Binary time series classification with Bayesian convolutional neural networks when monitoring for marine gas discharges

The world’s oceans are under stress from climate change, acidification and other human activities, and the UN has declared 2021–2030 as the decade for marine science. To monitor the marine waters, with the purpose of detecting discharges of tracers from unknown locations, large areas will need to be covered with limited resources. To increase the detectability of marine gas seepage we propose a deep probabilistic learning algorithm, a Bayesian Convolutional Neural Network (BCNN), to classify time series of measurements. The BCNN will classify time series to belong to a leak/no-leak situation, including classification uncertainty. The latter is important for decision makers who must decide to initiate costly confirmation surveys and, hence, would like to avoid false positives. Results from a transport model are used for the learning process of the BCNN and the task is to distinguish the signal from a leak hidden within the natural variability. We show that the BCNN classifies time series arising from leaks with high accuracy and estimates its associated uncertainty. We combine the output of the BCNN model, the posterior predictive distribution, with a Bayesian decision rule showcasing how the framework can be used in practice to make optimal decisions based on a given cost function.publishedVersio

Semi-conditional variational auto-encoder for flow reconstruction and uncertainty quantification from limited observations

We present a new data-driven model to reconstruct nonlinear flow from spatially sparse observations. The proposed model is a version of a Conditional Variational Auto-Encoder (CVAE), which allows for probabilistic reconstruction and thus uncertainty quantification of the prediction. We show that in our model, conditioning on measurements from the complete flow data leads to a CVAE where only the decoder depends on the measurements. For this reason, we call the model semi-conditional variational autoencoder. The method, reconstructions, and associated uncertainty estimates are illustrated on the velocity data from simulations of 2D flow around a cylinder and bottom currents from a simulation of the southern North Sea by the Bergen Ocean Model. The reconstruction errors are compared to those of the Gappy proper orthogonal decomposition method.publishedVersio

Experimental design for parameter estimation in steady-state linear models of metabolic networks

Metabolic networks are typically large, containing many metabolites and reactions. Dynamical models that aim to simulate such networks will consist of a large number of ordinary differential equations, with many kinetic parameters that must be estimated from experimental data. We assume these data to be metabolomics measurements made under steady-state conditions for different input fluxes. Assuming linear kinetics, analytical criteria for parameter identifiability are provided. For normally distributed error terms, we also calculate the Fisher information matrix analytically to be used in the D-optimality criterion. A test network illustrates the developed tool chain for finding an optimal experimental design. The first stage is to verify global or pointwise parameter identifiability, the second stage to find optimal input fluxes, and finally remove redundant measurements.publishedVersio

Covering tour problem with varying coverage: Application to marine environmental monitoring

In this paper, we present a novel variant of the Covering Tour Problem (CTP), called the Covering Tour Problem with Varying Coverage (CTP-VC). We consider a simple graph = ( ,), with a measure of importance assigned to each node in . A vehicle with limited battery capacity visits the nodes of the graph and has the ability to stay in each node for a certain period of time, which determines the coverage radius at the node. We refer to this feature as stay-dependent varying coverage or, in short, varying coverage. The objective is to maximize a scalarization of the weighted coverage of the nodes and the negation of the cost of moving and staying at the nodes. This problem arises in the monitoring of marine environments, where pollutants can be measured at locations far from the source due to ocean currents. To solve the CTP-VC, we propose a mathematical formulation and a heuristic approach, given that the problem is NP-hard. Depending on the availability of solutions yielded by an exact solver, we evaluate our heuristic approach against the exact solver or a constructive heuristic on various instance sets and show how varying coverage improves performance. Additionally, we use an offshore CO2 storage site in the Gulf of Mexico as a case study to demonstrate the problem’s applicability. Our results demonstrate that the proposed heuristic approach is an efficient and practical solution to the problem of stay-dependent varying coverage. We conduct numerous experiments and provide managerial insights.publishedVersio

Survey strategies to quantify and optimize detecting probability of a CO2 seep in a varying marine environment

AbstractDesigning a marine monitoring program that detects CO2 leaks from subsea geological storage projects is challenging. The high variability of the environment may camouflage the anticipated anisotropic signal from a leak and there are a number of leak scenarios. Marine operations are also costly constraining the availability of measurements. A method based on heterogeneous leak scenarios and anisotropic predictions of chemical footprint under varying current conditions is presented. Through a cost function optimal placement of sensors can be given both for fixed installations and series of measurements during surveys. Ten fixed installations with an optimal layout is better than twenty placed successively at the locations with highest leakage probability. Hence, optimal localizations of installations offers cost reduction without compromising precision of a monitoring program, e.g. quantifying and reduce probabilities of false alarm under control. An optimal cruise plan for surveys, minimizing transit time and operational costs, can be achieved

Assessing Model Uncertainties Through Proper Experimental Design

This paper assesses how parameter uncertainties in the model for rise velocity of CO2 droplets in the ocean cause uncertainties in their rise and dissolution in marine waters. The parameter uncertainties in the rise velocity for both hydrate coated and hydrate free droplets are estimated from experiment data. Thereafter the rise velocity is coupled with a mass transfer model to simulate the fate of dissolution of a single droplet. The assessment shows that parameter uncertainties are highest for large droplets. However, it is also shown that in some circumstances varying the temperature gives significant change in rise distance of droplets.publishedVersio

PVTx Properties of a Two-phase CO2 Jet from Ruptured Pipeline

Span and Wagner equation of state (SW EOS) have been used to investigate changes in the thermodynamic properties of CO2 during a depressurization process from a pipeline into marine environment. The process is assumed to be isenthalpic, as only the thermodynamic change at the moment of depressurization is considered. The calculations show that the depth location of the pipeline influences greatly the density, temperature and volume changes, because of the difference in the surrounding pressures. In general the two-phase area is reached at depths shallower than 600 meters, which yields for the Norwegian Continental Shelf, as it is mainly shallower than 500 meters depth. There is a rapid decrease in density in the two-phase area causing a rapid expansion in the volume of CO2 from 4 MPa to 1 MPa. At the shallowest depth considered (100m) the volume fraction consist almost entirely of gas, and the density change give a significant increase in volume.publishedVersio

Optimal sensors placement for detecting CO2 discharges from unknown locations on the seafloor

Assurance monitoring of the marine environment is a required and intrinsic part of CO2 storage project. To reduce the costs related to the monitoring effort, the monitoring program must be designed with optimal use of instrumentation. Here we use solution of a classical set cover problem to design placement of an array of fixed chemical sensors with the purpose of detecting a seep of CO2 through the seafloor from an unknown location. The solution of the problem is not unique and different aspects, such as cost or existing infrastructure, can be added to define an optimal solution. We formulate an optimization problem and propose a method to generate footprints of potential seeps using an advection–diffusion model and a stoichiometric method for detection of small seepage CO2 signals. We provide some numerical experiments to illustrate the concepts