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Calibration of a Bed Load Transport Rate Model in Streams of NE Greece

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Calibration of a Bed Load Transport Rate Model in Streams of NE Greece European Water 55: 125-139, 2016. © 2016 E.W. Publications Calibration of a bed load transport rate model in streams of NE Greece T. Papalaskaris1*, V. Hrissanthou1** and E. Sidiropoulos2 1 Department of Civil Engineering, Democritus University of Thrace, Kimmeria Campus, 67100 Xanthi, Greece 2 Department of Rural and Surveying Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece * e-mail: [email protected] ** e-mail: [email protected] Abstract: Measurements of stream discharge and bed load transport rate were carried out at the outlets of the mountain parts of Kosynthos River basin and Kimmeria Torrent basin (NE Greece). Specifically, 27 measurements of stream discharge and bed load transport rate were carried out in Kosynthos River and 37 measurements in Kimmeria Torrent. Apart from the measurements, the bed load transport rate was calculated by means of Meyer-Peter and Müller formula, after calibrating the above formula manually in terms of roughness coefficient. A comparison between calculations and measurements of bed load transport rate was made on the basis of the following statistical criteria: Root Mean Square Error (RMSE), Relative Error (RE), Efficiency Coefficient (EC), linear correlation coefficient, determination coefficient and discrepancy ratio. The comparison results are satisfactory. A less satisfactory, although more physically sound, calibration of the Meyer-Peter and Müller formula resulted on the basis of the least squares method. Key words: bed load transport rate, measurements, calculations, Meyer-Peter and Müller formula, calibration. 1. INTRODUCTION During the last decade, an effort to conduct stream bed load and suspended load transport rate measurements is on the way by the Division of Hydraulic Engineering, Department of Civil Engineering, Democritus University of Thrace (Greece), at the outlets of the mountainous parts of stream basins discharging to Kosynthos River and Kimmeria Torrent (northeastern Greece), in the framework of diploma theses (Metallinos and Hrissanthou, 2010; Kaffas and Hrissanthou, 2015). The outlets of those stream basins are located in proximity to the city of Xanthi. Due to the fact that both bed load transport rate as well as suspended load transport rate depend on, among other factors, stream flow rate, the measurements of stream flow rate preceded the measurements of bed load and suspended load transport rate. Measurements of bed load transport rate in streams or rivers were conducted in the last years, also by others, e.g., in the USA (Duan and Scott, 2007; Kuhnle et al., 2014), in Spain (López et al., 2014), in Iran (Haddadchi et al., 2012), in China (Yu et al., 2009). Additionally, investigations of bed load transport in laboratory flumes were conducted recently, e.g., Patel et al. (2015); De Vincenzo et al. (2016); Li et al. (2016). In the present study, 27 pairs of stream flow rate and bed load transport rate measurements of Kosynthos River and 37 pairs of stream flow rate and bed load transport rate measurements of Kimmeria Torrent are presented. Apart from the measurements, the bed load transport rate was calculated by means of Meyer-Peter and Müller formula (1948), which is considered one of the most reliable formulae in order to calculate the bed load transport rate. Thus, by the end of the procedure, it was possible to compare calculated to site-measured stream bed load transport rate. The formula or the concept of Meyer-Peter and Müller was applied also, in the last years, to streams or rivers of other countries for the calculation of bed load transport rate and the comparison with measurements, e.g., in France (Claude et al., 2012), Spain (Vázquez-Tarrío and Menéndez- Duarte, 2015). 126 T. Papalaskaris et al. 2. STUDY AREA Kosynthos River basin considered in this study drains an area of 237 km2 (Figure 1). The basin outlet is located at the city of Xanthi. The basin terrain is covered by forest (74%), bush (4.5%), urban area (1.5%) and no significant vegetation (20%). The maximum altitude of the basin is approximately 1700 m. The length of the main watercourse of the basin is 35 km, whereas the mean slope of the main watercourses of the ten natural sub-basins the Kosynthos River basin is divided to is approximately 5%. Figure 1. Kosynthos River basin divided into ten sub-basins. Figure 2. Kimmeria Torrent basin. European Water 55 (2016) 127 Kimmeria Torrent basin considered in this study drains an area of 35 km2 (Figure 2). The basin outlet is located at the village of Kimmeria which lies northeast of the city of Xanthi. The basin terrain is covered by forest (55%), bush (33%), urban area (1%) and no significant vegetation (11%). The maximum altitude of the basin is approximately 800 m. The length of the main watercourse of the basin is 10 km, whereas the mean slope of the main watercourse is approximately 6%. From the physiographic characteristics mentioned above, the bed slope of Kosynthos River and Kimmeria Torrent impacts directly bed load transport, while the soil cover impacts runoff generated from rainfall and stream discharge which again influences bed load transport. 3. STREAM FLOW RATE AND BED LOAD TRANSPORT RATE MEASUREMENTS The stream flow rate measurements were conducted as follows: The site cross section was divided into sub-sections and the average stream flow velocity was measured at the middle of each sub-section by means of a current meter. The average stream flow velocity of each cross sub-section is then multiplied by the area of the sub-section (wetted area), yielding the individual stream flow rate of the specific sub-section. The stream flow rate of the entire cross section is the outcome of the summation of the individual sub-sections stream flow rates. The stream bed load transport rate measurements were conducted by means of a Helley-Smith bed load sampler which was placed at the middle of each stream bed cross section. The above device consists of an expanding nozzle, a sample bag and a wading rod. In order to determine the bed load transport rate in kg/(m s), the trapped bed load dry mass is divided by the trap width and the measurement time duration. The stream flow and bed load transport rate measurements concerning Kosynthos River were conducted at a location 4 km upstream of the city of Xanthi (e.g., Efthymiopoulou and Tsamis, 2012; Giannelou et al., 2012). The average width of the cross sections of all measurements is about 22 m. The dates of all measurements as well as the stream flow rates and bed load transport rates of Kosynthos River are presented in Table 1. The stream flow and bed load transport rate measurements concerning Kimmeria Torrent were conducted at a location nearby the village of Kimmeria (e.g., Vallianatos and Giannakos, 2012; Alexandridis and Tourkas, 2013; Zilelidis and Polyhroniadis, 2014). The average width of the cross sections of all measurements is about 7 m. The dates of all measurements as well as the stream flow rates and bed load transport rates of Kimmeria Torrent are presented in Table 2. The mountainous part of Kosynthos River has a torrential behaviour. The bed of both streams, Kosynthos River and Kimmeria Torrent, consists of gravel and sand. However, the trapped bed load in both cases belongs to sand category, because the measurement sites are located near the basin outlets. 4. BED LOAD TRANSPORT RATE CALCULATIONS In order to calculate the bed load transport rate, the following formula of Meyer-Peter and Müller (1948) was employed, which is considered one of the most reliable available: ! !! ! !/! �! = (�! − �!,!") (1) ! !!!!! !! where: �! = �!��!�! (2) �!,!! = 0.047�′�!��! (3) 128 T. Papalaskaris et al. ! ! �! = !! ! (4) !! !!" !/! �! = ( ) � (5) !! !" �! = ! (6) !!" where: mG: bed load transport rate per unit width [kg/(m s)] g: gravity acceleration (m/s2) 3 ρF: sediment density (kg/m ) 3 ρW: water density (kg/m ) 2 το: actual shear stress (N/m ) 2 το,cr: critical shear stress (N/m ) dm: bed load particles mean diameter (m) Ir: energy line slope due to individual particles Rs: hydraulic radius of the specific part of the cross section under consideration which affects the bed load transport (m) I: energy line slope due to individual particles and stream bed forms 1/3 kr: coefficient, whose value depends on the roughness due to individual particles (m /s) kst: Strickler coefficient, whose value depends on the roughness due to individual particles as well as to stream bed forms (m1/3/s) d90: characteristic grain size diameter (m) (in case of taking a sample of stream bed load, 90% of the sample weight is comprised by grains with size less or equal to d90) Table 1. Stream flow rate and bed load transport rate measurements of Kosynthos River - Calculated bed load transport rate Bed load Bed load transport rate Bed load transport rate Bed load transport rate Stream flow transport rate [kg/(m s)] [kg/(m s)] [kg/(m s)] No. Date rate (m3/s) [kg/(m s)] Calculated Calculated Calculated Measured (manual calibration) (parameter α) (parameter β) 1 24-3-2006 11.115 0.0030 0.0328 0.1057 0.0590 2 26-3-2006 5.993 0.0350 0.0039 0.0744 0.0581 3 3-7-2006 2.970 0.0039 0.0053 0.0313 0.0559 4 28-3-2007 7.710 0.0024 0.0219 0.0695 0.0579 5 29-3-2007 6.570 0.0016 0.0189 0.2309 0.0576 6 30-3-2007 5.310 0.0093 0.0070 0.0503 0.0571 7 1-5-2007 2.244 0.0033 0.0032 0.0274 0.0555 8 2-5-2007 2.891 0.0040 0.0059 0.0320 0.0559 9 3-5-2007 3.425 0.0042 0.0058 0.0310 0.0559 10 4-5-2007 2.436 0.0035 0.0025 0.0241 0.0552 11 11-5-2007 1.647 0.0030 0.0017 0.0208 0.0549 12 18-9-2008 0.756
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