Update index.md

docs/index.md

@@ -2,20 +2,24 @@
 
 ## Summary
 
-Dean (1991) have proposed the concept of an equilibrium beach profile. Dean (1991) derived the equilibrium beach profile model with the wave energy dissipation similar to other previous works (e.g., Bruun, 1954). The equilibrium beach profile equation is very simple, but has been used by many researchers for coastal engineering.
+Meso- and macro-tidal beaches, which constitute a large proportion of beaches in the world, are characterized by separated beach profiles. Many researchers, including Bruun (1954) and Dean (1991), have proposed the concept of an equilibrium beach profile. However, they considered the wave condition without tidal influence. Therefore, Bernabeu et al. (2003) proposed a two-section equilibrium beach profile model (2S-EBP) based on the concept of the previous studies. This model is useful for predicting the equilibrium beach profile under various conditions.
 
 ## Model formula
 
-Dean (1991) suggested a simple equilibrium beach profile equation based on the wave energy dissipation as follows:
+Bernabeu et al. (2003) proposed the 2S-EBP to predict static beach profile for two separated sections (i.e., surf and shoaling profiles) as follows:
 
 ```text
-h=Ay^(2/3)
-
-h : the water depth
-y : the seaward distance
-A : the Dean parameter
+Surf profile:
+x = (h/A)^(3/2) + B/A^(3/2)h^3   for   0 ≤ x ≤ x_r
+Shoaling profile:
+X = x - x_0 = (h/C)^(3/2) + D/C^(3/2)h^3   for   x_r ≤ x ≤ x_a
+
+h : the water depth from mean sea level
+x : the cross-shore distance from the shoreline
+A,B,C,D : the calibration parameters that depend on the energy dissipation and the reflection process
+x_0 : the cross-shore distance between the beginning of the surf profile and the virtual origin of the shoaling profile over the mean sea level.
 ```
 
 ![Definition sketch of equilibrium beach profile model](_static/images/Imagen1.png)
 
-Fig. Definition sketch of equilibrium beach profile model (Dean, 1991).
+Fig. Definition sketch of equilibrium beach profile model (Bernabeu et al, 2003).