Environ Monit Assess (2015) 187:466 DOI 10.1007/s10661-015-4687-z

Development of a decision-making methodology to design a water quality monitoring network Jongho Keum & Jagath J. Kaluarachchi

Received: 11 November 2014 / Accepted: 9 June 2015 # Springer International Publishing Switzerland 2015

Abstract The number of water quality monitoring stations in the USA has decreased over the past few decades. Scarcity of observations can easily produce prediction uncertainty due to unreliable model calibration. An effective water quality monitoring network is important not only for model calibration and water quality prediction but also for resources management. Redundant or improperly located monitoring stations may cause increased monitoring costs without improvement to the understanding of water quality in watersheds. In this work, a decision-making methodology is proposed to design a water quality monitoring network by providing an adequate number of monitoring stations and their approximate locations at the eight-digit hydrologic unit codes (HUC8) scale. The proposed methodology is demonstrated for an example at the Upper Colorado River Basin (UCRB), where salinity is a serious concern. The level of monitoring redundancy or scarcity is defined by an index, station ratio (SR), which represents a monitoring density based on water quality load originated within a subbasin. By comparing the number of stations from a selected target SR with the available number of stations including the actual and the potential stations, the suggested number of stations in each subbasin was decided. If monitoring stations are primarily J. Keum (*) Department of Civil Engineering, McMaster University, Hamilton, Ontario L8S 4K1, Canada e-mail: [email protected] J. J. Kaluarachchi College of Engineering, Utah State University, Logan, UT 84322, USA

located in the low salinity loading subbasins, the average actual SR tends to increase, and vice versa. Results indicate that the spatial distribution of monitoring locations in 2011 is concentrated on low salinity loading subbasins, and therefore, additional monitoring is required for the high salinity loading subbasins. The proposed methodology shows that the SR is a simple and a practical indicator for monitoring density. Keywords Hydrometic network . Water quality . Monitoring . Station ratio

Introduction Hydrometry includes all aspects of water-related measurements providing information, such as water levels, shape and level of waterways, surface water and ground water discharge, water quality, etc. (Boiten 2000; Herschy 1999; Mishra and Coulibaly 2009). Since one measurement in a location cannot represent all the information of a large region, a hydrometric network, defined as a combined system of spatially distributed observations, is required. The primary purpose of gathering information from a hydrometric network is to conduct an appropriate analysis to answer specific questions (Moss 1979), where the ultimate goal is to support decision-making. Gathering more data may be often considered as the best strategy to improve hydrologic information, but in some cases, combining inadequate or redundant data can worsen the monitoring quality from a network (Davis et al. 1979; Langbein 1979). In

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addition, a hydrometric network requires capital and human resource investments for installation, maintenance, and operation of monitoring stations including sample collections. Therefore, within a limited financial budget and human capital, finding an optimal number and locations of monitoring stations is important to design an effective hydrometric network (Husain 1989; Moss 1979). The World Meteorological Organization (2008) categorized monitoring stations into principal, secondary, and special stations. The secondary stations are operated intermittently to establish stable measurements for complementary purposes. Special stations are installed only for cases where specific information is required. However, principal stations are the most important stations for analysis and should be maintained continuously. The principal stations define the minimum size of a hydrometric network. World Meteorological Organization (2008) recommended the minimum network densities of precipitation, evaporation, streamflow, sediment, and water quality for various physiographic regions. Therefore, it is recommended that analyses to find the optimum network should be applied only after the minimum network is satisfied (World Meteorological Organization 2008). There are numerous methods for the design of hydrometric networks. Mishra and Coulibaly (2009) summarized network design approaches, incorporating statistical analysis, spatial interpolation, entropy, optimization, basin physiographic characteristics, sampling strategies, etc. In general, hydrometric network design faces difficulties due to the lack of understanding of how to establish objective measures (Harmancioglu and Alpaslan 1992). In addition, most methods are applied to the networks for precipitation and streamflow observations and these methods are sometimes difficult to apply to water quality monitoring networks. For example, spatial interpolation is reasonable for precipitation, but it is not applicable to streamflow or water quality monitoring because of geographical effects. Strobl and Robillard (2008) provided a review of previous studies, which showed lack of a consistent methodology for water quality network design. Most statistical approaches have targeted the methods to reduce the errors from monitoring networks. Harmancioglu and Alpaslan (1992) applied an entropybased method to assess the existing water quality monitoring network and quantify the benefits from the enhanced network. Entropy in the network design addresses

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an uncertainty measure of hydrologic information and has been used to assess the efficiency and costeffectiveness of the existing network. Ammar et al. (2008, 2011) developed a methodology using a Bayesian framework with relevance vector machines to analyze a groundwater quality monitoring network. Strobl et al. (2006) developed a critical sampling point methodology to design water quality monitoring networks for small agricultural or forested watersheds by using a total phosphorus simulation model. Because the sources and transport of total phosphorus are closely related to the interactions between land use, topography, hydrology, vegetation, and soil, a normalized index, called the potential stream pollution index, was used to evaluate and prioritize target regions. Moss and Gilroy (1980) and Gilroy and Moss (1983) developed cost effective stream gauging strategies and applied these to the Lower Colorado River Basin. The objective was to allocate resources in order to reduce parameter uncertainties at monitoring stations, which is a function of visiting frequencies. Hence, the uncertainty is minimized by maximizing the number of samples from frequent visits. In order to manage salinity in the Colorado River Basin, a number of studies have been conducted. 'Spatially Referenced Regressions on Watershed Attributes (SPARROW) surface water quality model developed by Schwarz et al. (2006) was used to simulate salinity sources and transport in the Upper Colorado River Basin (UCRB) (Anning et al. 2007; Kenney and Buto 2012; Kenney et al. 2009, 2012; Keum and Kaluarachchi 2015). After the initial SPARROW salinity analysis in the western USA by Anning et al. (2007), Kenney et al. (2009) focused on the UCRB and simulated salinity for water year 1991, which was estimated as a hydrological normal year. Kenney and Buto (2012) and Kenney et al. (2012) extended the SPARROW salinity model for the salinity in the UCRB until 1998 but not any further due to the lack of evapotranspiration data. The recent work by Keum and Kaluarachchi (2015) extended SPAR ROW modeling to 2011, and they identified the need for better data collection method for improved model calibration and verification. The results also identified the increasing uncertainty due to the decreasing availability of the number of monitoring stations and corresponding data. The goal of this work is to develop a decision-making methodology for design of water quality monitoring networks to gather essential data effectively. For this purpose, spatially referenced salinity data in the UCRB

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will be used with the assistance of the water quality model SPARROW. The methodology will discuss the opportunities to identify the number and approximate locations of the monitoring stations; therefore, the redundancy and scarcity of the existing water quality monitoring network will be assessed. In addition, the relationship between the number of monitoring stations and the model uncertainty from the SPARROW will be estimated. The major contribution of this research is to provide a practical framework to estimate priorities for installing or maintaining monitoring stations, so that decision-makers can use these priorities to better use the available resources.

Methodology Description of salinity monitoring in the UCRB Monitoring networks in the USA have been shrinking significantly during the recent decades due to financial limitations (Kenney et al. 2009; Keum and Kaluarachchi 2015; US Geological Survey 1999). US Geological Survey (USGS) (1999) estimated that 33 to 43 % of funds for monitoring networks in the USA have been eliminated, and these budget reductions resulted in a significant loss of monitoring stations or fewer sampling visits. Figure 1 shows the decrease in the number of monitoring stations in the UCRB, where the total dissolved solids (TDS) concentration as a salinity measure was observed during the past two decades. There were 218 active stations in 1991; however, this number decreased 70 % to approximately 50 stations after 2006. This decreasing trend may increase calibration uncertainty (Keum and Kaluarachchi 2015). Figure 2 shows the active baseline monitoring stations, which represents currently active stations that observe both TDS and discharge (64 stations in 2011). Additional monitoring stations can be used from the existing unused stations to enhance the effectiveness of the existing water quality monitoring network. Detailed descriptions about these additional stations are given and discussed in the Scenario development section. The predicted TDS loads using SPARROW are also shown in Fig. 2. Station ratio World Meteorological Organization (2008) recommended a general guideline of minimum hydrometric

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network densities of precipitation, evaporation, streamflow, sediments, and water quality stations. In specific, the minimum densities are given by coverage area per station, such that water quality stations in mountains or interior plains, like the UCRB, should cover 20,000 or 37,500 km2 at most, respectively (World Meteorological Organization 2008). However, the areal density of monitoring stations is not always practical without meticulous studies regarding spatial distribution of the nonpoint sources. Application of the minimum density method by the WMO for the water quality network design may lead to install monitoring stations where there is no source of pollutants, while monitoring may be scarce in the highly impairing regions. Therefore, we are proposing a simple index between the number of monitoring stations and the water quality load rather than area. The index, called the station ratio (SR), is defined by SR ¼ N = M

ð1Þ

where N is the number of water quality monitoring stations within an area and M is the water quality load (units of mass per unit time) originated within the same area. SR is a number that can use any units of mass that are convenient to the users. In this work, million tons per year will be used to describe the TDS load such that the unit of SR is the number of monitoring stations per million tons of TDS per year. SR is more meaningful than the minimum density by the WMO for water quality monitoring, because mass, M, is the ultimate product of all of the water quality related parameters including areal effects. Scenario development Similar to most other studies related to the optimal monitoring locations, the methodology proposed in this work determines the reduction of monitoring from a given network status (Dymond 1982; Harmancioglu and Alpaslan 1992; Husain 1989; Mooley and Mohamed Ismail 1981; Spence et al. 2007). Considering the total drainage area of the UCRB is 280,000 km2, the network density from 64 active TDS monitoring stations in 2011 meets the WMO minimum density requirements. However, given the importance as a primary water resource in the western USA and the socioeconomic damages due to salinity in the UCRB, scenarios that increase the total number of monitoring stations are considered. There have been 1143 USGS

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Fig. 1 Annual changes of the number of TDS monitoring stations in the UCRB from 1991 to 2011

Fig. 2 Spatial distribution of monitoring stations and the predicted salinity loads in the UCRB in 2011

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water data sites in the UCRB, and 426 stations among the sites are located at or near the outlets of catchments delineated by the Enhanced River Reach File 2.0 (Nolan et al. 2003; US Geological Survey 2013). However, not all of the 426 stations have monitored both streamflow and TDS and some of them have been discontinued. Among the 426 stations, 169 stations are still active for monitoring streamflow. As mentioned earlier, only 64 stations are active for both streamflow and TDS observations. Therefore, this work proposes two scenarios for the potential monitoring stations. In scenario 1, the 169 stations, which are active streamflow stations, are considered as the potential TDS monitoring stations. In scenario 2, the 426 stations, which consist of inactive stations as well as active stations, are considered. Accordingly, these numbers are the maximum numbers of TDS monitoring stations for both scenarios. The locations of these potential stations for both scenarios are shown in Fig. 2. The potential stations are located primarily in the mountainous regions of Colorado and northeastern Utah, while only a few stations exist in the northern and southwestern regions of the UCRB.

Selection of monitoring stations If there is no limitation to add potential stations, the number of monitoring stations in each subbasin can be directly calculated by setting a target SR with a given budget. However, since the number of available potential stations may or may not be sufficient in each subbasin, the target SR is selected using trial-and-error such that the total number of monitoring stations becomes equal to the available number of stations within the given budget. For example, if there is a budget for ten additional stations, the target SR can be set to have ten more stations in the entire basin. Then, the SR calculation in each basin will spatially distribute where the additional stations should be located in order to be an effective network. Since the SR is formulated from the relationship between the number of monitoring stations and water quality load, the number of monitoring stations to be operated varies with changes in the target SR. Accordingly, NSR;i ¼ SRs  Mi

ð2Þ

where NSR,i is the number of monitoring stations corresponding to a target SR in subbasin i, SRs is the target SR of a scenario, and Mi is the water quality load originated

from the subbasin i (million tons of TDS per year in this study). This relationship is a transposition of Eq. (1), and represents the target number of monitoring stations with a given SR for a specific scenario. Then, the applicable number of monitoring stations can be estimated by comparing NSR,i with the total number of available active and potential monitoring stations.
 ð3Þ Ni ¼ min Nmax;i ; NSR;i where Ni is the suggested number of monitoring stations in subbasin i, and Nmax,i is the total number of available monitoring stations in subbasin i. The spatial distribution of the suggested number of monitoring stations consists of a set of Ni, which is calculated for each subbasin. Then, the monitoring redundancy or scarcity can be determined by comparing the suggested number of monitoring stations with the currently active network. Hydrologic units were introduced to identify watershed units for effective watershed managements (Seaber et al. 1987) and include watershed delineations, codes, and names. The hydrologic unit codes divided the USA successively into four levels of hierarchy: regions (two-digit codes), subregions (four-digit codes), accounting units (basins, six-digit codes), and cataloging units (subbasins, eight-digit codes). These levels extended to six levels by adding watersheds (ten-digit code) and subwatersheds (12digit code). The UCRB is equivalent to the HUC14-Upper Colorado Region, and consists of 59 subbasins. Considering that the range of the number of monitoring stations in the UCRB during the past two decades is from 38 to 218, subbasin scale is selected as the spatial group of monitoring. Therefore, the suggested number of monitoring stations is calculated within each subbasin.

Estimation of water quality loads in subbasins In order to apply the SR method to the water quality network design, estimation of the water quality load originated within each subbasin is essential. While the typical water quality models calculate in-stream water quality, the SPARROW water quality model is able to predict loads from catchments as well as in-stream loads. The SPARROW water quality model is a hybrid model that consists of statistical nonlinear least squares regression and spatially distributed deterministic parameters (Schwarz et al. 2006). The model parameters are divided into two categories: (1) source variables including point sources, and land areas that are occupied by water quality

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inducing parameters such as land cover and geology, and (2) landscape delivery variables that represent solute transport from the location of the pollutants released to the outlet of catchment. The governing equation of SPAR ROW is a mass balance, in which the load at the outlet of a catchment is equal to the sum of loads released within the catchment and loads delivered to the catchment from upstream catchments. Keum and Kaluarachchi (2015) calibrated the SPAR ROW model parameter coefficients to estimate the TDS in the UCRB using data from 1999 to 2011. In this study, the calibration results for the most recent year 2011, called SPARROW 2011 hereafter, were used to calculate the TDS loads of each subbasin in the UCRB (Table 1). The model parameters included the loads from saline springs and the areas of geologic units that were classified by lithology and yield classes as source parameters. Landscape delivery parameters are mostly based on the geomorphological and hydrological parameters such as precipitation, evapotranspiration, catchment elevation, soil thickness, soil characteristic code, and land cover. The SPARROW governing equation applied to model TDS in the UCRB was given by 0 Li ¼ @

X

1 L j Aδ i þ 0

j∈ J ðiÞ

NS X

S n;i αn exp

n¼1

MD X

!! ωn;m Dm;i θm

ð4Þ

m¼1

where Li is the TDS load leaving reach i (kg), L′j is the TDS load delivered from upstream reaches J(i) to the reach i (kg), δi is the fraction of delivered load due to diversions (dimensionless), Sn,i is the source n in reach i (kg or km2 depending on the type of source), αn is the coefficients of the source n, ωn,m is the indicator variable (which is 1 only if the landscape delivery parameter m is related to the source variable n and 0 if not), Dm,i is the landscape delivery parameter m in the reach i, and θm is the corresponding parameter coefficient for parameter m (Keum and Kaluarachchi 2015).

Results and discussions Station ratio The SR can be calculated in several ways. First, if we consider the SR in its entirety, the total loads from the entire basin and the total number of monitoring stations are used to calculate the SR (i.e., lumped SR). Considering that the total number of TDS monitoring stations was

64 and the TDS load at the outlet of the UCRB was 8.5 million tons per year in 2011 (Keum and Kaluarachchi 2015), the lumped SR was calculated at 7.5 using Eq. (1). On the other hand, the SR can be calculated for each subbasin (i.e., individual SR), and then the representative SR can be calculated by taking their average (i.e., average SR). Using the incremental TDS load and the number of monitoring stations in each subbasin, the SR ranged from 0 to 115 and the average SR was estimated at 14.7. The HUC 14070004, Dirty Devil subbasin has the largest individual SR of 115 from one TDS monitoring station and 8.7 thousand tons per year of the incremental TDS load. On the other hand, there are 24 subbasins that do not have any TDS monitoring stations and their SRs become zero. The difference between the lumped SR and the average SR indicates that the water quality monitoring network can be improved more effectively. The term effectiveness is used here to represent an equitable distribution in the context of similar SR values among subbasins, and then the spatial distribution of the monitoring stations will be similar to that of the TDS loads. If monitoring stations are excessively located in high TDS loading subbasins compared to the low TDS loading subbasins, the average SR tends to decrease, and vice versa. In other words, if the individual SRs of high loading subbasins are generally greater than the individual SRs of low loading subbasins, the average SR will be smaller than the lumped SR. The maximum number of monitoring stations for scenarios 1 and 2, including both active and potential stations, are 169 and 429, respectively. Therefore, the corresponding lumped and averaged SRs are 19.9 and 27.6 for scenario 1, and 50.1 and 68.2 for scenario 2, respectively. For both scenarios, the average SRs are greater than the lumped SRs, indicating that the potential monitoring stations of both scenarios are concentrated in the low TDS loading subbasins, similar to the spatial distribution of the active TDS monitoring stations in 2011. Figure 3 shows the distributions of the individual SRs and the lumped SR for the active TDS monitoring stations in 2011, and scenarios 1 and 2. The active and the potential stations were assumed to construct the monitoring networks for both scenarios 1 and 2. The results show that the medians of the individual SRs are similar to the lumped SRs, respectively. Therefore, higher average SRs were caused by the extreme values of the individual SRs, resulting in ineffective spatial distribution of monitoring stations throughout the UCRB.

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Table 1 Parameter coefficients of the SPARROW TDS model and the TDS load observed at the outlet of the UCRB Types Source variables

Landscape delivery variables

TDS load

Model parameters

Coefficients

Units

Point sources

0.22

Dimensionless

Crystalline and volcanic rocks

1086

1000 kg/km2

High-yield Cenozoic sedimentary rocks

16,517

1000 kg/km2

High-yield Mesozoic sedimentary rocks

4848

1000 kg/km2

Low-yield Mesozoic sedimentary rocks

7394

1000 kg/km2

High-yield Paleozoic and Precambrian sedimentary rocks

3425

1000 kg/km2

Low-yield Paleozoic and Precambrian sedimentary rocks

1303

1000 kg/km2

Irrigated sedimentary clastic Mesozoic lands

152,071

1000 kg/km2

Irrigated sedimentary clastic Tertiary lands

554,954

1000 kg/km2

Irrigated lands of other lithology

199,641

1000 kg/km2

Minimum catchment elevation

−0.0020

1/m

Mean catchment total precipitation

0.0628

year/cm

Mean catchment total precipitation, maximum catchment elevation ratio

−100

100 years

Mean catchment total evapotranspiration

0.0001

year/mm

Mean catchment cumulative thickness of soil

−0.07

1/in.

Mean catchment hydrologic soil characteristic code

−2.3

Dimensionless

Fraction of catchment area covered by forest

0.91

Dimensionless

Observed at the outlet of the UCRB

7.6

106 t/year

Note: Data from Keum and Kaluarachchi (2015)

Proposed monitoring stations Tables 2 and 3 show the proposed numbers of monitoring stations of the seven selected subbasins when the target SR was chosen as 25. The subbasins were selected from the top 1, 10, 20, 30, 40, 50, and 59 subbasins among 59 total subbasins according to the incremental TDS load from each subbasin. The target SR of 25 was arbitrarily selected for demonstration purposes and can Fig. 3 Distributions of the lumped SR and the individual SRs for the existing network in 2011 and the scenarios 1 and 2

be changed to other numbers according to the monitoring budget. Column 5 of Table 2 shows the required number of monitoring stations to satisfy the target SR using Eq. (2). The next column (column 6) shows the monitoring redundancies or deficits by calculating the differences between the required number from the target SR (column 5) and the number of active stations (column 3). A positive value suggests the number of potential stations that should be added to meet the target SR,

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Table 2 Sample calculations for the suggested number of monitoring stations using the scenario 1 and a target SR of 25 Subbasin (HUC8)

TDS Load in 2011 (t/year)

Number of monitoring stations Existing in 2011

Available under scenario 1

No. of stations required for target SR

Deficit or redundancy from target

Suggested number under scenario 1

14060003

687,564

5

7

17

12

7

14070006

232,175

1

1

6

5

1

14050003

166,062

0

1

4

4

1

14040102

110,891

0

2

3

3

2

14060008

56,222

1

1

1

0

1

14020003

27,266

1

3

1

0

1

14070004

8685

1

1

0

−1

1

In all cases, a minimum threshold of one station is maintained in each subbasin. The positive numbers represent deficit and negative represent redundancy

while a negative value indicates the redundant number of stations. Then, the proposed numbers of monitoring stations (column 7) were calculated using Eq. (3) by comparing the available and the required number of stations (columns 4 and 5). Among the seven selected subbasins, HUC 14060003, 14070006, 14050003, and 14040102 have an insufficient number of monitoring stations for the target SR, such that they require additional monitoring stations under scenario 1. The available stations under scenario 1 in HUC 14020003 is three while the required number is one; therefore, the number of stations in the subbasin does not have to be changed. In HUC 14060008, the required number of monitoring stations was estimated as one, while the number of active stations is also one. Therefore, it can be assumed that there is an adequate number of monitoring

stations in HUC 14060008 under scenario 1 with a target SR of 25. The required number of stations in HUC 14070004 using the target SR of 25 was calculated as zero because of the relatively low TDS loading. However, a minimum threshold of at least one station is maintained in each subbasin. Similarly, Table 3 describes the water quality monitoring network for scenario 2. The target SR of 25 was used in Table 3. Accordingly, the number of monitoring stations from the baseline condition of 2011 and from the target SR remained the same, but the available number of monitoring stations was increased under scenario 2. Because of sufficient availability, HUC 14050003 and 14040102 meet the requirement of the target SR while HUC 14060003 and 14070006 still need additional monitoring.

Table 3 Sample calculations for the proposed number of monitoring stations using the scenario 2 and a target SR of 25 Subbasin (HUC8) TDS load in Number of monitoring stations 2011 (t/year) Existing in 2011 Available under No. of stations Deficit or redundancy Suggested number scenario 2 required for target SR from target under scenario 2 14060003

687,564

5

16

17

12

14070006

232,175

1

2

6

5

16 2

14050003

166,062

0

11

4

4

4

14040102

110,891

0

4

3

3

3

14060008

56,222

1

1

1

0

1

14020003

27,266

1

5

1

0

1

14070004

8685

1

2

0

−1

1

In all cases, a minimum threshold of one station is maintained in each subbasin. The positive numbers represent deficit and negative represent redundancy

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The SR method was able to determine whether the monitoring network was scarce or redundant for the subbasin scale by comparing the TDS loads from the individual subbasins and the number of monitoring stations in the subbasins. Then, the results suggested that transferring the monitoring efforts from redundant subbasins to the scarce subbasins for an effective TDS monitoring network. The SR method is based on both water quality loads and the active and potential monitoring stations in subbasins, and therefore, it provides a consistent approach to allocate resources for a long-term monitoring network design.

scenario 1, HUC 14010005, Colorado HeadwatersPlateau, was the subbasin that required the highest number of additional stations for both target SRs of 25 and 50, which were 12 and 23 stations, respectively. The subbasin with the most number of redundant stations for scenario 2 was the same as scenario 1, which was HUC 14050006, White-Yampa, and the numbers of redundant stations were 3 and 2 for the target SRs of 25 and 50, respectively.

Spatial distributions of monitoring stations

Figure 5 shows the relationship between the target SR, the suggested number of monitoring stations from the target SR, and the average SR from the suggested network. The range of the target SR was selected by considering from the no-action to the maximum number of potential stations in each scenario. Then, the suggested numbers of monitoring stations were calculated for each arbitrarily selected target SR within the range. The average SRs were calculated from the suggested number of monitoring stations to see the differences between the target SR and the average SR from the suggested networks. In addition, points from the average SR and the number of monitoring stations from the existing TDS monitoring network in the UCRB in 2011 were added in each plot of Fig. 5. The curves in Fig. 5 can be considered as the effective distribution of the monitoring station using SR method. If too many monitoring stations are located in the low TDS loading subbasins and too few stations are located in the high TDS loading subbasins, the corresponding points in Fig. 5 will move below the curves of effective distribution. On the contrary, a water quality monitoring network that excessively focuses on high TDS loading subbasins makes the relationship to move above the curves of the effective distribution. In all plots in Fig. 5, the relationship points from the existing TDS monitoring network in 2011 were located below the curves of effective distribution, so the additional monitoring stations are recommended for the high TDS loading subbasins.

Figure 4 shows the spatial distributions of the differences between the suggested number of monitoring stations for both scenarios and the existing network in 2011, and the two target SRs of 25 and 50 were applied in each scenario, respectively. The numbers in Fig. 4 represent the redundant or scarce number of monitoring stations in subbasins. The subbasins colored blue required more monitoring stations and the corresponding number of required stations were indicated inside each subbasin. Numbers in red subbasins represent the number of redundant stations in each subbasin. White subbasins had the adequate number of monitoring stations. Using a target SR of 25 in scenario 1 (Fig. 4a), 28 subbasins required an additional 72 stations, while 7 subbasins had 10 redundant stations. By changing the target SR to 50, the suggested number of monitoring stations increased. Thirty subbasins required additional monitoring stations, and the total number of monitoring stations to be added was estimated at 95. The number of redundant stations decreased to 6 from 5 subbasins. The scarcity in HUC 14010001, Colorado Headwaters, was the highest, which required nine additional monitoring stations with a target SR of 25, or 14 additional monitoring stations with a target SR of 50. On the contrary, the redundancy was the highest in HUC 14050006, White-Yampa, where redundancies were 3 and 2 with target SRs of 25 and 50, respectively. Since scenario 2 considered approximately twoand-a-half times more potential stations than scenario 1, there was more opportunity to meet the given target SR. This feature of scenario 2 produced more scarcity for the same SR than in scenario 1. Contrary to

Changes of the number of monitoring stations and the target SR

Impacts of monitoring on water quality modeling This work was motivated by the decreasing trend of monitoring stations, which can affect model reliability. For example, the results from the SPARROW TDS

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ƒFig.

4 Spatial distributions of the suggested TDS monitoring network for the scenarios 1 and 2 with target SR values of 25 and 50: a scenario 1 with target SR of 25, b scenario 1 with target SR of 50, c scenario 2 with target SR of 25, and d scenario 2 with target SR of 50. The numbers inside subbasins indicate the numbers of monitoring stations to be added or reduced

model for the UCRB showed considerable uncertainty when the network density was low (Keum and Kaluarachchi 2015). Since the SR requires incremental TDS loads from subbasins and the loads were estimated using the SPARROW model, noise was added to the predicted loads to introduce model uncertainty. For the SPARROW 2011 model, the differences between the observed and predicted loads were close to a normal distribution. Therefore, the noise was calculated using the same statistical distribution with residuals of the SPARROW 2011 model. Then, the noise was added to the predicted TDS loads distribution of SPARROW 2011. Fifteen SPARROW model runs were conducted for each selected target SR and each scenario to determine

Fig. 5 Relationships between the target SR, the number of stations and the average SR

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model uncertainty. If the number of monitoring stations was suggested in a subbasin, then the monitoring stations were randomly selected for each model run. Figure 6 shows the SPARROW model statistics by changing the target SR for scenarios 1 and 2, and Table 4 gives the relationship between the target SR and the corresponding number of monitoring stations. The statistics, such as root mean square error (RMSE) and the coefficient of determination of TDS yield, also called Yield R2 (Eqs. 5 and 6, respectively, of Schwarz et al. (2006)), describe that the model uncertainty decreases with the increase of target SR and the number of monitoring stations. It should be noted that the Yield R2 is the R2 value of the logarithm of TDS yield by removing the strong correlation between source variables and drainage area.

RMSE ¼

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX 2 u ^ e t i∈I i N −K

ð5Þ

where RMSE is the dimensionless root mean square error, ê is the estimated residual in log space, N is the

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Fig. 6 The SPARROW simulation statistics from 15 runs for randomly selected monitoring stations with changing the target SRs: a, b Scenario 1; c, d scenario 2. The central lines are medians, the edges of the boxes are the 25th and 75th percentiles, and the whiskers are drawn with maximum whisker length of 1.5 to show the most extreme values that are not outliers

number of observations, and K is degrees of freedom. XN Yield R ¼ 1− X N n 2

i¼1

e2 i¼1 i

o2   f *i − f * − d i −d

ð6Þ

where ei is the residual at monitoring station i in log scale, N is the number of monitoring stations, f*i is the observed flux at monitoring station i in log scale, f * is the mean observed flux over N observations, di is the drainage area of monitoring station i in log scale, and d is the mean drainage area over N monitoring stations. In specific, if the target SR is 10, the range of RMSE between whiskers in Fig. 6 is greater than 0.1 and 0.15 for scenarios 1 and 2, respectively. However, the range of RMSE is around or less than 0.01 if the target SR is 150. The boxplots using the Yield R2 show similar patterns indicating the ranges are large with a limited number of monitoring stations and vice versa. As shown in Fig. 6, the ranges of statistical parameters noticeably change between SR of 25 and 50. Therefore, a minimum SR target of 25 is recommended for reliable SPARROW

TDS modeling in the UCRB using existing network in 2011. Consequently, it is shown that the existing network in 2011 from 64 active TDS monitoring stations in the UCRB produces a large statistical uncertainty. This observation suggested that the SPARROW 2011 model results could be made more reliable if monitoring stations were added in a manner similar to the proposed approach.

Table 4 Target SR and the corresponding total number of monitoring stations in the UCRB for scenarios 1 and 2 Target SR

Number of monitoring stations Scenario 1

Scenario 2

10

68

77

15

91

116

25

126

186

50

153

297

100

164

380

150

167

404

Environ Monit Assess (2015) 187:466

Summary Due to the financial and other management concerns, the number of active water quality monitoring stations in the USA has decreased significantly during the past few decades. This decreasing trend is a concern in modeling, forecasting, and management, because model uncertainty increases with limited observations. Therefore, developing an effective monitoring strategy is important for management purposes. In this work, a simple decision-making framework for design of an effective water quality monitoring network was developed. As a metric of effectiveness, the SR, which represents the relationship between the number of monitoring stations and the incremental water quality load produced within a hydrologic unit such as a subbasin, was proposed. If the total number of monitoring stations of a basin is set from the available resources, the number of monitoring stations in individual subbasins can be suggested using the proposed SR method. This proposed SR method was conducted to identify the adequacy of the existing water quality monitoring network and to propose the potential revisions for TDS monitoring in the UCRB at an 8-digit HUC scale. The results from the SR method demonstrated that the existing network in 2011 could be improved by establishing a denser network in high TDS loading subbasins, because the monitoring within those subbasins was typically scarce. More specifically, the scarcity was the highest in HUC 14010001, Colorado Headwaters, while the redundancy was the highest in HUC 14050006, White-Yampa. The uncertainty analysis about the SPARROW TDS model concluded that the existing network in 2011 required additional monitoring stations in order to reduce model uncertainty. The ranges of RMSE and R2 were considerable between the target SR values of 25 and 50. Therefore, it can be assumed that a target SR of no less than 25 is recommended for TDS monitoring in the UCRB. The proposed decision-making procedure is scalable to any other water quality monitoring network and provides the information required to allocate available resources to design an effective monitoring network. However, the procedure proposed in this research has limitations too. This work has focused exclusively on optimizing the monitoring network for the TDS in the UCRB. However, water quality interests in other watersheds or basins can be a combination of one or many water quality parameters, and can be dependent on site-specific

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conditions. Future works in this aspect need to be conducted to understand how multiple water quality parameters can be accommodated in the overall design of monitoring networks. In addition, this simple and pragmatic approach of developing a monitoring strategy is able to identify the monitoring needs at subbasin scale but the actual locations within subbasins cannot be specified. Additional analysis may be needed to identify the specific locations of these additional monitoring stations.

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