A web-based software tool to estimate unregulated daily streamflow at ungauged rivers

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Introduction
Streamflow information at ungauged rivers is needed for any number of hydrologic applications; this need is of such importance that an international research initiative known as Prediction in Ungaged Basins (PUB) has been underway for the past decade (Sivapalan et al., 2003).Concurrently, there has been increasing emphasis on the need for daily streamflow time series to understand the complex response of ecology to river regulation and to develop streamflow prescriptions to restore and protect aquatic habitat (Poff et al., 1997(Poff et al., , 2010)).Basin-wide water allocation decisions that meet both human and ecological demands for water require daily streamflow time series at river locations that have ecological constraints on water (locations where important or protected fish or ecological communities reside or rely on for life), human constraints on Introduction

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Full water (locations on the river that are dammed or otherwise managed), or locations that have both constraints.Often times, these locations are unmonitored and no information is available to make informed decisions about water allocation.Methods to estimate daily streamflow time series at ungauged locations can be broadly characterized under the topic of regionalization (Bl öschl and Sivapalan, 1995), an approach which pools information about streamgauges in a region and transfers this information to an ungauged location.Generally there are two main categories of information that is pooled and transferred: (1) rainfall-runoff model parameters that are calibrated at gauged catchments and transferred in some way to an ungauged location (see Zhang and Chiew, 2009 for a review) and (2) gauged streamflows, or related streamflow properties, are directly transferred to ungauged locations.Examples of this type of regionalization approach include geostatistical methods such as top-kriging (Skøien and Bl öschl, 2007) and more commonly used methods such as the drainage-area ratio method (as described in Archfield and Vogel, 2010), the MOVE method (Hirsch, 1979), and a non-linear spatial interpolation method, applied by Fennessey (1994), Hughes and Smakhtin (1996), Smakhtin (1999), Mohamoud (2008), Archfield et al. (2010), and Shu and Ourda (2012).For the software tool presented in this paper, a hybrid approach combining the drainage-area ratio and non-linear spatial interpolation methods is used to estimate daily streamflow time series.
When streamflow information is presented in an easy-to-use, freely-available software tool, this information can provide a scientific framework for water-allocation negotiation amongst stakeholders.Software tools to provide streamflow time series at ungauged locations have been previously published for predefined locations on a river; however few -if any -tools currently exist that provide daily streamflow time series at any stream location for which this information is needed.Smakhtin and Eriyagama (2008) and Holtschlag (2009) introduced software tools to provide monthly streamflows for ecological streamflow assessments at predefined river locations around the globe and in the Great Lakes region of the United States, respectively.Williamson et al. (2009) developed The Water Availability Tool for Environmental Introduction

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Full Resources (WATER) to serve daily streamflow information at fixed stream locations in non-karst areas of Kentucky.These existing tools provide valuable streamflow information; yet, in most cases, at the monthly -not daily -time step and, in all cases, for only predefined locations on a river that may not be coincident with a river location of interest.The US Geological Survey StreamStats tool (Ries and others, 2008) does provide the utility to delineate a contributing area to a user-selected location on a river; however, only streamflow statistics -not streamflow time series -are provided for the ungauged location.
The software tool presented here is one of the first such tools to provide daily streamflow time series at ungauged locations in a regional framework for any user-desired location on a river.The software tool has a map-based user interface and leverages recently published methods to estimate daily streamflow at ungauged river locations.This paper first briefly describes the methods used by the software tool.The software tool is then presented and its functionality is described.Lastly the utility of the software tool to provide reliable estimates of daily streamflow is demonstrated for a large basin in the northeast United States.

Methods underlying the software tool
Streamflow is estimated in the software tool using information from an index streamgauge and catchment characteristics computed for the contributing area to the ungauged stream location of interest (Fig. 1).Catchment characteristics and the selected index streamgauge are first used to estimate a continuous, daily flow-duration curve (FDC) at the ungauged location (Fig. 1).The estimated FDC is then transformed to a time series of streamflow values by the index streamgauge (Fig. 1).The methods to estimate the FDC, select the index streamgauge, and transform the FDC to a time series of daily streamflow are explained in detail in the following sections.Introduction

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Full Estimation of the daily FDC at an ungauged location remains an outstanding challenge in hydrology.Castellarin et al. (2004) provides a review of several methods to estimate FDCs at ungauged locations and found that no particular method was consistently better than another.For this study, an empirical, piece-wise approach to estimate the FDC is used in the software tool (Fig. 2).This overall approach is similar to that used by Mohamoud (2008), Archfield et al. (2010), and Shu and Ourda (2012) in that the FDC is estimated by first developing regional regressions relating catchment characteristics to selected FDC quantiles and then interpolating between those quantiles to obtain a continuous FDC.
With the exception of streamflows having less than or equal to a 0.01 probability of being exceeded (streamflows with a probability of being exceeded more than 1 percent of the time), selected quantiles on the FDC are estimated from regional regression equations and a continuous FDC is log-linearly interpolated between these quantiles to obtain a continuous FDC (Fig. 2).Relations between streamflow quantiles at the 0.02, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.7, 0.75, 0.8 and 0.85 exceedance probabilities were estimated by independently regressing each streamflow quantile against catchment characteristics (Fig. 2).Following the approach in Archfield et al. (2010), relations between streamflow quantiles at the 0.9, 0.95, 0.98, 0.99 and 0.999938 were estimated by regressing streamflows at these quantiles against one another and using these relations to recursively estimate streamflows (Fig. 2).Recursively estimating low streamflows, as was done in Archfield et al. (2010), exploits the strong structural relation between the streamflow quantiles (Fig. 2) and enforces the constraint that streamflows must decrease as the exceedance probability increases.Mohamoud (2008) and Archfield et al. (2010) observed that when regression is done against catchment characteristics, there is increased potential for the estimated quantiles to violate the constraint that streamflows must decrease as the exceedance probability increases because the uncertainty in the flow estimates is greatest at the lowest portion of the FDC.Introduction

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Full Regressing quantiles against one another ensures that this constraint is not violated.This is an alternative approach to that used by Mohamoud (2008), who suggested discarding any estimated quantiles that violate the constraint.All regressions were fit using methods outlined in Archfield et al. (2010).Archfield et al. (2010) showed that estimated streamflows determined by log-linear interpolation for exceedance probabilities of 0.01 or less do not match the shape of the FDC in this range and this interpolation method creates a bias in the estimated streamflows, which can substantially overestimate the peak streamflows.The shape of the FDC at the highest streamflows is so complex that, instead of using another interpolation method, streamflows from an index streamgauge are scaled to estimate the highest streamflows at the ungauged location.The assumption here is that the shape of the left tail of the FDC is better approximated by the streamflow quantiles at an index streamgauge than by a curve fit.Therefore, for streamflows having less than or equal to a 0.01 probability of being exceeded, streamflows are scaled by a drainagearea ratio approach (Eq. 1) in conjunction with the selected index streamgauge: where q p u is the value of the streamflow quantile at the ungauged location for exceedance probability, p, A u is the contributing drainage area to the ungauged location, A g is the contributing drainage area to the index streamgauge, and q p g is the value of the streamflow quantile at the index streamgauge for exceedance probability, p.

Selection of the index streamgauge
As shown in Fig. 1, the index streamgauge is used for two purposes in the streamflow estimation approach: (1) to estimate streamflows that have less than a 1-percent chance of being exceeded, and (2) to transform the estimated FDC into a time series of streamflow at the ungauged location.The index streamgauge is selected by the Introduction

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Full map-correlation method (Archfield and Vogel, 2010).The map-correlation method selects the index streamgauge estimated to have the highest cross-correlation between streamflow time series at the index streamgauge and the ungauged location.Archfield and Vogel (2010) showed that the selection of the index streamgauge using crosscorrelation between streamflow time series outperformed the selection of the nearest index streamgauge when used with the drainage-area ratio method to estimate daily streamflow time series at ungauged locations.This finding supports the use of the mapcorrelation method for two reasons: (1) the drainage-area ratio approach is also used to estimate streamflows that have less than a 1-percent chance of being exceeded, and (2) because the streamflow time series is constructed by transferring the timing of the streamflows at an index streamgauge to the ungauged location, it follows that one would seek to select the index streamgauge that maximizes the cross-correlation between the streamflows at the ungauged location and the index streamgauge.Details of the map correlation method are described in Archfield and Vogel (2010).

Generation of streamflow time series
With an index streamgauge and estimated daily FDC at the ungauged location, a time series of daily streamflow for the simulation period is then constructed by use of the QPPQ transform method (Fennessey, 1994;Hughes and Smakhtin , 1996;Smakhtin, 1999;Mohamoud, 2008;Archfield et al. 2010;Shu and Ourda, 2012).The term QPPQtransform method was coined by Fennessey (1994); however, this method has been by published Smakhtin (1999), Mohamoud (2008), and Archfield et al. ( 2010) under names including "non-linear spatial interpolation technique" (Hughes and Smakhtin, 1996;Smakhtin, 1999) and "reshuffling procedure" (Mohamoud, 2008).The method assumes that the exceedance probability associated with a streamflow on a given day at the index streamgauge also occurred on the same day as the ungauged location.
For example, if the streamflow on 1 October 1974 was at the 0.9 exceedance probability at the index streamgauge, then it is assumed that the streamflow on that day at the ungauged location also was at the 0.9 exceedance probability.To implement the Introduction

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Full QPPQ-transform method in the software tool, a FDC is constructed from the observed streamflows at the index streamgauge, and then the FDC and the daily flow time series are used together to construct a daily time series of exceedance probabilities for the streamgauge.The exceedance probability for each day at the streamgauge is then entered sequentially into the estimated FDC for the ungauged location to construct the daily streamflow time series there.

Software tool
All data underlying the software tool and methods are freely available across the United States and, therefore, the software tool can be considered a general framework to provide daily streamflow time series at ungauged locations in other regions.The software tool initially interfaces with the US Geological Survey StreamStats tool (Ries et al., 2008) to delineate a catchment area for any user-selected location on a river and to compute the catchment characteristics needed to estimate the FDC at the ungauged location (Fig. 1).The selection of the index streamgauge, the computation of the FDC and the estimate of the time series of daily streamflow is executed by a Microsoft Excel spreadsheet program with Visual Basic for Applications (VBA) coding language.
The spreadsheet itself, which contains the VBA source code, can be used independently of the StreamStats interface and is, therefore, able to be customized to interface with other watershed delineation tools or with any study area for which the methods in Sect. 2 have been applied.
The StreamStats tool operates within a web browser, and is accessible at http:// streamstats.usgs.gov.The StreamStats home page provides a general description of the application.A gray box on the left side of the page contains a series of links to pages that document how to use the application, define terminology, and so forth.The map navigation tools provided in the StreamStats user interface should be used to locate a point along the stream of interest.In addition to the stream network, users can view satellite imagery, topographic maps, and street maps to find the river location

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Full of interest.With the map zoomed into a scale of at least 1:24,000, pressing on the Watershed Delineation button, and then on the map at location of interest will cause the catchment boundary for the selected location to be delineated and displayed on the map (Fig. 3A).Once the catchment is delineated, pressing on the Basin Characteristics button will result in the appearance of a new browser window that contains a table of the catchment characteristics for the selected location (Fig. 3B).StreamStats uses the processes described by ESRI, Inc. (2012) for catchment delineation and computation of catchment characteristics.StreamStats also provides a Download tool to export a shapefile of the contributing catchment (Fig. 5A) for use in other mapping applications.
The Microsoft Excel spreadsheet used to estimate daily streamflow for the stream location of interest contains five worksheets (Figs.3C-F).The spreadsheet opens on the MainMenu worksheet, which provides additional instruction and support contact information (Fig. 3C).The user enters the catchment characteristics summarized by StreamStats into the BasinCharacteristics worksheet (Fig. 3D) and then presses the command button to compute the unregulated daily streamflows.The program then follows the process outlined in Fig. 1 and Sect. 2. The estimated streamflows are, in part, computed from regional regression equations that were developed using the catchment characteristics from the approach discussed in Sect.2.1.Streamflows estimated for ungauged catchments having characteristics outside the range of values used to develop the regression equations are highly uncertain because these values were not used to fit the regression equations.Therefore, the software tool includes a message in the BasinCharacteristics worksheet (Fig. 3D) next to each characteristic that is outside the respective ranges of those characteristics used to solve the regression equations.
The ReferenceGaugeSelection worksheet (Fig. 3E) displays information about the ungauged catchment and index streamgauge that was selected from the method described in Sect.2.2, including the percent difference between catchment characteristics at the ungauged and index streamgauge, the distance between the catchment characteristics at the ungauged location and index streamgauge, and the estimated crosscorrelation resulting from the map-correlation method.Whereas the tool automatically Introduction

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Full selects the index streamgauge estimated to be most correlated with the ungauged location, the five index streamgauges estimated to be most correlated with the ungauged location are also reported (Fig. 3E).The tool also allows users to choose from any of the potential index streamgauges in the study (Fig. 3E).Users select a new index streamgauge from a pull-down list and then choose the update button (Fig. 3E).
The ContinuousFlowDuration worksheet (Fig. 3F) displays the estimated continuous exceedance probabilities, and the ContinuousDailyFlow worksheet (Fig. 3G) displays the estimated daily time series for the ungauged site.

Demonstration area
The methods described in Sect. 2 were applied to the Connecticut River Basin (CRB), located in the northeast United States, and incorporated into a basin-specific tool termed the Connecticut River UnImpacted Streamflow Estimator (CRUISE) tool.The CRUISE tool is freely available for download at http://webdmamrl.er.usgs.gov/s1/sarch/ctrtool/index.html.The CRB is located in the northeast United States and covers an area of approximately 29 000 km 2 (Fig. 1).The region is characterized by a temperate climate with distinct seasons.Snowfall is common from December through March, with generally more snow falling in the northern portion of the CRB than in the south.The geology and hydrology of the study region are heavily affected by the growth and retreat of glaciers during the last ice age, which formed the present-day stream network and drainage patterns (Armstrong et al., 2008).The retreat of the glaciers filled the river valleys with outwash sands and gravel as well as fine-to coarse-grained lake deposits (Armstrong et al., 2008), and these sand and gravel deposits have been found to be important controls on the magnitude and timing of base flows in the southern portion of the study region (Ries and Friesz, 2000).The CRB has thousands of dams along the mainstem and tributary rivers that are used for hydropower, flood control, and water supply just as the CRB is home to a number of important fish species that rely on the river for all or part of their life cycle.These competing interests for water required daily Introduction

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Full streamflow time series at ungauged locations to understand how dam management can be optimized to meet both human and ecological needs for water.Data from streamgauges located within the CRB and surrounding area are used in the CRUISE tool to estimate daily streamflow time series at ungauged locations (Table 1).The study streamgauges have at least 20 yr of daily streamflow record and have minimal regulation in the contributing catchment to the streamgauge (Armstrong et al., 2008;Falcone et al., 2010).Previous work in the southern portion of the study area by Archfield et al. (2010) showed that the contributing area to the streamgauge, percent of the contributing area with surficial sand and gravel deposits, and mean annual precipitation values for the contributing area are important variables in modeling streamflows at ungauged locations.For this reason, these characteristics were summarized for the study streamgauges and used in the streamflow estimation process.Contributing area to the study streamgauges ranges from 0.5 km 2 to 1845 km 2 with a median value of 200 km 2 .Mean annual precipitation ranges from 101 cm per year to 157 cm per year with a median value of 122 cm per year.Percent of the contributing area with surficial sand and gravel ranges from 0 percent to 67 percent with a median value of 9.5 percent.Streamflow in the CRUISE tool is estimated for a 44-yr daily period spanning 1 October 1960 through 30 September 2004 using the methods described in Sect. 2. Estimated regression coefficients and variogram model parameters are shown in Tables 2-4, respectively.

Performance of estimated streamflows
To evaluate the utility of the underlying methods to estimate unregulated, daily streamflow at ungauged locations, a leave-one-out cross validation for 31 streamgauges (Fig. 4) was applied in conjunction with the methods described in Sect. 2. Goodness of fit between observed and estimated streamflows for the entire simulation period was evaluated using the Nash-Sutcliffe efficiency value (Nash and Sutcliffe, 1970), which was computed from both the observed and estimated streamflows as well as the natural logarithms of the observed and estimated streamflows (Fig. 4A).The natural logarithms Introduction

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Full of the observed and estimated streamflows were taken to scale the daily streamflow values so that the high and low streamflow values were more equally weighted in the calculation of the efficiency metric.Efficiency values were mapped to determine if there was any spatial bias in the model performance (Fig. 4B).Selected hydrographs were also plotted to visualize the interpretation of the efficiency values (Figs.4C-E).
The values in Fig. 4 show that the streamflows estimated by the CRUISE tool generally have good agreement with the observed streamflows at the 31 validation streamgauges.The minimum efficiency computed from the transformed daily streamflows is 0.69 and the maximum value is 0.92 (Fig. 4A), with an efficiency value equal to 1 indicting perfect agreement between the observed and estimated streamflows.The efficiency values for the untransformed observed and estimated streamflows range from 0.04 to 0.92 (Fig. 4A).This decrease in efficiency between the transformed and untransformed observed and estimate streamflows suggest that the fit between the observed and estimated streamflows from the CRUISE tool at high streamflow values is more of a challenge than the fit at the other streamflow values.Despite this, the CRUISE tool appears to result in high efficiency values across all validation sites (Fig. 4).Streamgauges in the northern portion of the basin have lower efficiency values than streamgauges in the middle and southern portions of the basin; however, it should be noted from the hydrographs in Fig. 4 that the CRUISE tool is able to represent the daily features of the hydrographs at the validation streamgauges even though the efficiency values are relatively lower in the northern portion of the study area.The efficiency values and hydrograph comparisons demonstrate that the CRUISE tool can provide a reasonable representation of natural streamflow time series at ungauged catchments in the basin.

Summary and conclusions
This paper presents one of the first software tools to provide daily streamflow time series for any user-selected river location in a region.The software tool is freely-available Introduction

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GMDD Introduction Conclusions References
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Full  Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |and requires only an internet connection, a web browser program, and Microsoft Excel version 2000 or higher.Furthermore, the underlying data used to develop the tool and the source code are freely-available and adaptable to other regions of the United States.Daily streamflow is estimated by a four-part process: (1) delineation of the drainage area and computation of the basin characteristics for the ungauged location,(2) selection of an index streamgauge, (3) estimation of the daily flow-duration curve at the ungauged location, and (4) use of the index streamgauge to transfer the flowduration curve to a time series of daily streamflow.The software tool, when applied to a river basin in the northeastern United States, provided reliable estimates of observed daily streamflows at 31 validation streamgauges across the basin.This software framework and underlying methods can be used to develop map-based, daily-streamflow estimates needed for water management decisions at ungauged stream locations for other regions.
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Fig. 2 .
Fig. 2. Diagram showing the methods used to estimate a continuous, daily flow duration at an ungauged location.

Fig. 4 .
Fig. 4. Range of efficiency values computed between the observed and estimated streamflows at the 31 validation streamgauges (A), spatial distribution of efficiency values resulting from logtransformed observed and estimated daily streamflow at 31 validation streamgauges (B) and selected hydrographs of observed and estimated streamflow for the period from 1 October 1960 through 30 September 1962 (C-E).
Fig. 1.Diagram of the process to estimate unregulated, daily streamflow at ungauged locations.Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |