Remote Monitoring of Atmospheric and Hydrophysical Characteristics of the Water Surface Based on Microwave Radiometric Measurements

Abstract

This work summarizes the main characteristics of atmospheric and hydro-physical parameters of the water surface derived from microwave radiometric data. First, current knowledge based on experimental measurements and model calculations of emissivity of the atmosphere and water surface in the microwave spectrum is presented. Emphasis is placed on remote radio-physical methods that have the peculiarity of being related to atmospheric radio-transparency which is one of the main advantages of the microwave radiometric method compared to optical and infrared methods. A detailed presentation is attempted with specific examples of classification of water surface phenomena using software modules included in the system used for the processing of data of radio-physical experiments by the Cosmos-1500 satellite. In addition, the statistical characteristics of the “spotting” of radio-brightness temperatures obtained for the most informative thresholds are analyzed and it is argued that these characteristics for the Pacific areas can also be used to detect abnormal phenomena on the water surface of the Mediterranean Sea. Finally, it is emphasized that the results obtained from this work make it possible to rapidly evaluate various parameters such as temperature, water surface waves, foam formation areas, etc., providing predictions and allocating irregular areas.

1. Introduction

Nowadays, the development of experimental radio-physical methods for the study of the environment is often characterized by the transition from the passive collection of information about the object under study to the design of intentional experiments. In conducting such experiments, the organization of the mass collection of information about the system under study, the efficiency of its processing, and the reliable interpretation of the observed data, acquire the utmost importance.

Depending on the nature of the detected electromagnetic radiation, active and passive sounding methods are used. Active methods are based on the analysis of the signals reflected by the objects under study and use the relationship between the backscattering characteristics and the physical parameters of the objects. Passive methods are based on receiving the radiation itself from the objects under study, the characteristics of which are closely related to the physical and geometric properties of the natural objects.

The present work mainly focuses on the remote radio-physical methods related to the atmospheric radio transparency that is the main advantage of the microwave radiometric method compared to the optical and infrared methods [1,2,3,4,5,6,7,8].

In this context, it should be emphasized that the potential of infrared and optical methods is strongly limited by the absorption and scattering properties of the atmosphere. The main obstacles to these methods are clouds, which often prevent the collection of operational data on the state of the land cover and water area.

Note that, to some extent, the radio transparency of the atmosphere is relative. At a wave of 1.35 cm there is an absorption line for water vapor, and in the wavelength range 0.5 cm for oxygen. But the presence of these resonant absorption zones in the microwave range allows remote retrieval of meteorological parameters of the atmosphere such as vertical temperature and humidity profiles, integral meteorological parameters—total mass of water vapor and cloud water storage and identification of precipitation zone. The ability to obtain information not only about the characteristics of the water and earth surface, but also about its surface layer, depends on the depth of penetration of the electromagnetic wave. In the infrared spectrum, all the radiation is formed in a very thin surface layer. The electromagnetic waves in the microwave range are strongly absorbed by the earth and water surfaces. The penetration depth varies from centimeters to one millimeter in the case of water surface research. At the same time, in dry soils and on continental ice, dry snow, the penetration depth reaches several tens of wavelengths. This makes it possible to carry out remote sensing studies of soil, ice, and snow covers at considerable depths. The penetrating power of radio waves gives advantages especially when the earth’s covers are sounded directly. Loose vegetation (grass, cereals, etc.) generally weakly absorbs and scatters the radio waves, and therefore it is possible to make “radio observation” of soil cover through it. Radio waves can penetrate the soil (especially dry) and carry out sounding at a depth of about one meter.

The main disadvantage of radio-physical methods of remote sensing is the relatively low spatial resolution compared to the optical method. In the radio bands, high resolution is achieved in specialized and advanced radio systems, and in other cases, only coarse resolution is achieved. Therefore, radio-physical methods of remote sensing from space are applicable mainly for areas of the earth with high spatial homogeneity [1]. In this context, airplanes are used for higher resolution.

At present, it is possible to achieve high resolution in the radio range only with the help of aperture synthesis due to the motion of devices (satellites, aircraft) by sequential signal accumulation (or Doppler filtering, which is equivalent) and temporal resolution. The system requires coherence of radio waves and therefore it is currently implemented in synthetic aperture radars.

Aperture synthesis is also possible when receiving noise signals, for example, radiothermal radiation. However, it is necessary to have at least two systems with independent antennas moving relative to each other and synchronized constantly or periodically on certain communication channels. The feasibility of such systems is beyond doubt (especially since radio astronomers have experience in this field). However, their technical implementation, for example, in space execution, is not an easy task.

Therefore, it can be concluded that high resolution is achieved in radio bands in specialized (expensive) and advanced radio systems, and in other cases only coarse resolution is achieved [1].

2. Materials and Methods

2.1. Estimates of Atmospheric Characteristics Based on Microwave Radiometry Data

The presence in the microwave spectrum of areas of resonant absorption of water vapor and oxygen determines the fundamental ability to estimate integrated meteorological parameters: the total mass of water vapor in the atmosphere Q and the water content of clouds W, to solve the problem of restoring vertical profiles of temperature, water content, humidity, etc. At the same time, the zones of possible rainfall can be easily identified by different temperature contrasts in the studied areas [3,5,9,10].

The absorption and self-radiation of the atmosphere depend on both the cloud layer parameters and the content of water vapor of the atmosphere. The average drop radius of stratus clouds and fair-weather cumulus clouds is 2.5–7 µm [10], and the maximum contribution to the water content is made by drops with a radius of 10–20 µm. In the wavelength range λ ≥ 0.8 cm, the Rayleigh scattering conditions are satisfied in the clouds with good accuracy [10]:

$$\frac{2\pi a}{\lambda }<<1;\underset{}{{\displaystyle }}\left|m\right|\frac{2\pi a}{\lambda }<<1,$$

where a is the radius of drops; |m| is the modulus of the refractive index.

The main gaseous components of the atmosphere that absorb microwave radiation are molecular oxygen and water vapor. The absorption of other atmospheric gases can be neglected due to their low concentration and the weakness of the absorption lines [9,11].

The expression for the radio-brightness temperature of the “ocean–atmosphere” system in the absence of precipitation, taking into account the ascending $T_b^{\uparrow }$ and descending $T_b^{\downarrow }$ radiation of the atmosphere and the intrinsic radiation of the surface, attenuated by the atmosphere, has the form [3,9,10]:

$$T_b=\ae T_0{e}^{-{\tau }_{\lambda }}+T_b^{\uparrow }+(1-\ae )T_b^{\downarrow }{e}^{-{\tau }_{\lambda }},$$

(1)

where æ, T₀ are the emissivity and temperature of the underlying surface, respectively.

$${\tau }_{\lambda }={\displaystyle \underset{0}{\overset{\infty }{\int }}{\alpha }_{\lambda }(z)dz}$$

τ_λ—optical thickness of the atmosphere; α_λ(z)—vertical profile of the absorption coefficient in the atmosphere.

The brightness temperatures of the ascending $T_b^{\uparrow }$ and descending $T_b^{\downarrow }$ radiation of the atmosphere are expressed by the formulas:

$$\begin{array}{l}{T}_b^{\uparrow }={\displaystyle \underset{0}{\overset{\infty }{\int }}T(z){\alpha }_{\lambda }(z)\exp \left[-{\displaystyle \underset{z}{\overset{\infty }{\int }}{\alpha }_{\lambda }(z^{\prime })d{z}^{\prime }}\right]}dz;\\ T_b^{\downarrow }={\displaystyle \underset{0}{\overset{\infty }{\int }}T(z){\alpha }_{\lambda }(z)\exp \left[-{\displaystyle \underset{0}{\overset{z}{\int }}{\alpha }_{\lambda }(z^{\prime })d{z}^{\prime }}\right]}dz,\end{array}$$

(2)

where T(z) is the vertical air temperature profile.

In the absence of precipitation, α_λ(z) can be represented as the sum of the absorption coefficients in water vapor ${\alpha }_{\lambda }^{H_{2}O}(z)$, in oxygen ${\alpha }_{\lambda }^{O_2}(z)$, and in liquid drop clouds α_λ^cl(z):

$${\alpha }_{\lambda }(z)={\alpha }_{\lambda }^{O_2}(z)+{\alpha }_{\lambda }^{cl}(z)+{\alpha }_{\lambda }^{H_{2}O}(z)$$

The values ${\alpha }_{\lambda }^{H_{2}O}(z)$ and ${\alpha }_{\lambda }^{cl}(z)$ are related to the vertical profiles of humidity Q(z) and water content W(z) with the formulas [10]:

$$\begin{array}{l}{\alpha }_{\lambda }^{H_{2}O}(z)=C_Q(\lambda ,T)Q(z);\\ {\alpha }_{\lambda }^{cl}(z)=C_W(\lambda ,T)W(z),\end{array}$$

here C_Q(λ,T), C_W(λ,T) are known functions of temperature and wavelength. The oxygen absorption coefficient ${\alpha }_{\lambda }^{O_2}$ at a given temperature T and pressure P can be estimated by the expression [9,10,11]:

$${\alpha }_{\lambda }^{O_2}=C_{\lambda }{p}^2{T}^{-2,8}, at 0.8\le \lambda \le 3\mathrm{cm}.$$

The Equations (1) and (2) are the main ones for solving the inverse problem of microwave radiometric sounding of the “ocean–atmosphere” system. Let us consider the possibility of determining some integral meteorological parameters, such as the total mass of water vapor in the atmosphere Q and the water content of clouds W. These parameters can be estimated from simpler relationships obtained from (1) and (2) with some simplifications by introducing the so-called weighted average effective atmospheric temperatures $T_{\lambda }^1$ and $T_{\lambda }^2$ [1,12]. The radio-brightness temperatures $T_b^{\uparrow }$ and $T_b^{\downarrow }$ are expressed through them as:

$$\begin{array}{l}{T}_b^{\uparrow }=T_{\lambda }^1(1-e^{-{\tau }_{\lambda }});\\ T_b^{\downarrow }=T_{\lambda }^2(1-e^{-{\tau }_{\lambda }}).\end{array}$$

and the total absorption of the atmosphere τ_λ is represented as a linear function of Q and W:

$${\tau }_{\lambda }={\tau }_{\lambda }^{O_2}+K_{1\lambda }\widehat{Q}+K_{2\lambda }(T_{cl})\widehat{W},$$

where K_1λ, K_2λ(T_cl) are the weight coefficients of absorption of water vapor and liquid-drop water, T_cl is the effective temperature of the cloud. The values of the parameters T_λ¹, T_λ², K_1λ, K_2λ(T_cl) are estimated using standard atmospheric models [1,13]. Thus, to estimate the unknowns Q and W from the results of microwave radiometric measurements, the number of channels λ_i must be at least two. The main source of error in estimating the unknowns Q and W from (3) is the inaccurate assignment of the value of T_cl.

The possibilities of joint determination of the parameters Q, W, and T_cl are considered in [1,3,9,10,11]. Estimates of the accuracy of determining these parameters can be found in [9,10,11]. From a practical point of view, it is also preferable to use regression relationships directly between Tn and the desired parameters

$$\widehat{W}=\left\{\begin{array}{c}0.056T_b-7.13{{\displaystyle }}^{}\hspace{1em}in \mathrm{clear} \mathrm{weather}\\ 0.052T_b-6.59{{\displaystyle }}^{}\hspace{1em}cloudy\hspace{1em}z\le 250 \mathrm{m}, \widehat{Q}<0.1 {\mathrm{kg}/\mathrm{m}}^2\\ 0.041T_b-5.03{{\displaystyle }}^{}\hspace{1em}cloudy\hspace{1em}z>250 \mathrm{m}, \stackrel{}{}0.1\le \widehat{Q}\le 0.5 {\mathrm{kg}/\mathrm{m}}^2\end{array}\right.$$

2.2. Estimates of the Main Hydrophysical Characteristics of the Water Surface Based on the Data of Microwave Radiometric Measurements

The main hydrophysical parameters of the water system are surface temperature T, salinity S, and wave intensity related to wind speed V. Methods for remote determination of these parameters are considered in [3,8,9,14,15].

The radiation of scattering media occurs against the background of earth covers (soil, water) and, moreover, sometimes under conditions of absorption by the atmosphere. This process is described with a certain degree of accuracy by the transport equation.

For remote sensing to the nadir, the approximate solution of the transport equation has the form [15]:

$$T_b=T_{ob}\exp \left\{-{\displaystyle \underset{0}{\overset{H}{\int }}\left[{\sigma }_{t_H}(z)+\gamma (z)\right]dz}\right\}+{\displaystyle \underset{0}{\overset{H}{\int }}T(z)\left[{\sigma }_a(z)+\gamma (z)\right]}\exp \left\{-{\displaystyle \underset{0}{\overset{H}{\int }}\left[{\sigma }_t(S)+\gamma (S)\right]dS}\right\}dz$$

Here To is the brightness temperature of the surface; γ(z)—coefficient of absorption by atmospheric gases; T(z)—altitude distribution of atmospheric temperature. The scattering cross sections σ_t and absorption σ_ɑ, the absorption coefficient γ are functions of frequency. Therefore, the brightness temperature also depends on the frequency. This means that, depending on the frequency, one or the other parameter acquires dominant values. From this it follows that in order to determine certain properties of the medium, it is necessary to select frequencies corresponding to the dominant role of the parameter under study for recording radio-thermal radiation.

Using microwave radiometric methods, it is necessary to determine the surface temperature of the ocean. To do this, it is best to choose a range of waves that are not absorbed and not scattered in the atmosphere. These are waves of frequency below 10 GHz (λ > 3 cm) and then:

T_b = T_ob; λ = λ₁

If we need to know the integral content of water vapor in the atmosphere, then at wavelength λ = 1.35 cm there is a relatively weak water vapor absorption line. This wave is not very strongly scattered and is absorbed in the clouds. Then:

$$T_b\cong T_{ob}+\overline{T}{\displaystyle \underset{0}{\overset{\infty }{\int }}\gamma (z)dz,\lambda ={\lambda }_2}$$

where T is the atmospheric temperature averaged over the thickness of the water vapor. In the first approximation, it can be taken equal to the surface temperature. The value of T_ob obtained on the wave λ₁ can be recalculated on the T_ob wave λ₂. Then it is possible to determine the optical depth of water vapor proportional to the vapor content of the atmosphere.

$$\rho ={\displaystyle \underset{0}{\overset{\infty }{\int }}\gamma (z)dz}$$

If it is necessary to know the water content of the clouds; then, it is convenient to carry out observations at a wavelength of 0.8 cm, where absorption by water vapor and oxygen is not significantly affected, but absorption in clouds is noticeable. In the first approximation of this wave, the following relationship holds:

$$T_b=T_{ob}+\overline{T}{\displaystyle \underset{0}{\overset{L}{\int }}{\sigma }_a(z)dz,\lambda ={\lambda }_3,}$$

where L is the thickness of the cloud layer and T is its average temperature.

Similar considerations make it possible to state that it is possible to determine the water content of clouds from microwave radiometric data.

Characteristic in the above reasoning is that the problem of remote sensing is often multi-parametric and for its successful solution requires the creation of a multi-channel system. In this case, the system must be multi-channel, even if only one parameter is to be determined.

For example, to find out with relative accuracy the surface temperature from the T_oя value obtained at λ = λ₁, it is necessary to introduce “corrections for waves”. For this, a second channel is needed, which measures, for example, the height of the waves, etc.

The problem of determining the ocean temperature in a complex environment, taking into account the main interference factors, was first considered theoretically in relation to multi-channel microwave measurements in [15].

With a four-channel system (λ₁ = 0.8 cm, λ₂ = 1.35 cm, λ₃ = 3.4 cm, λ₄ = 8.5 cm), according to the data of the Kosmos-243 satellite, a linear expression was found for the temperature (not too large parameters variations), which is a solution of a linear system of algebraic equations [15].

$$T=T_0+0.21\Delta T_b^{(0.8)}+0.04\Delta T^{(1.35)}-3.57\Delta T_b^{(3.4)}+8.68\Delta T_b^{(8.5)}$$

where T₀ is the temperature value at the linearization point, ΔT_b is the increase in brightness temperature relative to the linearization levels.

For the set of measuring channels we consider, the system of equations for temperature calculations is ill-conditioned. This is manifested at high values of coefficients at radio-brightness temperatures at wavelengths of 3.4 and 3.5 cm. Poor conditionality means that the solution is extremely sensitive to inaccuracies in the original data and model representations. This circumstance makes it impossible to obtain ocean surface temperature under uncontrolled conditions with an accuracy greater than a few degrees using nadir measurements.

Additional possibilities for conducting multi-channel measurements in the microwave range are provided by using angular measurements of radiation of different polarization.

In [15], an analysis of the dependence of radiation intensity at a wavelength of 3.2 cm on temperature and wind speed, as well as on the characteristics of the atmosphere, shows that the effect of the atmosphere is relatively small and the inverse problem of temperature calculation from measurements at a wavelength of 3.2 cm in two polarizations are well conditioned.

The ocean surface temperature is expressed in terms of measured quantities as follows:

$$T=T_0+{\alpha }_1\Delta I^{ver.pol.}+{\alpha }_2\Delta I^{hor.pol.}$$

where T is the temperature of the ocean surface; T₀—reference level; ΔI^vert.pol. and ΔI^hor.pol.—variations in the sensor readings for vertical and horizontal polarization, respectively, expressed on a conditional scale, corrected according to internal calibration standards. The coefficients α₁ and α₂ are determined using the regression method using the climatic values of the ocean surface temperature along the flight path of the aircraft. The reference level T₀ is taken equal to the integral average value of the climatic temperature of the water surface along the aircraft’s flight path. As shown in [15], the root-mean-square error of an individual determination of the water surface temperature according to microwave radiometer data during polarization measurements at a wavelength of 3.2 cm does not exceed 1.6 °C. The reduction in the error of a single determination of the water surface temperature is achieved by using polarization measurements at long wavelengths and considering the effect of cloudiness on radiation from measurements at a wavelength of 0.8 cm.

Let us consider the possibility of remote sensing methods of the intensity of waves (V) of the water surface. Wind is one of the important factors of the water cycle, which affects the intensity of precipitation, evaporation from the surface of water bodies, and many other hydrological phenomena. Microwave radiometric measurements make it possible to determine the values of the wind speed modulus under certain assumptions about the relationship between the roughness and foaming of the water surface and the wind.

In [8,14,16], based on real measurements and model calculations, the following radiation-wind dependence is proposed:

$$\Delta T_{b\lambda }=0.9(V-V_0)/(1+0.01{\lambda }^2),$$

where V₀ = 5−10 m/s, ΔTя_λ is the increase in the brightness temperature of the water surface. The value of V₀ has the meaning of the “critical” wind speed at which foaming begins. In [3] for ΔTя_λ another dependence is given:

$$\Delta T_{b\lambda }=T_0{S}_{F\lambda }\Delta A_{\lambda },$$

(3)

here ΔA_λ is the contrast value of the sea surface emissivity with and without foam, S_Fλ is the relative area of the sea surface covered with foam (0 < S_Fλ < 1). Based on the dynamic model of sea foam, the values S_Fλ and ΔA_λ are related to the near-water wind speed V. The dependencies of the values S_Fλ and ΔA_λ from V are as follows:

$$\begin{array}{l}{S}_{F\lambda }\cong 6.75\ast {10}^{-4}{(V-3)}^2;\\ \Delta A_{\lambda }\cong 0.45{\lambda }^{-0.5}\exp \left[-a(V-10)\right],\\ where\\ a=\left\{\begin{array}{c}0.32\hspace{1em}at\hspace{1em}V\ge 10 \mathrm{m}/\mathrm{s}\\ 0\hspace{1em}at\hspace{1em}V<10 \mathrm{m}/\mathrm{s}\end{array}\right.\end{array}$$

(4)

From (3) and (4) we get:

$$\Delta T_{b\lambda }=3\cdot {10}^{-4}{T}_0{\lambda }^{-0.5}{(V-3)}^2\exp \left[-a(V-10)\right]$$

(5)

In [17], the accuracy of determining the near-water wind speed using formula (5) is estimated. The optimal wavelength for the determination of V should be in the range from 1.7 to 1.8 cm, while the root-mean-square error in estimating V is quite large and amounts to 6–7 m/s for the optimal wavelength. As noted, the microwave radiometric method makes it possible to estimate only the surface wind speed modulus. However, when solving many hydrophysical problems, it is preferable to determine both the modulus and the direction of the wind speed over the water surface. This problem is solved by the active method of remote sensing of the “ocean–atmosphere” system with the help of satellites. In [11], a technique for estimating the field V is developed based on processing of a radar image of the water surface. The algorithm applies a graphical-analytical calculation procedure using known relationships between the specific effective scattering area and V, at different angles between the sounding direction and the wind, while the direction of the wind speed in the first approximation is determined using optical analysis of the radar image of the water surface, taking into account its structural features. This work provides a method for determining the direction of wind speed from radiometric measurements.

It is often convenient to define the above parameters together. In these cases, when setting inverse problems, it becomes possible to take into account certain relationships between unknown parameters. The inverse problem of joint determination of geophysical parameters from microwave measurements is limited to solving an ill-conditioned system of linear equations [3]. Therefore, analyzing the effect of measurement errors, as well as studying the possibilities for improving the stability of parameter estimates, is important. Using this approach, the main parameters T, S, and V are determined in [8,14,16]. In particular, it was shown in [14] that in the absence of influential atmospheric components in the range 0.8 ≤ λ ≤ 30 cm, the solutions of T, V, and S are the most stable in the parts of the spectrum λ₁ = 5–10; λ₂ = 0.8–1.6 and λ₃ = 25–30 cm; at 0 ≤ T₀ ≤ 30 °C; 0 ≤ S ≤ 40%, 0 ≤ V ≤ 25 m/s.

3. Results and Discussion

3.1. Processing Results of Satellite Measurements for Certain Areas of the Pacific Ocean

The data for the “Cosmos-1500” satellite (with radiometers of our design) were used as initial data for the thematic processing of the remote sensing measurements of the subsystem [1,2].

Satellite-performed radiophysical experiments make it possible to determine ocean parameters such as surface temperature, waves, wind speed, water surface condition, ice cover, and atmospheric parameters.

The “Cosmos-1500” satellite was launched on 28 September 1983 with the following orbital parameters: altitude at the apogee 679 km; at the perigee 649 km; orbital inclination 82.60; the orbit period is 97.7 min [1,2].

The satellite is oceanographic. Its main tasks are:

-

Development and improvement of means for remote sensing of ocean surface and ice fields;

-

Development of methods and means of sub-satellite support for space oceanographic systems;

-

Accumulation of experience by consumers of satellite information on the use of remote sensing data.

The following were installed on board: a radiometric complex consisting of a side-scanning radar station and a scanning microwave radiometer (λ = 0.8 cm); multi-zone scanning device of the visible range; path type microwave radiometric complex with three channels: λ₁ = 0.8 cm; λ₂ = 1.35 cm; λ₃ = 8.5 cm.

Modulation radiometers were used as receivers in all spectrometer channels, in which the source of the reference signal (temperature) and the source of the “cold” calibration signal are weakly directed horn antennas aimed at the open space. Information about the radio-brightness temperature of the “ocean–atmosphere” system is provided to the satellite memory device in both digital (8-bit binary code) and analog code. The root-mean-square error of measuring the radio brightness temperature is 20 K. The resolution at λ₁ = 0.8 cm is 17 km, λ₂ = 1.35 cm is 20 km, λ₃ = 8.5 cm is 85 km.

The range of measured temperatures on a coarse scale for all channels is 100–330 K.

In the present paper, we present the results of data processing from a microwave path type radiometric complex with three channels: λ₁ = 0.8 cm; λ₂ = 1.35 cm; λ₃ = 8.5 cm.

Let us look at some aspects of data processing received from the “Cosmos-1500” satellite in February 1984. The thematic processing of the remote sensing data was carried out in the following order. According to the synoptic map, a specific area (−48°S, −35°S; 110°W, 130°W) or (48°S, 35°S; 110°W, 130°W) over the Pacific Ocean was selected as the object of study (see Figure 1). Then, according to the given or the calculated thresholds {X_i}, samples of l⁺ and l⁻ characteristics were formed [1,18,19,20]. The scheme for measuring the characteristics of “spotting” of the aquatic environment is shown in Figure 2 (details are given in the block diagram of Figure 3).

The most obvious way to identify spots is the method of setting thresholds. In this case, the area of the spot refers to that part of the space in which the media display for a given channel exceeds (l⁺-characteristic) or does not exceed (l⁻-characteristic) the threshold value.

In real conditions, studying the “spots”, obtaining statistical data about them and using this data in the detector is a rather complicated and cumbersome task. It is necessary to develop criteria to distinguish “spots” from other phenomena, in particular, it is necessary to set a threshold, the exceeding of which is a sign of a characteristic parameter of a spot.

In quasi-stationary modules, one way to set the threshold is as follows:

$$X_k=T_{b\min }+k\frac{T_{b\max }-T_{b\min }}{d}$$

where is the T_bmin—minimum value of the radio brightness temperature;

• T_bmax—maximum value of radio brightness temperature;
• k—a parameter that determines the number of thresholds (for example, k = 1.9);
• d is a parameter determined in the following way d = k_max + 1.

Let us introduce the following notation: m_l⁺—frequency of hit values from the sample of positive spots in the sampling interval; m_l⁻—hit frequency of values from a sample of negative spots in the sampling interval; m_l⁺l⁻—is the frequency of the combination hit of pairs of negative and positive spots in the respective sampling interval. Then, {m_l⁺}, {m_l⁻} are the distribution histograms of positive and negative spots, respectively, {m_l⁺l⁻} is the histogram of the joint distribution of the positive and negative spots.

Thus, for each X_i threshold, samples of positive and negative spots were formed according to the selected feature.

We will consider the case when the sign is the length of the spot (the number of measuring points).

Then, various statistical characteristics were calculated for the obtained samples: mean value (M), variance (σ²), skewness (A), kurtosis (K), central moments, etc. In the next step, histograms of the empirical distribution function {m_l⁺} and {m_l⁻} and the type of sampling distribution were analyzed. A joint sample of positive and negative spots was then formed. For this sample, a histogram of the empirical distribution function {m_l⁺l⁻} was also constructed, and statistical characteristics calculated. The correlation coefficient was calculated using the formula:

$$\begin{array}{l}\rho =\frac{\frac{1}{n}{\displaystyle \sum l^{+}{l}^{-}{m}_{l^{+}{l}^{-}}+\frac{1}{n^2}{\displaystyle \sum l^{+}{m}_{l^{+}}{\displaystyle \sum l^{-}{m}_{l^{-}}}}}}{{\sigma }_{+}{\sigma }_{-}},where\\ {\sigma }_{+}={\left[\frac{1}{n}{\displaystyle \sum _{l^{+}}{m}_{l^{+}}{(l^{+}-{\overline{l}}^{+})}^2}\right]}^{\frac{1}{2}},{\overline{l}}^{+}=\frac{1}{n}{\displaystyle \sum m_{l^{+}}{l}^{+}},\\ {\sigma }_{-}={\left[\frac{1}{n}{\displaystyle \sum _{l^{-}}{m}_{l^{-}}{(l^{-}-{\overline{l}}^{-})}^2}\right]}^{\frac{1}{2}},{\overline{l}}^{-}=\frac{1}{n}{\displaystyle \sum m_{l^{-}}{l}^{-}}\end{array}$$

n is the joint sample size. The confidence interval limits were calculated for the correlation coefficient. The 99% confidence interval was calculated using the formulas [1,7,18,21,22]:

ξ₁ = z − u₉₉σ_z, ξ₂ = z + u₉₉σ_z,

where z = ½ln(1 + ρ)/(1 − ρ) is an auxiliary value, where σ_z = (n − 3)^−½, standard error z, n—sample size. Furthermore, (n − 3) is the number of degrees of freedom for z. The values obtained by z correspond to the values of r₁ and r₂, which are the 99% confidence limits for the general correlation coefficient. After that, the joint distribution was analyzed for independence. The results of a comparison of the empirical and theoretical distribution functions were also used for the final decision.

As a result of the thematic processing of radiometric information, the following results were obtained:

• Tables of statistical characteristics of positive and negative spots (l⁺, l⁻)-characteristics).
• Tables of statistical characteristics for average amplitude values of positive and negative “spots”.
• One-dimensional histograms of (l⁺, l⁻)-characteristics (both in terms of the width of the outliers and in terms of the average amplitude values of the outliers).
• Two-dimensional histograms (l⁺, l⁻)-characteristics (both in terms of the width of the outliers and in terms of the average amplitude values of the outliers).
• Results of the analysis of the joint distribution of (l⁺, l⁻)-characteristics for independence.
• Results of the analysis of the distribution type (l⁺, l⁻)-characteristics.

One of the variants of the block diagram of remote information processing is shown in Figure 2. Systems consist of three subsystems: Holder, Resolver, and the Searcher. The functions of Systems are as follows: (1) periodic view of the elements of the phase space; (2) fixing of “suspicious” elements, which requires subsequent additional analysis; (3) accumulation in time of data for several views from fixed elements in the corresponding memory cells; (4) analysis of the results of accumulation and the final decision on the noise or signal character of the element; and (5) localization of the location of anomalies.

Due to the dynamic variation in the image, the System is much quicker to perform a periodic review of the elements of the sea surface. Further, the Holder with the Resolver on some rule allocates “suspicious” elements of the sea surface. After this, a temporary rigid connection is established between the elements of the phase space in the memory cells of the block Holder, in which the data is accumulated for several views up to the final decision in the solver block about the noise or signal character of the elements of the sea surface. After making the final decision on the signal character of the analyzed element, the signal is given to the Searcher block for more accurate localization of the anomaly site and the corresponding memory cells are cleared and can receive new data. All this creates a dynamic mode of memory of the Holder determined by the probabilistic regularities [19,20].

More details on the above-mentioned analysis are given in the following subsections.

3.2. The Case of Calm Surface Water

Table 1. Statistical characteristics of “spot” (l⁺, l⁻) of the Pacific Ocean region according to satellite data “Cosmos-1500” (channel λ₁ = 0.8 cm, pressure 1025 mb, wind speed V < 5 m/s).

Threshold	Sample Size		M	σ2	MIN	MAX	RAZ	A	K	ρ
147.8	13	+	11	326	1	69	68	2.53	5.27	−0.101
		−	1.08	0.08	1	2	1	3.02	7.09
149.6	18	+	6.72	162.31	1	54	53	2.99	7.84	0.074
		−	2.06	3.7	1	9	8	2.74	7.07
151.4	19	+	4.79	116.9	1	48	47	3.4	10.52	−0.234
		−	3.61	7.9	1	13	12	1.87	4.17
153.2	9	+	6.56	205.36	1	47	46	2.45	4.07	−0.266
		−	12.13	107.61	3	34	31	1.16	−0.16

presents the results of statistical data processing for the spotting of radio- brightness temperatures at a wavelength of λ₁ = 0.8 cm, obtained by cross-sectional analysis for an area with high pressure (1025 mb) and wind speed V < 5 m/s (calm area) (data from “Cosmos-1500” satellite for 8–9 February 1984).

The maximum value of radio-brightness temperature T_bmax = 162.3 K, the minimum value of temperature T_bmin = 144.2 K. The most informative are the thresholds, whose values range from 149 K to 152 K. It is worth noting that the more threshold intersections (the more “Spots”), the more informative the threshold (see Figure 1).

For these thresholds, there is a greater convergence of the average sizes of positive and negative spots. For the threshold X = 151.4, the difference between the average values of the spot sizes is ΔM = 1.18. The minimum value of the correlation coefficient was also set for the most informative thresholds. Therefore, for the threshold X = 149.6 ρ_min = 0.074.

In this case, it can be argued with high probability that the distributions of the positive and negative spots are independent.

We can limit ourselves to the study of one-dimensional histograms (l⁺, l⁻)-characteristics. An analysis of the theoretical and empirical distribution of negative spots also showed their independence for the most informative thresholds. Thus, the mean theoretical and empirical distribution for the threshold value X = 149.6 was Δ = 0.048, and for X = 151.4, Δ = 0.016.

Figure 4 illustrates one-dimensional histograms for characteristics l⁺ and l⁻. Figure 5 shows the corresponding two-dimensional histograms for characteristics l⁺ and l.

3.3. The Case of Moderate Surface Water Waves

Table 2. As in Table 1, but for channel λ₁= 0.8 cm, pressure 1010 mb, wind speed 6 < V ≤ 10 ms⁻¹.

Threshold	Sample Size		M	σ2	MIN	MAX	RAZ	A	K	ρ
159.9	16	+	12.31	257.09	1	61	60	1.82	2.66	−0.351
		−	1.4	0.37	1	3	2	1.26	0.51
161.8	35	+	4.09	23.79	1	22	21	2.45	5.66	−0.198
		−	2.21	5.28	1	13	12	3.31	11.99
163.7	37	+	1.81	3.5	1	11	10	3.46	13.23	−0.020
		−	4.08	35.16	1	34	33	3.67	14.95
165.6	8	+	2.57	3.10	1	6	5	0.82	−0.61	−0.266
		−	25	1268.5	1	117	116	2.06	2.63

shows the statistical characteristics of the Pacific Ocean “spot” for an area with a normal pressure of 1010 mb and a wind speed of 6 m/s ≤ V ≤ 10 m/s (moderate waves). For this area, the extreme values of radio-brightness temperature are as follows: T_bmin = 156.8 K, T_bmax = 175.8 K.

The most informative thresholds range from 161 K to 164 K. For the same thresholds, there is also a sharpness of the average sizes of positive and negative spots. For X = 161.8 the difference ΔM gets the value 1.88. The correlation coefficient reaches the minimum value ρ = −0.02 for the threshold X = 163.7, which indicates the independence of the distribution of positive and negative spots. The mean deviation of the theoretical and empirical joint distribution is Δ = 0.01, which also confirms this. For this threshold, as well as for the threshold X = 161.8 (ρ = −0.198), one can limit himself to the study of one-dimensional histograms, and for the rest it is desirable to study two-dimensional histograms. Figure 6 shows one-dimensional histograms for the l⁺ and l⁻ characteristics while Figure 7 depicts the respective two-dimensional histograms for the l⁺ and l⁻ characteristics.

3.4. The Case of Storm Surface Water Waves

Table 3. As in Table 1, but for channel λ₁ = 0.8 cm, pressure ≤ 1005 B, wind speed V ≈ 16 m/s.

Threshold	Sample Size		M	σ2	MIN	MAX	RAZ	A	K	ρ
162	6	+	13.5	333.25	1	52	51	1.42	0.39	0.1
		−	1.5	1.25	1	4	3	1.79	1.2
163.5	12	+	5.5	157.25	1	47	46	2.99	7.01	0.034
		−	2	1	1	4	3	0.5	−1
166.5	7	+	7.5	96.58	1	29	28	1.63	0.89	0.16
		−	7.5	86.58	1	23	22	0.78	−1.29

presents the statistical characteristics of the “spot” of the Pacific Ocean with low pressure (<1005 mb) and wind speed V ≈ 16 m/s (storm zone) for the channel λ₁ = 0.8 cm.

The extreme values of radio-brightness temperature are the following: T_bmin = 160.6 K, T_bmax = 220.1 K.

The most informative thresholds are in the range from 163 K to 164 K. However, the average sizes of positive and negative spots are closer for the threshold X = 166.5 and ΔM = 0, while for X = 163.5 ΔM = 3.5. The correlation coefficient reaches its minimum ρ_min = 0.034 for the X = 163.5 threshold, which indicates the independence of the distributions of positive (l⁺) and negative (l⁻) spots.

For the same threshold, the minimum deviation of the joint theoretical and empirical distributions Δ = 0.007 was obtained, which confirms this independence. Figure 8 shows one-dimensional histograms for l⁺ and l⁻ characteristics and Figure 9 shows the corresponding two-dimensional histograms for the l⁺ and l⁻ characteristics.

From the analysis of the statistical characteristics of the “spot” of three types of Pacific Ocean areas, obtained for the most informative thresholds, with the statistical characteristics of the “spot” of the same areas, selected from the minimum value of the correlation coefficient of the joint sample of positive and negative spots, an interesting conclusion is revealed. It appears that for areas with moderate waves and storm zones, the statistical characteristics of the “spot” coincide, i.e., the minimum of the correlation coefficient ρ_min is achieved for the most informative thresholds. As for a quiet area, this is not the case.

From the above it follows that the statistical characteristics of the “spot” of radio-brightness temperatures can be used to detect and classify phenomena on the ocean surface that differ in the degree of waves.

3.5. The Case of Averaged Values

Table 4. As in Table 1, but for the average amplitude values of spots of radio brightness temperatures according to the satellite data “Cosmos-1500” (channel λ₁ = 0.8 cm).

Threshold	Sample Size		M	σ2	MIN	MAX	RAZ	A	K	ρ
147.8	13	+	150.55	3.71	148.7	155.9	7.2	1.5	1.97	−0.373
		−	146.7	0.87	144.2	147.2	3	−1.68	1.53
149.6	18	+	151.3	2.86	150.2	157.5	7.3	2.67	6.98	0.21
		−	148	0.93	145.7	148.7	3	−1.43	0.97
151.4	19	+	152.5	2.58	151.4	158.3	6.9	2.54	6.14	0.336
		−	149.2	0.61	147.8	150.2	2.4	−0.64	−0.68
153.2	9	+	154.9	3.14	153.3	158.5	5.2	0.61	−0.77	0.471
		−	150.5	1.46	149.1	152.5	3.4	0.44	−1.30

shows the statistical characteristics for the average amplitude values of the “spots” of radio-brightness temperatures according to the data of the satellite “Cosmos-1500” for 8–9 February 1984. As shown in Table 4, for all thresholds it is necessary to study two-dimensional histograms.

The analysis of the empirical distributions (histograms) of the “spot” of radio brightness temperatures shows that in most cases (l⁺, l⁻) the characteristics are consistent with the exponential distribution, and the amplitude characteristics are normal [1,7,18,20], Therefore, to detect and classify ocean surface phenomena, it is necessary to use optimal algorithms for machine learning to make statistical decisions for the above distributions [12,23,24,25,26,27]. A similar procedure may be used to explore the remotely sensed atmospheric and hydro-physical characteristics of the water surface of the Mediterranean Sea.

4. Conclusions

According to the analysis presented above, one of the important points of geoinformation monitoring is the automation of remote sensing data processing with the ultimate goal of solving the problem of detecting and classifying a specific phenomenon on the water surface. An effective solution of these problems is impossible without the widespread introduction into the practice of researching automated systems for collecting, storing, and processing data based on modern computers using open systems technology. Thus, the automation of geoinformation monitoring in all its stages, from information collection to the creation of an appropriate automated data processing system equipped with the necessary algorithms and software, is an urgent scientific task of great practical importance.

The developed algorithms and software for the detection and classification of surface water phenomena according to geoinformation monitoring data significantly increases the efficiency of environmental studies due to the integrated and rational use of experimental equipment, the optimal use of remote sensing data.

A feature of remote measurements is the collection of information when the input of the processing system receives data during the flight route of the aircraft. As a result, a set of implementations of random processes is obtained, the processing of which with spatiotemporal interpolation makes it possible to form a two-dimensional image of the object under study. One of the models of this image is the statistical model of the “spot” of the studied space.

A sub-block of an automated system for geoinformation monitoring has been developed that implements the algorithm for statistical modeling of the “spot”.

The statistical characteristics of the “spot” of radio-brightness temperatures obtained for the most informative thresholds are analyzed. It is argued that these characteristics can be used to detect anomalous phenomena on the water surface.

Based on the developed “spot” model, the processing of geoinformation monitoring data makes it possible to identify the probabilistic characteristics of the “spot”, which are informative signs for the detection and classification of anomalous phenomena on the ocean or sea surface.

The statistical characteristics for the “spottiness” of brightness temperatures in the microwaves can be used for detection and classification of the phenomena on the ocean surface, caused by a degree of sea roughness. Analysis of the empirical histograms for the “spottiness” of “brightness temperatures in microwaves” shows, that in most cases (l⁺, l⁻)-characteristics will be in tune with the exponential distribution, and amplitude characteristics will be in tune with the normal distribution. Therefore, for the detection and classification of phenomena on an ocean surface it is necessary to apply optimal training algorithms for statistical decision making for the aforementioned distributions [1,7,19,20,22,28,29,30,31,32].