A simple approach is assuming a homogeneous plane wave coming from free space which has a certain polarization (parallel or orthogonal) and a certain angle of incidence .For this case the reflected and also transmitted wave (into the water) can rather easily be calculated. Of course there will be refraction and the angle (wrt surface normal of the boundary) of the transmitted wave is different compared to the incident wave and there is also a different polarization state to be expected. Afterwards you may calculate the frequency dependent losses in the water depending on the length of the propagation path . And to refine the result (if more precision is required)over the entire angular spectrum of homogeneous (and possibly also inhomogeneous plane waves) keeping in mind reciprocity (S21=S12).

Javad Bolboli , I agree with Fritz Caspers , you can calculate the interaction of EM waves at a boundary by looking at the various vector components and their angle of incidence. You can kind of think of it like a load impedance. When the wave encounters a material with different attenuation and propagation parameters, it will behave differently. You can calculate the reflection of that boundary if you know the indices of refraction for the medium (http://electron6.phys.utk.edu/optics421/modules/m1/reflection_and_refraction.htm). The transmitted portion would then be something like (1-Reflected).

I'd also recommend looking at a link budget. It allows for all elements of gain and attenuation between receiver and transmitter to be calculated. I've attached some links that may be of assistance to you! Best of luck!

http://www.sis.pitt.edu/prashk/inf1072/Fall16/lec5.pdf

https://www.ihe.kit.edu/img/studium/Wave_Propagation.pdf

-Adam

I agree with other answers in addition to considering the water composition, (which would become extremely precise as you requested above the water surface and another transceiver underwater). The parameters mentioned by Fritz Caspers and Adam Weidling would influence the path loss plus constructive and destructive interference. Please have a look at

https://www.researchgate.net/publication/352846612_Comparison_of_the_Self-Piloting_Constructive_and_Destructive_Interference_in_7_and_23_GHz_Band_Over_the_Seawater_Surface

Path loss can be estimated by Geometricsl Optic solution for microwave trough Refection Coeffient and Penteration Death, formulas are avialable.

From transceiver in air to boundary betwen air and water you can use classical Friis transmission equation. But only if wavelength of transmitted signal is much smaller than distance between transmitter and boundary.

Reflection loss from boundary depends on polarization of wave and angle of incidence. Value of reflection coeficient depends on signal frequency as permittivity of water itself is frequency-dependent.

When signal travels through water then it is ususally strongly attenuated - again attenuation coeficient depends on frequency.

If there is not other objects in the path or nearby then we are talking about one-path model.

Ivo Müürsepp Eanass Al-Shabkhoon Imadeldin Elmutasim Adam Weidling Fritz Caspers

Hello everyone

Thank you for your answers and help. Based on your answers I understood exactly what happens when an EM wave incidence to the water surface.

Also, I find some books and papers explaining the mentioned situation. In addition to your answers in this post, I mention these references here in case some researchers need it

Hattab, G., El-Tarhuni, M., Al-Ali, M., Joudeh, T. and Qaddoumi, N., 2013. An underwater wireless sensor network with a realistic radio frequency path loss model. International journal of distributed sensor networks, 9(3), p.508708.

F. Ulaby, R. Moore, and A. Fung, Microwave Remote Sensing: Radar Remote Sensing and Surface Scattering and Emission Theory, Remote Sensing, Addison-Wesley, Reading,Mass, USA, 1981.

Great , because the difficulty behind reflecting factor is oblique angle and traditionally it is taken for normal incidents.

you may be interested to read my old thesis (1982)[sorry in german] on this kind of subject

https://cds.cern.ch/record/2110245/files/Thesis-1982-Caspers.pdf

Fritz Caspers Eanass Al-Shabkhoon Ivo Müürsepp Imadeldin Elmutasim Adam Weidling

Would you please do me a favaour.

I am looking for this book, it is the reference of many same research papers. Would you please share it with me? Thanks in advance.

J. B. Hasted, “Aqueous Dielectrics,” Chapman and Hall, New York, 1973.

And also thank you Fritz Caspers for sharing the thesis with me.

Solving this problem has become really serious for me. It is a personal project but I am working on it even on Sunday and Saturday. in the first step, I am trying to see the real and imaginary part of Debye's model based on the equations mentioned in these papers:

1- Path Loss Analysis of RF Waves for Underwater Wireless Sensor Networks [Saini-2017]

2- An Underwater Wireless Sensor Network with Realistic Radio Frequency Path Loss Model [Hattab-2013]

But my result is different from their results (using MATLAB). I find some typos and I think the mentioned equations in their papers are not current.

Fritz Caspers Eanass Al-Shabkhoon Ivo Müürsepp Imadeldin Elmutasim Adam Weidling

Hello Everyone,

I hope you are doing well,

I know your time is valuable, so I don't want to waste your time and I want to confess that I did a stupid mistake, and because of that my result was different from the result of the mentioned references in my previous message.

I just did not know that for plotting in MATLAB they used semilogx and loglog.

Have a good day

kind regards

Javad Bolboli glad you got it figure out!

-Adam

Hi Javad Bolboli , I know the book by Hasted on aqaueous dielectrics quite well since 40+ years and at least I had it long time..its a very good book..but even if I found it again on my shelf..what to do.?.perhaps you can get it on loan from some university library..perhaps you have a specific question which we can discuss either privately or in public via research gate.

please also have a look to

https://ieeexplore.ieee.org/abstract/document/9266731

https://scholar.google.com/scholar?cluster=17493322674227653429&hl=en&oi=scholarr

Regards,

Imadeldin Elmutasim Thank you so much

Most welcome and Good luck