Iniciativas Internacionales

Both at the gully-flume and at the sediment plot high dirty water concentrations were measured, at the gully-flume 600 g/l (table 4.11), at the plot about 750 g/l (table 4.12).

Both flumes are H-flumes that were constructed according to literature instructions (Bos, 1989).

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

13:40 13:48 13:55 14:02 14:09 14:16 14:24 14:31 14:38 14:45 14:52 15:00 time

Q (m^3/s)

0 100 200 300 400 500 600

C (g/l)

fluid discharge (Qf) clear water discharge (Qw) dirty water concentration (Cf)

5.5.1 Velocity and discharge

The discharge equations of H-flumes are based on previous calibrations. This should mean that if the flume is constructed according to the literature instructions the discharge equation is the same as given in the literature. Like for the weir, however, high viscosity might decrease the discharge in comparison to the calibration conditions, while on the other hand higher density and momentum might increase it. The net effect for the discharge equation could in principle be evaluated by comparing the calculated total discharge (from the sensor data) with the total discharge amounts that have been collected using the divisor system (see chapter 4). Assuming that all water was collected in the barrels a difference in total discharge as calculated from the barrel-data and from the water level data could be ascribed to the effect of viscosity. In practice, however, this will not be possible because of uncertainty about measured water level data, sediment levels in the flumes and concentration in the barrels. The discharge equations were therefore not changed.

5.5.2 Sediment content

After an event there is usually a layer of sediment present in the flumes, as shown in figure 5.5. Cantón et al. (2001) tried to solve similar problems by using tilted false floors in their flumes in the Tabernas badlands of southern Spain. This, however, was only partially successful and they were forced to correct the falling limbs of the measured hydrographs. In the Danangou catchment this was also necessary. To be able to determine discharge from the sensor signal one needs to know when the sediment layer developed.

Because of the assumption that the discharge equations are correct the total discharge from the barrels can be used to guess at the build-up of sediment. The procedure is to estimate sediment levels during the event based on the levels observed in the flume after the event. By changing the timing of sediment-buildup the total amount of discharge changes and can be made to fit the observed barrel-totals as closely as possible. In this process two assumptions were adopted:

1) That sediment build-up always started after the runoff-peak

2) That the hydrograph should maintain a probable shape, i.e. that it will show an approximately exponential decrease after the peak.

Figure 5.6 shows the results of this procedure for the event of 990710. As can be seen from the figure the measured water level levelled off at about 0.018 m (1.8 cm). This was assumed to be due to a sediment layer of that thickness in the flume. Measurements of the sediment level on the day after the event gave an average sediment level of 1.35 cm in the flume, while at the sensor the sediment thickness was above average. To assume a

sediment level of 1.8 cm was therefore acceptable.

Discharge was calculated by applying the discharge equation of the flume (equation 4.9) to the uncorrected measured water level and to the estimated sediment level. Discharge was then calculated as discharge from the uncorrected measured water level minus the hypothetical sediment discharge. This is necessary because of the v-shaped aperture of an

Figure 5.5 Thick sediment layer (about 10 cm) in the gully-flume after the event of 980712. At this time the barrels below the flume had not yet been installed. Picture by E. van de Giessen and

J. Snepvangers

Figure 5.6 Measured water level, estimated sediment level and corrected water level for the event of 990710, sediment plot

H-flume (see figure 5.5). If the discharge equation were applied to the corrected water level discharge would be too low because the water is not flowing over the bottom of the flume, but over the sediment that deposited inside the flume. After the discharge was calculated with the discharge equation, it was corrected to clear water discharge using equation 5.16. Because no timeseries of sediment concentrations were available for the

-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

15:00 15:07 15:14 15:21 15:28

time

water level (m) and sediment level (m)

water level (sensor data) estimated sediment level water level (corrected)

sediment plot the average concentration as determined from the barrels was used. For the gully-flume the data collected with the turbidity sensor could not be used because

concentrations were far outside the range of the sensor (chapter 4), so that for the gully-flume the barrel data should also be used. Finally, concentrations expressed in gram per litre clear water were calculated in the same way as described for the weir (equation 5.19).

5.5.3 Settling velocity

Application of the Stokes equation (equation 5.11) for the conditions of the Danangou catchment (d50 about 35 mu) showed that settling velocity in clear water would be about 1 mm/s. Considering the concentrations measured at the flume real settling velocity could be about half that, i.e. 0.5 mm/s. This shows that settling velocity reduction is not likely to be important in shallow flows with depths of several millimetres only.

5.6 Conclusions

High sediment concentrations are a characteristic feature of the Loess Plateau. These high concentrations are probably caused by a combination of factors, in particular the

occurrence of erodible materials on steep slopes, the structure and chemical constitution of the loess and the harsh climate that causes plant cover to be low.

When sediment concentration increases fluid density increases, viscosity increases and settling velocity decreases. The effect of this becomes increasingly important with increases in concentration and can result in flow behaviour that is quite different from that of normal streamflow. For large concentrations transport capacity might for example increase. The net effect of these changes on the flow is not always evident, for example the effect on flow velocity and flow resistance remains unclear. Despite this, erosion models that are dealing with high sediment concentrations cannot afford to neglect these effects altogether.

The data collected in the Danangou catchment indicate that even though sediment concentrations were considerable this did not change the fluid flow to such extent that special adaptations are needed to soil erosion models such as LISEM. A number of corrections are, however, necessary to be able to compare field measurements with results of soil erosion models. For the weir sediment volume should be subtracted from runoff volume and a density correction is needed to use data from the pressure transducer. For the flumes, the measured water level should be corrected by subtracting the sediment level in the flume from the water level, while the sediment volume should also be subtracted from the discharge. Finally, measured concentration should be corrected to give concentration expressed as gram per litre clear water.

Literature data show that for the sediment concentrations occurring in the catchment the settling velocity will be significantly reduced, so that soil erosion models should be adapted to incorporate a correction for settling velocity.

133 6 FLOW VELOCITY

Based on: Hessel, R., Jetten, V. & Zhang Guanghui (in press) Estimating Manning’s n for steep slopes. Catena

6.1 Introduction

Hydrological and soil erosion models need to calculate the flow velocity to be able to simulate the flow of water over the land surface. These models generally use a separate water balance for each spatial element, in which the water depth available for runoff is calculated by subtracting interception, infiltration and surface storage from precipitation.

Several equations are available to calculate overland flow velocity from this water depth.

The most widely used of these equations are the Darcy-Weisbach and Manning equations.

Most field and laboratory studies on overland flow seem to use the Darcy-Weisbach f, whilst most studies of channel flow use Manning’s n. This division, however, is not clear-cut, as the choice for either formula is also influenced by personal preference.

Furthermore, there is no reason to assume major differences in results between the two methods. Both are calculated from the same variables and both suffer from the limitations of having to characterise flow patterns that are highly variable in space and time. On hill slopes, overland flow will occur as a shallow sheet of water, with faster flowing,

diverging and converging flow threads around obstacles. Flow depth and velocity will therefore be highly variable in space. Abrahams et al. (1990) studied Darcy-Weisbach f for desert hill slopes and found that it varies with the rate of flow. Since the rate of flow is highly variable in space, so too is f. Resistance to flow will also be variable in time, as it depends on continuously changing flow conditions. This dependence is often expressed by developing relationships between the Darcy-Weisbach f and Reynolds number (e.g.

Abrahams et al., 1990, Gilley et al., 1992). As Takken & Govers (2000) have noted, Manning’s n is likely to behave in the same way as f. The flow will also tend to

concentrate in the downslope direction, which is likely to decrease resistance to flow in that direction (Abrahams et al., 1990).

Contrary to field studies, most hydrological and soil erosion models use Manning’s n, probably because the literature provides more data for n than for f. Another reason could be that the use of Manning’s equation for overland flow is more or less accepted, while Darcy-Weisbach appears not to have been used for streamflow. It is obviously preferable to use only one equation for any one model application, and the choice for Manning’s equation in modelling is therefore generally accepted. Table 6.1 shows some literature values for Manning’s n. Morgan et al. (1998b) used the same values for Manning’s n in the case of overland flow and channel flow. They stated, however, that the values for overland flow are likely to be relatively close to the ‘high’ value mentioned by them.

Table 6.1 Literature values of Manning’s n

Land use Source^a Low Mean High

Mountain streams 1 0.030 0.040 0.050

Major rivers 1 0.035 0.100

Concrete or asphalt 3 0.010 0.011 0.013

Bare soil 2 0.010 0.020 0.030

Bare cropland 1 0.020 0.030 0.040

Fallow – no residue 3 0.006 0.050 0.160 Mature row crops 1 0.025 0.035 0.045 Mature field crops 1 0.030 0.040 0.050

Wheat 2 0.100 0.125 0.300

Sorghum 2 0.040 0.090 0.110

Short grass 1 0.025 0.030 0.035

Short Bermuda grass 2 0.030 0.046 0.060 Long Bermuda grass 2 0.040 0.100 0.150 Natural rangeland 3 0.100 0.130 0.320

Scattered brush 1 0.035 0.050 0.070

Dense brush (summer) 1 0.070 0.100 0.160

a 1: Ven Te Chow (1959), 2: Morgan et al.. (1998b), 3: Engman (1986)

Engman (1986) summarised a number of studies on friction factors. The effects of rainfall, tillage and vegetation on friction factors have all been studied. Despite this, considerable uncertainty about the values of friction factors remains. An important subject of discussion is the applicability of the friction factors to different types of flow.

Two distinctions in flow type deserve attention: laminar versus turbulent (defined with Re) and sub-critical versus super-critical (defined with Froude number, Fr). Ven Te Chow et al. (1988), for example, stated that Manning’s equation is only valid for fully turbulent flow, when Darcy-Weisbach f is independent of Reynolds number. Abrahams et al. (1990), Gilley et al. (1992) and Nearing et al. (1997) found many different

relationships between f and Re for overland flow, but apparently there was always some dependency. Similarly, the Manning and Darcy-Weisbach equations have been applied to laminar flow, and not always with different values for the friction factor than used for turbulent flow (Engman, 1986). The distinction between sub-critical and super-critical flow has received much less attention (if any). This is surprising since super-critical flow has both smaller water depth and larger velocity than sub-critical flow at the same discharge. This is contrary to the Manning and Darcy-Weisbach equations since both predict that if water depth is smaller velocity should be smaller. Thus, either n and f should be smaller for super-critical flow, or the equations would not be applicable at all.

Nearing et al. (1997) performed a series of experiments in which both sub-critical and super-critical flow occurred. In some cases they found different relationships between f and Re for laminar and turbulent flow, but they paid no attention to the distinction

135 between sub-critical and super-critical flow. However, for their uniform sand experiments they found a clear increase of Fr with an increase of Re as well as a decrease of f with an increase of Re. Thus, f decreased with increasing Fr. Giménez & Govers (2001) did not question the applicability of Manning’s equation for their super-critical flow. Their data for non-eroding rills show that Fr increased from sub-critical values to super-critical values with an increase in slope angle from 3 to 12 degrees, but that Manning’s n was independent of slope angle. Thus, n was apparently independent of Fr. These different studies suggest that the Manning and Darcy-Weisbach equations can be applied to all types of flow, but that the values of the friction factors might be different for different flow conditions.

Ven Te Chow (1959) noted that Manning’s n, which is often assumed to be constant, can actually vary for a number of reasons. The same will be true for Darcy-Weisbach f. The dependency of n and f on flow conditions has already been discussed above. Some other factors that can cause Manning’s n to vary are (Ven Te Chow, 1959):

- Vegetation. The effect of vegetation on Manning’s n depends on height, density, distribution and type of vegetation. Petryk & Bosmajian (1975) developed equations to calculate Manning’s n as a function of flow depth and vegetation density for partially submerged vegetation. They found that if the vegetation density over height is constant Manning’s n will increase with increasing flowdepth. Jin et al. (2000) tested these equations with flume experiments in which vegetation was simulated with propylene bristles. They found that the equations performed well. It should be noted that these equations only apply when flow depth is smaller than vegetation height. If this is not the case Manning’s n usually decreases with increasing water level because of increasing submergence and because of bending plants (Petryk & Bosmajian, 1975).

- Silting and scouring. According to Ven Te Chow (1959) silting generally smoothens the channel so that Manning’s n becomes lower, while scouring increases Manning’s n because the channel becomes rougher.

- Stage and discharge. Manning’s n usually decreases with increasing water level, at least if the roughness elements are fully submerged. In fact, the degree of submergence of obstacles determines whether roughness increases or decreases with increasing stage, as found by e.g. Abrahams et al. (1990), Gilley et al. (1992) and Takken & Govers (2000).

- Suspended material and bedload. Suspended material and bedload consume energy and cause head loss, so that Manning’s n should be higher. Chapter 5, however, showed that there are also indications that the transport of suspended material does not cause head loss. Which is true probably depends on local flow conditions.

If friction factors are measured under natural conditions the values that are obtained are effective friction factors, since they include effects of raindrop impact, flow

concentration, litter, crop ridges, rocks, tillage roughness, frictional drag and erosion and transport of sediment (Engman, 1986). However, from a viewpoint of simulating the hydrograph, such an effective friction factor is adequate. Determining Manning’s n from field plots is complicated by the fact that assumptions about infiltration are needed.

Engman (1986) assumed a constant infiltration rate, while Mohamoud (1992) modelled infiltration with the Philips equation. Both used rainfall experiments on plots, so that even without infiltration discharge would not be constant along the plot. Runon-experiments, on the other hand, neglect the effect rainfall might have on the friction factor. These problems are almost unavoidable for field measurements. Values of friction factors obtained from laboratory experiments are, however, difficult to compare to field

conditions. Emmett (1970), for example, found a tenfold increase in resistance on natural plots compared to laboratory plots. If the objective is to use erosion models, it is

appropriate to use effective friction factors obtained for field conditions.

Research into the flow resistance on slopes as steep as in the Danangou catchment has been scant. Abrahams et al. (1990) measured f values on slopes of 6 – 33^o, but they focussed on soil roughness effects and did not investigate the effect of slope itself.

The aims of the research project described in this chapter were the following. 1) To evaluate the use of Manning’s equation for steep slopes. For this purpose, Manning’s n was measured on slopes ranging from 6 to 64%. 2) To find out if Manning’s equation can be used or if the Darcy-Weisbach equation is more suitable because of its relationship with the Reynolds number. 3) To obtain values of Manning’s n or Darcy-Weisbach f for different types of land use in the Danangou catchment. The values obtained for different land uses and slopes were intended to be used as input for soil erosion models.