RU2319205C1 - Method for determining thickness of ice in freezing water areas - Google Patents

Abstract

FIELD: hydrology, possible use for determining thickness of ice cover over freezing water areas on basis of data of remote measurement instruments, installed on meteorological Earth satellites.

SUBSTANCE: in accordance to the invention, provided mathematical formulas are used to a priori calculate a set of standards of nonlinear similarity coefficients between relief of true ice thickness and relief of temperature field of ice cover. Then similarity coefficients are determined on basis of data of infrared image being analyzed, where test sections are selected, surface temperature of which corresponds to sections of water at freezing temperature and to sections of "thick" (thickness > 120 cm) snow-covered ice. Under identical hydro-meteorological conditions from a set of standard values for data for the time of image receipt, similarity coefficients are selected which are equal to the calculated ones, and temperature intervals, which correspond to selected discrete intervals of ice thickness, are determined. On the image of ice cover, sections with given ice thickness intervals are singled out using a color pattern. As test sections on the infrared image which correspond to surface temperature or brightness of pixels of "thick" snow-covered ice, sections of image of snow-covered earth surface, which is positioned closely to ice cover being examined, are selected.

EFFECT: creation of monitoring over thickness of ice in freezing water areas on basis of images in heat channel of infrared range of frequencies of meteorological Earth satellites, which is automated in interactive mode.

3 cl, 1 dwg

Description

The invention relates to the field of hydrology and is associated with determining the thickness of the ice cover of freezing water areas according to remote sensing instruments installed on meteorological satellites, which allow determining the physical characteristics of geophysical objects from the intensity of their own or reflected radiation. The interpretation of the recorded energy characteristics into the physical characteristics of the objects under observation is a process of deciphering the information received.

The problem of monitoring the thickness of the ice cover is very relevant from the point of view of ensuring the safe operation of hydraulic structures in freezing waters under the influence of ice formations on them; providing navigation of vessels in ice; solving the problems of the interaction of the atmosphere and the ocean in the presence of ice cover. Remote research methods fundamentally allow us to solve this problem, especially sounding with satellite. Therefore, for all sections of the electromagnetic spectrum in which useful information about the thickness of the ice in the water areas can be obtained, special techniques are being developed. The ice cover of the water area has a complex physical composition, structure and structure, varying in time and space depending on environmental conditions, which does not allow to obtain high accuracy of measuring ice thickness using remote monitoring tools, comparable to contact methods. In addition, the natural averaging of the measured value on the local resolution element of the equipment leads to a result that can be called the conditional thickness. In most cases, using remote monitoring tools, as applied to measuring the thickness of the ice cover, some arbitrary distinguishable intervals of thickness are determined, as well as its age gradations. As a rule, the following age gradations of the ice cover are distinguished: initial and nilas (with a thickness h <10 cm), young (with h = 10 ÷ 30 cm), thin annuals (with h = 30 ÷ 70 cm), annual average thickness (with h = 70 ÷ 120 cm), thick annuals (with h = 120 ÷ 250 cm), biennial and perennial ice (with h> 250 cm).

Among the remote technical means and methods used to determine the age gradations of the ice cover, the following can be noted:

1. Means of observation in the visible range of the electromagnetic frequency spectrum (with wavelengths of 380-760 nm). In this range, the contrast of the observed objects is determined by their albedo and the position of the sun. Using satellite images of medium resolution, it is possible to determine the above age-related gradations of ice in the daytime in the absence of cloudiness, if the size of the homogeneous sections of the ice cover significantly exceeds the size of the elementary areas of the image [1]. Moreover, the accuracy of determining age gradations of ice largely depends on the subjective assessment of the received images by an expert decoder.

2. Means of observation in the microwave frequency range (active and passive), recording the thermal radiation of the ice cover in the wavelength range of 1 mm - 40 cm, allow the identification of annual thin, medium, thick ice and perennial ice [2]. However, such possibilities are available only if homogeneous sections of the ice cover are greater than the local resolution of the radiometers. Meanwhile, satellite microwave radiometers have a resolution on the terrain of about 10-80 km.

3. Means of radar sensing (radar BO) measure the energy of the reflected radar signal, determined by the reflectivity of the objects or the effective scattering area (EPR). With regard to the location of the ice cover, the EPR depends on the complex dielectric constant of the ice, the relief of its surface and its humidity, as well as on the parameters of the observation equipment — wavelength and polarization of the emitted and received signal. The practice of using BO satellite radars indicates that age-based gradations of mainly three types of ice can be determined from radar images obtained at wavelengths of 0.8-5.0 cm: young, one-year-old, and old [3].

4. Means of infrared sounding in the heat channel measure the intrinsic thermal radiation of the ice cover at the maximum of this radiation at natural air temperature values for the earth's cover. The intrinsic thermal radiation of ice is determined by its radiation temperature, which is very close to the actual surface temperature. Since the ice cover of the water area is an intermediate layer between water at freezing temperature and the atmosphere, the thickness of the ice can be calculated from the difference in surface temperature. This is confirmed by classical theoretical laws. The optimal range of measured ice thickness is the interval from the film to 60 ÷ 100 cm (according to various authors), i.e. young, thin and medium annual ice. However, the physical and mathematical interpretation of satellite images in this range in order to determine the thickness of the ice cover of the waters is very difficult. The problem is associated with the numerous (from 8 to 10), usually unknown, physical characteristics of ice and environmental conditions that significantly affect the final result [4]. Therefore, calculations become very time-consuming and economically unjustified. The solution to such multifactorial problems is considered optimal when determining dimensionless parameters that can significantly reduce the number of required measured parameters.

5. The closest to the proposed method is to determine the thickness of the ice cover according to the heat channel of the PC of the AVHRR radiometer (AES-NOAA) with a total distribution of ice up to 80 cm thick [5]. Based on the physical model, the authors developed an algorithm for the proportionality of the radiation temperature of thin, slightly snow-covered sea ice to their thickness. The measured radiation temperature of the ice surface T _s from the satellite is recalculated into data on the ice thickness h _i using empirical dependences T _s = F (h _i ). At the same time, hydrometeorological elements such as atmospheric transmission, surface air temperature, effective ice cover radiation, the presence and depth of snow cover, thermal conductivity of snow and ice, and wind speed should be taken into account. The algorithm for thin ice was tested by comparing the results of interpretation of thermal images of sea ice cover obtained from a satellite in a cloudless sky with the data of a sonar (Upward Looking Sonar) in various regions of the Arctic and confirmed its reliability. One of the practical applications of this algorithm was its use in validating the results of interpreting the thickness of thin ice obtained using RADARSAT data with AVHRR data. These studies were carried out by a team of authors from the Polar Science Center for Applied Physics, University of Washington and the Jet Propulsion Laboratory (report: RWLindsay, Y. Yu, HLStern, DARothrock, R. Kwok, 2000. RADARSAT Geophysical Processor System Products: Evaluation and Validation. January 31, 2000, p.13). The disadvantages of this method include a direct solution to the problem, requiring the measurement of many hydrometeorological elements, which is associated with great technical difficulties and an increase in the total measurement error.

The objective of the proposed method is the creation of an automated interactive monitoring of the ice thickness of freezing waters in the range from film to 100-120 cm with a resolution that is limited by the sensitivity of the method and above 120 cm - without a resolution that is averaged over a local resolution element according to images in the heat channel IR frequency range of meteorological satellites in a cloudless atmosphere and negative air temperature. The solution to this problem is achieved by creating a physical model that includes dimensionless parameters that combine various hydrometeorological elements and establishes new physical relationships. At the same time, the number of required measured elements is significantly reduced and the solution of the problem is simplified. The main result of physical and mathematical modeling is the establishment of a nonlinear similarity of the relief of the field of intrinsic thermal radiation of the ice cover at the altitude of the satellite flight to the relief of the field of “true” ice thickness and the determination of the coefficients of this similarity. The relief of the field of the true thickness of the ice cover is understood as a virtual relief, which occurs when the lower bases of all the ice floes of different thicknesses entering the ice cover of the waters are located on the same plane. Under the term “ice thickness”, a conventional value is accepted in the model that is equivalent in its thermal characteristics to the thickness of an even ice plate within the resolution element of an artificial satellite radiometer.

The initial one in this model is the solution of the heat balance equation on the surface of snowy ice, considered as a two-layer plate (a solution is also obtained for a multi-layer plate), provided that the heat flux is continuous. The equation is presented in integral form. The transition to finite increments and analysis of all components allowed us to obtain an expression for the surface temperature T _{0 of} ice in the water in the form [6]:

where t _p is the thickness of snow-covered ice converted to the thickness of non-snowy ice under the condition of equivalent heat transfer;

λ is the thermal conductivity of ice;

k is the heat transfer coefficient of the ice surface with the atmosphere;

Θ - freezing temperature of water;

T _a - ambient temperature;

I _ef - effective radiation of the ice surface;

I ^' - solar radiation absorbed in the upper centimeter layer of snow or ice.

To go from the converted ice thickness to true, a dimensionless parameter ξ is introduced, which has an average statistical value. In physical terms, this parameter determines the attenuation of the heat flux passing through the ice caused by the presence of snow. The current values of the parameter ξ are determined by the relation:

where λ _s , t _s - respectively, the thermal conductivity of the snow and the depth of the snow cover on a given ice,

λ, t _E - thermal conductivity and thickness of ice.

From expressions (1) and (2), we can obtain equation (3) for calculating the true ice thickness t _E :

The surface temperature of the “thick” (t _E > 1.2 m) snow-covered ice of the T ₂ water areas is practically independent of thickness. The surface temperature of degenerate ice (t _E = 0) can be considered equal to the freezing temperature of water Θ. Then the expression of the dimensionless parameter ψ _r represented by relation (4),

based on the expression (1), with an error not exceeding 10%, can be expressed by equation (5)

Under the same hydrometeorological conditions, ψ _r = ψ.

The calculation of the dimensionless parameter ψ by expression (5), where the values of hydrometeorological elements were calculated using empirical formulas, showed that this parameter is a factor that is practically independent of air temperature, effective radiation, and transmission of radiation to the atmosphere. This can be seen from the table in which cloudiness N ₀ appears only as a meteorological element affecting the effective radiation.

Table
The values of the factor ψ for various values of the converted ice thickness t _p , air temperature T _a , wind speed V and cloud cover N ₀ . Temper. air, t _p , ° С Wind speed, V, m / s Cloud cover, N ₀ , rel. one Converted ice thickness, t _p , m 0.01 0.1 0.25 0.5 1,0 -fifteen 2 one 0,033 0.280 0.493 0.680 0.833 -25 2 one 0,033 0.251 0.465 0.650 0.806 -35 2 one 0,030 0.234 0.439 0.623 0.792 The average value of the factor Ψ 0,032 0.253 0.466 0.650 0.810 -fifteen 2 0 0,035 0.274 0.488 0.677 0.826 -25 2 0 0,034 0.253 0.460 0.646 0.804 -35 2 0 0,029 0.230 0.435 0.615 0.783 The average value of the factor Ψ 0,032 0.253 0.461 0.646 0.804 -fifteen 5 0 0,073 0.450 0.677 0.823 0.915 -25 5 0 0,068 0.420 0.650 0,800 0.904 -35 5 0 0,068 0.414 0.646 0.796 0,900 The average value of the factor Ψ 0,070 0.430 0.660 0.810 0.910 -fifteen 10 0 0.150 0.640 0.830 0.910 0.960 -25 10 0 0.140 0.620 0.810 0.910 0.960 -35 10 0 0.130 0.610 0,800 0,900 0.950 The average value of the factor Ψ 0.140 0.620 0.810 0.910 0.960

To prove the independence of the factor ψ from the atmospheric transmission function in the absence of cloudiness, it suffices to analyze expression (4). It can be seen from it that all the parameters included in this expression, corresponding to various temperature values located on the gentle part of the Planck curve, form radiation that equally interacts with the atmosphere. Therefore, the factor ψ does not depend on the transmission function of the atmosphere.

Under conditions of different (negative in ° C) values of air temperature and effective radiation, the factor ψ is a nonlinear similarity coefficient between the topography of the field of true ice thickness t _E and the topography of the temperature field on its surface. The conversion of the converted ice thickness t _p to the true ice thickness t _{E is} carried out using expression (3).

Like the calculated values of the factor ψ given in the table, depending on the transformed ice thickness t _p, one can calculate many standards ψ = f (t _p ), a priori determined for further calculations of the true ice thickness. You can also use the regression equations and determine their coefficients.

To further simplify the solution of the problem and refuse to calculate the surface temperature of the ice sheet, we introduce the factor β _r , equivalent to the factor ψ _r , in which the temperature characteristics are replaced by the brightness of the pixels of the IR image of the ice sheet in accordance with expression (6).

where α ₀ is the brightness of the pixel corresponding to the diagnosed ice;

α _w is the brightness of the pixel corresponding to water at freezing temperature;

α ₂ is the brightness of the pixel corresponding to thick snowy ice.

The concept of "thick snowy ice" is introduced only for reasons of distinguishability of the surface temperature of ice of different thicknesses using infrared radiometry. In this context, this upper limit is the thickness of the ice of the order of 120-150 cm. The correction of the absolute error that occurs when the factor ψ _{r is} replaced by the factor β _r is introduced by substituting the calculated coefficients in the model software product. As a result, the calculation error with this replacement of factors decreases to 1-2% in the entire range of the determined ice thickness. Therefore, the calculations and conclusions made with respect to the factor ψ _r are valid for the dimensionless corrected parameter β _r . Therefore, β _{r is} also a factor. Moreover, the factor β _{r is} also independent of air temperature, effective radiation, and the transmission function of a layer of a uniform cloudless atmosphere.

Similar to the proposed definition of the factor ψ _r , the factor β _r can be called the nonlinear similarity coefficient of two reliefs: the relief of the field of true ice thickness of water areas and the relief of the field of their brightness in the IR image of the satellite and practically use it to determine the ice thickness according to the data of the original IR images of the ice cover. Using the similarity of the two fields, the algorithm for solving the problem can be constructed in two ways. It is possible to calculate factors β _r from the IR image of the ice sheet and calculate the ice thickness from known values of β _r taking into account real meteorological conditions. However, it is more convenient to do this in the reverse order, i.e. for given intervals of ice thickness, select the boundary values β _r using the set of a priori standards ψ = f (t _p ), and then determine the brightness values of pixels in the original image corresponding to the given intervals. Then the expression for calculating the brightness of pixels corresponding to the boundaries of the intervals of the determined ice thickness can be obtained from equation (6) in the form:

Classification of the ice thickness distribution of freezing water areas according to the satellite imagery IR data in accordance with the proposed method allows one to choose an arbitrary discretization of the ice thickness intervals within the sensitivity of the method, which decreases with increasing wind and increasing depth of snow cover on ice and increases with decreasing air temperature. The sensitivity of the method decreases with increasing ice thickness. Thus, an extremely possible discretization of the intervals of ice thickness through 10 cm was obtained in the region of thin and medium thickness annual ice. A similar result is unique in comparison with the methods described above for determining the ice thickness by deciphering the data of remote sensing of ice in the water areas.

The practical feasibility of the proposed method is confirmed by test tests on the interpretation of satellite images in the thermal channel of the IR range for various water areas and by comparing the results with actual measurements of the thickness of the ice cover in the surveyed areas during the registration of satellite images [7].

Information sources

1. Sea ice. Collection and analysis of observational data, physical properties and forecasting of ice conditions (reference manual). - St. Petersburg: Gidrometeoizdat, 1997 .-- 402 p.

2. Darovsky A.P., Martynova E.A., Spitsyn V.A. Probability distributions of radio brightness temperature of snow-ice cover of various ages. On Sat Electrophysical and physico-mechanical properties of ice. - L .: Gidrometeoizdat, 1989. - P.72-77.

3. Bushuev A.V., Bychenkov Yu.D., Loshchilov B.C., Masanov A.D. The study of ice cover using side-scan radars (RLS BO) // Methodical manual. -L .: Gidrometeoizdat, 1983 .-- 120 p.

4. Bogorodsky VV, Martynova EA Own thermal radiation from the snow-ice cover of the Arctic seas. - L .: Gidrometeoizdat, 1978.- 39 p.

5. Y. Yu and D.A. Rothrock. Thin ice thickness from satellite thermal imagery. // J. Geophs. Res., 1996, 101 (C10), 25, 753-25, 766.

6. Lebedev G.A., Paramonov A.I. Determination of the physical characteristics of sea ice according to infrared sounding with satellite. // Meteorology and hydrology, 2001. - No. 2. - S. 72-80.

7. Paramonov A.I., Lebedev G.A. An algorithm for nonlinear similarity of the reliefs of the radiation field and the field of true thickness of sea ice for studying age-related gradations of sea ice cover according to satellite observations in the thermal channel of the infrared range // Collection of reports of the Second All-Russian Scientific Conference “Remote Sensing of the Earth's Coverings and Atmosphere by Aerospace Means,” 16-18 June 2004, St. Petersburg. - T.2. - S. 71-75.

Claims (3)

1. The method for determining the ice thickness of freezing waters in the range from film to 100-120 cm with a resolution that is limited by the sensitivity of the method and above 120 cm - without a resolution averaged over a local resolution element, according to satellite images in the thermal channel of the infrared frequency range with cloudless atmosphere, meteorological data of the averaged surface wind speed V during the sounding period and the average values of the dimensionless parameter

, where λ _s and t _s are respectively the thermal conductivity and depth of snow cover on ice with a thickness t _E and thermal conductivity λ at negative air temperature, characterized in that a priori many standards of non-linear similarity coefficients ψ are calculated that are practically independent of the surface air temperature, effective radiation of the underlying surface and the transmission function of the atmosphere for radiation in the thermal IR channel,

Where

- the thickness of snow-covered ice converted to the thickness of non-snowy ice, subject to equivalent heat transfer; λ is the thermal conductivity of ice; k is the heat transfer coefficient of the ice surface with the atmosphere; T _a - ambient temperature; Θ - freezing temperature of water; I _ef is the effective radiation of the surface of the studied ice; I ₂ is the effective radiation of the surface of the "thick" ice (t _E > 120 cm), between the relief of the true thickness of the ice for the selected discrete intervals of thickness and the relief of the temperature field of the ice cover, the similarity coefficients of which

, where T ₀ , T ₂ are the surface temperatures of the studied ice and “thick” ice, respectively, are determined by the data of the analyzed IR image, where test sections are selected whose surface temperature corresponds to the sections of water at freezing temperature and the sections of “thick” snowy ice; under identical hydrometeorological conditions ψ = ψ; ψ equal to the calculated values of ψ are selected from the set of reference values for the data at the time of receiving the image of the surface wind speed V and the average statistical values of ξ, and the temperature intervals corresponding to the selected discrete intervals of ice thickness are determined; on the analyzed image of the ice cover, sections with specified intervals of ice thickness are highlighted using the color palette. 2. The method according to claim 1, characterized in that the non-linear similarity coefficients on the decryptable images are calculated using the expression

, where α ₀ is the brightness of the pixel corresponding to the diagnosed ice; α _w is the brightness of the pixel corresponding to water at freezing temperature; α ₂ - the brightness of the pixel corresponding to the "thick"ice; and correction factors are introduced when ψ is replaced by β. 3. The method according to claim 1 or 2, characterized in that as the test areas in the IR image corresponding to the surface temperature or pixel brightness of the "thick" snowy ice, image areas of the earth's snowy surface located near the investigated ice cover are selected.