Online Calibration of Deep Learning Sub-Models for Hybrid Numerical Modeling Systems

Artificial intelligence and deep learning are currently reshaping numerical simulation frameworks by introducing new modeling capabilities. These frameworks are extensively investigated in the context of model correction and parameterization where they demonstrate great potential and often outperform traditional physical models. Most of these efforts in defining hybrid dynamical systems follow {offline} learning strategies in which the neural parameterization (called here sub-model) is trained to output an ideal correction. Yet, these hybrid models can face hard limitations when defining what should be a relevant sub-model response that would translate into a good forecasting performance. End-to-end learning schemes, also referred to as online learning, could address such a shortcoming by allowing the deep learning sub-models to train on historical data. However, defining end-to-end training schemes for the calibration of neural sub-models in hybrid systems requires working with an optimization problem that involves the solver of the physical equations. Online learning methodologies thus require the numerical model to be differentiable, which is not the case for most modeling systems. To overcome this difficulty and bypass the differentiability challenge of physical models, we present an efficient and practical online learning approach for hybrid systems. The method, called EGA for Euler Gradient Approximation, assumes an additive neural correction to the physical model, and an explicit Euler approximation of the gradients. We demonstrate that the EGA converges to the exact gradients in the limit of infinitely small time steps. Numerical experiments are performed on various case studies, including prototypical ocean-atmosphere dynamics. Results show significant improvements over offline learning, highlighting the potential of end-to-end online learning for hybrid modeling

Assessing the potential impact of assimilating total surface current velocities in the Met Office’s global ocean forecasting system

Accurate prediction of ocean surface currents is important for marine safety, ship routing, tracking of pollutants and in coupled forecasting. Presently, velocity observations are not routinely assimilated in global ocean forecasting systems, largely due to the sparsity of the observation network. Several satellite missions are now being proposed with the capability to measure Total Surface Current Velocities (TSCV). If successful, these would substantially increase the coverage of ocean current observations and could improve accuracy of ocean current forecasts through data assimilation. In this paper, Observing System Simulation Experiments (OSSEs) are used to assess the impact of assimilating TSCV in the Met Office’s global ocean forecasting system. Synthetic observations are generated from a high-resolution model run for all standard observation types (sea surface temperature, profiles of temperature and salinity, sea level anomaly and sea ice concentration) as well as TSCV observations from a Sea surface KInematics Multiscale monitoring (SKIM) like satellite. The assimilation of SKIM like TSCV observations is tested over an 11 month period. Preliminary experiments assimilating idealised single TSCV observations demonstrate that ageostrophic velocity corrections are not well retained in the model. We propose a method for improving ageostrophic currents through TSCV assimilation by initialising Near Inertial Oscillations with a rotated incremental analysis update (IAU) scheme. The OSSEs show that TSCV assimilation has the potential to significantly improve the prediction of velocities, particularly in the Western Boundary Currents, Antarctic Circumpolar Current and in the near surface equatorial currents. For global surface velocity the analysis root-mean-square-errors (RMSEs) are reduced by 23% and there is a 4-day gain in forecast RMSE. There are some degradations to the subsurface in the tropics, generally in regions with complex vertical salinity structures. However, outside of the tropics, improvements are seen to velocities throughout the water column. Globally there are also improvements to temperature and sea surface height when TSCV are assimilated. The TSCV assimilation largely corrects the geostrophic ocean currents, but results using the rotated IAU method show that the energy at inertial frequencies can be improved with this method. Overall, the experiments demonstrate significant potential benefit of assimilating TSCV observations in a global ocean forecasting system

The impact of simulated total surface current velocity observations on operational ocean forecasting and requirements for future satellite missions

Operational forecasts rely on accurate and timely observations and it is important that the ocean forecasting community demonstrates the impact of those observations to the observing community and its funders while providing feedback on requirements for the design of the ocean observing system. One way in which impact of new observations can be assessed is through Observing System Simulation Experiments (OSSEs). Various satellite missions are being proposed to measure Total Surface Current Velocities (TSCV). This study uses OSSEs to assess the potential impact of assimilating TSCV observations. OSSEs have been performed using two global ocean forecasting systems; the Met Office’s (MetO) Forecasting Ocean Assimilation Model and the Mercator Ocean International (MOI) system. Developments to the individual systems, the design of the experiments and results have been described in two companion papers. This paper provides an intercomparison of the OSSEs results from the two systems. We show that global near surface velocity analysis root-mean-squared-errors (RMSE) are reduced by 20-30% and 10-15% in the MetO and MOI systems respectively, we also demonstrate that the percentage of particles forecast to be within 50 km of the true particle locations after drifting for 6 days has increased by 9%/7%. Furthermore, we show that the global subsurface velocities are improved down to 1500m in the MetO system and down to 400m in the MOI system. There are some regions where TSCV assimilation degrades the results, notably the middle of the gyres in the MetO system and at depth in the MOI system. Further tuning of the background and observation error covariances are required to improve performance in these regions. We also provide some recommendations on TSCV observation requirements for future satellite missions. We recommend that at least 80% of the ocean surface is observed in less than 4 to 5 days with a horizontal resolution of 20 to 50 km. Observations should be provided within one day of measurement time to allow real time assimilation and should have an accuracy of 10 cm/s in the along and across track direction and uncertainty estimates should be provided with each measurement

Measuring currents, ice drift, and waves from space: the Sea Surface KInematics Multiscale monitoring (SKIM) concept

We propose a new satellite mission that uses a near-nadir Ka-band Doppler radar to measure surface currents, ice drift and ocean waves at spatial scales of 40?km and more, with snapshots at least every day for latitudes 75 to 82, and every few days otherwise. The use of incidence angles at 6 and 12 degrees allows a measurement of the directional wave spectrum which yields accurate corrections of the wave-induced bias in the current measurements. The instrument principle, algorithm for current velocity and mission performance are presented here. The proposed instrument can reveal features on tropical ocean and marginal ice zone dynamics that are inaccessible to other measurement systems, as well as a global monitoring of the ocean mesoscale that surpasses the capability of today?s nadir altimeters. Measuring ocean wave properties facilitates many applications, from wave-current interactions and air-sea fluxes to the transport and convergence of marine plastic debris and assessment of marine and coastal hazards

SKIM, a candidate satellite mission exploring global ocean currents and waves

The Sea surface KInematics Multiscale monitoring (SKIM) satellite mission is designed to explore ocean surface current and waves. This includes tropical currents, notably the poorly known patterns of divergence and their impact on the ocean heat budget, and monitoring of the emerging Arctic up to 82.5°N. SKIM will also make unprecedented direct measurements of strong currents, from boundary currents to the Antarctic circumpolar current, and their interaction with ocean waves with expected impacts on air-sea fluxes and extreme waves. For the first time, SKIM will directly measure the ocean surface current vector from space. The main instrument on SKIM is a Ka-band conically scanning, multi-beam Doppler radar altimeter/wave scatterometer that includes a state-of-the-art nadir beam comparable to the Poseidon-4 instrument on Sentinel 6. The well proven Doppler pulse-pair technique will give a surface drift velocity representative of the top meter of the ocean, after subtracting a large wave-induced contribution. Horizontal velocity components will be obtained with an accuracy better than 7 cm/s for horizontal wavelengths larger than 80 km and time resolutions larger than 15 days, with a mean revisit time of 4 days for of 99% of the global oceans. This will provide unique and innovative measurements that will further our understanding of the transports in the upper ocean layer, permanently distributing heat, carbon, plankton, and plastics. SKIM will also benefit from co-located measurements of water vapor, rain rate, sea ice concentration, and wind vectors provided by the European operational satellite MetOp-SG(B), allowing many joint analyses. SKIM is one of the two candidate satellite missions under development for ESA Earth Explorer 9. The other candidate is the Far infrared Radiation Understanding and Monitoring (FORUM). The final selection will be announced by September 2019, for a launch in the coming decade

Altimetry for the future: Building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the ‘‘Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

Altimetry for the future: building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the “Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

Couplage des observations spatiales dynamiques et biologiques pour la restitution des circulations océaniques : une approche conjointe par assimilation de données altimétriques et de traceurs

High resolution sensors of tracers such as the Sea Surface Temperature or the Ocean Color reveal small structures at the submesoscale, which are not seen by altimetry. Therefore, this thesis explores the feasibility of using tracer information at the submesoscales to complement the control of ocean dynamic fields that emerge from altimeter data analysis at larger scales. To do so, an image data assimilation strategy (i.e. inversion of images) is developed in which a cost-function is built that minimizes the misfits between image of submesoscale flow structure and tracer images. In the present work, we have chosen as an image of submesoscale flow structure the Finite-Size Lyapunov Exponents (FSLE). This method has been successfully tested on several areas using tracer and altimetric observations from space A high resolution physico-biogeochemical coupled model of process and a high resolution realistic model of the Solomon sea have been used to assess the error associated with the inversion and the efficiency of the correction on the oceanic circulation. These results show the benefits of the joint use of tracer image and altimetric data for the control of ocean circulations.Depuis quelques années, les observations spatiales des traceurs, comme la température de surface de l'océan (SST) ou la couleur de l'océan, ont révélé la présence de filaments à sous-mésoéchelle, qui ne peuvent être détectées par les satellites altimétriques. Ce travail de thèse explore la possibilité d'utiliser les informations dynamiques contenues dans les images traceur haute résolution pour compléter l'estimation de la dynamique océanique de surface effectuée par les satellites altimétriques. Pour ce faire, la méthode d'inversion développée est inspirée de l'assimilation de données images. A l'aide d'une fonction coût, on mesure la distance entre une image du flot dynamique et l'image des structures présentes sur le traceur. On a choisi pour cette étude d'utiliser le FSLE (Finite-Size Lyapunov Exponents) comme proxy image de la dynamique. Cette méthode est testée avec succès sur plusieurs cas test d'observations spatiales. Un modèle de processus couplé physique-biogéochimie ainsi qu'un modèle réaliste de la mer des Salomon sont utilisés pour estimer l'erreur associée à la méthode d'inversion et la pertinence de la correction effectuée. L'utilisation conjointe d'images traceurs et de données altimétriques présente un fort intérêt pour le contrôle de la circulation océanique

Coupling of dynamical and biological space observations for the control of ocean circulations : a joint approach through assimilation of altimeter and chlorophyll data

Depuis quelques années, les observations spatiales des traceurs, comme la température de surface de l'océan (SST) ou la couleur de l'océan, ont révélé la présence de filaments à sous-mésoéchelle, qui ne peuvent être détectées par les satellites altimétriques. Ce travail de thèse explore la possibilité d'utiliser les informations dynamiques contenues dans les images traceur haute résolution pour compléter l'estimation de la dynamique océanique de surface effectuée par les satellites altimétriques. Pour ce faire, la méthode d'inversion développée est inspirée de l'assimilation de données images. A l'aide d'une fonction coût, on mesure la distance entre une image du flot dynamique et l'image des structures présentes sur le traceur. On a choisi pour cette étude d'utiliser le FSLE (Finite-Size Lyapunov Exponents) comme proxy image de la dynamique. Cette méthode est testée avec succès sur plusieurs cas test d'observations spatiales. Un modèle de processus couplé physique-biogéochimie ainsi qu'un modèle réaliste de la mer des Salomon sont utilisés pour estimer l'erreur associée à la méthode d'inversion et la pertinence de la correction effectuée. L'utilisation conjointe d'images traceurs et de données altimétriques présente un fort intérêt pour le contrôle de la circulation océanique.High resolution sensors of tracers such as the Sea Surface Temperature or the Ocean Color reveal small structures at the submesoscale, which are not seen by altimetry. Therefore, this thesis explores the feasibility of using tracer information at the submesoscales to complement the control of ocean dynamic fields that emerge from altimeter data analysis at larger scales. To do so, an image data assimilation strategy (i.e. inversion of images) is developed in which a cost-function is built that minimizes the misfits between image of submesoscale flow structure and tracer images. In the present work, we have chosen as an image of submesoscale flow structure the Finite-Size Lyapunov Exponents (FSLE). This method has been successfully tested on several areas using tracer and altimetric observations from space A high resolution physico-biogeochemical coupled model of process and a high resolution realistic model of the Solomon sea have been used to assess the error associated with the inversion and the efficiency of the correction on the oceanic circulation. These results show the benefits of the joint use of tracer image and altimetric data for the control of ocean circulations