Construction of the stage-discharge rating curve and the SSC-turbidity calibration curve in San Antonio Coapa 2009 hydrological season

Transcription

1 Construction of the stage-discharge rating curve and the SSC-turbidity calibration curve in San Antonio Coapa 009 hydrological season C. Duvert, N. Gratiot, September Introduction Study site The gauging station of San Antonio Coapa (SAC) stands at the outlet of a 90-km catchment that is part of the larger Cointzio basin (Fig. 1). It was equipped and tested during the 008 season; water and suspended sediment fluxes could then be measured all throughout 009. The material consists of a water level floating gauge (Thalimede OTT) and a turbidity sensor (Visolid WTW) connected to a Campbell datalogger. The gauging site was visited on a weekly basis, during which all data were downloaded, and equipments were checked and maintained when necessary. Figure 1: Location of the study site. The blue area corresponds to SAC subcatchment. The Undameo station is situated 5 km downstream, at the outlet of the Cointzio catchment 1

2 A number of technical difficulties were faced at this monitoring station. The major problem was the instability of the river cross-section because of frequent in-channel sediment deposition occurring all along the rainy season (Fig. ). The site lies within the alluvial plain of the Cointzio catchment and its river section, which is deep-channelled, was fully dredged during winter to minimize the flooding potential (Fig. a). As a consequence, the stream constantly deposited material during 008 and 009 floods until getting back to its original equilibrium (Fig. b). a) b) Figure : (a) View of the gauging station of SAC with turbidity sensor (left). (b) View of recent fine sediment deposits left by a flood and water level gauge Given the cross-section area changed during the rainy season, we had to adapt various stagedischarge rating curves in order to obtain some discharge estimates as reliable as possible. Similar difficulties were encountered for the calibration of the turbidity probe. The methodologies used to improve both the stage-discharge rating curve (Section ) and the SSCturbidity calibration curve (Section ) are presented hereafter.. Stage-discharge rating curve.1. Discharge measurements During 009, 8 discharge measurements were obtained using the tracer dilution method (Fig., black squares; Appendix 1). A rating curve of polynomial type was drawn, and the fitting of the curve with all discharge measurements is satisfying (Fig. ). Eight measurements had also been performed during the previous season (Fig., grey diamonds), but a high scattering is visible between the sets of data. This is undoubtedly an expression of the interseasonal unsteadiness of the cross-section area. Those 008 values were evidently not accounted for in the rating curve construction.

3 6000 Gauging 009 y = 4E-4x + 0.0x x Gauging 008 Discharge (l/s) Water level (cm) Figure : Discharge measurements performed in 008 and 009 at San Antonio Coapa. Error bars correspond to ± 10% uncertainties on each measurement At first sight, a total of 8 rating values could be considered low for the construction of a valid stage-discharge law. However, changes in the section did not only occur between 008 and 009, but also regularly all along the year: a scour chain survey carried out in 008 on the river banks of SAC showed that fine sediment deposition could reach up to cm weekly. Given these frequent variations of the section, the achievement of more measurements would certainly not have provided a better precision, but rather, would have increased the scattering (each gauging having only an ephemeral validity). Following this idea, the rating displayed in Fig. might be considered as appropriate only for the period encompassing the event during which those measurements were done. The 6 highest values were measured during a flooding event on 1 st July; the relationship found is therefore expected to be relevant only for the beginning of the wet period. Indeed, when applying the same rating to the entire 009 data, discharges appeared to be strongly under-estimated during the second part of the rainy season. A significant and increasing bias was found when the obtained data were compared with discharge values recorded at Santiago Undameo, especially for high values occurring during floods. Thus, some other appropriate ratings had to be elaborated for the rest of the season.

4 .. Inter-comparison with Undameo data Because of the geographical proximity between the gauging stations of Santiago Undameo and SAC (Fig. 1), and because of the geomorphological similarities between those two stations (they are both located in the lowland alluvial plain), we decided to use the discharge data obtained at Santiago Undameo as an indicator for the improvement of discharge estimates at SAC. The discharge values recorded at Undameo were used as markers of the maximum quantity of water that may have flowed through the SAC station. The blue squares and red triangles in Fig. 4 correspond to peak discharges measured in Undameo, to which water levels recorded in SAC during the same event were compared. These points therefore represent some maximum values that should not be overstepped by the rating. The exercise showed that a significant change occurred after the first major flood of the year, corresponding to the third highest of the season in terms of water level, on 1 st July 009 (shifting from blue squares to red triangles). The fitting curve that was established from the discharge measurements (see Section, black curve in Figs. and 4) is only adequate for data recorded until that event. Then, the equation would provide a constant underestimation of discharges. On the basis of the discharge records available at Undameo during the second part of the rainy season (red triangles in Fig. 4), the adjustment of 1 other fitting curve (red line in Fig. 4) appeared to be satisfactory until the end of the season Gauging Q Undameo before Q Undameo after Discharge (l/s) Eq () 4000 Eq (1) Water level (cm) Figure 4: Adjustment of the stage-discharge law by means of data from Undameo 4

5 To adjust this second rating curve with the best accuracy, we carefully analyzed the timing of floods in Undameo, inferring that each subcatchment had a distinct transit time. Some characteristic events were identified, in which various contributions could be individualized in Undameo hydrograph (i.e. double- or triple-peak floods; Fig. 5). During the peak that was expected to correspond to SAC subcatchment contribution only, we considered that there should not be a significant difference between the discharge measured in SAC and the discharge flowing down to the outlet at Undameo. The red law in Fig. 4 was therefore adjusted in order to obtain a good fitting of the hydrographs. Various examples of this technique are given in Fig. 5. Note that a shifting of.5 hours ( transit time between SAC and Undameo) was applied to the discharge values of Undameo in order to obtain a better visual synchronicity of both hydrographs. 6 5 contribution from other subcatchments Q Undameo Q San Antonio 5 (B) Considering a 10% uncertainty on discharge values, Q SAC is not significantly higher than Q Unda Q (m s -1 ) 4 contribution expected to be exclusively from SAC subcatchment Q (m s -1 ) 4 1 (A) 1 Q Undameo Q San Antonio 1/07 1/07 /06 (C) Q Undameo Q San Antonio Q (m s -1 ) 1 Here SAC subcatchment is probably not the only contributor 08/09 Figure 5: Hydrograph adjustment in San Antonio Coapa for various floods We then followed a trial-and-error process, repeating the same analysis for all the multi-peak events of the second part of the season. The obtained law was time after time adjusted to get the best compromise among all events. 5

6 .. Rating curves Overall, two equations were used to adjust water depth and discharge values. Equations (1) and () are cubic polynomials: Q = 0.4H H H (1) Corresponds to the black curve in Fig. 4 Q = 0.5H H H () Corresponds to the red curve in Fig. 4 with Q in m /s and H in m. Equation (1) was used from the beginning of the year 009 until the recession phase of the 1 st July event, and Eq. () was used from the end of the 1 st July event up to the end of the year 009. Data acquired through that procedure were then carefully checked in order to point out any anomaly or aberration. We principally verified that there were no floods during which discharge values in SAC were significantly higher than in Undameo..4. Conclusions It is also important to mention that several floods were not recorded in SAC all throughout the rainy season, mostly because of considerable siltation leading to the burying of the water level gauge. The main ungauged events correspond to the following days: 18/07, 0/07 and 14/09/009 (only turbidity peak was recorded during those flooding events). This might explain the relatively lower mean annual specific discharge encountered at SAC than at Undameo (respectively, 1.5 l/s/km and.1 l/s/km ). Overall, the discharge values at SAC estimated by the method presented here are of moderate reliability (uncertainty ± 0%). They were further used for yield and flux calculations, but these estimates should systematically be associated with error bars to prevent misinterpretations. 6

7 Figure 6 shows the 009 hydrographs obtained at Undameo and SAC: 15 Q Undameo Q San Antonio Coapa Discharge (m /s) /04 01/07 01/10 01/01 Figure 6: Hydrographs at Undameo and SAC during the 009 hydrological season. SSC-turbidity calibration curve A temporal evolution of the relationship between turbidity and suspended sediment concentration (SSC) was identified during the 009 season in SAC. Such phenomenon is well known and has already been evidenced by a number of authors (e.g. Gippel, 1995; Lewis, 1996; Eder et al., 010). It requires successive calibrations of the measuring device all throughout the season. In our case, various abrupt changes occurred: the first one was recorded around mid-july, and the second one occurred in late August. This might be a consequence of a clogging of the probe after concentrated flood events. Three adjustments were applied all along the rainy season in order to ensure continuity in the calculated SSC time series. The first adjustment corresponds to data covering the period January mid-july 009 (red circles in Fig. 7). The calibration used in Santiago Undameo (catchment outlet, 5 km downstream SAC) was applied on this first period. Indeed, both series of data present a goodquality overlapping (see Fig. 7, red and black circles). As the scattering was lower and the number of values was higher in Undameo, we chose to use this last relationship for the determination of SSC values in SAC, from the beginning of the year until 1th July

8 10 1 Undameo SAC jusqu'au 1/07 SAC entre 1/07 et /08 SAC après /08 MES (g/l) Turbidité (g/l de SiO ) Figure 7: Relation between turbidity and SSC values in Undameo and SAC Furthermore, couples of values measured in SAC and corresponding to the second (intermediary) part of the season (from 1th July till nd August; blue circles in Fig. 7) follow a significantly diverging trend. For similar values of turbidity, SSC values indeed undergo an upward translation. A second adjustment (Ajust. ) was therefore created, to account for this positive bias. This second law is presented in Fig. 8; it takes the shape of a simple linear function SSC (g/l) y = 0.65x Turbidity (g/l SiO ) Figure 8: Calibration of the values extracted from the intermediary period 8

9 Ajust. relation is therefore as follows: SSC = 0.65 * Turbidity A verification of this new adjustment was undertaken, by comparing the high frequency SSC data obtained from the two calibrations, to the values measured from water samples. This comparison is displayed in Fig. 9. While the initial calibration would introduce a high under-estimation of suspended sediment fluxes (mean error between measured value and value deduced from the calibration > 400%), the second law provides a better adequacy between measured values and values obtained from the calibration (mean uncertainty 40%). SSC (g l -1 ) Mean bias 40% Before adjustment 0.5 SSC (g l -1 ) /07 6/07 0/08 Mean bias 40% After adjustment /07 6/07 0/08 Figure 9: Comparison of the error related to the calibration selected: the initial adjustment obtained in Undameo is used in the upper graph, and Ajust. is used in the lower graph. The red circles correspond to the values obtained from manual sampling From the end of August 009, the bias between high frequency turbidity data and SSC seemed to increase again (see Fig. 7, green circles). The number of witness SSC-turbidity couples is very low during this period; however, a thorough analysis of the time series confirms that if using Ajust., an under-evaluation of the fluxes recorded during the last floods of the rainy season is very likely to happen (i.e. period September-October). We therefore had to apply a third calibration to the high frequency turbidity records (Ajust. ). 9

10 Rather than relying on a linear function elaborated from the (low) number of SSC-turbidity values, this last adjustment was realized by simply multiplying three times the gradient of Ajust.. Indeed, the study of events exhibiting similar discharge records in both Undameo and SAC proves that the underestimation is threefold for this period. An example of one of these events is presented in Fig SSC Undameo Q Undameo Q San Antonio SSC San Antonio with Ajust. SSC San Antonio with Ajust. Q (m/s) - SSC (g/l) /09 Figure 10: Adjustment achieved for the last part of the rainy season (Ajust. ) and comparison with Ajust. for the 7th September 009 flood event It appears that the SSC peak obtained from Ajust. (blue line) is analogous to the one recorded in Undameo a few hours later (red line), and this for a flood with very similar discharge pattern (both in terms of Q max and V tot ). Eventually, this method ensures a better adequacy with the few measured data (obtained from manual sampling). Ajust. relation is therefore as follows: SSC = 1.95 * Turbidity Overall, the results obtained after using these three calibration laws are satisfying. The annual flux recorded in SAC amounts to Mg (in comparison, the flux recorded at the outlet of the catchment over the same period is Mg). However, it is worth mentioning that a total of 1 events were not measured throughout the season. Those 1 events can be compared to the events for which discharge and sediment flux have been properly measured (i.e. 71% of events occurring in 009 were measured). A significant underestimation of the 009 annual export from SAC is therefore to be expected (a value of around Mg would rather be expected). 10

11 Appendix 1 Discharge measurements obtained at SAC by means of the dilution gauging method Distance from injection (m) : 0 NaCl mass (g) : 450 Sum C(t) 1.78 Staff : Julien Némery, Clément Duvert Discharge (l/s) 5.0 Water level (cm) : /1/009 11:4 09/1/009 11:6 09/1/009 11:9 09/1/009 11:4 09/1/009 11:45 Distance from injection (m) : 55 NaCl mass (g) : 996 Sum C(t) Staff : Nicolas Gratiot, Clément Duvert Discharge (l/s) 6.81 Water level (cm) : /10/009 1:46 1/10/009 1:48 1/10/009 1:49 1/10/009 1:50 1/10/009 1:5 1/10/009 1:5 1/10/009 1:55 11

12 Distance from injection (m) : 100 NaCl mass (g) : 000 Sum C(t) Staff : Nicolas Gratiot, Clément Duvert Discharge (l/s) Water level (cm) : :41 0:4 0:44 0:45 0:47 0:48 Distance from injection (m) : 100 NaCl mass (g) : 000 Sum C(t) 0.85 Staff : Nicolas Gratiot, Clément Duvert Discharge (l/s) Water level (cm) : :40 01:4 01:4 01:45 01:46 01:48 1

13 Distance from injection (m) : 100 NaCl mass (g) : 115 Sum C(t) 1.5 Staff : Nicolas Gratiot, Clément Duvert Discharge (l/s) 54.6 Water level (cm) : :4 00:44 00:46 00:47 00:48 00:50 Distance from injection (m) : 100 NaCl mass (g) : 090 Sum C(t) 1.18 Staff : Nicolas Gratiot, Clément Duvert Discharge (l/s) Water level (cm) : :07 00:08 00:10 00:11 00:1 00:14 00:15 1

14 Distance from injection (m) : 100 NaCl mass (g) : 000 Sum C(t) 0.69 Staff : Nicolas Gratiot, Clément Duvert Discharge (l/s) 46.5 Water level (cm) : :48 1:50 1:51 1:5 1:54 1:56 1:57 Distance from injection (m) : 100 NaCl mass (g) : 000 Sum C(t) 0.51 Staff : Nicolas Gratiot, Clément Duvert Discharge (l/s) Water level (cm) : : 1:4 1:6 1:7 1:8 1:40 14