Measuring Flood Discharge
Summary and Keywords
With a continuous global increase in flood frequency and intensity, there is an immediate need for new science-based solutions for flood mitigation, resilience, and adaptation that can be quickly deployed in any flood-prone area. An integral part of these solutions is the availability of river discharge measurements delivered in real time with high spatiotemporal density and over large-scale areas. Stream stages and the associated discharges are the most perceivable variables of the water cycle and the ones that eventually determine the levels of hazard during floods. Consequently, the availability of discharge records (a.k.a. streamflows) is paramount for flood-risk management because they provide actionable information for organizing the activities before, during, and after floods, and they supply the data for planning and designing floodplain infrastructure. Moreover, the discharge records represent the ground-truth data for developing and continuously improving the accuracy of the hydrologic models used for forecasting streamflows. Acquiring discharge data for streams is critically important not only for flood forecasting and monitoring but also for many other practical uses, such as monitoring water abstractions for supporting decisions in various socioeconomic activities (from agriculture to industry, transportation, and recreation) and for ensuring healthy ecological flows. All these activities require knowledge of past, current, and future flows in rivers and streams.
Given its importance, an ability to measure the flow in channels has preoccupied water users for millennia. Starting with the simplest volumetric methods to estimate flows, the measurement of discharge has evolved through continued innovation to sophisticated methods so that today we can continuously acquire and communicate the data in real time. There is no essential difference between the instruments and methods used to acquire streamflow data during normal conditions versus during floods. The measurements during floods are, however, complex, hazardous, and of limited accuracy compared with those acquired during normal flows. The essential differences in the configuration and operation of the instruments and methods for discharge estimation stem from the type of measurements they acquire—that is, discrete and autonomous measurements (i.e., measurements that can be taken any time any place) and those acquired continuously (i.e., estimates based on indirect methods developed for fixed locations). Regardless of the measurement situation and approach, the main concern of the data providers for flooding (as well as for other areas of water resource management) is the timely delivery of accurate discharge data at flood-prone locations across river basins.
Given the critical role played by discharge in water resource management, the development of methods for its measurement started in Egyptian and Greek antiques times (e.g., Frazier, 1974). Today, the discharge measurements in streams (a.k.a. streamflows) benefit from a much wider variety of instruments and techniques compared to other hydrologic/hydraulic variables. Among all discharge data beneficiaries, the areas of flood forecasting and monitoring are of critical importance, as they inform society about one of the largest natural disasters. The current streamflow data, along with the datasets acquired over extended time periods, are important for understanding and investigating floods as a physical process, estimating flood hazard levels, assessing the risk posed by floods for the socioeconomic activities ongoing in the river floodplains, and producing timely warnings. The role of monitoring is central as it is the only source for valid records of all variations in the streamflow. Records of flood events serve as the basis for the design of river infrastructure (from bridges to reservoirs) and for floodplain delineation. The streamflow records provide data for the planning and design of river-related projects and are also used after the projects have been completed for management and operation purposes. Streamflow records provide the requisite ground-truth data for the calibration and validation of hydrological models used for streamflow, hazard, and risk forecasting.
Measurements of discharges for supporting flood hazard mitigation are made at gauging stations by specialized agencies using well-established protocols and programs (WMO, 2010a, 2010b). The acquired data are most often assembled into regional or national streamflow monitoring networks that provide a general perspective on the status of the river network in real time. For example, the national monitoring system of the United States falls under the supervision of the U.S. Geological Survey (USGS), which manages discharge data produced by many agencies for 18,500 U.S. locations. Out of these locations, about 8,000 stations are used for providing real-time river flow measurements. Almost half of the stations issue forecasts of flow conditions on major rivers and small streams in urban areas (Mason & Weiger, 1995). The information produced by forecasting stations is especially critical during floods, when timely and accurate estimations of the flood spatiotemporal evolution over large scales are paramount.
Discharge, as a flow variable, is a function of flow geometry and its velocity. There is no single-sensor instrument to directly measure discharge in streams. Traditionally, the discharge has been computed from direct measurements of stream width, stream depth, and flow velocity, all separately acquired with several different instruments. With the advent of modern sensors, the streamflow can be directly acquired through “autonomous” (i.e., anytime, at any stream location) measurements using just one instrument and one deployment. For example, the Acoustic Doppler Current Profiler (ADCP) can provide discharge measurements in a fraction of the time required by any of the previous measurement methods from one river passing. Other methods for directly measuring discharges (such as weirs and sluice gates) are available, but they are typically utilized at fixed locations in the streams.
For the present context, it is useful to make the distinction between “discrete” and “continuous” discharge measurements as, in general, the instruments and techniques have been designed to support one or the other type of measurements. “Discrete” discharge measurements are acquired for characterizing the status of the flow at a given time. While it is easy to obtain this characterization for normal flow conditions, during high flood events the direct measurements are difficult, unsafe, or impossible. The means to acquire discrete discharge measurements and the ancillary protocols for data acquisition have been complemented by ample guidelines developed continuously over time by the hydrology community (see, for example, WMO, 2010a).
“Continuous” flow measurements over shorter or longer time intervals are common for most water resource areas, and essential for flooding events (NAS, 2012). Continuous discharge estimations are typically made in conjunction with discharge rating curves (RCs) or “ratings”. An RC can be a simple relationship between stage and discharge, or a more complex relationship in which discharge is a function of other factors (slope, rate of change of stage, etc.). The RCs are constructed by acquiring simultaneously direct measurements of the discharge and the other variables involved in the relationship. Obtaining reliable relationships can be attained by repeatedly acquire direct measurements spanning a wide range of stream discharges. After the RCs are constructed and consolidated, they are used as stand-alone direct-measurement surrogates that provide discharges using only the continuously measured variable(s) for which the RCs were built (e.g., stage). The established RCs can be affected by multiple factors that might occur at the gaging site, such as vegetation growth, changes in flow dynamics and channel morphology. Verification of the initial RC is therefore needed by periodically inspecting the gaging site to ensure that these factors do not affect the accuracy of the RC estimates. If differences between new measurements and the RC estimates occur, corrections (a.k.a. “shifts”) are applied to account for the changes produced at the gauging site.
At a time when flooding frequency and intensity have dramatically increased globally, the measurement methods for discharge in streams continue to seek for improvements, pressed by the societal need for more accurate measurement of streamflows during these hazardous situations. Fortunately, significant advancements of new nonintrusive technologies (such as those based on acoustics or images) in the last several decades hold great promise to revolutionize both the discrete and continuous autonomous discharge measurements in normal and extreme flows (Muste et al., 2007; Mueller et al., 2013). The availability of increased high-quality amounts of streamflow data, in conjunction with improved modeling and communication means, can ensure the delivery of timely information for flood mitigation in flood-prone areas, regardless of their size (from local to regional and continental), location, and hazard level.
Presentation, or even the listing, of all conventional methods for discharge measurement is beyond the scope of this article. Instead, we describe essential elements of selected instruments and methods for discrete and continuous measurement of discharge with a focus on those capable of providing measurements over the range of flows of interest for flood monitoring and investigations. For readers interested in the whole range of methods used for various flow measurement situations, a wide selection of books is available for consultation (WMO, 2010a, 2010b; Rantz et al., 1982b; Herschy, 2009).
Discrete Autonomous Measurements
For most of the past century, discrete discharge measurements were determined using velocity-area methods whereby point velocities and flow depths were acquired over subsections of the stream cross-section, followed by the summation of the discharges for all subsections. The velocity-area method is widely covered in the hydrometry literature (e.g., Rantz et al., 1982a; Herschy, 2009). The advent and subsequent development of new acoustic technologies in the last few decades has gradually changed the way in which hydraulic data (including discharges) are collected in streams and human-made channels, as the new instruments are efficient, performant, and safe to operate during normal and extreme flows (e.g., Muste et al., 2007). As instruments such as ADCPs have already demonstrated their measurement capabilities (e.g., Muste et al., 2007) and are most likely to become the new standard, this discussion is limited to measurements acquired with this type of acoustic instrument.
ADCPs were introduced in the riverine environment in the 1980s with the goal of measuring discharge, and they continue to expand their presence throughout the world. Downward-looking ADCPs estimate velocities by releasing acoustic (sound) pulses (a.k.a. pings) toward the stream bottom and “listening” to the return signal backscattered by suspended matter in small water volumes (bins) located along the acoustic beam path (see Figure 1a). The scattering particles, assumed to move with the same velocity as the flow, produce a Doppler shift in the signal returned to the instrument receiver that is subsequently converted to velocity by a customized processing algorithm. The velocity component resolved from the Doppler shift is aligned with the acoustic beam path. Each depth cell (a.k.a. bin) has a velocity associated with it (i.e., in-bin velocity). The location of the depth cell is determined by multiplying the speed of sound in water with the time that it takes for the sound to return to the probe.
Given that one beam provides just one velocity component, ADCPs are designed using a multibeam arrangement. The number of beams in the arrangement varies (three, four, or more), depending on the instrument manufacturer. Figure 1a displays a four-beam arrangement used by one of the main ADCP producers (TeledyneRDI Inc.). Only three beams are needed to completely define the velocity vector. Additional beams are devised to improve the accuracy of the measurement and making the instrument more versatile for measurements in various field conditions. The in-beam velocities are measured in instrument coordinates and may then be translated to Earth coordinates using a calibrated internal or external compass and an estimate of the local magnetic declination. Velocities measured in each beam for the same cell depth are subsequently combined to obtain a resultant vector for that depth. The final result of the measurement is a three-dimensional velocity profile assigned to the instrument axis that is the equivalent to the profile obtained with repeated point-velocity measurements in that vertical, therefore the measurement is considerable faster. An important assumption associated with the ADCP velocity measurement is that the flow within the ADCP footprint (the pyramid enclosed by the four beams in Figure 1a) is homogeneous in horizontal planes throughout the flow depth. If this assumption is violated (for example, by a strong three-dimensional flow created in the ADCP footprint), the error in velocity estimates can be substantial (Vermeulen et al., 2014).
The approach most often used to measure discharges with downward-looking ADCPs is to install the instrument on a boat that crosses the river, as illustrated in Figure 1a. This approach is also known as the “transect” or “moving-boat” method (Mueller & Wagner, 2009). Measurements of the vertical velocity profiles are repeated at high sampling rates during the ADCP bank-to-bank movement, resulting in a spatially dense dataset covering almost the entire stream section, as illustrated in Figure 1c. The discharge is determined for each individual bin and then summed up for the entire stream cross-section by microprocessors embedded in the instrument hardware. ADCPs cannot measure very close to the river banks, near the bottom, or near the surface, as indicated in Figures 1b and 1c. The flows in the unmeasured areas are estimated using analytical extrapolation algorithms that the users select from a set of options. Mueller et al. (2013) provide detailed guidance on procedures for conducting moving boat ADCP discharge measurements. Typically, several transects traversed in both directions are acquired to determine a mean value for the stream discharge. The accuracy of moving-boat ADCP discharge measurements depends on many factors, and estimation of the measurement uncertainty remains an area of active research (e.g., Gonzalez-Castro & Muste, 2007). An alternative approach for determining discharge with ADCPs is to measure velocities with the boat set at fixed points across the section and using the such-obtained velocity profiles in conjunction with the conventional velocity-area method to determine the stream discharge. This acquisition approach is labeled as the section-by-section method.
Continuous Measurements with the Stage-Discharge Method
While autonomous direct flood measurements are desirable and increasingly possible, currently most of the real-time data for flood monitoring are provided by continuous flow estimation methods. These methods emerged at the beginning of the 20th century with the expansion of electricity-based technologies that also provided a means to record the acquired data collected at the sites (Rantz et al., 1982b). Besides their capacity to continuously estimate discharges, the introduction of the continuous monitoring methods gradually replaced the previous nonrecording gauging stations due to their superior efficiency (as they do not require an observer at the site) and accuracy (Rantz et al., 1982a). Taking advantage of the advancements in electronic and communication technologies in the last half-century, gauging stations have been linked in networks covering large areas of many countries. Today’s modern gauging stations are outfitted with telemetry equipment, which allows the stations to communicate the streamflow information in real time for the entire network.
The methods for continuous streamflow measurement are based on empirical or semi-empirical relationships, called rating curves (or “ratings”), that pair direct discharge measurements with direct measurements of some other variables acquired at gauging stations located at carefully selected river locations. The independent variables selected for developing the ratings are those that are the most sensitive to changes in discharge magnitude (i.e., stage, velocity, or free-surface slope). They are valid only for the site where they have been developed. The stage-discharge method is the most popular conventional approach for continuous discharge estimation. Stage-discharge ratings are built and consolidated over time being displayed as diagrams. Rating construction assumes that the stream gauge sites fulfill the requirements formulated by the best domain practice (e.g., Rantz et al., 1982a). In particular, these guidelines assume careful site selection, minimal changes of the morphological characteristics at the gauging site, and limited changes in the flow structure passing through the station over short and long time intervals.
The core element of the simple stage-discharge method is the rating curve (RC) relating the water-surface level above a local datum (H) to the discharge in the stream (Q), which explains the HQRC label used herein for the rating. The HQRC is established from a series of direct stage and discharge measurements (a.k.a. calibration measurements) acquired over a wide range of flows passing through the gaging station. Figure 2 illustrates the steps involved in the construction and use of HQRCs for the medium-to-high streamflow range. The curves are typically monotonically increasing functions up to the bankfull stage when the stream overflows into the floodplain. The HQRC ratings in this area are rarely derived by means of regression applied to the calibration measurements. Traditionally, the staff of the hydrometric agencies uses the calibration data in conjunction with expert judgment to shape the curves. Consequently, conventional means for statistical assessment of the rating quality (goodness-of-fit measure such as the sum of squares due to error, R-square, and root mean squared error) are rarely used. Supplementary measurements in the vicinity of the gauging site in conjunction with analytical methods can be employed to verify the quality of the constructed rating (Holmes, 2017).
For low flows, the HQRC rating can have different shape and slope, as shallow flows might be governed by a different flow mechanism. Specifically, the flow is predominantly controlled by geometrical features of the station’s cross-section and its vicinity (e.g., the presence of natural bumps or similar obstacles), not by the channel friction, as is the case for medium-to-high flows (Holmes, 2017). The shape of the rating curve in this area can be guided by an exponential function of the form, , where is the stage for the zero flow. This zero-flow stage, obtained by a detailed channel survey in the vicinity of the station, is the stage where the flow in the channel ceases. The coefficients are obtained from applying regression to the measured Q–H data pairs. In general, complex geometry at the stations requires the use of complex fitting functions and calls for a larger stage-discharge survey dataset. An often-used regression alternative is based on a polynomial function, but this approach may increase the uncertainty of the parameter estimation. The uncertainty can be somewhat limited by increasing the number of data points used in the regression.
Once a suitable RC is established, discharge can be estimated continuously by directly measuring only the river stage and determining the corresponding discharge from the established rating. The station has to be continuously inspected to ensure the strict application of the guidelines for gauge operation (Rantz et al., 1982a). Deviations from these guidelines might overlook flow disturbances that can occur at the gauging location and are not accounted for in the assumptions of the RC construction. An example of such disturbance is common in small streams where significant vegetation growth on the banks and, for some situations, even in the main channel may occur. The seasonal changes associated with vegetation growth affect the shape of the RC, as demonstrated by Gunavan (2010). Regardless of their nature, disturbances adversely affect the quality of the measurement results without notice as they are no part of the data collection process.
The HQRC is reliable only over the flow range where calibration measurements were taken. Often the in-situ flow velocity measurements are unavailable for extreme conditions; thus, the RCs lack data in the area of high flows that is typically associated with flood situations. The conventional method for extending the RC for high flows is the slope-area method discussed below. Without the additional information provided by this method, extrapolation of RCs above the bankfull stages is risky. It is worth mentioning that the introduction of new measurement instruments such as ADCPs greatly facilitate the acquisition of data for a notably larger flow range and with much increased efficiency. Therefore, it is expected that the quality of the RCs improves over time.
Extension of the Stage-Discharge Ratings for Flow through Floodplains
The HQRC behavior becomes more complex when the water stage rises and overflows into the floodplain as the shape of the cross-section is dramatically changed, as illustrated in Figure 3a (USACE, 2017). Typically, the stage corresponding to bankfull becomes an inflexion point in the RC, as illustrated in Figure 3b. The portion of the HQRC above the bankfull stage is difficult to extrapolate as there are few measurements available for conditions when the floodplain is inundated, for reasons discussed later in this section. Changes in the RCs are typically based on expert knowledge accounting for the open-channel mechanics in compound channels with variable roughness (e.g., Schmidt & Garcia, 2003) and a good familiarity with the gauging site local hydraulics.
The best approach for filling data in the missing portion of the HQRC in the overflow area is to conduct direct measurements during floods. However, there are several operational obstacles involved when measurements are acquired for flows exceeding the bankfull stage. The first obstacle is related to accessibility of the gauging sites as the roads during flooding can be blocked (Le Boursicaud et al., 2016). Other obstacles are related to the flow conditions and instrument operational aspects that might occur during the floodplain measurements. Irrespective of the instrument, the major problems related to the flow are their high velocities and, in many situations, the presence of the floating debris. Both factors pose threats to boats and measurement instrumentation. Furthermore, the small depths and irregular bathymetry can severely obstruct the collection of direct flow measurements in a floodplain. Moreover, during floodplain flows rapid morphological changes occur, which can drastically restrict boat movement. These problems are common for most of the instruments and methods, but for illustration purposes we will restrict our discussion to ADCP measurements increasingly used for HQRC constructions.
ADCPs can acquire accurate data in simple and compound channels, as demonstrated by Admiraal and Demissie (1996). However, measurements in shallow flows, as is the case in inundated floodplains, face various limitations. First, the boat-mounted ADCPs require a minimum submergence (a.k.a draft) of about 0.1 m to keep the sensor head under water when the boat tilts under the action of wind or water waves. Second, the instrument cannot read close to the instrument sensor due to ringing, an inherent effect for ADCP sensors (Muste et al., 2010); therefore, an additional distance from the sensor is discarded from depth measurements. The combination of these two factors precludes acquiring ADCP velocities closer than about 0.2 m from the water surface even with a stable boat and small instrument draft. Furthermore, ADCPs cannot measure in the lower 6% of the water column (see, for example, Gordon, 1989). The limited ADCP capabilities to measure near the stream surface and bottom, and the relatively shallow depth of the water in the floodplain, lead to just a few valid measurements over the flow vertical. Taking into account that the floodplains are typically vegetated, an additional concern is that the quality of the measurements can deteriorate (Warren & Perterson, 2007). To make the situation worse, more complexities arise in situations where the floodplain bottom is nonuniform (Vermeulen et al., 2014). Finally, when sediment concentration is excessively high, the ADCP measurements cannot be taken at all.
The many problems associated with the direct measurements in the floodplain leaves no alternatives for filling data points above the bankfull stage other than using numerical simulations. Numerical models vary in their complexity from one-dimensional steady approaches (USACE, 2017; Kean & Smith, 2005) to more models that capture the momentum exchange between the stream and its floodplains (e.g., Lang et al., 2010; Shiono & Muto, 1998). For illustration purposes, Figure 3b compares the USGS stage-discharge rating with the one obtained with a one-dimensional HEC-RAS model (USACE, 2017). As the figure shows, this model can be reliably used to provide data for the RC extrapolation.
Indirect Peak Discharge Estimation
The most popular approach to extend the HQRC above the bankful stage is to use the high-water mark stages left by the flood passage (i.e., flood peaks) in conjunction with the slope-area method. The slope-area method estimations are based on the Manning equation, applied over three or more channel cross-sections that are assumed to maintain as close as practically possible the flow uniformity over a wide range of discharges (Dalrymple & Benson, 1984; ISO 1070, 1992). Selection of the site for implementing the method should take into account the availability of high-water marks, the absence of major changes in the channel configuration during flood wave propagation, and the lack of upstream or downstream flow controls. In addition, the reach should be long enough to develop a fall in the free surface elevation that is beyond the range of uncertainty in measuring the elevation of the high-water marks. All of the above conditions are needed to make reliable use of the Manning equation. While it is obvious that attaining all these considerations is difficult, there are internal consistency checks within the method (i.e., use of the energy equation) to confirm that the departure of the actual flow situation from the assumed one is within an acceptable range.
The peak discharge is estimated by plugging into the Manning equation the values for the measured cross-sections, channel roughness, and the friction (or energy) slope (derived from the measured fall divided by the distance between the in-situ identified high-water marks). Given that natural channels are invariably nonuniform, the slope-area method application has to account for the factors that might affect the friction slope (Darlymple & Benson, 1984). This is done by computing the geometric mean of the conveyance for the series of cross-sections considered along the reach. Overall, the slope-area method has proven to be reliable, provided an accurate Manning’s roughness coefficient has been selected (Dalrymple & Benson, 1967). The slope-area method shows potential for further improvement by taking advantage of the emerging technologies. For example, regular cellular phones can acquire georeferenced photographs of the water levels obtained during floods. Subsequent processing using camera specifications and customized software is achievable for converting the camera coordinates to actual stages in the stream that are equivalent of the high-water marks (Le Coz et al., 2016). Such information, centralized through crowdsourcing for multiple ungauged stream locations, offers a good opportunity to supplement the discharge data provided by the existing stream gauging networks.
Even though the newer technologies such as ADCPs are increasingly capable of acquiring data during high-flow events, the slope-area method is still popular for peak discharge estimations, as severe flood events are relatively rare and the majority of the alternative measurement methods/instruments face difficulties in acquiring reliable sample data during floods. Moreover, the time at which the flood peak occurs cannot be known with sufficient precision to reach the site at the proper time, not to mention that frequently it is impossible to access the gauging sites because of traffic interruptions. Consequently, the slope-area method remains a useful indirect method to estimate discharge after the passing of the flood events.
Complexities in Monitoring Flood Flows
Use of the simple HQRCs is limited to uniform and steady flow conditions. During floods, it is most likely that neither of the flow conditions exists, as flood wave propagation is associated with large variations of flow in time and/or space. With the increase of the stage, the flow becomes nonuniform owing to the irregularity of the natural channels (e.g., cross-sectional geometry, channel-bed roughness) and the development of backwater in the stream. Furthermore, the rapid variations in the streamflows associated with storm events produce unsteady flows. Addressing the deviations from the conditions assumed in the simple HRQC construction requires either alternative measurement approaches (for nonuniform flows) or adjustments made to the ratings (for unsteady flows). More complexities are involved if the floods occur in tidal rivers where the unsteadiness effects can extend over hundreds of kilometers inland (Hoitink & Jay, 2016).
The presence of local hydraulic controls such as river confluences, weirs, dams, and naturally occurring features such as riffles are likely to cause backwater or drawdown that cannot be handled with the simple stage-discharge relationships that are valid only for uniform flows (Hidayat et al., 2011). The discharge for these conditions is a function of both the stage and slope of the stream energy gradient (Rantz et al., 1982b). For such observation sites, stage-fall-discharge ratings are developed by directly measuring the discharge and stages at a base gauge and another auxiliary gauge (typically downstream from the base). The water-surface slope (determined from the two-stage readings) is measured with high frequency during nonunifrom flow conditions to capture the variation in the slope with the change in discharge. By analyzing the relationship between the slope and discharge established from direct measurements, one can determine whether or not the fall marked against each measurement is affected by backwater at all stages, or only above a given value of the stage/discharge. Construction details of each of these special rating cases are provided in Rantz et al. (1982b).
Another complexity affecting the simple stage-discharge rating is the occurrence of flow unsteadiness, which can be irregular (as produced by flood waves and river structure operations) or periodic (as produced by tides). The first type of unsteadiness is discussed in this section while the second type is discussed next. Among the random unsteadiness category, the unsteady flows produced by storm runoff directed to inland rivers are the most frequent. The passage of a storm wave can last minutes, hours, days, or even longer, depending on the location of the river site in the watershed as well as on the storm intensity and duration.
Typically, the rising stage of the flood wave is much shorter than the falling stage, and the associated acceleration rates are different for the two limbs of the hydrograph (see Figure 4a). Laboratory experiments conducted by Song and Graf (1996) show that during the passage of the hydrograph the velocities on the rising limb are higher than on the falling limb for the same flow depth (Tu & Graf, 1992; Nezu & Nakagawa, 1995). Consequently, the depth-averaged velocities and the velocity over the entire cross-section are also different, leading to a nonunique relationship between stage and mean channel velocity.
The above changes are not accounted for in the simple HQRC that assumes the river flows under steady and uniform conditions. For such flow regimes, the relationship between the steady RCs’ variables are unique for the rising and falling limbs of a flood hydrograph, even if the flow is slightly nonuniform and quasi-steady. Figure 4b illustrates this situation; it should be noted that for steady flows the maximum cross-sectional velocity (Umax), the discharge (Qmax), and the depth (hmax) reach their peak at the same time. For unsteady flow situations, the three peaks are separated, as illustrated in Figure 4c, with Umax peaking first, followed by Qmax and hmax (Graf & Qu, 2004).
Flow unsteadiness creates separate stage-discharge relationships for the rising and falling limbs of the hydrograph that are distinct from the unique, monotonically increasing RC for steady flows, as it is graphically illustrated in Figure 4d. The departure of the unsteady limbs from the one-to-one rating is called a “loop” (Henderson, 1966) or “hysteresis” (a general term defining changes of the status of the system that depend not only on the present state but also on its past state). The available experimental data show that the differences between steady and unsteady HQRCs are more significant for low-gradient channel slopes exposed to large flow unsteadiness (Faye & Cherry, 1980; Fread, 1975; Di Baltassarre & Montanari, 2009; Dottori et al., 2009; Hidayat et al., 2011). The latter condition is quite typical during flood events when the RC’s accuracy matters most.
Tidal Rivers and Estuaries
Rivers located in coastal areas might be subject to tide action, a process that produces periodic flow variations. Discharge monitoring in tidal rivers and estuaries requires a different strategy than the one described in Flow Nonuniformity for inland rivers (Hidayat et al., 2014). Tidal channels tend to widen toward the coast, in the transitional region where the tidal velocity is high and the stream velocity decreases because of the increased storage capacity in this area (Sassi et al., 2012). The head gradient required to achieve a constant discharge through the river and estuary increases with the tidal velocity amplitude (Dronkers et al., 1964; Jay et al., 2016). Consequently, the tides elevate the mean surface-water levels, creating a time-varying setup whereby the mean water levels are highest during spring tide and smallest during neap tide (e.g., Sassi et al., 2013; Hoitink & Jay, 2016).
When a rain-induced flood wave reaches the tidal river, the combined effect of the two sources of unsteadiness results is an attenuation of the tidal motion. The rise in mean water levels will be partly canceled by the drop in water-level elevation caused by attenuation of the tides, which reduces the time-varying setup. Through attenuation of the tides, tidal channels may accommodate the peak river discharge without reaching conditions of overbank flow. Attempts to better understand the dynamic interplay between river discharge and the tidal motion have been made by analyzing the ratio of tidal amplitude in the river and at sea (Jay & Kukulka, 2003). Recent studies have shown that this approach can be adopted to retrieve historical peak discharges (Moftakari et al., 2013, 2015), albeit with limited accuracy. The method relies on a regression analysis for fitting the friction parameters for the estuary in a theoretical model for the tide, which is subsequently inverted to estimate discharge.
An increasing trend for obtaining more accurate estimations of tidal river discharge is to directly acquire flow velocities (Hoitink et al., 2009; Sassi et al., 2011). While acoustic instruments are suitable for these kinds of measurements, they may be challenged by the presence of salinity gradients and the associated estuarine circulation (Bechle et al., 2011). The vertical and horizontal circulations are driven by the density difference between freshwater and saltwater (e.g., Dyer, 1997). The presence of density gradients produces refraction of the acoustic beams traveling through the flow, which in turn affect the accuracy of the ADCP’s output (e.g., Medwin & Clay, 1997). Given the large width-to-depth ratios of estuarine channels, these density gradients are particularly relevant for measurements acquired with horizontal ADCP deployments.
This technique can account for the refraction patterns occurring in the beam path using analytical methods. Proof of concept analyses show promising results (Kawanisi et al., 2010, 2012), especially for weak to mildly stratified conditions in which acoustic rays are homogeneously distributed over the cross-section. For strong stratification, the acoustic rays may reflect at the pycnocline, leaving part of the cross-section ungauged.
Subcritical and Supercritical Flow
During the development of extreme discharge events, the flow may alternate between subcritical and supercritical flow (Henderson, 1996). The distinction between the two regimes is made by the Froude number, , where V is flow velocity, g is the gravity acceleration, and H denotes water depth. Subcritical or slow flow occurs when Fr < 1, flow is critical for Fr = 1, and the flow is supercritical when Fr > 1, which is also referred to as “fast” or “shooting” flow. Froude numbers can exceed the critical value for high velocities in shallow flows. The flow in the main channel of a river is, however, unlikely to become supercritical, as Lumbroso and Gaume (2012) illustrated. Their analysis on flash floods led to the conclusion that many hydrological and hydraulic analyses assume supercritical flood flow conditions where conditions appear subcritical after reanalysis. This misperception is similar to the assumption that the channel roughness does not change during extreme conditions, which is also untrue. However, the submerged vegetation on shallow floodplains causes an increased hydraulic roughness, which in turn leads to higher water levels that preclude the formation of supercritical flow for the channel as a whole. Several other investigators confirmed Lumbroso’s and Gaume’s (2012) findings by arguing that in natural channels supercritical flow cannot be sustained over reaches longer than about 20 m (Jarrett, 1984, 1987; Grant, 1997; Tinkler, 1997).
The shallow zones of a channel reach can, however, become more often supercritical. When the stage reaches the level that produces flow overrun in the floodplain, the shallow flow protruding in the floodplain from the main channel can be supercritical because the velocities and the slope driving the local flow are high (Peltier et al., 2013). Local features in the floodplain topography can result in scattered transitions from subcritical to supercritical flow that can switch in time, leading to the formation of hydraulic jumps, as illustrated in Figure 6. These transitions complicate the relationship between local depth and discharge. In general, supercritical flows are highly irregular and difficult to gauge. Without other measurement alternatives at hand, image-based techniques can be used to monitor floodplain supercritical flow, as illustrated by Sun et al. (2010).
The alternation between supercritical and subcritical flow is also relevant in the context of flow measurement with hydraulic structures. Structures such as broad-crested weirs are suitable for monitoring flows in small streams being designed in many configurations (e.g., Bos, 1989; Henderson, 1996). Discharge measurement structures generate critical flow conditions, for which a theoretical relationship between stage and discharge can be obtained. The discharges measured with these structures are typically accurate, provided that sufficient fall is available and free flowing conditions occur at a critical depth (Bos, 1989). However, peak discharges may cause tailwater to reach the upper limit of the calibration range of measurement weirs and flumes. This is exemplified in Figure 7, which shows an H-flume during low and high flows (Brauer et al., 2011).
The H-flumes are designed to measure a wide range of conditions, but during high flows, the rising tailwater increases their submergence, which may lead to a violation of the assumptions underlying their stage-discharge relationships.
Shifting in the Ratings
Even if the gauging site is selected following the best practices, natural streams display a wide variety of complexities that often makes it impossible to fulfill all the guidelines (Holmes, 2016). Moreover, changes at the station may occur owing to a variety of reasons (scour/fill in the stream channel or accumulation of debris). Many of these changes are associated with dynamic flows events such as flood passage through the station. The changes may produce deviations from the established ratings, especially in the low-flow portion of the rating curves as the flow control might change. The deviations can be gradual or abrupt, temporary or permanent (Kennedy, 1984). These changes can be detected visually by plotting new discrete discharge measurements acquired at the station on the existing rating graphs. The current practice assumes that if the discharge measurements during verification display a change larger than ±5% of the value indicated by the rating, corrections and/or shifts to RCs are required (Rantz et al., 1982a).
The hydrometric agencies in charge with the operation of the gauging stations conduct periodic verifications of the ratings to make sure that the equipment is in working condition. Even if they perform well in steady and uniform flow conditions, the status of the ratings needs to be inspected by direct observations after each major storm propagating through the station, as they might be affected by one or more morphological changes. The adjustment of the ratings is typically made on the basis of hydrologic judgment applied to visual observations and with consideration of the site morphology behavior over time. Guidance on shift detection, establishment of periods for shift controls, and application of corrections to the rating as a whole are extensively covered by guidelines (e.g., in WMO, 2010b; Rantz et al., 1982b).
Emerging Streamflow Monitoring Methods
Most of the emerging discharge estimation approaches result from rejuvenating conventional approaches by adding new instruments or enhanced sensor configurations. Another emerging trend in monitoring flows is the combination of in-situ measurements with hydrodynamic models. As described above, some form of modeling is already in place for extrapolating the ratings in their unmeasured portion corresponding to extreme events. The most advanced contemporary discharge estimation protocols combine data from in-situ monitoring and/or remote sensing with hydrodynamic models that have an appropriate level of sophistication to more accurately replicate flow complexity in areas and situations where the capabilities of conventional methods are limited. Recently, attempts are made to measure discharges based only on satellite remote sensing (Durand et al., 2016).
Index-Velocity Method using Horizontal Acoustic-Doppler Profilers
The index-velocity method has been conventionally used with velocities measured by mechanical, electromechanical, and travel-time-based acoustic instruments (Rantz et al., 1982b; Patino & Ockerman, 1997). The development of the method was triggered by measurement situations in areas that experience periodic or random unsteady flows. For this areas, developing discharge ratings associated with the direct measurement of an index velocity in addition to stage is beneficial (Levesque & Oberg, 2012). The index velocity can be continuously acquired in a point (Chiu, 1987), along a line (Rantz et al., 1982b), or over a surface in the stream (Muste et al., 2008). Recently, the method that has increased considerably its presence with the development of the horizontal ADCPs, a new configuration of acoustic velocimeter brought in the riverine environment in early 1980s (Morlock et al., 2002; Le Coz et al., 2008; Hoitink et al., 2009). This method is used here for illustration of the index-velocity measurement approaches.
The protocol for obtaining discharge estimates using the index-velocities acquired with horizontal ADCPs is schematically illustrated in Figure 8. Repeated calibration measurements of stages (H), stream discharge (Q), and index velocities (Vindex) are used to construct the RCs associated with the channel cross-section (A) and mean channel velocity (V), respectively. A “stage-area” rating curve (HARC) is obtained by relating the depth to the corresponding cross-sectional area. The channel cross-section is determined with a detailed survey of the river bathymetry at the gauge location. The mean channel velocity is determined by dividing the discharge measured during calibrations with the stream cross-sectional area. Discharges can be measured with any of the conventional methods (e.g., point-velocity current meters); however, discharges are increasingly acquired with vertically positioned ADCPs mounted on small boats as described in Discrete Autonomous Measurements and schematically illustrated in Figure 8 (top figure). Multiple mean-channel velocities derived from the measured discharges along with the simultaneously acquired index velocities are paired to build the index-velocity rating curve (VQRC), typically by using least-squares regression.
After the index-velocity ratings establishment, direct measurements of depth and index-velocity acquired continuously with permanently deployed instruments in conjunction with the two RCs provide area and mean channel velocity. Multiplication of the mean velocity with the cross-sectional area gives continuous discharge estimates. Stages are measured with methods used by the stage-discharge method described in Continuous Measurements with the Stage-Discharge Method. Continuous observations of the index velocity are obtained by averaging velocities acquired in individual bins along the line of sight of the horizontal ADCP.
The accuracy of the index-velocity method discharge estimates is intrinsically linked to the quality of the regression model adopted to translate index velocity to cross-sectional averaged velocity. For channels with a simple geometry, this relationship is often linear. Compound channels require more complex relations, which is an ongoing field of research (e.g., Uchida & Shoji, 2014). For example, if the RC is developed as a continuum for the main channel and its floodplain, a bimodal rating should be constructed, as described in Ruhl and Simpson (2005). A new methodology for estimating mean velocities for VQRC is proposed by Chiu (1987), Chiu and Said (1995), and Chen (2013). Based on the probabilistic concept of entropy, Chiu and Chen (2003) argue that a direct relationship between the maximum velocity in a cross-section and the cross-sectional averaged velocity exists for channels with simple geometry. Following this argumentation, an acoustic profiler can be deployed at the location of the maximum velocity across the section to continuously collect vertical profiles of velocity. With the availability of more calibration data acquired at the relatively new index-velocity method stations, more complex empirical or semi-deterministic model functions relating Vindex, H and V might be developed.
For flood situations, the relationship between Vindex and V may differ for the rising and falling limbs of the flood hydrograph (i.e., a hysteresis effect) because of inertia in the process of floodplain inundation and emptying. To account for such circumstances, a more complex relationship for the VQRC is proposed (Ruhl & Simpson, 2005; Levesque and Oberg (2012). Based on the analyses conducted so far, the index-velocity method seems to capture the hysteresis with increased accuracy (e.g., Muste & Lee, 2013) compared with the HQRC. Some degree of improvement in the accuracy of index-velocity method used in unsteady flows is expected, as it is based on two direct and simultaneous measurements collected continuously at a high sampling rate, i.e., stage and velocity. The remaining question is if the index-velocity to channel-velocity relationship (i.e., the VQRC) is also subject to hysteresis. The novelty of the VQRC method compared to the more often and extensively used HQRCs does not provide sufficient experimental and analytical data to definitively answer the above question or to anticipate potential complexities associated with the use of unique RCs for unsteady events.
Continuous Slope-Area Method
The conventional slope-area method was developed to extend the HQRC usability for high flows (see Indirect Peak Discharge Estimation). The method is used in conjunction with high-water marks produced by flood events and has been streamlined by the USGS for computer implementation (Fulford, 1994). Slope-area method estimates can replicate discharge within 10% accuracy or better (Dalrymple & Benson, 1967). However, the single most important step in successfully applying the method is the selection of suitable channel reaches for its implementation (e.g., Rantz et al., 1982b; ISO 1070, 1992). These recommendations are numerous and quite difficult to fulfill in natural streams.
With the advent of low-cost recording pressure transducers, the slope-area method has resurfaced as a new approach for continuous measurement of the streamflow (Smith et al., 2010). The new approach is labeled here as the continuous slope-area (CSA) method. Recent tests conducted by Stewart et al. (2012) for estimating peak flows in ephemeral streams found that this method has uncertainties ranging from 12.3 to 15.5%. Another benefit of the CSA method is that it provides direct measurements of free surface during the rise and fall of the event hydrograph, hence the potential to capture the loop in the stage-discharge rating curve (Stewart et al., 2012). While these CSA method features are promising, evaluation of the CSA method performance for steady and unsteady flow conditions is still in its infancy.
A simplified continuous slope-area (SCSA) method has been more recently tested by Muste et al. (2016) for sites that feature quasi-uniform flow up to bankfull water levels. Figure 9 provides essentials of the measurement protocol for the simplified method. The SCSA approach is based on continuous measurement of the stream stages at only two locations (rather than three or more as specified by the CSA implementation guidelines). The difference between the stages at the two locations (i.e., the fall) divided by the distance between the sensors provides continuous estimates of the water-free surface slope. A one-time survey of one of the cross-sections (preferably the one located downstream) as well as the measurement of the distance between sensors is conducted at the time of equipment installation. The Manning’s roughness coefficient can be obtained from lookup tables (Yochum et al., 2014). For a gauging station located on a morphologically stable stream reach, the one-time survey of the cross-sectional area is sufficient. Periodic inspections of the measurements site are needed to detect possible changes in the stream configuration. The SCSA does not use an RC per se, but a synthetic stage-discharge rating curve can be readily available as the continuous measurements are acquired.
Comparison of the SCSA method estimates, along with those provided by a stage-discharge method available at a collocated USGS gauging station, is illustrated in Figure 3b. The overall agreement in the two ratings is relatively good up to the bankfull stage, which is the maximum stage for SCSA method validity. These preliminary results indicate that the less expensive synthetic rating curve obtained from the one-time instrumentation deployment can be used in certain situations as a surrogate for the more expensive stage-discharge or index-velocity methods. The major limitations of the SCSA method are its sensitivity to the accuracy of the Manning’s coefficient selection and the slope measurements. Special caution is required when Manning’s coefficients are selected from generic sources (books, tables, or expert judgment) rather than based on in-situ estimates.
The stage measurements to be used in conjunction with the SCSA method benefit from a wide variety of nonintrusive (radar- or acoustic-based) or intrusive (strain-gauged based) sensors, some of which are relatively inexpensive. Given that the operating cost of the SCSA method compared with that of most of the other discharge monitoring approaches is also lower (as it does not require direct and repeated contact of equipment and personnel with the stream for building the ratings) makes the method attractive. The gain in deploying a dense, less expensive, and ready-to-use network of discharge stations, even if the uncertainty is not at the same level with HQRC- or VQRC-based methods, might be beneficial for some applications such as validation of numerical models simulating flood events over large-scale basins.
Direct Measurements Coupled with Numerical Models
Numerical flow models used in conjunction with velocity-based approaches have the potential to improve the relationships between local velocities (acquired in a point, along a line, or over a surface as described in Index-Velocity Method) and the cross-sectional velocity in complex flows. For example, Nihei and Kimizu (2008) developed an approach, which they refer to as the dynamic interpolation and extrapolation (DIEX) method, based on a simplified streamwise momentum equation. They start from an equation representing steady, uniform flow and solve for a velocity profile across the channel, using as baseline the data acquired with an ADCP. The ADCP measurements are needed to optimize a coefficient added in the momentum equation, which accounts for flow unsteadiness and nonuniformity at the gauging site. Furthermore, by assuming a logarithmic vertical velocity profile and a simple model that accounts for turbulence, they demonstrated that the results can be further improved. Iwamoto and Nihei (2009) extended the original DIEX method for compound channels subjected to flooding.
The DIEX approach and its improvements can be considered as first steps toward efficiently combining numerical flow models with direct velocity measurements for estimating discharges in complex flow situations such as flood events. These examples are signaling an emerging trend in discharge flow estimation that exploits data assimilation techniques applied to models operated in real time (e.g., Weerts et al., 2010). More improvements are expected from combining direct measurements with more advanced floodplain flow modeling approaches (such as those based on flexible meshes that allow an increase of the spatial resolution in regions of strong bed-level gradients). These hybrid measurement-modeling approaches may dramatically improve our capabilities to estimate discharges in overbank flow situations, where reliance on only direct measurements faces numerous adversities, as described in Extension of the Stage-Discharge Ratings for Flow through Floodplains.
Web-Based Platforms for Measurement Communication
Most of the contemporary gauging systems communicate stream discharges in real time for immediate use of the data by multiple stakeholders: from decision makers in various areas of water resource and emergency management to scientists and general public (e.g., waterdata.usgs.gov). While all stakeholders are seeking good quality and timely, accessible discharges, their interests, data needs, and levels of detail regarding the data vary widely. For example, hydrologists and scientists might be more interested in being able to mine long-term datasets that shed insights into flow processes than in having access to data in real time. The opposite holds for a flood emergency manager.
Current advancements in computing and communications enable new, innovative means to share and visualize the same incoming data using widely different granularity, structure, and formats using web platforms. The emergence of web-based central management approaches, as well as web services, enable agencies and groups to pool their resources, share costs, increase the availability of the high-resolution data, and provide smaller groups with data they otherwise could not afford (Voinov et al., 2016). More benefits will become available (especially in flood situations) when the data acquisition is complemented by crowdsourcing (Le Coz et al., 2016). Critically important for advancing the use of common datasets, such as the ubiquitous discharge-stage data streams discussed herein, is the use of consistent methods for data synthesis, understanding the user needs, their level of technical preparation, and the specifics of the human–computer interaction for each of the targeted stakeholders.
Illustrations of the means to accomplish this customization of the information communication are provided in Figure 10 (Xu et al., 2016). Figure 10a displays a web interface that contains a manager/scientist-level view of the data whereby time series for stage recordings at several stations located on the same stream are displayed, along with the associated statistical parameters (i.e., a box plot) for the time records. The plotted data can be downloaded for further analysis from the same web interface. This interface can retrieve other variables (e.g., flow discharge, water quality parameters) defining the process under investigation.
Using the same raw data on stream stages, customized interfaces can visualize that data in other formats, allowing presentation of the data in a context that is more appropriate for the general public, as illustrated in Figures 10b and 10c. Specifically, the real-time stage measurements at the gauging station (located on a culvert) are converted in dynamically adjusted free-surface water layers superposed on a realistic image of the site. The interactive images shown in Figures 10b and 10c were obtained from a drone-based photogrammetric survey of the gauge site. This more realistic and understandable visualization can readily convey the level of hazard produced by various stages in the stream without the need of any technical preparation.
The measurement of flood discharge has a long history of serving authorities responsible for monitoring, forecasting, and planning in the riverine landscape. Flood discharge holds a strong relation with water level, which is relatively easy to gauge continuously. Consequently, the first, and still widely used, conventional method for continuous discharge monitoring is based on relating river stage to discharge, in the form of a stage-discharge rating curve. Rating curves are built using discrete measurements repeated throughout the lifetime of the gauging station and covering a wide range of flows. Simple stage-discharge relations hold for steady, uniform flow conditions, which do not fully apply to extreme discharge events when floodplains are inundated. Unfortunately, it still remains difficult to collect direct flow measurements during high in-bank and overbank flows.
There is a continuous search for innovative solutions to overcome the operational limitations of the conventional approaches and improve the estimation of discharge accuracy. These innovations target new avenues for both gauging streamflows continuously and making discrete measurements. So far, the most promising results are obtained with in-situ nonintrusive instruments (based on optical, underwater acoustics, and radar) acquired with underwater, airborne, or remote-sensing platforms. These new measurement techniques have different pros and cons in terms of accuracy, costs, processing complexity, and robustness of deployment. None of the new approaches captures the flow velocity over the full cross-section, which would yield a direct estimate of the flood discharge. Consequently, the accuracy of the discharge estimates reflects the skills of the method by which the directly measured variables (i.e., stages, velocities, and slopes) are combined in discharge estimation models. A highly sophisticated method may be required to outperform a much simpler rating curve approach.
Recent decades have seen advancements and innovations in multiple areas of science and technology that have led to a swift development of new discharge sensing technologies, methods to combine measured data with hydrodynamic models for increased accuracy. Collectively, these developments promise to continuously enhance our capabilities to forecast and mitigate floods over a wide range of temporal and spatial scales. For the coming decades, the challenge is to create synergy between monitoring methods and efficient means of assimilating multi-instrument data with appropriate hydrodynamic models. Increased computer power allows adopting such a data assimilation approach. In parallel, the current advancements in computer and communication science and technologies enable new, innovative means to assemble, communicate, and visualize the flood-related data, through a web-based platform capable of accommodating stakeholders with a widely different level of technical preparation. The creation of these digital environments uniquely enables production of the knowledge that will enrich the scientific understanding and the actionable knowledge on flood mitigation, closing the gap between state-of-the-art flood science and flood control decision making and policy.
Funds for Marian Muste were provided by the Iowa Flood Center, IIHR-Hydroscience & Engineering, at the University of Iowa. This research has benefited from cooperation within the network of the Netherlands Centre for River studies. Ton Hoitink acknowledges Rijkswaterstaat for sharing documentation.
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