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Other model :

• Elvira model : model 4 with river >2nd order
  

Log10(Wet width + 1) = 0.22734+ 0.20045 (log10 catchment area) + 0.25939 (log 10 Shreve index)

• Thornton model : W = 4.98 CA0.47
  

Models tested:
Linear regression

• Model 1 : width ~ a*catchment_area + b
• Model 2 : log(width) ~ a*log(up_area)+ b
• Model 3 : log(width) ~ a*log(up_area) + uga + b
• Model 4 : log(width) ~ a*log(up_area) + b*log(shreve index) + c
• Model 5 : log(width) ~ a*log(up_area) + b*log(shreve index) + uga + c

Non linear regression with library(nlme)

• Model 1: width~alpha*up_area^beta
• Model 2 : width~gamma*shreve^{lambda (à tester : width~gamma*strahler}lambda

• Data extraction :
  • year > 1987 (RHP)
  • Period : april-october
  • complete sampling method
  • shreve >1

Model Validation for linear regression

• Residuals versus fitted values to verify homogeneity
• QQ-plot or histogrqam of the residuals for normality
• Residuals versus each explanatory variable to check independence

Up cathcment area ~stream order

Up catchment area ~ shreve	Up catchment area ~ strahler

Width ~stream order

River width ~ shreve	River width ~ strahler