4.4. Evaluation and applicability of the procedure

4.4.1. Evaluation of the procedure

The present analysis with the scaling factor developed and used here was applied, for verification, to the results of several fishway types and studies. Verification data was found in the literature (appendices 2-5). All the data were prepared for analysis in a similar way.

The statistical analysis was carried out using the Student’s paired t-test of the differences between the discharge measured and the discharge estimated by the rating curve. The test is used to check whether a rating curve, on the average, gives significant overestimates or underestimates compared with the discharge measurements on which the curve is based (Tilrem 1997). The basic assumptions underlying this test are that the percentage differences between the measured values and the values estimated by the curve are independent of the magnitude of the discharge and normally distributed about a mean value of zero. The mean deviation, p_m, in per cent, is tested against its standard error to see whether it differs significantly from zero. The analysis was carried out for all the data and for several subdata on different fishway types and studies.

According to the statistical analysis, the mean percentage deviation for all fishway types is very close to zero denoting that, on the average, this procedure gives good results (Table 1). The standard percentage deviation, on the other hand, is large denoting that the calculated discharge may differ to a large extent from the measured value.

Possible reasons for the large standard deviation may be that measurements are taken in scale models. For low discharges, when the depth of flow is very small, in addition to gravity, viscosity also begins to take effect. In addition, with high discharges the water surface fluctuates, making it difficult to define the water depth at any point of the fishway.

To find equations for other fishway types, the present analysis with the scaling factor developed and used here was applied to the results of several fishway types and studies (appendices 2-5). Equations were obtained from the regression lines (Table 2, Fig. 18).

Table 2. The comparison of the scaling factors and dimensionless equations created according to them.

Fishway model Reference	N	The used scaling factor	R2	The used scaling factor	R2
Pool-and-weir fishway Appendix 2	181		0.62		0.68
Pool-and-weir Section 3.2	115		0.79		0.81
Pool-and-weir with V-crest Section 3.2	172		0.94		0.93
Denil fishway Appendix 3	27		0.89		0.75
Denil fishway Appendix 1/ Heikkinen	121		0.93		0.93
Denil fishway Appendix 1/ Isohaara (unpublished)	29		0.99		0.87
Vertical slot fishway Appendix 1	15		0.92		0.91
Vertical slot fishway Appendix 4	201		0.84		0.69

Comparing figures 17 and 18, it is obvious that results of these other studies do not as readily fit the curve, rather the scatter is higher. One, and maybe the most important, factor could lie on the different measuring methods for water depths or heads. This is especially true for studies on pool-and-weir fishways (Appendix 2).

An attempt was made to compare the scaling factor and the procedure developed in this study with the previously developed scaling factor, and to apply the same procedure. All the data was used for evaluation. Discharges were transformed for dimensionless discharges using equation 5. As a length scale, the width of the free opening b_o was used. Dimensionless discharges Q_* were plotted against relative water depths y_o/b_o (Fig. 19). In the analysis, a power regression was applied for all the data. The dimensionless discharge equations for both of the scaling factors and for each data are given in a summary table (Table 2). It can be seen that the correlation values for the new procedure are higher for almost all fishway types than those calculated with the previously developed scaling factor. The only exception is the pool-and-weir fishway, where the flow depths have been measured in a way that is not necessarily suitable for the present analysis. In addition, it can be seen that in both the procedures the slope of the regression line for vertical slot fishway differs from the slopes of the other lines.

According to the Student’s paired t-test, the dimensionless discharge equation calculated using the scaling factor given in equation 5 does not give good results for all the data (Table 3). The mean percentage deviation p_m is over 7 and the standard percentage deviation of p_m is over 70%. In addition, the value of the test statistic t is too high. For the author’s data, the results are better, but the standard percentage deviation of p_m is very high, 77%.

This model and procedure which include the new scaling factor for predicting fishway flows, describes the physical situation in different types of fishways well. Flow depths can already be compared by using dimensionless values. It should be noted already here, that the general equation (22) should not be used in analyzing flows in pool-and-weir fishways. A more fitting result would be obtained by using dimensionless equations for each of the fishway types.

4.4.2. Applicability to the flows in pool-and-weir fishways

Pool-and-weir fishways are very sensitive to water level fluctuations. In these fishways, low tailwater levels will result in high drops at the lowest weir. High tailwater levels will lead into drowning of the fishway entrance and, consequently, poor attraction for fish. Changes in the upper water level drastically affects the flow conditions inside the fishway, and accordingly, the fish passage conditions. A very low upper water level will result in low discharges and very low water depths at the weir. With very high upper water levels the flow becomes streaming, and the depth of flow actually decreases with the increase in discharge, resulting in high water velocities at the weir. A simple example of this is given in Fig. 20. The measurements were made in a pool-and-weir fishway model for one slope (S_o=10 %). The study arrangements are described in Section 3.1. With high water depths when the flow is streaming, the effect of approach velocity becomes significant. In the model, this causes the discharge to increase faster than the water depths. Because of this, depth of flow may not be a good measure of discharges in pool-and-weir fishways.

The Student’s paired t-test was carried out for the data on pool-and-weir fishways (Table 4). According to this test, the mean percentage deviation p_m is reasonably close to zero for all the equations used, but the standard percentage deviation of p_m is high, around 50%. When using special equations for pool-and-weir fishways, for the author’s data on experimental observations (Sections 3.1 and 3.2), the standard percentage deviation of p_m is lower, 37% for pool-and-weir fishways with a horizontal crest and 28% for a V-crest.

In the normal range of dimensionless water depths y_o/L from about 0.02 to 0.4, pool-and-weir fishways are sensitive to changes in the model parameters. This means that a small change in model parameters gives a significant change in the dimensionless discharges and water depths.

Pool-and-weir fishways are very sensitive to upper water level fluctuations. In the model for calculating dimensionless discharges, this increases the scatter in the discharge rating curve. Even though the upper water level effect is not as strong for pool-and-weir fishways with a V-shaped crest as for those with a horizontal crest, the effect still exists and makes the predictability of this kind of an analysis quite poor. A better measure for the flow rate would be the upper water level. It predicts the discharges in the fishway better than the water depth at the weir, which was measured in these studies (Fig. 20).

An experienced designer may also use equations for weir flows with good success when the flow is in the plunging mode and the flow over the weirs is not affected by the adjacent weirs. In addition to the upper water level, water depths inside fishways are important for fish passage, and so analysis of water depths would be useful, too.

4.4.3. Applicability to the flows in Denil fishways

Denil fishways are referred to as efficient energy dissipators. Energy dissipation is created by vanes at the bottom and at the sides. With extremely low discharges, the flow in Denil fishways can be considered as plunging. With higher water depths the flow becomes streaming, but unlike in pool-and-weir fishways, flow friction is higher and the flow is more stable. Even though the flow is streaming, the increase in water depth does not result in excessively increased average water velocities.

The model developed describes flows in Denil fishways reasonably well. The slope of the fitting curves of Denil fishways are almost equal and for most of the data, the fitting curves agree with the fitting curve of all the author’s data (Fig. 18). According to the t-test, even the general equation gives good results (Table 5). For the author’s data on experimental observations (App. 1), the standard percentage deviation of the relative difference in dimensionless discharge is less than 15% in all confidence intervals. Slightly better results are obtained by using a special equation for Denil fishways.

In Denil fishways, the normal range of dimensionless water depths y_o/L varies from about 0.5 to 2.0. In the range of y_o/L = 0.5…1.2, Denil fishways are not very sensitive to changes in the model parameters.

4.4.4. Applicability for the flows in vertical slot fishways

The energy dissipation pattern in vertical slot fishways is different than that in pool-and-weir and Denil fishways. This can also be seen in all the separate fitting curves (Figs. 17, 18, and 19). The slope of the fitting curves for vertical slot fishways is noticeably different than the slopes for the other studied fishway types. Because of this, the general dimensionless discharge equation does not give a very good fit due to a high standard percentage deviation of the mean (Table 6). The use of the special equation for vertical slot fishways gives better results. For the author’s data (App. 1 and 7), standard percentage deviation of the mean p_m decreases to 14% (with the mean p_m being 2.2%) and to 21% for the reference data (App. 4). The reason for trend lines being located some distance from each other may be due to differences in the measuring methods of water depths. The slopes of the lines are, however, almost equal.

A closer analysis of the results on vertical slot fishways reveals that the general model is not so readily suitable for some of the fishway types, while for other types the model gives better results. This could be due to improper energy dissipation (the model gives usually too high dimensionless discharges). Another reason may be the poor appropriacy of the model parameters for that special fishway type, so that new parameters should be defined for it. In the normal range of dimensionless water depths y_o/L, from about 0.15 to 1.5, vertical slot fishways tolerate changes in model parameters quite well.