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<br />1132
<br />
<br />T, C. GRAND ET AL
<br />
<br />removed from the backwater (Pi,!, unitless) each hour was equal to the proportion of the backwater's total water
<br />volume that flowed into the mainstem during that hour (PI',!, unitless; equal to 0 if mainstemflow was steady or
<br />increased during the hour) multiplied by a calibration parameter, fe (unitless):
<br />
<br />Pi,/ = fe ' Pv,/
<br />
<br />(5)
<br />
<br />Hence, the proportion of the original population of inveltebrates remaining at the end of the hour (p,:!, unitless) was equal to:
<br />
<br />Pr.t = Pr.tmJ ' (1 - Pi,,)
<br />
<br />(6)
<br />
<br />The parameterfe can be thought of as representing the fraction of a backwater's invertebrate biomass that is in the
<br />water column instead of attached to the bottom and, therefore, susceptible to being flushed out of the backwater
<br />when river flow decreases. At our study sites, and during the time period of interest, mainstem flow changes are
<br />usually gradual and result in backwater velocities that are typically too low to dislodge invertebrates attached to the
<br />bottom. Although we used chironomid larvae to represent the entire community of invertebrate prey, pikeminnow
<br />do consume other species of invertebrates, including insects that are feeding in the water column and planktonic
<br />invertebrates, Values of!_ are unknown, but are expected to be relatively low at our study site because most of the
<br />fish food base appears to be benthic invertebrates.
<br />Thus, at the end of each day, the number of invertebrates available for consumption by fish (n,., prey) will be equal to:
<br />
<br />nj = Pr,24 . (~) 'Amin
<br />
<br />(7)
<br />
<br />and the density of invC11ebrates available for consumption by fish (di, prey' m-2) will be equal to:
<br />
<br />n'
<br />di =::d:
<br />A
<br />
<br />(8)
<br />
<br />where Amin (m2) is the daily minimum wetted area of the backwater and A (m2) is the daily mean wetted area, Note
<br />that Equation (7) implies that backwater cells that become dried out at any time during the day do not contribute to the
<br />total daily production of invertebrates in the backwaters, This assumption allowed us to capture the potential effects of
<br />substrate exposure due to within-day flow fluctuations on the availability of invertebrate prey to fish. We believe this is
<br />a conservative assumption, and underestimates the actual production of invertebrates in temporarily exposed cells.
<br />
<br />Backwater temperature model calibration
<br />
<br />Due to the importance of water temperature to both invertebrate production (see above) and fish bioenergetics
<br />(Elliott, 1982; Hanson et aI., 1997), we conducted a calibration and sensitivity analysis of the backwater
<br />temperature model prior to its inclusion in the full model. Our primary goals in calibrating the water temperature
<br />model were to (1) find satisfactory values for the two calibration parameters Ie and We, (2) evaluate the uncertainty
<br />in temperature calculations and (3) determine the temperature model's sensitivity to these parameters,
<br />Two of the six modelled backwaters were selected for use in calibrating the temperat.ure model; backwater 5 (a
<br />small, relatively shallow backwater) and backwater 6 (a large, relatively deep backwater; see Figure 2) were chosen
<br />because these backwaters had the longest uninterrupted time series of temperature data and because of the size
<br />range represented. We ran 49 simulations using all pair-wise combinations of seven candidate values for each
<br />calibration parameter (Ie = 0.4,0,5,0.6,0,7,0,8,0,9 and 1.0; We = 0.5,0.75, 1,0, 1.25, 1.5, 1.75 and 2.0). For each
<br />simulation run, we compared the predicted backwater temperatures to those measured between 22 August and 26
<br />October 2003. Comparisons were made by squaring the hourly differences between observed and predicted
<br />temperatures and summing those squares over the entire modelled period, The parameter values resulting in the
<br />smallest sum of squared differences were deemed the 'best fit' values (i,e. the calibration parameter values resulting
<br />in the closest agreement between predicted and observed backwater temperatures), The first 4 days of each
<br />simulation were excluded from the analysis to avoid the effects of initial conditions. We then estimated the water
<br />temperature model's accuracy by comparing the hourly backwater temperatures predicted by the model (using the
<br />best. fit calibration parameter values as described below) with those obtained from the temperature recorders in both
<br />backwaters 5 and 6.
<br />
<br />Copyright t, 2006 John Wiley & Sons, Ltd,
<br />
<br />Ri rer Res, Applic, 22: 1125-1142 (2006)
<br />DOl: IO,lOO2lrra
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