added

Author: arunp77

assets/img/remote-sensing/ssvt_math.png

@@ -191,13 +191,112 @@ <h1>Physical Quantity of Interest: Sea Surface Temperature</h1>
                     </div>
 
 
+                    <div class="box">
+                      <h3>Sea Surface Temperature (SST): A Detailed Mathematical Description</h3>
+                      To understand Sea Surface Temperature (SST) mathematically, we must view it as the thermodynamic result of the energy balance at the interface between the ocean and the atmosphere.
 
 
 
 
 
 
 
+                    </div>
+
+In physical oceanography, SST is not a single value but a vertical profile. We differentiate between the **Skin Temperature** () and the **Bulk Temperature** ().
+
+---
+
+## 1. The Governing Thermodynamic Equation
+
+The rate of change of temperature () in the upper ocean layer (the mixed layer) is governed by the conservation of heat energy. The heat budget equation for a water column of depth  is:
+
+Where:
+
+* : Density of seawater ().
+* : Specific heat capacity of seawater ().
+* : Net surface heat flux.
+* : Heat loss/gain due to horizontal advection ().
+* : Vertical diffusion or entrainment at the base of the mixed layer.
+
+---
+
+## 2. The Net Surface Heat Flux ()
+
+The  is the most critical component for SST. It is the sum of four distinct flux terms:
+
+### A. Shortwave Radiation ()
+
+This is the solar energy absorbed by the ocean. It depends on the solar constant, albedo (), and solar zenith angle ().
+
+
+
+However, not all  stays at the surface; it penetrates the water column according to **Beer’s Law**:
+
+
+
+where  is the attenuation coefficient.
+
+### B. Longwave Radiation ()
+
+The ocean emits infrared radiation as a blackbody (modified by emissivity ). According to the **Stefan-Boltzmann Law**:
+
+
+* : Stefan-Boltzmann constant ().
+* : Absolute sea surface temperature.
+* : Atmospheric temperature.
+
+### C. Latent Heat Flux ()
+
+This is the heat lost due to evaporation. It is mathematically modeled using the **Bulk Aerodynamic Formula**:
+
+
+* : Air density.
+* : Latent heat of vaporization.
+* : Transfer coefficient for moisture.
+* : Wind speed.
+* : Specific humidity gradient between the surface and the air.
+
+### D. Sensible Heat Flux ()
+
+This is the direct heat transfer due to the temperature difference between air and water:
+
+
+* : Stanton number (transfer coefficient for heat).
+
+---
+
+## 3. The "Cool Skin" Phenomenon
+
+Because heat loss () occurs exactly at the surface, while heat gain () is distributed through depth, the very top layer (the "skin") is usually cooler than the water 10 cm below. This is described by the **Fourier Law of Conduction** in the molecular sublayer:
+
+* : Thickness of the molecular sublayer ().
+* : Thermal conductivity of water.
+
+---
+
+## 4. Summary Table of Variables
+
+| Variable | Description | Typical Units |
+| --- | --- | --- |
+|  | Sea Surface Temperature |  or  |
+|  | Latent Heat (Evaporation) |  |
+|  | Sensible Heat (Conduction) |  |
+|  | Surface Wind Speed |  |
+|  | Albedo (Reflectivity) | Dimensionless |
+
+---
+
+## 5. Why this matters for your research
+
+If you are applying to the research centers mentioned earlier (like **IITM** or **INCOIS**), you will likely deal with **Coupled Models**. In these models, the SST is the "boundary condition." If the math in your model incorrectly calculates  (evaporation), your Monsoon predictions will fail.
+
+**Would you like me to explain how these equations are discretized for use in numerical climate models like WRF or ROMS?**
+
+
+
+
+