Regional regression models for estimating monthly streamflows

STOTEN-135729; No of Pages 11 Science of the Total Environment xxx (xxxx) xxx

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Science of the Total Environment journal homepage: www.elsevier.com/locate/scitotenv

Regional regression models for estimating monthly streamflows Zhenxing Zhang a,⁎, John W. Balay b, Can Liu b a b

Illinois State Water Survey, Prairie Research Institute, University of Illinois at Urbana-Champaign, Champaign, IL 61822, USA Susquehanna River Basin Commission, 4423 N. Front Street, Harrisburg, PA 17110, USA

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• Comprehensively assess regional regression models for estimating environmental flows • Exam contributions of various watershed characteristics for environmental flows • Provide scientific guidance for prioritizing streamflow monitoring

a r t i c l e

i n f o

Article history: Received 11 September 2019 Received in revised form 7 November 2019 Accepted 22 November 2019 Available online xxxx Editor: José Virgílio Cruz Keywords: Susquehanna River Monthly streamflow Environmental flow Prediction in ungagged basins

a b s t r a c t Environmental flow science has attracted significant attention in recent years and has become more widely implemented by various agencies responsible for managing water resources. In addition to annual environmental flows, monthly environmental flows have been increasingly used to protect aquatic ecosystems. Regional regression analysis is commonly used to estimate streamflows when long-term continuous streamflow records are not available. While literature related to regional regression models for estimating annual flows is relatively rich, studies focused on regional regression analysis for estimating monthly flows are rare. This study contributes a comprehensive assessment of regional regression models for estimating monthly flows. A comprehensive database of watershed characteristics was developed, and a suite of monthly and annual flows were estimated using long-term continuous streamflow records from 72 watersheds within or adjacent to the Susquehanna River Basin. Regional regression models were developed for 104 flows, including 96 monthly flow statistics and 8 annual flow statistics. The performance of regional regression models for estimating various monthly flows, as well as which watershed characteristics were most important for estimating them, was investigated. The results showed regional regression analysis performed better for wet months than dry months, and better for high and medium flows than low flows. Drainage area and precipitation were the most important watershed characteristics for estimating flows. The performance of regional regression models for estimating annual flow was often better for estimating monthly flows of dry months but worse than for estimating monthly flows of wet months. The study also provides guidance for water resources managers regarding where to focus streamflow monitoring efforts with limited resources, considering flow estimation error is greatest for low flow statistics in dry weather months. © 2019 Elsevier B.V. All rights reserved.

1. Introduction

⁎ Corresponding author. E-mail address: [email protected] (Z. Zhang).

Environmental flow is “the flow regime required in a river to achieve desired ecological objectives” (Acreman and Dunbar, 2004). Environmental flow science, which is focused on the concepts of environmental

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flow as well as methods, tools and models to determine environmental flow, has attracted much attention in the last several decades and has been applied in water resources management and planning to help balance human and ecosystem water needs (Richter et al., 1996; Richter, 2010). Ideally, site-specific environmental flow studies are conducted to determine environmental flow standards, but this process is often time consuming and financially prohibitive (Zhang et al., 2016). Poff et al. (2010) developed the ecological limits of hydrologic alteration (ELOHA) framework, which could be used to establish environmental flow standards for a region when site-specific studies are not feasible. Both site-specific and regional environmental flow criteria are often based on seasonal and/or monthly streamflow statistics. The most commonly used monthly streamflow statistics include monthly mean flow, which is the average flow for a specific month, and monthly percent exceedance flow, which is the flow that has been exceeded a certain percentage of time for a specific month. For example, September P75 flow represents low flow conditions because 75% of all daily flows in September have been greater than that amount. It is important to be able to accurately estimate monthly environmental flows for water resources management applications. When there are long-term continuous streamflow records available, flow frequency analysis is typically conducted to estimate monthly streamflow statistics using mean daily flow data for specific months. If no long-term streamflow records are accessible, regional regression analysis is commonly utilized to estimate monthly streamflow statistics. Regional regression models have long been employed in hydrologic analyses, especially for prediction in ungauged basins (PUB) and prediction in changing environments (Sivapalan, 2003; Zhang et al., 2008). Annual streamflow statistics have been used for a wide range of purposes, including water allocation, wastewater discharge, water quality management, flood control, drought management, water supply planning, reservoir design, etc. There are many studies and practical applications highlighting the use of regional regression analysis for estimating high, medium, and low flows at national, state, regional, and watershed scales (Benson and Matalas, 1967; Hirsch, 1979; Vogel and Kroll, 1990; Vogel et al., 1999; Kroll et al., 2004; Stuckey, 2006; Roland and Stuckey, 2008; Archfield et al., 2010). Regional regression models often perform well for predicting high flows, such as the 100-year flood, while errors associated with estimating low flows, such as the 7-day-10-year low flow, are often much greater (Vogel and Kroll, 1990; Vogel et al., 1999; Zhang and Kroll, 2007). Monthly mean flows have long been used to characterize seasonal hydrologic patterns and adopted for water resources management purposes such as reservoir operation and water allocation. Estimates of monthly mean flows in ungauged basins have also attracted much attention in the literature. Farmer and Vogel (2013) compared the drainage area ratio and regional regression methods, among other approaches, for estimating monthly mean flows and proposed a performance-weighted method for estimating monthly streamflow in ungauged sites. Erdal and Karakurt (2013) used ensemble learning paradigms to improve monthly streamflow prediction accuracy with Classification and Regression Tree (CART) models. Use of monthly percent exceedance flows is relatively new compared to the traditional use of annual flood flow, annual low flow, and monthly mean flow statistics for water resources management applications. However, use of monthly percent exceedance flows by federal, state, and local resources agencies for establishing environmental flow criteria has been increasing recently, subsequent to having been advocated by academia and environmental groups for years. For example, the Susquehanna River Basin Commission (SRBC), among other agencies, has used regional regression models for estimating monthly percent exceedance flows for a broad range of purposes including water availability analysis, low flow operations, and water use management. There are many situations in which monthly streamflow statistics are needed but long-term continuous streamflow records are not available. In this case, regional regression analysis is often employed to estimate

the monthly percent exceedance flows. It is often assumed that regional regression models perform similarly for estimating monthly percent exceedance flows and annual streamflow statistics, though the performance of regional regression analysis for predicting monthly flows is not well understood. StreamStats, developed by the U.S. Geological Survey (USGS) since 1997, is a widely used map-based application that incorporates a Geographic Information System (GIS) to provide a user interface for site selection. It is a valuable tool for water resources planning and management and provides a range of streamflow statistics for ungaged sites based on regional regression and/or drainage area ratio (Ries et al., 2017). To develop StreamStats, a range of streamflow statistics have been analyzed. StreamStats for the Susquehanna River Basin does not currently provide monthly percent exceedance flows. The study attempts to explore the performance of regional regression models for estimating monthly flows, including monthly mean flow and monthly percent exceedance flows, which are often used to determine environmental flows. Specifically, the study aimed to address the following scientific questions with respect to regional regression analysis for estimating monthly flows: (1) Do regional regression models perform better for some months than others? If so, for which months do they perform better?; (2) Does regional regression analysis performance vary for different flow regimes, i.e., what is the difference in performance for estimating high, medium, and low monthly flows?; (3) Which watershed characteristics are most important for estimating monthly flows?; and (4) Does regional regression analysis perform similarly for monthly and annual streamflow statistics? To address these questions, regional regression equations were developed for a range of monthly flow statistics (including high, medium, and low flows) using data from long-term, continuous USGS stream gages within and near the Susquehanna River Basin (SRB). A suite of watershed characteristics were developed using available digital elevation models, geology, land use, soil, and climate data for use in conducting the regional regression analysis. The following sections describe the study area, watershed and streamflow data, regional regression analysis methodology, and key study results. The study contributes to the literature by exploring which months, flow conditions, and watershed characteristics practitioners need to allocate more resources to monitor in order to improve environmental flow estimates for water resources management applications. The study will also provide a scientific basis for applying monthly environmental flow statistics for water resources management, in general. 2. Study area The Susquehanna River is the largest river within the United States that drains into the Atlantic Ocean with a drainage of 27,510 mi2. The basin covers portions of the states of Pennsylvania, New York and Maryland. It is the largest tributary of the Chesapeake Bay and provides 50% of Chesapeake Bay's freshwater. The Susquehanna River is about 444 miles long. Zhang et al. (2009 and 2010) provided detailed descriptions of the Susquehanna River Basin which is shown in Fig. 1. To assess the regional regression models for estimating monthly flows, regional regression equations were developed for a set of monthly percent exceedance and mean flows using long-term continuous USGS stream gages that met the following criteria: (1) located within or adjacent to the Susquehanna River Basin; (2) contain at least 10-years of continuous, daily streamflow records; (3) reflect unregulated conditions with minimum hydrologic alteration; and (4) possess drainage areas less than 1000 mi2 (Balay et al., 2016). Based on these criteria, 72 references gages shown in Fig. 1 were used for the study. The average drainage area of the gages is 183 mi2, with a minimum of 1.8 mi2 and a maximum of 981.7 mi2. The drainages associated with the 72 reference gages are distributed throughout the study area. A histogram of the drainage areas associated with the reference gages used in the study is shown in Fig. 2. It can be seen that small to medium

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Fig. 1. Reference gages used for assessing the regional regression analysis.

sized watersheds are well represented, so the resulting regression equations would be applicable for similar watersheds throughout the

Susquehanna River Basin. The USGS station number, gage name, and drainage area for each reference gage are summarized in Appendix A.

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Nuber of refrence gages

4

Frequency

18 16 14 12 10 8 6 4 2 0

100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

Cumulave %

10

50

100 200 Drainage Area (sq mi)

500

1000

Fig. 2. The distribution of drainage area for the reference gages used in the study.

3. Regional regression analysis Regional regression analysis is one of the most commonly used applications in hydrology, which develops regional regression models by relating a specific hydrologic index to watershed characteristics. To form a near-linear relationship, streamflow statistics and watershed characteristics are log transformed. For watershed characteristics with units of percentages, 1.0 was added to the decimal form of the percentages to avoid the occurrence of zero values before they were transformed. The linear regression equation in log-space is expressed as follows: Logy ¼ β0 þ β1 Logx1 þ β2 Logx2 þ β3 Logx3 þ …

ð1Þ

The equation could be converted to real-space to estimate y as follows: y ¼ 10β0 x1 β1 x2 β2 x3 β3 …

ð2Þ

where: Log is log to base 10; y is the flow statistic of interest; x1, x2, x3… are watershed characteristics; and β0, β1, β2, β3… are regression coefficients. Vogel and Kroll (1992) showed that Eq. (2) is consistent with the linear solution to the Boussinesq equation for groundwater discharge. The form of Eq. (2) has been extensively used to model streamflow regimes in literature as well. A log-transformed relationship of streamflow statistics and watershed characteristics are often consistent with the linear relationship in Eq. (1). The observed monthly flows which are computed using frequency analysis with long-term continuous streamflow records for the reference gages were regressed against watershed characteristics using the ordinary least squares (OLS) regression technique. The watershed characteristics are the explanatory variables and the observed flows are the independent variables. The OLS procedure estimates regression parameters by minimizing the sum of the squared residuals. By the Gauss Markov theorem, if the residuals have a mean of zero, a constant variance, and are independent of each other, the OLS estimators are the best linear, unbiased estimators. When the regression models are used to estimate monthly flows, the estimated flows are referred to as predicted flows. The SAS®, version 9.3 software package, was used to conduct the step-wise regression, which reduces the number of explanatory variables to those significant at the 95% confidence level. Outliers, and the overall validity of the regression equations, were examined graphically. The assumptions of OLS (e.g., uncorrelated errors with a mean of 0 and constant variance) were examined on the residuals. R-squared and adjusted R-squared were employed to test the goodness of fit. Variance inflation factors (VIF) were examined to identity potential multicollinearity issues. The prediction residual error sum of squares (PRESS) was explored to show the regression model's predictive ability. Standard error estimates, in percentages, were primarily used for evaluating the performance of the regional regression models, so that the evaluation was consistent for different months and for varying flow

regimes. The standard error in percentages are calculated as 100(exp (S2)-1)1/2, where S is an estimate of the variance of the residuals (Kroll et al., 2004). The standard error has been extensively used for assessing performance of various approaches and models. Environmental flows are often determined based on low flows as aquatic ecosystem can be stressed during low flow conditions due to low oxygen content and high water temperature. Thus, it is important for this study to understand the performance of regional regression for estimating low flows. Use of standard error in percentage would reduce impact of high flows so that the assessment of performance is not dominated or skewed by high flows. In addition, the performance metrics of root mean square error (RMSE) and PRESS were examined as well. They showed similar patterns as standard error and, thus, were not discussed in detail in the following section. Kroll et al. (2004) and Zhang and Kroll (2007) also showed that results of relative error, impacted by both the error and mean flows, are generally consistent with other performance metrics. 4. Streamflows and watershed characteristics A suite of monthly flows was used in the study to comprehensively examine the performance of regional regression analysis. The flows analyzed included monthly P5, P10, P25, P50, P75, P90, and P95, which covered high, medium, and low flows. Monthly mean flows were analyzed as well. Totally 96 monthly flows were analyzed to comprehensively understand regional regression models for estimating monthly flows. The corresponding annual percent exceedance flows were also examined in the study and compared with the monthly flows. The 96 monthly flow statistics are denoted as the combination of streamflow and month representing by numerals. For example, January P95 is denoted as P95_1. The eight annual flow statistics are denoted as the combination of streamflow and number 0. For example, annual P95 is denoted as P95_0. The 104 flow statistics were calculated for each of the 72 reference gages via flow frequency analysis using the longterm, continuous streamflow records obtained from the USGS National Water Information System (NWIS). The flows calculated from streamflow records are referred to as observed flows. The observed flows were the independent variables used in the regional regression models. A broad range of watershed characteristics including climate, topography, land use/land cover, soil, geology, geomorphology, and hydrogeology were compiled from various sources. To ensure consistency and accuracy, the watershed characteristics were obtained directly or calculated from existing geographic information systems (GIS) datasets. Table 1 shows the data sources and units for the watershed characteristics used in the study. To summarize watershed scale characteristics, the drainage area for each gage is the total drainage area upstream of the USGS gage. All the other watershed characteristics are averaged through the watershed. Using the watershed scale averaged characteristics may induce additional uncertainties due to the geographic distribution or structure of the characteristics. For example, forests located upstream or downstream of a watershed could result in very different flow regimes. The same average soil thickness through a watershed could result in different flow regimes as the soil thickness variability changes. Regional regression could only use the summary information without fully capturing the spatial distribution of these watershed characteristics or their variances. It is noteworthy that baseflow index (BFI) was used in the study as it is available for ungaged sites in the conterminous United States since USGS developed BFI grid data in 2003. For locations where estimated BFI is not available for undaged sites, BFI should not be used as an explanatory variable. To generate unique regression parameter estimators, the watershed characteristics should be linearly independent. However, multicollinearity often exists in hydrology applications of regional regression as watershed characteristics are often correlated (Kroll and

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Table 1 Watershed characteristics used in the regional regression analysis. Basin characteristic

Abbreviation Units

Source

Average slope Available water capacity Base flow index Carbonate bedrock Base flow index Coal Drainage area Soil erodibility factor Mean fault per square mile

AVSLP AWC BFI CARB CLAY COAL DA ERODE FAULT

Degrees Inch/inch Percentage Percentage Percentage Percentage Square mile Unitless Count per square mile

Forest biomass Forest Mean elevation Percent of impervious area Average karst density Liquid limit Mean potential evapotranspiration Soil permeability Mean precipitation Specific capacity

FORBIO FOREST ELEV IMPER KD LL PE

Megagram/hectare Percentage Feet Percentage Count per 50 square meters Percentage Inch

National Elevation Dataset (NED) State Soil Geographic (STATSGO) USGS USGS STATSGO Pennsylvania Department of Environment Protection (PADEP) NED STATSGO Pennsylvania Department of Conservation and Natural Resources (PA DCNR), NY Museum, MD Geological Survey Moderate Resolution Imaging Spectroradiometer (MODIS) Image Dataset National Land Cover Database (NLCD) NED USGS PA DCNR STATSGO MODIS Global Evapotranspiration (MOD16)

PERM PREC_ia SCAP

STATSGO Parameter-Elevation Regressions on Independent Slopes Model (PRISM) SRBC

Soil thickness Mean daily maximum temperature Mean daily minimum temperature Topographic position index ridge area Topographic position index slope area Topographic position index valley area

THICK TMAX_ia

Inch/hour Inch Gallon per minute per foot of drawdown Inch Fahrenheit

TMIN_ia

Fahrenheit

PRISM

TPIRDG

Percentage

Jenness, 2006; NED

TPISLP

Percentage

Jenness, 2006; NED

TPIVAL

Percentage

Jenness, 2006; NED

a

STATSGO PRISM

i = 1 through 12, representing the months of January through December, respectively; I = 0, representing annual statistics.

Song, 2013). For example, the correlation between temperature and evaporation, drainage area and stream length, as well as average slope and slope area are typically correlated throughout a region. Many approaches exist to address multicollinearity in hydrology such as using VIFs to screen watershed characteristics (Kroll et al., 2004), principal component regression (PCR) (Jolliffe, 2011), and ridge regression (Hoerl and Kennard, 2000). Kroll and Song (2013) demonstrated that complex, biased regression techniques such as PCR, do little to improve regression models' predictions when compared with OLS for hydrologic regional regression confronted with multicollinearity. As the present study aims to explore the general pattern of region regression to

estimate monthly streamflow, only VIFs were used to examine and screen watershed characteristics. More complex methods such as PCR or ridge regression were not employed. 5. Results For each regression model, the regression performance was assessed statistically and graphically. The satisfactory models were selected and used for comparing model performance to address the four scientific questions listed in the introduction section. As an example, the regression performance for December average flow is presented here. Fig. 3

Predicted streamflow (cfs)

10,000

1,000

100

10

1 1

10

100

1,000

10,000

Observed streamflow (cfs)

Fig. 3. The predicted streamflow and observed streamflow for December mean flows.

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0.15

0.10

Residual in log

0.05

0.00 1

10

100

1,000

-0.05

-0.10

-0.15

Drainage area (mi2)

Fig. 4. The residuals v.s. drainage areas for December mean flow.

shows the predicted values vs. the observed values for all the gages in the study area and demonstrates the predicated values match the observed values well. Fig. 4 graphically shows the residuals vs. corresponding drainage areas and demonstrates the residuals generally satisfy the assumption of OLS. The following 4 subsections address individual scientific questions listed in the introduction section. The first subsection compares the regional regression model performance for each month. In the second subsection, the model performance is compared with respect to streamflow regimes to assess the performance for high, medium, and low flows. In the third subsection, significant watershed characteristics are explored and compared with respect to each month and the different flow regimes. The fourth subsection compares the performance of regional regression models between annual and monthly flows. 5.1. Do regional regression models perform better for some months than others? The standard errors of the regional regression models for various monthly and annual flows are shown in Fig. 5. The performance of the various regression models, including P5, P10, P25, P50, P75, P90, P95, and Qavg, reflects very similar monthly patterns. The results show that the regression models performed better for wet season, such as March, April, and May, and worse for the dry season, such as July, August, and September. For example, for the monthly P95 low flows, the standard errors for March, April, and May were 22%, 20%, and 28%, respectively, while those for July, August, and September were 67%, 84%, and 80%, respectively. A paired sample t-test was conducted to examine whether the mean performance was significantly different between the dry season and wet season. The results showed the regional regression performs significantly better for wet months at significant level of 0.01. The difference in regional regression model performance between wet and dry months was notable for low flow statistics such as monthly P95 and P90. In contrast, the difference in model performance between wet and dry months was less significant for high flow statistics such as monthly P5 and P10. For instance, regarding the monthly P5 high flows, the minimum standard error was 10% for May and the maximum standard error was 29% for August, reflecting a difference of only 19%. In contrast, with respect to the monthly P95 low flows, the standard errors ranged from 20% to 84%, indicating a much greater difference.

5.2. Does regional regression analysis performance vary for different flow regimes? The standard errors associated with regional regression models for different flow regimes within each month were compared, and the results are shown in Fig. 6. Generally, regional regression analysis performance improved for estimating medium and high flow statistics such as monthly P5 and P10 but decreased for estimating low flow statistics such as monthly P95. From January to December, the performance of the regional regression models for monthly P95 was always the worst in comparison to the other flow statistics. As an example, for January, the standard errors for P95, P90, P75, P50, P25, P10, and P5 were 37%, 28%, 20%, 16%, 12%, 13%, and 16%, respectively. The pattern of performance for the other months was the same as that for January. Paired sample t-tests demonstrated that the regional regression performs significantly better to estimate high flows than medium flows at the significance level of 0.01. The paired t sample test also showed that regression performance was significantly better for estimating medium flows than low flows at the significance level of 0.01. This finding is consistent with conclusions in Zhang (2017) regarding estimation of percent exceedance flows using the index gage method. The performance of regional regression models for estimating monthly average flows was better than for estimating low and medium monthly percent exceedance flows. The performance for estimating monthly average flows was similar to that of estimating high monthly percent exceedance flows such as P10 and P25. This implies that it is relatively easier to estimate monthly average flows than monthly low flows, which suggests the assumption that regional regression analysis performs similarly for estimating monthly percent exceedance flows and monthly average flows is not valid. Therefore, it is important to investigate how regional regression models perform for estimating monthly percent exceedance flows. 5.3. Which watershed characteristics are most important for estimating monthly flows? The comprehensive database of watershed characteristics allowed for exploration into which watershed characteristics were most important for estimating flows for different months and flow regimes. For the total of 104 regressions, the number of the final regression models, in which the specific watershed characteristic is significant at 5%, is employed to represent the importance of the watershed characteristics. The overall results for all flows and individual flows are shown in

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100%

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80% 60% 40% 20%

20% P90_12

P90_10

P90_11

P50_10

P90_8

P90_9 P50_9

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P10_9 Qavg_9

Qavg_12

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P10_11

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Qavg_10

P10_5 Qavg_5

Qavg_11

P10_4 Qavg_4

P5_12

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P25_12

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0% P25_1

0%

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40%

P95_12

P95_11

P95_10

P95_8

P95_9

P95_7

P95_6

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100%

Standard error

60%

0% P95_1

0%

80%

Qavg_0

Standard error

100%

7

100% 80% 60% 40% 20% 0%

Fig. 5. Comparison of standard errors (%) of regional regression models for monthly and annual flows. The y-axes of all charts indicate standard error (%).

Table 2. The detailed results for individual months and annual regression models are shown in Table 3. As expected, the most important watershed characteristic is the drainage area which is statistically significant for every single regional regression. The second most important watershed characteristic is the precipitation which is statistically significant in 91 regional regressions. Baseflow Index (BFI), coal, and soil thickness are the 3rd, 4th and 5th most important watershed characteristics in that BFI, coal, and soil thickness are statistically significant for 61, 42 and 39 regional regressions, respectively. For drainage area and precipitation, they are important for high, medium, and low flow statistics. BFI, coal and soil thickness are primarily important for estimating low flows such as P95 and P90. Coal is important for 8 regional regressions for P95, P90, and P75, demonstrating that coal mined areas are highly impacting low flows. Interestingly, soil thickness is not important for P50 at all and is important for average flows for 2 regional regressions. This implies the soil thickness impact on average flow or median flow in the basin is minimal though its impact on low flow is greater. One interesting finding is that all the 25 watershed characteristics are statistically significant for at least one regional regression.

From Table 3, drainage area, precipitation, BFI, and soil thickness are the most important watershed characteristics for annual flow. For monthly flows, drainage area and precipitation are the most important watershed characteristics while precipitation is not in each monthly flow for May through October, which covers the low flow months in the basin. The percentage of forest area is an important variable for estimating monthly flows for March, May, and June. BFI is an important watershed characteristic for estimating monthly flows for May through August. In addition, the percentage of area with coal mines is remarkably important for May through October in that it is significant in 4 to 7 monthly regressions for each of these 6 months. Interestingly, air temperatures (maximum or minimum) do not play key roles in the regional regressions. Consistent with regional regression studies on annual streamflow statistics in literature, the drainage area and precipitation are the two most important watershed characteristics. The coefficients of these two variables are examined in depth to explore how they influence monthly flow regressions. Tables 4 and 5 list the coefficients of the drainage area and precipitation, respectively. The coefficients for drainage area are narrowly ranged from 0.99 to 1.25. For high and medium

Please cite this article as: Z. Zhang, J.W. Balay and C. Liu, Regional regression models for estimating monthly streamflows, Science of the Total Environment, https://doi.org/10.1016/j.scitotenv.2019.135729

Standard error

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Standard error

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Fig. 6. Comparison of standard errors (%) of regional regression models for difference flow regimes. The y-axes of all charts indicate standard error (%).

Please cite this article as: Z. Zhang, J.W. Balay and C. Liu, Regional regression models for estimating monthly streamflows, Science of the Total Environment, https://doi.org/10.1016/j.scitotenv.2019.135729

Z. Zhang et al. / Science of the Total Environment xxx (xxxx) xxx Table 2 Watershed characteristics included in the final regression models for each flow. The values indicate the number of final regression models in which the corresponding watershed characteristics were significant at 5%. The values are color coded with the high frequency numbers in red and low frequency numbers in green. Variable All Qavg P95 P90 P75 P50 P25 P10 P5 AVSLP 5 0 0 1 0 1 1 1 AWC 5 0 0 0 1 0 0 2 61 5 12 11 10 7 4 5 BFI CARB 16 0 2 3 4 3 2 2 CLAY 3 1 0 0 0 0 2 0 COAL 42 5 8 8 8 6 4 3 104 13 13 13 13 13 13 13 DA ERODE 10 2 0 0 0 1 2 3 FAULT 5 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 FORBIO FORREST 35 4 3 4 3 5 7 5 IMPER 16 2 2 2 0 1 0 4 24 3 0 1 1 7 4 4 KD LL 2 0 0 1 0 0 0 0 MNSLP 8 3 0 0 0 0 2 1 PE 24 2 3 4 5 5 4 1 PERM 14 0 1 2 3 4 2 1 91 13 8 9 11 13 13 12 PREC_i SCAP 13 3 0 3 2 2 1 1 39 2 9 10 8 0 1 5 THICK TMAX_i 6 1 0 0 0 0 0 2 TMIN_i 16 3 1 1 1 2 2 3 TPIRDG 6 0 0 0 0 0 1 1 23 4 1 4 2 4 5 2 TPISLP 11 0 3 0 3 3 2 0 TPIVAL

1 2 7 0 0 0 13 2 1 0 4 5 4 1 2 0 1 12 1 4 3 3 4 1 0

9

Table 4 The coefficients for drainage area used in the final regression models. Month

P5

P10

P25

P50

P75

P90

P95

Qavg

January February March April May June July August September October November December Annual

1.03 1.03 1.05 1.07 1.02 1.01 1.10 1.04 1.12 1.00 1.03 1.03 1.04

1.05 1.03 1.05 1.06 1.02 1.02 1.11 1.04 1.02 1.00 1.02 1.04 1.04

1.04 1.03 1.00 1.00 1.02 1.03 1.05 1.03 1.03 1.01 1.03 1.04 1.04

1.04 1.04 1.04 1.06 1.02 1.02 1.04 1.04 1.08 1.04 1.03 1.02 1.03

1.07 1.05 1.04 1.06 1.01 1.05 1.11 1.11 1.10 1.07 1.06 1.02 1.07

1.09 1.04 1.05 1.07 1.04 1.08 1.17 1.17 1.25 1.11 1.07 1.04 1.12

1.08 1.05 1.08 1.06 1.05 1.10 1.23 1.21 1.16 1.14 1.09 1.04 1.16

1.03 1.02 1.01 1.06 1.02 0.99 1.03 1.02 1.02 1.00 1.08 1.07 1.03

that monthly precipitation is not a key player in estimating low flows for summer and fall months for the study area. It is noted that the coefficients for high flows in July, August, September, October, and November are often greater, ranging between 2 and 3. This reveals that precipitation is critical in estimating high flows in summer and fall months.

5.4. Does regional regression analysis perform similarly for monthly and annual streamflow statistics? flows such as P5, P10, P25, and P50, the coefficients for drainage area are usually very close to 1 which is very similar to the coefficients for drainage area in annual flow regressions. For low flows such as P95 and P90, the coefficients are often between 1.1 and 1.2, and the largest coefficients are usually for the low flows for the dry months such as July, August, and September. This demonstrates that the commonly used drainage area ratio method in water resources and environmental flow management practices with the assumption of the coefficient of 1 may produce relatively large errors for estimating monthly low flows. The coefficients for precipitation, ranging from 0.57 to 3.27, have greater range in the final regression models than those for drainage area. In addition, precipitation is not even statistically significant in the final regression models for P95 of May, June, August, September, and October and for P90 of May, June, August, and October. This implies

Table 3 Watershed characteristics included in the final regression models for each month. The values indicate the number of final regression models in which the corresponding watershed characteristics were significant at 5%. The values are color coded with high frequency numbers in red and low frequency numbers in green. Variable Annual Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVSLP 0 0 0 0 1 0 0 0 0 2 1 0 1 AWC 0 0 2 0 1 0 0 0 0 0 1 1 0 5 6 5 2 2 6 7 8 6 4 3 3 4 BFI CARB 1 0 1 0 2 0 4 4 1 2 1 0 0 CLAY 0 0 0 0 0 1 0 0 0 0 2 0 0 4 0 1 2 0 4 6 7 6 7 5 0 0 COAL DA 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 2 3 1 0 0 0 1 1 0 0 2 ERODE FAULT 0 0 0 0 1 2 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 FORBIO FORREST 4 2 0 5 2 8 6 3 0 1 4 0 0 IMPER 2 0 1 3 4 1 0 0 0 0 0 2 3 KD 1 2 3 3 0 2 1 1 4 2 0 2 3 0 0 0 0 2 0 0 0 0 0 0 0 0 LL MNSLP 0 0 0 2 1 0 0 2 0 1 0 1 1 2 4 1 1 7 3 0 0 0 0 0 4 2 PE PERM 1 3 2 3 4 0 0 0 0 0 0 1 0 PREC_i 8 8 8 6 8 6 5 8 6 6 6 8 8 SCAP 2 0 0 1 1 0 0 2 0 3 2 1 1 THICK 5 2 4 1 2 4 3 2 3 3 3 3 4 0 0 0 0 2 0 0 1 2 0 1 0 0 TMAX_i 1 1 0 3 0 0 1 1 0 2 0 1 6 TMIN_i TPIRDG 1 0 3 0 0 0 1 0 0 1 0 0 0 2 1 4 1 1 0 1 0 2 2 3 3 3 TPISLP TPIVAL 2 1 0 0 2 3 0 0 0 1 0 1 1

The comparison of annual and monthly percentile flows is shown in Figs. 5 and 6. For the same percentile flows, the standard error for annual flow statistics is smaller than those of dry months but often greater than those of wet months. When the standard errors of annual percentile flows are compared with the average standard error of 12 monthly flows, it is smaller than monthly average standard error for P75, P50, P25, P10, and P5, and greater than monthly average standard error for P95 and P90 (Table 6). Paired sample t-test results demonstrate that regression performs significantly better in estimating annual flows than in estimating dry season monthly flows at the significance level of 0.01. Regression performs significantly better in estimating wet season monthly flows than in estimating annual flows at the significance level of 0.10. The standard errors of annual and monthly average flows are graphically demonstrated in Fig. 5. Interestingly, the standard error for annual average is smaller than those of monthly average flows which suggests it is easier to estimate annual average flow than monthly average flows with regional regression. This finding implies that the assumption of regional regression performs similarly for estimating monthly and annual flows are not valid and it is valuable to examine the performances of regressions in different flows.

Table 5 The coefficients for annual and monthly precipitation in the final regression models. Month

P5

P10

P25

P50

P75

P90

P95

Qavg

January February March April May June July August September October November December Annual

1.35 0.61

1.29 0.83

1.15 1.06 1.21 3.00 3.04 2.85 1.59 2.74 1.53 1.24

0.57 1.01 1.72 3.00 3.58 3.25 1.78 2.38 1.63 1.49

1.14 1.06 0.81 0.64 1.19 1.25 2.71 2.48 3.48 2.41 2.58 1.69 1.88

1.47 1.41 1.11 1.11 1.40 0.96 1.90 2.17 2.50 3.13 2.99 1.77 2.53

1.62 1.27 1.37 1.27 1.32

1.96 1.48 0.70 1.39

2.07 1.74 0.78 1.12

1.76 1.83

1.90

2.18

1.44 1.03 1.04 0.93 0.90 1.16 2.28 2.14 2.45 1.72 2.41 1.68 1.62

2.35 1.83 3.48 1.95 3.27

2.63 2.55 2.90

2.25 2.75 2.23

Please cite this article as: Z. Zhang, J.W. Balay and C. Liu, Regional regression models for estimating monthly streamflows, Science of the Total Environment, https://doi.org/10.1016/j.scitotenv.2019.135729

10

Z. Zhang et al. / Science of the Total Environment xxx (xxxx) xxx

Table 6 The standard errors for estimating annual flows and the average standard errors for estimating monthly flows. Flow

Annual

Monthly average

P95 P90 P75 P50 P25 P10 P5 Qavg

59% 47% 30% 16% 10% 9% 12% 9%

48% 41% 32% 24% 18% 17% 18% 16%

6. Conclusions This study contributes a comprehensive assessment of regional regression models for estimating monthly streamflows. While monthly percent exceedance flow applications have recently attracted considerable attention in the literature and water resources management, the performance of regional regression analysis for estimating monthly flows has not been systematically examined. In this study, a comprehensive database of watershed characteristics was developed, and a suite of monthly and annual flow statistics was estimated, using longterm continuous streamflow records from 72 USGS reference gages located within or adjacent to the Susquehanna River Basin. Regional regression models were developed for 104 flow statistics, including monthly and annual high, medium, and low flows. The following conclusions were reached based on the results of the study: (1) Regional regression models performed better for wet months than dry months. (2) Regional regression models performed better for high and medium flows than low flows. (3) Drainage area and precipitation were the first and second most important watershed characteristics for estimating monthly flows. In addition, BFI and soil thickness were particularly important for estimating low flows. (4) The performance of regional regression models for estimating annual flows was often better than for estimating monthly flows of dry months and worse than for estimating monthly flows of wet months.

This study also demonstrated that the performance of regional regression models for estimating monthly flows cannot simply be assumed to be similar with that of estimating annual flows. It also provides guidance for water resources managers regarding where to focus streamflow monitoring efforts given limited resources, considering flow estimation error is greatest for low flow statistics in dry weather months. In addition, the results imply that the drainage area ratio method, which assumes a unit area of drainage generates the same amount of streamflow, may produce relatively large errors in estimating low flows for dry months, and warrants further study in the future. Acknowledgements The authors would like to thank Andrew Dehoff, Andrew Gavin, and the Susquehanna River Basin Commission (SRBC), at large, for their support of this work. We are grateful to Jeffrey Zimmerman, Jr. for his assistance in conducting GIS analyses, generating watershed characteristics, and preparing study maps. We also appreciate Hilary Hollier for completing a comprehensive editorial review of this paper. Any opinions, findings, and conclusions do not necessarily reflect the views of the SRBC or University of Illinois and no official endorsement should be inferred.

Appendix A. Pertinent information for reference gages used in the regional regression analysis. Gage ID is the ID number used in the map and DA is the drainage area

Gage ID

USGS station number

Gage name

1 2 3

0142400103 01426000 01428750

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

01447500 01468500 01469500 01470779 01500500 01502000 01502500 01505000 01510000 01514000 01516350 01516500 01518862 01527000 01527500 01528000 01529500 01532000 01534000 01537500 01538000 01539000 01540200 01541000 01541308 01542000 01542810 01543000

32 33 34 35 36 37

01544500 01545600 01546400 01546500 01547100 01547200

38 39 40 41 42 43 44 45 46 47 48 49

01547700 01547950 01548500 01549500 01550000 01552000 01552500 01553130 01554500 01555000 01555500 01556000

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

01557500 01558000 01559000 01560000 01562000 01565000 01565700 01566000 01567500 01568000 01570000 01571500 01572000 01573000 01573086 01574000 01576500

Trout Creek near Trout Creek, NY Oquaga Creek at Deposit, NY West Branch Lackawaxen River near Aldenville Lehigh River at Stoddartsville Schuylkill River at Landingville Little Schuylkill River at Tamaqua Tulpehocken Creek near Bernville Susquehanna River at Unadilla Butternut Creek at Morris Unadilla River at Rockdale Chenango River at Sherburne Otselic River at Cincinnatus Owego Creek near Owego, NY Tioga River near Mansfield Corey Creek near Mainesburg Cowanesque River at Westfield Cohocton River at Cohocton Cohocton River at Avoca Fivemile Creek near Kanona Cohocton River near Campbell Towanda Creek near Monroeton Tunkhannock Creek near Tunkhannock Solomon Creek at Wilkes-Barre Wapwallopen Creek near Wapwallopen Fishing Creek near Bloomsburg Trexler Run near Ringtown West Branch Susquehanna River at Bower Bradley Run near Ashville Moshannon Creek at Osceola Mills Waldy Run near Emporium Driftwood Br Sinnemahoning Cr at Sterling Run Kettle Creek at Cross Fork Young Womans Creek near Renovo Spring Creek at Houserville Spring Creek near Axemann Spring Creek at Milesburg Bald Eagle Creek below Spring Creek at Milesburg Marsh Creek at Blanchard Beech Creek at Monument Pine Creek at Cedar Run Blockhouse Creek near English Center Lycoming Creek near Trout Run Loyalsock Creek at Loyalsockville Muncy Creek near Sonestown Sand Spring Run near White Deer Shamokin Creek near Shamokin Penns Creek at Penns Creek East Mahantango Creek near Dalmatia Frankstown Br Juniata River at Williamsburg Bald Eagle Creek at Tyrone Little Juniata River at Spruce Creek Juniata River at Huntingdon Dunning Creek at Belden Raystown Branch Juniata River at Saxton Kishacoquillas Creek at Reedsville Little Lost Creek at Oakland Mills Tuscarora Creek near Port Royal Bixler Run near Loysville Sherman Creek at Shermans Dale Conodoguinet Creek near Hogestown Yellow Breeches Creek near Camp Hill Lower Little Swatara Creek at Pine Grove Swatara Creek at Harper Tavern Beck Creek near Cleona West Conewago Creek near Manchester Conestoga River at Lancaster

DA (mi2) 20.2 67.5 40.6 91.8 133.1 43.9 70.5 985.3 59.9 520.3 262.3 147.1 186.6 152.6 12.1 90.0 52.0 155.9 66.9 467.4 216.2 393.0 15.5 42.0 271.6 1.8 315.2 6.8 68.8 5.2 272.0 137.1 46.2 58.0 85.9 145.4 267.4 44.1 152.6 601.4 37.9 172.9 436.7 23.4 4.6 54.5 305.8 162.4 289.3 44.6 220.4 816.6 171.7 753.7 163.0 6.6 209.9 15.0 206.7 466.4 212.7 34.1 336.1 7.9 512.4 322.0

Please cite this article as: Z. Zhang, J.W. Balay and C. Liu, Regional regression models for estimating monthly streamflows, Science of the Total Environment, https://doi.org/10.1016/j.scitotenv.2019.135729

Z. Zhang et al. / Science of the Total Environment xxx (xxxx) xxx (continued) Gage ID

USGS station number

Gage name

DA (mi2)

67 68 69 70 71 72

01578400 01580000 01613050 01639000 03026500 03034000

Bowery Run near Quarryville Deer Creek at Rocks Tonoloway Creek near Needmore Monocacy River at Bridgeport Sevenmile Run near Rasselas Mahoning Creek at Punxsutawney

6.0 94.4 10.7 173.2 7.9 157.5

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Please cite this article as: Z. Zhang, J.W. Balay and C. Liu, Regional regression models for estimating monthly streamflows, Science of the Total Environment, https://doi.org/10.1016/j.scitotenv.2019.135729