Radiation-temperature dependence of water at microwaves

Pure water radiation-temperature dependence at wavelength 8 mm in the temperature range of 30-50 °C has been experimentally investigated. Measurements were made with the microwave radiometer with central frequency 37.5 GHz (wavelength 8 mm). The absolute method of measuring the intensities of distributed radiation was used. A horn with a 30x30 mm opening was used as an antenna. Calibration of the intensity of the received radiation was carried out by its own radiation of a black body at different temperatures. The equipment had a sensitivity (fluctuation threshold) 0.2 K at a time constant τ = 1 sec. An increment of the radio-brightness contrast is about 3 K in this temperature range. The water radio-emission depends non-linearly on the kinetic temperature. It was measured, that effective temperature of the skin-depth layer increases from 0.28 up to 0.4 °C per degree of water heating. It was shown, that the radiation temperature of the water surface for the 8 mm waves and temperature range 30-50 °C is determined not by the bulk kinetic water temperature, but by the effective temperature of the skin-depth layer formed under the influence of heat exchange with the atmosphere.


Introduction
Water is an element experienced phase transitions under natural temperature changes on the Earth's surface.The phase transition of the water state occurs under small natural temperature fluctuations.They can occur with a high frequency in areas with moderate and cold climates (transitions "through zero": daily and seasonal).During phase transitions, the conditions of reflection and transmittance of electromagnetic waves through an aqueous medium change dramatically, because the complex permittivity of water, ice and water vapor differ significantly.If the phase state of water changes at the water surface-atmosphere boundary, the radiation-thermal exchange of atmosphere and water media change significantly too.To predict the behavior of heat exchange at the air-water interface under water phase transitions, it is necessary to know the temperature-radiation dependence of water in its different phase states, because such data give possibility to find from experiment the complex water dielectric permittivity, its temperature and radiation frequency dependence.Interaction of radiation with matter in the solid [1][2][3][4] and liquid [5] state, reflection and transmission of electromagnetic waves in water for various wavelengths [6][7] are the subjects of theoretical [8][9] and experimental [10][11] researches.The subjects of study are also dielectric permittivity [12][13] and water skin-depth [14].
The radiation-temperature dependence of water at a wavelength of 8 mm has been studied repeatedly [15].However, the temperature range of 30-50 degrees remains insufficiently studied.Due to the small difference in radio brightness temperatures in this range, researchers neglect it and consider only the range with high values of the radio brightness temperature gradient.The need for research is also dictated by the mismatch of experimental and theoretical data for this temperature range.

Materials and Methods
We need to report experimental investigation of the radiation-temperature dependence for pure water at a wavelength 8 mm in the temperature range 30 О C -50 О C.

Theory
The brightness temperature of the radiation of the water surface is determined by the ratio: ) R (λ, t o , θ) -reflection coefficient of the surface, γ (ߣ, ‫ݐ‬ ) -absorption coefficient of electromagnetic radiation in water, T A (θ) -radio emission temperature of atmosphere, ܶ(‫-)ݖ‬water temperature depth profile, θ -azimuth angle.If the temperature does not change vertically, then T (z) = T = const, And the effective temperature is T eff.= T. Expression (1) takes the form: A 1-4 mm temperature layer is formed under the surface of the water.In this layer, there is a temperature gradient from the water temperature at the atmosphere-water boundary to the water temperature measured in the water depth.Moreover, the water temperature on the surface is determined by several factors, namely: air temperature, evaporation and heat flow.
The temperature profile characterizes the temperature distribution in the temperature layer.The amount of heat transfer at the water-air interface and its direction is determined by grad T(z).
Thermal radio emission is formed in a skin-depth layer, into which electromagnetic radiation penetrates.The skin-depth depends on the wavelength λ and temperature For the absorbing medium, the absorption coefficient is ε(ߣ, ‫ݐ‬ ) -the dielectric constant of the medium.The permittivity in the form of the Debye equation has the form ߝ ∞ -high-frequency dielectric constant, ߬ -relaxation time, sec., ݂wave frequency, ߪ -permeability of free space, ߪ -ionic conductivity.The skin depth for water at a wavelength λ = 8 mm is δ = 0.3 mm, so the radio emission of water on the waves of the millimeter range is formed within the temperature layer, that is 1-4 mm thickness.
As can be seen from (1-5), the radio brightness temperature is a function of the temperature of the medium.Even with an isothermal temperature profile, the radio-brightness temperature T br.varies not proportionally to the kinetic temperature T. The effective transformation of the kinetic temperature of the medium into the radio-brightness temperature is characterized by a radiation-temperature dependence and is described by a derivative ܶ ୠ୰.ʹ =

డ்ୠ୰. డ்
The calculation of this value is difficult due to insufficient information about the temperature profile T(z) in the surface layer in the experiment conditions.
Calculations of the brightness temperature were carried out for fresh water under the assumption of an isothermal vertical temperature profile.The dielectric permittivity was calculated using the Stogryn model [16].

Experiment
The radiation-temperature dependence for pure water at a wavelength λ= 8 mm in the temperature range from 30 О C to 50 О C was investigated.The absolute method of measuring the intensities of distributed radiation was used [16].A horn with a 30x30 mm opening was used as an antenna.In the wave zone of the horn, at a distance of 250 mm, radiating bodies were installed, completely overlapping the directional pattern of the horn.The receiving equipment had a sensitivity (fluctuation threshold) of 0.2 K at a time constant τ = 1 sec.During measurements, the signal was recorded in relation to the temperature of the calibration standard, the duration of recording the signal was 1 minute.As a result, the random measurement error was about 0.03 K, the systematic error was determined by the measurement errors of the temperature standards, which was 0.15 K. Systematic errors remained the same in all measurements.Calibration of the intensity of the received radiation was carried out by its own radiation of a black body [17] at different temperatures.

Figure1. Experiment scheme
Figure2.Signal recording scheme The absorbing coating (black body) was cooled in the freezer to a temperature of -16 О C and installed in front of the horn.After that, it was heated naturally to the ambient temperature.In the experiment, the temperature change of a black body was 44 K.Then, in front of the horn, instead of the absorbing body, a cuvette with water was installed, the temperature of which was measured.
The readings of radio emission temperature of water were made relative to the radiation level of the black body, which was at temperature t = 34 О C. The water surface was flat, not distorted by wind.

Results
In table 1 n is the increment of the amplitude of the signal from the water relative to the black body, which had a temperature of 34 О C, the calibration multiplier k = 1,22 In addition, the horn has a fairly wide directional pattern and, therefore, the reflection coefficients may differ from those calculated for a normal fall.In order to clarify the influence of these factors, additional measurements were made with a metal sheet.Radiation with T background reflected from the sheet was received by a horn.
T black body.(34 О C) -T background = 260 K Note that the temperature of the sky at the zenith was measured at this time T atmosphere (zenith) = (27 ±0.2) K That is, 20 K was received additionally due to the re-reflection of the surrounding radiation by the sheet.
At a water temperature equal to the ambient temperature, in accordance with (*), the brightness temperature is: This temperature coincides completely with the measured radiation temperature.Temperature changes of the reflection coefficient, according to the calculation, does not exceed (3 ÷ 5) •10 -3 , therefore, the corresponding change in brightness temperature does not exceed 0.2-0.3K, which does not exceed the error of reading signal levels during recording.
The last column of table 1 shows the brightness temperatures calculated in accordance with (*) at the actual measured values of T background .
Table 2.The water temperature corresponding to the observed brightness temperature of its own radiation.1 shows a graph of water radiation temperatures deviations from the water kinetic temperature, experiment and theory.It can be seen from the graph that the real ability of water's own radiation during heating is significantly less than expected.Based on the results of the experiment it can be concluded that the radio emission of the water surface is formed in a skin-depth layer near the air-water boundary.
At λ= 8 mm, the thickness of the skin layer of water is about 0.3 mm.Using (*), we calculate the water temperature corresponding to the observed brightness temperature of its own radiation.The radiation-temperature dependence was measured in windless dry sunny weather at t = 34 О C of air.At a water temperature of 29.9 О C, the effective temperature of the skin layer was higher (32.Experimental research of the radiation-temperature dependence for fresh water in the temperature range of 30-50 degrees Celsius have shown an increment of the radio-brightness contrast about 3 K is in this temperature range.

Table 1.Experiment and theory data
The radio brightness temperature of water radiation is determined by the kinetic temperature of the skin-depth layer.The ratio of the thickness of the skin layer and the temperature layer at the water surface is an important parameter characterizing the process of formation of the radio brightness temperature.Since the skin depth depends on the wavelength of the detected radiation, its size can be either bigger than temperature layer depth or smaller than it.
In the case when the skin depth is much smaller than the size of the temperature layer depth, the spatial temperature distribution at the surface of the liquid can be neglected and the temperature of the skin-depth layer can be considered as a constant.In cases where the skin-depth is comparable with the temperature layer depth, or exceeds it, it is necessary to take into account the vertical temperature distribution at the surface of the liquid when calculating the radio brightness temperature.
Temperature contrasts [18] of the studied range can be recorded on the water surface on the waves of the millimeter range in the temperature range from 30 О C to 50 О C, what was demonstrated in the experiment.The obtained dependence of the water brightness temperature from the kinetic temperature at wavelengths of the millimeter range, makes it possible to use heated and cooled water to create thermal standards necessary for antenna calibrations in natural conditions.

Conclusions
The radiation temperature of the water surface on the waves of the millimeter range is determined not by the bulk water temperature, but by the effective temperature of the skin-depth layer formed under the influence of heat exchange with the atmosphere.The experiment demonstrates the possibility of remote detection of thermal anomalies of hydro objects by radio brightness contrasts on their surface in the millimeter wavelength range.This has an important practical application for remote search of temperature anomalies caused by contamination of the water surface.
The actual intrinsic radio emission of water when heated is significantly less than its theoretically predicted value.The reason for this discrepancy may be that the vertical distribution of kinetic temperature in the near-surface layer cannot be considered as a constant.

Figure 3 .
Figure 3.The dependence of the deviation of the brightness temperature on the temperature of water heating (redline-theory, blue -experiment).

Figure 4 .
Figure 4. Dependence of the brightness temperature deviation from the water heating temperature.The red line is for the brightness temperature of the water (theory), the green line is for the brightness temperature of the skin layer (theory), the blue line is the brightness temperature of the sample (experiment).
5 О C) due to surface heating.With a subsequent increase in the water temperature (above the air temperature), the effective temperature of the skin layer of water rises slowly.In the range of water temperatures Δtwater=40.3-35.5(О C) effective temperature of the skin-depth layer increases by 0.28 degrees per degree of water heating, in the interval this value is 0,4 О C per 1 О C. National Conference on Physics and Chemistry of Materials (NCPCM 2023) Journal of Physics: Conference Series 2603 (2023) 012014