Modeling of the SOA MCW and IR Characteristics and Their Relations With the Air–Sea Heat Interaction

Abstract

In this chapter, we present some results of modeling an intensity of natural microwave radiation of the system ocean-atmosphere at microwaves (in the millimeter and centimeter range of wavelengths) and infrareds (in the window of relative transparency 8–12 μm). These characteristics computed for various levels of observations used in practice (satellite, aircraft, and vessel) were compared with the surface vertical turbulent fluxes of sensible, latent, and total heat. A search of spectral intervals providing most close correlations of radiation characteristics and heat fluxes over various time scales (mesometeorological, synoptic, seasonal, and intra-annual) was considered as a separate task. The models of the system ocean-atmosphere were constructed taking into account accessible oceanographic and meteorological data required for computation of the radiation characteristics.

2.1 Sensitivity of Microwave and Infrared Radiation of the System Ocean-Atmosphere to Mesometeorological Variations of Heat Interchanges Between the Oceanic and Atmospheric Boundary Layers

2.1.1 Model of Heat Interchanges Between the Oceanic and Atmospheric Boundary Layers

To study the thermal response of the atmospheric and oceanic boundary layers (hereafter, ABL and OBL, respectively) to a heat perturbation at their interface:

$$\begin{array}{l}dT_1/dt = (q_{h{\rm a}} - q_{h{\rm s}})/(\rho_{\rm a} c_{\rm a} h_1),\\ dT_2 / dt = (q_{h{\rm s}} - q_{h{\rm w}} - Le_{\rm s} + R)/(\rho_{\rm w}\; c_{\rm w}\; h_2),\\ dq/dt = (e_{\rm a} - e_0) / (\rho_{\rm a}\; h_1),\end{array}$$

(2.1)

$$T_1 = T_{10},\; T_2 = T_{20},\; q = q_o \; (t = 0)$$

(2.2)

Here, the values T ₁ and T ₂ are denoted as the temperatures of the atmospheric and oceanic boundary layers, respectively; q is the specific humidity in the ABL; h ₁ and h ₂ are the thickness of the ABL and OBL, respectively; ρ _a and ρ _s are the air water densities; C _a and c _w are the air and water specific capacities, respectively; q _haа and q _hw are the latent heat fluxes at the sea-air interface; e _s is the moisture flux (rate of evaporation/condensation) at the water surface; L is the specific heat of evaporation; and R is the sun shortwave radiation flux heated the water surface.

The temperature-moisture regime of the SOA is parameterized under the following assumptions:

• The simulated system is laterally homogeneous

• The boundary layers of the atmosphere and ocean are well mixed, so that T ₁, T ₂, and q values are independent of the height (depth) within the ABL and OBL

• The boundary-layer thicknesses h ₁ and h ₂ remain unchanged with time

• The ABL heat budget is controlled only by sensible heat fluxes q _haа and q _hs

• The OBL heat budget is controlled only by sensible heat q _hw and q _hs and also by the latent heat Le _s, resulting from a water surface evaporation (condensation), and by the solar radiation flux R, which is entirely absorbed within the OBL

• The ABL moisture budget is determined by the surface evaporation e _s and the moisture exchange e _a with the overlying air layer; phase conversions of water do not occur in the ABL

• ABL and OBL temperature regime is independent of the electromagnetic radiation intensity in the ocean-atmosphere system

The problem is formulated analogously to Grankov and Resnjanskii (1998), with the only difference that in the evolution of the ABL moisture regime, the respective component of the OBL heat budget is taken into account inconvenience.

To close the problem, it is necessary to express the fluxes q _h , q _hs, q _ha, q _hw, e _s, and e _a in terms of the sought variables and q as well as the external conditions. The radiation flux R is assumed to be specified. It serves as a thermal perturbation. The simulation of the response to this perturbation is the essence of the given problem. To determine the fluxes, the following expressions are used:

$$\begin{array}{l}q_{{\rm hs}} = c_1\;\rho_{\rm a}\;c_{\rm a}\;V_{\rm a} (T_1 - T_2),\\ e_0 = c_2 \; \rho_{\rm a} \; V_{\rm a}\; (q - q_{\rm s}),\\ q_{{\rm ha}} = c_3\;\rho_{\rm a}\;c_{\rm a}\;V_{\rm a} (T_{\rm a} - T_1),\\ e_{\rm a} = c_4 \; \rho_{\rm a} \; V_{\rm a}\; (q_{\rm a} - q),\\ q_{{\rm hw}} = c_5\;\rho_{\rm w}\;c_{\rm w}\;u_{\rm w} (T_2- T_{\rm w}),\end{array}$$

(2.3)

where the first two are conventional bulk formulas, and the last three are based on the assumption that the fluxes q _ha, q _he, and q _hw at the outer boundaries of the ABL and OBL, to first approximation, can be expressed similarly through the values of the q _hs and q _hs and q _es with a proper choice of the transfer coefficients c ₃, c ₄, and c ₅.

In formulas (2.3), T _a is the air temperature just above the ABL; T _w is the water beneath the OBL; q _w is the saturation specific humidity at the water temperature T ₂; V _a is the mean near-surface wind speed; u _w is the mean oceanic current; c ₁, c ₂, …, c ₅ are some nondimensional transfer coefficients.

Using one more assumption of the linearized dependence of a saturation humidity q _w vs. the temperature T ₂,

$$q_{\rm w} = q_{\rm r} + a (T_2 - T_{\rm r})$$

(2.4)

where, q _r and T _r are the reference humidity and temperature; the set of equations (2.1) taking into account (2.3) and (2.4) can be rewritten in a vector form as follows:

$$d{\rm {\bf y}}/dt = A{\rm {\bf y}} + {\bf f},$$

(2.5)

where y = (T ₁, T ₂, q) is the vector of the sought variables; f = (f ₁, f ₂, f ₃) is the vector of three terms:

$$\begin{array}{l}f_1 = (c_3\;u_{\rm a} /h_1)T_{\rm a},\\f_2 = [R + c_5 \; \rho_{\rm w}\; c_{\rm w}\; T_{\rm w} - c_2 \;\rho_{\rm a} \; u_{\rm a}; L (q_{\rm r} - a\; T_{\rm r}))];\\f_3 = (u_{\rm a} /h_1) [c_4 q + c_2 (q_{\rm r} - aT_{\rm r})];\end{array}$$

(2.6)

A = |a _ik |, i, k = 1, 2, 3, is the matrix of coefficients. Unlike f, the expressions for a _ik comprise only the model parameters h ₁, h ₂, a, c ₁, c _2, …, but not R, T _a, T _w, and q _a, which characterize the external conditions of forcing with respect to the ABL (OBL).

The solution of (2.5) is written as follows:

$$\begin{array}{l}T_1 = C_1 \; e ^{{\rm r \ t}}_ {\ 1} + C_2 \; e^{{\rm r \ t}}_ {\ 2} + C_3 \; e^{{\rm r \ t}}_ {\ 3} + T^*_1,\\ T_2 = C_1 \; p_1 \; e^{{\rm r \ t}}_ {\ 1} + C_2 \; p_2 \; e^{{\rm r \ t}}_{\ 2} + C_3 \; p_3 \; e^{{\rm r \ t}}_ {\ 3} + T^*_1,\\ q = C_1 \; s_1 \; e^{{\rm r \ t}}_ {\ 1} + C_2 \; s_2 \; e^{{\rm r \ t}}_ {\ 2} + S_3 \; C_3 \; e^{{\rm r \ t}}_ {\ 3} +q^*,\end{array}$$

(2.7)

Here, r _i (i = 1, 2, 3) are the roots of a characteristic equation of the homogeneous system (2.5) as shown in the Table 2.1.

Table 2.1 Matrix of the coefficients a _ij characterized the equation of the system (2.7)

The values T ^*₁ , T ^*₂ , and q are the partial solutions of the inhomogeneous system (2.7), sought by the method of variation of constants and expressed in terms of a _ik , f _i , and r _i.; p _i , s _i and C _i are some combinations of coefficients and initial values T ₁₀, T ₂₀, and q ₀ from condition (2.2).

Numerical estimates show that for typical values of the model parameters, the determinant of the characteristics of (2.8) is negative, and all its roots r _i , (j = 1, 2, 3) are real, different, and negative. Hence, the solution (2.7) describes the adaptation of the ABL-OBL system to the external conditions (factors) R, T _a, T _w, q _a, which tend with time to a stable state (T ^*₁ , T ^*₂ , q ^*). The characteristic adaptation time [min (ú r _i ú )]⁻¹ is about 18 h for typical values of the parameters: ρ _a= 1.25 kg m⁻³; ρ _w = 10³kg m⁻³; c _a= 10³J kg deg⁻¹; c _w= 4,100 Jkg deg⁻¹; h ₁= 1,500 m; h ₂= 30 m; L  =  2.4  ×  10⁶  J kg⁻¹; R  =  200 W m⁻²; V _a  = 10 m s⁻¹; u _w = 0.1 ms⁻¹; c _i = 1.3 × 10⁻³ (i = 1, 2, …, 5); T _r = 10°C; q _r= 7.5 × 10 ⁻²  kg kg⁻¹; and a = 5 × 10 ⁻⁴ deg⁻¹.

2.1.2 Interrelations of MCW and IR Radiation Fluxes with Heat Fluxes in the System Ocean-Atmosphere

In the framework of a plane-layered model of thermal radiation (absorption) in the ocean-atmosphere system (Fig. 2.1), it is possible to analyze the processes of the electromagnetic energy transfer in various layers, as well as to estimate an intensity of these radiation components, which can be registered with satellite (A), airplane (B), and shipboard (C) equipment.

Fig. 2.1

Parameterization scheme of the main characteristics of thermal and electromagnetic energy transfer in the ocean-atmosphere system

A: In satellite observations, the ocean-atmosphere natural microwave radiation I _sat is composed of the intensity of the free-atmosphere radiation I _a and an intensity of the up-going radiation flux I ₁ʿ at the top of the ABL attenuated in the free atmosphere (multiplier G _a):

$$I_{\rm sat} = I_{\rm a} + I_1^ {\ \uparrow} G_{\rm a},$$

(2.8)

where I ^ʿ₁= I ₁+(I ₁¯ R ₂₁+ I ₂ ) G ₁ is an intensity of the up-going radiation flux at the top of the ABL; I ^↓₁= I ₁+ I _a; G ₁ is an intensity of the down-going radiation flux at the bottom of the ABL; I ₁(G ₁) is an intensity of the integral (total) attenuation in the ABL; I ₂ is an intensity of the ABL natural radiation; G ₁ is the integral attenuation of radiation in the ABL; and R ₂₁ is the coefficient of reflection of the down-going radiation flux I ^¯₁ from the water surface.

It is assumed that the electrophysical parameters of the ABL and the free atmosphere, in spite of the difference (in a general case) between their temperature and humidity characteristics, are consistent with each other, that is, the reflectivity at their interface is absent or negligibly small compared with R _21.

B: In observations from an aircraft (at the top of the ABL), the ocean-atmosphere radiation intensity I _air is determined solely by the component I ^ʿ₁ :

$$I_{\rm air} = I_1^ {\ \uparrow}$$

(2.9)

C: In shipboard observations (at the lower boundary of the ABL), an intensity of radiation I _ship is computed as follows:

$$I_{\rm ship} = I_2 + I_1^ {\ \uparrow} R_{21}$$

(2.10)

The characteristics of natural radiation of the boundary (I ₁) and free (I _a) atmosphere in expressions (2.8)-(2.10) are related to the corresponding values of temperature T ₁, T _a and of the integral absorption G ₁, G _a of this media:

$$I_1 = T_1 (1-G_1 \ ); I_{\rm a} = T_{\rm a} (1-G_{\rm a \ }).$$

(2.11)

An intensity of the thermal radiation of the water surface I ₂ is proportional to

$$\begin{array}{l}I_2 = {\ae} \ T_2 in \; the \; MCW \; wavelength \; range;\\ I_2 = \delta \ B(T_2) \ in \; the \; IR - band,\end{array}$$

where T ₂ is the OBL temperature; B(T ₂) is the Planck’s function with T ₂ as an argument; æ is the emissivity of the water surface at microwaves; and δ is the IR-emissivity of the ocean surface.

In the MCW range of wavelengths, where the Rayleigh-Jeens approximation is valid, respective values of the brightness temperature T ^b are used as a measure of the radiation intensity of different components of the ocean-atmosphere system. To characterize the IR radiation intensity I here and below, we will use the concept of the effective (radiation) temperature T ^r, defining it from the equation B(T ^r), that is, as a thermodynamic temperature of the absolute (ideal) black body with a radiation intensity is equal to I.

2.1.3 Results of Numerical Analysis of the Dynamics of Thermal and Electromagnetic Fluxes and Their Correlations in the Ocean-Atmosphere System

The numerical estimates were obtained for the temporal evolutions of fluxes q _h and q _e at the ABL-OBL interface boundary and the radiation fluxes I _sat, I _air, and I _ship in terms of the corresponding values of the brightness temperature at the wavelength range (5 mm-3 cm) and infrared radiation temperatures (8–12 mcm) after the ocean-atmosphere system was forced out of the state of a thermal equilibrium. They were obtained for typical values of thermal constants (air humidity and density, heat capacity, specific heat of evaporation (condensation), heat and humidity interchange coefficients), ABL and OBL thickness, mean wind, and current velocities, given above.

The computations were performed in the following sequence: (a) derivation of the system solution (2.7) as related to the tasks (2.1), (2.2) in terms of the ocean-atmosphere interface layer variables T ₁, T ₂, and q _a for given values of the thermodynamic parameters T _w, T ₁, and q _a at the outer boundaries of the ABL and OBL and of the solar heat flux R at the water surface; (b) determination of heat fluxes q _h and q _e at the ocean-atmosphere interface from the defined values of T ₁, T ₂, and q _a; and (c) determination of electromagnetic fluxes I _sat, I _air, and I _ship from the calculated values of parameters T ₁, T ₂, and q _a and specified values of T ₁, T ₂, and q _a; and (d) regression analysis of the interrelation between the evolutions of the q _h and q _e parameters and the evolutions of the I _sat, I _air, and I _ship values in various MCW and IR spectral bands.

The analysis of the ocean-atmosphere brightness temperature has been carried out for the range of wavelengths from 5 mm to 3 cm, where the natural MCW radiation of the system is most sensitive to variations of thermal and humidity characteristics, the radiation temperature being used as a measure of natural IR radiation in the atmospheric window of 8–12 mcm. The atmospheric absorption was computed with an account of the effect of the water vapor content (in MCW and IR bands), molecular oxygen (in the MCW bands), and the aerosol component (in the IR band) on the basis of theoretical relations (Zhevakin and Naumov 1964, 1965) and semi-empirical relations (Arefjev 1991; Paramonova 1985) mainly used at infrareds.

The simulation of the dynamics of thermal and electromagnetic fluxes and an analysis of their interrelations have been performed for several variants differing in the character of the thermal energy outflow from the ocean-atmosphere interface toward the outer boundaries of the ABL and OBL and beyond their borders. This was achieved by a proper choice of parameters of the free atmosphere and of the lower quasi-homogeneous ocean in reference to the initial ABL and OBL conditions invariant in all cases (T ₁₀ = T ₂₀ = 10°C, q _o = 6 g kg⁻¹). The results given below illustrate the following variants: (1) T _w = T _a = 5°C; q = 4 g kg⁻¹ (the heat propagates toward the outer boundary of the ABL and simultaneously to the outer boundary of the OBL); (2) T _w = 5°C; T _a = 10°C; q = 6 g kg⁻¹ (heat propagates only to the lower oceanic layer); and (3) T _w = 10°C; T _a = 5°C; q = 4 g kg⁻¹ (heat propagates only to the free atmosphere).

Figure 2.2 demonstrates the results of an analysis of the response of the ABL and OBL parameters T ₁, T ₂, and q, which determine a natural MCW and IR radiation of the SOA, for the first (most general of the above-mentioned) variant.

Fig. 2.2

The response of (1) ABL temperature T ₁, (2) OBL temperature T ₂, and (3) ABL humidity q to the thermal excitation of the SOA in the case of heat outflow from the ocean-atmosphere interface toward the outer boundaries of the ABL and OBL

As seen from the figure, the complete adaptation of the SOA parameters to the impact of the solar radiation flux R occurs during 1–2 days; the adaptation of the ABL temperature occurs about twice as fast as that of the ABL parameters T ₁ and q.

The analysis of corresponding variations of sensible and latent heat fluxes q _h and q _e shows that the response of heat fluxes and of the ocean-atmosphere brightness (radiation) temperature is also formed during 1–2 days, that is, it agrees with the time of adaptation of the ocean-atmosphere characteristics to the external influx R.

A regression analysis has been performed to derive some relations between variations of sensible and latent heat fluxes, Δq _h and Δq _e, and brightness ΔT  ^b (radiation ΔT ^r ) temperature variations at microwaves and infrareds, accordingly, for versions I, II, III at different observation levels (from satellites, aircrafts, vessels). In particular, the feasibility of an approximation of Δq _h and Δq _e has been examined for the case of the heat outflow in both directions from the ocean-atmosphere interface; the approximations were constructed as linear pair combinations of ΔT in different spectral bands (if meaning the satellite level) and are shown in Fig. 2.3. The solution of this problem involves: (1) determination of regression coefficients between Δq _h , Δq _e, and ΔT in the initial stage of formation of the SOA response to a thermal perturbation (hatched area in Fig. 2.3); (2) approximation of Δq _h and Δq _e using the computed regression coefficients; and (3) extrapolation (prediction of the subsequent evolution) of Δq _h and Δq _e with the regression relations derived in the initial stage with an account for the evolution of ΔT in the final stage of formation of the ocean-atmosphere response. As seen from the Fig. 2.3, the variations of an intensity of the ocean-atmosphere natural radiation in the spectral windows ∼10 microns and ∼5.7 mm provide the best reconstruction of the q _h and q _e fluxes in the entire time interval (2 days) of a formation of the radiation and heat response.

Fig. 2.3

Simulated results of approximation and extrapolation of sensible q _h and latent q _e fluxes (1) with the data of satellite passive radiometric measurements at the spectral intervals: 10 mcm, 5.7 mm (2), 10 mcm and 1.35 cm (3), 1.35 and 3.2 cm (4), 5.7 mm and 3.2 cm (5)

The results of a regression analysis for different versions of heat outflow from the interface to the outer boundaries of the ABL and OBL are given more completely in Table 2.2.

Table 2.2 Approximation errors δq _h and δq _e for Fluxes q _h and q _e in different spectral bands for overall (2-day) cycle of the SOA response as observed from satellite

It follows from the table that the lowest estimation errors δ(q _h ) and δ(q _e) (a few percent of the amplitude of natural variations of these parameters) correspond in most cases to spectral intervals 10 and 5.7 micrometers microns as well as 1.35 and 3.2 cm; the increase in the number of spectral intervals as degrees of freedom from two to three or more in the approximation of heat fluxes by MCW and IR radiation characteristics does not lead to any significant reduction of the errors.

The results of a regression analysis of heat fluxes at the micrometers (mycrons) ocean-atmosphere interface and electromagnetic fluxes at the top of the ABL (the aircraft level) are quite close to those given in the table. At the same time, the results of regression analysis of the heat and electromagnetic fluxes at the lower boundary of the ABL (the vessel level), where the atmosphere influence is minimal, differ from the data in the table by substantially larger values of q _h and q _e, which in this case equal 5–6 W m⁻² and are scarcely affected by the selection of the spectral intervals.

As a whole, the idea of studying the response of the ABL heat features on the air-sea boundary perturbations give us the following results:

• 1. The heat and water exchange processes in the ocean-atmosphere interface layer have a profound effect on the MCW and IR radiation characteristics not only in the interface layer, but also in the entire atmosphere. This is evident from analysis of the evolutions of the SOA brightness temperatures at the top of the ABL and in the free atmosphere, as well from comparison of these data with the evolutions of heat fluxes at the ocean-atmosphere interface. One can see that the response of thermal and electromagnetic fluxes to the excitation of the system is developing during about the same time period (several days, typically).

• 2. A connection of brightness and radiation temperatures at the top of the ABL and in the free atmosphere with sensible and latent heat fluxes in the SOA interface is best pronounced in certain spectral intervals; the main effect of the outflows from the ocean-atmosphere interface toward the outer boundaries of the ABL and OBL becomes more apparent in the regions of the atmospheric resonance absorption by molecular oxygen (∼5 mm) and in the water vapor line 1.35 cm. Hence, the oxygen and water vapor atmospheric factors can serve as some transient parameters (“bridges”) between the natural radiation of the SOA and the heat exchange intensity at its interface not only on seasonal and synoptic scales, but also on smaller (daily, for example) time scales.

• 3. Because of theoretical analysis fulfilled in the framework of the plane-layered problem, the brightness (radiation) temperature variations at the top of the ABL and in the free atmosphere caused by vertical transfer of heat and water transfer in the interface of the system are of a few degrees of Kelvins (K). At the same time, as it will be shown below, the satellite-derived estimates of the SOA brightness temperature variations can reach the tens of K measured at the wavelength 1.35 cm.

2.2 Correlation of the Brightness Temperature with an Intensity of the Ocean-Atmosphere Heat Interaction in the Synoptic Range of Time Scales

2.2.1 Initial Data

We will use in this study the results of the experiments ATLANTEX-90 and NEWFOUEX-88 obtained from the research vessels (R/Vs) Victor Bugaev, Musson, and Volna, which manifested and completed a final phase of the scientific project “RAZREZY” devoted to an analysis of the large-scale air-sea heat and dynamic interaction in the North Atlantic energy active zones.

First of all, from these unique experiments, we extracted the data that are obtained during the so-called stationary phases (April 4–21, 1990 and March 3–23, 1988), which are distinguished by the following features:

• (a) Maximum regularity of the meteorological and, especially, aerologic measurements fulfilled during this period

• (b) Possibility of a fine analysis of the temporal dynamics of the oceanic and atmospheric parameters due to the fixed (stationary) positions of the R/Vs Victor Bugaev, Musson, and Volna

The research vessels were settled in the three areas of the Gulf Stream delta: in a southern periphery of the basic Gulf Stream water flow (R/V Victor Bugaev), in its southern stream (R/V Musson), and in an eastern branch of the Labrador Current (R/V Volna). This zone is characterized by a strong synoptic variability of the oceanic and atmospheric parameters, which is caused by an influence of the subpolar hydrological front (SHF) as a result of interaction between the cold Labrador Current and the warm quasi-stationary anticyclone rings of the Gulf Stream. The important attribute of this zone is an intensive horizontal circulation of the atmosphere - about 50% of all the time this area of the North Atlantic feels an influence of the powerful midlatitude cyclones, which excite intensive variations of the atmospheric temperature and humidity as well as the boundary heat fluxes (Lappo et al. 1990).

The fragments of stationary phases of the experiments ATLANTEX-90 (from April 8 to 13, 1990) and NEWFOUEX-88 (from March 10 to 15, 1988) were analyzed in details, because just in these periods one could see a synchronous response of all vessel oceanographic and meteorological sensors on the strong mid latitude cyclones in this area of the North Atlantic.

2.2.2 Methods of Computation of the SOA Radiation

We compared the results from the two methods of calculating the average daily values of the SOA brightness temperature in the spectral regions affected by absorption in molecular oxygen (5−6 mm) and the atmospheric water vapor line (1.35 cm) for the case of satellite-borne observations.

In the first case, the simplified model (2.8) was used, which cannot take into account a detailed information on the atmospheric characteristic vertical distribution, but is more accessible for various oceanic regions in every times.

In another case, the plane-layer model of radiation (Basharinov et al. 1974) similar to the model described in Sect. 1.1 of Chap. 1 was used. In terms of this model, proper for MCW range as well as the infrareds, for observations in the nadir direction from an altitude H, the SOA natural radiation I consists of three components:

$$I = I_1 + I_2 + I_3,$$

(2.12)

where the components I ₁, I ₂, and I ₃ can be determined by the relationships (1.12)-(1.15).

Here, in comparison with the model used in Sect. 2.1, this one enable us to assimilate the spacious data on vertical distribution of the air temperature, humidity, and pressure obtained from the aerologic measurements. But the sample frequency specific for the aerologic measurements (every 6 h) is less in comparison with the first case where the SOA brightness temperature is computed based on the 1-hourly values of the oceanographic and meteorological measurements.

An intensity of the SOA radiation I at the level h is determined as follows:

$$\begin{array}{l}\ \ at\,microwaves\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,at\,infareds \\ \begin{array}{*{20}c}{I_{\rm a} (h) = T_{\rm a} (h)\,\gamma \,(h);\,\,\,\,\,\,\,\,\,\,} & {I_{\rm a} (h) = B[T_{\rm a} (h)]\,\gamma \,(h)}, \\\end{array}\\ \end{array}$$

(2.13)

where T _a(h) is the thermodynamic temperature of the atmosphere at the level h; B[T _a(h)] is the Plank function with the argument T _a(h).

Relationships (2.12), (2.13) and formulas figured in Chap. 1 (1.11–1.15) will be used later in Sect. 2.3 of this chapter.

Right now, using this model, we will analyze the daily and synoptic variations of the SOA brightness and radiation temperatures in the wavelength range 0.5–5.0 cm at the stationary phases of the experiments ATLANTEX-90 and NEWFOUEX-88 aboard the Victor Bugaev, Musson, and Volna.

From the field data we extracted the following:

• Hourly values of the oceanic water surface temperature T _w and near-surface wind speed V to calculate the brightness (radiation) temperature of the surface.

• Total water vapor content in the troposphere to evaluate the integral absorption τ both with and without cloudiness.

• The temperatures T _a, relative humidity q (or water vapor pressures e), and the air pressures P measured at 20 levels between 10 and 16,000 m every 6 h to estimate not only the total absorption τ, but also the linear absorption factor γ(h), from which the accurate estimates of the atmospheric transfer function and, hence, the SOA brightness (radiation) temperature can be found.

• Estimates of turbulent sensible q _h and latent q _e heat at the SOA interface, which were calculated in the State Institute of Oceanography using parameterizations (Gulev et al. 1994) based on hourly observational data for T _w, T _a, V, and e.

The contributions from different layers to radiation properties of the SOA and their interrelations with the heat fluxes at the interface on the synoptic time scale were evaluated theoretically for various cases. In the first case, the down-looking sensors (radiometers) are placed in free air to simulate satellite observations. In the second case, which simulates measurements aboard an aircraft, the down-looking sensors are placed at the boundary between free air and the atmospheric boundary layer. In the third case, the up- and down-looking sensors are placed 10–20 m above the water surface to simulate aboard the vessels.

One more method of calculating the satellite-derived SOA brightness temperature in the spectral regions caused by the absorption of oxygen (∼5 mm) and water vapor (1.35 cm) in the atmosphere was tested in our investigations. The idea was to use the minimum data on the atmosphere absorption characteristics - without any detailed information on its vertical temperature and humidity distribution within the ABL (see Fig. 2.4).

Fig. 2.4

Comparison of the SOA brightness temperature calculated from integral MCW radiometric (1) and aerologic (2) measurements of the temperature and humidity characteristics of the atmosphere at the wavelengths 5.6 mm (a) and 1.35 cm (b)

Partial interest of comparison of these data with the results of more accurate procedures of calculating the SOA brightness temperature was obtained with an account of the temperature and humidity vertical distribution in the ABL.

It follows from a comparison of the results of the calculations that both methods give a similar picture of the variations of the daily averaged brightness temperature at the wavelengths 5.6 mm and 1.35 cm during the stationary phase of the experiment ATLANTEX-90, though individual differences between the results may account to several Kelvin degrees at the wavelength 5.6 mm and of 15−20 K at the wavelength 1.35 cm.

2.2.3 Results of Computations of the SOA Brightness Temperatures and Their Comparison with Heat Fluxes (Experiment ATLANTEX-90)

The response of the SOA natural MCW radiation to the variability of heat fluxes at the ocean-atmosphere interface was the most distinct in April 8–13, 1990, when the strong cyclone was ranged.

Over this period, the variations of the total (sensible + latent) heat fluxes were more than 800 W m⁻² for the Victor Bugaev, 500 W m⁻² for the Musson, and about 400 W m⁻² for the Volna (Gulev et al. 1994). Among the spectral ranges used to calculate the SOA brightness temperature (5.4, 5.6, 5.9 mm, 0.8, 1.0, 1.35, 1.6, 3.2, and 5.0 cm), the temperature brightness contrasts over this time interval was found to be the greatest in the wavelength range 0.59−1.60 cm, which corresponds to the resonant effect of the atmospheric oxygen and water vapor on the water surface up-going radiation (Fig. 2.5).

Fig. 2.5

Spectral dependence of the SOA brightness temperature contrast ΔT ^b in the wavelength range 5 mm-5 cm during the passage of a cyclone (April 8–13) through the places of location of the RV/s V. Bugaev (1), Musson (2), and Volna (3)

One can observe in this piece of electromagnetic spectrum a close correlation between estimates of variations of the SOA brightness temperature T ^b and near-surface heat fluxes q _he at the satellite, aircraft, and vessel levels of simulated results of outer observations.

This idea is illustrated by Figs. 2.6a, b, c, which compare the values of the q _he, and T ^b_0.59 (the brightness temperature at a wavelength of 5.9 mm) and T ^b_1.35 (the brightness temperature at a wavelength of 1.35 cm) obtained aboard the V: Bugaev, Musson, and Volna.

Fig. 2.6

(a) Comparison of the total heat flux q _he with the simulated SOA brightness temperature estimates T ^b_0.59 and T ^b_1.35 in the places of location of the R/V V. Bugaev during the period April 8–13, 1990 (experiment ATLANTEX-90). Simulation of satellite (1), aircraft (2), and vessel (3) observations Fig. 2.6 (continued) (b) The same as in (a), but for the vessel Musson. Fig. 2.6 (continued) (c) The same as in (a) and (b), but for the vessel Volna

It is seen that, in response to the increase in the fluxes q _he, the SOA microwave radiation diminishes its brightness temperature T ^b and vice versa: as the value of q _he decreases, T ^b grows. Over this period, the brightness temperature variations are, on average, 15−20 K at the wavelength 5.9 mm and 30−40 K at 1.35 cm.

We analyzed more rigorously the phenomena of a time delay of the SOA brightness temperature response in the resonant spectral domains 0.59 and 1.35 cm compared to the variations of surface heat fluxes resting upon the results adjusted above (see Fig. 2.7).

Fig. 2.7

Sensitivity of the SOA brightness temperature at the wavelengths 0.59 and 1.35 cm to heat flux variations (in K W m⁻²)⁻¹days⁻¹ in the areas observed by the R/Vs - V. Bugaev (a), and Volna (b)

The Duamel’s integral equation let us to calculate the function r(t) of the brightness temperature T ^b response (sensitivity) to the total heat flux q _he variations:

$$T^{\rm b}(t) = \cdot \int\limits_0^t q(\tau)\cdot r(t - \tau)\cdot d\tau$$

(2.14)

One can consider (2.14) as a modification of the classic Volterra’s equations of the first kind inherent to the class of equations of the convolution type. We proposed some iterative procedure determining the function r(t) as a linear superposition of the exponential functions:

$$r(t) = \sum\limits_{i=1}^N a_i \exp(-b_it)$$

(2.15)

where coefficients a _i and b _i are calculated from the condition of minimal discrepancy between the SOA brightness temperature values and their approximations, characterized by values of the root-mean square (rms) error.

The calculations show that the value N = 6 in the formula (2.15) is acceptable for this task; a mean value of the rms error in this case does not exceed 5–7%.

The result shown in the Fig. 2.7b for the vessel Volna is especially useful for us due to a fuzziness of variations of the parameters T ^b and q _he (see Fig. 2.6c). This case is distinguished from the cases illustrated in the Figs. 2.6a and b where the fact of the time shift between these parameters is obviously noticeable without any mathematical analysis.

Table 2.3 illustrates results of an analysis of the role of a time delay of the SOA response on the synoptic surface heat fluxes. Here, we presented the data of a regression analysis (the coefficient of correlation R and discrepancy d (rms)) between simulated estimates of the SOA brightness temperatures at the wavelengths 0.59 and 1.35 cm and the heat fluxes data collected from the vessel Musson during the stationary phase of the experiment ATLANTEX-90. Thus, while carrying out comparison of these data, we have to take into account the factor of a time shift between the surface heat fluxes and the SOA brightness temperature variations in the synoptic range of time scales.

Table 2.3 Influence of the time shift Dt between the time samples of the SOA brightness temperature at the wavelengths 0.59 cm (1) and 1.35 cm (2) and heat fluxes on their correlation R and rms d (R/V Musson). The peak of heat flux variations is of 900 W m⁻²

We studied regression relationships in the form of linear correlations between 6-h samples (Fig. 2.8) of the total heat flux q _he at the ocean-atmosphere interface and the brightness temperature of the SOA microwave radiation (the simulation of satellite measurements) at wavelengths of (a) 5.9 mm and (b) 1.35 cm (the temperature was calculated from the oceanographic and aerologic measurements aboard the Volna), and the model estimates of the SOA brightness temperature. It is seen that there is an intimate relation between the synoptic variations of the heat fluxes (recorded by the Volna) and the model estimates of the SOA brightness temperature. For the 6-h samples of the parameters q _he and T ^b in the resonance ranges of molecular oxygen and atmospheric water vapor, the least absolute error of approximating the total heat flux q _he by the brightness temperature T ^b is of 26–28 W m⁻² for a flux variation amplitude of 320 W m⁻².

Fig. 2.8

Six-hour samples of the total heat fluxes q _he, as the linear combinations of the SOA brightness temperatures at the wavelengths 0.59 and 1.35 cm computed from the meteorological and aerologic data obtained during the stationary phase of the experiment ATLANTEX-90 (R/V Volna)

The relative variations of the regression coefficients c ₁ and c ₂ are of 13–15%, with the regression coefficient c ₂ being negative in both cases. This means that the heat flux and the brightness temperature vary in antiphase: an increase in the parameter q _he causes T ^b to decrease and vice versa. It is remarkable that the intensity variations of the SOA natural microwave radiation correlate well with variations of the heat fluxes in this case, though the accuracy of finding the brightness temperature, and especially, the heat fluxes is not very high. The relative error involved in the model brightness temperature values found under the hydrometeorological conditions of the ATLANTEX-90 experiment is estimated as 5–10%, while that of the heat fluxes determined by the bulk-parameterizations (1.11–1.13) given in Chap. 1 may be as great as several tens of percent (Gulev et al. 1994). This factor substantiates the idea of using passive MCW radiometric data as natural characteristics of ocean-atmosphere heat interaction.

2.2.4 On the Mechanism of a Correlation Between the SOA Brightness Temperature and Interfacial Heat and Momentum fluxes

The problem of how the SOA brightness temperature (simulated or satellite-measured), for which an effectively radiating 2- to 5-km-thick stratum is responsible, can be related to the temperature and humidity properties of a much thinner (roughly 10-m-thick) near-water atmospheric layer has been repeatedly discussed by teams at the Institute of Radioengineering and Electronics, Russian Academy of Sciences; the Institute of Space Research, Russian Academy of Sciences; and the Institute of Oceanology, Russian Academy of Sciences.

Here, we will study the importance (priority) of water surface parameters and some parameters of different atmospheric layers, i.e., their effect on the correlation between the heat and humidity exchange characteristics and the MCW radiation of the SOA on the synoptic time scales. To this end, the regression analysis of relationships between variations of simulated brightness temperatures ΔT ^b and total heat fluxes Δq _he was made based on the data accumulated from the R/V Volna at the ATLANTEX-90 experiment stationary phase with the following formulas:

$$\Delta q_{\rm he} = k_1 \ \Delta T_{\rm i1} + k_2 \ \Delta T_{\rm i2}; \ i = 1,\ldots, \ 4,$$

(2.14)

where the indices 1 and 2 are attached to the SOA brightness temperature of natural radiation in certain pieces of the MCW spectrum characterized by the wavelengths λ ₁ and λ ₂; due to the index i we can divide an influence of parameters forming the air-sea heat interaction such as the sea surface temperature T _w (i = 1), the near-surface wind speed V (i = 2) and temperature T _a (i = 3), as well as the total water vapor content Q (i = 4); ΔT _i1 and ΔT _i2 are the brightness temperature variations at these wavelengths caused by variations of these parameters.

Then, we used the ordered elimination method to reveal the contribution of one or another parameter simultaneously to the heat exchange process and the SOA natural radiation in different parts of the MCW range of wavelengths. Table 2.4 lists the errors due to the approximation of the total heat fluxes q _he by the brightness temperatures of the SOA radiation in the wavelength range 0.56–3.2 cm.

Table 2.4 Root-mean-square errors of approximation of the total heat fluxes by the sea brightness temperatures simulated with various radiation models (the generalized model - the column “d,” and the simplified ones - the other columns)

Here, the column d is the discrepancy (rms) between the parameter q _he and the linear combinations of the parameters ΔT _i1 and ΔT _i2, whose values were computed from the formulas of the least-squares method taking into account variations of all the basic parameters of the SOA (T _w, T _a, V, and Q) in the frames of generalized and simplified radiation models.

In the columns d_T _w, d_V, d_T _a, and d_Q, the effects of the ocean surface temperature T _w, the near-surface wind speed V and temperature T _a, and the integral water vapor content Q, respectively, are excluded (neutralized). Table 2.4 shows that an influence of the sea surface temperature is more easy in comparison with the atmospheric parameters T _a and Q (this question was one of actual point in our regular discussions conducted with some leading specialists of the P.P. Shirshov’s Oceanologic Institute Russian Academy of Sciences, in particular, with Prof. Vadim Pelevin and Dr. Sergey Pereslegin).

We analyzed also the relations between synoptic variations of the parameter q _he and the model estimates of variations of the SOA brightness temperature derived as a result of an imitation of satellite and aircraft measurements with the down-looking MCW sensors, as well as the ship measurements with up-looking (1) and down-looking (2) sensors (antennas): these results are presented in Table 2.5. Computations of the SOA brightness temperatures were performed using the radiation model (2.8)-(2.11) for the 6-hourly samples taken from the measurements of the parameters T _w, V, T _a, and Q observed aboard the vessel Volna at the stationary phase of the experiment ATLANTEX-90.

Table 2.5 Correlation between simulated values of the SOA brightness temperature from various levels of observations at the millimeters and centimeters and the parameter q _he controlled from the vessel volna in April 1990

The results given in Tables 2.4 and 2.5 point to the primary role of the parameters T _a and Q in forming relations between the SOA brightness temperatures in the atmospheric resonance lines 1.35 cm and in the regions (5.4–5.9 mm) of the oxygen (O₂) attenuation (radiation) with the near-surface heat fluxes. This analysis also shows that independently from the methods of observations used (satellite, aircraft, or vessel), an influence of the sea surface temperature on the SOA brightness temperature is the passive factor in comparison with an influence of the atmospheric parameters T _a and Q in the synoptic range of time scales.

Figures 2.9a, b, c, given below, illustrate an important role of the air temperature parameter T_1500 measured at the height of 1,500 m (the top of the ABL) and the atmospheric total water vapor content Q as the transient (transmitting) factors forming relations between the SOA brightness temperatures and the near-surface heat fluxes.

Fig. 2.9

(a) Results of comparison the heat fluxes q _he, the atmosphere temperature t_1500 at the top of the ABL, the total water vapor content of the atmosphere Q, and the SOA brightness temperature at the wavelengths 5.9 mm and 1.35 cm at the point of location of the R/V Victor Bugaev during 8–13 April, 1990. Fig. 2.9 (continued) (b) The same as (a), but for the vessel Musson. Fig. 2.9 (continued) (c) The same as (a) and (b), but for the vessel Volna

We estimated the parameters T_1500 and Q from aerological measurements carried out with the R/Vs Victor Bugaev, Musson, and Volna during April 8–13, 1990.

A close correlation between the vertical turbulent flux of momentum q _v and the near-surface wind speed V is observed. Figure 2.10 demonstrates this effect with data of the experiment ATLANTEX-90 derived from the R/V Volna.

Fig. 2.10

Results of comparison of the near-surface wind speed and momentum fluxes observed during the stationary phase of the experiment ATLANTEX-90 with the 1-h time resolution of these parameters

This regularity predetermines a clear direct correlation between the SOA brightness temperature and the momentum fluxes. For example, we revealed a close interrelation between the momentum fluxes at the ocean-atmosphere interface and the model estimates (corresponding to the satellite level of observations) of the SOA brightness temperature in the wavelength range between 3 and 5 cm, which is not affected by the atmosphere, and where the brightness temperature variations are governed mainly by variations of an intensity of a wind stress of the water surface (see Fig. 2.11).

Fig. 2.11

Comparison of the momentum fluxes q _v with simulated ocean-atmosphere brightness temperature at 3.2 cm in the areas where the R/Vs Victor Bugaev, Musson and Volna were resided during April 8–13, 1990

During April 8–13, the correlation coefficient of variations of the brightness temperature T ^b at the wavelength 3.2 cm and the parameter q _v observed from the vessel Victor Bugaev was as high as R = 0.96 and the discrepancy (rms error) between such variations was of d = 0.043 for the values of parameter q _v varying from 0.044 to 0.9 N m⁻² (in Newton per square meter). For the R/V Musson, the corresponding parameters were as R = 0.95 and d = 0.05 in the range of variations of q _v 0.013–0.57 N m⁻². At last, for the vessel Volna, the values of its corresponding parameters were of R = 0.89 and d = 0.06 for q _v varying from 0.014 to 0.42 N m⁻². Hence, we can observe a direct correlation between the SOA natural MCW radiation (its brightness temperatures estimated in the millimeter and centimeter range of wavelengths) and the impulse (momentum) fluxes in the synoptic scales.

2.2.5 Response of the SOA Heat and MCW Radiation Characteristics on the Atmospheric Horizontal Circulation

It follows from illustrations shown at the Figs. 2.5 and 2.6 as well as from an analysis of characteristics of spatial and temporal variability of the atmosphere that the SOA brightness temperature contrasts in the oceanic areas observed where the experiment ATLANTEX-90 was made are strongly dependent on the processes of the horizontal circulation in the near-surface atmosphere, which produce, in particular, intensive advection fluxes of heat and water. We have discovered that this effect exceeds in an order an influence of the factor of vertical turbulent heat and water transfer, which was analyzed and demonstrated in Sect. 2.1 of this chapter. The processing of the aerological data array gained afloat has made it possible to put forward a concept of the large-scale horizontal (advective) heat and water transfer as a factor provoked the vertical turbulent fluxes arising for regulating the heat balance between the ocean and atmosphere. The essence of this idea is that the horizontal heat transfer leads to a periodical sharp heating (cooling) of air in a given oceanic area. This effect (1) intensifies heat fluxes directed from the atmosphere to the ocean (or vice versa) because of a greater difference between the water and air; and (2) increases (or decreases) the integral absorption of electromagnetic fluxes, based on the model of the SOA brightness temperature (2.12). Such a supposition follows from the comparison of synoptic variations of the enthalpy (heat content), kinetic, and potential energy in the ABL, which experience the regular influence of the horizontal heat and energy transfer, with the vertical heat fluxes at the SOA interface and the brightness temperature of the system.

Figure 2.12 compares the values of the ABL enthalpy (computed from the aerologic sounding data for horizons on altitude of 10, 100, 200, 300, 400, 500, 900, and 1,000 m gathered aboard the V. Bugaev and Musson vessels and estimated with the methods stated in Pinus (1982) and Perevedentsev (1984)) with the total heat fluxes excited by the deep cyclone originated during the stationary phase of the experiment ATLANTEX-90 in April 8–13, 1990. Figure 2.13 illustrates relations between the ABL enthalpy J and the SOA brightness temperature variations at the wavelengths 5.9 mm and 1.35 cm over this period.

Fig. 2.12

Total heat fluxes q _he vs. the enthalpy J_1000 of the ABL during the passage of a cyclone (April 8–13, 1990) through the location of the (a) Victor Bugaev and (b) Musson

Fig. 2.13

Results of modeling the response of the SOA brightness temperature at the wavelengths 5.9 mm and 1.35 cm to variations of the ABL enthalpy J_1000 during the passage of a cyclone (April 8–13, 1990) through the places of locations of the R/Vs V.Bugaev and Musson

One can see from Fig. 2.13 that synoptic variations of the enthalpy of the ABL stimulate an appreciable reaction of the SOA brightness temperature in the ranges of effect of atmospheric oxygen (5−6 mm) and water vapor (1.35 cm), which varies from 12 to 45 K, respectively; moreover, the response of the brightness temperature lags behind the enthalpy variation by 18–24 h. This property becomes especially apparent during the periods of a cyclonic activity of the atmosphere, when the ABL temperature and humidity are sharply and strongly varied.

For summarizing this stage of our investigations, one ought to keep in mind the following:

• 1. The data obtained confirm a close correlation between the synoptic variations of the atmospheric temperature and humidity, and an intensity of the ocean-atmosphere heat interaction, which were demonstrated earlier in Laihtman (1976) and Lebedeva 1991), for example.

• 2. Correlation between the SOA brightness temperature and an intensity of the surface vertical turbulent heat fluxes at the mid- and high latitudes of the North Atlantic, if formed, mainly due to the horizontal (advective) large-scale heat and water movements in the ABL; an influence of the vertical heat transfer on the SOA brightness temperature is much more less (in an order) in comparison with the advective factor.

• 3. Based on results of the analysis obtained in the experiment ATLANTEX-90, we concluded that the variations of temperature and humidity characteristics in the ABL caused by a large-scale horizontal heat and water transfer in the atmosphere rule over the vertical turbulent heat and water fluxes at the SOA interface as well as the intensity of natural MCW radiation of the system.

Moreover, to all appearances, the SOA brightness temperature formed in the atmospheric oxygen and water vapor resonance regions can be used not only for determining the near-surface heat fluxes, but also for estimating some characteristics of energy horizontal transfer in the ABL in the range of synoptic time scales.

2.3 Relations Between Monthly Mean Air-Sea Temperature Differences and SOA MCW and IR radiation

2.3.1 Statement of the Problem

The main objective of this study is modeling the seasonal dynamics of monthly mean characteristics of the SOA natural MCW and IR radiation and analyzing their correlations with seasonal dynamics of monthly mean differences between surface (water) temperature of the ocean T _w and the near-surface atmosphere temperature T _a. As is known, the parameter ΔT = T _w − T _a directly determines the vertical turbulent fluxes of sensible and latent heat in the case of large-scale interaction of the ocean and atmosphere, as well as the average multiyear (climatic) values of ΔT in the North Atlantic (except its tropical zones) agree well with the average multiyear values of heat exchange between ocean and atmosphere. In the center of the study is the energy-active zone Gulf Stream, which is characterized by spacious oceanographic, meteorological, and other archives.

The following tasks are in a focus:

• Computing the MCW and IR temperatures of the SOA and their seasonal dynamics: (simulation of MCW and IR passive radiometric measurements from satellites with archival data of oceanographic and hydrometeorological measurements) in the Gulf Stream energy-active zone of the North Atlantic.

• Analysis of influence of the SOA parameters (with emphasizing the parameters T _w and T _a) on the MCW and IR radiation intensity at centimeters, millimeters, and infrareds in this area of the North Atlantic.

• Analysis of steadiness of relations between the MCW and IR radiation intensity in various pieces of spectrum and the parameter ΔT.

• Exposure of spectral pieces at centimeters, millimeters, and infrareds, which provide a top steadiness of the dependence “MCW radiation vs. parameter ΔT” and its interannual (seasonal) dynamics.

In the analysis were used the long-term data of oceanographic and meteorological measurements gathered in the fragment of Gulf Stream EAZO - the 5-degree square centered about the point (vessel station) with coordinates 38^oN, 71^oW - so called point H (HOTEL).

To compute the SOA radiation characteristics and their temporal dynamics at microwaves and infrareds we used the plane-layer model (2.12).

2.3.2 Approximations and Limitations Used

The analysis of the SOA radiation characteristics is made with the assumption that the ocean surface is calm (flat) and the atmosphere is cloudless. The relative frequency of these situations in SOA is around 50% (Shutko 1986). In addition, the results of special study show that the monthly mean values of brightness temperature of the SOA as well as the estimates of monthly mean parameters its system retrieved from satellite sensors (at microwaves) are practically inert to the wind speed, cloudiness, and precipitation intensity.

An intensity of the water surface radiation is computed within a wide range of its temperature variations in accordance with the well-known methods cited in Handbook (1977)) and Basharinov et al. (1974). Numerical estimates of the atmosphere attenuation γ are obtained with an account of the water vapor content (at microwaves and infrareds), molecular oxygen (at microwaves), and aerosol (at infrareds) on the basis of theoretical (Zhevakin and Naumov 1964, 1965) and empirical (Arefjev 1991; Paramonova 1985) relationships.

In accordance with Arefjev (1991)), Paramonova (1985), and Zhevakin and Naumov (1964, 1965), the attenuation of natural emission in the atmosphere in the microwave and infrared ranges of wavelengths is caused mainly by its parameters as the air temperature T _a, humidity ρ, and pressure P as well as their vertical distribution. As the monthly mean parameters T _a, ρ, and P are considered in our study, the model of standard atmosphere (Xrgian 1978) is appropriate:

$$T_{\rm a}(h) = T_{\rm a}(0)\exp[-0.02h];$$

(2.15a)

$$P(h) = P(0) \exp [-0.125h];$$

(2.15b)

$$\rho(h) = {\rm r}(0)\exp[-ah].$$

(2.15c)

Monthly mean values of the parameter a in (2.15c) can be determined from the monthly mean values of near-surface water vapor pressure e(0) and integral water vapor content $Q = \int\limits_0^H \; \rho(h)\; dhQ = \int\limits_0^H \; \rho(h)$ in the atmosphere cited in Zhevakin and Naumov (1964) with an account of the next relationship between e(0) (in mb) and ρ(0) (in kg m⁻³):

$$\rho(0) = 0.22 \; e(0)/T_{\rm a}(0).$$

(2.16)

It follows from (2.15c) and (2.16):

$$a = 0.22\; e(0) / Q \; T_{\rm a} (0), \; {\rm km}^{-1}.$$

(2.17)

The near-surface atmospheric pressure is taken as equal to its standard value P(0) = 1,013 mbar for all seasons, because the seasonal variations of P(0) are of 10–15 hPa for the main active zones of the North Atlantic including its Gulf Stream zone (Handbook 1979). These variations are the cause of small variations of the line absorption of natural electromagnetic radiation, which does not exceed 0.5–0.7% of their averaged per year (climatic) absorption at the wavelength 1.35 cm and 1–1.5% in the IR band 8–12 mcm, respectively.

Let us note that variations of the near-surface air humidity yield the effect of tens of percents in seasonal variations of absorption at microwaves and infrareds.

The monthly mean parameters T _w, T _a(0), e(0), a, Q and ρ(0) shown in Table 2.6 are used as the initial data for calculations of natural MCW and IR radiation in the Gulf Steam active zone for various seasons.

Table 2.6 Monthly mean (climatic) temperature and humidity characteristics in the gulf stream active zone of the North Atlantic

The data presented in Table 2.6 help us compute a vertical distribution of attenuation γ(h) and intensity of radiation I _a(h). The resulting values of brightness and radiation temperature are determined by integration of γ(h) and I _a(h) from h = 0 meters to H = 10,000 m.

2.3.3 Relations Between Natural Radiation and SOA Characteristics

We computed the monthly mean values of brightness temperature at wavelengths 3 mm-8.5 cm and radiation temperature at the window 8.5–14 mcm corresponding to monthly mean values of parameters T _w, T _a(0), a, ρ(0), and Q presented in Table 2.6. It follows from calculations that the SOA natural IR- and MCW radiation is most sensible to seasonal variations of the near-surface atmospheric temperature and humidity variations of the SOA, which are closely related to the SOA natural radiation intensity in the spectral interval 9–10 mcm, at the vicinity of the 5 mm - line of resonant absorption by molecular oxygen, and in the 1.35-line of resonant absorption by a water vapor as well as in nonresonant spectral interval 3–8 cm (see Fig. 2.14 illustrating these features at the microwaves).

Fig. 2.14

Seasonal dynamics of monthly mean values of the brightness temperature in the Gulf Stream active zone (a) and the relative contribution of the parameters T _w, T _a(0), and Q in the T ^b variations (b)

This figure shows also the results of the linear regression analysis between the monthly mean values of the SOA brightness temperatures and parameters T _w, T _a(0), and Q in a form of diagrams illustrating a relative contribution of variations of these parameters in variations of the parameter T ^b at the wavelengths 5.7 mm, 1.35 cm, and 5 cm during the winter-summer period.

Let us note that the parameter Q is a more reliable factor governing the brightness temperature at the wavelength 1.35 cm in comparison with the parameter ρ(0), as the parameter T ^b depends not only on the near-surface air humidity, but also on its vertical distribution. That is why the integral water vapor content Q appears in Fig. 2.14 along with parameters T _w and T _a(0). The results of a regression analysis clarify some important peculiarities of relations between MCW and IR radiation and the SOA parameters. For example, seasonal variations of an intensity of natural radiation in spectral intervals 10 mcm and 5 cm are well-correlated first of all with seasonal variations of the ocean surface temperature T _w. Parameter T _a shows its worth at the wavelengths 5.7 mm, and the parameter Q - in the line 1.35 cm of water vapor absorption; at these wavelengths, the values of T ^b and T ^r are increasing linearly with increasing parameters T _w, T _a, and Q. The coefficient of regression ΔT ^b/ΔT _w for the dependence “brightness temperature vs. water surface temperature” is about 0.4–0.45 K ^oC⁻¹ at the wavelength 5 cm; the coefficient of regression ΔT ^b/ΔQ for the dependence “brightness temperature vs. integral vapor content of the atmosphere” at the wavelength 1.35 cm is varied from 14.4 K g^-1 cm⁻² between May and August to 17.3 K g^-1cm⁻² between February and May. These results are in agreement with their well-known estimates obtained on the more short periods (hours, weeks) (Basharinov et al. 1974; Shutko 1986).

2.3.4 Correlation Between Monthly Mean Differences of the Ocean Surface and Atmosphere Near-Surface Temperatures and the SOA Natural Radiation

The fact that natural radiation of the SOA brings an information on the ocean surface temperature and the near-surface air temperature in appropriate spectral intervals suggests the idea of their usage for the determination of the difference between parameters T _w and T _a, which is the key factor of heat and water exchange in the ocean-atmosphere interface. In fact, the parameter T _w can be determined directly with the data of measurements of brightness temperature at the wavelength 5 cm or radiation temperature at the wavelength 10 mcm; estimates of the parameter T _a can be derived directly from the brightness temperature at the vicinity of the resonance line 5 mm or indirectly from the brightness temperature at the wavelength 1.35 cm (if to take into account a close correlation between parameters T _a and Q in a wide range of time scales shown in Chap. 1).

We examined the possibility of using the SOA intensity radiation at microwaves and infrareds for an analysis of seasonal dynamics of the monthly mean difference ΔT = T _w − T _a by means of studying a steadiness of relationships between this parameter and various pairs of monthly mean values of I(λ ₁), I(λ ₂) for different combinations of λ ₁ and λ ₂ and the parameter ΔT for the Gulf Stream active zone. The initial for such examination values ΔT and estimates of seasonal variations of month mean brightness (radiation) temperatures are computed taking month mean values of parameters T _w, T _a, a, and ρ(0) into account (Table 2.7)

Table 2.7 Seasonal variations of monthly mean values of the parameter Δt and brightness (radiative) temperatures in the active zone Gulf Stream

On the basis of the data shown in Table 2.7, we analyzed the following regression:

$$\Delta_{\rm i}(\Delta T) = k_1\Delta T_{\rm i1} + k_2 \ \Delta T_{\rm i2}; \; i = 1,\ldots, 4,$$

(2.18)

where the indices i ₁, i ₂ applied to brightness (radiation) contrasts mean one or another wavelength, and the index i applied to the parameter ΔT means one or another season of a year; it is supposed that the coefficients k ₁ , k ₂ remain the same invariable of all seasons.

To evaluate an effectiveness of the procedure (2.18) of estimating the seasonal variations of ΔT, the next criteria are used:

• 1. The index k, which displays a steadiness of estimates of Δ _i (ΔT) to errors of the values ΔT _i1, ΔT _i2 determination:

  $$k = (k_1 + k_2)^{1/2};$$

• 2. The discrepancy δT between the left-hand and right-hand and right-hand members of (3.18), that is, between real values of Δ _i (ΔT) and their estimates:

  $$\delta T = [1/4 \ \Sigma \; \Delta_{\rm i} - (k_1 \; \Delta_{\rm i1} + k_2 \; \Delta_{\rm i2})]^{1/2}; \; {\rm i} = 1,\ldots,4.$$

The results of computations of the criteria δT and k for several pairs of λ ₁ and λ ₂ are listed in Table 2.8.

Table 2.8 Values of the criteria k and δT for different cases of combining the wavelengths

As follows from Table 2.8, the parameter δT and, especially, k gets greatly increased if the spectral intervals λ ₁ and λ ₂ duplicate one another. For example, it is true for the case 3, as both wavelengths (10 mcm and 5 cm) bring similar information, mainly on the ocean surface temperature T _w and its seasonal variations.

An increase of the number of spectral intervals from 2 to 3 results in decrease of the value δT approximately in 3 times; at the same time, the coefficient k is increasing in 2-3 times. The minimum values of the criteria k are ensured if only one wavelength is used; however, the value of δT becomes unacceptable in this case. For example, for λ = 10 mcm, δT = 3.1°C and k = 0.16, and for λ = 1.35 cm, δT = 1.4°C and k = 0.067.

The best results (minimum values of k and δT) ensure the pairs of λ ₁ and λ ₂, which include the wavelength 1.35 cm: 10 mcm and 1.35 cm (case 2), 5.7 mm and 1.35 cm (case 4), 1.35 cm and 5 cm (case 6). Here, as typical for modern radiometers values of errors ΔT _i1, ΔT _i2, it is possible to amount the accuracy of the parameter δT estimates to 0.25-0.3°C and, therefore, to derive the reliable estimates of seasonal variations of the monthly mean differences ΔT, which are varied from 0.5 to 3°C in the EAZO Gulf Stream.

And more results of our study show that it is sufficient to use merely a pair of wavelengths to estimate the parameter ΔT and its seasonal variations with a use for oceanologist’s and climatologist’s accuracy, in spite of the fact that the SOA radiation characteristics depend not only on the parameters T _w and T _a, but also on the air humidity. This fact, which is substantial for understanding the capabilities of remote diagnostics of the SOA interface at microwaves and infrareds, can be justified solely by close correlation between monthly mean temperature and humidity characteristics of the atmosphere appearing in this zone and in the middle and high latitudes generally.

2.4 Brightness Temperature as the Characteristic of Seasonal and Interannual Dynamics of the Ocean-Atmosphere Heat Interaction

2.4.1 T _w, T _a - loops as Characteristics of Heat Exchange Between the Ocean and Atmosphere

Here, we state one approach of the utilization of the data of long-term MCW radiometric measurements settled on (described in Lappo et al. (1990)) the method of determination of integral (averaged per year) sensible and latent fluxes at the SOA interface, which is prevailing in climatic studies. The method is based on the fact discovered by authors that a magnitude of integral heat flux depends not only on values of monthly mean water surface and air near-surface temperatures, but on forestalling (lag) one of these with respect to another during a year cycle. We ought to keep in mind the fact that parameters T _w and T _a are adapting one to another over a 1-year and more long periods; their average values during these periods are practically equal. In the seasonal time scales, when intending to estimate an intensity of the ocean-atmosphere heat exchange and the character of this process in various situations (either a heat influx is directed from the ocean to atmosphere or from the atmosphere to ocean), we certainly require to take into account the degree of match (dismatch) of these parameters (Lappo et al. 1990). The interannual variations of monthly mean parameters T _w and T _a can be visually presented in the form of specific trajectories - (T _w, T _a) loops in the two-dimensional system of coordinates (see Fig. 2.15). Namely, an availability of the time shift between the evolutions of the parameters T _w and T _a predetermines the folded kind of their visual presentation.

Fig. 2.15

Annual evolutions of monthly mean parameters T _w and T _a (a, b) and their phase trajectories (c, d) the figures denotes the months of year

It was shown that such geometric characteristics as the loop squares and their orientations, the degree of distinctions of their forms from the rectangular ones, etc. can be served as the quantitative characteristics of intensity of heat processes in the SOA interface.

Taking into account a close correlation between the SOA own (oceanolographic, meteorological, and aerologic characteristics) and its MCW and IR radiation characteristics, we can expect that this method is effective in the case when we will use in place of parameters T _w and T _a suitable values of brightness (radiation) temperatures of the SOA for estimating an intensity of heat interchanges between the ocean and atmosphere in different areas of the World ocean and estimate the annual heat fluxes and their intraannual variability.

2.4.2 Ways to Use the Brightness Temperature Loops for Estimation of Annual Heat Fluxes

So, due to a sensitivity of the SOA natural MCW and IR radiation to variations of the oceanic surface and atmospheric near-surface atmospheric temperature, we can construct some analog of the processes existent in the system interface of heat processes in the SOA interface, that is, to build the radiation images of the annual T _w, T _a - cycles using as initial data, for example, the brightness temperature in the spectral interval 3-8 cm, where the highest possible values of sensitivity of the parameter T ^b to variations of the parameter T _w is observed, and the brightness temperature at the wavelength 1.35 cm, which is a considerable source of information on the atmospheric temperature and humidity characteristics.

In comparison with traditional methods of estimating the annual heat fluxes based on the separated determination of the parameters T _w, T _a as the input values used in the bulk-formulas, the peculiarity of this approach consists in a more high stability of the estimates sought under effect of accidental errors. In this case, the final estimates of heat fluxes is based not only on the selected (monthly mean) samples, but assimilates their seasonal dynamics as a whole, that is, the possibility of accumulation of these data is used. If the data of measurements of the SOA brightness temperature are compared to the values of heat fluxes gathered a few times in a year in reference zones of the World ocean, we can successfully estimate the annual heat fluxes and their intraannual variability.

We studied the possibilities of MCW radiometric methods of determination of the annual sensible heat fluxes by way of comparing the characteristics of the brightness temperature annual loops computed with the climatic values of the SST, the atmospheric near-surface, and integral humidity in the Norwegian, Newfoundland, and Gulf Stream active zones of the North Atlantic taken from Handbook (1977)) and Tuller (1968)) (see Fig. 2.16 with the Newfoundland and Gulf Stream EAZOs taken as the examples).

Fig. 2.16

Seasonal evolutions of the SOA monthly mean brightness temperatures at the wavelengths 1.35 and 3.4 cm in the Newfoundland and Gulf Stream active zones of the North Atlantic: figures - the months of the year cycle, counted from the January

The calculations were made with the radiation model (2.8) for the wavelengths 1.35 and 3.4 cm, which are traditionally used in meteorological and oceanographic satellites; it is seen from these results that the ratio between the loop squares for these EAZOs is of 1: 1.25: 2.33. The results of analysis of climatic (archival) data show:

• 1. The ratio between annual fluxes of sensible heat in the Newfoundland and Norwegian active zones is equal to 1.08 (estimations of the State Oceanographic Institute - SOI), to 1.16 (the Main Geophysical Observatory), and to 1.41 (the Institute of the Water Problems - IWP).

• 2. The ratio between annual fluxes of sensible heat between Gulf Stream and Norwegian active zones is varied from 1.24 (SOI) to 1.59 (IWP).

Excessive values of the annual sensible heat flux (a square of the T  ^b_1.35-T ^b_3.4 loop) in the Gulf Stream EAZO can be explained by the specific of this oceanic area, namely by dominating the component of a latent heat in comparison with a sensible heat as a result of intensive evaporations from the water surface.

Let us note that the estimates of annual heat fluxes made by oceanologists strongly differ from one to another versions (see Table 2.9); it gives rise to some problems in validation of results of the MCW radiometric sensing the heat processes in the SOA interface.

Table 2.9 Estimates of the annual heat fluxes in active zones of the North Atlantic

2.5 Use of Satellite MCW Radiometric Methods to Determine the Role of Energy-Active Zones in the North Atlantic in Forming the Weather Conditions in the ETR

2.5.1 Initial Point

The concept of energy-active zones of the oceans (EAZOs) due to academician Marchuk (1979, 1989) and the problems of modeling short-period climatic changes and of early estimations of weather anomalies are currently occupying many researches. For example, Strokina et al. (1983) identified a significant link between Spring/Summer temperature and precipitation in the main agricultural regions of the Russia and changes in the water heat content (enthalpy) in a number of EAZOs of the North Atlantic over the previous winter and winter-spring periods. In Andrianova (1986)), based on joint analysis of a series of sea surface temperature (SST) and the near-surface air temperature at individual points of the European territories of Russia (ETR), it was shown that the SST anomalies in the regions of Gulf Stream and Newfoundland are manifest in the form of large-scale changes in the air temperature over the ETR after 2-3 months. The research in Vazhnik and Chistyakova (1989) confirms the existence of active areas in the North Atlantic and shows that it is possible theoretically to forecast anomalies of the winter (January) air temperature over the Western Part of ETR 2 months beforehand. The important role of EAZO in relation to the development of weather trends and short-period variations of the climate is also confirmed by the results of research expeditions carried out within the framework of the RAZREZY program (Marchuk, 1989). Remote, and in particular, satellites methods of studying the physical processes in the Earth’s weather (climatic) system have a special value (Dymnikov et al. 1984; Becker and Seguin 1985; Malkevich, 1986; Kozoderov 1989). Significant experience in the use of national and international satellite facilities has been recognized when applying it to the following:

• Determination of meteorological parameters of the atmosphere

• Retrieval of the ocean surface temperature

• Monitoring of the state of the oceanic surface using the MCW and IR passive radiometric methods

• Analysis of synoptic and mesoscale properties of hydrophysical fields in the ocean suing radar and high-resolution optical and IR scanners

• Estimation of the radiation balance of the SOA in the IR band

Numerous results have confirmed also the effectiveness of using satellite passive radiometric means to determine some climatic-mean characteristics of the system “land covers-atmosphere” from space at microwaves.

2.5.2 Our Approach

To analyze the effect of the EAZO on the weather conditions over the adjacent continents to these areas, we associated the latter with parameters such as the air temperature, the form and the quantity of clouds and the soil moisture content, or with the deviations of these from the monthly mean norms (Strokina 1983; Andrianova 1986; Vazhnik and Chistyakova 1989; Nikolaev 1981). As a generalized parameter characterizing the balance of heat and humidity, we will use the so-called radiation index of dryness R = Pinc/Pevap, which is the ratio of the heat incident on a given area of the earth surface (Pinc) to the amount of heat required to evaporate the precipitation falling in this area over a specific period (Pevap) introduced long ago in Grigor`ev and Budyko (1956). As the theoretical and experimental results show, the MCW and IR radiometric methods can provide us the reliable information on the soil humidity, the temperatures of the atmosphere, and of the land surface and enable us to reliably recognize the precipitation zones.

It was the especially important observation made in Reutov and Shutko (1987) and Reutov (1989) that an intensity of natural MCW radiation of the land surface for specific scales of spatial and temporal averaging can serve as a direct (natural) measure of the parameter R. The physical uniformity of this parameter and the enthalpy of the oceanic upper layer Q _Σ is the reason to carry out an analysis of these characteristics as having a similar heat and energy nature and depending on the processes of heat transfer between the underlying surface and atmosphere. This fact means that the choice of the value of radiation index of dryness R as the parameter describing the reaction of atmospheric processes over continents to the effects of EAZOs is promising, in particular, in studying the influence of the North Atlantic EAZO on the weather conditions of the ETR.

We compared the variations (from month to month) of the average multiyear values of the parameter R for the ETR and the intensity of the heat exchange at the points “M” (Norwegian EAZO) and “E” (Gulf Stream EAZO) in the North Atlantic (Grankov and Shutko 1992, 1997). In this comparison we considered both components of the heat exchange between the ocean and the atmosphere, namely, the vertical turbulent fluxes of sensible heat and the so-called heat loss (latent heat) due to evaporation (which is significant for the point “E”); the necessary data are taken from Nikolaev (1981)). The estimates of the radiation index (in arbitrary units) were obtained by calculating the relationship between the amount of heat in the air and the loss of heat due to evaporation (thawing) of the precipitation, taking into account data about the monthly mean air temperature and the precipitation intensity given in Handbook (1964). The mean values of this index for the ETR and some other regions were determined from partial values for the towns Murmansk, Leningrad (St. Petersburg), Kiev, Kirov (Vyatka), Sverdlovsk (Ekaterinburg), and Moscow. The results obtained for the point “E” shown at Fig. 2.17 confirm that the variations of monthly mean values of the parameter R in these territories with a delay of 2-3 months are correlated with changes in the monthly mean heat of a heat content of the oceanic upper layer exchanges in the given area of the North Atlantic. There is a less strict correlation between the value ΔQ _Σ and the variations of the air temperature ΔT _a, which only reflects the component of the radiation index of dryness associated with transformations of the flux of sensible heat in the atmosphere and does not take into account the latent heat associated with precipitation. At the same time, the results of the atmospheric circulation and their comparative analysis show that it is possible to use the difference between the monthly values of the oceanic surface and the near-surface air temperatures as equivalent to the intensity of the heat exchange processes at the point “E” in the North Atlantic in studies of their effects on variations of the weather characteristics over the ETR (Fig. 2.18).

Fig. 2.17

Comparison of the variations of monthly mean values of the oceanic heat content in the upper oceanic layer at the point “E” ΔQ _Σ and the radiation index of dryness ΔR (in relative units) for conditions: (a) variations of ΔR synchronous with that of ΔQ _Σ; (b) ΔR is 1 month behind ΔQ _Σ; (c) 2 months behind (1) and 3 months behind (2); and (d) ΔR is 1 month ahead of ΔQ _Σ

Fig. 2.18

Comparison of the variations of monthly mean values of: (a) an intensity of heat content in the oceanic upper layer ΔQ _Σ at the point “E” (excluding the winter months) and the averaged over the ETR air temperature ΔT _a; and (b) the difference between the oceanic surface and the atmospheric near-surface temperatures ΔT and radiation index of dryness ΔR (in relative units) for conditions that the weather changes over the ETR are (1) 2 months and (2) 3 months later than the ΔQ_Σ variations

We observed also the influence of the heat properties of the ocean at the point “M” of the North Atlantic on the radiation index of dryness of the ETR; in this case the time delay between the parameters ΔQ _Σ and ΔR is minimal due to their geographical closeness to the ETR. Thus, we can test a separate idea of influence of the energy active zones in the oceans on the weather characteristics of the adjacent continents for various systems such as the “Gulf Stream outflow in the Norwegian sea/the North Europe territories,” the “Kuroshio current source/the East Asia territories,” etc. It is hard to propose that these phenomena might be useful as the long-term predictors of weather changes in these territories, but we assume their usefulness when analyzing the sources of their current (synoptic and seasonal) developments in these systems.

So it seems to be perspective the using of satellite MCW and IR means and methods in studies of the influence of heat processes in the North Atlantic EAZOs on the radiation index of dryness at the territory of ETR as a whole as well as at some of its adjoining points as the Ekaterinburg (trans-Ural area), Kiev (Ukraine). Let us note that both processes are accessible for the MCW radiometric measurements in the millimeter and centimeter range of wavelengths (related to the parameter ΔQ _Σ) and at the decimeter range of wavelengths (related to the parameter ΔR).

This conception can be entirely realized using various satellite systems with moderate spatial resolution comparable with the sizes of EAZOs (of 300–500 km) and considerable time averaging during of 30-40 days.

2.6 Conclusion

An influence of the oceanic water surface temperature T _w on the SOA brightness temperature is the passive factor in comparison with the near-surface air temperature and integral water vapor content of the atmosphere observed in the experiments NEWFOUEX-88 and ATLANTEX-90 in the range of synoptic time scales. This fact possibly is not evident for oceanologists and climatologists in their traditional understanding of the role of using the remote sensing methods, when only the partial parameters of the SOA interface are used in retrieving the heat fluxes in the ocean-atmosphere interface with the well-known procedures such as the bulk-formulas. Such result can be justified by an intensive variability of the atmospheric parameters T _a, e, and Q, as well as their close correlation determined by the processes of the horizontal air movements in the near-surface and the boundary layers masses typical for middle and high latitudes. This effect excites the brightness contrasts at the synoptic time scales exceeding in ten times the contrasts produced by variations of the parameter T _w because the influence of the vertical heat transfer on the MCW radiation characteristics is weaker in comparison with the effect of the horizontal heat transfer on the atmosphere.

The significant and unique effect observed in these tasks is a high sensitivity of the SOA brightness temperature at the wavelength 1.35 cm to variations of the atmospheric parameters determining the processes of heat transfer through the ocean-atmosphere boundary.