Search

Sea surface temperature (SST) is a critical parameter in the global climate system and plays a vital role in many marine processes, including ocean circulation, evaporation, and the exchange of heat and moisture between the ocean and atmosphere. As such, understanding the variability of SST is important for a range of applications, including weather and climate prediction, ocean circulation modeling, and marine resource management.The dynamics of SST is the compound of multiple degrees of freedom that interact across a continuum of Spatio-temporal scales. A first-order approximation of such a system was initially introduced by Hasselmann. In his pioneering work, Hasselmann (1976) discussed the interest in using a two-scale stochastic model to represent the interactions between slow and fast variables of the global ocean, climate, and atmosphere system. In this paper, we examine the potential of machine learning techniques to derive relevant dynamical models of Sea Surface Temperature Anomaly (SSTA) data in the Mediterranean Sea. We focus on the seasonal modulation of the SSTA and aim to understand the factors that influence the temporal variability of SSTA extremes. Our analysis shows that the variability of the SSTA can indeed well be decomposed into slow and fast components. The dynamics of the slow variables are associated with the seasonal cycle, while the dynamics of the fast variables are linked to the SSTA response to rapid underlying processes such as the local wind variability. Based on these observations, we approximate the probability density function of the SSTA data using a stochastic differential equation parameterized by a neural network. In this model, the drift function represents the seasonal cycle and the diffusion function represents the envelope of the fast SSTA response.

The aim of the TOPVOYS project supported by the MarTERA ERA-Net Cofund program within the European Commission is to advance and implement analyses tools and decision support system for voyage optimisation. Based on marine weather analyses and forecasts combined with near real time satellite-based observations of wind, wave and surface current conditions as well as sea surface temperature fields the best shipping route are examined. The proposed approach aims to identify the optimum balance between minimisation of transit time and fuel consumption as well as reduction of emissions without placing the vessel at risk to damage and or crew injury. As such it is compliant with the International Maritime Organization guidelines [6] for ship routeing to keep the traffic smooth and avoid accidents, notably in the presence of unfavorable marine meteorological conditions. The tool performances will be demonstrated both in post-voyage analyses and real time operations for the North Atlantic Ocean crossings, voyages from Europe through the Mediterranean Sea and the Suez Channel to the Far East (e.g. China, South Korea) and voyages around Southern Africa.

When considering the modeling of dynamical systems, the increasing interest in machine learning, artificial intelligence and more generally, data-driven representations, as well as the increasing availability of data, motivated the exploration and definition of new identification techniques. These new data-driven representations aim at solving modern questions regarding the modeling, the prediction and ultimately, the understanding of complex systems such as the ocean, the atmosphere and the climate. In this work, we focus on one question regarding the ability to define a (deterministic) dynamical model from a sequence of observations. We focus on sea surface observations and show that these observations typically relate to some, but not all, components of the underlying state space, making the derivation of a deterministic model in the observation space impossible. In this context, we formulate the identification problem as the definition, from data, of an embedding of the observations, parameterized by a differential equation. When compared to state-of-the-art techniques based on delay embedding and linear decomposition of the underlying operators, the proposed approach benefits from all the advances in machine learning and dynamical systems theory in order to define, constrain and tune the reconstructed sate space and the approximate differential equation. Furthermore, the proposed embedding methodology naturally extends to cases in which a dynamical prior (derived for example using physical principals) is known, leading to relevant physics informed data-driven models.

We propose a new strategy for dissecting the macroeconomic time series, provide a template for the propagation mechanism that best describes the observed business cycles, and use its properties to appraise models of both the parsimonious and the medium-scale variety. Our findings support the existence of a main business-cycle driver but rule out the following candidates for this role: technology or other shocks that map to TFP movements; news about future productivity; and inflationary demand shocks of the textbook type. Prominent members of the DSGE literature also lack the propagation mechanism seen in our anatomy of the data. Models that aim at accommodating demanddriven cycles under flexible prices appear promising.

The complexity of real-world geophysical systems is often compounded by the fact that the observed measurements depend on hidden variables. These latent variables include unresolved small scales and/or rapidly evolving processes, partially observed couplings, or forcings in coupled systems. This is the case in ocean-atmosphere dynamics, for which unknown interior dynamics can affect surface observations. The identification of computationally-relevant representations of such partially-observed and highly nonlinear systems is thus challenging and often limited to short-term forecast applications. Here, we investigate the physics-constrained learning of implicit dynamical embeddings, leveraging neural ordinary differential equation (NODE) representations. A key objective is to constrain their boundedness, which promotes the generalization of the learned dynamics to arbitrary initial condition. The proposed architecture is implemented within a deep learning framework, and its relevance is demonstrated with respect to state-of-the-art schemes for different case-studies representative of geophysical dynamics.

Wind-generated waves strongly interact with sea ice and impact air-sea exchanges, operations at sea, and marine life. Unfortunately, the dissipation of wave energy is not well quantified and its possible effect on upper ocean mixing and ice drift are still mysterious. As the Arctic is opening up and wave energy increases, the limited amount of in situ observations is a clear limitation to our scientific understanding. Both radar and optical remote sensing has revealed the frequent presence of waves in ice, and could be used more systematically to investigate wave-ice interactions. Here we show that, in cloud-free conditions, Sentinel-2 images exhibit brightness modulations in ice-covered water, consistent with the presence of waves measured a few hours later by the ICESat-2 laser altimeter. We show that a full-focus SAR processing of Sentinel-3 radar altimeter data also reveals the presence and wavelengths of waves in sea ice, within minutes of Sentinel-2 imagery. The SWIM instrument on CFOSAT is another source of quantitative evidence for the direction and wavelengths of waves in ice, when ice conditions are spatially homogeneous. In the presence of sea ice, a quantitative wave height measurement method is not yet available for all-weather near-nadir radar instruments such as altimeters and SWIM. However, their systematic co-location with optical instruments on Sentinel-2 and ICESat-2, which are less frequently able to observe waves in sea ice, may provide the empirical transfer functions needed to interpret and calibrate the radar data, greatly expanding the available data on wave-ice interactions. Key Points Wave patterns in sea ice can be found in radar and optical remote sensing data We provide a quantitative estimation of wave height, wavelength and direction from ICESat-2 and Sentinel-2 data Wavelengths and directions in full-focus SAR altimetry and CFOSAT SWIM are consistent with other sensors Plain Language Summary Waves generated by winds over the ocean propagate in ice-covered regions where they can be strongly attenuated and can contribute to breaking up the ice and pushing the ice around. Wavy patterns are clearly visible in remote sensing data collected by different instruments including the ICESat-2 laser altimeter, Sentinel-1 imaging radar, the Sentinel-2 optical imager, Sentinel-3 radar altimeter, and CFOSAT wave-measuring instrument SWIM. Here we show examples of such patterns and propose an quantitative interpretation of ICESat-2 and Sentinel-2 that is consistent with waves generated by storms in the Barents sea that are observed to travel under the ice over hundreds of kilometers. For Sentinel-3 and SWIM, a quantification of wave heights will have to be validated, possibly based on data from the other two instruments. This may strongly expand the quantity of available information for scientific investigations and operational applications.

The reconstruction of sea surface geophysical variables typically relies either on Optimal Interpolation (OI) or on model-based approaches which explicitly exploit a dynamical model. While the optimal interpolation suffers from smoothing issues making it unreliable in retrieving fine scale variability, the selection and parametrization of a dynamical model, when considering model based data assimilation strategies, remains a complex issue since several trade-offs between the models complexity and its applicability in sea surface data assimilation need to be carefully addressed. In this work, and motivated by the success of artificial intelligence algorithms in various signal processing fields as well as the increasing amounts of observations and simulation datasets, we explore a data driven Koopman model and formulate the reconstruction problem as solution of the classical Kalman filter in a space of observables. The proposed architecture although linear, is shown to outperform state-of-the-art non linear data-driven filtering schemes such as the Analog Data Assimilation (AnDA).

We study optimal policy in an economy in which public debt serves as collateral or buffer stock. Issuing more public debt can raise welfare by easing the underlying friction; but it also reduces the premium that the private sector is willing to pay for this service, which in turn raises interest rates. This trade off shapes the optimal long-run quantity of public debt. It justifies larger deficits during financial crises. It may subsume other considerations, such as whether public debt crowds out, or in, capital. And it clarifies the circumstances under which a low risk-free rate represents an opportunity of cheap borrowing by the government. * This paper supersedes an earlier paper, entitled "Optimal Public Debt Management and Liquidity Provision" (Angeletos et al, 2016). We are grateful to Behzad Diba for his collaboration on the early stages of this project; to Pedro Teles and Per Krusell for discussing our paper in conferences; to numerous seminar participants for their comments; and, last but not certainly not least, to Harald Uhlig and three anonymous for their extensive feedback. Angeletos also thanks the University of Bern, the Study Center Gerzensee, and the Swiss Finance Institute for their hospitality.

Spatio-temporal interpolation applications are important in the context of ocean surface modeling. Current state-of-the-art techniques typically rely either on optimal interpolation or on model-based approaches which explicitly exploit a dynamical model. While the optimal interpolation suffers from smoothing issues making it unreliable in retrieving fine-scale variability, the selection and parametrization of a dynamical model, when considering model-based data assimilation strategies, remains a complex issue since several trade-offs between the model's complexity and its applicability in sea surface data assimilation need to be carefully addressed. For these reasons, deriving new data assimilation architectures that can perfectly exploit the observations and the current advances in signal processing, modeling and artificial intelligence is crucial.In this work, we explore new advances in data-driven data assimilation to exploit the classical Kalman filter in the interpolation of spatio-temporal fields. The proposed algorithm is written in an end-to-end differentiable setting in order to allow for the learning of the linear dynamical model from a data assimilation cost. Furthermore, the linear model is formulated on a space of observables, rather than the space of observations, which allows for perfect replication of non-linear dynamics when considering periodic and quasi-periodic limit sets and providing a decent (short-term) forecast of chaotic ones. One of the main advantages of the proposed architecture is its simplicity since it utilises a linear representation coupled with a Kalman filter. Interestingly, our experiments show that exploiting such a linear representation leads to better data assimilation when compared to non-linear filtering techniques, on numerous applications, including the sea level anomaly reconstruction from satellite remote sensing observations.

Microseisms in the dominant double-frequency band, around 5 s period and their ubiquitous presence makes them an interesting signal for exploring the solid Earth and associated natural hazards (e.g. Olivier et al. 2019). These microseisms are generated by opposing ocean waves of equal frequencies (Hasselmann 1963) that generally arise within the locally generated sea state at high frequencies (class I, Ardhuin et al. 2011), due to coastal reflection (class II) or when swell from a distant storm collides with another wave system, which generally corresponds to the strongest microseism sources (class III). Improving on solid Earth knowledge and natural hazard monitoring can benefit from a better quantitative knowledge of these sources. Similar applications to the study of the stratosphere can use atmospheric infrasound that are generated by the same opposing ocean waves, the microbaroms (Brekhovskikh et al. 1973, De Carlo et al. 2020). So far, very few direct measurements of wave properties have been able to quantify the presence of waves in opposite directions, and the magnitude of microseism sources has relied on numerical simulations. Here we use sun glitter measurements from the Copernicus-Sentinel 2 satellites, as processed in the SARONG project (http://www.sarong.global/). We show that the presence of opposing waves gives a strong anomaly in the phase of co-spectra of optical images from Sentinel 2 (S2). When using only 2 time-lagged images this feature generally limits the possibility to measure surface currents from waves shorter than about 25 m, that always have a significant energy in opposing directions (class I microseism sources).Caption: Processing from Sentinel 2 Level-1c images to phase speeds. Top: data from Copernicus Sentinel 2 on 29 April 2016 off California (See Figs. 3-9 in Kudryavtsev et al. 2017). Bottom: simulated S2 data based on in situ wave spectrum determined from directional moments using the Maximum Entropy Method. The phase speed anomalies, highlighted with the dashed magenta circle near the Nyquist wavelength L = 20 m, disappear when no energy propagates in opposing directions.The same also happens for longer components when strong (class III) microseism sources are present. However this signature is also an opportunity to directly measure the sources of microseisms and quantify the energy in opposing directions using 2 or more different time lags (Ardhuin et al., in 2021). Given its coastal coverage, we find that S2 is particularly well suited for estimating reflection coefficients of waves off the coast, which is a major source of uncertainty for microseism and microbarom source modelling. Ardhuin, F., Stutzmann, E., Schimmel, M., & Mangeney, A. (2011). Ocean wave sources of seismic noise. Journal of Geophysical Research, 116(C9). doi:10.1029/2011jc006952Kudryavtsev, V., Yurovskaya, M., Chapron, B., Collard, F., & Donlon, C. (2017). Sun glitter imagery of ocean surface waves. Part 1: Directional spectrum retrieval and validation. Journal of Geophysical Research: Oceans, 122(2), 1369–1383. doi:10.1002/2016jc012425 Olivier, G., Brenguier, F., Carey, R., Okubo, P., & Donaldson, C. (2019). Decrease in seismic velocity observed prior to the 2018 eruption of Kīlauea volcano with ambient seismic noise interferometry. Geophysical Research Letters. doi:10.1029/2018gl081609

The Pilot Mission Exploitation Platform (Pi-MEP) for Salinity (www.salinity-pimep.org) has been released operationally in 2019 to the broad oceanographic community, in order to foster satellite sea surface salinity validation and exploitation activities.Specifically, the Platform aims at enhancing salinityvalidation, by allowing systematic inter-comparison of various EO datasets with a broad suite of in-situ data, and also at enabling oceanographic process studies by capitalizing on salinity data in synergy with additional spaceborne estimates. Despite Pi-MEP was originally conceived as an ESA initiative to widen the uptake of the Soil Moisture and Ocean Salinity (SMOS) mission data over ocean, a project partnership with NASA was devised soon after the operational deployment, and an official collaboration endorsed within the ESA-NASA Joint Program Planning Group (JPPG). The Salinity Pi-MEP has therefore become a reference hub for SMOS, SMAP and Aquarius satellite salinity missions, which are assessed in synergy with additional thematic datasets (e.g., precipitation, evaporation, currents, sea level anomalies, ocean color, sea surface temperature). Match-up databases of satellite/in situ (such as Argo, TSG, moorings, drifters) data and corresponding validation reports at different spatiotemporal scales are systematically generated; furthermore, recently-developed dedicated tools allow data visualization, metrics computation and user-driven features extractions. The Platform is also meant to monitor salinity in selected oceanographic “case studies”, ranging from river plumes monitoring to SSS characterization in challenging regions, such as high latitudes or semi-enclosed basins. The two Agencies are currently collaborating to widen the Platform features on several technical aspects - ranging from a triple-collocation software implementation to a sustained exploitation of data from the SPURS-1/2 campaigns. In this context, an upgrade of the satellite/in-situ match-up methodology has been recently agreed, resulting into a redefinition of the validation criteria that will be subsequently implemented in the Platform. A further synthesis of the three satellites salinity algorithms, models and auxiliary data handling is at the core of the ESA Climate Change Initiative (CCI) on Salinity and of ESA-NASA further collaboration.

An assessment of variance in ocean current signal and noise shared by in situ observations (drifters) and a large gridded analysis (GlobCurrent) is sought as a function of day of the year for 1993-2015 and across a broad spectrum of current speed. Regardless of the division of collocations, it is difficult to claim that any synoptic assessment can be based on independent observations. Instead, a measurement model that departs from ordinary linear regression by accommodating error correlation is proposed. The interpretation of independence is explored by applying Fuller's (1987) concept of equation and measurement error to a division of error into shared (correlated) and unshared (uncorrelated) components, respectively. The resulting division of variance in the new model favours noise. Ocean current shared (equation) error is of comparable magnitude to unshared (measurement) error and the latter is, for GlobCurrent and drifters respectively, comparable to ordinary and reverse linear regression. Although signal variance appears to be small, its utility as a measure of agreement between two variates is highlighted. Sparse collocations that sample a dense grid permit a first order autoregressive form of measurement model to be considered, including parameterizations of analysis-in situ error cross-correlation and analysis temporal error autocorrelation. The former (cross-correlation) is an equation error term that accommodates error shared by both GlobCurrent and drifters. The latter (autocorrelation) facilitates an identification and retrieval of all model parameters. Solutions are sought using a prescribed calibration between GlobCurrent and drifters (by variance matching). Because the true current variance of GlobCurrent and drifters is small, signal to noise ratio is near zero at best. This is particularly evident for moderate current speed and meridional current component., Comment: 24 pages, 14 figures

Should a central bank deviate from price stability to promote financial stability? We study this question through the lens of a textbook New Keynesian model augmented with capital accumulation and search–for–yield behaviors that give rise to endogenous financial crises. Our main findings are fourfold. First, monetary policy affects the probability of a crisis both in the short run (through aggregate demand) and in the medium run (through savings and capital accumulation). Second, the central bank can lower the probability of a crisis and increase welfare compared to strict inflation targeting by responding to output and an index of financial fragility (the “yield gap”) in addition to inflation. Third, “backstop” policy rules that prevent credit market collapses can further increase welfare. Fourth, financial crises may occur after a long period of unexpectedly loose monetary policy as the central bank abruptly reverses course.

This paper addresses the data-driven identification of latent representations of partially observed dynamical systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications and long-term asymptotic patterns. Whereas state-of-the-art data-driven approaches rely in general on delay embeddings and linear decompositions of the underlying operators, we introduce a framework based on the data-driven identification of an augmented state-space model using a neural-network-based representation. For a given training dataset, it amounts to jointly reconstructing the latent states and learning an ordinary differential equation representation in this space. Through numerical experiments, we demonstrate the relevance of the proposed framework with respect to state-of-the-art approaches in terms of short-term forecasting errors and long-term behavior. We further discuss how the proposed framework relates to the Koopman operator theory and Takens' embedding theorem., This work was supported by Labex Cominlabs (grant SEACS), Region Bretagne, CNES (grant OSTST-MANATEE), and Microsoft (AI EU Ocean awards) and by MESR, FEDER, Région Bretagne, Conseil Général du Finistère, Brest Métropole, and Institut Mines Télécom in the framework of the VIGISAT program managed by “Groupement Bretagne Télédétection,” CNES (grant OSTST-MANATEE), and ANR (Melody and OceaniX grants). It benefited from HPC and GPU resources from Azure (Microsoft EU Ocean awards) and from GENCI-IDRIS (Grant No. 2020-101030).

The forecasting and assimilation of sea surface dynamics from satellite-derived data is a challenging issue. Data-driven approaches have arisen as promising schemes to fully exploit satellite observations. A key feature of sea surface dynamics is that they relate to partially-observed dynamics. Here, guided by physical and mathematical considerations of the underlying dynamics of a given system, we propose a novel neural networks architecture for the identification of ordinary differential equations (ODE) of partially observed systems. Numerical experiments for toy models and a sea level anomaly dynamics illustrate the relevance of the proposed scheme for forecasting and assimilation issues w.r.t. other state-of-the-art data-driven models.

International audience; The Chinese-French oceanography satellite, CFOSAT, was launched on October 2018. Two Ku-band scatterometers are on-board: SCAT for the wind observation and SWIM for the wave observation. This paper presents the most recent results on the SWIM data quality analysis a few months after the end of the CAL/VAL phase.