Volume 45, Issue 15 p. 7551-7560
Research Letter
Free Access

Global Estimates of River Flow Wave Travel Times and Implications for Low-Latency Satellite Data

George H. Allen

Corresponding Author

George H. Allen

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

Correspondence to: G. H. Allen,

[email protected]

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Cédric H. David

Cédric H. David

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

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Konstantinos M. Andreadis

Konstantinos M. Andreadis

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

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Faisal Hossain

Faisal Hossain

Department of Civil and Environmental Engineering, University of Washington, Seattle, WA, USA

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James S. Famiglietti

James S. Famiglietti

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

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First published: 26 April 2018
Citations: 39

Abstract

Earth-orbiting satellites provide valuable observations of upstream river conditions worldwide. These observations can be used in real-time applications like early flood warning systems and reservoir operations, provided they are made available to users with sufficient lead time. Yet the temporal requirements for access to satellite-based river data remain uncharacterized for time-sensitive applications. Here we present a global approximation of flow wave travel time to assess the utility of existing and future low-latency/near-real-time satellite products, with an emphasis on the forthcoming SWOT satellite mission. We apply a kinematic wave model to a global hydrography data set and find that global flow waves traveling at their maximum speed take a median travel time of 6, 4, and 3 days to reach their basin terminus, the next downstream city, and the next downstream dam, respectively. Our findings suggest that a recently proposed ≤2-day data latency for a low-latency SWOT product is potentially useful for real-time river applications.

Key Points

  • We present the first global estimate of latency requirements for satellite observations of rivers for time-sensitive management decisions
  • Global flow waves moving at max speed reach their basin outlet, the next city, and the next dam in a median of 6, 4, and 3 days, respectively
  • A recently proposed ≤2-day latency for a low-latency SWOT data product is potentially useful for real-time river management applications

Plain Language Summary

Satellites can provide upstream conditions for early flood warning systems, reservoir operations, and other river management applications. This information is most useful for time-sensitive applications if it is made available before an observed upstream flood reaches a downstream point of interest, like a basin outlet, city, or dam. Here we characterize the time it takes floods to travel down Earth's rivers in an effort to assess the time required for satellite data to be downloaded, processed, and made accessible to users. We find that making satellite data available within a recently proposed ≤2-day time period will make the data potentially useful for flood mitigation and other water management applications.

1 Introduction

The past decade has witnessed increasing use of near-real-time (NRT) satellite data products for time-sensitive applications like disaster monitoring and real-time resource management (Davies et al., 2017). A subset of these applications focuses on flood mitigation and river resource management using a variety of satellite-based river remote sensing systems. For example, NRT monitoring of rivers can be achieved using optical imagers (e.g., Brakenridge & Anderson, 2006; Cooley et al., 2017), passive microwave radiometers (e.g., De Groeve, 2010), radar altimeters (e.g., Hossain et al., 2014), or synthetic aperture radar altimeters (e.g., Twele et al., 2016). Online platforms including the Dartmouth Flood Observatory (http://floodobservatory.colorado.edu/), National Aeronautics and Space Administration (NASA)'s Near Real-Time Global Flood Mapping Program (https://floodmap.modaps.eosdis.nasa.gov/), and the Global Flood Monitoring System (http://flood.umd.edu/) have made flood remote sensing NRT products easily accessible to the public. As innovation continues to improve the performance of data processing, data distribution, and sensor technology, we expect that the use of low-latency river remote sensing products will continue to grow.

Satellite data latency refers to the time period between when a satellite makes an observation and when that information is available to the user in an actionable format. Multiple technological factors contribute to the latency of satellite products including the time necessary to acquire, store, downlink, process, and distribute the data (Brown et al., 2014). For example, product geolocation accuracy depends on the precise knowledge of a spacecraft's ephemeris position during an observation, which benefits from later location information collected post acquisition (Davies et al., 2017). Hence, trade-offs exist between satellite data latency and data quality, such that longer latency products are more internally consistent and of higher quality. Interested readers will find additional details on the value and challenges related to timely access to satellite data in Davies et al. (2017).

The Surface Water and Ocean Topography (SWOT) mission (Alsdorf et al., 2007), expected for launch in 2021, is the first satellite specifically designed jointly by the oceanographic and hydrologic science communities. SWOT will use a novel sensor, a radar swath interferometer, to provide elevation and extent measurements of global surface water bodies at an unprecedented spatial resolution (6–60 m pixel size) and vertical accuracy (<10 cm when averaging over water area >1 km2; Biancamaria et al., 2016). With a 21-day repeat orbit cycle and a 120-km-wide edge-to-edge swath, SWOT is anticipated to be able to observe river conditions night and day, and during cloudy weather conditions. The SWOT mission is designed for a 45-day latency, allowing for sufficient time to provide high-quality data and fulfill its science requirements (https://swot.jpl.nasa.gov). However, a 45-day latency may impede the usefulness of SWOT data for time-sensitive river water management applications.

Recent discussions with stakeholder agencies have led to the recognition that a potential low-latency SWOT data product could spur some of the most innovative societal applications and could improve many current operational systems (Hossain, Andral, et al., 2017). These applications include flood risk mitigation, early flood warning systems, reservoir operations management, optimization of fishing activity, and riverine navigation. An outcome of the discussions was that participants generally preferred a latency period of two days or less (Hossain, Andral, et al., 2017; Hossain, Srinivasan, et al., 2017). However, this timespan was based on end user perception and conjecture rather than a scientific analysis of the rates of the global surface water dynamics that SWOT will observe. Such an analysis has yet to be considered because SWOT is the first satellite mission with specific terrestrial hydrology focus, and hence, it differs from the past ocean altimetry missions with hydrology by-products (e.g., Paris et al., 2016; Tourian et al., 2017). Regardless, flow propagation in rivers must first be characterized at the global scale to understand the latency requirements of time-sensitive river applications that use remote sensing information.

Large changes in river flow take the form of waves that move down river networks faster than the velocity of water itself. The speed at which large waves propagate downstream, termed wave celerity, has long been studied in fluvial hydrology both empirically (e.g., Brakenridge et al., 1998; Seddon, 1900; Wong & Laurenson, 1983) and theoretically (e.g., Lighthill & Whitham, 1955; Woolhiser & Liggett, 1967). Celerity is a core variable in a variety of hydrologic models and flow-routing algorithms that simulate changes in river discharge (e.g., David et al., 2013; Olivera et al., 2000; Turner-Gillespie et al., 2003). However, while studies measuring river wave propagation time have found that wave celerity ranges between ~0.25 and 10 m/s, they have only worked at the reach to basin scale, often only focusing a handful of events, thereby limiting their ability to inform the latency requirements of global-scale satellite observations (e.g., Brakenridge et al., 1998; David et al., 2011; Sriwongsitanon et al., 1998; Turner-Gillespie et al., 2003; Wong & Laurenson, 1984).

Thus, in an effort to characterize the usefulness of low-latency existing and future satellite observations of rivers, we present a global quantification of bankfull river wave celerity and travel time. Maximum celerity occurs at or near bankfull flow conditions (Anderson et al., 2006; R. Price et al., 1973; Sriwongsitanon et al., 1998; Wong & Laurenson, 1983, 1984), and thus, we are assessing the worst-case scenario in terms of latency requirements by estimating, under simple assumptions, the minimum time that waves are expected to propagate downstream. We apply this knowledge to the spatial distribution of the largest global cities and dams to determine the timescales involved in flood risk and reservoir operation management. Finally, we take into consideration the spatial and temporal constraints of the planned SWOT mission to understand the potential latency needs for SWOT data to be useful in real-time river management applications.

2 Methods

Flow wave celerity can be approximated using a range of models with varying levels of complexity (Chow, 1959). In this analysis we use a kinematic wave model to estimate the celerity of global flow waves. While a kinematic wave is a simplified representation of the highly-complex full dynamic wave, the kinematic wave solution gives accurate results during supercritical flow conditions and is commonly used for first-order approximations of hydrological processes (Morris & Woolhiser, 1980; Singh, 2001; Woolhiser & Liggett, 1967). Following the derivation of a kinematic wave originally presented in Lighthill and Whitham (1955), celerity (c) is linearly related to flow velocity (u) for inbank flow,
urn:x-wiley:00948276:media:grl57184:grl57184-math-0001(1)
where β is a constant equal to 5/3 when applying Manning's flow resistance formula to a rectangular channel cross section (see Text S1 in the supporting information for detailed derivation). In the equation above, we also use Manning's formula with the assumption of a rectangular channel cross section to estimate flow velocity,
urn:x-wiley:00948276:media:grl57184:grl57184-math-0002(2)
where w is flow width, h is flow depth, and S is the water surface slope equal to the bed slope with the kinematic wave approximation. Manning's roughness coefficient, n, is assumed to have a mean equal 0.035 s/m1/3, a reasonable approximation in river systems at the global scale (Arora et al., 1999; Barnes, 1967; Chow, 1959).

We characterize global patterns of river wave celerity by applying equation 1 to a river flowline hydrography data set (HydroSHEDS; Lehner et al., 2008) enhanced with information regarding river length, bankfull width, and bankfull depth (Andreadis, 2016; Andreadis et al., 2013; GRDC, 2017; Moody & Troutman, 2002; see Text S2 for model implementation and geographic information system details). Note that bankfull width and depth monotonically increase downstream in this data set. We calculate river slope by extracting river elevations from the hydrologically conditioned 15-arcsec HydroSHEDS digital elevation model (DEM) (Durand et al., 2008; Emery et al., 2016). To account for the tendency of flowline data sets to underestimate the length of rivers by short circuiting fine-scale meanders present in real rivers (Fekete et al., 2001), we multiply downstream river length by an mean factor of 1.25 (e.g., Allen et al., 2013; da Paz et al., 2008; Schulze et al., 2005). We exclude from our analysis flowlines in desert regions after Andreadis et al. (2013), as classified by the Global Land Cover Characteristics Database V2 (https://lta.cr.usgs.gov/glcc/), because these regions typically lack rivers. We also exclude river networks that drain north of 60°N latitude, where the Shuttle Radar Topography Mission-derived flowline and DEM data sets are devoid of data (Farr & Kobrick, 2000).

To quantify the timescales over which flow waves travel down the world's rivers, we divide river length by the estimated celerity and then cumulatively sum travel time upstream along river networks. We characterize our results in terms of stakeholder points of interest by quantifying the travel times over which waves will reach the next downstream city with a population >100,000 inhabitants (Bright et al., 2012) and separately, the next downstream dam (Lehner et al., 2014). In analyzing wave travel time in context of the SWOT mission, we exclude rivers that are typically unobservable by the sensor on SWOT (KaRIn; Enjolras & Rodriguez, 2009; Fjørtoft et al., 2014), specifically rivers that are narrower than 100 m during bankfull flow (Pavelsky et al., 2014). SWOT's 77.6° orbit inclination will overpass regions in high latitudes more frequently than regions in lower latitudes (Figure S1). To account for this heterogeneity in overpass frequency, we count each river segment the number of times that the segment is observed per 21-day repeat orbit cycle (see Text S2). We conduct a Monte Carlo simulation to quantify model error due to the uncertainty of the input parameters (see Text S3 and Figures S3 and S4).

We validate the kinematic model-derived celerities by applying a lagged cross-correlation analysis to discharge records from U.S. Geological Survey gauge stations (https://waterdata.usgs.gov/nwis). We join 2,271 gauge records to the flowline river network and compare the hydrographs of all pairs of upstream and downstream gauges (N pairs = 3.9 million). We then cross correlate each pair of hydrographs over a lag window from 0 to 200 days (Figure S2). We set the maximum lag to 200 days because we observed that longer lags tend to become influenced by annual seasonality. We then find which lag time has the maximum correlation, corresponding to the average travel time of waves moving downstream between the two gauges (Smith & Pavelsky, 2008). Note that the distance used here also accounts for the aforementioned sinuosity correction. We remove from the analysis gauge pairs with <5 years of overlapping discharge records, with poor maximum correlations (R < 0.5), or with correlations that do not exhibit substantial variation with different lag times (cross-correlation range R < 0.5). Of the 931 pairs of gauges that met these criteria, we calculate gauge-derived celerity by dividing the downstream distance by the lag time between the pair of gauges. We then assign the celerity to each downstream segment along the flowline between of the two gauges and compare the model and gauge-derived celerities, segment-by-segment and weighted by segment length.

3 Results

3.1 River Flow Wave Celerity

Running the kinematic wave model on 17.7 million kilometers of Earth's rivers allows for an examination of the geographic distribution of flow wave celerity estimates (Figure 1a). Statistically, the distribution of celerity is right-skewed with a median celerity of urn:x-wiley:00948276:media:grl57184:grl57184-math-0003 m/s (confidence interval is first and third quartiles hereinafter). Note that this value corresponds to celerity at bankfull flow, which has been theoretically and empirically shown to be the approximate hydrological condition that waves exhibit their peak velocity (Price, 1982; R. Price et al., 1973; Turner-Gillespie et al., 2003; Wong & Laurenson, 1983, 1984). These studies have shown that during higher discharge, overbank flooding occurs, which increases hydraulic roughness and decreases the hydraulic radius, thereby reducing celerity. The model likely overestimates celerity in steep, mountainous rivers because these environments tend to have greater hydraulic roughness than mean n = 0.035 s/m1/3, as we assume here (Barnes, 1967). Conversely, the average hydraulic roughness used here is likely overestimated in large, lowland river systems.

Details are in the caption following the image
River flow wave celerity model output and validation. (a) Global map of river flow wave celerity at bankfull discharge. Large and steep rivers have the fastest celerities. (b) Map of U.S. Geological Survey gauge-based celerity estimates. (c) Map of model-based celerity along corresponding river segments. (d) Distribution of gauge-based and modeled celerities. Differences between the two celerity estimates are discussed in section 3.2. All maps have the same color scale.

3.2 Model Validation

Previous empirical studies have found that celerity in natural river channels ranges from 0.25 to 10 m/s (Brakenridge et al., 1998; David et al., 2011; Sriwongsitanon et al., 1998; Turner-Gillespie et al., 2003; Wong & Laurenson, 1984). Brakenridge et al. used orbital synthetic aperture radar remote sensing (ERS-1) to determine that the celerity of a large flood wave in the Upper Mississippi Valley was 0.25 m/s. Sriwongsitanon et al. found that inbank flow celerity reached ~10 m/s during a high-flow event in the Herbert River, Queensland. The kinematic model used here estimates celerities that are almost entirely within a range previously reported. However, past studies measured celerity at a relatively small number of locations, often spanning a limited time period. To better characterize the full range of celerity, we analyze discharge records from over 20,000 U.S. Geological Survey gauge stations along over 64,000 km of diverse river systems in the United States (Figure 1b). The statistical distribution of the gauge-based celerities is right skewed with a median value of is urn:x-wiley:00948276:media:grl57184:grl57184-math-0004 m/s. The median modeled celerity for the same segments is urn:x-wiley:00948276:media:grl57184:grl57184-math-0005 m/s.

The mean error between the modeled and gauge-based celerities is 1.5 m/s. A primary cause of this substantial difference in celerity is that the model is estimating celerity at a constant-frequency bankfull flow, while the gauge-derived data are estimating celerity using the entire range of recorded discharge. Since bankfull discharge corresponds to conditions of maximum celerity, this bias is expected. Another probable source of this discrepancy is that the kinematic wave model neglects to represent diffusive processes and backwater effects, which can accelerate or slow down flow wave propagation (Getirana & Paiva, 2013; Price, 1982; Tsai, 2005). The standard error and the root-mean-square error between the model and gauge celerities are 2.8 and 3.2 m/s respectively, rates that reflect the significant difference in hydrological conditions between the gauge-based and modeled celerity estimates. Further, uncertainty stemming from a range of factors including the assumptions of constant hydraulic roughness, channel shape, averaging gauge-based celerity over a range of discharge, and differences in length averaging between the two methods of estimating celerity also contribute to this difference. Reservoir operations and water diversions also impact the comparison. Thus, the differences between the model and gauge-based celerities are expected given the complexity of the system being simulated. The higher relative values of modeled celerity are also in line with a conservative quantification of latency needs.

3.3 River Flow Wave Travel Time

Analyzing flow wave travel time over the entire global river network, we find that flow waves take a median of urn:x-wiley:00948276:media:grl57184:grl57184-math-0006 days to reach their basin outlet (Figure 2a). We emphasize that this is the minimum time that waves traverse their river networks and so we expect that this travel time to be longer during lower inbank flows or during overbank floods. Spatially, wave travel time increases monotonically with upstream distance but not linearly due to varying celerity along river networks. This effect generally produces patterns where coastal regions have a wave travel time of less than a day while continental interiors have longer travels times, except for rivers within endorheic basins. However, inland rivers near high-order, high-celerity trunk rivers often have shorter travel times than catchments located closer to the coast (e.g., see the Amazon basin in Figure 2a). The longest basin travel times occur in the upper reaches of large river basins with abundant downstream lakes and/or reservoirs. The upper reaches of the Nile, Mississippi, and Niger river basins have the longest wave travel times globally.

Details are in the caption following the image
Global map of river flow wave travel time to (a) basin outlets, (b) the next downstream city, and (c) the next downstream dam. Travel time refers to the minimum temporal interval over which flow waves reach a given basin outlet, city, or dam. All maps have the same color scale.

While basin outlet flow wave travel time is an important metric in understanding the timescales over which waves reach their termini, it is less directly applicable for characterizing time intervals involving human flood risk and reservoir operations management. This is because most population centers and reservoirs are not located at the outlets of river basins but rather are distributed throughout river basins. Thus, we conduct similar travel time analyses but with regard to the next downstream city (Figure 2b) and next downstream dam (Figure 2c) rather than basin outlet. We find that flow waves take an median time of urn:x-wiley:00948276:media:grl57184:grl57184-math-0007 days to reach the closest downstream city and urn:x-wiley:00948276:media:grl57184:grl57184-math-0008 days to reach the closest downstream dam, travel times that are shorter than for basin outlets (see Figure S5 for statistical distributions). Put another way, waves in urn:x-wiley:00948276:media:grl57184:grl57184-math-0009% of the global river network seen in Figure 2a will take longer than one day to exit the river basins, urn:x-wiley:00948276:media:grl57184:grl57184-math-0010% for five days, and urn:x-wiley:00948276:media:grl57184:grl57184-math-0011% for 10 days (Table 1).

Table 1. Data Latencies and the Corresponding Probability That an Observed Flow Wave Will not Have Reached its Basin Outlet, the Next Downstream City, and Next Downstream Dam
All rivers SWOT-observable rivers
Latency Basin outlet City Dam Basin outlet City Dam
1 day urn:x-wiley:00948276:media:grl57184:grl57184-math-0012% urn:x-wiley:00948276:media:grl57184:grl57184-math-0013% urn:x-wiley:00948276:media:grl57184:grl57184-math-0014% urn:x-wiley:00948276:media:grl57184:grl57184-math-0015% urn:x-wiley:00948276:media:grl57184:grl57184-math-0016% urn:x-wiley:00948276:media:grl57184:grl57184-math-0017%
2 days urn:x-wiley:00948276:media:grl57184:grl57184-math-0018% urn:x-wiley:00948276:media:grl57184:grl57184-math-0019% urn:x-wiley:00948276:media:grl57184:grl57184-math-0020% urn:x-wiley:00948276:media:grl57184:grl57184-math-0021% urn:x-wiley:00948276:media:grl57184:grl57184-math-0022% urn:x-wiley:00948276:media:grl57184:grl57184-math-0023%
3 days urn:x-wiley:00948276:media:grl57184:grl57184-math-0024% urn:x-wiley:00948276:media:grl57184:grl57184-math-0025% urn:x-wiley:00948276:media:grl57184:grl57184-math-0026% urn:x-wiley:00948276:media:grl57184:grl57184-math-0027% urn:x-wiley:00948276:media:grl57184:grl57184-math-0028% urn:x-wiley:00948276:media:grl57184:grl57184-math-0029%
4 days urn:x-wiley:00948276:media:grl57184:grl57184-math-0030% urn:x-wiley:00948276:media:grl57184:grl57184-math-0031% urn:x-wiley:00948276:media:grl57184:grl57184-math-0032% urn:x-wiley:00948276:media:grl57184:grl57184-math-0033% urn:x-wiley:00948276:media:grl57184:grl57184-math-0034% urn:x-wiley:00948276:media:grl57184:grl57184-math-0035%
5 days urn:x-wiley:00948276:media:grl57184:grl57184-math-0036% urn:x-wiley:00948276:media:grl57184:grl57184-math-0037% urn:x-wiley:00948276:media:grl57184:grl57184-math-0038% urn:x-wiley:00948276:media:grl57184:grl57184-math-0039% urn:x-wiley:00948276:media:grl57184:grl57184-math-0040% urn:x-wiley:00948276:media:grl57184:grl57184-math-0041%
10 days urn:x-wiley:00948276:media:grl57184:grl57184-math-0042% urn:x-wiley:00948276:media:grl57184:grl57184-math-0043% urn:x-wiley:00948276:media:grl57184:grl57184-math-0044% urn:x-wiley:00948276:media:grl57184:grl57184-math-0045% urn:x-wiley:00948276:media:grl57184:grl57184-math-0046% urn:x-wiley:00948276:media:grl57184:grl57184-math-0047%
45 days urn:x-wiley:00948276:media:grl57184:grl57184-math-0048% urn:x-wiley:00948276:media:grl57184:grl57184-math-0049% urn:x-wiley:00948276:media:grl57184:grl57184-math-0050% urn:x-wiley:00948276:media:grl57184:grl57184-math-0051% urn:x-wiley:00948276:media:grl57184:grl57184-math-0052% urn:x-wiley:00948276:media:grl57184:grl57184-math-0053%
  • Note. The SWOT percentages do not correspond to the likelihood that SWOT will observe a flow wave, but rather the likelihood that if a flow wave is observed, SWOT observations will be available before the wave reaches the given point of interest.

To cast flow wave travel time in terms of the SWOT mission, we only consider rivers that are wide enough for SWOT to measure (rivers with width >100 m) and we resample the travel times to account for the SWOT's overpass frequency (Figure S1). Of these rivers that are observable to SWOT, we find that a urn:x-wiley:00948276:media:grl57184:grl57184-math-0054% have a basin travel time of one day or less, meaning that if SWOT observes a river, and there is a one-day NRT product latency, there is an urn:x-wiley:00948276:media:grl57184:grl57184-math-0055% chance that the observed wave will still exist in the basin (Table 1). Similarly, of the rivers that are upstream of cities and that are observable by SWOT, there is an urn:x-wiley:00948276:media:grl57184:grl57184-math-0056% chance that an observed wave will have not reached a city within a one-day latency time interval. In the case of dams, there is only a urn:x-wiley:00948276:media:grl57184:grl57184-math-0057% chance that an observed wave will have not reached the next downstream dam. The median travel times for flow waves observable by SWOT are urn:x-wiley:00948276:media:grl57184:grl57184-math-0058 days, urn:x-wiley:00948276:media:grl57184:grl57184-math-0059 days, and urn:x-wiley:00948276:media:grl57184:grl57184-math-0060 days to reach the basin outlet, the next downstream city, and next downstream dam, respectively. With increasing data latency, the likelihood that NRT observations of rivers could be used by stakeholders decreases, precipitously for the first few days, then more slowly as the latency increases (Table 1 and Figure S5).

4 Discussion

This study's findings can be used to inform preliminary latency requirements for existing and future river-observation NRT satellite products, as well as inform gauge-based early warning systems, reservoir operations management, and hydrological models. In the case of SWOT, we find that latencies of on the order of days rather than weeks would significantly enhance SWOT's potential to aid early flood warning systems in cities and reservoir operation management at dams (Table 1). Specifically, our simulations suggest that the recently proposed ≤2-day latency (Hossain, Andral, et al., 2017; Hossain, Srinivasan, et al., 2017) would allow a SWOT NRT product to be available before at least urn:x-wiley:00948276:media:grl57184:grl57184-math-0061% and urn:x-wiley:00948276:media:grl57184:grl57184-math-0062% of SWOT-observable flow waves reach the next downstream city and dam, respectively. The current SWOT latency requirement of 45 days has virtually no practical use for real-time applications (Table 1), although we emphasize that this high latency does not reduce the expected scientific value of SWOT data a posteriori. We also stress that just like any other Earth-orbiting satellite, the observations are useful to flood mitigation management only if they coincide with a flood event on the ground. As mentioned above, we are effectively simulating the worst-case scenario, and in most cases, real flood waves will move slower than what is estimated here. Note that our approach likely overestimates hydraulic roughness in large, lowland river systems that are expected to be most observable by SWOT. However, the Monte Carlo simulation incorporates lower roughness values to estimate uncertainty (Figure S4), so readers wishing to err on the side of caution can use the lower uncertainty bounds shown in Table 1. In addition, our analysis does not take into account the time it takes to implement flood mitigation measures, although such implementation time should also be considered when selecting an optimum latency.

Regions of high population density (e.g., China, India, and Europe) have the lowest average city travel times causing their latency requirements to be the greatest in terms of flood risk. However, these highly populated regions typically maintain well-developed gauge networks, which may prove more effective for early warning systems than satellite-based early warning systems. Satellite-based early flood warning systems likely have the greatest utility for cities that are located far downstream from basin headwaters and do not have well-developed gauge networks in place. This being said, we note that low-latency remote sensing observations can still greatly benefit cities located in relatively small basins with well-developed infrastructure (e.g., Schumann et al., 2016). Similar to cities, areas containing fewer dams or dams with larger contributing areas will potentially benefit the most from NRT satellite products, at least when considering data latency alone. Interestingly, dams have a very precipitous initial drop in the frequency of travel time, primarily because dams are typically not located on very large rivers, and if they are, they tend to have more dams upstream, with some notable exceptions like the Aswan Dam on the Nile (Figure 2c). Together, cities and dams located along transboundary rivers where data sharing is poor stand to benefit the most from NRT river remote sensing satellite products (Gleason & Hamdan, 2017).

This study is the first effort to characterize the distribution of wave celerity and travel time at the global scale in the context of satellite data latency requirements. As such, it is a first-order approximation with significant assumptions and uncertainties that should be better constrained in future work. The simplified hydraulic geometry and uniform estimates of hydraulic roughness that we used in the kinematic model could be improved by using more realistic representations of global river hydromorphology (e.g., Allen & Pavelsky, 2015). Future work could also focus on regional calibration of model parameters for improved validation. The recent development of fully global and accurate DEMs (e.g., Yamazaki et al., 2017) could potentially be used to create globally complete hydrographic data sets, allowing for future evaluations to be extended into high latitudes. In-channel backwater effects can increase or decrease flow wave celerity and are often pronounced in large, low-land fluvial systems (Getirana & Paiva, 2013; Tsai, 2005), where satellites are most adept at observing rivers. Thus, in these systems, it is uncertain that the modeled celerities are within the worst-case scenario for inbank flow waves.

Modeling celerity using more realistic, but far more computationally costly, hydrodynamic flow simulations could substantially improve the characterization of global wave travel times and incorporate important processes like backwater effects and wave attenuation (e.g., Bates et al., 2010; Paiva et al., 2011; Yamazaki et al., 2011). Sophisticated hydrodynamic models can also simulate overbank flow dynamics like river-floodplain interactions and floodplain inundation processes, which are especially important in context of floods and flood mitigation applications. Finally, accounting for the complex, nonlinear behavior of actively managed reservoirs could substantially improve the accuracy of future studies (e.g., Hanasaki et al., 2006; Yoon et al., 2016).

5 Conclusions

In this study, we use a kinematic wave model to estimate flow wave celerity and travel time throughout the world's river network. We find that waves moving at their maximum speed reach their basin outlet, a city, or a dam in a median time of 6, 4, and 3 days, respectively. This information can be used to assess the usefulness of existing and future satellite data for real-time river applications including a potential SWOT low-latency product by capturing the timescales involved with the downstream propagation of flow waves. Taking into account the spatial and temporal resolutions of the SWOT satellite, we find that a 2-day or shorter latency as suggested by Hossain, Srinivasan, et al. (2017) would significantly enhance SWOT's potential to aid early flood warning systems in cities and reservoir operation management at dams compared to the current 45-day latency requirement. Note that this study does not consider the likelihood that SWOT will observe a flow wave, but rather the timescales involved in the propagation of a flow wave toward downstream points of interest if the wave is indeed observed. These results also can be used to inform other potential NRT products like those of the NISAR and ICESat-2 satellite missions and can be used to assess the utility of existing NRT satellite products as well as in situ river monitoring systems. Yet more work is needed to understand the trade-offs between data latency and data quality in satellite-derived products as well as the timescale necessary to implement NRT information in real-world applications.

Acknowledgments

G. H. Allen, C. H. David, K. M. Andreadis, and J. S. Famiglietti were supported by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA; including grants from the NASA SERVIR Applied Sciences Team and the NASA SWOT Science Team. The data produced in this study are openly available from Allen et al. (2018) under a Creative Commons Attribution License. The software used to analyze the data and produce the figures is available from Allen (2018) under a Berkeley Software Distribution 3-Clause License. We thank Editor M. Bayani Cardenas, Paul D. Bates, and an anonymous reviewer whose comments helped improve the manuscript. © 2017. All rights reserved.