Feasibility of Fish Passage at Alameda Creek Diversion Dam

Feasibility of Fish Passage at Alameda Creek Diversion DamModel 17:Model 18:Model 19:Y =α ⎛ X ⎞× ⎜β+ X⎟⎝ ⎠α+β Xδ×Y = ηφ+γ×X=α−β δXY ×( )Model 20: Y = ( α−β× X ) × 1−exp( −φ × X)δγThese models were fitted to the 1994–2004 data using least squares, assuming that the residuals are normallydistributed with mean 0 and standard deviation σ. Table B-1 displays the values of the parameter estimates,the estimated standard deviation of the residuals:N( σ= ˆ ∑ residual N )as well as the coefficient of determination (r²) of the fits for the 20 models.i=1The best of the 20 fitted models was selected using Akaike’s Information Criteria (AIC). AIC was calculatedusing the formula:( ˆ 2)AIC = N × ln σ + 2 × K (Burnham and Anderson, 2002),where K is the number of estimated parameters, and N is the sample size (i.e., N = 3,653).as the square of ˆσ .Table B-2 displays the AIC for the 20 fitted models, together with the AIC differences (i.e.,i2ˆσ was estimatedΔ AICimodel likelihoods (i.e., Λ i ) and the relative model probabilities or Akaike’s weights (i.e., w i ). The modelselected as the best model for the data out of the 20 models corresponds to the model whose fit produced theΔ AIC = AIC − min AIC , while the modelsmallest AIC. The AIC differences were calculated as ( )likelihoods were calculated as:and the Akaike’s weights as:⎛ 1L iα exp ⎜−× ΔAICi⎝ 2i⎞⎟⎠i), thewi= Li20∑i = 1LiThese three additional quantities provide an insight on the relative performance of each fitted model withinthe set of 20 chosen models.ACDD Passage June 2009 Page B-4