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Effects of grid spacing on habitat hydraulic complexity metricsThe sensitivity of the habitat hydraulic complexity metrics to Δs was examined by calculating the metrics for Δs = 0.06, 0.12, 0.18, and 0.24 m (for M4, Δs = Δx = Δy). Figure 3 shows the variation of the metrics with grid spacing for scenarios with boulders. A preliminary assessment of no-boulder scenarios (S1-L and S1-H) showed that all the metrics decreased by increasing the grid spacing. However, because the metrics are mostly used in complex rather than non-obstructed and 1-D flows, the plots only include scenarios with boulder placement to highlight the effects of grid spacing on the metrics in complex flows. All the metrics generally decreased as Δs increased. At the low flow rate, by changing the Δs from the smallest to largest, i.e., 0.06 m to 0.024, the mean decreases in the M1, M2, and M4 metrics (averaged over all the scenarios with boulders) were 45.1, 9.9, and 74.7%, respectively. At the high flow rate, these reductions were 34.8, 14.7, and 82.5% for M1, M2, and M4, respectively. Table 2 shows the p-values associated with the changes in the metrics due to increasing Δs from 0.06 to 0.24 m for all scenarios. The table indicates that changes in M1 and M4 were statistically significant while for M2 they were not (p-values  > 0.05 for all scenarios except for S2-H). This result indicated the considerable influence of grid spacing on M1 and M4 metrics in the reaches with boulder placement. Additionally, the differences in the reported average reductions due to changing the flow rate were less than 10%, indicating an insubstantial effect of flow rate on the habitat hydraulic complexity metrics’ sensitivity to the grid spacing. The significant sensitivity of the metrics M1 and M4 to the grid spacing in this study is contrary to the findings of a previous study in which an insignificant correlation was found between the habitat hydraulic complexity metrics and Δs29. This difference can be attributed to different topographic features in the studied reaches. In the previous findings, measurements were mainly taken around the bends and reaches with no significant obstruction29, in which a more uniform flow with smaller velocity gradients is expected. However, in this study, the systematic boulder placement generated more complex flow patterns with noticeable velocity gradients. Therefore, due to the variations of flow velocities in the zone studied, substantially different values for the metrics are anticipated by computing the metrics over different spatial scales.Figure 3Variation of the habitat hydraulic complexity metrics with grid spacing (Δs) for scenarios with boulder placement. (a) kinetic energy gradient metric, M1, (b) normalized kinetic energy gradient metric, M2, (c) modified recirculation metric M4.Full size imageTable 2 p-values associated with changing the grid spacing from 0.06 to 0.24 m.Full size tableStatistical distribution of habitat hydraulic complexity metricsTable 3 lists the mean, minimum, maximum, and standard deviations of the habitat hydraulic complexity metrics (Δs = 0.06 m) for all the scenarios. To complement the results from Table 3 and assess whether the influences of solely changing the boulder concentration or flow rate on the metrics were statistically significant, Table 4 shows p-values associated with changing flow rate from low to high for a given boulder concentration, and Table 5 shows p-values associated with gradually increasing the boulder concentration for a given flow rate.Table 3 The statistical parameters of the habitat hydraulic complexity metrics in the detailed measurement zone.Full size tableTable 4 p-values from a t-test associated with changes in flow rate for a given boulder concentration.Full size tableTable 5 p-values from a t-test associated with changes in boulder concertation for a given flow rate.Full size tableFor metric M1, the mean M1 values for scenarios incorporating boulders showed the same order of magnitude as values from previous studies for reaches with single and multiple boulders27 but they were about one order of magnitude larger than calculated values in the confluence of two rivers11. Using a larger grid spacing in the study in the confluence of two rivers11 can be the reason for this difference. For a scenario at the higher flow rate, the mean M1 was on average (averaged for all the scenarios) 36% greater than its counterpart at the lower flow rate and this change in M1 values was statistically significant with p  More