Kosynthos River basin with an area of about 237 km2 and Kimmeria Torrent basin with an area of about 35 km2. Measuring data of rainfall depth, rainfall ...
Regression relationships between sediment yield and hydraulic and rainfall characteristics for two basins in northeastern Greece A. Metallinos & V. Hrissanthou Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece
ABSTRACT: Simple non-linear regression relationships between sediment transport on the one hand and water discharge, rainfall depth and rainfall intensity on the other hand were established for two basins located near Xanthi (Thrace, northeastern Greece): Kosynthos River basin with an area of about 237 km2 and Kimmeria Torrent basin with an area of about 35 km2. Measuring data of rainfall depth, rainfall duration, water discharge and sediment transport for the outlets of the above basins were available. The relatively high values of the correlation coefficients resulted from the regression analysis indicate that sediment yield at the outlet of the studied basins can be predicted satisfactorily as a function of the water discharge in the main streams of the basins on the one hand and the rainfall characteristics (rainfall depth, rainfall intensity) on the other hand. 1 INTRODUCTION Sediment yield at the outlet of a basin is mainly due to soil erosion and to stream bed erosion in the basin. Soil erosion, again, is caused by the rainfall impact on the soil surface and the shear stresses of the overland flow exerted also on the soil surface. Furthermore, stream bed erosion is caused by the shear stresses of streamflow exerted on the bed surface. Since overland flow, induced by runoff on the soil surface, and direct runoff in the streams depend mainly on the rainfall characteristics, regression relationships between sediment transport on the one hand and water discharge, rainfall depth and rainfall intensity on the other hand could be established for a basin. In concrete terms, simple non-linear regression relationships between the above mentioned variables were established for two basins located near Xanthi (Thrace, northeastern Greece): Kosynthos River basin with an area of about 237 km2 and Kimmeria Torrent basin with an area of about 35 km2. Measuring data of rainfall depth, rainfall duration, water discharge and sediment transport for the outlets of the above basins were available. A simple empirical way to find out the interdependence, linear or non-linear, between two measuring variables consists in the regression analysis. A pair of measuring variables can be represented by a point in a rectangular coordinates system. The interdependence between the two variables is depicted graphically by a regression curve. The degree of the linear or nonlinear dependence is expressed by the correlation coefficient. The ideal value of 1.0 for the correlation coefficient indicates that all points representing pairs of measuring variables lie on the regression curve; in other words, the adaptation of the regression curve to the measuring points is perfect. Numerous regression relationships between suspended load concentration or suspended load transport rate on the one hand and water discharge on the other hand, for different regions in the world, can be found in the literature (e.g. Walling 1977; Griffiths 1982; Córdova & González 1997; Asselman 2000; Achite & Ouillon 2007; Sadeghi et al. 2008).
While regression analysis is a very useful tool to predict sediment yield at the outlet of a basin as a function of hydraulic and hydrologic properties of the basin, the mechanisms of the physical processes of rainfall – runoff, soil erosion and stream sediment transport are not considered and quantified.
2 MEASURING DATA 2.1 Kosynthos River basin The basin of Kosynthos River has an area of about 237 km2 consisting of forest (74%), bush (4.5%), urban area (1.5%) and an area with no significant vegetation (20%). The highest altitude of the basin is about 1700 m. The length of the main stream of the basin is about 35 km. The whole basin can be divided into ten natural sub-basins with areas between 16 and 35 km2. The mean soil slope gradient of the sub-basins is about 37%, while the mean slope gradient of the main streams of the sub-basins is about 5%. On certain days, measurements of water discharge, suspended load transport and bed load transport, after rainfall events, were performed near the outlet of Kosynthos River basin (Garip & Hafouz 2006; Konstantinidis & Dimakoyiannis 2007; Lambrou & Dramalidis 2007; Gountanas & Lambrianou 2008). Rainfall data (daily rainfall depth and rainfall duration) were available from the meteorological station of the Laboratory of Hydrology and Hydraulic Engineering (Department of Civil Engineering, Democritus University of Thrace), located in the centre of gravity (Oreo) of the basin. The mean width of the cross sections, where the measurements were performed, was 22 m. The cross section was divided into subsections, and the mean velocity was measured separately in each subsection by means of a propeller device. The water discharge in each subsection results as the product of the mean velocity and the cross-sectional area of the subsection. The water discharge of the whole cross section is the sum of the water discharges of the subsections. Measurements of suspended load transport and bed load transport were carried out in the same time as the water discharge measurements. In this time, water samples were taken from each subsection. In the Laboratory of Ecological Engineering and Technology (Department of Environmental Engineering, Democritus University of Thrace), the concentration of suspended load for each subsection was determined. The concentration of suspended load for the whole cross section was determined from the following equation: m
m
C s = ∑ C si Qi / i =1
∑ Qi
(1)
i =1
where C s = concentration of suspended load for the whole cross section (kg/m3); C si = concentration of suspended load for the subsection i (kg/m3); Qi = water discharge for the subsection i (m3/s); and m = number of the subsections. The transport rate of suspended load for the whole cross section, m s (kg/s), was determined from the following relationship: m
m s = C s ∑ Qi i =1
(2)
For the measurement of bed load transport, a sediment trap was put on the bed, in the middle of the whole cross section. In order to determine the bed load transport rate in kg/(m s), the dry mass of the trapped sediment has to be divided by the measurement duration and the width of the sediment trap. In Table 1, the date of the measurements, the daily rainfall depth, the rainfall intensity, the water discharge, the suspended load transport rate and the bed load transport rate are given.
Table 1. Rainfall data and measured values of water discharge, suspended load and bed load transport rate near the outlet of Kosynthos River basin. Date Daily rainfall Rainfall Water Suspended Bed load depth (mm) intensity discharge load transport transport rate (mm/hr) (m3/s) rate (gr/s) [kg/(s m)] 26-10-2005 0.43 0.37 0.0018 02-11-2005 0.43 0.007 0.0021 30-11-2005 2.79 26.80 0.0031 07-12-2005 2.74 12.00 0.0045 14-12-2005 0.99 11.80 0.0034 24-03-2006 11.15 no measurem. 0.0030 26-03-2006 5.99 no measurem. 0.0035 08-04-2006 7.80 3.34 3.20 no measurem. 0.0044 20-04-2006 1.80 4.50 2.68 no measurem. 0.0070 01-05-2007 4.60 3.45 2.24 678.9 0.0033 02-05-2007 5.60 2.80 2.89 1976.2 0.0040 03-05-2007 15.2 2.17 3.43 2336.2 0.0042 04-05-2007 0.80 1.60 2.44 1383.0 0.0035 1.80 3.60 1.65 455.5 0.0030 11-05-2007 17-04-2007 1.52 12.93 no measurem. 18-04-2007 1.09 13.90 no measurem. 23-04-2007 0.25 6.00 1.06 20.10 no measurem. 25-04-2007 0.65 12.50 no measurem. 26-04-2007 1.53 26.55 no measurem.
2.2 Kimmeria Torrent basin The basin of Kimmeria Torrent has an area of about 35 km2 consisting of forest (55%), bush (33%), urban area (1%) and an area with no significant vegetation (11%). The highest altitude of the basin is about 800 m. The length of the main stream of the basin is about 10 km. The mean soil slope gradient of the basin is about 45.5%, while the mean slope gradient of the main stream of the basin is about 6%. Similar measurements, as described above for Kosynthos River basin, were performed at the outlet of Kimmeria Torrent basin (Rasim et al. 2004; Gesoulis & Papantoniou 2006; Chatzinikolakis & Koulanis 2006). Rainfall data were available from the meteorological station of the Laboratory of Ecological Engineering and Technology (Department of Environmental Engineering, Democritus University of Thrace), located near the outlet of Kimmeria Torrent basin. The mean width of the cross sections, where the measurements were performed, was 7.0 m. In Table 2, the date of the measurements, the rainfall depth, the rainfall intensity, the water discharge, the suspended load transport rate and the bed load transport rate are given.
Table 2. Rainfall data and measured values of water discharge, suspended load and bed load transport rate at the outlet of Kimmeria Torrent basin. Date Daily rainfall Rainfall Water Suspended Bed load depth (mm) intensity discharge load transport transport rate (mm/hr) (m3/s) rate (gr/s) [kg/(s m)] 19-06-2004 2.80 2.80 0.67 403.2 0.0005 21-06-2004 18.4 36.80 3.05 2225.0 0.0008 22-06-2004 5.00 2.86 0.65 262.0 0.0005 23-06-2004 6.40 19.39 0.40 369.2 0.0005 30-06-2004 4.00 5.33 0.81 379.0 0.0006 22-06-2004 5.00 2.86 13.0 13.00 no measurem. 23-06-2004 6.40 19.39 0.59 757.9 no measurem. 20-05-2005 1.60 3.85 0.23 3.58 no measurem. 13-06-2005 5.80 13.94 0.20 7.04 no measurem. 21-09-2007 3.20 2.56 0.04 0.004 0.00008 20-11-2007 0.06 0.07 0.000014 20-11-2007 8.40 2.58 1.26 15.28 0.042 11-12-2007 5.20 5.68 0.805 9.52 0.1013 06-04-2008 49.0 3.67 3.09 148.6 0.2156
3 REGRESSION RELATIONSHIPS Sediment transport in the streams is classified into bed load transport and suspended load transport on the basis of the two different motion patterns. While bed load transport depends mainly on the hydraulic characteristics of the streams, e.g. water discharge, suspended load transport depends on both hydraulic and rainfall characteristics, e.g. rainfall depth, rainfall intensity. This fact can be justified as follows: when soil erosion products, created by rainfall and runoff, reach the streams, then they are transported in the streams as suspended materials, because they are very fine. Contrarily, bed load consists mainly of coarse material, and originates from stream bed erosion. On the basis of the above thoughts, the following simple non-linear regression relationships were established for the basins of Kosynthos River and Kimmeria Torrent (Metallinos 2009): • Suspended load transport rate versus water discharge • Suspended load transport rate versus daily rainfall depth • Suspended load transport rate versus rainfall intensity • Bed load transport rate versus water discharge For the basins of Kosynthos River and Kimmeria Torrent, the variables of the regression analysis, the types of the regression curves, the values of the correlation coefficients and the numbers of pairs of measuring data are given in Tables 3 and 4, respectively. Table 3. Simple non-linear regression relationships for Kosynthos River basin. Suspended load Suspended load Suspended load transport rate transport rate transport rate (gr/s) (gr/s) (gr/s) versus versus versus water discharge daily rainfall depth rainfall intensity (m3/s) (mm) (mm/hr) Type of regression hyperbolic hyperbolic exponential curve y=7.012x4.119 y=251.0x0.915 y=13545e-1.00x Correlation coefficient Number of pairs of measuring data
Bed load transport rate [kg/(m s)] versus water discharge (m3/s) exponential y=0.002e0.284x
0.82
0.79
0.89
0.88
15
7
8
14
Table 4. Simple non-linear regression relationships for Kimmeria Torrent basin. Suspended load Suspended load Suspended load transport rate transport rate transport rate (gr/s) (gr/s) (gr/s) versus versus versus water discharge daily rainfall depth rainfall intensity (m3/s) (mm) (mm/hr) Type of regression polynomial polynomial polynomial curve y=84.4x2+156.8x y=7.491x2-24.27x y=2.332x2-30.52x +63.1 +137.4 +204.4 Correlation coefficient Number of pairs of measuring data
Bed load transport rate [kg/(m s)] versus water discharge (m3/s) polynomial y=0.316x2-0.949x +0.392
0.96
0.93
0.96
0.97
13
12
13
11
In Figure 1, the regression exponential curve representing the interrelationship between bed load transport rate and water discharge for Kosynthos River basin is indicatively given, while in Figure 2, the regression polynomial curve showing the interrelationship between suspended load transport rate and daily rainfall depth for Kimmeria Torrent basin is indicatively illustrated.
Figure 1. Regression exponential curve for Kosynthos River basin.
Figure 2. Regression polynomial curve for Kimmeria Torrent basin.
4 DISCUSSION - CONCLUSION For Kimmeria Torrent basin, the correlation coefficient obtains very high values, greater than 0.90, for all the regression cases investigated (Table 4). For Kosynthos River basin, the values of the correlation coefficient vary between 0.79 and 0.89, which are also high (Table 3). The higher values of the correlation coefficient for Kimmeria Torrent basin compared to those for Kosynthos River basin are propably due to the smaller basin area of Kimmeria Torrent compared to that of Kosynthos River. For both basins, an increasing trend of - suspended load transport rate versus water discharge - suspended load transport rate versus daily rainfall depth (Fig. 2) - bed load transport rate versus water discharge (Fig. 1) is observed. Concerning the interrelationship between suspended load transport rate and rainfall intensity, a decreasing trend for Kosynthos River basin and an increasing trend for Kimmeria Torrent basin is observed. This contradictory remark is probably due to the fact that both rainfall depth and rainfall duration are daily cumulative values. The high values of the correlation coefficients (Tables 3 and 4) indicate that sediment yield at the outlet of the studied basins can be satisfactorily predicted as a function of the water discharge in the main streams of the basins on the one hand and the rainfall characteristics (rainfall depth, rainfall intensity) on the other hand. The reliability of the regression equations were higher if more measuring data were available. REFERENCES Achite, M. & Ouillon, S. 2007. Suspended sediment transport in a semiarid watershed, Wadi Abd, Algeria (1973-1995). Journal of Hydrology 343(3-4): 187-202. Asselman, N.E.M. 2000. Fitting and interpretation of sediment rating curves. Journal of Hydrology 234(3-4): 228-248.
Chatzinikolakis, D. & Koulanis, P. 2006. Measurements of bed load transport rate and suspended load transport rate in Kimmeria Torrent. Diploma Thesis, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece (in Greek). Córdova, J.R. & González, M. 1997. Sediment yield estimation in small watersheds based on streamflow and suspended sediment discharge measurements. Soil Technology 11(1): 57-65. Garip, H.A. & Hafouz, H.T. 2006. Measurements of water discharge and sediment transport rate in Kosynthos River. Diploma Thesis, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece (in Greek). Gesoulis, K. & Papantoniou, D. 2006. Measurements of water discharge and suspended load transport rate at the outlet of Kimmeria Torrent basin. Diploma Thesis, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece (in Greek). Gountanas, K. & Lambrianou, S. 2008. Measurements of water discharge, suspended load transport rate and water quality parameters in Kosynthos River basin. Diploma Thesis, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece (in Greek). Griffiths, G.A. 1982. Spatial and temporal variability in suspended sediment yields of North Island basins, New Zealand. Water Resources Bulletin 18(4): 575-584. Konstantinidis, D. & Dimakoyiannis, E. 2007. Measurements of bed load transport rate and suspended load transport rate in Kosynthos River. Diploma Thesis, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece (in Greek). Lambrou, A. & Dramalidis, C. 2007. Measurements of sediment transport rate under basisflow conditions. Diploma Thesis, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece (in Greek). Metallinos, A. 2009. Application of regression methods to stream sediment transport. Diploma Thesis, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece (in Greek). Rasim, S., Amet, R. & Nouri, S. 2004. Measurements of water discharge and sediment transport rate in Kimmeria Torrent. Diploma Thesis, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece (in Greek). Sadeghi, S.H.R., Mizuyama, T., Miyata, S., Gomi, T., Kosugi, T., Fukushima, T., Mizugaki, S. & Onda, Y., 2008. Development, evaluation and interpretation of sediment rating curves for a Japanese small mountainous reforested watershed. Geodema 144(1-2): 198-211. Walling, D.E. 1977. Assessing the accuracy of suspended sediment rating curves for a small basin. Water Resources Research 13(3): 531-538.
