Evolution of river-routing schemes in macro-scale models and their potential for watershed management

Figures & data

Figure 1. Pathways of deriving river discharge information from GCMs. Based on downscaling method pathways reviewed in Xu (1999).

Table 1. Conceptual underpinnings of the river-routing models arranged in chronological order.

	River-routing method	Routing stage	In-grid routing/storage	Subsurface contribution	Channel routing method
1	Lohmann routing [Lohmann et al. 1996]	(1) In-grid routing to outflow point; (2) Channel/river routing	Routing using impulse response function (IRF) for grid box	The IRF has a “slow” component to reflect baseflow	IRF derived from linearized Saint Venant equations (1D diffusive wave equation)
2	Total runoff integration pathways (TRIP) river runoff model [Oki and Sud 1998]	Change in storage per grid cell and grid routing	Storage for grid cell based on linear reservoir linked to grid routing	Deep drainage from LSM	Linear cell-by-cell transport using continuity equation with fixed constant velocity (v = 0.5 m/s) and fixed river meandering ratio (1.4)
3	River transport model (RTM) [Branstetter 2001]	Change in storage per grid cell and grid routing based on slope	Storage for grid cell based on liquid or ice water considering inflow from neighboring cells and runoff from LSM	LSM drainage	Linear cell-by-cell transport using continuity equation with fixed constant velocity (v = 0.35 m/s)
4	Grid-to-grid routing Model (G2G) [Bell et al. 2007]	(1) Land-pathways routing (2) River routing	Grid-cells classified as “Land” under land-pathways routing parameters using linear form of continuity equation in 2D with constant velocity	2D kinematic flow for groundwater below both land and river – connected via a “return” flow variable	Grid-cell classified as river under river-routing parameters using linear form of continuity equation in 2D with constant velocity
5	Total runoff integration pathways (TRIP2) river-routing model [Pappenberger et al. 2010]	Change in storage per grid cell and grid routing	Storage for grid cell based on linear reservoir linked to grid routing	Deep drainage from LSM and linear groundwater storage reservoir	1D kinematic wave routing with variable velocity (determined by Manning’s equation based on rectangular cross-section)
6	TRIP CHS river-routing model [Decharme et al. 2010]	(1) Change in storage per grid cell and grid routing (2) Floodplain interaction	Storage for grid cell based on linear reservoir linked to grid routing	Deep drainage from LSM and linear groundwater storage reservoir	1D kinematic wave routing with variable velocity (determined by Manning’s equation based on rectangular cross-section)
7	Catchment-based macro-scale floodplain model (CaMa-Flood) [Yamazaki et al. 2011]	(1) Change in floodplain and river storage for each grid (2) Main channel routing	“Unit catchment” derived for outlet point for each grid cell using 1-km resolution DEM. Change in storage for river and flood plain solved for each unit catchment (thus, for each grid)	No	Diffuse wave approximation of the 1D Saint Venant equations
8	Paiva et al. (2011)	(1) Routing in each sub-basin/HRU (2) River routing	Linear reservoirs to route baseflow and surface flow from HRU to stream network	Linear reservoirs to route subsurface flow from HRU	Hydrodynamic model using full Saint Venant equations
9	RAPID [David et al. 2011]	River routing	Surface runoff from LSM summed into lateral flow to channel	Subsurface runoff from LSM added as lateral flow	Muskingum method with parameters calibrated using gauge data
10	Wen et al. (2012)	(1) Overland routing (2) Main channel routing	1D kinematic wave routing with variable velocity and statistical distribution derived from DEM used to describe “length” of flow for in-grid overland flow to reach channel	No	1D kinematic wave routing with variable velocity and multidirectional flow possible in river channel
11	WaterGAP routing [Verzano et al. 2012]	Change in storage of river segment per grid cell and grid routing	Storage for river segment in each grid cell based on linear reservoir linked to grid routing	No	1D kinematic wave routing with variable velocity (determined by Manning’s equation assuming trapezoidal cross-section)
12	Model for scale-adaptive river transport (MOSART) [Li et al. 2013]	(1) Hillslopes to tributaries; (2) Tributaries to main channel; (3) Main channel routing	1D kinematic wave routing with variable velocity for hillslopes and tributaries	No	1D kinematic wave routing with variable velocity for main channel
13	HydroROUT [Lehner and Grill 2013]	Main channel routing	No	No	Multidirectional routing with network tracing using weights, barriers and decay functions
14	Kinematic wave routing (KWR CLM) [Ye et al. 2013]	(1) Catchment based slope routing (2) Main channel routing	Grids are mapped to catchments; in each catchment, the kinematic approximation of the Saint Venant equations is used to route water over slopes till it enters river	No	Kinematic approximation of 1D Saint Venant equations
15	ALMIP-2 river-routing scheme (ARTS) [Getirana et al. 2014]	(1) Surface, subsurface and deep groundwater in each grid (2) Main channel routing	Storage using a linear reservoir with time delay to capture in-grid routing	Linear reservoir for baseflow generation and deep groundwater infiltration reservoir	Nonlinear Muskingum-Cunge method
16	Dominant river tracing-based runoff routing (DRTR) model [Wu et al. 2014]	(1) Tributaries at in-grid level (2) Main channel routing between grids	Routing using kinematic wave equations (for tributaries only); assumes overland surface runoff and baseflow enter the corresponding dominant river intervals and tributaries within each time step	Adds to in-grid routing	Kinematic wave equations
17	mizuRoute [Mizukami et al. 2016]	(1) Hillslope routing (2) Main channel routing	Routing using impulse response function (gamma-distribution-based unit hydrograph)	No	(1) Kinematic wave tracking (KWT) routing procedure; and/or (2) impulse response function routing procedure
18	HYPERstream [Piccolroaz et al. 2016]	(1) Hillslope routing (2) Main channel routing	Routing using impulse response function for each “macrocell” (sub-division of grids) identified as land draining into channel macrocells	Depends on runoff model selected	Geomorphologically-based accumulation using constant (user-defined/calibrated) velocity

Table 2. Structural components and known applications of the river-routing models (RRM).

	RRM	Resolution	River network	Intervention, flooding or transport	Applications/coupled with
1	Lohmann routing	Spatial: Multiscale; reported for 0.5° in Lohmann et al. (1998) Temporal: Hourly	Derived river flow network	Basic capability of representing interventions on river	Standard routing scheme used with variable infiltration capacity (VIC) LSM
2	TRIP RRM	Spatial: 1° Temporal: Daily	TRIP network	No	Standard coupling with Interactions between Soil, Biosphere and Atmosphere (ISBA) Demonstrated with Minimal Advanced Treatments of Surface Interaction and Runoff (MATSIRO) LSM [Pokhrel et al. 2012]
3	RTM	Spatial: 0.5° Temporal: Daily or lower	Based on slope of terrain model	No	Standard routing scheme used with Community Land Model (CLM)
4	G2G	Spatial: 1 km Temporal: Daily or sub-daily (computational time step: 15 min)	Derived from HYDRO1K digital elevation data	No	Demonstrated for a simple LSM forced by RCM/Observed data Applied for the British Isles
5	TRIP2 RRM	Spatial: 1° Temporal: Daily/hourly	TRIP network	No	Demonstrated as coupled with hydrological component of European Centre for Medium-Range Weather Forecasts (ECMWF)
6	TRIP CHS RRM	Spatial: 2° Temporal: 3-hourly	TRIP network	Floodplain reservoir for two-way interaction with LSM	Demonstrated as coupled with ISBA [Decharme et al. 2010, 2012]
7	CaMa-Flood	Spatial: 0.25° Temporal: Daily	Based on Global Drainage Basin Database [Masutomi et al. 2009]	Exchange with storage for flood plain	Demonstrated for the Amazon Basin [Yamazaki et al. 2012] using runoff from MATSIRO land surface model. Hirabayashi et al. (2013) demonstrated on 29 major basins globally
8	Paiva routing	Spatial: Multiscale Temporal: Daily	Derived from SRTM data	Floodplain interchange	Demonstrated on the Purus River Basin (tributary of the Amazon River)
9	RAPID	Spatial: Vector river layer Temporal: 900 s	NHDPlus network [Horizon Systems Corporation 2007]	No	Applicable to contiguous United States, demonstrated using runoff input from Noah LSM
10	Wen routing	Spatial: Multiscale; Reported for 1/32° to 1° Temporal: Daily and hourly	Multidirectional network scheme from Guo et al. (2004)	No	Demonstrated on the Blue River Basin, the Illinois River near Watts Basin, and the Elk River Basin while coupled with VIC −3L LSM
11	WaterGAP routing	Spatial: 0.0833° Temporal: Daily	HydroSHEDS river network	Retention storage representing lakes, reservoirs, wetlands	Developed for WaterGAP Global Hydrology Model; demonstrated for Europe
12	MOSART	Spatial: Multiscale; Reported for 1/16–1/2° Temporal: Hourly or daily	HydroSHEDS data with DRT algorithm	No	Columbia River basin with VIC [Li et al. 2013] Global streamflow with CLM4 [Li et al. 2015]
13	HydroROUT	Spatial: Vector river layer at 15 s resolution, runoff downscaled to 500 m resolution Temporal: Monthly averages	HydroSHEDS river network	Accounts for lake volume; includes contaminant fate model	Coupled with runoff generated from WaterGAP Applied for studying fragmentation of river globally and specifically for the Mekong, contaminant transport in China and Saint Lawrence River Basin, Canada
14	KWR CLM	Spatial: Catchment size depends on topography; reported minimum sub- basin area of >100 km^2 Temporal: Not reported; study used data at 3-h resolution	Derived	No	Demonstrated on China while coupled with Community Land Model (CLM) LSM
15	ARTS	Spatial: 0.05° Temporal: Daily (computational time steps: a few min to several hours)	Derived from SRTM data	No	Ouémé River basin (in Benin) with Interactions between Soil, Biosphere, and Atmosphere (ISBA) [Getirana et al. 2014]
16	DRTR	Spatial: ~12 km Temporal: 3-hourly	1 km hydrographic inputs through hierarchical DRT	Two-way exchange with LSM is possible but not activated	Global Flood Monitoring System (GFMS) with VIC [Wu et al. 2014]
17	mizuRoute	Spatial: Multiscale; applicable for fine (~1 km) to coarse (>10 km) resolutions Temporal: Hourly or daily	User defined; Grid-based or vector networks	No	Developed as a stand-alone routing model, demonstrated for spatially distributed streamflow simulations over Contiguous United States (CONUS)
18	HYPERstream	Spatial: Multiscale Temporal: Reported; sub-hourly	User defined; hybrid grid-based or vector networks	No	Demonstrated on the Upper Tiber Basin, Italy Developed as a possible stand-alone routing method

Table 3. Governing equations for storage-based routing schemes.

Equation type	Applied by
Kinematic wave routing (KWR) with constant/simplified velocity
	RTM TRIP RRM G2G^a
KWR with variable velocity
	WaterGAP routing Wen routing MOSART^b DRTR^b KWR CLM^b
KWR with variable velocity and other storage in cell
	TRIP2 RRM TRIP CHS RRM
Diffusion wave
	CaMa-Flood
Dynamic wave
	Paiva routing

x is river segment [L] estimated differently for different methods, q is discharge per unit length [L² T⁻¹], h is height above datum [L], r is per unit surface runoff from LSM [L T⁻¹], v is mean velocity [L T⁻¹], β is grid cell topographic slope [-], n is Manning’s roughness coefficient [-], R is channel hydraulic radius [L], a_c is grid cell area, G is groundwater storage [L³], Q_sb is deep drainage from LSM [L³ T⁻¹], S_o and S_f are bed slope [-] and friction slope, respectively [-], q_cat is the lateral flow into the river [L² T⁻¹], q_fl is the river–floodplain flow exchange [L² T⁻¹], b is river cross-section width at free surface elevation [L], A is cross-section area [L²], g is acceleration due to gravity [L T⁻²].

^a G2G splits the KWR into sets for land, river and subsurface with constant velocity.

^b These routing schemes divide routing by stages (hillslope/overland/river, etc.).

Figure 2. Dongjiang basin and validation of model with and without basic reservoir representation for the two main reservoirs based on discharge at downstream gauge at Boluo.

Table 4. Range of parameters of the abcd model for Monte Carlo simulations.

Parameter	Definition	Min value	Max value
a	Propensity to generate runoff before the soil layer is fully saturated	0.7	1.0
b	Estimate of the upper bound of storage in the unsaturated zone	0.0	300 mm/d
c	Ratio of groundwater recharge to surface runoff	0.0	1.0
d	Proportion of groundwater that seeps back into the stream	0.0	1.0

Figure 3. Average monthly discharge at Boluo with Pearson correlation coefficient and NSE between monitored data and simulated results.

Figure 4. High-resolution tracking of surface water dynamics using remotely sensed optical imagery, demonstrated using 30-m resolution LandSAT imagery over the Pearl River Estuary and Lower Dongjiang River Basin. Map extracted from results of an algorithm tracking change of Water Occurrence Change Intensity between 1984 and 2015 developed by Pekel et al. (2016).

Figure 5. Annual average total phosphorus (TP) load generation and routing through the river network.

Xu, C.-Y., 1999. From GCMs to river flow: a review of downscaling methods and hydrologic modelling approaches. Progress in Physical Geography, 23 (2), 229–249. doi:10.1191/030913399667424608

 Web of Science ®Google Scholar

Lohmann, D., NolteHolube, R., and Raschke, E., 1996. A large-scale horizontal routing model to be coupled to land surface parametrization schemes. Tellus Series a-Dynamic Meteorology and Oceanography. doi:10.1034/j.1600-0870.1996.t01-3-00009.x

 Web of Science ®Google Scholar

Oki, T. and Sud, Y.C., 1998. Design of total runoff integrating pathways (TRIP)—A global river channel network. Earth Interactions, 2 (1), 1. doi:10.1175/1087-3562(1998)002<0001:DoTRIP>2.0.CO;2

 Google Scholar

Branstetter, M.L., 2001. Development of a parallel river transport algorithm and applications to climate studies PhD Dissertation. University of Texas.

 Google Scholar

Bell, V.A., et al., 2007. Development of a high resolution grid-based river flow model for use with regional climate model output. Hydrology and Earth System Sciences, 11 (1), 532–549. doi:10.5194/hess-11-53two-2007

 Web of Science ®Google Scholar

Pappenberger, F., et al., 2010. Global runoff routing with the hydrological component of the ECMWF NWP system. International Journal of Climatology, 30 (14), 2155–2174. doi:10.1002/joc.2028

 Web of Science ®Google Scholar

Decharme, B., et al. 2010. Global evaluation of the ISBA-TRIP continental hydrological system. Part II: uncertainties in river routing simulation related to flow velocity and groundwater storage. Journal of Hydrometeorology, 11 (3), 601–617. doi:10.1175/2010JHM1212.1

 Web of Science ®Google Scholar

Yamazaki, D., et al., 2011. A physically based description of floodplain inundation dynamics in a global river routing model. Water Resources Research, 47 (4), 1–21. doi:10.1029/2010WR009726

 Web of Science ®Google Scholar

Paiva, R.C.D., Collischonn, W., and Tucci, C.E.M., 2011. Large scale hydrologic and hydrodynamic modeling using limited data and a GIS based approach. Journal of Hydrology, 406 (3), 170–181. doi:10.1016/j.jhydrol.2011.06.007

 Web of Science ®Google Scholar

David, C.H., et al., 2011. River network routing on the NHDPlus dataset. Journal of Hydrometeorology, 12 (5), 913–934. doi:10.1175/2011JHM1345.1

 Web of Science ®Google Scholar

Wen, Z., Liang, X., and Yang, S., 2012. A new multiscale routing framework and its evaluation for land surface modeling applications. Water Resources Research, 48 (8). doi:10.1029/2011WR011337

 Web of Science ®Google Scholar

Verzano, K., et al. 2012. Modeling variable river flow velocity on continental scale: current situation and climate change impacts in Europe. Journal of Hydrology, 424–425, 238–251. Elsevier B.V. doi:10.1016/j.jhydrol.2012.01.005

 Web of Science ®Google Scholar

Li, H., et al., 2013. A physically based runoff routing model for land surface and earth system models. Journal of Hydrometeorology, 14 (3), 808–828. doi:10.1175/JHM-D-1two-015.1

 Web of Science ®Google Scholar

Lehner, B. and Grill, G., 2013. Global river hydrography and network routing: baseline data and new approaches to study the world’s large river systems. Hydrological Processes, 27 (15), 2171–2186. doi:10.1002/hyp.9740

 Web of Science ®Google Scholar

Ye, A., et al., 2013. Improving kinematic wave routing scheme in community land model. Hydrology Research 44 (January 2016): 886, 44, 886. doi:10.2166/nh.2012.145

 Google Scholar

Getirana, A.C.V., Boone, A., and Peugeot, C., 2014. Evaluating LSM-based water budgets over a west african basin assisted with a river routing scheme. Journal of Hydrometeorology, 15 (6), 2331–2346. doi:10.1175/JHM-D-14-0012.1

 Web of Science ®Google Scholar

Wu, H., et al. 2014. Real‐time global flood estimation using satellite‐based precipitation and a coupled land surface and routing model. Water Resources Research, 50 (3), 2693–2717. doi:10.1002/2013WR014710

 Web of Science ®Google Scholar

Mizukami, N., et al., 2016. mizuRoute version 1: a river network routing tool for a continental domain water resources applications. Geoscientific Model Development, 9, 2223–2238. doi:10.5194/gmd-9-2223-2016

 Web of Science ®Google Scholar

Piccolroaz, S., et al., 2016. HYPERstream: a multi-scale framework for streamflow routing in large-scale hydrological model. Hydrol Earth Systems Sciences, 20, 2047–2061. doi:10.5194/hess-20-2047-2016

 Web of Science ®Google Scholar

Lohmann, D., et al., 1998. Regional scale hydrology: I. Formulation of the VIC-2l model coupled to a routing model. Hydrological Sciences Journal, 43 (1), 131–141. doi: 10.1080/02626669809492107

 Web of Science ®Google Scholar

Pokhrel, Y., et al. 2012. Incorporating anthropogenic water regulation modules into a land surface model. Journal of Hydrometeorology, 13 (1), 255–269. doi:10.1175/JHM-D-11-013.1

 Web of Science ®Google Scholar

Decharme, B., et al., 2012. Global off-line evaluation of the ISBA-TRIP flood model. Climate Dynamics, 38 (7–8), 1389–1412. doi:10.1007/s0038two-011-1054-9

 Web of Science ®Google Scholar

Masutomi, Y., et al. 2009. Development of highly accurate global polygonal drainage basin data. Hydrological Processes, 23 (4), 57two–584. doi:10.1002/hyp.7186

 Web of Science ®Google Scholar

Yamazaki, D., et al., 2012. Analysis of the water level dynamics simulated by a global river model: a case study in the Amazon River. Water Resources Research, 48 (9), 1–15. doi:10.1029/2012WR011869

 Web of Science ®Google Scholar

Hirabayashi, Y., et al., 2013. Global flood risk under climate change. Nature Climate Change, 3 (9), 816–821. Nature Publishing Group. doi:10.1038/nclimate1911

 Web of Science ®Google Scholar

Horizon Systems Corporation, 2007. National Hydrography Dataset Plus: Documentation. Available from: http://www.horizon-systems.com/nhdplus/[Accessed January 2018].

 Google Scholar

Guo, J., Liang, X., and Leung, L.R., 2004. A new multiscale flow network generation scheme for land surface models. Geophysical Research Letters, 31 (23). doi:10.1029/2004GL021381

 Web of Science ®Google Scholar

Li, H., et al., 2015. Evaluating global streamflow simulations by a physically based routing model coupled with the community land model. Journal of Hydrometeorology, 16 (2), 948–971. doi:10.1175/JHM-D-14-0079.1

 Web of Science ®Google Scholar

Pekel, J.-F., et al., 2016. High-resolution mapping of global surface water and its long-term changes. Nature, 540, 418–422. doi:10.1038/nature20584

 PubMed Web of Science ®Google Scholar