Computerized method and system for determining a map of a velocity field of a maritime surface

Abstract

The computerized method for determining a map of a velocity field of a maritime surface comprises providing a low-resolution satellite map (1032) representative of a velocity field of the maritime surface, and a high-resolution topological satellite map (104) of the current lines of the maritime surface. A computerized determination module determines the map (108) of the velocity field of the maritime surface, comprising an ageostrophic component, having a resolution higher than the low resolution, based on said satellite map (1032) representative of a velocity field, on said topological satellite map (104), and on a numerical model (107).

Description

Method and computerized system for determining a velocity field map of a maritime surface. SCOPE OF THE INVENTION

[0001] The present invention relates to computerized methods and systems for determining a velocity field map of a maritime surface. "Maritime" refers to a sea or ocean. TECHNOLOGICAL BACKGROUND

[0002] In large bodies of water, particularly seas and oceans, flows are governed by complex geophysical laws. To understand these flows, complex observation systems are used, notably satellite data acquisition. Thus, it is well-established to use satellite altimetry observations to evaluate the surface displacement fields of the water body. The geostrophic approximation is used to determine the velocity field from the height irregularities identified by the satellite observation. However, the acquisition is dependent on the satellites' trajectories and the resolution of the sensors used. This results in good accuracy of the evaluation directly under the satellite's trajectory, but uncertainty in the fields evaluated far from the satellites' trajectories, which are obtained by extrapolation. Consequently, the uncertainty of the determined velocity field is inhomogeneous.However, a good understanding of flows is of interest from an industrial perspective, for example for optimizing maritime transport, monitoring pelagic species or concentrations of microplastic waste, or search and rescue at sea, or other purposes.

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

[0004] However, the aim is to obtain a more accurate representation of marine flows, using as many available satellite observations as possible. This involves, on the one hand, obtaining a high-resolution assessment of the flows, estimating the total current vector field, of which the geostrophic component is only a part (hereafter referred to as "complete flows"), and reducing the uncertainty associated with certain assessments. SUMMARY OF THE INVENTION

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

[0006] These measures allow for the creation of a complete map of sea surface flows, taking into account the ageostrophic component of the flow. This results in a more reliable estimate of the flow.

[0007] Depending on various aspects, it is possible to predict one and / or the other of the characteristics below taken alone or in combination.

[0008] According to one implementation, the numerical model was previously obtained by learning, the learning being carried out by comparing results of the numerical model with results obtained by an objective geophysical numerical model.

[0009] According to one achievement, during the learning process, synthetic second mapping data was generated from the results of the geophysical numerical model. [09a] According to one embodiment, the objective geophysical numerical 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.

[0010] According to one realization, the digital model is a multi-modal and multi-task model. [10a] According to one embodiment, the numerical model uses satellite mapping data representative of a velocity field and satellite mapping data of streamline topology contemporaneous with and prior to the velocity field maps for the sea surface. [10b] According to one embodiment, the computerized determination module determines a predicted map of the sea surface velocity field, from said satellite mapping representing a velocity field, said satellite topology mapping, and a numerical model relating data from satellite mapping representing a velocity field, satellite mapping data of streamline topology, and subsequent velocity field maps for the sea surface. [10c] According to one embodiment, the computerized determination module determines a predicted map of the sea surface velocity field from ensemble predictions of multiple such maps.

[0011] According to one realization, low-resolution satellite mapping representative of a sea surface velocity field includes cloud cover of between 10% and 40%, and in which high-resolution satellite mapping of sea surface streamline topology includes cloud cover of between 10% and 40%.

[0012] According to one realization, the training input data includes cloud cover synthetically added onto a cloud-free map.

[0013] According to one embodiment, a low-resolution satellite map representing a sea surface velocity field is provided, or a map of a sea surface altimetry field, with a regular or irregular grid along satellite tracks.

[0014] According to one implementation, a map of surface temperature, chlorophyll concentration and / or concentration of suspended particulate matter at the sea surface is provided as a high-resolution satellite mapping of the topology of sea surface current lines. [14a] According to one embodiment, a high-resolution satellite map of sea surface streamline topology is provided, along with a map of chlorophyll concentration and / or suspended particulate matter concentration at the sea surface, and the numerical model is generated by self-supervised learning using the surface temperature map.

[0015] According to another aspect, the invention relates to a computer program comprising portions of program code for the execution of the steps of this process when said program is executed on a computer.

[0016] In another aspect, the invention relates to a computerized system for determining a velocity field map of a sea surface, comprising: - A computerized determination module adapted to determine the mapping of the sea surface velocity field, including an ageostrophic component, from low-resolution satellite mapping representative of a sea surface velocity field, a high-resolution satellite mapping of sea surface streamline topology 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 sea surface velocity field mapping having a resolution higher than the low resolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Embodiments of the invention will be described below with reference to the drawings, briefly described below:

[0018] [Fig. 1] schematically represents a computerized system according to one embodiment of the invention.

[0019] [Fig. 2] represents a satellite-acquired map of sea surface altimetry.

[0020] [Fig. 3] represents a satellite-acquired map of sea surface temperature.

[0021] [Fig. 4] represents a flow map obtained from a trained numerical model.

[0022] [Fig. 5] represents a set of maps used to train the numerical model.

[0023] [Fig. 6] represents the schematic of an observation system simulation experiment used to obtain synthetic data for the first surface altimetry mapping.

[0024] [Fig. 7] represents an example of synthetic simulation of cloud cover.

[0025] [Fig. 8] represents a satellite-acquired map of chlorophyll concentration. [25a] [Fig. 9] is a figure similar to figure 1 which schematically represents a computerized system according to an embodiment of the invention. [25b] [Fig. 10] represents a time series of images superimposing a satellite temperature map and a dynamically modeled map juxtaposed for several respective time intervals. [25c] [Fig. 11] is a figure similar to figure 1 which schematically represents a predictive computerized system according to an embodiment of the invention.

[0026] In the drawings, identical references designate identical or similar objects. DETAILED DESCRIPTION

[0027] Figure 1 schematically represents a computerized system for determining the velocity field of a sea surface. A sea surface is defined as a surface layer of a sea or ocean extending typically 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 sea surface in question is not necessarily enclosed. For example, the sea surface could be the Mediterranean Sea, or a part of it, particularly one with an area of ​​at least 250 km x 250 km. However, the invention is applicable to other seas or oceans, such as the Atlantic Ocean.

[0028] The flow can be characterized by a velocity field that we wish to determine. Specifically, we want to determine the horizontal components {U; V} of this velocity field in a horizontal orthonormal plane coordinate system (O; X; Y). The velocity field {U; V} is defined as the sum of a geostrophic component and an ageostrophic component.

[0029] The geostrophic term corresponds to the component that results from the balance between the Coriolis force and the force due to the pressure gradient.

[0030] The term ageostrophic corresponds to other equilibria, such as that between the Coriolis force and the centrifugal force. In this case, we are interested in the ageostrophic term averaged over a time period relevant to the application, for example, from 6 to 48 hours.

[0031] The computerized system 100 includes a processor 101 adapted to execute a computer program stored in a memory 102. Data, which will be described in more detail later, can also be stored in the memory 102. The processor 101 and / or the memory 102 can be located in the same device or distributed across a network.

[0032] Figure 2 schematically represents a first 1032 satellite map representing a sea surface velocity field. The planar orthonormal coordinate system is used for orientation within this first map. This first 1032 satellite map is stored in memory 102. This first 1032 satellite map can, for example, be represented as a set of points {(x; y); h(x; y)}, where (x; y) denote the coordinates of a point along the X and Y axes of the orthonormal coordinate system, respectively, and h denotes the altitude at the point with coordinates (x; y).

[0033] The first 1032 satellite map is obtained for a period To. The duration of this period is typically from 6h to 36h, notably from 12h to 24h.

[0034] The first 1032 satellite map is obtained from a satellite altimetry image. According to this first embodiment, the raw satellite altimetry image is obtained from one or more satellite tracks over the sea surface during the period T0. The sea surface height field of the first 1032 satellite map is obtained by extrapolating the satellite altimetry data measured along the satellite tracks onto a regular grid. From this sea surface height field, the geostrophic component of the sea surface velocity field can be calculated by approximating the geostrophic component, transforming the height field into a pressure field. Due to the spacing of the satellite tracks, the first 1032 satellite map 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, compared to the resolutions of the other maps considered. Furthermore, the uncertainty associated with these points is inhomogeneous. The first satellite map, 1032, is therefore a map averaged over the period T0.

[0035] Figure 3 schematically represents a second satellite map 104 representative of a surface temperature field of the fluid volume.

[0036] For example, the same orthonormal coordinate system (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 as a set of points {(x; y); 0(x; y)}, where 0 denotes the surface temperature.

[0037] The second satellite map 104 is also obtained for the period To.

[0038] The second satellite map 104 is obtained from a satellite image of ocean surface temperature (observed by infrared sensors). According to this first embodiment, the satellite temperature image is obtained from one or more satellite tracks passing over the fluid volume during the period T0. Due to the swath spacing and the infrared sensor acquisition technology, 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. Furthermore, the uncertainty associated with these points is homogeneous. The satellite map 104 resulting Infrared observation is likely to be covered by clouds that obscure sampling, inducing missing data points on unsampled pixels.

[0039] The processor implements a computerized determination module adapted to determine a velocity field map for the sea surface. This computerized determination module implements a numerical model 107 relating first satellite mapping data 1032, second satellite mapping data 104, and velocity field maps 108 for the sea surface.

[0040] In particular, the 108 velocity field map for the sea surface has a better resolution than the first satellite mapping data 1032. The 108 map from the numerical model 107 is shown in Figure 4. In addition, the 108 velocity field map for the sea surface corresponds to the complete flows, including both the geostrophic component and an ageostrophic part of the flows.

[0041] Numerical model 107, for example, was obtained through machine learning. It can also be described as a "statistical" model. In the example presented, it is a deep convolutional neural network. This numerical model defines a relationship between a set of input and output images, as illustrated in Figure 5. Numerical model 107 thus learns the statistical link between a set of images that correspond to satellite maps ("input" - Figures 5(a), 5(b) and 5(c)) and the complete flows ("output" - Figures 5(d) and 5(e)).

[0042] Learning phase

[0043] A geophysical numerical model (GNM) 1007 is available for the area under consideration. This GNM 1007 can be described as "objective" in that it implements explicitly defined functions. This GNM 1007 allows for the simulation of geophysical phenomena occurring in the area under consideration. For example, the GNM 1007 implements primitive equations, such as: - the Navier-Stokes equations in a rotating frame of reference, which express the conservation of momentum, - the continuity equation which expresses 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. [43a] Such a geophysical model, which solves the primitive equations, is capable of simulating all the forces and physical laws that lead to ocean flows. This means that the model reproduces a realistic simulation of the geostrophic and ageostrophic components of velocities, while also reproducing an exact correspondence between the velocity output field and the temperature output field resulting from advection. [43b] For example, the model known at the priority date as the "ROMS" model, for "Regional Ocean Modeling System", can be translated into French as "Système régional de modèlenage océanique tel que descriptive par exemple dans Alexander F. Shchepetkin et al. "the Regional oceanic modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model", Ocean modelling, 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", can be translated into French as "Nucleus pour la modèlenage européenne de l'océan", 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,” as described, for example, in Debreu et al., “Two-way nesting in split-explicit ocean models: Algorithms, implementation and validation,” Ocean modelling, 49–50, 1–21, and Auclair et al., “Some recent developments around the CROCO initiative for complex regional to coastal modelling,” in Comod 2018 – Workshop on coastal ocean modelling (pp. 1–47). All these references are incorporated here in their entirety for any purpose.This geophysical numerical model 1007 takes as input an initial state (e.g., bathymetry, atmospheric forcing, radiative flux, and boundary conditions) for a certain domain (e.g., the Mediterranean Sea or the Atlantic Ocean), and determines modeled maps 1008i of the liquid flow velocity field, IOO82 of the water depth, and 1009 of the ocean surface temperature in the modeled area by applying a set of fluid mechanics equations. The resulting modeled maps IOO82 and IOO81 are shown in Figures 5(d) and (e), respectively. The resulting modeled map 1009 is shown in Figure 7(a). The flows determined by the geophysical numerical model 1007 are the complete flows, including the ageostrophic component of the flow. These modeled maps can, for example, be presented as a set of points {(x; y); (u; m (x ;y) ;v m (x ;y)) ; tm (x; y)}, where (x; y) denote the coordinates of a point along the X and Y axes of the orthonormal coordinate system, respectively, u m and v m denote the components of the flow velocity field projected onto the X and Y axes, respectively, obtained from the geophysical numerical model 1007, and t m denotes the temperature at that point. The modeled maps IOO82, IOO81, and 1009 exhibit a high equivalent resolution to that of satellite map 104. Furthermore, the modeled maps IOO82, IOO81, and 1009 present geophysical representations (currents, eddies, fronts) analogous to those found in satellite maps 1032 and 104, thus enabling the learning process. It should be noted that the geophysical model is not necessarily assimilated; that is, it may deviate from the observed real-world conditions. However, the relationship between the modeled maps respects the laws of physics.

[0044] During the learning phase, a training dataset is provided, synthetic first mapping data 10032, 1003i, synthetic second mapping data 1004, and modeled mapping data IOO82, IOO81 of velocity field for the sea surface generated by the geophysical numerical model 1007. By synthetic data, we mean data obtained through a process that reproduces synthetic satellite observations from modeled data. This process is called an "observation system simulation experiment." In the example implementation presented, the synthetic data for the first map 10032 and the synthetic data for the second map 1004 are determined from the modeled map data IOO82, IOO81, and 1009.

[0045] Regarding the synthetic data for the initial 10032 mapping, a synthetic altimetric observation is reproduced, analogous to that used to obtain the 1032 satellite map. Thus, to obtain the synthetic 10032 data, a subset of points (x; y) 1003' is selected from the modeled sea surface height map IOO82 by simulating synthetic satellite tracks. From these points (x; y), a 10032 sea surface height map is obtained by extrapolation, and the 1003i geostrophic velocity component map is obtained by approximation using exactly the same procedure as that used to obtain the geostrophic flow component from the 1032 satellite map. This process is illustrated in Figure 6.

[0046] Regarding the synthetic data from the second map 1004, which represents a temperature field of the surface under consideration, a synthetic infrared observation is reproduced, analogous to that used to obtain the satellite map 104. The modeled map 1009 is used as the simulation basis, on which the effect of cloud cover, apparent in the satellite map 104, is synthetically simulated. Thus, for each sample of the modeled map 1009, we reproduce several Samples of a synthetic map 1004 are created by adding cloud cover masks identical to those found in samples of the satellite map 104. The cloud cover of these masks can, for example, be up to 80% of the total map area. Higher cloud cover could negatively impact training quality. Clouds are represented numerically by a constant value, which can be, for example, 0. The cloud simulation is illustrated in Figure 7.

[0047] The goal of the training is to build a numerical model 107 which, from the synthetic data of first mapping 10032, 1003i and the synthetic data of second mapping 1004, generates an output close to the modeled mapping data IOO82, IOO81.

[0048] The modeled and synthetic data pairs mentioned above are divided into training and validation data.

[0049] The numerical model 107 is thus trained, using this training data, to generate velocity field maps 108 from first satellite mapping data 1032 and second satellite mapping data 104. The numerical model 107 includes, for example, a convolutional neural network, architected with weights 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 features via convolution operators. According to one embodiment, this architecture can, for example, correspond to an encoder-decoder such as the Unet, a neural network architecture such as that 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 in its entirety by reference for any purpose. Visually, such a network has a shape approximating the form of a “U.” The architecture is symmetrical and consists of three sections: the contraction section, the choke section, and the expansion section. The contraction section may include an assembly of convolutional and max-pooling layers tailored to capture the features of an image and reduce its size to minimize the number of parameters in the neural network. For example, two 3x3 convolutional layers are repeatedly applied. Each layer is followed by a ReLU activation function and batch normalization. Then, a 2x2 max pooling operation is applied to reduce the spatial dimensions. The bottleneck section connects the contraction section to the expansion section. It includes, for example, two 3x3 convolution layers, where each layer is followed by a ReLU activation function. The expansion section implements transposed convolution. This section might begin with oversampling of the feature map followed by a transposed 2x2 convolution layer. Afterward, two 3x3 convolution layers are used, where each convolution is followed by a ReLU activation function. [49a] According to another 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 this particular case, the volumetric dimension is obtained by stacking two-dimensional images, each associated with successive time points. For example, we use an architecture called "3D UNET", 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, integrated here by reference in its entirety for any purpose. [49b] Thus, for example, a time series of n input triplets is generated, each comprising synthetic first-map data 10032, 1003i, synthetic second-map data 1004, and associated modeled map data IOO82, IOO81, as described above, with n between 2 and Nmax, Nmax being, for example, between 3 and 30. A volume triplet is generated, comprising, for the first, a stacking of the n synthetic first-map data 10032, 1003i, for the second a stacking of the n synthetic second-map data 1004, and, for the third, a stacking of the n associated modeled map data IOO82, IOO81. The training set consists of a plurality of such triplets. This takes advantage of the fact that the geophysical model is a dynamic model.These triplets are obtained from the geophysical model, by retrieving the maps generated for various times by the same model. The goal of the training is to build a numerical model 107 which, from the synthetic data stacks of the first mapping 10032, 1003i and the synthetic data stacks of the second mapping. 1004, generates an output close to the IOO82, IOO81 modeled mapping data stacks.

[0050] Alternatively, the numerical model 107 can include a so-called "transformer" neural network, comprising self-attention layers adapted to track long-range dependencies in images. Transformers allow, in particular, the integration of multimodal representations of satellite maps, such as two-dimensional images or one-dimensional satellite traces, with the corresponding positional encodings of the geographic location in question. The implementation of transformers can be achieved, for example, through vision transformers, using an architecture such as that 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 here in its entirety by reference for any purpose.

[0051] These two networks can exhibit an encoder-decoder architecture.

[0052] According to one embodiment, the numerical model 107 is a multimodal and multitask model. For training, the multimodal input data is normalized. In a specific example, the numerical model 107 takes four modalities as input and provides three outputs (i.e., its training consists of assimilating three tasks). The input modalities for a simulation performed using the geophysical numerical model 1007 are the synthetic second-stage mapping data 1004, the synthetic first-stage mapping data 10032, 1003i, and the X and Y components of the flow velocity field from the modeled mapping data IOO82, IOO81 from the same simulation. The tasks determined are the high-resolution X and Y components of the velocity field and the high-resolution elevation.Using high-resolution altitude as a training task facilitates better convergence of the model towards the main task of interest in this process, namely the reconstruction of the high-resolution velocity field. For training purposes, the X and Y components of the high-resolution velocity field determined by the numerical model 107 from the synthetic second-map data 1004 and the synthetic first-map data 10032, 1003i are compared with the components of the modeled map data IOO82, IOO81.

[0053] Usage phase

[0054] 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 should be close to the modeled mapping 1008i obtained by the geophysical numerical model 1007 for these input data.

[0055] The performance of the trained numerical model 107 is estimated by comparing the difference between the resulting velocity field maps 108 from the numerical model 107 for a synthetic validation dataset 10032, 1003i, 1004, with the corresponding modeled mapping IOO82, IOO81, 1009 for the same dataset. This difference is evaluated using simple metrics such as the root mean square deviation between all pixels of the two images 108 and IOO81. An equivalent difference is calculated between the synthetic validation data pairs 10032, 1003i of the velocity and altimetry field and the modeled validation maps IOO82, IOO81, to calculate the equivalent deviation of a synthetic altimetry.

[0056] Through this validation process, it can be demonstrated that the numerical model 107 produces velocity field results 108 that are more faithful to the velocity fields IOO81 compared to the synthetic data from the first mapping 1003i. This fidelity can be represented in terms of the correct representation of the vector angles as well as their intensities.

[0057] Under operational conditions, the trained numerical model 107 can be applied to a set of satellite maps 1032-104 acquired by satellite for a period Tj, 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 cloud cover in the satellite map 104 not exceeding 50%. [57a] In the embodiment where the digital model 107 generates a volume, the slice of the volume that corresponds to the time considered is selected, that is typically the top slice of the stack, which corresponds to the most recent time. [57b] The numerical reference 107 generically designates numerical models relating satellite mapping data 1032 representing a velocity field, satellite mapping data 104 of streamline topology, and velocity field maps 108 for the sea surface. The numerical model presented above for a first embodiment may be designated by the reference 107i.

[0058] Variant

[0059] In the example shown, the surface height and velocity field of the fluid volume has a uniform mesh determined by extrapolation from raw data from satellite measurements along satellite tracks.

[0060] Alternatively, synthetic first-stage mapping data 10032 can be produced by selecting a subset of points (x, y) from the modeled sea surface height map IOO82 and simulating synthetic satellite tracks, without extrapolation. This simulates an upstream phase of satellite mapping 1032, where only the raw satellite measurements along satellite tracks, as shown in Figure 6(b), are retained, while the remaining image pixels are left blank, providing a non-uniform mesh. This alternative requires that the numerical model has been trained using this input data. For operational application, the corresponding satellite map must be used.

[0061] The surface temperature field allows for the characterization of the fluid volume streamline topology. Alternatively, the fluid volume streamline topology 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 Figure 8, ocean color reflectance, or suspended particulate matter. This variant complements the satellite mapping by combining the infrared measurement image with a visible measurement image. To complete the training scheme, the synthetic data from the second mapping 1004 must also reproduce the visible measurement. This variant therefore requires that the geophysical numerical model 1007 model the corresponding biogeophysical phenomena.Specifically, compared to the geophysical numerical model 1007 presented above, an advective module is added to model particle advection on velocity fields obtained through simulation. Chlorophyll concentration can be obtained from pigment concentration data by applying a biogeochemical model. Cloud cover is simulated on visible images in the same way as for infrared images. This variant requires that the numerical model 107 be trained using these synthetic data from the second mapping 104, which includes both infrared and visible images.

[0062] For this embodiment, the numerical model 107 can be generated by self-supervised learning. The neural network learns in two stages. 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, an intermediate numerical model 109 is first generated, adapted to determine a high-resolution map of the sea surface velocity field from a low-resolution satellite map 1032. representative of the velocity field and a high-resolution satellite map of surface temperature. To achieve this, the process described above can be implemented, in which triplets consisting of the high-resolution sea surface velocity field map, the low-resolution 1032 satellite map representing the velocity field, and the high-resolution 104i satellite map of surface temperature 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 107i numerical model presented above, except that it is only an intermediate model in this variant.

[0063] This intermediate numerical model 109 is used to generate high-resolution velocity field maps from low-resolution satellite velocity field maps and satellite surface temperature maps, as shown above, for a number of times.

[0064] In addition, for each of these moments, we have satellite mapping of chlorophyll concentration.

[0065] The 1072 numerical model in this embodiment is trained from data triplets comprising, for a given instant, the low-resolution satellite mapping of the velocity field, the satellite mapping of chlorophyll concentration, and the high-resolution mapping of the velocity field for that instant determined by the intermediate module, as shown above.

[0066] This gives us a 1072 numerical model relating 1032 satellite mapping data representing a low-resolution velocity field, 1042 satellite mapping data of chlorophyll concentration representing the topology of streamlines, and 108 high-resolution velocity field maps for the sea surface.

[0067] In a particular case, the training of the numerical model 1072 is trained from a selection of training triplets, the selection being based on the relevance score associated with the high-resolution velocity field mapping determined by the intermediate numerical model 109. In other words, the numerical model 1072 is trained only from datasets including a prediction deemed sufficiently reliable of the high-resolution velocity field maps 108.

[0068] This same method can be used for any 104 streamline topology mapping alternative to chlorophyll concentration, such as particulate matter concentration mapping or other.

[0069] According to the embodiments above, the 108 velocity field map of the determined sea surface is a map contemporaneous with the 1032 and 104 satellite maps. That is to say, 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 between 1 hour (h) and 48 h. This means that the 1032 and 104 satellite maps were obtained within this same time interval, even if, from a practical point of view, they may not be exactly simultaneous, for example, because they were obtained using two different satellites flying over the region of interest at different times within the time interval in question.

[0070] According to another embodiment, the determined sea surface velocity field map 108 is a map predicted from satellite maps 1032 and 104. That is, 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 12 hours, for example, at least 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.

[0071] In this embodiment, a numerical forecasting model 107s 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 numerical forecasting model 107s can, for example, determine a map 108_J+1 associated with the day following the satellite maps (called "J+1") and a map 108_J+2 associated with the following day (called "J+2"), as shown in Figure 10. In this figure, by way of example, other images can correspond to other time intervals.

[0072] 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.

[0073] If necessary, in addition to determining one or more predicted maps, the 107s numerical forecasting model can also determine the contemporary map as shown above (leftmost thumbnail in Figure 10).

[0074] In the example above, the predicted map(s) are determined from the most recent set of satellite maps. However, alternatively, the 107s numerical forecasting model can use satellite maps. Previous events are used to determine the predicted map. Maps 1032 and 104 are associated with a time interval prior to the moment the determination is implemented. The difference between the moment the determination is implemented and the time interval associated with maps 1032 and 104 is at least 12 hours, for example, at least 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.

[0075] Where appropriate, the 107s numerical forecasting model uses several sets of satellite maps (1032 and 104), corresponding to different past time intervals, to determine the predicted map. The 107s numerical forecasting model can, for example, determine a predicted map associated with the day following the most recent satellite maps (referred to as "D+1") and / or a map associated with the following day (referred to as "D+2") from the most recent satellite map data (referred to as "D") or from the previous day (referred to as "D-1").

[0076] Alternatively, the 107s numerical forecasting model can determine a predicted map for day "D" from satellite mapping data associated with one or more past time intervals, for example associated with "D- 1" and / or at "D-2".

[0077] In summary, the 107s numerical forecasting model links one or more satellite mapping datasets 1032 representing a low-resolution velocity field (103_J-1, 103_J in Figure 11), one or more satellite mapping datasets 104 of streamline topology (104_J-1, 104_J in Figure 11), and one or more high-resolution velocity field mapping datasets 108 for the sea surface (108_J, 108_J+1, 108_J+2 in Figure 11). The satellite mapping datasets 1032 representing a low-resolution velocity field and 104 of streamline topology are paired at the same time points (e.g., 103_J-1 and 104_J-1 in Figure 11). If there are several, they are each associated with a different time (for example, also 103_J and 104_J in Figure 11). If there are several 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 time different from the times associated with the satellite mapping datasets 1032 representing a low-resolution velocity field and satellite mapping datasets 104 of streamline topology.

[0078] The numerical model 107s is thus trained, using this training data, to generate predicted velocity field maps 108 from first satellite mapping data 1032 and data from second satellite mapping 104. According to an example of implementation, the digital model 107s can 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.

[0079] According to another example of implementation, the 107s digital model could have a so-called "transformer" architecture, where the temporal dimension is raised by positional encodings.

[0080] In another implementation example, the 107s numerical model could employ a generative "diffusion" model architecture that progressively reconstructs the temporal evolution of the maps by considering the maps from an input time (e.g., day "D") and reconstructing a subsequent time (e.g., the following day "D+1") through a process of adding and denoising noise. This 107s numerical model has learned the latent structure of the dataset by modeling how 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 here in its entirety by reference for any purpose.

[0081] Alternatively, the 107s numerical model, with a generative "diffusion" model architecture, takes a given input for a specific time point (e.g., day "D") and provides several outputs for a later time point (e.g., the following day "D+1") by varying the amount of noise added during the denoising process. These multiple map outputs are called ensemble forecasts for the later time point (e.g., day "D+1") in question. Ensemble forecasts offer various possible scenarios for the future evolution of the marine flows under consideration, allowing for probabilistic approaches to the use of this forecast data. Alternatively, one can use inputs for several contemporary and / or past times to obtain outputs for several contemporary and / or future times points. LIST OF REFERENCE SIGNS 100: Computerized system 101: Processor 102: Memory 1032: First satellite map 104: Second satellite map 107: Digital model 1072: Digital model 1073: Digital Model 108: Dynamic modeled mapping (height or velocity field) 109: Intermediate digital model 10032, 1003i: Synthetic data from the first mapping; 1004: Synthetic data from the second mapping 1007: Geophysical Numerical Model IOO82, IOO81: Dynamic modeled mapping (height, velocity field) 1009: Modeled Temperature Mapping 1003': Synthetic data from the initial mapping

Claims

CLAIMS 1. Computerized method for determining a map of a speed field of a maritime surface, in which: - A low-resolution satellite map (1032) representative of a sea surface velocity field is provided, - High-resolution satellite mapping (104) of the topology of the current lines of the sea surface is provided, - A computerized determination module determines the 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 topology of streamlines, and velocity field maps (108) for the maritime surface.

2. Computerized method according to claim 1, in which the digital model (107) has 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.

3. Computerized method according to claim 2 wherein, during the learning, synthetic second mapping data (1004) were generated from the results of the geophysical digital model.

4. Computerized method according to claim 2 or 3 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.

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

6. A computerized method according to any one of claims 1 to 5, 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 maps (108) for the sea surface.

7. Computerized method according to any one of claims 1 to 6, in which the computerized determination module determines a predicted mapping (108) of the velocity field of the maritime surface, 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 mappings (108) for the maritime surface.

8. A computerized method according to claim 7, wherein the computerized determination module determines a predicted map (108) of the sea surface velocity field from ensemble predictions of multiple such maps.

9. Computerized method according to one of claims 1 to 8, in which the low-resolution satellite mapping (1032) representative of a sea surface velocity field comprises a cloud cover of between 10% and 40%, and in which the high-resolution satellite mapping (104) of the topology of the streamlines of the sea surface comprises a cloud cover of between 10% and 40%.

10. A computer-implemented method according to claim 9, and according to claim 2 or a claim dependent thereon, wherein the training input data comprises cloud cover synthetically added onto a cloud-free map.

11. Computerized method according to one of claims 1 to 10, 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.

12. Computerized method according to one of claims 1 to 11, in which, as high-resolution satellite mapping (104) of the topology of the current lines of the maritime surface, a surface temperature mapping, of chlorophyll concentration and / or suspended particulate matter concentration at the sea surface.

13. Computerized method according to claim 12, in which, as high-resolution satellite mapping (104) of the topology of the streamlines of the sea surface, a mapping of chlorophyll concentration and / or of suspended particulate matter concentration at the sea surface is provided, and in which the digital model (107) is generated by self-supervised learning using the surface temperature mapping.

14. Computer program comprising portions of program code for executing the steps of the method according to one of claims 1 to 13 when said program is executed on a computer.

15. Computerized system for determining a map of a velocity field of a maritime surface, comprising: - A computerized determination module adapted to determine the 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 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.

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