This invention relates to apparatus and method for characterizing sea ice and, in particular, to estimating a thickness of the sea ice.
As land based hydrocarbon reservoirs become depleted, reserves in more remote and hostile locations of the earth are being explored. Many of these new locations are marine based and include cold regions such as the Arctic and Antarctic regions. These regions can be very cold especially in the winter time. Cold temperature can cause the formation of sea ice and ice floes, which is sea ice that drifts due to ocean currents and wind. It is noted that in many regions such as the North Atlantic and the Baltic, sea floes are traditionally a seasonal event, appearing in winter and vanishing in warmer seasons.
Ice floes can have dimensions that range from tens of meters to several kilometers and an associated mass. Drifting sea ice with such a large mass can pose significant problems to hydrocarbon production platforms in those regions subjected to ice floes. Accordingly, there is a need to accurately model ice floes in order to study them to increase understanding of their dynamics and ice load distributions, and further understand the forces they may impact on the production platforms.
In one embodiment, a method for estimating a total thickness of sea ice floating in sea water having a sea water level is disclosed. The method includes obtaining a set of surface topographic data points of the sea ice representing elevation of those surface topographic data points with reference to a sea water level using a surface topography acquisition system, and estimating, using a processor, the total thickness of the sea ice above and below the sea water level using the elevation of each of the points.
The invention, together with further advantages thereof, may best be understood by reference to the following description taken in conjunction with the accompanying figures by way of example and not by way of limitation, in which:
Reference will now be made in detail to embodiments of the invention, one or more examples of which are illustrated in the accompanying drawings. Each example is provided by way of explanation of the invention, not as a limitation of the invention. It will be apparent to those skilled in the art that various modifications and variation can be made in the present invention without departing from the scope or spirit of the invention. For instance, features illustrated or described as part of one embodiment can be used on another embodiment to yield a still further embodiment. Thus, it is intended that the present invention cover such modifications and variations that come within the scope of the appended claims and their equivalents.
Disclosed are method and apparatus for generating a total thickness profile of sea ice. The sea ice having a density that is less than the density of the sea water that it is in floats in the sea water and has a portion that is above the surface of the sea water and another portion that is below the surface of the sea water. The method and apparatus relate to generating a surface thickness profile, referred to as the surface profile, of the surface portion of the sea ice and an undersea thickness profile, referred to as the undersea profile, of the undersea portion of the sea ice. The surface profile and the undersea profile are then combined using a processor to generate the total thickness profile.
Referring now to
Still referring to
In one or more embodiments, the total thickness of the sea ice may be estimated from the surface topography using an isostasy method. The isostasy method is based on the principle of buoyancy where the sea ice immersed in sea water is buoyed with a force equal to the weight of the displaced sea water. Hence, assuming approximately constant sea ice density, the volume of sea ice and associated depth necessary to support the amount of sea ice above the sea water level may be calculated. Assuming a complete isostatic compensation (i.e., free floating ice), the total thickness H of the sea ice may be calculated using Airy's formula:
where ei is the elevation of the sea ice above the sea water level, ρw is the average density of the sea water, and ρi is the average density of the sea ice. Assuming ρw=1.025×103 kg/m3 and pi=0.91×103 kg/m3, variations in ice thickness in excess of 10 meters may be detected in one or more embodiments.
As discussed above, the STAS 2 obtains data points delineating the surface topography of the sea ice above the sea water level and the UTAS 5 obtains data points delineating the topography of the sea ice surface below the sea water level. The data points are three-dimensional coordinates, which may include x-y-z coordinates where the x-y plane is the plane of the sea water level and the z coordinate represents elevation above the sea water level or depth below the sea water level. The processing system 3 processes these data points to provide a total thickness of the sea ice from below the sea water level to above the sea water level. In one or more embodiments, the elevation of one STAS data point is added to the depth of one UTAS data point when those data points have the same x-y coordinates in order to calculate the total thickness of the sea ice at that x-y coordinate. In some situations an STAS data point may not line up exactly with a UTAS data point in the x-y plane. In these situations, the elevation and the depth may be added as long as the x-y coordinate of the STAS data point and the UTAS data point are within a selected range or distance of each other such as being within a distance of each other that is less than half the distance to the next adjacent STAS or UTAS data point. Alternatively, an elevation of a STAS data point and/or a depth of a UTAS data point may be interpolated from adjacent data points in order get the x-y values of elevation and depth to line up with each other.
Synthetic Aperture Radar interferometric processing to derive the topography of the sea ice is now discussed in more detail referring to
z(y)=h−ρcos θ (1)
A SAR interferogram, viewed as a fringe pattern, shows the relative difference between phases of the two images obtained by A1 and A2. The phase difference φ depends on the geometry of the tracks of the two antennas and the image point and thus is proportional to the difference in path times (or delays) from the two antennas imaging the same point and is given by equation (2) where λ, is the wavelength of the radar waves.
φ=4π(ρ−(ρ+δρ))/λ (2)
To determine z, the interferometric processing steps that are generally followed are (a) selection of a suitable pair of SAR images, (b) geometric registration of the images, (c) interferogram generation based on the two images, (d) phase unwrapping of the interferogram, and (e) extraction of elevations from the phases.
In support of the teachings herein, various analysis components may be used, including a digital and/or an analog system. For example, the processing system 3 may include digital and/or analog systems. The system may have components such as a processor, storage media, memory, input, output, communications link (wired, wireless, optical or other), user interfaces, display, software programs, signal processors (digital or analog) and other such components (such as resistors, capacitors, inductors and others) to provide for operation and analyses of the apparatus and methods disclosed herein in any of several manners well-appreciated in the art. It is considered that these teachings may be, but need not be, implemented in conjunction with a set of computer executable instructions stored on a non-transitory computer readable medium, including memory (ROMs, RAMs), optical (CD-ROMs), or magnetic (disks, hard drives), or any other type that when executed causes a computer to implement the method of the present invention. These instructions may provide for equipment operation, control, data collection and analysis and other functions deemed relevant by a system designer, owner, user or other such personnel, in addition to the functions described in this disclosure.
Further, various other components may be included and called upon for providing for aspects of the teachings herein. For example, a power supply (e.g., at least one of a generator, a remote supply and a battery), cooling component, heating component, magnet, electromagnet, sensor, electrode, transmitter, receiver, transceiver, antenna, controller, optical unit, electrical unit or electromechanical unit may be included in support of the various aspects discussed herein or in support of other functions beyond this disclosure.
Elements of the embodiments have been introduced with either the articles “a” or “an.” The articles are intended to mean that there are one or more of the elements. The terms “including” and “having” are intended to be inclusive such that there may be additional elements other than the elements listed. The conjunction “or” when used with a list of at least two terms is intended to mean any term or combination of terms.
The preferred forms of the invention described above are to be used as illustration only, and should not be used in a limiting sense to interpret the scope of the present invention. Modifications to the exemplary embodiments, set forth above, could be readily made by those skilled in the art without departing from the spirit of the present invention.
This application is a non-provisional application which claims benefit under 35 USC §119(e) to U.S. Provisional Applications Ser. No. 61/914,565 filed Dec. 11, 2013, entitled “DERIVATION OF SEA ICE THICKNESS USING ISOSTACY AND UPWARD LOOKING SONAR PROFILES,” which is incorporated herein in its entirety.
Number | Date | Country | |
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61914565 | Dec 2013 | US |