Baseflow separation in a small watershed in New Brunswick, Canada ...

HYDROLOGICAL PROCESSES Hydrol. Process. 27, 2659–2665 (2013) Published online 8 June 2012 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/hyp.9417

Baseflow separation in a small watershed in New Brunswick, Canada, using a recursive digital filter calibrated with the conductivity mass balance method Ruigang Zhang,1 Qiang Li,2 Thien Lien Chow,3 Sheng Li2,3* and Serban Danielescu3 1

3

Institute of Geographic Sciences and Nature Resources Research, Chinese Academy of Sciences, Datun Road, Chaoyang District Beijing 100101, China 2 Faculty of Forestry and Environmental Management, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada Potato Research Center, Agriculture and Agri-Food Canada, 850 Lincoln RD, PO Box 20280, Fredericton, New Brunswick, E3B 4Z7, Canada

Abstract: Baseflow separation is important for obtaining critical parameters for hydrological models. As measuring the baseflow component directly is difficult, various analytical and empirical baseflow separation methods have been developed and tested. The recursive digital filter (RDF) method is commonly used for baseflow separation due to its simplicity and low data requirement. However, parameters used in the RDF method are often determined arbitrarily, resulting in high uncertainty of the estimated baseflow rate. A more accurate method is the conductivity mass balance (CMB) method, which is established based on the differences in physical processes between baseflow and surface runoff. In this research, the output of the CMB method was used to calibrate the parameters of an RDF model, and the calibrated RDF model was used to estimate monthly, seasonal and annual baseflow rate and baseflow index for the past 19 years using streamflow discharge records. The characteristics of the baseflow hydrographs were found to be consistent with the hydrological and hydrogeological conditions of the research area. Research results indicated that the accuracy of the RDF model has been greatly enhanced after being calibrated with the CMB method so that the RDF model can provide more reliable baseflow separation results for a long-term study. Copyright © 2012 John Wiley & Sons, Ltd. KEY WORDS

baseflow separation; conductivity mass balance; recursive digital filter; parameter estimation

Received 8 November 2011; Accepted 20 April 2012

INTRODUCTION Separation of the baseflow component from total streamflow is critical for understanding the water budget in a watershed (Stewart et al., 2007). Baseflow separation is also required to estimate groundwater discharge in hydrological models and to accurately estimate long-term nutrient loading during water quality assessments (e.g. Yu and Schwartz, 1999; Muller et al., 2003; Schilling and Zhang, 2004; Tan et al., 2009). Many methods have been developed for baseflow separation, and great efforts have been made to improve the efficiency and accuracy of these methods (e.g. Nathan and McMahon, 1990; Nejadhashemi et al., 2003; Stewart et al., 2007). These baseflow separation methods can be generally grouped into three categories: analytical, empirical and mass balance (MB) methods. Analytical methods are normally constructed based on the fundamental theories of groundwater and surface water flows. Examples of such theories are the analytical solution of the Boussinesq equation, the unit hydrograph model and the theories for reservoir yields from aquifers (Boussinesq, 1877; Su, 1995; Nejadhashemi et al., 2003). Analytical

*Correspondence to: Sheng Li, Potato Research Centre, Agriculture and Agri-Food Canada, 850 Lincoln RD, PO Box 20280, Fredericton, New Brunswick E3B 4Z7, Canada. E-mail: [email protected] Copyright © 2012 John Wiley & Sons, Ltd.

methods can be easily implemented with computers, thus making the baseflow separation automatic. However, analytical methods are normally based on assumptions of ideal conditions that may not always be true (Halford and Mayer, 2000; Rutledge, 2005). In practice, empirical methods are probably the most widely used methods for baseflow separation. Empirical methods are normally developed based on calibration of a hypothetical model with field measurements or simply based on experience. Although mathematically simple, a high correlation between estimated and measured data for surface and subsurface flow can be achieved with empirical methods (Nejadhashemi et al., 2003). The low-pass filter methods (Stewart et al., 2007) and graphical methods are two main types of empirical methods. For example, the commonly used hydrograph separation program HYSEP (Sloto and Crouse, 1996) is built based on low-pass filter principles. The HYSEP program includes the choice of fixed-interval, sliding-interval and local minimum options for filtering. These methods generally use moving time windows to find successive discharge minima on a hydrograph and assume that baseflow can be derived by connecting lines between selected low-flow points on a streamflow hydrograph. Another type of the low-pass filter method is the recursive digital filter (RDF) method adapted from the signalprocessing theory (Nathan and McMahon, 1990; Chapman, 1999; Eckhardt, 2005). In the RDF method, surface runoff is

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considered to be high-frequency signals, whereas baseflow is considered to be low-frequency signals. By filtering out the high-frequency signals (surface runoff) from the streamflow, the low-frequency signals (baseflow) can be revealed (Nathan and McMahon, 1990). The filtering result is largely dependent on some watershed-specific parameters. These parameters can be calibrated based on measured data on baseflow. Unfortunately, measured data are rare, and in practice, these parameters are often determined arbitrarily (Nejadhashemi et al., 2003). There are some other filter methods developed based on the Boussinesq equation (Huyck et al., 2005) or the hillslope MB equations (Furey and Gupta, 2001). However, these filer methods are in fact semianalytical methods and require basin-specific parameters. These parameters are often difficult to obtain, and therefore, these semianalytical methods are rarely used (Stewart et al., 2007). The MB method is based on the assumption that baseflow normally has different chemical characteristics compared with surface runoff due to the different flow paths of these two types of flows. As a result, different flow components can be separated based on the constituent concentrations in the water. (Pinder and Jones, 1969; Cey et al., 1998; Stewart et al., 2007). In addition to discharge rate, the MB method requires constituent concentration data, which are not widely available, especially over a long period. This makes the application of the MB method in large basins impractical over a long period (Stewart et al., 2007). The need to collect and analyse water constituent concentrations also adds to the cost of the MB method (Nejadhashemi et al., 2003). One of the most popular MB methods is the conductivity mass balance (CMB) method. The conductivity (also termed specific conductance) of the streamflow water is a comprehensive index of the composite chemicals in the water. In general, conductivity of the baseflow water is substantially greater than that of the surface runoff water, and therefore, conductivity can be used as a natural indicator of the sources of the flows. The CMB method uses the conductivity measurements to quantify the sources of the flows and, therefore, separates baseflow from surface runoff at the watershed scale (Pilgrim et al., 1979; Matsubayashi et al., 1993; Stewart et al., 2007). Baseflow separation using the CMB method is considered to be objective because it is based on basin-specific physical processes. Because continuous measurement of streamflow conductivity is difficult, long-term conductivity records are not widely available. This limits the application of the CMB method for long periods. In summary, the RDF method only requires the stream discharge data as input and, therefore, is one of the most readily available methods for baseflow separation in longterm studies. However, the parameters for the RDF method are often subjectively determined, resulting in high uncertainties in the baseflow separation estimations. On the other hand, the CMB method is considered to be more objective because it is based on the direct measurements of streamflow conductivity. However, the data required for the CMB method may not be available for long periods. A linkage between the RDF and the CMB methods can be Copyright © 2012 John Wiley & Sons, Ltd.

established by using the baseflow data estimated with the CMB method to calibrate parameters for the RDF model. The calibrated RDF model can then be used for baseflow separation over a longer period when only discharge data are available. The objectives of this research were (1) to evaluate and compare the RDF and the CMB method for baseflow separation in a small agriculture dominant watershed; (2) to use baseflow estimated with the CMB method to calibrate the parameters used in the RDF model; (3) to use the calibrated RDF model for baseflow separation for a longer period; and (4) to validate the calibrated RDF model using other hydrogeological measurements.

METHODS Study site and data collection

The study is carried out in the Black Brook Watershed (BBW) located near the town of Grand Falls in northwest New Brunswick, Canada. The watershed covers an area of 14.5 km2, with 65% agricultural land, and the remainder of the watershed divided between forested areas (21%) and other land uses (i.e. residential, transportation, wetlands) (Chow et al., 2011). Elevation in the BBW ranges from 180 to 260 m above sea level. The primary hydrogeological unit is highly fractured limestone bedrock, which is overlain by a relative thin layer of glacial drift (Kierstead, 1993). The climate is considered to be humid cool boreal. Significant amounts of stream discharge and groundwater recharge are from snowmelt in the spring (Gallagher, 1997). A gauging station was established at the outlet of the BBW in 1992. There are 19 years of 1-h interval stream discharge data from 1992 to 2010. Stream discharge rate and conductivity of the stream water were continuously measured at 5-min intervals from 15 July to 25 November 2010. Groundwater levels were continuously measured at 1-h intervals in 5 piezometers (Pez7-11) established in the central part of the watershed. These raw data were averaged to daily values of stream discharge, conductivity and groundwater level to fit the needs of the baseflow separation carried out in this study. The RDF method

For the RDF method, we used the theoretical framework proposed by Eckhardt (2005), which was based on the assumption that the outflow from an aquifer is linearly proportional to its storage: BFt ¼

ð1 BFI max ÞaBFt 1 þ ð1 aÞBFI max Qt 1 aBFI max

(1)

Subject to BFt < Qt t ,where

BF t

the total baseflow (m3 day–1) the time step number (day) Hydrol. Process. 27, 2659–2665 (2013)

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the total streamflow (m3 day–1) the recession constant parameter (dimensionless), and BFImax the maximum value of the BFI (ratio of baseflow to total streamflow) that can be modelled by the algorithm (dimensionless). Two parameters, a and BFImax, need to be determined in Equation (1). Generally, the BFImax value influences the total baseflow amount, whereas the a value influences the shape of the baseflow hydrograph (e.g. steep versus gentle slope of the hydrograph). The value of a is often determined using a recession analysis (Rutledge, 1993, 1998; Eckhardt, 2005). In this study, two declining slopes associated with baseflow were identified on the recession curves following each surface runoff event. One declining slope (af) is associated with the fast groundwater flow in the shallow fractured zone, and the other declining slope (am) is associated with slow matrix groundwater flow (Figure 1). The values of the declining slopes were calculated using the RECESS method proposed by Rutledge (1993, 1998). As the RDF method only accounts for one recession constant parameter, an average recession constant parameter (aavg) was calculated by averaging am and af. The calculated baseflow is also sensitive to the parameter BFImax. However, BFImax cannot be measured directly. In practice, indirect method, such as using the results of tracer experiments, is recommended (Eckhardt, 2005). In this study, the initial value of BFImax used in the RDF method was set as the maximum BFI value determined using the CMB method, as will be described.

BF ¼ Q

Q a

The CMB method

In theory, surface runoff has lower conductivity than baseflow because baseflow water percolates through soil and bedrock and, therefore, accumulates higher concentrations of ions. Based on this principle, the baseflow fraction in the total streamflow can be calculated using an MB approach.

Copyright © 2012 John Wiley & Sons, Ltd.

(2)

where BF the total baseflow (m3 day–1) Q the total streamflow (m3 day–1) the conductivity of the streamflow (ms cm–1) Qc BFc the conductivity of the baseflow (ms cm–1), and ROc the conductivity of the surface runoff (ms cm–1). Parameters BFc and ROc can be directly measured in groundwater and surface runoff, respectively (Matsubayashi et al., 1993; Yu and Schwartz, 1999). In this study, the values of BFc and ROc were selected based on direct measurements using the method proposed by Stewart et al. (2007). BFc is considered to be the streamflow conductivity during the extreme low-flow periods when baseflow represents up to 100% of the total streamflow, whereas ROc is equivalent to the streamflow conductivity during the extreme high-flow periods when surface runoff makes up close to 100% of the total flow. The 5-min interval measurements of conductivity at the BBW outlet gauging station were used to determine the parameters BFc and ROc. Calibration of the RDF method with the CMB method

In the RDF method, the procedures used to determine the initial values of the two parameters (a and BFImax) described earlier were mostly empirical. More accurate estimates were expected once these two parameters were calibrated with results obtained from the CMB method. In this study, the calibration started from the initial values of a and BFImax. During the calibration, the BFImax value was adjusted first to minimize the difference in total baseflow amount between the RDF method and the CMB method. The a value was then adjusted for obtaining a better fit of the ‘shapes’ of the two hydrographs. By repeating these two steps, the two parameters were systematically adjusted to minimize the differences between the baseflow hydrographs produced by the RDF method and the CMB method. The root mean square difference (RMSD) was used to assess the relative difference between the two hydrographs. RMSD ¼

Figure 1. Recession curve and typical double declining slopes in Black Brook Watershed

Qc ROc BFc ROc

X 1 2 1 N RDF CMB 2 Q Q i i i¼1 N

(3)

where Qi RDF and Qi CMB are baseflow estimated by the RDF method and the CMB method, respectively. N is the number of daily data. The calibrated RDF model was used to estimate the baseflow rate and the BFI for the BBW over the period from 1992 to 2010. The results were aggregated into annual, seasonal and monthly data. Three seasons were defined in this study. The fall–winter season includes October to February, the spring season includes March to May, and the summer season includes June to September. Hydrol. Process. 27, 2659–2665 (2013)

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RESULTS The initial application of the RDF and the CMB methods

For the initial application of the RDF method, the recession constant associated with the fractured water recession af was 0.91, and recession constant associated with the matrix water recession am was 0.98. The average recession constant aavg was 0.95. For the CMB method, the baseflow conductivity (BFc) and surface runoff conductivity (ROc) were 0.57 and 0.20 mS cm–1, respectively. The average baseflow index (BFIavg) of the 4-month period was 0.62. For the calibration of the RDF method with the CMB method, the optimum values for a and BFImax were 0.85 and 0.64, respectively, when the RMSD between the two methods reached its lowest value (1457 m3 day–1) (Table I). As shown in Figure 2, high flow peaks of streamflow are always associated with low conductivity of the stream water. The RDF method, with recession constant estimated with the aavg, tended to underestimate baseflow at high flow periods and overestimate baseflow during low flow periods compared with the CMB method. Through calibration with the results from CMB model, baseflow estimated with digital filter method matched very well with baseflow estimated with the CMB method. Long-term assessment based on the calibrated RDF model

Based on the calibrated RDF model, annual average daily baseflow rate varied from 9190 m3 day–1 in 2002 to 22 040 m3day–1 in 2008 (Table II). The variation pattern of baseflow was found to be strongly correlated with the pattern of streamflow. Variation in annual average BFI was found to be relatively small. The lowest annual average BFI was 0.48, which occurred in 1994, and the highest value was 0.64, which occurred in 2004. The overall annual average BFI was 0.61, with a standard deviation of 0.04. Averaged over the years, baseflow rates were high during spring snowmelt period in March, April, and May and were low during summer months from June to September (Tables III and IV). Baseflow during the fall– winter months and the summer months only accounted for 30% and 16% of the annual baseflow, respectively, whereas baseflow during the spring snowmelt period contributed more than 54% towards the annual baseflow. Seasonal average BFI values did not vary very much (Table IV). The monthly BFI values of March and May were the lowest and the highest of the year, respectively, but both are in the spring season.

Figure 2. Stream water conductivity, streamflow daily discharge and baseflow rates separated by the conductivity mass balance (CMB) method and the recursive digital filter (RDF) method with different recession constant (a) values

DISCUSSION The implications of the baseflow and streamflow hydrographs

The baseflow separation results indicate that baseflow forms a large portion of the total streamflow (>60% in most years) in the BBW. As such, groundwater reservoirs should respond quickly during storm events. The shape of the baseflow hydrographs and the fact that more than half of the baseflow came from high flow spring season support this hypothesis. This assumption is also supported by the pattern of unconfined groundwater level fluctuation characteristics of piezometers located in the middle area of the BBW. As shown in Figure 3, dynamics of the hydrographs of streamflow and groundwater levels were quite similar. The rapid rise and fall of the groundwater table levels should be attributed to the high percolation capacities of the thin upper soil layer, the high hydraulic conductivity of the fractured aquifer, as well as the good connectivity between the groundwater system and the stream channels. The similar responses of groundwater table levels and streamflow to recharge events support the baseflow separation result in that the baseflow hydrograph closely follows the streamflow hydrograph, and baseflow is a significant component of the streamflow during the peak flow events. The baseflow and streamflow hydrographs (Figure 2) also showed that there is a daily surface runoff component during the entire research period. These phenomena have been explained by Spongberg (2000) from a signal analysis standpoint—the spectrum of direct runoff has a broad bandwidth with a non-zero low-frequency component. In our research, this observed response may also be related to the frequent rainfall events during the 4-month observation period.

Table I. Parameters for the recursive digital filter method estimated with the initial procedure and calibrated with the CMB method Method

a

BFImax

BFIavg

RMSD (m3 day–1)

RMSD/Streamflow

RECESS CMB

0.95 0.85

0.65 0.64

0.63 0.62

2930 1457

0.14 0.07


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Table II. Annual average daily rates of total streamflow, surface runoff and baseflow and annual average BFI measured or estimated for the Black Brook Watershed from 1992 to 2009 Year

Streamflow (m3 day–1)

Runoff (m3 day–1)

Baseflow (m3 day–1)

BFI

29 990 29 050 30 320 19 350 31 180 22 890 20 180 21 220 20 590 15 350 15 050 26 000 15 410 31 250 24 510 19 440 35 640 27 600 24 170 6073

11 500 13 010 15 870 7110 12 220 8510 7880 7850 7940 5910 5850 9680 5620 12 140 9060 7620 13 610 10 270 9540 2870

18 490 16 040 14 450 12 240 18 960 14 380 12 300 13 360 12 660 9450 9190 16 320 9790 19 110 15 450 11 820 22 040 17 330 14 630 3543

0.62 0.55 0.48 0.63 0.61 0.63 0.61 0.63 0.62 0.62 0.61 0.63 0.64 0.61 0.63 0.61 0.62 0.63 0.61 0.04

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Average Standard deviation

Table III. Monthly average daily rates of streamflow, runoff, baseflow, BFI and percentage of monthly baseflow to annual baseflow measured or estimated for the Black Brook Watershed from 1992 to 2010 Month January February March April May June July August September October November December Average Standard deviation


Surface runoff (m3 day–1)


Percentage of the whole year

BFI

24 840 17 930 41 960 157 180 48 650 19 510 17 710 15 680 11 920 22 750 35 240 32 150 37 130 39 435

9290 7270 19 270 70 790 11 790 6660 6230 5420 4500 9490 13 140 11 610 14 620 18 155

15 550 10 660 22 690 86 390 36 860 12 850 11 480 10 250 7420 13 260 22 100 20 550 22 500 21 654

5.76 3.95 8.40 31.99 13.65 4.76 4.25 3.80 2.75 4.91 8.18 7.61 — —

0.63 0.59 0.54 0.55 0.76 0.66 0.65 0.65 0.62 0.58 0.63 0.64 0.61 0.06

Table IV. Seasonal average daily rates of streamflow, surface runoff, baseflow, BFI and percentage of seasonal baseflow to annual baseflow measured or estimated for the Black Brook Watershed from 1992 to 2010

Seasons Fall–Winter (October–February) Spring (March–May) Summer (June–September)



Surface runoff (m3 day–1)


Percentage of the whole year

BFIavg

26 580 82 590 16 200

10 160 33 950 5700

16 420 48 650 10 500

30.41 54.04 15.56

0.62 0.59 0.65

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Figure 3. Comparison of hydrographs of streamflow rate at the outlet of the Black Brook Watershed and the groundwater table levels measured at 5 piezometers (Pez 7–11) located in the middle of the Black Brook Watershed

The impact of errors in conductivity estimations

In this study, the parameters for the CMB method were estimated based on the method proposed by Stewart et al. (2007), in which it was assumed that the baseflow conductivity is equal to the stream water conductivity during the period of the lowest flows, and the surface runoff conductivity is equal to the stream water conductivity during the period of the highest flows. In addition, both baseflow and runoff conductivities were assumed to be unchanged during the study period. However, these assumptions may not always be true because the hydrological and geological conditions vary with time and space. For example, there should always be a small amount of baseflow during the highest flow period. Therefore, estimated ROc should be higher than the true value of surface runoff conductivity. This may lead to an underestimation of the baseflow. Similarly, the determination of BFc may also have some errors. BFc was set as the highest conductivity value during the low flow period. The baseflow component could come from different pathways with different chemistry. Water constituting the lowest baseflow likely comes from the regional flow, which had a much longer flow path than the local baseflow. The regional flow could pick up more ions along the long flow path and thus has higher conductivity. Therefore, the BFc value estimated from the highest conductivity during the entire measurement period likely is higher than the average baseflow conductivity. This may also result in an underestimation of the baseflow. On the other hand, the inclusion of a small portion of surface runoff during the low flow period would underestimate BFc and leads to an overestimation of the baseflow. Moreover, because the conductivity was only recorded for 4 months, the calculated BFc according to the ‘lowest flow’ period may not be that for the lowest flow over a longer period of time, and this could lead to an underestimation of the ‘highest conductivity’ and thus an overestimation of the baseflow. The two potential errors would compensate each other to some degree. As Copyright © 2012 John Wiley & Sons, Ltd.

such, the potential error caused by BFc estimation was considered to be low. It has been found that BFIavg was fairly sensitive to BFc. For example, if BFc had been underestimated by 20% due to the inclusion of surface runoff components during the low flow period, BFIavg would have been overestimated by 26%. Overestimation of BFc, however, would have less impact on BFIavg compared with underestimation of the same parameter. On the other hand, BFIavg was not very sensitive to ROc. For example, if surface runoff conductivity were overestimated by 20% due to the inclusion of baseflow components during the highest flow period, BFIavg would have been underestimated only by 5%. These results are consistent with the result of Stewart et al. (2007), who determined that CMB-derived cumulative baseflow is not sensitive to errors associated with the estimation of ROc. Overall, our results indicate that the CMB-derived baseflow is much more sensitive to BFc than to ROc so that for accurate baseflow separation, BFc needs to be determined accurately.

CONCLUSION The value of the recession constant a estimated with the traditional recession curve analysis is higher than the value estimated with the CMB method. Without the CMB calibration, the RDF method tends to underestimate baseflow during high flow seasons and overestimate baseflow during low flow season. After proper calibration with the CMB model, the RDF method was able to produce more accurate baseflow separation results, as evidenced in the similarities between the estimated baseflow hydrograph and the field measured groundwater table levels. The application of the calibrated RDF model over a 19-year period using stream discharge records suggested that baseflow constitutes a large portion of the stream discharge, particularly during the period of spring snowmelt. Overall, our results indicate that it is feasible to use the CMB method with a short period of conductivity data to calibrate the parameters of the RDF model and then use the calibrated RDF model to estimate long-term annual, seasonal and monthly baseflow based on stream discharge records.

ACKNOWLEDGEMENTS

This study was funded by the Agriculture and Agri-Food Canada (AAFC) through the Watershed Evaluation of Beneficial Management Practices (WEBs) project, the 2009 MOE-AAFC PhD Research Program and the Watershed-Based Assessment of the Impacts of Intensive Potato Production on Nitrate Levels of Groundwater A-Base project. Special thanks are given to Dr Fan-Rui Meng from the University of New Brunswick for synthesizing the manuscript and Dr Yefang Jiang for his valuable comments during the research. Hydrol. Process. 27, 2659–2665 (2013)


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