Global Estimates of River Flow Wave Travel Timesand Implications for Low-Latency Satellite DataGeorge H. Allen1 , Cédric H. David1 , Konstantinos M. Andreadis1 , Faisal Hossain2 ,and James S. Famiglietti1
1Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 2Department of Civil andEnvironmental Engineering, University of Washington, Seattle, WA, USA
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 reservoiroperations, provided they are made available to users with sufficient lead time. Yet the temporalrequirements 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 futurelow-latency/near-real-time satellite products, with an emphasis on the forthcoming SWOT satellite mission.We apply a kinematic wavemodel to a global hydrography data set and find that global flowwaves traveling attheir maximum speed take a median travel time of 6, 4, and 3 days to reach their basin terminus, the nextdownstream 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.
Plain Language Summary Satellites can provide upstream conditions for early flood warningsystems, reservoir operations, and other river management applications. This information is most usefulfor time-sensitive applications if it is made available before an observed upstream flood reaches adownstream point of interest, like a basin outlet, city, or dam. Here we characterize the time it takes floodsto 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 recentlyproposed ≤2-day time period will make the data potentially useful for flood mitigation and other watermanagement 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). Asubset of these applications focuses on flood mitigation and river resource management using a variety ofsatellite-based river remote sensing systems. For example, NRT monitoring of rivers can be achieved usingoptical 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://floodobserva-tory.colorado.edu/), National Aeronautics and Space Administration (NASA)’s Near Real-Time Global FloodMapping 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. Asinnovation continues to improve the performance of data processing, data distribution, and sensor technol-ogy, 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 thatinformation is available to the user in an actionable format. Multiple technological factors contribute to thelatency of satellite products including the time necessary to acquire, store, downlink, process, and distributethe data (Brown et al., 2014). For example, product geolocation accuracy depends on the precise knowledgeof a spacecraft’s ephemeris position during an observation, which benefits from later location informationcollected post acquisition (Davies et al., 2017). Hence, trade-offs exist between satellite data latency and dataquality, such that longer latency products are more internally consistent and of higher quality. Interestedreaders will find additional details on the value and challenges related to timely access to satellite data inDavies et al. (2017).
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RESEARCH LETTER10.1029/2018GL077914
Key Points:• We present the first globalestimate of latency requirements forsatellite observations of rivers fortime-sensitive management decisions
• Global flow waves moving at maxspeed reach their basin outlet, thenext city, and the next dam in amedian of 6, 4, and 3 days,respectively
• A recently proposed ≤2-day latencyfor a low-latency SWOT data productis potentially useful for real-time rivermanagement applications
Supporting Information:• Supporting Information S1
Citation:Allen, G. H., David, C. H., Andreadis, K. M.,Hossain, F., & Famiglietti, J. S. (2018).Global estimates of river flowwave travel times and implications forlow-latency satellite data. GeophysicalResearch Letters, 45, 7551–7560. https://doi.org/10.1029/2018GL077914
Received 13 MAR 2018Accepted 3 APR 2018Accepted article online 26 APR 2018Published online 30 APR 2018
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 measurementsof global surface water bodies at an unprecedented spatial resolution (6–60 m pixel size) and vertical accu-racy (<10 cm when averaging over water area >1 km2; Biancamaria et al., 2016). With a 21-day repeat orbitcycle and a 120-km-wide edge-to-edge swath, SWOT is anticipated to be able to observe river conditionsnight 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 watermanagement applications.
Recent discussions with stakeholder agencies have led to the recognition that a potential low-latency SWOTdata product could spur some of the most innovative societal applications and could improve many currentoperational systems (Hossain, Andral, et al., 2017). These applications include flood risk mitigation, early floodwarning 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 userperception and conjecture rather than a scientific analysis of the rates of the global surface water dynamicsthat SWOT will observe. Such an analysis has yet to be considered because SWOT is the first satellite missionwith specific terrestrial hydrology focus, and hence, it differs from the past ocean altimetry missions withhydrology by-products (e.g., Paris et al., 2016; Tourian et al., 2017). Regardless, flow propagation in rivers mustfirst be characterized at the global scale to understand the latency requirements of time-sensitive river appli-cations that use remote sensing information.
Large changes in river flow take the form of waves that move down river networks faster than the velocityof water itself. The speed at which large waves propagate downstream, termed wave celerity, has longbeen 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). Celerityis a core variable in a variety of hydrologic models and flow-routing algorithms that simulate changesin river discharge (e.g., David et al., 2013; Olivera et al., 2000; Turner-Gillespie et al., 2003). However, whilestudies measuring river wave propagation time have found that wave celerity ranges between ~0.25 and10 m/s, they have only worked at the reach to basin scale, often only focusing a handful of events, therebylimiting 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 riv-ers, we present a global quantification of bankfull river wave celerity and travel time. Maximum celerityoccurs 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 latencyrequirements by estimating, under simple assumptions, the minimum time that waves are expected to pro-pagate downstream. We apply this knowledge to the spatial distribution of the largest global cities and damsto determine the timescales involved in flood risk and reservoir operation management. Finally, we take intoconsideration the spatial and temporal constraints of the planned SWOT mission to understand the potentiallatency 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. Whilea kinematic wave is a simplified representation of the highly-complex full dynamic wave, the kinematic wavesolution gives accurate results during supercritical flow conditions and is commonly used for first-orderapproximations 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,
where β is a constant equal to 5/3 when applying Manning’s flow resistance formula to a rectangular channelcross section (see Text S1 in the supporting information for detailed derivation). In the equation above, we alsouse Manning’s formula with the assumption of a rectangular channel cross section to estimate flow velocity,
u ¼ w h�wþ2 h
� �2=3S1=2=n; (2)
where w is flow width, h is flow depth, and S is the water surface slope equal to the bed slope with thekinematic wave approximation. Manning’s roughness coefficient, n, is assumed to have a mean equal0.035 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 hydrographydata 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; seeText S2 for model implementation and geographic information system details). Note that bankfull widthand depth monotonically increase downstream in this data set. We calculate river slope by extracting riverelevations 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 underestimatethe length of rivers by short circuiting fine-scale meanders present in real rivers (Fekete et al., 2001), we multi-ply downstream river length by anmean 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 bythe Global Land Cover Characteristics Database V2 (https://lta.cr.usgs.gov/glcc/), because these regions typi-cally lack rivers. We also exclude river networks that drain north of 60°N latitude, where the Shuttle RadarTopography Mission-derived flowline and DEM data sets are devoid of data (Farr & Kobrick, 2000).
To quantify the timescales over which flowwaves travel down the world’s rivers, we divide river length by theestimated celerity and then cumulatively sum travel time upstream along river networks. We characterize ourresults in terms of stakeholder points of interest by quantifying the travel times over which waves will reachthe next downstream city with a population >100,000 inhabitants (Bright et al., 2012) and separately, thenext 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 inlower latitudes (Figure S1). To account for this heterogeneity in overpass frequency, we count each riversegment the number of times that the segment is observed per 21-day repeat orbit cycle (see Text S2). Weconduct 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 dis-charge records from U.S. Geological Survey gauge stations (https://waterdata.usgs.gov/nwis). We join 2,271gauge records to the flowline river network and compare the hydrographs of all pairs of upstream and down-stream gauges (N pairs = 3.9 million). We then cross correlate each pair of hydrographs over a lag windowfrom 0 to 200 days (Figure S2). We set the maximum lag to 200 days because we observed that longer lagstend 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 maxi-mum correlations (R < 0.5), or with correlations that do not exhibit substantial variation with different lagtimes (cross-correlation range R < 0.5). Of the 931 pairs of gauges that met these criteria, we calculategauge-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 gaugesand compare the model and gauge-derived celerities, segment-by-segment and weighted by segment length.
3. Results3.1. River Flow Wave Celerity
Running the kinematic wave model on 17.7 million kilometers of Earth’s rivers allows for an examination ofthe geographic distribution of flow wave celerity estimates (Figure 1a). Statistically, the distribution of
celerity is right-skewed with a median celerity of 1:6þ1:7�0:9 m/s (confidence interval is first and third quartiles
hereinafter). Note that this value corresponds to celerity at bankfull flow, which has been theoretically andempirically 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 studieshave shown that during higher discharge, overbank flooding occurs, which increases hydraulic roughnessand decreases the hydraulic radius, thereby reducing celerity. The model likely overestimates celerity insteep, mountainous rivers because these environments tend to have greater hydraulic roughness thanmean n = 0.035 s/m1/3, as we assume here (Barnes, 1967). Conversely, the average hydraulic roughnessused here is likely overestimated in large, lowland river systems.
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
Gauge-based Celerity
Model-based Celerity Celerity (m/s)
Riv
er N
etw
ork
Leng
th (
km)
0 2 4 6 8 10
020
0040
0060
00
Celerity (m/s)
0.05
4
>8
2
6
a
b
c
d
GaugeModel
Figure 1. River flow wave celerity model output and validation. (a) Global map of river flow wave celerity at bankfull dis-charge. Large and steep rivers have the fastest celerities. (b) Map of U.S. Geological Survey gauge-based celerity esti-mates. (c) Map of model-based celerity along corresponding river segments. (d) Distribution of gauge-based and modeledcelerities. Differences between the two celerity estimates are discussed in section 3.2. All maps have the same color scale.
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determine that the celerity of a large flood wave in the Upper Mississippi Valley was 0.25 m/s. Sriwongsitanonet 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 rangepreviously 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 dischargerecords from over 20,000 U.S. Geological Survey gauge stations along over 64,000 km of diverse river
Travel Time (days)
a. Basin Outlets
b. Cities
c. Dams
0
12
79
6
24
Figure 2. Global map of river flow wave travel time to (a) basin outlets, (b) the next downstream city, and (c) the nextdownstream dam. Travel time refers to the minimum temporal interval over which flow waves reach a given basinoutlet, city, or dam. All maps have the same color scale.
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systems in the United States (Figure 1b). The statistical distribution of the gauge-based celerities is right
skewed with a median value of is 1:3þ1:1�0:8 m/s. The median modeled celerity for the same segments is
3:0þ1:6�1:7 m/s.
The mean error between the modeled and gauge-based celerities is 1.5 m/s. A primary cause of this substan-tial difference in celerity is that the model is estimating celerity at a constant-frequency bankfull flow, whilethe gauge-derived data are estimating celerity using the entire range of recorded discharge. Since bankfulldischarge corresponds to conditions of maximum celerity, this bias is expected. Another probable sourceof this discrepancy is that the kinematic wave model neglects to represent diffusive processes and backwatereffects, 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 2.8and 3.2 m/s respectively, rates that reflect the significant difference in hydrological conditions betweenthe gauge-based and modeled celerity estimates. Further, uncertainty stemming from a range of factorsincluding the assumptions of constant hydraulic roughness, channel shape, averaging gauge-based celerityover a range of discharge, and differences in length averaging between the two methods of estimatingcelerity also contribute to this difference. Reservoir operations and water diversions also impact the compar-ison. Thus, the differences between the model and gauge-based celerities are expected given the complexityof the system being simulated. The higher relative values of modeled celerity are also in line with a conser-vative quantification of latency needs.
3.3. River Flow Wave Travel Time
Analyzing flowwave travel time over the entire global river network, we find that flowwaves take amedian of
6þ7�4 days to reach their basin outlet (Figure 2a). We emphasize that this is the minimum time that waves tra-
verse their river networks and so we expect that this travel time to be longer during lower inbank flows orduring overbank floods. Spatially, wave travel time increases monotonically with upstream distance butnot linearly due to varying celerity along river networks. This effect generally produces patterns where coastalregions have a wave travel time of less than a day while continental interiors have longer travels times, exceptfor rivers within endorheic basins. However, inland rivers near high-order, high-celerity trunk rivers oftenhave shorter travel times than catchments located closer to the coast (e.g., see the Amazon basin inFigure 2a). The longest basin travel times occur in the upper reaches of large river basins with abundantdownstream lakes and/or reservoirs. The upper reaches of the Nile, Mississippi, and Niger river basins havethe longest wave travel times globally.
While basin outlet flow wave travel time is an important metric in understanding the timescales over whichwaves reach their termini, it is less directly applicable for characterizing time intervals involving human floodrisk and reservoir operations management. This is because most population centers and reservoirs are notlocated at the outlets of river basins but rather are distributed throughout river basins. Thus, we conduct simi-lar 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 4þ4�2 days to reach the
closest downstream city and3þ4�2 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 82þ2�1% of the global
river network seen in Figure 2a will take longer than one day to exit the river basins, 52þ3�3% for five days,
and 32þ5�4% for 10 days (Table 1).
To cast flow wave travel time in terms of the SWOT mission, we only consider rivers that are wide enough forSWOT 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 85þ2�2% have a
basin travel time of one day or less, meaning that if SWOT observes a river, and there is a one-day NRT pro-
duct latency, there is an85þ2�2% 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 80þ4�4% 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 73þ4�6% chance that an observed wave will have not reached the next downstream dam. The median
travel times for flowwaves observable by SWOT are6þ6�4 days, 3
þ3�2 days, and2
þ3�1 days to reach the basin outlet,
the next downstream city, and next downstream dam, respectively. With increasing data latency, the
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likelihood that NRT observations of rivers could be used by stakeholders decreases, precipitously for the firstfew 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 opera-tions management, and hydrological models. In the case of SWOT, we find that latencies of on the orderof days rather than weeks would significantly enhance SWOT’s potential to aid early flood warning sys-tems in cities and reservoir operation management at dams (Table 1). Specifically, our simulations suggestthat 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 63þ6�6% and 53þ5
�7% of SWOT-observableflow waves reach the next downstream city and dam, respectively. The current SWOT latency requirementof 45 days has virtually no practical use for real-time applications (Table 1), although we emphasize thatthis high latency does not reduce the expected scientific value of SWOT data a posteriori. We also stressthat just like any other Earth-orbiting satellite, the observations are useful to flood mitigation managementonly if they coincide with a flood event on the ground. As mentioned above, we are effectively simulatingthe 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 areexpected to be most observable by SWOT. However, the Monte Carlo simulation incorporates lowerroughness values to estimate uncertainty (Figure S4), so readers wishing to err on the side of cautioncan use the lower uncertainty bounds shown in Table 1. In addition, our analysis does not take intoaccount the time it takes to implement flood mitigation measures, although such implementation timeshould 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 timescausing their latency requirements to be the greatest in terms of flood risk. However, these highly populatedregions typically maintain well-developed gauge networks, whichmay provemore effective for early warningsystems than satellite-based early warning systems. Satellite-based early flood warning systems likely havethe 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 observationscan 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
Table 1Data Latencies and the Corresponding Probability That an Observed Flow Wave Will not Have Reached its Basin Outlet, theNext Downstream City, and Next Downstream Dam
All rivers SWOT-observable rivers
Latency Basin outlet City Dam Basin outlet City Dam
1 day82þ2
�1% 87þ2�3% 78þ3
�3% 85þ2�2% 80þ4
�4% 73þ4�6%
2 days72þ2
�2% 73þ3�5% 62þ4
�4% 75þ3�3% 63þ6
�6% 53þ5�7%
3 days64þ2
�2% 60þ5�5% 49þ4
�4% 67þ3�4% 50þ6
�6% 40þ6�6%
4 days58þ3
�3% 50þ6�4% 40þ4
�4% 60þ4�5% 40þ7
�5% 32þ5�5%
5 days52þ3
�3% 42þ5�5% 33þ4
�4% 54þ4�5% 31þ6
�5% 25þ6�5%
10 days32þ5
�4% 16þ3�5% 16þ3
�2% 30þ6�5% 10þ4
�3% 10þ3�3%
45 days 1þ1�1% 0þ0
�0% 0þ0�0% 1þ1
�1% 0þ0�0% 0þ0
�0%
Note. The SWOT percentages do not correspond to the likelihood that SWOT will observe a flow wave, but rather thelikelihood that if a flow wave is observed, SWOT observations will be available before the wave reaches the given pointof interest.
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areas will potentially benefit the most from NRT satellite products, at least when considering data latencyalone. Interestingly, dams have a very precipitous initial drop in the frequency of travel time, primarilybecause dams are typically not located on very large rivers, and if they are, they tend to have more damsupstream, with some notable exceptions like the Aswan Dam on the Nile (Figure 2c). Together, cities anddams located along transboundary rivers where data sharing is poor stand to benefit the most from NRT riverremote 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 scalein the context of satellite data latency requirements. As such, it is a first-order approximation with significantassumptions and uncertainties that should be better constrained in future work. The simplified hydraulic geo-metry and uniform estimates of hydraulic roughness that we used in the kinematic model could be improvedby using more realistic representations of global river hydromorphology (e.g., Allen & Pavelsky, 2015). Futurework could also focus on regional calibration of model parameters for improved validation. The recent devel-opment of fully global and accurate DEMs (e.g., Yamazaki et al., 2017) could potentially be used to createglobally 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 riv-ers. Thus, in these systems, it is uncertain that the modeled celerities are within the worst-case scenario forinbank flow waves.
Modeling celerity using more realistic, but far more computationally costly, hydrodynamic flow simulationscould substantially improve the characterization of global wave travel times and incorporate important pro-cesses 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-floodplaininteractions and floodplain inundation processes, which are especially important in context of floods andflood mitigation applications. Finally, accounting for the complex, nonlinear behavior of actively managedreservoirs could substantially improve the accuracy of future studies (e.g., Hanasaki et al., 2006; Yoonet al., 2016).
5. Conclusions
In this study, we use a kinematic wave model to estimate flow wave celerity and travel time throughout theworld’s river network. We find that waves moving at their maximum speed reach their basin outlet, a city, or adam in a median time of 6, 4, and 3 days, respectively. This information can be used to assess the usefulnessof existing and future satellite data for real-time river applications including a potential SWOT low-latencyproduct by capturing the timescales involved with the downstream propagation of flow waves. Taking intoaccount the spatial and temporal resolutions of the SWOT satellite, we find that a 2-day or shorter latency assuggested by Hossain, Srinivasan, et al. (2017) would significantly enhance SWOT’s potential to aid early floodwarning systems in cities and reservoir operation management at dams compared to the current 45-daylatency requirement. Note that this study does not consider the likelihood that SWOT will observe a flowwave, but rather the timescales involved in the propagation of a flow wave toward downstream points ofinterest if the wave is indeed observed. These results also can be used to inform other potential NRT productslike those of the NISAR and ICESat-2 satellite missions and can be used to assess the utility of existing NRTsatellite products as well as in situ river monitoring systems. Yet more work is needed to understand thetrade-offs between data latency and data quality in satellite-derived products as well as the timescale neces-sary to implement NRT information in real-world applications.
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