Method and computerized system for determining a map of a velocity field of a maritime surface

Abstract

The computerized method for determining a velocity field map of a sea surface comprises providing a low-resolution satellite map (1032) representing a sea surface velocity field and a high-resolution satellite map (104) of the sea surface streamline topology. A computerized determination module determines the sea surface velocity field map (108), including an ageostrophic component, with a resolution higher than the low resolution, from said satellite velocity field map (1032), said topology satellite map (104), and a numerical model (107). Figure for the abstract: Figure 1

Description

Title of the invention: Method and computerized system for determining a map of a velocity field of a maritime surface FIELD OF THE INVENTION

[0001] The present invention relates to computerized methods and systems for determining a mapping of a velocity field of a maritime surface. By "maritime" is meant a sea or an ocean. TECHNOLOGICAL BACKGROUND

[0002] In large bodies of water, particularly seas or oceans, flows are governed by complex geophysical laws. To understand these flows, complex observation systems are used, particularly satellite acquisitions. Thus, conventionally, it is known to use satellite altimetry observations to evaluate the displacement fields of the surface of the body of water. The geostrophic approximation is used to determine the velocity field from the height irregularities determined by satellite observation. However, the acquisition is dependent on the trajectory of the satellites, and the resolution of the sensors used. This results in good accuracy of the evaluation at the satellite, but uncertainty in the fields evaluated far from the trajectory of the satellites, which are obtained by extrapolation. As a result, the uncertainty of the determined velocity field is inhomogeneous.However, a good knowledge of flows is of interest on an industrial level, for example for the optimization of maritime transport, the monitoring of pelagic species or concentrations of micro-plastic waste, or search and rescue at sea, or other.

[0003] The paper “Super-resolving ocean dynamics from space with computer vision algorithms”, Nardelli et al., Remote Sens. 2022, 14, 1559 describes a computer-based method in which the geostrophic currents of a sea surface are determined with improved resolution by a numerical model based, among other things, on sea surface height data.

[0004] However, an attempt is being made to obtain a more faithful representation of marine flows, using the maximum number of available satellite observations. This involves, on the one hand, obtaining a high-resolution assessment of the flows, estimating the total vector field of the currents, of which the geostrophic component is only a part (hereinafter referred to as "complete flows"), and reducing the uncertainty relating to certain assessments. Summary of the invention

[0005] Thus, the invention relates to a computerized method for determining a map of a speed field of a maritime surface, in which: - A low-resolution satellite map representative of a sea surface velocity field is provided, - High-resolution satellite mapping of the topology of the current lines of the sea surface is provided, - A computerized determination module determines the mapping of the velocity field of the maritime surface, including an ageostrophic component, having a resolution higher than the low resolution, from said satellite mapping representative of a velocity field, from said satellite mapping of topology, and from a digital model relating satellite mapping data representative of a velocity field, satellite mapping data of streamline topology, and velocity field maps for the maritime surface.

[0006] Thanks to these provisions, a map of the complete flows of the maritime surface is determined, taking into account the ageostrophic component of the flow. This provides a more reliable estimate of the flow.

[0007] According to different aspects, it is possible to provide one and / or the other of the characteristics below taken alone or in combination.

[0008] According to one embodiment, the digital model has been previously obtained by learning, the learning being carried out by comparing results of the digital model with results obtained by an objective geophysical digital model.

[0009] According to one embodiment, during the learning, synthetic second mapping data was generated from the results of the geophysical digital model.

[0010] [09a] According to one embodiment, the objective geophysical digital model implements at least one of the Navier-Stokes equations, the continuity equation reflecting the conservation of mass, energy and / or salt, or the equation of state relating density, temperature and salinity.

[0011] According to one embodiment, the digital model is a multi-modal and multi-task model.

[0012] [10a] According to one embodiment, the digital model uses mapping data representative satellite velocity field and streamline topology satellite mapping data contemporary with and prior to the velocity field mapping for the sea surface.

[0013] [10b] According to one embodiment, the computerized determination module determines a predicted mapping of the sea surface velocity field, from said satellite mapping representative of a velocity field, from said mapping satellite topology, and a numerical model linking satellite mapping data representative of a velocity field, satellite mapping data of streamline topology, and subsequent velocity field mappings for the sea surface.

[0014] [10c] According to one embodiment, the computerized determination module determines a predicted mapping of the sea surface velocity field from ensemble forecasts of multiple such maps.

[0015] According to one embodiment, the low-resolution satellite mapping representative of a sea surface velocity field comprises a cloud cover of between 10% and 40%, and in which the high-resolution satellite mapping of the topology of the streamlines of the sea surface comprises a cloud cover of between 10% and 40%.

[0016] According to one embodiment, the training input data comprises cloud cover synthetically added to a non-cloud map.

[0017] According to one embodiment, a low-resolution map of a sea surface velocity field or a map of a sea surface altimetry field, with regular or irregular meshing along satellite traces, is provided as low-resolution satellite mapping representative of a sea surface velocity field.

[0018] According to one embodiment, a map of surface temperature, chlorophyll concentration and / or suspended particulate matter concentration at the sea surface is provided as high-resolution satellite mapping of the topology of the streamlines of the sea surface.

[0019] [14a] According to one embodiment, there is provided, as high-resolution satellite mapping sea ​​surface streamline topology resolution, chlorophyll concentration and / or suspended particulate matter concentration mapping at the sea surface, and the numerical model is generated by self-supervised learning using surface temperature mapping.

[0020] According to another aspect, the invention relates to a computer program comprising portions of program code for executing the steps of this method when said program is executed on a computer.

[0021] According to another aspect, the invention relates to a computerized system for determining a mapping of a velocity field of a maritime surface, comprising: - A computerized determination module adapted to determine the mapping of the sea surface velocity field, including an ageostrophic component, from a low-resolution satellite mapping representative of a sea surface velocity field, from a high-resolution satellite mapping of streamline topology of the sea surface and a numerical model relating satellite mapping data representative of a velocity field, satellite mapping data of streamline topology, and modeled velocity field maps for the sea surface, said resulting velocity field mapping of the sea surface having a resolution greater than low resolution. Brief description of the drawings

[0022] Embodiments of the invention will be described below with reference to the drawings, briefly described below:

[0023] [Fig.l] schematically represents a computerized system according to an embodiment of the invention.

[0024] [Fig.2] represents an acquired satellite map of altimetry of the maritime surface.

[0025] [Fig.3] represents a satellite map acquired of sea surface temperature.

[0026] [Fig.4] represents a flow map obtained from a trained numerical model.

[0027] [Fig.5] represents a set of maps used to train the digital model.

[0028] [Fig.6] represents the diagram of an observation system simulation experiment used to obtain the synthetic data of the first surface altimetry mapping.

[0029] [Fig.7] represents an example of synthetic simulation of cloud cover.

[0030] [Fig.8] represents an acquired satellite map of chlorophyll concentration.

[0031] [25a] [Fig.9] is a figure similar to [Fig.l] which schematically represents a computerized system according to one embodiment of the invention.

[0032] [25b] [Fig. 10] represents a time series of images superimposing a mapping temperature satellite and dynamic modeled mapping juxtaposed for several respective time intervals.

[0033] [25c] [Fig.l 1] is a figure similar to [Fig.l] which schematically represents a predictive computerized system according to one embodiment of the invention.

[0034] In the drawings, like references designate identical or similar objects. DETAILED DESCRIPTION

[0035] [Fig.l] schematically represents a computerized system 100 for determining a velocity field of a maritime surface. By maritime surface, we mean refers to a surface layer of a sea or ocean typically extending from the surface (interface with the atmosphere) to a depth of between 1 meter (m) and 20 m, typically between 5 m and 15 m. Thus, the maritime surface concerned is not necessarily closed. For example, the maritime surface may be the Mediterranean, or a part of the Mediterranean, in particular with an area at least equal to 250 km x 250 km. However, the invention is applicable to another sea or ocean, for example the Atlantic Ocean or other.

[0036] The flow can be characterized by a velocity field that we wish to determine. We wish in particular to determine the horizontal components {U; V] of this velocity field in an orthonormal horizontal plane frame (O; X; Y). The velocity field {U; V] is defined as the sum of a geostrophic component and an ageostrophic component.

[0037] The geostrophic term corresponds to the component which results from the balance between the Coriolis force and the force due to the pressure gradient.

[0038] The ageostrophic term corresponds to other equilibria, such as that between the Coriolis force and the centrifugal force. In the present case, we are interested in the ageostrophic term averaged over a period of time relevant to the application, for example from 6h to 48h.

[0039] The computer system 100 comprises a processor 101 adapted to execute a computer program stored in a memory 102. In the memory 102 may also be stored data which will be described in more detail later. The processor 101 and / or the memory 102 may be arranged in a single device, or distributed within a network.

[0040] [Fig.2] schematically represents a first satellite map 103 2 representative of a sea surface velocity field. The plane orthonormal reference frame is used to locate oneself in this first map. This first satellite map 1032 is stored in memory 102. This first satellite map 1032 may, for example, be presented in the form of a set of points {(x; y); h(x; y)}, where (x; y) designate the coordinates of a point along the X and Y axes of the orthonormal reference frame, respectively, and h designates the altimetry at the point with coordinates (x; y).

[0041] The first satellite map 1032 is obtained for a period To. The duration of this period is typically from 6h to 36h, in particular from 12h to 24h.

[0042] The first satellite map 1032 is obtained from an altimetry satellite image. According to this first embodiment, the raw altimetry satellite image is obtained from one or more satellite tracks flying over the maritime surface during the period To. The height field of the maritime surface of the first satellite mapping 1032 is obtained by extrapolation onto a regular grid of the satellite altimetry data measured along the satellite tracks. From said sea surface height field, the geostrophic component of the sea surface velocity field can be calculated by approximating the geostrophic component, by transforming the height field into a pressure field. Due to the spacing of the satellite tracks, the first satellite mapping 1032 has a resolution of at most one point every 5 kilometers (km), typically one point every 12 to 25 km. Such a resolution is described as "low" in this text, in comparison with the resolutions of the other maps considered. In addition, the uncertainty associated with these points is inhomogeneous. The first satellite mapping 1032 is therefore a mapping averaged over the period To.

[0043] [Fig. 3] schematically represents a second satellite map 104 representative of a surface temperature field of the fluid volume.

[0044] For example, the same orthonormal reference frame (0; X; Y) is used for this second satellite map 104. This second satellite map 104 is stored in memory 102. This second satellite map 104 can, for example, be presented in the form of a set of points {(x; y); 0 (x; y)}, where 0 designates the surface temperature.

[0045] The second satellite map 104 is also obtained for the period To.

[0046] The second satellite map 104 is obtained from a satellite image of ocean surface temperature (observation by infrared sensors). According to this first embodiment, the satellite temperature image is obtained from one or more satellite tracks flying over the fluid volume during the period To. Due to the spacing of the swath and the acquisition technology of the infrared sensors, the second satellite map 104 has a resolution of at least one point every 5 km, typically one point every 0.5 to 2 km. Such a resolution is described as “high” in this text, in comparison with the resolutions of the other maps considered. In addition, the uncertainty associated with these points is homogeneous. The satellite map 104 resulting from the infrared observation is likely to be covered by clouds which mask the sampling, leading to missing data points on the unsampled pixels.

[0047] The processor implements a computerized determination module adapted to determine a velocity field map for the maritime surface. This computerized determination module implements a digital model 107 relating first satellite mapping data 1032, second satellite mapping data 104, and velocity field maps 108 for the maritime surface.

[0048] In particular, the velocity field map 108 for the sea surface has a better resolution than the first satellite map data 1032. The map 108 from the digital model 107 is shown in [Fig. 4]. In addition, the velocity field map 108 for the sea surface corresponds to the complete flows, including both the geostrophic component and an ageostrophic part of the flows.

[0049] The digital model 107 was for example obtained by learning. It can also be called a “statistical” model. In the example presented, it is a deep convolutional neural network. This digital model defines a relationship between a set of input and output images, as illustrated in [Fig. 5]. The digital model 107 thus learns the statistical link between a set of images which correspond to satellite maps (“input” - input - figures 5(a), 5(b) and 5(c)) and the complete flows (“output” - output - figures 5(d) and 5(e)).

[0050] Learning phase

[0051] A geophysical digital model 1007 of the area under consideration is available. This geophysical digital model 1007 can be described as “objective” in that it implements explicitly defined functions. This geophysical digital model 1007 makes it possible to simulate the geophysical phenomena occurring in the area under consideration. The geophysical digital model 1007 implements, for example, the primitive equations, such as: - the Navier-Stokes equations in a rotating frame of reference, which reflect the conservation of momentum, - the continuity equation which reflects the conservation of mass, the conservation of energy, and / or the conservation of salt, - or the equation of state that relates the density of seawater to its temperature and salinity.

[0052] [43a] Such a geophysical model, which solves the primitive equations, is capable of simulate the full set of forces and physical laws that drive ocean flows. This means that the model reproduces a realistic simulation of the geostrophic and ageostrophic component of velocities, while also reproducing an exact match between the velocity output field and the temperature output field resulting from advection.

[0053] [43b] For example, the known model is implemented, at the priority date, under the model name “ROMS”, for “Regional Ocean Modeling System”, which can be translated into French as “Regional ocean modeling system as described for example in Alexander F. Shchepetkin et al. “the Regional oceanic modeling System (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model”, Ocean modeling, vol. 9, no. 4, pp. 347-404, 2005, or the model known, at the priority date, as the “NEMO” model, for “Nucleus for European Modelling of the Ocean,” which can be translated into French as “Nucleus for European Ocean Modeling,” as described for example in Madec, Gurvan, et al. “NEMO ocean engine.” (2017), or the model known, at the priority date, as the “Croco” model, for “Coastal and Regional Ocean COmmunity,” which can be translated into French as “COmmunauté d'Océan Régional et Côtier”), as described for example in Debreu et al. “Two-way nesting in split-explicit ocean models: Algorithms, implementation and validation,” Ocean modeling, 49-50, 1-21, and Auclair et al. “Some recent developments around the CROCO initiative for complex regional to Coastal modeling,” in Comod 2018 - Workshop on Coastal ocean modeling (pp. 1-47). All such references are incorporated herein by reference in their entirety for all purposes.This numerical geophysical model 1007 takes as input an initial state (e.g. bathymetry, atmospheric forcing, radiative flux and boundary conditions) for a certain domain (e.g. Mediterranean Sea or Atlantic Ocean), and determines modeled maps 10081 of the liquid flow velocity field, 10082 of the water height, and 1009 of the ocean surface temperature in the modeled area by applying a set of fluid mechanics equations. The obtained modeled maps 10082, 10081, are shown in Figures 5 (d) and (e), respectively. The obtained modeled map 1009 is shown in [Fig.7] (a). The flows determined by the numerical geophysical model 1007 are the complete flows, including the ageostrophic component of the flow.These modeled maps can for example be presented in the form of a set of points {(x; y); (um(x;y);vm(x;y)); tm(x;y)}, where (x;y) denote the coordinates of a point along the X and Y axes of the orthonormal reference frame, respectively, um and vm denote the components of the flow velocity field projected onto the X and Y axes, respectively, obtained from the numerical geophysical model 1007, and tm denotes the temperature at this point. The modeled maps 10082, 10081 and 1009 have a high resolution equivalent to that of the satellite map 104. In addition, the modeled maps 10082, 10081 and 1009 have geophysical representations (currents, eddies, fronts) similar to those present in the satellite maps 1032 and 104, which allows the learning process.It should be noted that the geophysical model is not necessarily assimilated, that is to say that it can deviate from the real conditions observed but that, however, the link between the modeled maps respects the laws of physics.

[0054] During the learning phase, a set of training data, synthetic first mapping data 10032, 10031, synthetic second mapping data 1004, and data of modeled maps 10082, IOO81 of velocity field for the sea surface generated by the digital geophysical model 1007.

[0055] By synthetic data, we mean data obtained from a process for reproducing synthetic satellite observations from modeled data. This process is called an "observation system simulation experiment". In the exemplary embodiment presented, the first mapping synthetic data 10032 and the second mapping synthetic data 1004 are determined from the modeled mapping data 10082, 10081 and 1009.

[0056] With regard to the synthetic data of first mapping 10032, a synthetic altimetric observation is reproduced, analogous to that used to obtain the satellite mapping 1032. Thus, to obtain the synthetic data 10032, a subset of points (x;y) 1003' of the mapping of the height of the modeled maritime surface 10082 is selected by simulating synthetic satellite traces. From these points (x;y), a mapping 10032 of the height of the sea surface is obtained by extrapolation and the mapping 10031 of the component of the geostrophic velocity is obtained by approximation with exactly the same procedure as that used to obtain the geostrophic component of the flow from the satellite mapping 1032. This process is illustrated in [Fig.6].

[0057] With regard to the synthetic data of second mapping 1004, which represents a temperature field of the surface considered, a synthetic infrared observation is reproduced, analogous to that used to obtain the satellite mapping 104. The modeled mapping 1009 is used as a simulation basis, on which the effect of cloud cover, apparent in the satellite mapping 104, is synthetically simulated. Thus, for each sample of modeled mapping 1009, we reproduce several samples of a synthetic mapping 1004, by adding cloud cover masks identical to those found in samples of the satellite mapping 104. The cloud cover of these masks can for example be of the order of up to 80% of the total surface area of ​​the mapping. A higher cloud cover could have a detrimental effect on the quality of the training.Clouds are represented numerically by a constant numerical value which can be for example 0. The simulation of clouds is illustrated in [Fig.7].

[0058] The aim of the training is to construct a digital model 107 which, from the synthetic data of first mapping 10032, 10031 and the data second mapping synthetics 1004, generates output close to modeled mapping data 10082, 10081.

[0059] The above-mentioned modeled and synthetic data pairs are divided into training and validation data.

[0060] The digital model 107 is thus trained, from this training data, to generate velocity field maps 108 from first satellite mapping data 1032 and second satellite mapping data 104. The digital model 107 comprises for example a convolutional neural network, an architecture whose weights are determined, during training, to take as input first satellite mapping data 1032 and second satellite mapping data 104 and to provide as output a velocity field map 108. This neural network produces a map of translationally equivariant characteristics via convolution operators. According to an exemplary embodiment, this architecture may for example correspond to an encoder-decoder such as Unet, a neural network architecture as described for example in Ronneberger, O., Fischer, P. and Brox, T., 2015, “U-net: Convolutional networks for biomedical image segmentation,” in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18 (pp. 234-241). Springer International Publishing, 2015, incorporated herein by reference in its entirety for any purpose. Visually, such a network has a shape approximating the shape of a “U.” The architecture is symmetrical and consists of three sections: the contraction section, the bottleneck section, and the expansion section. The contraction section may comprise an assembly of convolutional layers and “max pooling” layers tailored to capture the features of an image and reduce its size to reduce the number of parameters of the neural network. For example, two 3x3 convolutional layers are repeatedly applied. Each layer is followed by a ReLU activation function and batch normalization.Next, a 2x2 max pooling operation is applied to reduce the spatial dimensions. The bottleneck section connects the shrinkage section to the expansion section. It comprises, for example, two 3x3 convolution layers, where each layer is followed by a ReLU activation function. The expansion section implements the transposed convolution. This section can start with upsampling the feature map followed by a transposed 2x2 convolution layer. Afterwards, two 3x3 convolution layers are used, where each convolution is followed by a ReLU activation function.

[0061] [49a] According to another example of embodiment, this architecture can, for example: correspond to an encoder-decoder with a three-dimensional input dimension, where, in addition to the spatial dimensions, the temporal aspect of satellite maps is taken into account. For example, a neural network adapted to process three-dimensional images is implemented. In the particular case, the volumetric dimension is obtained by stacking two-dimensional images, each associated with successive instants. For example, an architecture called "3D UNET" is used, as described for example in Çiçek, Ôzgün, et al., "3D U-Net: learning dense volumetric segmentation from sparse annotation", Medical Image Computing and Computer-Assisted Intervention-MICCAI 2016: 19th International Conference, Athens, Greece, October 17-21, 2016, Proceedings, Part II 19, Springer International Publishing, 2016, incorporated herein by reference in its entirety for any purpose.

[0062] [49b] Thus, for example, we generate a time series of n input triplets each comprising synthetic data of first mapping 10032, 10031, synthetic data of second mapping 1004, and associated modeled mapping data 10082, 10081, as described above, with n included in 2 and Nmax, Nmax being for example between 3 and 30, and a triplet of volumes is generated comprising, for the first, a stack of the n synthetic data of first mapping 10032, 10031, for the second a stack of the n synthetic data of second mapping 1004, and, for the third, a stack of the n associated modeled mapping data 10082, 10081. The training set consists of a plurality of such triplets. Here, the fact that the geophysical model is a dynamic model is used. These triplets are obtained from the geophysical model, by recovering the maps generated for various instants by the same model.The goal of the training is to build a digital model 107 which, from the first mapping synthetic data stacks 10032, 10031 and the second mapping synthetic data stacks 1004, generates an output close to the modeled mapping data stacks 10082, IOOSl.

[0063] Alternatively, the digital model 107 may comprise a so-called "transformer" neural network, comprising self-attention layers adapted to track long-range dependencies in the images. The transformers make it possible in particular to integrate multimodal representations of satellite maps, such as, for example, two-dimensional images or one-dimensional satellite plots, with the corresponding positional encodings of the geographical location in question. The implementation of the transformers may be done, for example, by means of vision transformers, for example, using an architecture such as described in Dosovitskiy, Alexey, et al., "An image is worth 16x16 words: Transformers for image recognition at scale", arXiv preprint arXiv:2010.11929 (2020), incorporated herein by reference in its entirety for all purposes.

[0064] These two networks can have an encoder-decoder architecture.

[0065] According to an exemplary embodiment, the digital model 107 is a multimodal and multi-task model. For training, the multimodal input data are normalized. According to a particular example, the digital model 107 takes four modalities as input, and provides three results as output (i.e. its training consists of assimilating three tasks). The input modalities are, for a simulation carried out using the geophysical digital model 1007, the second mapping synthetic data 1004, the first mapping synthetic data 10032, 10031, and the X and Y components of the flow velocity field of the modeled mapping data 10082, 10081 from the same simulation. The tasks determined are the X and Y components of the high-resolution velocity field and the high-resolution altitude.The use of high-resolution altitude as a task facilitates, during training, a better convergence of the model towards the main task of interest to us in this method, i.e. the reconstruction of the high-resolution velocity field. For training, the X and Y components of the high-resolution velocity field determined by the numerical model 107 from the second-mapping synthetic data 1004 and the first-mapping synthetic data 10032, 10031 are compared with the components of the modeled mapping data 10082, 10081.

[0066] Use phase

[0067] Once the numerical model 107 is trained, if the trained numerical model 107 is applied to the synthetic validation data, the resulting velocity field map 108 from the numerical model 107 must be close to the modeled map 10081 obtained by the geophysical numerical model 1007 for these input data.

[0068] The performance of the trained digital model 107 is estimated by comparing the difference between the velocity field maps 108 resulting from the digital model 107 for a synthetic validation data set 10032, 10031, 1004, with the modeled map 10082, 10081, 1009 corresponding to the same set. This difference is evaluated using simple metrics such as for example the mean square deviation between all the pixels of the two images 108 and 10081. An equivalent difference is calculated between the pairs of synthetic validation data 10032, 10031 of the velocity field and altimetry and the modeled validation maps 10082, 10081, to calculate the equivalent deviation of a synthetic altimetry.

[0069] Through this validation process it can be demonstrated that the digital model 107 produces velocity field results 108 that are more faithful to the velocity fields 10081 compared to the synthetic first mapping data 10031. This fidelity can be represented in terms of correct representation of the angles of the vectors as well as their intensities.

[0070] In operational conditions, the trained numerical model 107 can be applied to a set of satellite maps 1032-104 obtained by satellite for a period T;, in order to obtain the high-resolution velocity field map 108 for the corresponding region and period. The numerical model 107 provides good results at least for a cloud cover of the satellite map 104 not exceeding 50%.

[0071] [57a] In the embodiment where the digital model 107 generates a volume, we select the slice of the volume which corresponds to the moment considered, that is to say typically the upper slice of the stack, which corresponds to the most recent moment.

[0072] [57b] The numerical reference 107 generically designates the models digital models relating satellite mapping data 1032 representative of a velocity field, satellite mapping data 104 of streamline topology, and velocity field maps 108 for the sea surface. The digital model presented above for a first embodiment may be designated by the reference 1071.

[0073] Variant

[0074] In the example presented, the surface height and fluid volume velocity field has a uniform mesh determined by extrapolation from raw data from satellite measurements along satellite tracks.

[0075] Alternatively, the synthetic first mapping data 10032 can be produced by selecting a subset of points (x;y) from the modeled sea surface height mapping 10082 by simulating synthetic satellite tracks, without performing an extrapolation. This simulates a phase upstream of the satellite mapping 1032, where only the raw satellite measurements along satellite tracks, as shown in [Fig.6] (b), are retained, while the rest of the image pixels are kept empty, providing a non-uniform mesh. This variant requires that the numerical model has been trained from this input data. For the operational application, the corresponding satellite mapping must be used.

[0076] The surface temperature field allows the topology of the streamlines of the fluid volume to be characterized. Alternatively, the topology of the streamlines of the fluid volume could be characterized by an image in one or more visible sensor bands. This could be an image of chlorophyll concentration 1042 as shown in [Fig.8], ocean color reflectance, or suspended particulate matter. This variant complements the satellite mapping by adding a visible measurement image to the infrared measurement image. To complete the learning scheme, the synthetic data of the second mapping 1004 must also reproduce the visible measurement. This variant therefore requires that the geophysical numerical model 1007 models the corresponding biogeophysical phenomena. In particular, compared to the geophysical numerical model 1007 presented above, an advective module is added to model the advection of particles on the velocity fields obtained by simulation.The chlorophyll concentration can be obtained from the pigment concentration data, by applying a biogeochemical model. A simulation of the cloud cover is carried out on the visible images in the same way as for the infrared images. This variant requires that the digital model 107 has been trained from these synthetic data of the second mapping 104 which include both infrared and visible images.

[0077] For this embodiment variant, the digital model 107 can be generated by self-supervised learning. The neural network learns in two steps. First, the task is solved based on pseudo-labels that help initialize the network weights. Second, the actual task is performed with supervised or unsupervised learning. More specifically, according to this embodiment, firstly, an intermediate digital model 109 is generated that is suitable for determining a high-resolution mapping of the sea surface velocity field, from a low-resolution satellite mapping 1032 representative of the velocity field and a high-resolution satellite mapping of surface temperature.For this, the method presented above can be implemented, in which triplets consisting of the high-resolution mapping of the sea surface velocity field, the low-resolution satellite mapping 1032 representative of the velocity field and the high-resolution satellite mapping of surface temperature 104i are synthetic maps generated from the geophysical model, and a neural network is trained to associate such triplets. Thus, the numerical model referred to here as intermediate can be the numerical model 107i presented above, except that it is only an intermediate in this variant.

[0078] This intermediate numerical model 109 is used to generate high-resolution velocity field maps from low-resolution satellite maps. resolution of the velocity field and surface temperature satellite maps, as presented above, for a number of instants.

[0079] In addition, for each of these moments, we have a satellite map of the chlorophyll concentration.

[0080] The digital model 1072 in this embodiment is trained from triplets of data comprising, for a time instant, the low-resolution satellite mapping of the velocity field, the satellite mapping of chlorophyll concentration, and the high-resolution velocity field mapping for that time instant determined by the intermediate module, as presented above.

[0081] A digital model 1072 is thus obtained linking satellite mapping data 1032 representative of a low-resolution velocity field, satellite mapping data 1042 of chlorophyll concentration representative of the topology of current lines, and high-resolution velocity field maps 108 for the sea surface.

[0082] In a particular case, the training of the digital model 1072 is trained from a selection of training triplets, the selection being based on the relevance score associated with the mapping of the high-resolution velocity field determined by the intermediate digital model 109. In other words, the digital model 1072 is only trained from data sets comprising a prediction deemed sufficiently reliable of the high-resolution velocity field mappings 108.

[0083] This same method can be used for any alternative streamline topology mapping 104 to chlorophyll concentration, such as particulate matter concentration mapping or otherwise.

[0084] According to the above embodiments, the determined maritime surface velocity field map 108 is a contemporary map of the satellite maps 1032 and 104. That is to say that the maps 1032, 104 and 108 can be associated with the same time interval. This time interval is defined on the scale of the temporal evolution of the phenomena studied. For example, the time interval in question is of a duration between 1 hour (h) and 48h. This means that the satellite maps 1032 and 104 were obtained in this same time interval, even if, from a practical point of view, they may not be exactly simultaneous, for example to be obtained using two different satellites flying over the region of interest at different times of the time interval in question.

[0085] According to another embodiment, the map 108 of the speed field of the determined maritime surface is a map predicted from the satellite maps 1032 and 104. That is to say that the map 108 is associated with a time interval later than that associated with maps 1032 and 104. The difference between the time interval associated with map 108 and that associated with maps 1032 and 104 is at least equal to 12 hours, for example at least equal to 24 hours. For example, it is equal to 1 day, 2 days, 3 days, 4 days, 5 days, 6 days, 7 days, 10 days, 15 days, or even 30 days.

[0086] In this embodiment, a digital forecasting model 1073 is used which can determine several maps 108, each associated with a different time interval, such as for example several of the time intervals presented above. The digital forecasting model 1073 can for example determine a map 108_D+1 associated with the day following the satellite maps (called “D+1”) and a map 108_D+2 associated with the following day (called “D+2”), as shown in [Fig. 10]. In this figure, by way of example, other images can correspond to other time intervals.

[0087] The time at which the determination is made is associated with the predicted maps. This allows the prediction to be made as soon as the most recent measurements are obtained.

[0088] Where appropriate, in addition to determining one or more predicted maps, the digital forecasting model 1073 may also determine the contemporary map as presented above (leftmost thumbnail in [Fig. 10]).

[0089] In the example above, the predicted map(s) are determined from a most recent set of satellite maps. However, as a variant, the digital forecasting model 1073 may use earlier satellite maps to determine the predicted map. The maps 1032 and 104 are associated with a time interval prior to the time at which the determination is implemented. The difference between the time at which the determination is implemented and the time interval associated with the maps 1032 and 104 is at least equal to 12 hours, for example at least equal to 24 hours. For example, it is equal to 1 day, 2 days, 3 days, 4 days, 5 days, 6 days, 7 days, 10 days, 15 days, or even 30 days.

[0090] Where appropriate, the digital forecasting model 1073 uses several sets of satellite maps 1032 and 104, corresponding to different past time intervals, to determine the predicted map. The digital forecasting model 1073 can, for example, determine a predicted map associated with the day following the most recent satellite maps (called “D+1”) and / or a map associated with the following day (called “D+2”) from data from the most recent satellite maps (called “D”) or from the previous day (called “D1”).

[0091] Alternatively, the digital forecasting model 1073 can determine a predicted map for day “D” from satellite map data associated with one or more past time intervals, for example associated with “D-1” and / or “D-2”.

[0092] In summary, the digital forecast model 1073 relates one or more satellite mapping data sets 1032 representative of a low-resolution velocity field (103_J-1, 103_J in [Fig. 11]), one or more satellite mapping data sets 104 of streamline topology (104_J-1, 104_J in [Fig. 1 1]), and one or more high-resolution velocity field mapping sets 108 for the sea surface (108_J, 108_J+1, 108_J+2 in [Fig. 1 1]). The satellite mapping datasets 1032 representing a low-resolution velocity field and satellite mapping 104 of streamline topology are associated two by two at the same times (for example, 103_J-1 and 104_J-1 in [Fig. 11]). If there are several, they are each associated with a different time (for example also 103_J and 104_J in [Fig. 11]).If there are multiple sets of high-resolution velocity field maps 108, they are associated with different times. At least one set of high-resolution velocity field maps 108 is associated with a different time than the times associated with the satellite mapping datasets 1032 representative of a low-resolution velocity field and satellite mapping 104 of streamline topology.

[0093] The digital model 1073 is thus trained, from this training data, to generate predicted velocity field maps 108 from first satellite mapping data 1032 and second satellite mapping data 104. According to an exemplary embodiment, the digital model 1073 may have a convolutional neural network architecture of “3D-unet” architecture, where the 3D dimension corresponds to the temporal aspect of the maps, as described above.

[0094] According to another exemplary embodiment, the digital model 1073 could have a so-called “transformer” architecture, where the time dimension is raised by positional encodings.

[0095] According to another exemplary embodiment, the digital model 1073 could have an architecture of a generative model called “diffusion” which progressively reconstructs the temporal evolution of the maps by considering the maps of an input instant (for example day “D”) and by reconstructing a later instant (for example the following day “D+1”) by learning a process of adding noise and denoising. This digital model 1073 learned the latent structure of the data set by modeling the way in which the data points diffuse in their latent space, as described in Ho, Jonathan, Ajay Jain, and Pieter Abbeel. “Denoising diffusion probabilistic models.” Advances in neural information processing Systems 33 (2020): 6840-6851, incorporated herein by reference in its entirety for all purposes.

[0096] Alternatively, the digital model 1073 with an architecture of a so-called “diffusion” generative model, taking into account a certain input for an input instant (for example for day “D”), proposes several outputs for a later instant (for example the following day “D+1”) by varying the noise added in the denoising process. These multiple mapping outputs are called ensemble forecasts for the later instant (for example day “D+1”) in question. The ensemble forecasts offer various possible scenarios for the future evolution of the maritime flows in question, which makes it possible to adopt probabilistic approaches for the use of these forecast data. Alternatively, it is possible to use inputs for several contemporary and / or past instants, and obtain outputs for several contemporary and / or future instants. List of reference signs

[0097] 100: Computerized system

[0098] 101: Processor

[0099] 102: Memory

[0100] 1032: First satellite mapping

[0101] 104: Second satellite mapping

[0102] 107: Digital model

[0103] 1072: Digital model

[0104] 1073: Digital model

[0105] 108: Dynamic modeled mapping (height or velocity field)

[0106] 109: Intermediate digital model

[0107] 10032, 10031: First mapping synthetic data

[0108] 1004: Second mapping synthetic data

[0109] 1007: Geophysical digital model

[0110] 10082, 10081: Dynamic modeled mapping (height, velocity field)

[0111] 1009: Modeled temperature mapping

[0112] 1003': Synthetic data of first mapping

Claims

Claims

1. Computerized method for determining a predicted mapping of a velocity field of a maritime surface, in which: - A low-resolution satellite mapping (1032) representative of a velocity field of the maritime surface is provided, - A high-resolution satellite mapping (104) of the topology of the streamlines of the maritime surface is provided, - A computerized determination module determines the predicted mapping (108) of the velocity field of the maritime surface, comprising an ageostrophic component, having a resolution greater than the low resolution, from said satellite mapping (1032) representative of a velocity field, from said satellite mapping (104) of topology, and from a digital model (107) relating satellite mapping data (1032) representative of a velocity field, satellite mapping data (104) of streamline topology,and subsequent velocity field maps (108) for the sea surface, - the digital model (107) having been previously obtained by learning, the learning being carried out by comparing results of the digital model (107) with results obtained by an objective geophysical digital model.,

2. Computerized method according to claim 1 in which, during the training, synthetic second mapping data (1004) were generated from the results of the geophysical digital model.

3. Computerized method according to claim 1 or 2 in which the objective geophysical digital model implements at least one of the Navier-Stokes equations, the continuity equation reflecting the conservation of mass, energy and / or salt, or the equation of state linking density, temperature and salinity.

4. Computerized method according to one of claims 1 to 3, in which the digital model (107) is a multi-modal and multi-task model.

5. A computerized method according to any one of claims 1 to 4, wherein the digital model (107) uses satellite mapping data (1032) representative of a velocity field and satellite mapping data (104) of streamline topology contemporary with and prior to the velocity field mappings (108) for the sea surface.

6. A computerized method according to any one of claims 1 to 5, wherein the computerized determination module determines a predicted map (108) of the sea surface velocity field from ensemble predictions of multiple such maps.

7. A computerized method according to one of claims 1 to 6, wherein the low-resolution satellite mapping (1032) representative of a sea surface velocity field comprises cloud cover of between 10% and 40%, and wherein the high-resolution satellite mapping (104) of streamline topology of the sea surface comprises cloud cover of between 10% and 40%.

8. The computerized method of claim 7, wherein the training input data comprises cloud cover synthetically added onto a cloud-free map.

9. Computerized method according to one of claims 1 to 8, in which, as low-resolution satellite mapping (1032) representative of a sea surface velocity field, a low-resolution mapping of a sea surface velocity field or a mapping of a sea surface altimetry field, with regular or irregular meshing along satellite traces, is provided.

10. Computerized method according to one of claims 1 to 9, in which, as high-resolution satellite mapping (104) of the topology of the current lines of the sea surface, a mapping of surface temperature, chlorophyll concentration and / or concentration of particulate matter suspended on the sea surface is provided.

11. A computerized method according to claim 10, wherein, as high-resolution satellite mapping (104) of streamline topology of the sea surface, a mapping of chlorophyll concentration and / or suspended particulate matter concentration at the sea surface is provided, and wherein the digital model (107) is generated by self-supervised learning using the surface temperature mapping.

12. Computer program comprising portions of program code for executing the steps of the method according to one of claims 1 to 11 when said program is executed on a computer.

13. A computerized system for determining a predicted mapping of a velocity field of a sea surface, comprising: - A computerized determination module adapted to determine the predicted mapping of the velocity field of the sea surface, comprising an ageostrophic component, from a low-resolution satellite mapping (1032) representative of a velocity field of the sea surface, a high-resolution satellite mapping (104) of the topology of the streamlines of the sea surface and a digital model relating satellite mapping data (1032) representative of a velocity field, satellite mapping data (104) of the topology of streamlines, and subsequent modeled velocity field maps (108) for the sea surface, said mapping of the velocity field of the sea surface obtained having a resolution greater than the low resolution,- the digital model (107) having been previously obtained by learning, the learning being carried out by comparing results of the digital model (107) with results obtained by an objective geophysical digital model.,

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