in posterior states. Initially, we evaluate the surrogate modeling capability of two distinct machine learning models, Fourier Neural Operators (FNOs) and Transformer UNet (T-UNet), in the context of CO₂ injection simulations within channelized reservoirs. We introduce the Surrogate-based hybrid ESMDA (SH-ESMDA), an adaptation of the traditional Ensemble Smoother with Multiple Data Assimilation (ESMDA). This method uses FNOs and T-UNet as surrogate models and has the potential to make the standard ESMDA process at least 50% faster or more, depending on the number of assimilation steps. Additionally, we introduce Surrogate-based Hybrid RML (SH-RML), a variational data assimilation approach that relies on the randomized maximum likelihood (RML) where both the FNO and the T-UNet enable the computation of gradients for the optimization of the objective function, and a high-fidelity model is employed for the computation of the posterior states. Our comparative analyses show that SH-RML offers a better uncertainty quantification when compared to the conventional ESMDA for the case study.

The particle filter is a data assimilation method based on importance sampling for state and parameter estimation. We apply a particle filter in two different quasi-static experiments with models of subsidence caused by a compacting reservoir. The first model considers uncorrelated model state variables and observations, with observed subsidence resulting from a single source of strain. In the second model, subsidence is a summation of subsidence contributions from multiple sources which causes spatial dependencies and correlations in the observed subsidence field. Assimilating these correlated subsidence fields may trigger weight collapse. With synthetic tests, we show in a model of subsidence with 50 independent state variables and spatially correlated subsidence a minimum of 10¹³ particles are required to have information in the posterior distribution identical to that in a model with 50 independent and spatially uncorrelated observations. Spatial correlations cause an information loss which can be quantified with mutual information. We illustrate how a stronger spatial correlation results in lower information content in the posterior and we empirically derive the required ensemble size for the importance sampling to remain effective. We furthermore illustrate how this loss of information is reflected in the log likelihood, and how this depends on the number of model state variables. Based on these empirical results, we propose criteria to evaluate the required ensemble size in data assimilation of spatially correlated observation fields.

The provinces of Bangkok, Samut Prakan, Samut Sakhon, and Nakhon Pathom in Thailand are experiencing subsidence caused by land subsidence, tectonic activity, and sea-level rise. INSAR result from 2015-2022 show that Bangkok and nearby provinces subsided up to 3 cm/yr in the past 20 years. GNSS results show absolute subsidence rates (below 20 m) up to 5 mm/yr in the past 25 years. According to satellite altimetry data, Bangkok is currently experiencing a sea-level rise of up to 5 mm per year in the Gulf of Thailand. Ground water pumping also play an important role on land subsidence.

This study presents a method to address the significant uncertainties in subsurface modeling that impact the efficiency of energy transition applications such as geothermal energy extraction and CO₂ geological sequetsration. The approach combines a physics-based geomechanical proxy model with an ensemble smoother with multiple data assimilation (ES-MDA), aimed at enhancing uncertainty quantification through the integration of vertical displacement measurements from fluid production and injection. The data from wells is limited in spatial coverage, while these measurements offer extensive spatial information, improving the understanding of subsurface behavior by reflecting changes in reservoir pressure and temperature. The open-DARTS simulator for fluid flow and a geomechanical proxy are used to perform data assimilation with ES-MDA. By generating an ensemble of model realizations with varied permeability, calculating vertical displacements at the surface, and applying ES-MDA, we effectively identify the probability distribution of the vertical displacement of the model conditioned to observed subsidence data. Entropy is used as a statistical measure to quantify the reduction of uncertainty of subsurface models based on observations. Our approach was tested on a 2D conceptual and 3D realistic datasets, demonstrating its capability to provide data assimilation. This workflow represents an advancement in subsurface modeling, supporting informed decision-making in geothermal energy production and CO₂ sequestration by offering an improved alternative for data assimilation and enhancing tools for uncertainty quantification.

Research into land subsidence caused by groundwater withdrawal is hindered by the availability of measured heads, subsidence, and forcings. In this paper, a parsimonious, linked data-driven and physics-based approach is introduced to simulate pumping-induced subsidence; the approach is intended to be applied at observation well nests. Time series analysis using response functions is applied to simulate heads in aquifers. The heads in the clay layers are simulated with a one-dimensional diffusion model, using the heads in the aquifers as boundary conditions. Finally, simulated heads in the layers are used to model land subsidence. The developed approach is applied to the city of Bangkok, Thailand, where relatively short time series of head and subsidence measurements are available at or near 23 well nests; an estimate of basin-wide pumping is available for a longer period. Despite the data scarcity, data-driven time series models at observation wells successfully simulate groundwater dynamics in aquifers with an average root mean square error (RMSE) of 2.8 m, relative to an average total range of 21 m. Simulated subsidence matches sparse (and sometimes very noisy) land subsidence measurements reasonably well with an average RMSE of 1.6 cm/year, relative to an average total range of 5.4 cm/year. Performance is not good at eight out of 23 locations, most likely because basin-wide pumping is not representative of localized pumping. Overall, this study demonstrates the potential of a parsimonious, linked data-driven, and physics-based approach to model pumping-induced subsidence in areas with limited data.

Bayesian-based data assimilation methods integrate observational data into geophysical forward models to obtain the temporal evolution of an improved state vector, including its uncertainties. We explore the potential of a variant, a particle method, to estimate mechanical parameters of the overriding plate during the interseismic period. Here we assimilate vertical surface displacements into an elementary flexural model to estimate the elastic thickness of the overriding plate, and the locations and magnitudes of line loads acting on the overriding plate to produce flexure. Assimilation of synthetic observations sampled from a different forward model than is used in the particle method, reveal that synthetic seafloor data within 150 km from the trench are required to properly constrain parameters for long wavelength solutions of the upper plate (i.e. wavelength ∼500 km). Assimilation of synthetic observations sampled from the same flexural model used in the particle method shows remarkable convergence towards the true parameters with synthetic on-land data only for short to intermediate wavelength solutions (i.e. wavelengths between ∼100 and 300 km). In real-data assimilation experiments we assign representation errors due to discrepancies between our incorrect or incomplete physical model and the data. When assimilating continental data prior to the 2011 Mw Tohoku-Oki earthquake (1997-2000), an unrealistically low effective elastic plate thickness for Tohoku of ∼5-7 km is estimated. Our synthetic experiments suggest that improvements to the physical forward model, such as the inclusion of a slab, a megathrust interface and viscoelasticity of the mantle, including accurate seafloor data, and additional geodetic observations, may refine our estimates of the effective elastic plate thickness. Overall, we demonstrate the potential of using the particle method to constrain geodynamic parameters by providing constraints on parameters and corresponding uncertainty values. Using the particle method, we provide insights into the data network sensitivity and identify parameter trade-offs.

Featured Application: This study emphasizes the importance of comprehensive monitoring, calibration, and optimization of storage strategies in a saline aquifer. It also highlights the need to manage geomechanical risks and uncertainties. By understanding these risks and employing suitable monitoring techniques, the integrity and safety of GCS can be ensured, contributing to the reduction of CO ₂ emissions. Geological Carbon Storage (GCS) involves storing CO ₂ emissions in geological formations, where safe containment is challenged by structural and stratigraphic trapping and caprock integrity. This study investigates flow and geomechanical responses to CO ₂ injection based on a Brazilian offshore reservoir model, highlighting the critical interplay between rock properties, injection rates, pressure changes, and ground displacements. The findings indicate centimeter-scale ground uplift and question the conventional selection of the wellhead as a monitoring site, as it might not be optimal due to the reservoir’s complexity and the nature of the injection process. This study addresses the importance of comprehensive sensitivity analyses on geomechanical properties and injection rates for advancing GCS by improving monitoring strategies and risk management. Furthermore, this study explores the geomechanical effects of modeling flow in the caprock, highlighting the role of pressure dissipation within the caprock. These insights are vital for advancing the design of monitoring strategies, enhancing the predictive accuracy of models, and effectively managing geomechanical risks, thus ensuring the success of GCS initiatives.

Different data assimilation schemes such as the ensemble Kalman filter (EnKF), ensemble smoother (ES) and ensemble smoother with multiple data assimilation (ESMDA) are implemented in a hydro-mechanical slope stability analysis. For a synthetic case, these schemes assimilate displacements at the crest and the slope to estimate strength and stiffness parameters. These estimated parameters are then used to estimate the system's state and factor of safety (FoS). The results show that EnKF provides an FoS estimation with a mean close to the truth and with the smallest standard deviation, with ESMDA using the largest amount of assimilation steps also providing a mean close to the truth but with less confidence. The ES and ESMDA with fewer assimilation steps underestimate the FoS approximation and have low confidence. Assimilating measurements over a longer period provides a more accurate parameter, state and FoS estimation. ES has the best computational performance, with ESMDA performing worse, with its performance dependent on the number of assimilation steps. The computational performance of the EnKF is better than ESMDA but around 50% worse than the ES. Non-linearity of the underlying problem is a key cause of the multi-step assimilation processes having a better performance.

Our ability to forecast earthquakes and slow slip events is hampered by limited information on the current state of stress on faults. Ensemble data assimilation methods permit estimating the state by combining physics-based models and observations, while considering their uncertainties. We use an ensemble Kalman filter (EnKF) to estimate shear stresses, slip rates and the state θ acting on a fault point governed by rate-and-state friction embedded in a 1-D elastic medium. We test the effectiveness of data assimilation by conducting perfect model experiments. We assimilate noised shear-stress and velocity synthetic values acquired at a small distance to the fault. The assimilation of uncertain shear stress observations improves in particular the estimates of shear stress on fault segments hosting slow slip events, while assimilating observations of velocity improves their slip-rate estimation. Both types of observations help equally well to better estimate the state θ. For earthquakes, the shear stress observations improve the estimation of shear stress, slip rates and the state θ, whereas the velocity observations improve in particular the slip-rate estimation. Data assimilation significantly improves the estimates of the temporal occurrence of slow slip events and to a large extent also of earthquakes. Rapid and abrupt changes in velocity and shear stress during earthquakes lead to non-Gaussian priors for subsequent assimilation steps, which breaks the assumption of Gaussian priors of the EnKF. In spite of this, the EnKF still provides estimates that are unexpectedly close to the true evolution. In fact, the forecastability for earthquakes for the same alarm duration is very similar to slow slip events, having a very low miss rate with an alarm duration of just 10 per cent of the recurrence interval of the events. These results confirm that data assimilation is a promising approach for the combination of uncertain physics and indirect, noisy observations for the forecasting of both slow slip events and earthquakes.