Integrating Hydrograph Modeling with Real-Time Flow Monitoring To

Journal of Hydrology 393 (2010) 331–340

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Journal of Hydrology

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Integrating hydrograph modeling with real-time ﬂow monitoring to generate hydrograph-speciﬁc sampling schemes ⇑ Heather E. Gall a, Chad T. Jafvert a, , Byron Jenkinson b a School of Civil Engineering, Purdue University, 3145 Civil Engineering Building, West Lafayette, IN 47907, USA b Jenkinson Environmental, LLC, West Lafayette, IN 47906, USA article info abstract

Article history: Automated sample collection for water quality research and evaluation generally is performed by simple Received 17 July 2009 time-paced or flow-weighted sampling protocols. However, samples collected on strict time-paced or Received in revised form 10 June 2010 flow-weighted schemes may not adequately capture all elements of storm event hydrographs (i.e., rise, Accepted 30 August 2010 peak, and recession). This can result in inadequate information for calculating chemical mass flux over storm events. In this research, an algorithm was developed to guide automated sampling of hydrographs This manuscript was handled by Philippe Baveye, Editor-in-Chief based on storm-specific information. A key element of the new ‘‘hydrograph-specific sampling scheme” is the use of a hydrograph recession model for predicting the hydrograph recession curve, during which flow-paced intervals are calculated for scheduling the remaining samples. The algorithm was tested at Keywords: Real-time monitoring a tile drained Midwest agricultural site where real-time flow data were processed by a programmable Automated sampling datalogger that in turn activated an automated sampler at the appropriate sampling times to collect a Tile drain total of twenty samples during each storm event independent of the number of sequential hydrographs Hydrograph modeling generated. The utility of the algorithm was successfully tested with hydrograph data collected at both a Recession analysis tile drain and agricultural ditch, suggesting the potential for general applicability of the method. This sampling methodology is flexible in that the logic can be adapted for use with any hydrograph recession model; however, in this case a power law equation proved to be the most practical model. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction also include chemical constituents that occur in natural waters in different forms, whose sum is the desired result, such as Total Kjel- Even though water is an essential resource, many of the ways dahl Nitrogen (TKN) or total phosphorus (TP), and whose determi- that it is affected by human activities are not well understood. nation requires sample digestion at high temperature. While such According to Montgomery et al. (2007), one of the reasons for this measurements are technologically feasible via automated sam- is that water is treated generally in a fragmented way that sepa- pling and other instrumentation installed in the field, it remains rates groundwater from surface water, and water quality from much more convenient and less expensive to collect water samples quantity. However, due to recent advances in affordable technolo- in the field with automated samplers and return these samples to gies (i.e., dataloggers, sensors, wireless communication devices), the lab for processing and analysis, especially if samples are col- our ability to simultaneously monitor watersheds for both water lected at multiple locations. quantity and quality has improved tremendously and will continue To implement an integrated monitoring plan for surface waters, to improve over time. Yet, there are many important water quality sample collection or in situ sensing of constituents of interest parameters for which in situ monitoring remains unfeasible due to should be performed in parallel with other in situ measurements, current instrument/sensor limitations or costs. This list of pollu- with discharge (i.e., volumetric flow rate) being of critical impor- tants includes many pesticides, antibiotics, hormones, and other tance. This is because changes in discharge due to precipitation organic contaminants that occur at trace levels in water for which events can result in rapid changes in water quality parameters. existing technologies may require samples to be concentrated, ex- Additionally, the calculation of mass fluxes requires corresponding tracted, or filtered prior to analysis by conventional chromatogra- information on discharge and constituent concentrations. When an phy, mass spectral, or photometric methods. These contaminants in situ sensor is deployed, the frequency at which the sensor collects the data is limited only by the sensor’s scanning interval or

⇑ Corresponding author. Address: 550 Stadium Mall Drive West Lafayette, IN by power limitations during extended deployment. When water 47907, USA. Tel.: +1 765 494 2196; fax: +1 765 496 1107. samples are collected, the number of discrete or composite E-mail address: [email protected] (C.T. Jafvert). samples collected for analysis may be limited: (i) by the number

Nomenclature

a recession sample number ti time of peak ﬂow rate c model parameter TS total number of sample bottles (20)

EN–S coefﬁcient of efﬁciency tsample time when a sample is triggered during the hydro- n model parameter graph’s recession

Oi observed flow rate V cumulative flow volume before the recession curve Oavg average observed flow rate Vr predicted cumulative flow volume during the recession Pi predicted flow rate curve from time ti to tend Pavg average predicted flow rate Vro observed cumulative flow volume during the recession Q(t) flow rate curve from time ti to tend Q(tend) 5% of the peak flow rate Vs observed volume of flow under the recession curve di- Qo peak flow rate vided by the number of remaining samples (out of 20) R2 coefficient of determination at the beginning of the recession curve

RS number of remaining samples (out of 20) at the begin- Vsample equal cumulative flow volume that each recession sam- ning of the recession curve ple is predicted to represent S(t) storage s storage coefficient tend time at which the flow rate is 5% of the peak flow rate

of bottles that the automated sampler holds, especially when the et al., 2008; Green and Wang, 2008; Manzoni and Porporato, sampling location is remote or (ii) by the cost of processing and 2009; Royer et al., 2006; Vanni et al., 2001). With the increasing analyzing the samples (Harmel et al., 2006). The sampling method- interest in studying emerging contaminants (e.g., hormones, phar- ology therefore is critical to obtain results that are representative maceuticals, etc.) whose transport mechanisms are not yet well of the hydrological characteristics of the study site, while at the understood, there is a need to develop a sampling methodology same time minimizing the costs associated with remote sample that collects discrete samples over hydrographs in their entirety. collection and laboratory analysis. Although a variety of simple and complex sampling methodol- Because the use of traditional time-paced sample collection is ogies have been reported, to our knowledge no reported sampling often ineffective in capturing events of interest, many researchers methodology uses volumetric flow data measured in real-time as have implemented some form of a flow-based sampling strategy, input to a hydrograph model to generate hydrograph-specific sam- ultimately leading to samples that more accurately represent con- pling schemes. The main objective of this study was to develop stituent loads during these events and during periods of high flow such a strategy. The main advantage of this approach for any dis- (Abtew and Powell, 2004; King and Harmel, 2003; King et al., 2005; crete sampling location is that the flow recession portion of both Rekolainen et al., 1991; Richards and Holloway, 1987). This is par- small and large hydrographs can be sampled at different flow-pro- ticularly true for smaller watersheds that have hydrographs of rel- portional frequencies, such that sufficient sampling occurs over atively short durations. For example, Kjær et al. (2007) used a real- smaller hydrographs, and less frequent sampling occurs over larger time monitoring system to study water quality at an agricultural hydrographs, avoiding filling all sample bottles before the hydro- field treated with manure. A datalogger (Campbell Scientific, Inc. graph recession is complete. We have implemented this sampling CR10X) was programmed to calculate the volumetric flow rate at methodology in an agricultural tile drain and ditch to collect sam- the discharge point of a tile drain based on the water level within ples for analysis of hormones and nutrients. the tile drain measured with a pressure transducer. The datalogger Tile drains are commonly used in Midwestern US states to drain triggered an automated sampler (ISCO 6700) to collect 200 mL excess water from agricultural landscapes. They typically are ori- subsamples based on volumetric flow after every 1500 or 3000 L, ented parallel to each other, spaced 12–24 m apart, and installed depending on the season, with the lower trigger of 1500 L used approximately 1 m below ground surface, lowering the water table during the summer months. Results of this work showed that hor- more quickly to this depth. They range in diameter from 10 to mones, 17b-estradiol and estrone, leached from the manure and 70 cm (approximately 4–24 in.), with smaller tile drains emptying were observed in tile drain effluent up to 11 months after slurry into larger collector drains before discharged into nearby drainage application. ditches. Although tile drains are an asset for improving crop yields, To prevent the over or under prediction of loads for constituents they can have negative environmental consequences as they expe- whose concentrations decrease or increase, respectively, over dite the transport of water, nutrients, and other chemicals to larger storm events, there is a need to sample storm events appropriately receiving streams, leading to lower water quality and declines in (Vidon et al., 2009). However, there are problems associated with fish populations (Orlando et al., 2004). current sampling techniques. These issues are described exten- sively by Harmel et al. (2006) and are summarized here. The limited number of sample bottles in automated samplers (typically 2. Site and monitoring station description 24 bottles) makes capturing samples over the entire duration of hydrographs extremely difficult, and significant errors are intro- The study area is located approximately 15 km northwest of duced into load calculations when any part of a hydrograph is Lafayette, IN on land that is part of Purdue’s Animal Science Re- missed. Using composite samples allows for more samples to be search and Education Center (ASREC). At the site, approximately collected, but does not provide information about constituent 55 ha are drained by a network of over 50 connected tile drains dynamics during storm events, thereby inhibiting the study of to a monitoring station referred to as D1 (Fig. 1). At D1, the transport processes. This is a major drawback of employing com- 30.5 cm (1 ft) diameter tile drain is outfitted with two risers. A flow posite sampling, as the relationship between the hydrological cycle sensor and sampling tube were deployed through the upstream ri- and biogeochemical cycles are not yet well understood (Breuer ser, and a simple circular-segment shaped dam, 7 cm in height, H.E. Gall et al. / Journal of Hydrology 393 (2010) 331–340 333

2.1. Monitoring equipment

Monitoring station D1 was equipped with a Campbell Scientific, Inc. CR1000 datalogger, PS100 12 V battery with charge regulator, RF401 900 MHz radio and antennas, temperature probe, a Marsh–McBirney Flo-Tote 3 and Flo-Station, an ISCO 3700 automated sampler, one 12 V DC deep-cycle battery, two CDT solar pan- els (one 20 W and one 50 W), and one SunSaver 10L 12 V charge controller. The 20 W solar panel and PS100 battery powered the datalogger and radio. The 50 W solar panel and 12 V deep-cycle battery supplied power to the ISCO 3700 via the SunSaver charge controller. The CR1000 was programmed in CRBASIC to scan each sensor every second and store 15-min average values. Water level and velocity were determined with the Flo-Tote 3’s pressure transducer and electromagnetic sensor. Using the water level and velocity, the Flo-Station datalogger computed the average flow rate for the fif- teen minute time interval and transferred all data to the Campbell Sci. datalogger via three 4–20 mA outputs. The 4–20 mA outputs were connected to input ports on the CR1000 via 100 ohm resis- tors, to provide the CR1000 with potentials within its input range of 0–5 V. The CR1000 uses these inputs to calculate the corresponding velocity, water level, and flow rate. Although there is some redundancy in data storage in the field with the two dataloggers, this arrangement allows for true supervisory control and data acquisition (SCADA) through the Campbell Sci. datalogger. The automated sampler was programmed to collect a 1L discrete sample upon receiving a contact closure pulse through a Crydom D1D07 solid-state relay connected to a 5 V output port on the Fig. 1. Map of tile drain network monitored by station D1. CR1000 datalogger. was deployed through the downstream riser to create sufficient water depth for accurate flow measurement and sampling during 2.2. Remote access to field data periods of low flow. Water within the tile discharges to Marshall Ditch and eventually to the Wabash River, approximately 25 km To enable near real-time wireless access to the field data, the to the southwest. In Marshall Ditch, 12 species of fish have been radio at D1 transmitted to a receiving radio installed at ASREC’s identified, and the Wabash River is home to over 150 fish species. Aquaculture building, located 1.6 km to the southeast. The base Most of the 55 ha site is planted in agricultural crops of corn and station at the Aquaculture building also included an NL100 soybeans, with a portion of the nutrients delivered to the site Ethernet link (Campbell Sci., Inc.) programmed with a static IP ad- through application of solid cattle manure and manure lagoon dress, connected to an Ethernet port. This arrangement allowed for water through a center pivot irrigation system. access to the data via the Internet and enabled two-way wireless

(a) 50 W Solar Antenna 20 W Solar Panel Panel

900 MHz Charge Radio 12 V Battery/ Regulator Charge Regulator

12 V Deep CR1000 100 Ohm Marsh- Cycle Battery Datalogger Current McBirney Shunts Flo-Station

ISCO Temperature Flo-Tote Area- Sampler Probe Velocity Meter

(b) Wall 12 V Battery/ NL100 900 MHz Antenna Outlet Charge Regulator Network Link Radio

Ethernet Port

Fig. 2. Equipment schematics for (a) monitoring station D1 and (b) the base station. 334 H.E. Gall et al. / Journal of Hydrology 393 (2010) 331–340 communication to the CR1000 datalogger. Fig. 2 shows a schematic (h1) and n (unitless) are model parameters, often treated as con- of the equipment at the monitoring station D1 and the base station. stants independent of field conditions or storm event characteris- For our convenience, the data collected over the most recent 48 h tics. This equation assumes that when t > 0, inflow to the field is were reported automatically on a website that updated every zero (Tallaksen, 1995) and thus it is only applicable if rainfall is neg- 15 min. ligible after the onset of the regression curve. It should be noted that the parameters in Eq. (1) may change seasonally and due to changes in land use. During the spring and summer, the recession 3. Developing a storm-specific sampling scheme curve often is more steep due to increased evapotranspiration and lower baseflow (Tallaksen, 1995). Antecedent moisture conditions To efficiently utilize the 24-bottle capacity of the typical auto- and rainfall patterns also influence the recession curve. A more de- mated sampler over hydrographs of various magnitudes, the flow tailed review of seasonal variations in recession modeling is dis- data collected in real-time were used to generate storm-specific cussed in Tallaksen (1995). flow-weighted sampling regimes. Because the increase in flow rate during each rising hydrograph was rapid, exceedance of specific flow rates on the rising hydrograph were used to trigger sampling 3.2. Determining sample times during hydrograph recession events, as any flow-weighted sampling scheme may completely miss the ‘‘first flush” component or the entirety of the sharp rise. Assuming the site-specific coefficients n and c are known and Once the hydrograph peak was observed using a 10% decrease in that Qo is determined via on-site measurement, the total cumula- flow criterion, a simple hydrograph recession model was used to tive volume under the predicted recession curve, Vr, can be deter- determine the timing of the remaining sampling events such that mined by substituting Eq. (1) into Eq. (2) and integrating each sampling interval corresponded to an equal volume of flow Z tend under the predicted hydrograph recession curve. The hydro- V r ¼ QðtÞdt ð2Þ graph-specific sampling scheme was developed with the capability to of automatically resetting in order to sample storms with multiple where to (h) is the time at which the peak flow rate was observed peaks based on the number of sample bottles remaining. and tend is the time at which the hydrograph recession is complete. The maximum flow rate at monitoring station D1 was observed For convenience, tend was set to the value where Q(t) equals 5% of to be approximately 3000 L/min and although it changed season- the peak flow rate, Qo. As will be shown in the next section, the ally, base flow was generally less than 50 L/min. Therefore, flow exponent n was nearly constant and equal to 1.0 over the initial values of 50, 200, 400, 800, 1600, and 2400 L/min were chosen as six hydrographs observed at the study site, leading to the following trigger flow rates for the rising hydrograph to effectively capture solution to Eq. (2) upon integration the rise during small and large storm events. This ensured that no more than six samples were collected on any rising hydrograph. 1 V ¼ Q lnððc t Þþ1Þ ð3Þ During the rising hydrograph, consecutive 15-min average flow r o c end rates were compared. Upon a 10% decrease in the flow rate, independent of the value of the peak flow rate, the datalogger triggered where the value of tend is independent of the peak flow rate and an additional sample and recognized that the hydrograph peak had dependent only on the value of c, as the rearrangement of Eq. (4) passed and recession had begun. During periods of very high flow Qðt Þ¼0:05 Q ¼ Q ½1 þ c t 1 ð4Þ that caused the tile drain to flow full for some time, the program end o o end recognized the start of the hydrograph recession when the flow results in Eq. (5). rate was reduced to less than 2900 L/min. In either case, the same hydrograph model was used to trigger samples after the recogni- 1 0:05 1 tend ¼ ¼ 19 c ð5Þ tion of recession onset, as described below. 0:05 c To appropriately sample hydrographs with multiple peaks, code Substitution of Eq. (5) into Eq. (3) yields the following equation was added to the program to automatically reset the variables that for Vr trigger samples on the rising limb after a peak has been observed. Each time the program executed after a peak has been observed, lnð20Þ V r ¼ Q ð6Þ the program compared the current flow rate to the trigger flow c o rates and resets the trigger flow rate variables if the current flow To determine the sampling schedule over the hydrograph reces- rate was less than the trigger flow rate (50, 200, 400, 800, 1600, sion, the datalogger program subtracts the number of samples al- and 2400 L/min). By adding this logic to the program, the datalog- ready taken from the total number of sample bottles (TS=) 20 to ger successfully triggered samples at the appropriate flow rates on obtain a value for the total number of available sample bottles to the rising side of sequential hydrographs and then created an up- be filled over the recession curve (RS). Although the maximum bot- dated sampling schematic for the new hydrograph based on the tle capacity in most commercially available automated samplers is most recent peak flow rate and the new number of empty bottles 24, TS was set to 20 to provide flexibility in case another storm in the sampler. event generated another hydrograph before the sample bottles were replaced. The volume of tile drain discharge that each sample

3.1. Hydrograph recession model is calculated to represent, Vs, is equal to the total volume under the recession curve divided by the number of samples to be collected

Many hydrograph recession curves for streams, near-ﬁeld (=Vr/RS). The datalogger program then calculates the time after ditches, and tile drains have been shown to conform to the follow- the peak, tsample, that each remaining sample will be collected ing non-linear equation (Brutsaert and Nieber, 1977; Tallaksen, exp 2:996a 1 1995) t ¼ RS ð7Þ sample c n QðtÞ¼Q oð1 þ c tÞ ð1Þ where a is the recession sample number that increased by one each where t (h) is the time since the peak ﬂow rate was observed, Q(t) time a sample was taken during the recession and varied from 1 to

(L/min) is the ﬂow rate at t, Qo is the peak ﬂow rate at t = 0, and c RS. The derivation of Eq. (7) is given in Appendix A. H.E. Gall et al. / Journal of Hydrology 393 (2010) 331–340 335

4. Model calibration Table 2 Coefﬁcients of determination and efﬁciency for the six hydrograph recessions.

4.1. Model parameters Event 123456 R2 0.90 0.94 0.98 0.98 0.97 0.92

The recession curve model (Eq. (1) was calibrated with six hyd- EN–S 0.25 0.65 0.76 0.89 0.93 0.54 rograph recessions observed at monitoring station D1. The values of the model parameters, c and n, were obtained by minimizing the sum of the squared residuals between the observed and pre- hi dicted flow rates. The optimum values for c and n for each of the P 2 N events are given in Table 1. Because the average value of n was i¼1ðOi Oavg ÞðPi PavgÞ R2 ¼ hiP hiP ð9Þ 1.04, it is set to 1.00 in all further calculations as mentioned N 2 N 2 ðO O Þ ðP P Þ above. Fig. 3 shows a comparison of the observed hydrograph i¼1 i avg i¼1 i avg recessions to the predicted recessions using the best-fit values of hiP c given in Table 1 and where n = 1. Events 1–3 and 5 each expe- N ðO P Þ2 hii¼1 i i rienced some additional rainfall during the hydrograph recession. ENS ¼ 1:0 P ð10Þ N 2 In each case, the additional precipitation was insufficient to initiate i¼1ðOi OavgÞ an increase in flow, which is consistent with the model’s assumptions. Substituting the average value of c (=0.193 h1) into Eq. (6), where Oi and Pi are the observed and predicted flow rates, and Oavg and P are the average observed and predicted flow rates, respec- the value of Vr at monitoring station D1 was calculated as avg tively. These coefficients have been used in various studies to com- V r ¼ 15:5 Q o ð8Þ pare predicted and observed hydrographs (Arabi et al., 2006; Kalin 1 Similarly, substituting the average value of c into Eq. (5) results et al., 2003). With the average values of c (=0.193 h ) and n (=1), Eq. (1) successfully predicted the hydrograph recessions as indi- in a value of tend equal to 4.1 days. 2 Using the average values of c and n, the coefficient of determi- cated by the high R values for each event (Table 2). These values 2 are high despite the differences between the predicted and ob- nation, R , and the coefficient of efficiency, EN–S, for each of the events’ recessions were calculated as (Arabi et al., 2006) served hydrographs because the coefficient of determination, using Eq. (9), calculates average discrepancies throughout the hydro-

graph. However, the values of EN–S are low for Events 1, 2, and 6, Table 1 indicating that the model is less successful at predicting the hydro- Site D1 best-fit model parameters. graph recessions for these events, even though they have high val- 2 Event c (h1) n ues of R . The value of EN–S can be improved by using storm-specific values of c to predict the hydrograph recession. Indeed, when using 1 0.072 1.00 2 0.097 1.00 the best-fit c values to predict the hydrograph recessions, each va- 3 0.101 1.00 lue of EN–S is greater than 0.97. 4 0.225 1.15 5 0.265 1.00 6 0.400 1.07 4.2. Sampling times Average 0.193 1.04 We applied the sampling logic described above to the complete hydrographs that correspond to the recession curves shown in Fig. 3. These hydrographs were generated by storm events that 3500 occurred from May to July 2008, and these six events include (a) 3000 Observed Recessions three that experienced full pipe flow. Fig. 4 shows the observed hydrographs, predicted hydrograph recessions (n = 1 Event 1 - Predicted 2500 and c = 0.193 h1), and the calculated sampling times as they cor- Event 2 - Predicted 2000 respond to the actual hydrographs. Table 3 provides a statistical Event 4 - Predicted summary for each of the six events’ recessions, from the time of 1500 the hydrograph peak, to,totend. The error on Q(t) was calculated 1000 at each sampling time, with the reported error being the average

Flowrate [L/min] percent error of the absolute values. The percent error on V was 500 r calculate from to to tend (calculated with the model) with the actual 0 sample volume determined using the trapezoidal rule with 0 10203040506070 Dt = 15 min. The error on Vs is the average absolute percent differ- ence between the volume of tile drain discharge (L) that each sam- 3000 ple should have represented based on the measured hydrograph (b) Observed Recessions 2500 and the actual volume of discharge that occurred between all sam- 2000 Event 3 - Predicted pling events. The errors presented in this table indicate that Event 5 - Predicted although the recession curve model often poorly predicts Q(t), 1500 Event 6 - Predicted especially as the flow recedes, the average error on Vs is generally 1000 less than 20% indicating that the model does reasonably well in 500 generating hydrograph-specific flow-weighted sampling schemes. Flowrate [L/min] Further, because constituent mass fluxes over the hydrographs 0 0 10203040506070 are determined ultimately from the measured values of flow and Time After Recession Began [hr] constituent concentration (sampled at relative flow-proportional time intervals), the magnitudes of the errors reported in Table 3 Fig. 3. Observed and predicted hydrographs for events that caused the pipe to (a) will have very little effect on the measured constituent mass flow full and (b) not flow full, with n = 1 and best-fit values of c. fluxes. 336 H.E. Gall et al. / Journal of Hydrology 393 (2010) 331–340

5000 0 4000 0 Event 1 Event 4

4000 Hyetograph 3000 Hydrograph 1 1 3000 Program Sample Times 2000 2000 Predicted Recession 2 2 1000 1000

0 3 0 3 0 20406080100 0 20406080100

5000 0 1000 0 Event 2 Event 5 4000 800 1 1 3000 600

2000 400 2 2

Flowrate (L/min) 1000 200 Rainfall (cm) 0 3 0 3 0 102030405060708090100 0 20406080100

3000 0 2000 0 Event 3 Event 6 2500 1500 2000 1 1 1500 1000 1000 2 2 500 500 0 3 0 3 0 20406080100 0 20406080100 Time After Rainfall Event Began (hr) Time After Rainfall Event Began (hr)

Fig. 4. Observed and predicted hydrographs and corresponding sample times for Events 1–6 using the average value of c given in Table 1 and n = 1.

Table 3 Events 7–10 show the ability of the hydrograph-speciﬁc sam- Average errors between measured and model calculated pling scheme to work successfully independent of season. Event 1 (c = 0.193 h ) values over the hydrograph recession curves. 7 provides an example of a small hydrographs that would have

Event Q(t) (%) Vr (%) Vs (%) tend been missed in its entirety even with conventional flow-paced 1 50.4 78.7 21.5 NAa sampling; however, it is sampled in its entirety with the hydro- 2 27.7 51.9 16.2 NA graph-specific methodology. Although it can be argued that miss- 3 36.5 36.5 14.0 NA ing small events may not introduce significant error when 4 59.2 36.6 17.2 82.7% calculating annual loads, the event occurred within a week after 5 19.7 19.1 9.1 24.6% the application of manure to fields in the drainage area. To study 6 119.1 45.3 16.6 124.9% the fate and transport of manure-borne constituents (e.g., hor- a NA indicates that a new hydrograph occurred before the flow mones, antibiotics, and nutrients), it is important to capture sam- rate decayed to 5% of the peak flow rate. ples over the first storm event after treatment, regardless of its magnitude. During Event 8, 13 samples were collected, with five on the rise and eight during the recession. Conventional sampling would have resulted in completely missing the rise. Events 9 and 5. Results and discussion 10 provide examples of the program’s ability to capture events with multiple peaks, regardless of magnitude. Samples were col- 5.1. Field implementation at monitoring station D1 lected over each recession using an updated value of RS and contin- ued to be collected until the next trigger flowrate was exceeded. A After training the model with the initial data collected at D1, we total of three and four peaks were observed during Events 9 and 10, programmed the datalogger to trigger sample collection every ten respectively, demonstrating the sensitivity of the program to suc- hours during baseflow and to activate the sampling logic described cessfully identify and capture multiple peaks. For each of these above at the designated change in baseflow. Fig. 5 shows the re- four events, samples representing 0%, 54%, 70%, and 92% of the to- sults of this programming logic implemented in real-time in the tal flow, respectively, would have been collected using the mini- field during several rainfall events in 2009. For comparison, sam- mum recommended conventional flow-paced sampling interval. ples that would have been collected if a conventional flow-paced The water samples collected during Events 8 and 9 were ana- methodology (1 mm depth of volumetric flow) had been invoked lyzed for nitrate + nitrite (N) and orthophosphate (P) using USEPA also are indicated in the figure. Methods 353.2 and 365.1, respectively, in order to compare the H.E. Gall et al. / Journal of Hydrology 393 (2010) 331–340 337

Event 7 Event 8

Hydrograph

Program Sample Times Traditional Sample Times

Event 9 Event 10 Flowrate (L/min)

Date

Fig. 5. Observed hydrographs and corresponding actual sampling times for Events 7–10.

Event 8 Event 9 Nitrate+Nitrite-N (mg-N/L) Flowrate (L/min) Orthophosphate-P (mg-P/L)

Date

Fig. 6. Nutrient and flow data for Events 8 and 9, with open circles representing actual nutrient concentrations for samples collected via the hydrograph-specific sampling scheme and closed circles representing nutrient concentrations estimated for traditional flow-paced samples. loads calculated for these events using the hydrograph-specific the conventional sampling methodology were 57% and 46% of sampling scheme to conventional flow-paced sampling. Fig. 6 the loads calculated from the hydrograph-specific sampling meth- shows the N and P chemographs and the hydrographs for each odology. For Event 9, conventional sampling encompassed 69% of event, with observed nutrient concentrations shown as open cir- the observed flow and 76% and 42% of the N and P loads calculated cles and concentrations estimated for the conventional samples from the hydrograph-specific sampling scheme. shown as closed circles. Loads were calculated by estimating the The utility of the hydrograph-specific scheme is evident when area (i.e., constituent mass) under the flux curves generated as a the concentrations of interest change significantly over the hydro- result of the hydrograph-specific and conventional sampling meth- graph. Such constituents include dissolved organic carbon and odologies. Conventional sampling encompassed 54% of the flow orthophosphate, whose chemographs generally trend with hydro- observed during Event 8 and the N and P loads estimated from graphs, and constituents typically associated with ground water 338 H.E. Gall et al. / Journal of Hydrology 393 (2010) 331–340

(e.g., magnesium), whose chemographs generally demonstrate in- power law decay function. To further examine the factors that verse relationships with hydrographs. This sampling methodology influence the value of c, the best-fit values of c given in Table 1 likely does not significantly improve load estimations for nitrate, were plotted as a function of the cumulative flow volume before whose concentrations generally remain more constant over hydro- the recession, V (L), and the peak flow rate, Qo (L/min). The results, graphs than most other constituents. Additionally, this sampling as shown in Fig. 7, indicate that the value of c for site D1 is inde- scheme may prove useful for studying contaminants of emerging pendent of the peak flow rate, Qo; however, it is dependent on concern (e.g., hormones, antibiotics, etc.) whose transport pro- the cumulative volume before the recession, V (m3) cesses are not yet well understood. c ¼ 0:08 þ 0:32 e0:00075V ð11Þ

5.2. Prospective application to monitoring Station S1 It is clear that Eq. (1) will vary between sites with different hydrogeological conditions and land uses. Our study site focused To assess the feasibility of applying the recession curve model on tile drained agricultural fields. These hydrographs tend to be and sampling logic to other sites, including agricultural ditches, ‘‘flashy” with sharp peaks and long tails, as the drains continue five hydrographs from a monitoring station located directly on to export water in the first meter of soil that would otherwise re- Marshall Ditch, designated as S1, were chosen for analysis. The cri- main in the soil profile. The tile drains do not capture any surface terion used to select these hydrographs was that no significant runoff, and therefore there is a maximum volume of water defined rainfall occurred during the recession, to be consistent with the by saturated soil conditions that can be observed once rainfall assumptions in the model’s development. Flow was continuously stops. These factors lead to a strong relationship between V and monitored at Station S1 with a 120° V-notch weir, stilling well, c. Study sites with natural drainage will likely need to include sur- and float and shaft-encoded system. Results from this analysis face runoff into an equation that defines c and are likely to observe are given in Table 4. a stronger relationship between c, antecedent moisture conditions, Similar to Site D1, the value of n at Site S1 was approximately and rainfall amounts than was observed in this study. 1, and the flow rate decreases with time at a similar rate for both the stream and drain hydrographs, with the average value of c for 5.4. Guide for adopting a storm-specific sampling regime both within 20% of each other. This may be expected as site S1 is influenced greatly by several large tile drains; however, it also Before this sampling methodology can be applied successfully experiences significant overland flow after high rainfall events. at additional study sites, it is necessary to have historic data available from which to choose flow rates appropriate for capturing samples on the rising side of the hydrograph and to calibrate an 5.3. Discussion of model parameters appropriate hydrograph recession model. Tallaksen (1995) provides a thorough review of various hydrograph recession models Eq. (1) was derived from a non-linear storage-discharge rela- from which a model can be chosen and calibrated. A numerical tionship, where n is the parameter of non-linearity (Brutsaert or analytical solution for the hydrograph recession model must and Nieber, 1977; Tallaksen, 1995; Wittenberg, 1999). The model then be developed to calculate Vr. This solution can then be pro- calibration resulted in a value of n 1, indicating a non-tradi- grammed directly into a programmable datalogger. The datalogger tional relationship between storage and discharge. The application program needs to contain a counter to keep track of the number of of Eq. (1) to tile drains implicitly assumes that the flow is not re- bottles remaining in the sampler. When samples are collected stricted by the tile drain, as its origin is for modeling reservoir out- from the field, this number needs to be reset in the program. The flow (Tallaksen, 1995). Khan and Rushton (1996) observed that the rate at which the water table falls depends on the maximum flow capacity of the tile drains, and that tile drains can greatly restrict (a) 0.5 this rate when they are flowing full. At this particular site, the main tile drain runs full frequently and can remain full for over 20 h, as 0.4 Best-fit c values shown in Fig. 4 during Events 1 and 2. It is likely that even when ) 0.3 the main tile drain is not full, many smaller tile drains are full, -1 Equation 11 leading to recession flow rates that do not follow the typical stor- 0.2 age-discharge model. The same non-traditional relationship be- c (hr tween storage and discharge also was observed at Site S1, as 0.1 Marshall Ditch is an agricultural ditch whose major source waters are large tile drain networks. Wittenberg (1999) characterized the 0 0 2,000 4,000 6,000 storage-discharge relationship for 80 gauging stations in Germany, 3 and found that two stations exhibited recession curves similar to Volume Before Recession, V (m ) those observed here. Some researchers (Cheng, 2008; Wittenberg, 1999) have de- (b) 0.5 fined c as a function of the peak flow rate, consistent with a general 0.4 )

-1 0.3 Table 4 0.2 Site S1 best-fit model parameters. c (hr 0.1 Event c (h1) n 0 1 0.111 1.018 0 1,000 2,000 3,000 4,000 2 0.331 1.007 3 0.289 1.314 Peak flowrate, Qo (L/min) 4 0.215 1.126 5 0.227 0.931 Fig. 7. Best-fit values of c when n = 1 for each event, plotted as a function of (a) Average 0.234 1.079 the cumulative flow volume before the hydrograph recession and (b) the peak flowrate. H.E. Gall et al. / Journal of Hydrology 393 (2010) 331–340 339 resetting of this sample number variable may be an issue if the Appendix A datalogger does not allow for manual resetting of the variables without resending the program. The value of the cumulative volume on the recession curve that is predicted to accumulate prior to triggering each sampling event can be calculated by dividing the volume of recession flow that 6. Conclusions accumulates before the recession sample is taken by the number of recession samples that have already been taken. The time after

This paper presents sampling scheme logic that uses real-time the peak, tsample, that each remaining sample is triggered can be cal- flow data for generating storm-specific sampling schemes for the culated as recession portion of storm events and that is easily encoded into R t¼t sample 1 programmable dataloggers. The code employs fixed flow intervals t t 0 QðtÞdt Q lnðc tsample þ 1Þ V ¼ ¼ i¼ ¼ o c ðA1Þ for triggering sample collection on the rising hydrograph, and a sample a a power law model (Brutsaert and Nieber, 1977; Tallaksen, 1995) where a is the recession sample number, t is the time at to calculate the times at which samples are triggered on the hyd- sample which recession sample a is triggered by the datalogger, Q is rograph’s recession curve. Regarding the two parameters within o the peak flow rate, and c is the model parameter. Solving Eq. the power law model, n was found to be constant over all storm (A1) for tsample gives events examined, whereas c was found to be dependent on the cumulative volume of flow prior to recession. As a result, using aVsamplec exp 1 the average value of c generally decreased the accuracy of the Qo tsample ¼ ðA2Þ predicted recession curves; however, this did not lead to signifi- c cant errors in the flow-weighted scheduling of sampling events. The predicted value of Vsample can also be calculated as Indeed, over- and under-predicting the recession curves still 1 resulted in nearly equal flow weighted samples over individual V r Q o c lnðc tend þ 1Þ V sample ¼ ¼ ðA3Þ hydrographs. RS RS A limitation of the simple regression curve model stems from where Vr is the predicted recession cumulative flow volume, RS is the assumption in its development that all rainfall ends before the number of remaining samples at the beginning of the reces- recession begins. For those storm events examined herein, this sion curve, and tend is the time after the peak at which the flow assumption did not appear to be an issue; however some simple rate is 5% of the peak flow rate. Substituting Eq. (A3) into modifications to the code may circumvent this limitation, as addi- Eq. (A2) gives tional input (rain) could be used to empirically increase time steps between sampling events. Indeed, at Site S1, precipitation was a½lnðctendþ1Þ exp RS 1 measured with a tipping bucket rain gauge, with the number of tsample ¼ ðA4Þ tips recorded by the same datalogger that monitors flow and that c triggered the sampler. Although the same basic logic may be suit- Eq. (A4) can be reduced further by substitution of Eq. (5) for tend. able for sampling the outflow of larger watersheds, recession Eq. (A4) then reduces to curves of larger watersheds tend to exhibit exponential decay rather than power law decay, necessitating use of an alternative exp 2:996a 1 t ¼ RS ðA5Þ recession curve algorithm. The proposed hydrograph recession sample c methodology may have limited applicability during snow-melt generated hydrographs and therefore it may be necessary to References change the model parameters seasonally or adopt a different hydrograph recession model during winter months; however in gen- Abtew, W., Powell, B., 2004. Water quality sampling schemes for variable-flow eral we found that the hydrographs were captured well canals at remote sites. J. Am. Water Resour. Assoc. 40 (5), 1197–1204. regardless of season, as is shown in Fig. 5. Independent of wa- Arabi, M., Stillman, J.S., Govindaraju, R.S., 2006. A process-based transfer tershed size, the hydrograph-specific sampling scheme presented function approach to model tile-drain hydrographs. Hydrol. 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Practical We would like to thank the EPA for funding this research under guidance for discharge and water quality data collection on small watersheds. Trans. ASABE 49 (4), 937–948. the Science to Achieve Results (STAR) Program grant number Kalin, L., Govindaraju, R.S., Hantush, M.M., 2003. Effect of geomorphologic RD833417. We also would like to extend our gratitude to the appli- resolution on modeling of runoff hydrograph and sedimentograph over small cation engineers at Campbell Scientific, Inc., especially Robert watersheds. J. Hydrol. 276, 89–111. Hyatt and Blake Farnsworth, for their valuable help and advice Khan, S., Rushton, K.R., 1996. Reappraisal of flow to tile drains III. Drains with limited flow capacity. J. Hydrol. 183, 383–395. regarding their company’s equipment; to Douglas Magers at Pur- King, K.W., Harmel, R.D., 2003. Considerations in selecting a water quality sampling due University, who was instrumental in establishing an Internet strategy. Trans. ASAE 47 (5), 1457–1463. connection at our base station; to Steven Smith and Jeffery Fields King, K.W., Harmel, R.D., Fausey, N.R., 2005. Development and sensitivity of a method to select time- and flow-paced storm event sampling intervals. J. Soil at Purdue’s Animal Science Research and Education Center for ac- Water Conserv. 60 (6), 323–331. cess to tile drain maps and the manure application database; and Kjær, J., Olsen, P., Bach, K., Barlebo, H.C., Ingerslev, F., Hansen, M., Sørensen, B.H., to Linda Lee at Purdue University. Additional thanks are extended 2007. Leaching of estrogenic hormones from manure-treated structured soils. Environ. Sci. Technol. 41 (11), 3911–3917. to three anonymous reviewers, whose comments and suggestions Manzoni, S., Porporato, A., 2009. Soil carbon and nitrogen mineralization: theory greatly improved this manuscript. and models across scales. Soil Biol. Biochem. 41, 1355–1379. 340 H.E. Gall et al. / Journal of Hydrology 393 (2010) 331–340

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