Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models

Recent progress in machine learning has shown how to forecast and, to some extent, learn the dynamics of a model from its output, resorting in particular to neural networks and deep learning techniques. We will show how the same goal can be directly achieved using data assimilation techniques without leveraging on machine learning software libraries, with a view to high-dimensional models. The dynamics of a model are learned from its observation and an ordinary differential equation (ODE) representation of this model is inferred using a recursive nonlinear regression. Because the method is embedded in a Bayesian data assimilation framework, it can learn from partial and noisy observations of a state trajectory of the physical model. Moreover, a space-wise local representation of the ODE system is introduced and is key to coping with high-dimensional models. It has recently been suggested that neural network architectures could be interpreted as dynamical systems. Reciprocally, we show that our ODE representations are reminiscent of deep learning architectures. Furthermore, numerical analysis considerations of stability shed light on the assets and limitations of the method. The method is illustrated on several chaotic discrete and continuous models of various dimensions, with or without noisy observations, with the goal of identifying or improving the model dynamics, building a surrogate or reduced model, or producing forecasts solely from observations of the physical model

Silicon cycle in Indian estuaries and its control by biogeochemical and anthropogenic processes

We study the silicon biogeochemical cycle and its associated parameters in 24 and 18 Indian estuaries during dry and wet periods respectively. We focus more specifically on dissolved Si (DSi), amorphous Si (ASi,) lithogenic Si (LSi), Particulate Organic Carbon (POC), Total Suspended Material (TSM), Dissolved Inorganic Nitrogen (DIN), salinity and fucoxanthin, a marker pigment for diatoms. Overall, we show that the estuaries have strong inter and intra variability of their biogeochemical parameters both seasonally and along salinity gradients. Based on Principal Component Analysis and clustering of categorised (upper and lower) estuaries, we discuss the four major processes controlling the Si variability of Indian estuaries: 1) lithogenic supply, 2) diatom uptake, 3) mixing of sea water and, 4) land use. The influence of lithogenic control is significantly higher during the wet period than during the dry period, due to a higher particle supply through monsoonal discharge. A significant diatom uptake is only identified in the estuaries during dry period. By taking into account the non-conservative nature of Si and by extrapolating our results, we estimate the fluxes from the Indian subcontinent of DSi, ASi, LSi to the Bay of Bengal (211 ± 32, 10 ± 4.7, 2028 ± 317 Gmol) and Arabian Sea (80 ± 15, 7 ± 1.1, 1717 ± 932 Gmol). We show the impact of land use in watersheds with higher levels of agricultural activity amplifies the supply of Si to the coastal Bay of Bengal during the wet season. In contrast, forest cover and steep slopes cause less Si supply to the Arabian Sea by restricting erosion when entering the estuary. Finally, Si:N ratios show that nitrogen is always in deficit relative to silicon for diatom growth, these high Si:N ratios likely contribute to the prevention of eutrophication in the Indian estuaries and coastal sea

Mechanics and thermodynamics of a new minimal model of the atmosphere

The understanding of the fundamental properties of the climate system has long benefitted from the use of simple numerical models able to parsimoniously represent the essential ingredients of its processes. Here, we introduce a new model for the atmosphere that is constructed by supplementing the now-classic Lorenz ’96 one-dimensional lattice model with temperature-like variables. The model features an energy cycle that allows for energy to be converted between the kinetic form and the potential form and for introducing a notion of efficiency. The model’s evolution is controlled by two contributions—a quasi-symplectic and a gradient one, which resemble (yet not conforming to) a metriplectic structure. After investigating the linear stability of the symmetric fixed point, we perform a systematic parametric investigation that allows us to define regions in the parameters space where at steady-state stationary, quasi-periodic, and chaotic motions are realised, and study how the terms responsible for defining the energy budget of the system depend on the external forcing injecting energy in the kinetic and in the potential energy reservoirs. Finally, we find preliminary evidence that the model features extensive chaos. We also introduce a more complex version of the model that is able to accommodate for multiscale dynamics and that features an energy cycle that more closely mimics the one of the Earth’s atmosphere

Combining data assimilation and machine learning to infer unresolved scale parametrization

In recent years, machine learning (ML) has been proposed to devise data-driven parametrizations of unresolved processes in dynamical numerical models. In most cases, the ML training leverages high-resolution simulations to provide a dense, noiseless target state. Our goal is to go beyond the use of high-resolution simulations and train ML-based parametrization using direct data, in the realistic scenario of noisy and sparse observations. The algorithm proposed in this work is a two-step process. First, data assimilation (DA) techniques are applied to estimate the full state of the system from a truncated model. The unresolved part of the truncated model is viewed as a model error in the DA system. In a second step, ML is used to emulate the unresolved part, a predictor of model error given the state of the system. Finally, the ML-based parametrization model is added to the physical core truncated model to produce a hybrid model. The DA component of the proposed method relies on an ensemble Kalman filter while the ML parametrization is represented by a neural network. The approach is applied to the two-scale Lorenz model and to MAOOAM, a reduced-order coupled ocean-atmosphere model. We show that in both cases, the hybrid model yields forecasts with better skill than the truncated model. Moreover, the attractor of the system is significantly better represented by the hybrid model than by the truncated model. This article is part of the theme issue 'Machine learning for weather and climate modelling'

54 years of microboring community history explored by machine learning in a massive coral from Mayotte (Indian Ocean)

International audienceCoral reefs are increasingly in jeopardy due to global changes affecting both reef accretion and bioerosion processes. Bioerosion processes dynamics in dead reef carbonates under various environmental conditions are relatively well understood but only over a short-term limiting projections of coral reef evolution by 2100. It is thus essential to monitor and understand bioerosion processes over the long term. Here we studied the assemblage of traces of microborers in a coral core of a massive Diploastrea sp. from Mayotte, allowing us to explore the variability of its specific composition, distribution, and abundance between 1964 and 2018. Observations of microborer traces were realized under a scanning electron microscope (SEM). The area of coral skeleton sections colonized by microborers (a proxy of their abundance) was estimated based on an innovative machine learning approach. This new method with 93% accuracy allowed analyzing rapidly more than a thousand SEM images. Our results showed an important shift in the trace assemblage composition that occurred in 1985, and a loss of 90% of microborer traces over the last five decades. Our data also showed a strong positive correlation between microborer trace abundance and the coral bulk density, this latter being particularly affected by the interannual variation of temperature and cumulative insolation. Although various combined environmental factors certainly had direct and/or indirect effects on microboring species before and after the breakpoint in 1985, we suggest that rising sea surface temperature, rainfall, and the loss of light over time were the main factors driving the observed trace assemblage change and decline in microborer abundance. In addition, the interannual variability of sea surface temperature and instantaneous maximum wind speed appeared to influence greatly the occurrence of green bands. We thus stress the importance to study more coral cores to confirm the decadal trends observed in the Diploastrea sp. from Mayotte and to better identify the main factors influencing microboring Frontiers in Marine Science frontiersin.org 0

Inversion of satellite ocean colour imagery and geoacoustic characterization of seabed properties: variational data inversion using a semi-automatic adjoint approach

In this paper a semi-automatic adjoint approach for variational data inversion is proposed. To demonstrate the effectiveness of the approach two illustrative examples are presented: the geoacoustic characterization of a Mediterranean shallow water environment using realistic experimental conditions and the estimation of oceanic and atmospheric constituents from satellite ocean colour imagery. In the first case geoacoustic parameters of the seabed (density, sound speed and attenuation) are determined from long/medium range underwater acoustic propagation data in the water column. In the second case the aerosol optical thickness in the atmosphere and the phytoplankton concentration in the ocean (chlorophyll-a) are estimated from solar reflectance measurements obtained with ocean colour sensors on board satellites. The general methodology for both applications is based on a modular graph concept that allows a straightforward adjoint computation by means of gradient backpropagation. Generation and coding of the adjoint models in both cases are accomplished with an algorithmic tool

First Evidence of Anoxia and Nitrogen Loss in the Southern Canary Upwelling System

The northeastern Atlantic hosts the most ventilated subsurface waters of any eastern boundary upwelling system, while coastal upwelling source waters are slightly above hypoxic levels. Anoxic conditions have previously been found offshore inside mesoscale eddies whose core waters undergo oxygen consumption for many months. Based on circumstantial in situ observations this study demonstrates that the Senegalese coastal ocean is subjected to episodic occurrence of zero dissolved oxygen concentration at depth along with elevated nitrite concentration (11 mmol/m3) and nitrate/nitrite deficit to phosphate, thereby indicating severe anoxia and intense nitrogen loss. The anoxic event was associated with a prolonged upwelling relaxation episode in March 2012 and a near shore diatom bloom that underwent degradation while being advected offshore in stratified waters. This is consistent with scenarios observed in other upwelling systems (Benguela and California) and such conditions are presumably frequent in the southern part of the Canary system. Plain Language Summary Oxygen is a key requirement for respiration by marine living organisms. Warming of the atmosphere and the ocean surface to reduces the oxygenation of offshore waters. Similarly, the extra load of nutrients from agriculture or waste waters modify algal production, particularly in coastal regionsoften resulting in oxygen‐depleted waters. Specific reactions affecting the ionic forms of nitrogen also occur within oxygen‐depleted waters also impact the nitrogen cycle by generating nitrite, which is poisonous for marine organisms, and nitrous oxide, a powerful greenhouse gas.We took measurements at sea to show that a poorly studied coastal sector of the North Atlantic Ocean, the Senegalese continental shelf, can be episodically subjected to complete depletion of subsurface oxygen (anoxia) as well as high nitrite concentrations, constituting the first report of anoxia for this oceanic region. We also show that this anoxia is likely the consequence of the decay of a bloom of diatoms, a group of microalgae common in this type of ecosystem thatinitially developed in shallow waters and transported offshore by anomalous currents associated with low‐wind conditions

First evidence of anoxia and nitrogen loss in the Southern Canary Upwelling System

The northeastern Atlantic hosts the most ventilated subsurface waters of any eastern boundary upwelling system, while coastal upwelling source waters are slightly above hypoxic levels. Anoxic conditions have previously been found offshore inside mesoscale eddies whose core waters undergo oxygen consumption for many months. Based on circumstantial in situ observations, this study demonstrates that the Senegalese coastal ocean is subjected to episodic occurrence of zero dissolved oxygen concentration at depth along with elevated nitrite concentration (11mmol/m(3)) and nitrate/nitrite deficit to phosphate, thereby indicating severe anoxia and intense nitrogen loss. The anoxic event was associated with a prolonged upwelling relaxation episode in March 2012 and a nearshore diatom bloom that underwent degradation while being advected offshore in stratified waters. This is consistent with scenarios observed in other upwelling systems (Benguela and California), and such conditions are presumably frequent in the southern part of the Canary system. Plain language summary Oxygen is a key requirement for respiration by marine living organisms. Warming of the atmosphere and the ocean surface reduces the oxygenation of offshore waters. Similarly, the extra load of nutrients from agriculture or waste waters modifies algal production, particularly in coastal regions, often resulting in oxygen-depleted waters. Specific reactions affecting the ionic forms of nitrogen also occur within oxygen-depleted waters, which also impact the nitrogen cycle by generating nitrite, which is poisonous for marine organisms, and nitrous oxide, a powerful greenhouse gas. We took measurements at sea to show that a poorly studied coastal sector of the North Atlantic Ocean, the Senegalese continental shelf, can be episodically subjected to complete depletion of subsurface oxygen (anoxia) as well as high nitrite concentrations, constituting the first report of anoxia for this oceanic region. We also show that this anoxia is likely the consequence of the decay of a bloom of diatoms, a group of microalgae common in this type of ecosystem that initially developed in shallow waters and transported offshore by anomalous currents associated with low-wind conditions