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--- en:manuel_reference:methode_micro:verif_habby [2021/11/29 15:20] – ylecoarer
+++ en:manuel_reference:methode_micro:verif_habby [2021/12/02 10:40] – ylecoarer
@@ Line 11: / Line 11: @@
 For a given variable, and for discrete values of the latter, the biological model provides suitability index SI given values between 0 and 1, qualifying the 'preference' of the fish, the suitability curve is thus constructed.
-Equation (1) allows the calculation of the habitat suitability index $\mathit{HSI_i}$ in a mesh of index i and area Ai of a hydraulic model, from the mean values of the variables (H,V,S) of this mesh noted $\mathit{H_i,V_i,S_i}$.
+Equation (1) is used to calculate the habitat suitability index $\mathit{HSI_i}$ according to the user options, in a mesh of index i and area Ai of a hydraulic model, from the mean values of the variables (H,V,S) of this mesh noted $\mathit{H_i,V_i,S_i}$.
-(1) \[HSI_i=SI_H(H_i)\times SI_V(V_i)\times SI_S(S_i)\]
+(1a) \[HSI_i=SI_H(H_i)\times SI_V(V_i)\times SI_S(S_i)\]
-(2) \[WUA=sum_{i=1}^M A_itimes HSI_i\]
+(1b) \[HSI_i=(SI_H(H_i)\times SI_V(V_i)\times SI_S(S_i))^\frac{1}{3}\]
-(3) \[OSI=frac{WUA}{sum_{i=1}^M A_i}\]
+(1c) \[HSI_i=\frac{SI_H(H_i)+ SI_V(V_i)+ SI_S(S_i)}{3}\]
-(4) \[{SI_{i,S}(S_{i,1},S_{i,2},..S_{i,K})}=\frac{\sum_{k=1}^K S_{i,k}\times SI_S(S_k)}{100} \]
+In case the user decides to use only two variables for example (H,V), these equations are adapted in HABBY and become :
+(1_a2) \[HSI_i=SI_H(H_i)\times SI_V(V_i)\]
+(1_b2) \[HSI_i=(SI_H(H_i)\times SI_V(V_i))^\frac{1}{2}\]
+(1_c2) \[HSI_i=\frac{SI_H(H_i)+ SI_V(V_i)}{2}\]
+The logics (a) product, (b) geometric mean and (c) mean are respected.
+In the case where the biological model is bivariate (H,V) equation (1) is written :
+(1_biv) \[HSI_i=SI_{H,V}(H_i,V_i)\]
 The  weighted useable area WUA of the hydraulic model is obtained from equation (2) and the overall suitability index OSI from equation (3)
+(2) \[WUA=\sum_{i=1}^M A_i\times HSI_i\]
+(3) \[OSI=\frac{WUA}{\sum_{i=1}^M A_i}\]
 Note that in the particular case of a description of the substrate in percentages per $\mathit{S_k}$ classes and a calculation of habitat in % of substrate, the value of $\mathit{SI_S(S_i)}$ in equation (1) must be replaced by the formulation in equation (4). In this equation $\mathit{S_{i,k}}$ represents the % of substrate of class $\mathit{S_k}$ in mesh i, the substrate being described by a number K of particle size classes k ∈ $\mathit{[1,K]_N}$.
+(4) \[{SI_{i,S}(S_{i,1},S_{i,2},..S_{i,K})}=\frac{\sum_{k=1}^K S_{i,k}\times SI_S(S_k)}{100} \]
 Let us now check a HSI calculation in any mesh of a hydraulic model.
@@ Line 50: / Line 69: @@
   * Substrate information S from your original data, in case your substrate is described in percentages of size classes, identify the coarser (Coarser) or dominant (Dominant) substrate that is required for the biological model.
   * In the case of a 2D finite volume hydraulic simulation, identify the mean height and mean velocity, which should be those of your original data.
-      * In the case of a 2D hydraulic simulation in finite elements, or a semi-wet mesh having been cut by HABBY, use the nodes layer and its attribute table to check them by calculating the mean values (H,V) of the 3 nodes defining the chosen mesh.
+      * In the case of a 2D hydraulic simulation in finite element, or a partly emergent mesh having been cut by HABBY, use the nodes layer and its attribute table to check them by calculating the mean values (H,V) of the 3 nodes defining the chosen mesh.
 Check the $\mathit{SI_H(H)}$ , $\mathit{SI_V(V)}$ values by performing linear interpolations with the biological model data.
@@ Line 57: / Line 76: @@
 Finally check the habitat value of the $\mathit{HSI}$ mesh using equation (1).
+You can also check the overall results of the hydraulic simulation from the mesh attribute table and equations (2) and (3).
 Clarification: