1. Introduction
The terrestrial water budget is a key component of the regional and global water cycle. Globally, about 65% of precipitation over land is returned to the atmosphere by evapotranspiration (Trenberth et al. 2007). The partitioning of precipitation into evapotranspiration and runoff has important implications to climate variability and change through various feedback mechanisms (Leung et al. 2010; Li et al. 2011). Although it is a smaller water flux compared to precipitation and evapotranspiration, runoff routing, which is the lateral transportation of surface water over land, facilitates water exchanges among the atmosphere, land surface, and ocean. Streamflow that results from runoff routing is also an important variable for evaluating land surface and hydrology models from small watershed to large river basin scales, as streamflow is one of the quantities in the global water budget that can be measured with good accuracy, especially compared to evapotranspiration (Lettenmaier and Famiglietti 2006). Driven by the increasing need for modeling capability to address climate change adaptation and mitigation questions, earth system models will require more accurate representations of river routing to capture human–earth system interactions, such as the impacts of dams and reservoirs on local and regional evapotranspiration and freshwater inputs to the oceans, and water cycle–carbon cycle interactions, such as impacts of irrigation and land use on the biogeochemistry of rivers, lakes, and coastal zones (Leung et al. 2006; Famiglietti et al. 2010; Moss et al. 2010; Li et al. 2012b). To meet these challenges, river routing models must be applicable across a wide range of spatial and temporal scales and should provide realistic estimates of not only streamflow but also key variables such as channel water depth and velocity to facilitate modeling and analysis of in-stream biogeochemistry, sediment transport, floods, etc.
The core algorithms underpinning existing runoff routing models can essentially be grouped into three categories: linear reservoir routing (LRR)-, impulse response function (IRF)-, and Saint Venant equation (SVE)-based methods. The LRR methods have been widely adopted in large-scale runoff simulations because they are easy to implement and computationally efficient (e.g., Miller et al. 1994; Oki et al. 1999; Branstetter and Erickson 2003; Wang et al. 2011). The LRR methods usually consist of a predefined channel velocity field that does not change with time. Channel velocity by nature contains high spatiotemporal variability that is almost impossible to prescribe over large areas. Most applications of the LRR algorithms either prescribe a constant uniform channel velocity (Branstetter and Erickson 2003; Coe 1998; Miller et al. 1994) or derive spatially variable but temporally constant velocities from empirical relationships based on mean annual discharge and topography (Arora et al. 1999; Bjerklie et al. 2003; Fekete et al. 2006). The lack of spatiotemporal variability inherently limits the predictive capability of the LRR-type models, especially at fine temporal scales. The accuracy of the LRR algorithms can be further reduced as most applications do not account for subgrid heterogeneities, which may be negligible for runoff travel time at fine spatial resolutions but are definitely important at coarse spatial resolutions (Gong et al. 2009; Zaitchik et al. 2010).
The IRF methods (or source-to-sink methods) typically perform well across a wide range of resolutions and are computationally more efficient than the LRR methods (Lohmann et al. 1996, 1998; Goteti et al. 2008; Gong et al. 2009; Zaitchik et al. 2010). Instead of simulating runoff transport cell by cell, the IRF methods predict the lumped response of the contributing area to any location of interest. The IRF methods, however, view the runoff transport system (i.e., landscape) as linear and stationary, which has been found not valid for either natural or managed hydrologic systems (e.g., Sivapalan et al. 2002; Botter and Rinaldo 2003; Milly et al. 2008). Since the parameters of the IRF methods are usually not easily available, considerable calibration is often required to reproduce the observed hydrograph. Another obvious limitation of the IRF methods is the difficulty to incorporate them in a land surface model to handle the interactions between water, energy, and other material fluxes. For example, the transport of sediment is governed by the dynamics of water fluxes such as depth and velocity variation, which are not easily extractable from the IRF methods.
The model introduced in this paper falls in the third category, the SVE-based methods. The SVE-based methods are rooted in the classic Saint Venant equations with simplifications at different levels, that is, kinematic wave method, diffusion wave method, etc. (e.g., Arnold et al. 1995; Arora and Boer 1999; Beighley et al. 2009; Lucas-Picher et al. 2003; Li and Sivapalan 2011; Yamazaki et al. 2011). The SVE models have been traditionally applied to small areas because of computational limitations and extensive data requirements. The work by Arora and Boer (1999) is among the first to couple the SVE routing approach with earth system models and applied it over large scales. By explicitly solving for velocities instead of prescribing or calibrating them, the SVE-based methods embrace the spatiotemporal variability of velocities without invoking the assumption of linearity or stationarity. This is of key importance to regional or global water cycle simulations (Decharme et al. 2010). Moreover, the SVE models explicitly estimate in-stream states such as water depth and velocity and therefore facilitate the coupling of water and other material fluxes in a land surface model or earth system model. Most of the existing SVE models either neglect the travel time within a grid cell (or subbasin) or discretize a grid or subbasin into a hillslope portion and a single channel (thus neglecting what happens in between); hence, conceptually, they are only applicable at fine spatial resolutions or coarse temporal resolutions. Among the very few exceptions is the Soil and Water Assessment Tool (SWAT) model (Arnold et al. 1995; Neitsch et al. 2004), which, however, has been designed for subbasin-based representation only, making it difficult to be coupled with large-scale land surface models. Here we propose a scalable, physically based framework to explicitly account for the effects of subgrid heterogeneity on runoff routing. Moreover, our model adopts a scale-independent river network dataset derived based on the Dominant River Tracing (DRT) algorithm (Wu et al. 2011, 2012). The DRT algorithm produces consistent estimation of flow directions, upstream areas, and flow lengths at various spatial resolutions (more details in section 2).
The remainder of this paper is organized as follows: section 2 introduces the model structure, section 3 describes the study area and model inputs, section 4 focuses on the results and discussion, and section 5 closes with a summary and discussion on the limitations and future directions for improvements.
2. Model description
a. A new routing model
Surface runoff after generation starts its journey first in the form of overland flow across hillslopes before entering the river channels. If a spatial unit is sufficiently large that its river network consists of more than one reach, the major reach can be treated as the main channel whose end node is the outlet of the whole spatial unit. The rest of the river network can be defined as tributaries, and they contribute to the main channel only. As shown in Fig. 1, we conceptualize the runoff routing pathways across a spatial unit as consisting of three components:
From hillslope to the tributaries: for each spatial unit, surface runoff routes as overland flow into the tributaries, while subsurface runoff after generation directly enters the tributaries, because the generation process of subsurface runoff already contains the memory of its residence time within hillslopes (Brutsaert and Nieber 1977; Harman et al. 2009; Wang and Cai 2009).
From the tributaries to the main channel: for each spatial unit, the tributaries are conceptualized as a single equivalent channel (denoted as subnetwork channel hereinafter), which has the same transport capacity as all tributaries within the spatial unit combined together (Snell and Sivapalan 1995). This subnetwork channel receives water from the hillslopes and discharges it into the main channel.
Main channel routing: it receives water from the tributaries within the spatial unit and/or water routed from the upstream spatial units (if any) and discharges the water to its downstream spatial unit or the ocean.
Conceptualization of river network in MOSART. The runoff generated first enters the tributaries (surface runoff via hillslope routing and subsurface runoff without hillslope routing); it is then routed through the tributaries (here conceptualized as a single equivalent channel, as shown by the light blue dashed lines) and is finally discharged into the main channel. The value Vh is the overland flow during hillslope routing, Vt is the channel velocity within the tributaries, and Vr is the channel velocity within the main channel.
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
The above conceptual model can be applied to either a grid-based or subbasin-based spatial representation. The grid-based representation discretizes a study area into a number of regularly shaped grid cells as the fundamental modeling units. The subbasin-based representation discretizes a study area into a number of subbasins. In this study we focus on the former, while the latter is being evaluated in another ongoing study. The grid-based routing model must be underpinned by a set of grid-based river network structures that facilitate the delineation of a study area into the fundamental units and provides linkage between these units. The DRT algorithm developed by Wu et al. (2011) is an automated procedure to upscale the baseline fine-resolution hydrography to any specified coarse resolution. The original baseline hierarchical drainage structure can be preserved consistently at various coarse resolutions by tracing each flow path (from headwater to river mouth) from the finescale structure. The higher-order reaches are given higher priority correspondingly. The baseline high-resolution hydrography dataset is Hydrological Data and Maps Based on Shuttle Elevation Derivatives at Multiple Scales (HydroSHEDS; Lehner and Döll 2004; Lehner et al. 2008). Figure 2 shows that the real river network in the Columbia River basin has been well preserved by the DRT algorithm. Note that here the “real” river network has been extracted from a different source, the National Hydrography Dataset Plus (NHDPlus; U.S. Geological Survey 2010).
River network within the Columbia River basin. The background layer is the upstream drainage area distribution at ⅙° resolution derived by the DRT algorithm. The purple lines are for the actual river channels extracted from the NHDPlus database, showing only the channels with upstream drainage areas larger than 30 000 km2. The green stars are the selected USGS streamflow stations where the model-predicted discharges are evaluated.
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
While designing and developing this new model, it is our goal that it is applicable at a broad range of spatial resolutions (e.g., fine to coarse) and scales (e.g., local to global) with relatively consistent performance. The knowledge gained from applications at one resolution can thus be transferred to another resolution without much adjustment (Guo et al. 2004; Wen et al. 2012). In this regard, we introduce a scalable framework of subgrid routing (mainly via a subnetwork channel) and between-grid routing (mainly via a scale-independent channel network structure). We therefore hereafter name this new model as Model for Scale Adaptive River Transport (MOSART).
b. Existing models for comparison
To assess the new river routing model described above and understand its behavior, it is valuable to compare it with commonly used methods including the LRR and IRF models. We chose two widely used models for comparison in this study: the River Transport Model (RTM) as part of the Community Land Model (CLM; Branstetter and Erickson 2003; Oleson et al. 2010) as a representative of the LRR approach, and the routing module, which is used as a postprocessor in the Variability Infiltration Capacity (VIC) model package for river routing (Lohmann et al. 1996, 1998) as a representative of the IRF approach (hereafter noted as the Lohmann routing model).
The Lohmann routing model explicitly represents the routing of surface and subsurface runoff within a grid using a unit hydrograph that contributes to the channel network. The unit hydrograph is, in principle, the distribution of travel time within a grid and implicitly incorporates the travel time both across hillslopes and through the tributaries that link the hillslopes and main channel. The channel network routing is simulated with a linearized Saint Venant equation (Lohmann et al. 1996, 1998), not for any specific channel segment, but for the whole network within the study area. Calibration of the parameters, mainly the unit hydrograph, channel velocity, and diffusion, is usually required, especially for any application at a daily time scale or finer.
3. Study area and data
a. Columbia River basin
The Columbia River basin is located in the U.S. Pacific Northwest. Originating from the Rocky Mountains of British Columbia, Canada, this river flows through Washington and Oregon and is the largest river from North America discharging into the Pacific Ocean. The hydrology of the basin is very rich because of the diverse climate zones and varied land uses, and it has been the subject of numerous studies (e.g., Cayan and Peterson 1989; Clark et al. 2001; Hamlet and Lettenmaier 1999a, 1999b, 2007; Naik and Jay 2011). Most of the Columbia River flows through stable rock-walled canyons, which lead to stable channel geomorphology and geometry therefore suitable for dam constructions. Since the 1930s, there have been more than 450 dams constructed in this basin for hydroelectric power production, irrigation, flood control, and other purposes.
The U.S. Geological Survey (USGS) gauge station near The Dalles (hereafter denoted as DALLE), Oregon, has an upstream contributing area of about 606 700 km2 that covers most of the Columbia River basin. For the convenience of model evaluation and comparison, we use the upstream contributing area of DALLE station, as shown in Fig. 2, as our study region. This area is divided into regular grids at ⅙°, ⅛°, ¼°, and ½° resolutions to investigate the effects of grid resolution on the model performance. Daily time series of runoff generation, which are inputs of the routing models, have been produced by the Surface Hydrology Group, University of Washington (UW; http://www.hydro.washington.edu/2860/) using the VIC model (Liang et al. 1994; Lohmann et al. 1996, 1998). The VIC model was calibrated for the period of approximately 1975–89 at the monthly scale at multiple flow stations to produce daily runoff generation time series at the ⅙° resolution (Elsner et al. 2010). For calibrating monthly mean discharges, only runoff generation parameters were calibrated while constant routing parameters were used (e.g., diffusivity of 800 m2 s−1 and velocity of 1.5 m s−1 according to the VIC webpage: http://www.hydro.washington.edu/Lettenmaier/Models/VIC/Documentation/Calibration.shtml#RoutCal).
Our study period was chosen as 1 November 1979 to 30 September 1989 since a 10-yr period will be sufficient for the model validation. In this study, the runoff generation time series produced by the VIC model were aggregated to various coarser resolutions, as shown in Table 1. Naturalized streamflow with human influences such as reservoir operation and surface water withdrawal removed is used to evaluate the simulated streamflow. The naturalized streamflow data are also obtained from the Surface Hydrology Group, University of Washington. Note that for stations with large contributing areas, naturalized streamflow data are only available at the monthly scale. Also displayed in Fig. 2 are the locations of selected major USGS streamflow gauges and a list of small natural basins from Model Parameter Estimation Experiment (MOPEX) for validation purposes (more details provided in section 4).
Spatial statistics of the daily runoff inputs (mean and standard deviation, the latter in parentheses). All statistics are weighted by the local drainage areas and are for all the pixels within the contributing area of DALLE station (i.e., the whole study area). Statistics are temporally averaged in either June or October 1980.
b. Network delineation and parameter estimation
Spatial statistics of the geographic inputs (mean and standard deviation, the latter in parentheses). All statistics are weighted by the local drainage areas. The statistics are for all the pixels within the contributing area of DALLE station (i.e., the whole study area), except for the last row, in which the statistics are for the pixels on the major channels only (i.e., those with an upstream drainage area larger than 50 000 km2).
4. Model results and discussion
a. Simulation of streamflow
MOSART was applied to the study area at different spatial resolutions. To minimize the impacts of the uncertainties in runoff generation simulation on runoff routing, we want to restrict our analysis to the locations where VIC reasonably captures both the magnitude and timing of runoff generation. Several USGS streamflow stations were thus selected on the basis of the following criteria:
The contributing areas should be sufficiently large because naturalized streamflow data at most stations are only available at the monthly scale, so routing is only important for larger areas.
The annual water balance should be reasonably preserved, that is,
The Lohmann routing model has good performance, that is, the Nash–Sutcliffe coefficient should be larger than 0.65 (Moriasi et al. 2007).
The selected stations are shown in Fig. 2 and listed in Table 3. For each station, the mask files have been derived at each coarse resolution based on the high-resolution digital elevation model (DEM) from the HydroSHEDS dataset. The purpose of the mask files is to ensure that the contributing area of each station (and thus the water balance) be well preserved during the routing process. The RTM routing approach has also been applied to different resolutions using the same network (mainly flow direction), runoff generation time series, and mask files used by MOSART. The Lohmann routing model results, which were simulated with the same runoff time series but different network and mask files, were directly obtained from the UW hydrology group.
Selected USGS flow stations.
Figure 3 shows the Nash–Sutcliffe coefficients and coefficients of determination between the models predicted and naturalized monthly streamflow. The performance of MOSART is clearly better than the RTM model for most stations, especially those with larger contributing areas. Also encouraging is that for these stations, MOSART performs no worse than the Lohmann routing model.
A comparison showing MOSART-, RTM-, and VIC-simulated monthly streamflow with naturalized streamflow for the period November 1979 to September 1989. From DALLE to ARROW, the contributing area decreases.
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
Since the most basic function of a routing model is to capture the time lag between runoff generation and streamflow, mean monthly hydrographs of the predicted and naturalized streamflow are compared and shown in Fig. 4. The RTM approach is overestimating the time lag between runoff generation and streamflow. This overestimation is more significant as the contributing area increases, that is, from Kootenay River at Boundary Dam (station name CORRA) to DALLE station. For stations with relatively small contributing areas, such as CORRA station, the difference of time lag between different model simulations becomes trivial at the monthly scale since the actual residence time of surface water through such small areas is usually much less than a month.
Mean monthly variations of streamflow simulations from different routing algorithms (at ⅙° resolution) and the naturalized streamflow for the period November 1979 to September 1989.
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
b. Simulation of travel velocity and water depth
The different behavior of MOSART, RTM, and Lohmann routing models as described above can be attributed primarily to the channel velocities used to transport water through the river network. For our study period (1979–89), the observed channel velocity time series under naturalized condition are not available at the major stations in Figs. 3 and 4 because the Columbia River system was subject extensively to the impacts of dams and reservoir operations during this period.
One way to validate the simulated channel velocities at major downstream stations is to utilize a hydraulic routing model under naturalized conditions. A hydraulic routing model solves the full Saint Venant equations to achieve the most complete process-level representation of channel routing (Chow et al. 1988), while hydrologic routing models (MOSART, RTM, and VIC all belong to this category) are simplifications of the former. When combined with a thorough field survey of channel geometry and geomorphology, a hydraulic routing model is expected to reproduce the variation of channel velocity well. Therefore, we applied a well-established hydraulic model called the Modular Aquatic Simulation System (MASS) (Richmond and Perkins 2009) for comparison with MOSART simulations. The MASS model has been extensively applied throughout the Columbia River basin based on high-resolution field surveys of channel geometry. During the period November 1917 to September 1921 (before the construction of dams along the Columbia River network began in the 1930s), USGS observed streamflow data are available for DALLE and PRIRA (Columbia River at Priest Rapids Dam) stations. Since the USGS-observed streamflow during that period does not differ significantly from the naturalized streamflow of our study period, and that the channel geometry should vary little over time because of the basalt bedrock, it is reasonable to compare the channel velocity simulated by the MASS model during November 1917 to September 1921 with our model simulations. The MASS model parameters were obtained via careful calibration under current conditions using detailed observations of water surface elevation, velocity, etc., and applied to the period November 1917 to September 1921. For more details about the MASS model and its application in this study, please refer to appendix A. Figure 5 shows that the magnitude of channel velocities simulated by MOSART compares reasonably well to that by MASS. More importantly, under naturalized conditions, the channel velocities within the Columbia River network exhibit strong seasonality. This seasonality has been well captured by MOSART across different resolutions.
Seasonal variations of channel discharge and velocity simulated by MOSART and MASS. The simulation period by MASS is 1 Nov 1917 to 30 Sep 1921 and by MOSART is 1 Nov 1979 to 30 Sep 1989.
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
We continue to evaluate MOSART simulations against the field measurements. A simple procedure has been developed to derive the channel velocity time series from the USGS observations. Details of this procedure are given in appendix B. We first apply this procedure to the major stations with the understanding that they are subject to significant human interferences. Limited by data availability, this procedure has been applied to two of the major stations shown in Figs. 3 and 4, namely, PRIRA and DALLE, for a relatively recent period November 1998 to September 2010. This period is close to our study period November 1979 to September 1989, and therefore, the corresponding velocity data are expected to reflect the actual velocity variation with our study period at a certain level.
As shown in Fig. 6, the most significant effects of dam constructions and operations on streamflow are to reduce the peak discharges when there is flooding and to maintain the low discharges when there is little precipitation and, thus, limited runoff to feed the channels. Surface water withdrawal from the main streams may also reduce the streamflow. The seasonal variation of channel velocity reflects similar effects of the dams and surface water withdrawal. Without human influences, the channel velocity would be significantly higher during the high-flow period, for example from April to July. Even attenuated by dam operation, the actual channel velocity is still mostly higher than 0.35 m s−1, which is the default channel velocity adopted by the RTM in CLM4.
Seasonal variations of channel discharge and velocity simulated by MOSART and derived from USGS observations. The period for MOSART simulation and naturalized streamflow is November 1979 to September 1989. The period for the USGS observation is November 1998 to September 2010.
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
We further apply this procedure and evaluate the MOSART-simulated channel velocities at some small natural basins from the MOPEX. The MOPEX basins are considered to be not affected by any noticeable human activities (Duan et al. 2006). Out of the 32 MOPEX basins within the Pacific Northwest region, we selected six where 1) the drainage area delineated by the DRT algorithm is close to the USGS estimated area; 2) the annual water balance is well simulated by the VIC runoff generation and MOSART routing, that is, 
Evaluation of MOSART at ⅙° and ½° resolutions for MOPEX basins. The vertical axis is for the model simulations, and the horizontal axis is for the USGS observations.
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
Figures 5–7, combined together, reveal the ubiquitous spatiotemporal variability of channel velocity, which is completely ignored by the RTM approach. The Lohmann routing model has some flexibility to capture the spatial variability of channel velocity, along with diffusion, unit hydrograph, etc. However, it requires considerable calibration efforts to achieve such spatial variability, and it has limitations in capturing the temporal variability of the routing parameters, which, as partially demonstrated in this study, is not negligible even at the monthly time scale. MOSART is shown capable of simulating the spatiotemporal variability of channel velocities across different spatial resolutions. In this study, the only calibration needed is for the hydraulic geometry relationships to estimate channel geometry.
Besides producing realistic channel velocity and, therefore, more accurate streamflow estimation, another significant advantage of MOSART as a physically based model is the ability to provide spatially distributed time series of water depth and velocity within hillslope, subnetwork, and main channels. In Figs. 8 and 9, these state variables were first averaged from the daily scale within June 1980 (a wet month) and October 1980 (a dry month), respectively, for each modeling unit (grid) to produce the spatial distributions for the two months. In both the wet month (Fig. 8) and dry month (Fig. 9), there is a strong similarity between the spatial distributions of overland flow velocities and runoff generation, especially for surface runoff. This is not surprising since overland flow follows immediately and is directly driven by the surface runoff generated. For the spatial pattern of subnetwork channel velocities, the impacts of surface runoff generation are more obvious under wet conditions than dry conditions. A possible explanation is that during wet periods the impacts of climate conditions dominate, while during dry periods the impacts of landscape properties such as channel slope distribution are at least equally important. The spatial structure of main channel water depth almost resembles the river network, that is, the larger the upstream drainage area, the deeper the channel water depth. This, however, is not the case for the main channel velocities, which are mainly controlled by the channel slope and water depth. The channel slope generally decreases from upstream to downstream, and this trend opposes the effect of increasing water depth with upstream drainage area.
Spatial distribution of model-simulated overland flow velocity (Vh), subnetwork velocity (Vt), main channel water depth (Hr), and main channel velocity (Vr) at ⅙° resolution, averaged for June 1980 (wet period); Qsur and Qsub are the surface runoff and subsurface runoff generation simulated by the VIC model.
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
As in Fig. 8, but for October 1980 (dry period).
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
c. Impacts of spatial resolutions
For any grid-based routing model, it would be of practical interest to understand how sensitive the model is to spatial resolutions. In this study, MOSART has been applied at ⅙°, ⅛°, ¼°, and ½° resolutions. The major outputs, streamflow time series, are produced at each grid within the study area. Also produced are the water depths and velocities at hillslope, subnetwork channel, and main channel within each grid cell. It is shown in Figs. 3 and 4 that MOSART reproduces the streamflow variation at the monthly scale reasonably well. More interestingly, the model-simulated monthly streamflow shows little sensitivity to spatial resolution. Note that the stations in Figs. 3–6 are mostly at the major reaches. Recall that one major advantage of the DRT algorithm is preserving the dominant channel network structure (inherited from the baseline hydrography) at any coarse resolution, that is, maintaining scale consistency of the channel network. Another important factor of streamflow simulation is the consistent representation of the contributing area of a targeted flow station across different resolutions. In this study, the contributing area of each station is consistently preserved within the mask files derived directly from the HydroSHEDS dataset.
The spatial statistics of the model outputs over the whole study area are listed in Table 4 for different resolutions. For overland flow velocities, there is a systematic increase of mean values with grid size, but this is not the case for the runoff generation (Table 1) or topographic slope (Table 2). If assuming steady conditions, overland flow velocity is a nonlinear function of runoff generation and topographic slope. Taking the relationship between overland flow velocity and topographic slope as an example, the relationship can be generalized by the formula 
Spatial statistics of the model outputs at daily scale (mean and standard deviation, the latter in parentheses). All statistics are weighted by the local drainage areas and are temporally averaged in either June or October 1980.
The mean values of subnetwork channel velocities decrease with coarser resolution. This is mainly because of the dominance of local channel slope that shows the same trend. Because the mean channel slope for each grid cell is calculated from the dominant river within the cell, the mean channel slopes of a grid cell at coarser resolutions (e.g., ½°) tend to be calculated using relatively larger rivers with longer river segments than for finer resolutions (e.g., ⅙° resolution), which explains the decrease of mean channel slope at coarser resolutions.
The model-generated main channel velocities show a systematic trend with spatial resolutions. The cause of this trend is not straightforward. The mean channel slopes averaged over the whole study area are decreasing from ⅙° resolution to coarser resolutions, while those averaged over the mainstream grids (here defined as those grids on the main stream, that is, with upstream drainage areas larger than a certain threshold, for example 50 000 km2) are rather similar across resolutions. The main channel velocity estimated from a grid at coarser resolution, nonetheless, appears to be larger than at finer resolution because of two factors: 1) a larger contributing area and, thus, more water in the channel, and 2) nonlinearity in the channel velocity formulation. The spatial statistics over the whole Columbia River basin are more influenced by the headwater grids simply because there are a much larger number of headwater grid cells than the number of downstream grids. The spatial statistics of main channel velocities over the mainstream grids, nevertheless, are rather consistent across different resolutions. This suggests that the impacts of spatial resolution on runoff routing are less significant for the locations with large upstream drainage areas.
Figure 10 shows the model sensitivity to spatial resolution and subgrid routing via daily hydrograph for one event during a wet period (June 1980) and another event during a dry period (November 1980) at the same set of stations as in Fig. 4. It is not surprising that the impacts of spatial resolution are more significant at daily scale. The daily hydrographs at ⅙° resolution exhibit more temporal variation and later time to peak than those at ½° resolution because of the greater spatial heterogeneity contained in the network parameters at ⅙° resolution. Also, the incorporation of subgrid routing introduces more spatial heterogeneity, which indeed helps reduce the impacts of spatial resolution; that is, the difference between daily hydrographs (e.g., rising limb and recession part) at different spatial resolutions are apparently less if subgrid routing is considered. This is most clearly shown in the top-right plot in Fig. 10 if one compares the rising limb of the daily hydrographs. The effects of separated representation of hillslope routing are not easy to illustrate via daily hydrograph since the travel time of overland flow across hillslopes is typically less than 1 day. But this will be critical if the coupling between water fluxes and other fluxes such as sediment or nutrients is of concern, since sediment or nutrients fluxes are usually triggered by precipitation events and the subsequent overland flow routing (Neitsch et al. 2004; Li et al. 2010).
Effects of subgrid routing at the daily scale. Case 1 is the simulation with subgrid routing at ⅙° resolution. Case 2 is the simulation without subgrid routing at ⅙° resolution. Case 3 is the simulation with subgrid routing at ½° resolution. Case 4 is the simulation without subgrid routing at ½° resolution.
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
d. Sensitivity analysis
Besides the channel geometry and parameters derived with DRT algorithm, two other parameters, the Manning’s roughness coefficients for overland flow routing and for channel routing, are fixed as constants across different resolutions in this study for simplicity. Sensitivity analysis has also been conducted on these two parameters. Figure 11 shows that MOSART is noticeably insensitive to the Manning’s roughness coefficient of channel flow for monthly streamflow. However, its sensitivity will be more significant for streamflow simulation at daily or finer temporal resolution or for simulation of channel velocities. The impacts of the Manning’s roughness coefficient on overland flow routing (results not shown) are trivial for streamflow simulation at the monthly scale.
Sensitivity of MOSART to the Manning’s roughness of channel flow at ⅙° and ½° resolution.
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
5. Summary and more discussion
This paper introduces a physically based runoff routing model that represents routing processes through hillslopes, subnetwork, and main channels. The model has been evaluated using monthly naturalized or observed streamflow at a number of USGS stations and channel velocities from reliable sources within the Columbia River basin. We show that MOSART is capable of not only capturing the seasonal variation of both streamflow and channel velocities at different spatial resolutions, but also providing reasonable estimation of water depth and velocities at hillslopes, subnetwork channels that are useful for lateral transport of biogeochemical fluxes. The scalability of a routing model hinges on its ability to represent spatial heterogeneity (subsequently temporal variability) within and between grid cells. That is, the better the model structure represents spatial heterogeneity, the less dependent the model is on spatial resolution. Because of the underlying assumption of spatially uniform constant velocity, RTM completely neglects spatial heterogeneity. Although one could improve such an LRR model by including spatially variable channel velocity, it still lacks subgrid representation, which affects model scalability significantly. The Lohmann routing model (and other IRF methods) explicitly represents subgrid routing via a subgrid IRF that implicitly combines the routing both at hillslopes and through subnetwork tributaries. Such a subgrid IRF is inherently scale dependent because of the increasing impacts of subnetwork tributaries at coarser resolutions. Moreover, IRFs are governed by both climate conditions and landscape properties, so their validity under climate change is questionable. MOSART explicitly parameterizes the subnetwork tributaries in a scalable way. We have illustrated that the subnetwork channel structure reduces scale dependence of the model (e.g., Fig. 7). Comparison between MOSART simulations and field measurements suggests that calibration could potentially improve MOSART’s performance, especially when it is applied to small catchments at finer spatial and temporal resolutions. We will explore such topics and report our results separately. Nevertheless, as we have discussed in this paper, all MOSART parameters are closely controlled by landscape properties only so they are less sensitive to climate change. Although the monthly time scale is considered sufficient for many applications of river routing in large river basins, it is important to understand how the model is dependent on spatial resolutions for finer temporal scales such as hourly or daily scales. We intend to investigate this in the future by applying MOSART to basins where both high-quality runoff generation and stream measurement data are available at fine temporal resolutions.
Several limitations revealed in this study deserve future attention:
The parameters required by this model are all physically based, and many of them can be derived from available information. Calibration, however, is recommended at least at the current stage. For example, accurate estimation of channel geometry remains a significant challenge for large-scale river routing. The hydraulic geometry relationship is handy to use but requires extensive field measurements to derive effective parameters, and a single relationship may not hold across a large area (Yamazaki et al. 2011). Efforts are also required to construct a global parameter database based on other available information. For example, by definition the hillslope length
As shown in Figs. 5–7, there are some differences among the simulated main channel velocities at different resolutions (e.g., the PRIRA station). According to Eq. (4), this difference is mainly caused by the local channel slope (estimated as the average slope of the cell containing the station), which is not necessarily consistent at different resolutions. A diffusion wave method, which explicitly incorporates the interactions between the upstream and downstream channels, would help to eliminate the overdominance of the local topography and improve the consistency of channel velocity simulation across different resolutions. However, the diffusion wave method is computationally expensive, so its utility is more warranted if an accurate simulation, such as inundation area variation, is of major concern and the spatial scales of interest are smaller.
When applying MOSART to small areas such as the MOPEX basins, the DRT-estimated drainage area is prone to significant errors, especially at coarse resolutions. Within a big grid cell (e.g., 1° × 1°), very often there are several river reaches. The current DRT algorithm assumes a single flow direction that corresponds to the most dominant river reach. When the outlet of a small basin is located on a tributary reach, significant drainage area error will arise. One possible way to solve this issue is to introduce a multiple flow direction approach into DRT (Guo et al. 2004), but this is left for future investigation.
The current representation of floodplain in MOSART is crude, even though it might be sufficient when only streamflow simulation is required, as in this study. When inundation dynamics are of interest, however, detailed floodplain topography needs to be better incorporated. One effective and feasible way is to incorporate a relationship between flooded area and water level and storage derived from high-resolution DEM (Yamazaki et al. 2011).
Acknowledgments
This study is supported by the Department of Energy Biological and Environmental Research (BER) Earth System Modeling (ESM) and Integrated Assessment Modeling (IAM) programs through the Integrated Earth System Modeling (iESM) and Climate Science for Sustainable Energy Future (CSSEF) projects. Development of the datasets used in this study is also partly supported by the Platform for Regional Integrated Modeling and Analysis (PRIMA) initiative. In addition, some data and information were provided by the Surface Hydrology Group, University of Washington (http://www.hydro.washington.edu/2860/). We thank Sara Kallio, William Perkins, and Marshall Richmond of PNNL for providing the simulation results from the MASS model. The Pacific Northwest National Laboratory is operated by Battelle for the U.S. Department of Energy under Contract DE-AC06-76RLO1830.
APPENDIX A
The MASS Model and Its Application at the Columbia River Basin
The velocity profiles were developed by using the Modular Aquatic Simulation System 1D (MASS1) software, developed at Pacific Northwest National Laboratory. MASS1 is an unsteady hydrodynamic model for river systems (Richmond and Perkins 2009) that calculates cross-sectional-averaged parameters of hydraulic conditions for riverine and reservoir systems. Since MASS1 uses cross-sectional area averaging, only single values of water surface elevation, velocity, and discharge were produced for each specified section.
Two-meter resolution bathymetry for the Columbia River from Rock Island Dam to McNairy Dam and the Snake River from Ice Harbor to the Columbia River confluence were used to digitize cross sections every 0.25 miles (mi). As shown in Fig. A1, the upstream boundary condition on the Columbia River was located at Rock Island Dam. The USGS gauge below Priest Rapids Dam (12472800) was used as the inflow discharge because of its records dating back to October 1917 and represents “natural flows” before dam constructions and flow alterations occurred. The Snake River upstream boundary condition was located at Ice Harbor Dam. The USGS streamflow observations at Clarkston (13343500) on the Snake River were used as the inflow discharge for its early, predam conditions as well. To compare with the simulations from MOSART, the results from MASS model were averaged within a 1-mi segment around the targeted USGS stations (five cross sections), instead of taking results from any single cross section.
The MASS model boundary conditions and USGS gauge locations.
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
APPENDIX B
Deriving Channel Velocities from USGS Observations
Throughout the Columbia River network, USGS has been regularly measuring and providing streamflow at various locations as early as the 1910s. After the 1990s, USGS has also been providing regularly measured gauge height, which can be considered as a surrogate of channel water depth. On top of these regular measurements, USGS has also conducted field measurements from time to time on the channel geometry such as channel width and channel (wetted) area. It is assumed that there is a one-to-one relationship between channel water depth and wetted area, as shown in Fig. B1. The average channel velocity 
Linear relationship between gauge height and channel (wetted) area measurements at the USGS stations.
Citation: Journal of Hydrometeorology 14, 3; 10.1175/JHM-D-12-015.1
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