In the first two groups of runs the modeled domain extends from the confluence with Deadwood Creek to the confluence with Grass Valley Creek (see Figure 2). These runs refer to dynamic equilibrium that the flow and the sediment transport reach downstream of the hydrograph boundary layer [Parker et al., 2008; Wong and Parker, 2006]. The simulations thus lasted for very long times (i.e., from 1800 to 15,000 years). The final results did not depend on the initial conditions because the river was modeled as a sediment feed flume [Parker and Wilcock, 1993]. In the last two sets of runs, however, the modeled domain is divided into two river segments (i.e., Lewiston and Bucktail/Lowden) because the input of sediment from the tributaries cannot be neglected. These runs refer to nonequilibrium conditions; the results are influenced by initial conditions because they describe the short term evolution of the river associated with an imposed change in the upstream boundary conditions.
4.1. Zeroing Runs
 The modeled reach of interest is approximately 11.5 km long. The number of computational nodes is 15, for a computational domain of 21 km. The length of the computational domain was set in order to have the downstream boundary condition far enough downstream of the reach of interest so as not to influence the dynamic equilibrium, and also to allow neglect of the first 4.5 km (three computational nodes) of the domain where the dynamic equilibrium is influenced by the upstream boundary conditions (i.e., the hydrograph boundary layer). In all the zeroing runs, the model was implemented so as to store and access the stratigraphy of the bed deposit.
 Results are reported in Table 1 and in Figures 9 and 10. All the output parameters presented in Table 1 and Figures 9 and 10 refer to the 11.5 km reach of interest, i.e., downstream of the hydrograph boundary layer and well upstream of the downstream boundary condition. In Table 1 the reference Shields number in the load relation , the value of atrans, the sediment feed rate Qfeed, the length of the hydrograph boundary layer Lhbl,, and the bed slope at equilibrium S are reported for each run. The characteristic diameters of the bed surface at equilibrium (i.e., Dsg, Ds50, and Ds90) are also presented in Table 1. Finally, in Figure 9 the criterion to estimate the length of the hydrograph boundary layer is shown, and in Figure 10 the grain size distribution of the new substrate, averaged over the thickness of the new deposit and the length of the modeled domain, is plotted.
Figure 9. Plot illustrating the nature of the hydrograph boundary layer for run Z4. Here “max” refers to the maximum flow of the hydrograph, and “end” refers to the end flow (equal to low flow here) of the hydrograph.
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Figure 10. (a) Grain size fractions and (b) cumulative distributions of the substrate averaged over the thickness of the new deposit and over the length of the modeled domain in the zeroing runs.
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 In all the runs, the surface predicted by the model at mobile bed equilibrium is noticeably coarser than the substrate but not unrealistically so: the predicted values of Dsg and Ds50 are very close to the D80 (77 mm) and the D90 (122 mm) of the substrate, respectively. This indicates that at mobile bed equilibrium most of the finer sediment has been removed from the surface layer, leaving a coarser pavement to regulate the transport of all size ranges [Parker et al., 1982; Parker and Klingeman, 1982].
 The length of the hydrograph boundary layer Lhbl was defined by comparing values of bed slope and geometric mean size Dsg in all the computational nodes at the maximum flow of the last hydrograph of the run and the low flow corresponding to the end of that hydrograph, as shown in Figure 9 for run Z4. It is assumed that the hydrograph boundary layer ends at the computational node where these values do not significantly change with the flow discharge. This means that the actual length of this region may be shorter than that reported in Table 1.
 The calibration of the model parameters can be summarized as follows.
 1. As reported by Gaeuman et al. , the bed load relation of Wilcock and Crowe  reasonably predicts bed load transport rates on the Trinity River, but it requires some calibration to be properly implemented in a numerical model that describes the transport of nonuniform sediment at field scale. In the zeroing runs, this calibration is done in terms of , computed with equation (12) in runs Z1 and Z3 but computed by multiplying the value given by equation (12) by 0.5 in runs Z2 and Z4. The channel slope at mobile bed equilibrium is found to be similar to the present slope of the Trinity River in runs Z2 and Z4. Assuming that after the closure of the dams the released discharge was too low to cause significant changes to the longitudinal profile [Gaeuman, 2008b], the current slope of the Trinity River below Lewiston dam should not be significantly different from the predam slope (i.e., 0.0024 m m−1). Thus the reference Shields number used here to apply the model to the Trinity River was computed by multiplying the value from equation (12) by 0.5 in order to bring the computed bed slope into agreement with the observed value. The consequences of lowering the reference Shields number in the bed load relation on the grain size distributions of the bed surface and of the substrate were also explored. In particular, comparing the results of the runs characterized by the same bed load feed rate, i.e., Z1 and Z2 and Z3 and Z4, it was found that (1) the value of the reference Shields number does not affect the grain size distribution of the substrate (Figure 10) and (2) the grain size distribution of the bed surface becomes coarser as the reference Shields number increases (see the characteristic diameters reported in Table 1).
 2. The value of the parameter atrans that governs the grain size distribution of the sediment transferred to the substrate during bed aggradation, equation (17), is set equal to 0.2 in runs Z1–Z4, according to the results of the laboratory experiments of Toro-Escobar et al. , who found 0.3, and Viparelli et al. , who obtained 0.2. As shown in Figures 10a and 10b, the model reasonably reproduces the grain size distribution of the bed surface, even if it tends to overestimate the fraction of coarse sediment. In runs Z5 and Z6, atrans is set equal to 0.4 and 0.6, respectively, resulting in a computed substrate that is noticeably coarser than that measured in the field (Figures 10a and 10b). This is because the fraction of coarse sediment transferred from the active layer to the substrate increases with increasing atrans. The grain size distribution of the bed surface does not depend on the value of atrans, i.e., the characteristic diameters of the bed surface do not change from runs Z4 to Z5 and Z6 (Table 1). In all subsequent numerical runs presented in this paper, the parameter atrans is set equal to 0.2.
 Channel slopes and characteristic diameters of the bed surface at equilibrium vary with the sediment feed rate. More specifically, the equilibrium slope steepens and the bed surface becomes finer as the feed rate increases (compare runs Z1–Z3 and Z2–Z4). The effects of the sediment feed rate on the grain size distribution of the bed surface are discussed in more detail in section 4.2.
4.2. Test Runs
 The length of the modeled domain, the initial conditions, the input hydrograph, and the grain size distribution of the bed load input rate are the same as those of the zeroing runs.
 The test runs are summarized in Table 2, and the bed load input rates are also reported. In runs T1–T4 and T11–T12, the model is allowed to store and access the stratigraphy of newly deposited sediment (“stored” in the stratigraphy column), while in runs T5–T10, the grain size distribution of the substrate was assumed to be constant in time and space and equal to the distribution represented in Figure 4 (“not stored” in the stratigraphy column). Finally, in runs T1–T10 the channel width is assumed to vary with the flow discharge according to equation (6) and Figure 7, while in the last two runs (T11 and T12) the width of the cross section is constant and equal to its predam reference value (i.e., 84 m).
Table 2. Description of the Test Runs
|Run||Qb (t yr−1)||Stratigraphy||B|
|T5||1,000||not stored||equation (6)|
|T6||16,199||not stored||equation (6)|
|T7||31,850||not stored||equation (6)|
|T8||300,000||not stored||equation (6)|
|T9||3,000,000||not stored||equation (6)|
|T10||30,000,000||not stored||equation (6)|
|T11||16,199||stored||const = 84 m|
|T12||31,850||stored||const = 84 m|
 The motivation for the runs with and without the storage of stratigraphy merits clarification. Parker et al.  present a similar calculation of the morphodynamic response of a gravel bed river to an imposed hydrograph. In their Figure 10.19, pertaining to mobile bed equilibrium, however, it is seen that the geometric mean of the bed load size distribution averaged over the hydrograph at the downstream end of the domain nearly, but not precisely, satisfies the necessary condition that it must be equal to that of the feed. This discrepancy is a result of the absence of a means to store and access stratigraphy in that model. The present model corrects this deficiency of that earlier model.
 In Figure 11, Dsg and the geometric mean diameter of the bed load Dlg at the maximum flow and the low end flow of the last hydrograph at the downstream node of the domain are plotted as functions of the bed load input rate (corresponding to runs T1, Z2, Z4, T2, T3, and T4 in order of increasing feed rate). The geometric mean diameter of the bed load input rate (Dlgfeed) and of the bed load transport rate averaged over the last hydrograph (Dlgav) are also shown in Figure 11. To interpret the results, two limiting cases need to be defined: static armor and unarmored bed [Parker et al., 2008]. Static armor is approached as the feed rate becomes increasingly smaller, with the fine grains essentially washed out from the bed surface so as to leave an immobile, coarse bed surface. When the transport rate becomes increasingly high, on the other hand, the bed surface tends to become unarmored and have the same grain size distribution as the feed (and thus of the substrate if the feed and substrate have the same grain size distribution).
 A comparison illustrating the extent of the hydrograph boundary layer Lhbl, the bed slope, and the grain size distribution of the bed surface averaged over the length of the modeled domain at equilibrium for the zeroing runs Z2 and Z4 and for the test runs T1–T4 is presented in Table 3 and in Figures 11, 12, and 13.
Figure 11. Variation during the last hydrograph of (1) the geometric mean diameter of the bed surface at the last computational node of the domain at the maximum flow (Dsgmax flow) and at the low-flow end of the run (Dsgend flow), (2) the geometric mean diameter of the feed (Dsgfeed), and (3) the geometric mean diameter of the load at the last computational node of the domain averaged over the hydrograph (Dlgaverage), at maximum flow (Dlgmax flow), and at the low flow at the end of the run (Dlgend flow).
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Figure 12. Variation in the downstream direction of channel slope S and geometric mean diameter of the bed surface Dsg at high (max) and low flow (end) during the last hydrograph for runs T3 and T4.
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Figure 13. Grain size distributions of the bed surface averaged over the channel length downstream of the boundary layer in the zeroing runs Z2 and Z4 and in the test runs T1–T4. Also shown is the grain size distribution of the sediment feed.
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Table 3. Length of the Hydrograph Boundary Layer Lhbl, the Bed Slope at Maximum Flow Smax flow and at the end Send flow of the Last Hydrograph, and the Reach-Averaged Geometric Mean Diameter of the Bed Surface at the End of the Last Hydrograph Dsg end flow for Zeroing Runs Z2 and Z4 and for Test Runs T1–T4
|Run||Qb (t yr−1)||Lhbl (m)||Smax flow (m m−1)||Send flow (m m−1)||Dsgend flow (mmol)|
 The results of this second group of numerical runs show that the following results occur as the bed load feed rate increases.
 1. The hydrograph boundary layer becomes longer, and, indeed, in runs T3 and T4 it is longer than the modeled domain (Figure 12). Therefore, bed slopes, geometric mean diameters, and grain size distributions of the surface layer reported in Table 3 and Figures 11 and 12 refer to (1) the reach outside of the boundary layer for runs Z2, Z4, T1, and T2 and (2) the downstream 12 computational nodes for runs T3 and T4 (i.e., the part of the domain where the channel slope does not vary too much during the hydrograph).
 2. The geometric mean diameters of the feed and of the bed load averaged over the last hydrograph are nearly equal for all the runs shown in Figure 11.
 3. Geometric mean diameters of the bed surface at high flow and at the end of the last hydrograph are noticeably different for run T4 only, for which the hydrograph boundary layer is much longer than the modeled domain (Figure 11).
 4. The bed load transport rate at high flow is always coarser than that corresponding to low flow (Figure 11).
 5. As the feed rate increases, unarmored conditions are approached (Figure 11). The bed surface becomes more and more similar to the feed rate (and the substrate), and the difference between the grain size distributions of the bed load at high and low flow decreases. As the feed rate becomes progressively smaller and conditions of static armor are approached, the opposite behavior is observed. That is, progressing in order from run Z4 to Z2 to T1, the predicted grain size distributions of the bed load at high and low flow tend to become similar to the grain size distribution of the feed. This inconsistency was also observed by Parker et al. , and it probably depends on the sediment transport equation implemented in the code, which has not been derived so as to represent such low transport conditions.
 6. The channel becomes steeper and its surface becomes finer (Table 3 and Figures 11 and 13). In particular, as the bed load input rate (equal to the sediment transport rate averaged over the last hydrograph for all the runs) increases, the geometric mean diameter of the bed surface tends to become equal to the geometric mean diameter of the sediment feed rate.
 The results of runs T3 and T4 for the last hydrograph of each run illustrate the changes in channel slope and grain size distribution in the hydrograph boundary layer (Figure 12).
 1. The grain size distribution of the bed surface becomes finer as the water discharge increases, and it then coarsens when the flow decreases and is no longer able to transport the coarser fractions.
 2. The channel slope strongly varies with the water discharge in the first three computational nodes (i.e., 3000 m) and then remains more or less constant over the downstream part of the domain. In particular, in the first three nodes the slope at high flow is milder than the slope at low flow. This is because the sediment is fed at a constant rate; at higher discharges the flow locally erodes part of the bed, but deposition occurs as discharges progressively decrease on the falling limb of the hydrograph.
 Figure 14, which has the same format as Figure 11, shows a comparison between runs with and without the storage of the stratigraphy. The values of Dsg at the last computational node at the end of the runs and the values of Dlg in the same computational node averaged over the last hydrograph are plotted as functions of the sediment feed rate for runs T1–T4, Z2, Z4, and T5–T10. In Figure 14, Dsg-withstrat and Dlgav-withstrat refer to values of Dsg and Dlg computed with the storage of stratigraphy implemented, and Dsg-nostrat and Dlgav-nostrat refer to the corresponding values with no stratigraphic storage implemented. In this latter case, the substrate is always assumed to have the same grain size distribution, regardless of the history of aggradation and degradation. Also shown in Figure 14 is Dlgfeed. Even in the runs with no storage of stratigraphy, the bed surface always becomes progressively finer as the sediment feed rate increases. At mobile bed equilibrium, the parameter Dlgav must be precisely equal to Dlgfeed. Figure 14 demonstrates that this condition is not satisfied in the absence of storage stratigraphy (as in the model of Parker et al. ) but is satisfied in the present model.
Figure 14. Comparison between the geometric mean diameter of the bed surface and of the bed load averaged over the last hydrograph for the runs, as computed with and without storage of the stratigraphy (Dsg_withstrat, Dsg-nostrat, Dlgav_withstrat, and Dlg-nostrat,, respectively).
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 In the last two runs in Table 2, T11 and T12, the channel width is assumed to be constant and equal to its predam bankfull value, and the input parameters are those of runs Z2 and Z4, respectively. In runs T11 and T12 and Z2 and Z4 the length of the boundary layer is practically the same (i.e., 4500 m). The bed slopes are milder in run T11 as compared to run Z2 (with respective values of 0.0022 and 0.0024). The same trend was observed in run T12 as compared to run Z4 (with respective slopes of 0.0023 and 0.0025). The corresponding bed surfaces are finer (with values of 79 versus 81 mm in runs T11 and Z2, respectively, and 75 versus 76 mm in runs T12 and Z4, respectively). These results can be explained considering that in the runs with constant width (T11 and T12) the water discharge and the sediment feed rate per unit channel width at high flow are higher than in the runs with variable width (Z2 and Z4). This results in a milder slope because of the increase in water discharge per unit width and in a finer bed surface for the higher sediment feed rate per unit width associated with high flows when conditions of constant width are imposed.
4.3. Postdam Run
 The modeled stretch of the Trinity River is divided in two segments: the Lewiston segment from the confluence with Deadwood Creek to the confluence with Rush Creek and the Bucktail/Lowden segment from the confluence with Rush Creek to the confluence with Grass Valley Creek. The Lewiston segment is approximately 5 km long, and the length of the modeled domain is equal to 9 km (in order to place the downstream boundary condition sufficiently far downstream so as not to influence the results of the simulations in the reach of interest). The modeled domain is divided in 13 segments bounded by 14 computational nodes. The Bucktail/Lowden segment is 7 km long, and the length of the numerical domain is set equal to 12 km, divided in 13 segments bounded by 14 computational nodes.
 The input hydrograph is reported in Figure 3. The sediment feed rates are 3861 and 5425 t yr−1 for the Lewiston and the Bucktail/Lowden segments, respectively, and their size distributions are plotted in Figure 6b. The downstream boundary condition (i.e., constant bed elevation) is again placed farther downstream so as not to influence the results in the domain of interest.
 For each segment, three numerical runs, PD1, PD2, and PD3, were performed, as summarized in Table 4. Each run actually consists of a pair of runs, i.e., one for the Lewiston segment and one for the Bucktail/Lowden segment. It has been necessary to run more than one numerical simulation for each segment. This is because (1) the predam grain size distribution of the bed surface is unknown and (2) for runs PD1 and PD2, which were of the short duration of 42 years, the results at the end of the computations depend on the initial conditions in that they refer to conditions of nonequilibrium.
Table 4. Description of the Postdam Runs
|Run||Surface Size Distribution||Lewiston Segment||Bucktail/Lowden Segment|
|Qbfeed (t yr−1)||Dlgfeed (mmol)||Duration (years)||Qbfeed (t yr−1)||Dlgfeed (mmol)||Duration (years)|
 Runs PD1 and PD2, although spanning the same period (from 1962 to 2004), differ in the initial grain size distribution of the bed surface. In run PD1, the initial bed has the same grain size distribution as the substrate, while in run PD2 it has the same grain size distribution as that of the bed surface computed at mobile bed equilibrium for run Z4. The values of Ds50 and Ds90 computed at mobile bed equilibrium (i.e., 125 and 223 mm, respectively, in both segments) are greater than the reach-averaged field values but smaller than the maximum recorded values (i.e., 190 and 380 mm). The initial condition for run PD1 is unrealistic because it means that the predam Trinity River did not show any armoring of the bed surface, which corresponds to a feed rate that is 3 or 4 orders of magnitude higher than our estimate (Figure 11). On the other hand, it represents the finest possible grain size distribution of the bed surface.
 The different initial grain size distributions of the bed surface of runs PD1 and PD2 result in opposite behavior for the 42 year simulation of regulated period.
 1. The bed surface becomes coarser during run PD1: at the end of the run, Ds50 and Ds90 are approximately equal to 85 and 202 mm, respectively, for both segments. These values are very close to the reach-averaged field values (i.e., Ds50 = 90 mm and Ds90 = 198 mm). On the other hand, at the end of run PD2, Dsg decreases in the two segments (from 76 to 59 mm in the Lewiston segment and to 55 mm in the Bucktail/Lowden segment). This decrease is specifically associated with an increase in the sand and very fine gravel content in the surface.
 2. The bed slope slightly decreased from 0.0024 m m−1 to approximately 0.0022 m m−1 in both segments during run PD1, while it did not change during run PD2.
 Run PD3 describes the mobile bed equilibrium for the postdam boundary conditions. The results outside the hydrograph boundary layer are independent of the initial conditions. The length of the hydrograph boundary layer was found to be approximately 2000 m for the Lewiston segment and 2500 m for the Bucktail/Lowden segment.
 The bed surface at mobile bed equilibrium for run P3 is finer than for the predam run Z4, as shown in Figure 15, because the fractions of sediment in the coarsest size ranges in the feed rate are smaller than those of the initial substrate. The bed slope at the end of run PD3 is 0.00097 m m−1 for the Lewiston segment and 0.00092 m m−1 for the Bucktail/Lowden segment because of the greatly reduced flow discharge as compared to predam conditions. Note that the duration of time necessary to achieve mobile bed equilibrium, i.e., 66,000 and 96,000 years for the Lewiston and the Bucktail/Lowden segment, respectively, is unrealistically long. The results of the run nevertheless give an idea of the direction in which the channel would evolve were postdam conditions continued indefinitely.
Figure 15. Grain size distributions of the bed surface averaged over the channel length (but outside the hydrograph boundary layer) at the end of run PD3. For the Lewiston segment, Dsg is 30 mm, Ds50 is 50 mm, Ds90 is 127 mm, the fraction of sediment finer than 6 mm is 21%, and the fraction of sand in the bed surface is 12.5%. For the Bucktail/Lowden segment, Dsg is 25 mm, Ds50 is 51 mm, Ds90 is 114 mm, the fraction of sediment finer than 6 mm is 25%, and the fraction of sand in the bed surface is 15.4%.
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 As underlined above, the result of the runs PD1 and PD2 strongly depend on the initial conditions because they refer to a very short time scale, so that channel morphodynamics and sediment transport do not have time to equilibrate (see duration columns in Table 4). Moreover, the input hydrograph has been derived from the flow duration curve based on the discharges measured at the USGS gauging station at Lewiston and thus is not entirely representative of the flow regime in the modeled domain. It does not consider, for example, that in the first decade after the closure of the dams, flow releases were very small (4−8 m3 s−1) and that they changed irregularly in the following years [U.S. Fish and Wildlife Service and Hoopa Valley Tribe, 1999]. Finally, the bed load input rate is assumed to be constant over the hydrograph and the historical gravel augmentations are not properly modeled.
 These limitations notwithstanding, an important result deserves mention. The model predicts an increase in the content of sediment finer than 6 mm in the surface layer in runs PD2 (13%−15% from an initial 6.5%) and also in the fraction of sand in the surface layer (7%−9% from an initial 2.5%). At equilibrium (run PD3) the fraction of sediment in the surface layer finer than 6 mm varies between 21% and 25%, and the corresponding fraction of sand varies between 12% and 16%. These results are in good agreement with the reduction of gravel quality due to the infiltration of fine sediment reported by Graham Matthews and Associates  and also with the visual estimate of an approximate reach-averaged content of sand in the surface layer of 10% based on the mapping of 2006 and 2007.
 To confirm the ability of the model to reproduce the infiltration of fine sediment in the substrate of the Trinity River in the regulated period, the grain size distributions of the topmost layer of the substrate at the end of runs PD2 and PD3 are plotted in Figure 16 along with the grain size distributions of the feed rate and initial substrate. During the 42 years of simulation of the run PD2, the model predicts an increase in sediment finer than 6 mm in the modeled domain from 29% to 36% in the Lewiston segment and to 39% in the Bucktail/Lowden segment. Kondolf  reports numerous research results on the fraction of material finer than 6 mm beyond which less than 50% emergence of salmonids is realized. In Kondolf's Table 1, this fraction is seen to range from 15% to 40%, depending upon the study in question, with an average value of 30%. With this in mind, the predictions of the model of 36% for the Lewiston segment and 39% for the Bucktail/Lowden segment are verging toward values that are too high for a healthy spawning environment.
Figure 16. Comparison between the grain size distributions of the topmost layer of the substrate in runs PD2 and PD3 for the Lewiston and the Bucktail/Lowden segments, the sediment feed rate, and the predam substrate.
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 When the flow and the sediment transport reach equilibrium (runs PD3), the grain size distribution of the substrate is very close to the grain size distribution of the bed load feed rate, and the fraction of sediment finer than 6 mm in the substrate is 68% in the Lewiston segment and 72% in the Bucktail/Lowden segment. These results highlight the tendency of postrun conditions to promote an unhealthy environment for salmonid spawning. The small difference between the grain size distribution of the bed load and the topmost layer of the substrate at the end of run PD3 that is apparent in Figure 16 corresponds to the loss of information due to the averaging process in the vertical direction associated with the procedure to store and access stratigraphy.
4.4. Augmentation Runs
 Four groups of runs were performed to investigate the consequences that the gravel augmentations proposed by Gaeuman [2008b] may have in the upstream part of the regulated Trinity River, i.e., runs AU1–AU4 in Table 5. These augmentations are characterized by two possible feed rates each (i.e., 9091 and 13,636 t yr−1) for the two different grain size distributions represented in Figure 17. The bed load input rates and their grain size distributions have been computed by adding the augmentation values to the postdam bed load input values for the Lewiston and Bucktail/Lowden segments, under the assumption that the gravel associated with augmentation is introduced in the Lewiston segment. The grain size distributions of the bed load input are shown in Figure 17 for the two modeled segments; the bed load input rates are reported in Table 5 along with other input parameters (i.e., augmentation feed rate, type of added gravel, and geometric mean diameter of the bed load input rate). The input hydrograph, reported in Figure 3, has been computed from the mandated ROD flow releases.
Figure 17. Grain size distributions of the augmented gravel (fine and coarse), of the postdam bed load feed rate, of the bed load input rates for the augmentation runs (AU1–AU4), and of the initial bed surface for (a) the Lewiston segment and (b) the Bucktail/Lowden segment.
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Table 5. Description of the Augmentation Runs
|Run||Augmentation Rate (t yr−1)||Augmentation Gravel||Lewiston Segment||Bucktail/Lowden Segment|
|Qbfeed (t yr−1)||Dlgfeed (mmol)||Qbfeed (t yr−1)||Dlgfeed (mmol)|
 The results of the augmentation runs strongly depend on the initial conditions because they describe the changes in the regulated Trinity River for an engineering time scale of 120 years, i.e., much shorter than the geological time scale required for the flow and the sediment transport to reach equilibrium. The initial river bed is the same as that assumed in the postdam runs (i.e., bed slope of 0.0024 m m−1 and substrate with the grain size distribution represented in Figure 4) and thus provides a reasonable approximation of the present conditions of the river. The initial grain size distribution of the bed surface (Figure 17) has been determined using the available field data (Ds50 = 90 mm, Ds90 = 198 mm, and 10% sand).
 The results of the augmentation runs are reported in Table 6 and Figure 18. In Table 6, for each modeled segment the channel slope S, the reach-averaged fraction of sand in the surface layer Fssurf and Ds50 and Ds90 are presented along with Dlgav. In Figure 18 the grain size distributions of the topmost layer of the substrate are compared with the predam substrate.
Figure 18. Grain size distributions of the topmost part of the substrate for the augmentation runs AU1–AU4 and of the postdam (but preaugmentation) substrate for (a) the Lewiston segment and (b) for the Bucktail/Lowden segment.
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Table 6. Results of the Augmentation Runsa
|Run||Lewiston Segment||Bucktail/Lowden Segment|
|S (m/m)||Fssurf||Ds50av (mmol)||Ds90av (mmol)||Dlgav (mmol)||S (m m−1)||Fssurf||Ds50av (mmol)||Ds90av (mmol)||Dlgav (mmol)|
 During the augmentation runs, the following occur.
 1. Noticeable channel bed aggradation (i.e., an increase in bed slope from 0.0023 to 0.0027) is evident for run AU4, for which the coarse gravel is added at the higher rate. In runs AU2 and AU3 the bed profile does not change significantly in the two segments. The aggradation predicted in the Lewiston segment is, to some extent, a numerical artifact related to the quick change of grain size distribution of the bed surface as the fine sediment is rapidly washed out. This results in a rapid increase in roughness height computed with equation (5), causing some bed steepening. As time passes and the flow and the sediment transport tend to reach equilibrium, the bed slope tends to return toward the initial value.
 2. The content of sand in the surface layer decreases, as shown in Table 6, and becomes smaller for the runs characterized by the coarser gravel feed rate. That is, this fraction decreases from an initial value of 10% to 2.2%−3.1% in the Lewiston segment and 3.5%−4.5% in the Bucktail/Lowden segment. The model thus indicates that gravel augmentation will help in removing fine sediment from the bed surface.
 3. The reach-averaged Ds50 becomes finer in all the runs, while the reach-averaged Ds90 becomes significantly finer only when the coarse gravel is added at the higher rate (i.e., run AU4).
 4. The geometric mean diameter of the bed load averaged over the last hydrograph is not too different from the same diameter of the bed load input rate (as can be seen by comparing Tables 5 and 6) in all the runs and in both modeled segments, showing that after 120 years the sediment transport regime may not be too far from a condition of mobile bed equilibrium. Another piece of evidence indicating that the conditions at the end of these runs may be close to equilibrium is the similarity between the grain size distributions of the substrate represented in Figure 18 and the grain size distributions of the feed rate shown in Figure 17.
 Figure 18 indicates that the major difference between the present-day (postdam) grain size distribution of the substrate and those at the end of the augmentation runs is a marked decrease in the content of fine sediment after augmentation. The fraction of sediment finer than 6 mm decreases in the Lewiston reach from an initial value of 29% to 25% and 22% in runs AU1 and AU2, respectively, and to 17% and 16% in runs AU3 and AU4, respectively. All of these postaugmentation values are below the average threshold value of 30% of Kondolf , beyond which less than 50% of salmonids emerge from redds. In the Bucktail/Lowden segment, the fraction of sediment finer than 6 mm does not change by the end of runs AU1 and AU2 but decreases to 25% and 21% for the higher augmentation rates of runs AU3 and AU4, respectively. Again, all these values are below the quoted threshold value of 30%. The median diameter of the substrate varies between 16 and 32 mm, which corresponds to a minimum length of the spawning fish of 200–300 mm [Kondolf, 2000], a value that is smaller than the characteristic length of the present-day salmonid population of the Trinity River [Kondolf et al., 1993].