A new multiscale routing framework and its evaluation for land surface modeling applications

Transcription

1 WATER RESOURCES RESEARCH, VOL. 48,, doi: /2011wr011337, 2012 A new multiscale routing framework and its evaluation for land surface modeling applications Zhiqun Wen, 1,2,4 Xu Liang, 2,3 and Shengtian Yang 1 Received 29 August 2011; revised 18 April 2012; accepted 24 June 2012; published 31 August [1] A new multiscale routing framework is developed and coupled with the Hydrologically based Three-layer Variable Infiltration Capacity (VIC-3L) land surface model (LSM). This new routing framework has a characteristic of reducing impacts of different scales (both in space and time) on the routing results. The new routing framework has been applied to three different river basins with six different spatial resolutions and two different temporal resolutions. Their results have also been compared to the D8-based (eight direction based) routing scheme, whose flow network is generated from the widely used eight direction (D8) method, to evaluate the new framework s capability of reducing the impacts of spatial and temporal resolutions on the routing results. Results from the new routing framework show that they are significantly less affected by the spatial resolutions than those from the D8-based routing scheme. Comparing the results at the basins outlets to those obtained from the instantaneous unit hydrograph (IUH) method which has, in principle, the least spatial resolution impacts on the routing results, the new routing framework provides results similar to those by the IUH method. However, the new routing framework has an advantage over the IUH method of providing routing information within the interior locations of a basin and along the river channels, while the IUH method cannot. The new routing framework also reduces impacts of different temporal resolutions on the routing results. The problem of spiky hydrographs caused by a typical routing method, due to the impacts of different temporal resolutions, can be significantly reduced. Citation: Wen, Z., X. Liang, and S. Yang (2012), A new multiscale routing framework and its evaluation for land surface modeling applications, Water Resour. Res., 48,, doi: /2011wr Introduction [2] Runoff routing, a process that transfers runoff to water flows in rivers, is important to land surface models (LSMs). Runoff routing, including overland and channel flow routing, integrates a watershed s distributed runoff into its channel streamflow which is one of the most accurate quantity that can be measured in the water budget. Thus, a good routing method can serve as an effective tool to link the results of a LSM to streamflow measurements for LSM model improvements and validations. In general, a routing model, a mathematical procedure used to represent the water movement from one place to another, includes two parts: (1) constructing a flow path (i.e., both overland and channel) network and (2) applying a mathematical method to calculate the water movement along the flow path network. 1 School of Geography, Beijing Normal University, Beijing, China. 2 Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania, USA. 3 State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, China. 4 Now at the State Information Center, Beijing, China. Corresponding author: X. Liang, Department of Civil and Environmental Engineering, University of Pittsburgh, 941 Benedum Hall, 3700 O Hara St., Pittsburgh, PA 15261, USA. (xuliang@pitt.edu) American Geophysical Union. All Rights Reserved /12/2011WR [3] Over the years, numerous runoff routing frameworks have been developed for large-scale applications with LSMs. Most of them, however, compute water movement through flow path networks obtained from the eight directions (D8) method [Guo et al., 2004] in which the flow direction (including both overland flow and channel flow) is determined by one of the eight directions of each modeling grid according to the steepest downward slope. For example, the flow path networks used in the River Transport Model (RTM) [Graham et al., 1999], the Total Runoff Integrating Pathways (TRIP) model [Oki and Sud, 1998], the overland flow routing module in Hydrology Laboratory Research Modeling System (HL-RMS) of the US national weather service [Koren et al., 2004; Wang et al., 2000], and the routing module in the Three-layer Variable Infiltration Capacity (VIC-3L) model [Lohmann et al., 1996] are all generated based on the D8 method. A common feature of most of the LSM applications using the D8 method is its rather coarse resolution, typically ranging from (10 10 km 2 )to5 5 ( km 2 ). Thus, impacts of the topography of each basin on the flows paths and the time it takes for the flow to travel cannot be adequately represented by the D8 method. Du et al. [2009] studied the effect of grid size on streamflow simulations for a watershed using the D8 method and concluded that different spatial resolutions affect the model-simulated streamflows due to the different representations of the flow path networks and their properties. Arora et al. [2001] 1of16

2 conducted a runoff routing comparison at 350 km and 25 km grid sizes with the same runoff input, and showed that the streamflow was biased at both high and low flows when the routing was applied to the coarser resolution case (i.e., 350 km resolution). Guo et al. [2004] and Guo [2006] provided detailed discussions on the limitations of the D8 method and a review of the strengths and weaknesses of other relevant routing methods that overcome some of the limitations of the D8-based (eight direction based) routing method. [4] The flow network generation method proposed by Guo et al. [2004] uses a concept of multidirections, as opposed to the concept of one of the eight directions (i.e., the D8 method), for the overland flow to simultaneously exit each modeling grid. They also introduced a new concept of using a tortuosity coefficient to reduce the spatial scale effect on the channel flow network lengths and other hydrologic characteristics. As a result, Guo et al. [2004] show, based on one watershed application, that not only can the flow directions and flow network be determined more accurately with their method than the widely used D8 method, but also their flow routing results, without calibrating the routing parameters at each individual spatial resolution, are much less affected by the different spatial resolutions than those by the D8-based routing method. Although there are successful applications of the D8-based routing method applied to different spatial resolutions, the routing results are calibrated at each given spatial resolution in each application [e.g., Du et al., 2009; Gong et al., 2009; Lohmann et al., 1998; Olivera and Maidment, 1999]. This makes the D8-based routing method less attractive, among other things, due to the large effort involved in the calibration process associated with each spatial resolution each time. Although the flow network generation method by Guo et al. [2004] has shown encouraging behaviors of its relative independence on the spatial scales, its results show a dependence on temporal scales. The river routing module in HL-RMS considers multiple directions for the river routing, but it does not consider multiple directions for the overland flow routing [Koren et al., 2004; Wang et al., 2000] in which the overland flow routing only allows flow to exist from one direction for each grid. Goteti et al. [2008] presented a macroscale hydrologic modeling system which is composed of a LSM and a river routing model with an explicit representation of the river channels and floodplains. In order to couple the LSM with the routing model, which includes catchment information from the 90 m Shuttle Radar Topography Mission (SRTM) DEM, to simulate river discharges, the LSM has to be transformed from a grid-based case to a catchmentbased case. Since most of the current LSMs and their inputs are constructed in a grid-based format, the transformation from a grid-based case to a catchment-based case introduces additional preparation work and scale uncertainty during its application. In addition, their routing method is scale dependent. Gong et al. [2009] proposed a large-scale runoff routing method with an aggregated network-response function, which was obtained from the GTOPO30 global elevation data set and had a spatial resolution of 30 arc sec (1 km). To be more efficient in computation, the cell-to-cell method was replaced by source-to-sink method in the routing model. Although the routing results were shown to be scale independent in space, discharge information for any interior locations of a river basin cannot be obtained from this routing method despite of its distributed nature on the runoff simulations. In addition, it is unclear if this method has any capability of being scale independent in time. [5] In this paper, we improve the routing method by Guo et al. [2004] to reduce the routing method s dependence on temporal scales, while the procedures related to the good features and concepts of the multiple directions and the tortuosity coefficient of Guo et al. [2004] are kept the same in this work as those of Guo et al. [2004]. That is, we propose a new routing framework which alleviates the scale impacts for both the spatial and temporal resolutions so that one does not need to calibrate the routing parameters given different spatial and temporal scales. [6] This paper is organized as follows: methodology of the new routing framework is presented in section 2. A brief description of the study areas, data sources and parameter calibrations is provided in section 3. In section 4, the new routing framework is applied to three river basins at six different spatial resolutions and two different temporal resolutions. Results of the new routing framework are discussed and also compared to those using the IUH method and those using the D8-based routing scheme in which the flow path networks are obtained using the D8 method. Sensitivity analysis of impacts of the resolutions of DEM (digital elevation model) data is also presented. Section 5 provides conclusions. 2. Methodology [7] The main idea behind to reduce impacts of different temporal scales on the routing results is to employ a distribution to statistically represent the different overland flow path lengths for each routing grid as opposed to use a mean average overland flow path length as is done in Guo et al. [2004]. In other words, we use a distribution instead of an average quantity to approximate the subgrid variabilities existed in reality for each large modeling grid size. In fact, this idea of employing a distribution has been indirectly shown to be effective based on previous studies. For example, Liang et al. [1996a] have shown that by considering the spatial subgrid variability associated with soil properties using a beta distribution, the VIC model is much less sensitive to the use of different precipitation distributions within the precipitation covered area than other LSMs in which a mean condition instead of a subgrid variable condition of soil properties is considered [Pitman et al., 1990]. Liang et al. [2004] have also shown that the simulation results (e.g., streamflow, evapotranspiration, soil moisture, etc.) of the VIC model are not sensitive to the different spatial scales used to calibrate the VIC model parameters due to its features of considering, in part, subgrid variabilities. Recently, Li et al. [2011] showed that the performance of the Community Land Model 4.0 (CLM4) is more sensitive to the spatial resolutions [e.g., Li et al., 2011, Figure 4] than the CLM4VIC model which is the CLM4 model but with the surface and subsurface runoff parameterizations of the VIC-3L model implemented in which the subgrid spatial variability of soil properties of the VIC-3L is included. In this study, we apply this idea to the flow path lengths in which a histogram is used to approximate the subgrid variability of the flow path lengths. We then test the effectiveness of this idea for the routing process through applications. 2of16

3 [8] Comparing to the method by Guo et al. [2004], the new method presented in this paper has three additional unique features. One is that the new method decides the overland flow path from each pixel s location to its river channel, which is more accurate than the one by Guo et al. [2004] which only considers the path from the four sides of a cell. The other is that our new method here allows multiple directions for a river channel cell as well, which is not adequately considered by Guo et al. [2004] if the flow network becomes complicated. The third one is that our new method employs a distribution to represent the overland flow path lengths for each routing grid as opposed to use a mean average overland flow path length that is performed by Guo et al. [2004] Flow Network Generation Scheme [9] We use, in general, the same flow network generation scheme by Guo et al. [2004], but have the scheme updated by considering more complicated natural flow network situations occurring in large river basins where the flow networks are typically more complicated than the ones the original computer codes considered [Guo et al., 2004]. The scheme allows overland flow and river channel flow to exit each modeling grid from multiple directions simultaneously, and it uses a concept of the tortuosity coefficient. Information of the flow directions, flow network lengths, slope, contributing areas, and the associated hydrologic characteristics is derived based on fine resolution of DEM data. To have this paper self-contained and easy to follow, basic descriptions, where necessary, of the scheme by Guo et al. [2004] and its improvements are all provided here. [10] Inputs to the flow network generation scheme are based on DEM data whose resolution is much finer than that of a LSM. The flow direction based on the high-resolution DEM can be easily obtained by commercially available Geographic Information System (GIS) software (e.g., Arc- GIS). Following the convention used by Guo et al. [2004], we define cells as grids at a specified coarse resolution, and pixels as grids at a high-resolution DEM. Because this scheme considers the channel flow and overland flow networks separately, the scheme consists of two main steps: (1) extracting the channel flow network for cells through which a true river passes and (2) extracting the overland flow network and its connections to the channel flow network for all of the cells. [11] The first main step of the flow network generation part is to generate the channel flow network at a specified coarse resolution to which the LSMs are applied based on a high-resolution DEM. The procedure can be briefly summarized as follows: [12] Step 1a is to derive the true river network based on a high-resolution DEM (e.g., National Atlas of the United States or the GTOPO30 30 arc sec global elevation data set) using commercially available GIS software. [13] Step 1b is to identify all the cells that include the true river pixels as river cells. [14] Step 1c is to identify the pixels where the true river network enters each river cell. [15] Step 1d is that within a river cell, trace each pixel identified in step 1c along the true river network in the downstream direction until the pixel where the true river leaves the river cell. Identify to which cell of its eight neighbors that the flow from the leaving pixel is going. When there are more than one cell in its eight neighbors to which the flow from the leaving pixels are going, this river cell then has multiple directions or multiple river reaches to be connected with its next grids. Each direction of a river cell is assigned with a river reach ID which is used to identify a river reach for routing the overland flow into the river reach and for routing the river flow to its next river reach until it arrives at the outlet of the watershed. [16] Step 1e is to calculate the length and slope of each true river reach included in the category of the river cell based on the high-resolution DEM data. An area-weighted average method was adapted to calculate the length and slope when there are more than one true river channel flowing into the same direction of a grid cell. [17] Step 1f is to repeat steps 1a 1e to obtain the channel flow network for the entire watershed. [18] The second main step of the flow network generation scheme is to generate the overland flow network and its connections to the channel flow network, based on the highresolution DEM, at a coarse resolution to which the LSMs are applied. The process to delineate the overland flow network for all the cells is summarized as follows: [19] Step 2a is to identify the overland flow path of each pixel in the cell from current pixel to its nearest river pixel. [20] Step 2b is to identify the river reach ID to which the nearest river pixel belongs. [21] Step 2c is that pixels that have the same river reach ID are then called to belong to the same overland flow group (or flow portion) within a model grid cell. [22] Step 2d is to calculate the accumulated contributing area and the slope of each portion that have the same river reach ID. The fraction of runoff that leaves this cell into the specific river reach is calculated as the ratio of the accumulated contributing area to the total area of the cell within the watershed. Histograms of the overland flow lengths are obtained and shown in Figure 1. [23] Step 2e is to repeat steps 2a 2d for all the cells within a study river basin. [24] The flow network generation scheme described above (i.e., steps 1a 1f and steps 2a 2e) is implemented in C programming language under Linux operation system. Therefore, it is not only easy to generate the flow network automatically, but also it makes the coupling of our new flow routing framework with a LSM (e.g., VIC) an easy task Representation of Flow Lengths [25] Runoff generated by a LSM is routed to the outlet of a study basin through a combination of an overland flow routing and a channel flow routing, in which different routing methods are available. In our study, the kinematic wave routing method is employed for both the overland flow and channel flow, which is briefly described as follows. [26] The velocity (v, m/s) of the overland flow and channel flow is calculated by the Manning s equation: v ¼ 1 n R2 3 S 1 20 where n is the Manning s coefficient for either the overland flow or the channel flow, R represents the hydraulic radius for the overland flow or the channel flow, and S 0 is the slope of the overland flow or the channel flow. For the overland flow, the Manning s coefficient is determined based on land ð1þ 3of16

4 iteration method, the unknown variable h in equation (4) is estimated. [29] With the calculation of the velocity (v in m/s), the time (t in s) required for the overland flow or channel flow can be obtained by t ¼ L v ð5þ Figure 1. Schematic representation of the distributions of overland flow path lengths for each flow portion. Histograms of the overland flow path lengths for each flow portion are indicated by the black curves, in which the corresponding average flow path lengths (i.e., mean) are also indicated for each case. A flow portion means an area consisting of pixels that flow into the same river reach ID. cover information, while for the channel flow, it is estimated through a model parameter calibration process which is discussed in section 3.2. [27] For the overland flow, R ¼ h w 2h þ w h w w ¼ h ð2þ where h (m) is the depth of the surface runoff in the cell which is obtained from a LSM at each time step and w (m) is the width of the overland flow. [28] For the channel flow, h w R ¼ 2h þ w where h (m) is the depth of the channel and w (m) is the width of the channel. In our case, the channel is assumed to have a rectangular shape. So the discharge in the channel is calculated by Q ¼ A v ¼ A 1 1 n R2 3 S20 ¼ h w 1 2 h w 3S ð4þ n 2h þ w where Q (m 3 ) is the discharge in the channel and A (m 2 )is the cross section area of the channel. Through Newton s ð3þ where L (m) is the length of the overland flow or the channel length. [30] After the travel time of the overland flow and the channel flow is calculated for each time step, the amount of the overland flow (generated at current time step T ) is then routed to the related river reach at the specific time (T + t) and the amount of water in the river reach is routed to the next river reach at the specific time (T + t), respectively, until the routed water arrives at the outlet of the river basin. [31] From equation (5), it can be seen that the magnitudes of the flow lengths (both for the overland flow and the channel flow) are critically important. This is especially true if we want to reduce the impacts of the spatial and temporal resolutions on the routing results, since for different resolutions, the routing length, L, can vary significantly from one resolution to another even if the velocity, v, is similar under different resolutions. For the estimation of the channel flow length, we employ the method of Guo et al. [2004] in which the concept of tortuosity coefficient is used to reduce the impacts of the spatial resolutions on both L and v [Guo et al., 2004]. For the overland flow length, we propose a new approach to estimate it in this study, which is described below. [32] For applications to large river basins that are associated with coarse spatial resolutions of a LSM, the amount of water associated with each time step s runoff may be very large. Routing such a large amount of water to the next river reach using an average overland flow length (i.e., a lumped approach) over a given small time step (e.g., at an hourly time step) would thus cause spiky peaks in the hydrograph time series. This problem is clearly evidenced when hourly or subdaily hydrograph time series are obtained using the scheme of Guo et al. [2004] (called old method hereafter) which uses an average overland flow path, similarly to other routing schemes [e.g., Du et al., 2009; Ducharne et al., 2003; Gong et al., 2009; Goteti et al., 2008; Olivera and Maidment, 1999; Wu et al., 2011]. This is because in reality, such a large amount of runoff generated from a LSM grid cell does not arrive at the channel together at the same specified time estimated by the average overland flow length, rather, it is spread out over time and arrives at the channel at different times. That is, runoff near the channel would arrive at the channel first and the runoff far away from the channel would arrive at the channel at a later time. To solve this spiky problem, we employ the idea, similar to that used in VIC [e.g., Liang et al., 1996a, 2004], of using a distribution to statistically represent the different overland flow path lengths. In this way, we can reduce effectively the impacts of different temporal scales (i.e., subtime variabilities) on the routing results. To this end, we use highresolution DEM data to obtain the statistical distributions (or histograms) of the overland flow path lengths. The main advantage of representing the overland flow path lengths by a statistical distribution versus representing the flow lengths 4of16

5 explicitly is its massive savings on the computer memories and at the same time, it can still adequately carry out the flow routing calculations. The saving is especially huge for large river basin applications. [33] Figure 1 shows a schematic representation of the histograms of the overland flow path lengths for each flow portion of the overland flow that is associated with each LSM grid for the Blue River basin in Oklahoma. Assume a LSM grid size applied to the Blue River basin is at 1 degree (i.e., km 2 ) resolution. Then the basin would be included within three modeling grid cells of the LSM. With the idea that the runoff generated for each cell from the LSM may exit the cell from multiple directions, each model grid cell (i.e., the one degree cell) can then be characterized by several overland flow portions based on their overland flow routing paths, which can be obtained from the fine resolution DEM data (i.e., m 2 DEM data in this case). For example, for the upper left cell in Figure 1, two overland flow portions (represented by two different colors) are identified based on the multidirection flow network generation scheme. Runoff from portion 1 (i.e., dark green) flows into the channel reach of the upper left grid cell (see Figure 1). Runoff from portion 2 (i.e., purple) flows into the channel reach of the lower left grid cell (see Figure 1). [34] Histograms for each flow portion shown in Figure 1 are obtained based on the overland flow routing length information of the individual pixels within each flow portion. The horizontal axis of the histogram represents the relative routing length, which is from 0 to 1. A pixel that is on the channel would have the shortest routing length within a given flow portion and it would have a value of 0, and a pixel with the longest routing length within the flow portion would be 1. Shapes of the histograms for each flow portion are generally different from each other, indicating relatively different physical information associated with the landscape topology. For example, for the histogram of flow portion 1 in Figure 1, a large number of the pixels are associated with large horizontal values (i.e., greater than their corresponding mean values). This shape of the histogram indicates that a large number of pixels within this flow portion are far away from the channel and thus, their flow lengths are relatively large. In contrast, for the histogram of flow portion 3 in Figure 1, many of the pixels are associated with small horizontal values, indicating that a large number of pixels are close to the channel. Thus, their flow lengths are relatively short. [35] In the new flow routing framework presented in this paper, the histogram of each flow portion, instead of the average overland flow length of each flow portion as in [Guo et al., 2004], is used in conjunction with the method of Guo et al. [2004] to represent the flow path network based on which to route the overland flow generated by a LSM. More specifically, information of the histograms of the overland flow path lengths for each portion is employed to determine what percentage of the overland flow would arrive at the river channel at each time step based on the corresponding calculated overland flow velocity. Therefore, the new proposed flow routing method distributes the runoff over a period of time according to the spreads of the histograms, which can significantly reduce the spikiness of the hydrograph time series at the outlet of a river basin when the hydrographs are represented at a subdaily time step. In addition, the new flow routing framework presented in this study updates the method by Guo et al. [2004] by considering more complicated channel network configurations over a river basin. For example, our new method here allows multiple directions for a river channel cell as well, which is not adequately considered by Guo et al. [2004] if the flow network becomes complicated. Moreover, our new method decides the overland flow path from each pixel s location to its river channel, which is more accurate than the one in Guo et al. [2004] which only considers the path from the four sides of a cell. 3. Case Studies 3.1. VIC-3L Land Surface Model [36] In this study, we obtain the runoff from the VIC-3L LSM [Cherkauer and Lettenmaier, 1999; 2003; Liang et al., 1994, 1996a, 1996b, 1999; Liang and Xie, 2001; Liang et al., 2003]. Features of the VIC-3L model include (1) representation of subgrid spatial variabilities of soil properties and precipitation; (2) accounting for both infiltration and saturation excess runoff generation mechanisms by considering subgrid spatial variabilities; (3) two time scale (quick and slow) characterization of the dynamics of runoff generation; (4) representation of the dynamic interactions between surface and groundwater and the impact of such interactions on surface fluxes and soil moisture state [Leung et al., 2011]; (5) simulation of snow and frozen soil processes for cold climate conditions, and (6) explicit characterization of multiple land cover types and a simple yet reasonable representation of ground heat fluxes both for bare and vegetated surfaces. The VIC-3L model has been extensively tested and successfully applied to various basins of different scales with good performance [Nijssen et al., 1997]. The VIC-3L model has also performed well in the various phases of the project for intercomparison of land surface parameterization schemes (PILPS) [Liang et al., 1998]. Furthermore, the VIC-3L model has been applied to a wide range of studies, including soil moisture estimation [Nijssen et al., 2001a], streamflow forecasting [Nijssen et al., 2001b], climate change impact analyses [Leung et al., 1999], and land use land cover change (LUCC) impact analyses [Mao and Cherkauer, 2009] Study Sites, Data, VIC-3L Model, and Parameter Calibration [37] The new routing framework described above is applied to three river basins to test its performance. They are the Blue River basin (1233 km 2 ) and the Illinois River near Watts basin (1231 km 2 ) in Oklahoma, and the Elk River basin (2212 km 2 ) in Missouri (see Figure 2). As can be seen from Figure 2, the river networks for the latter two watersheds are more complicated than that of the Blue River basin. Most of the data used for this study for these three basins are from the Distributed Model Intercomparison Project (DMIP) [Smith et al., 2004], which are provided by the Hydrology Laboratory (HL) of the National Weather Service (NWS) and are available from the DMIP project s website ( DMIP project compiled the various data from different data sources and conducted data quality control. The DEM data are at a resolution of 15 arc sec (approximately 400 m) and are used to generate the needed flow network information for each basin in this study. Vegetation information from the DMIP 5of16

6 Figure 2. A schematic of the location and surface elevation of the Blue River watershed, the Illinois River near Watts watershed, and the Elk River watershed. site is derived based on the NASA NLDAS vegetation data [Eidenshink and Faundeen, 1994] at about 1 km resolution, and the soil information from the DMIP site is extracted from the State Soil Geographic Database (STATSGO) [U.S. Department of Agriculture, Natural Resources Conservation Service, 1992] at about 1 km resolution. Precipitation data used to run VIC-3L are also from the DMIP s site, which are based on the NEXRAD Stage III Precipitation Data product. The other forcing data, including temperature, wind speed, needed to run VIC-3L, are extracted from the database for the conterminous United State [Maurer et al., 2002] at a 1/8 degree resolution. All of these data (vegetation, soil, and forcing) were aggregated or disaggregated to a specific resolution (i.e., one of the six spatial resolutions) using area weighted average method when running the VIC-3L model at the different spatial resolutions. The hourly forcing data are aggregated into daily data for running the VIC-3L at the daily time step. In addition, the hourly observed streamflow data from the U.S. Geological Survey (USGS) for each of the three river basins are aggregated to the daily streamflows as well when testing the new routing framework for its temporal resolution impacts. [38] The six different spatial resolutions at which the VIC- 3L model is run are 1/32, 1/16, 1/8, 1/4, 1/2, and 1 degree, respectively. For each spatial resolution, the VIC-3L model is run at both the hourly and daily time steps to generate the runoff for each of the three study basins. For the daily time step, VIC-3L is run from 7 May 1993 to 31 May 1999, while for the hourly time step, VIC-3L is run from 1 January to 31 December 1996 due to the data availability. The flow networks corresponding to each of the six different spatial resolutions are generated and coupled with our new routing framework. [39] In this study, the Shuffled Complex Evolution (SCE) [Duan et al., 1994] auto-optimization algorithm is applied to estimate six VIC-3L model parameters and two routing model parameters (see Table 1). The ranges listed for each model parameter in using the SCE method are based either on their typical application ranges if no specific information is available or on some physics. For example, the ranges for the river width and Manning s coefficient of the river channels are determined based on the limited measurements and pictures available from the DMIP website, while the ranges of the six VIC-3L model parameters are kept the same for all of the three test basins. [40] To assess the performance and effectiveness of reducing the impacts of spatial and temporal resolutions on the routing results, the new routing framework is compared to two other methods. One of them employs the widely used eight direction method (i.e., D8 method) to generate its flow path network for routing. That is, the main differences between this routing method (referred to as D8-based routing scheme/method hereafter) and our new routing method include (1) how the flow path network is generated and Table 1. A List of the Model Parameters for VIC-3L and the Routing Methods That Are Calibrated Using the SCE Method Category Parameters Meaning VIC-3L b The exponent (b) of the VIC-3L soil moisture capacity curve which describes the spatial subgrid variability of the soil moisture capacity d1 (m) The depth of the upper soil layer d2 (m) The depth of the lower soil layer Dmax The maximum velocity of the base flow Ds The fraction of Dmax at which nonlinear base flow occurs Ws The fraction of maximum soil moisture where nonlinear base flow occurs Routing w (m) The width of the channel used in the new or the D8-based routing methods n The channel s Manning coefficient used in the new or the D8-based routing methods K The storage delay time parameter used in the IUH routing method m The number of reservoirs used in the IUH routing method 6of16

7 (2) how such network information is used for routing, while both use the kinematic wave method to move the water through the flow path networks identified by their respective approaches. The other method used for comparison is the instantaneous unit hydrograph (IUH) method which lumps the impacts of the flow path network together with the mathematical calculations that move the water through the flow path network [Nash, 1957]. Although a routing method based on the unit hydrograph (UH) concept does not track the water movement along its flow path, the UH-based routing method has been widely used to represent the withingrid flow routing [e.g., Naden, 1992; Lohmann et al., 1996] before the runoff reaches the river network or to represent the routed lateral flow over areas between river reaches [e.g., Price, 2009]. If there is only one modeling grid, e.g., for a case of a small watershed or with a large modeling grid size, then it is a special case where the routing is simply represented by the UH method. The UH-based routing method (e.g., IUH method) is selected for comparison because it has, in principle, the least spatial resolution impacts on the routing results. This is due to the lumped nature of the UH-based method in which individual spatial resolutions within a basin are independent of the routing results at the basins outlets. Therefore, results associated with different spatial resolutions from the IUH method can serve as references for measuring the impacts of spatial resolutions on our new routing method and on the D8-based routing scheme as well. [41] In this study, all of the routing parameters associated with each of the three routing methods are calibrated, in combination with the six model parameters of VIC-3L, at the 1/8, 1/4, and 1/2 degree resolutions using the SCE method. The eight calibrated model parameters in each case are then applied to the other five spatial resolutions, at both daily and hourly time steps, respectively, for each routing method. In fact, for VIC-3L the model parameters only need to be calibrated at one resolution (e.g., 1/8 degree) rather than at each of the six different individual resolutions (i.e., 1/32, 1/16, 1/8, 1/4, 1/2, and 1 degree), respectively. This is because the 1/8 degree resolution may be a unique resolution for VIC-3L. Based on a comprehensive study, Liang et al. [2004] show that the VIC-3L model parameters calibrated at the 1/8 degree resolution may have the least overall effects on surface fluxes, soil moisture, streamflow, etc., when the calibrated parameters are applied to other spatial resolutions; that is, it may be a critical resolution determined by the precipitation and soil properties for study regions where the spatial variations of topography and vegetation are not large. In fact, Liang et al. [2004] show that not only does the VIC-3L model calibrated at each spatial resolution lead to similar performance to each other at the different spatial resolutions (e.g., 1/32, 1/16, 1/8, 1/4, and 1/2 degree) in terms of the Nash and Sutcliffe (N-S) coefficient but also the values of the calibrated VIC-3L model parameters are similar to each other at these different spatial resolutions. For the resolution of 1 degree case, although the differences in the N-S value and in the parameter values are larger than those for the other five resolutions (i.e., 1/32, 1/16, 1/8, 1/4, and 1/2 degree), they are still small [Liang et al., 2004]. In this study, we calibrate the eight model parameters (six for VIC- 3L and two for a routing scheme) at three different resolutions (i.e., 1/8, 1/4, and 1/2 degree) to investigate if similar conclusions as those by Liang et al. [2004] are still held. For other LSMs, e.g., those without the consideration of subgrid variabilities, calibration of the model parameters at each spatial resolution may be necessary since the model parameters associated with different resolutions may be quite different. 4. Results and Discussions [42] The VIC-3L land surface model is used to simulate the daily and hourly runoff as input to three different routing schemes which include the new routing framework presented here, the D8-based routing scheme, and the IUH method. The new routing framework firstly generates the flow path network and derives relevant network and topographical information (e.g., flow directions, flow network lengths, slope, contributing areas, tortuosity coefficient) based on a model specified spatial resolution and a fine resolution of DEM data. It then employs the kinematic wave routing method to route the flow simulated by the VIC-3L model to the basin outlet based on the flow path network and the other relevant network and topographical information as described in section 2. For the D8-based routing scheme, the VIC-3L model-simulated runoff is routed to the basin s outlet using the kinematic wave routing method based on the flow path network generated by the D8 method. For the IUH method, the VIC-3L simulated runoff is routed to the basin s outlet in a lumped way based on the UH concept. [43] The Nash and Sutcliffe (N-S) coefficient (E) is employed to evaluate the simulated results of the new routing framework and compare them with the results from the D8-based routing scheme and the IUH method. The N-S E value is expressed as [Nash and Sutcliffe, 1970] E ¼ 1:0 X N X N ðo i P i Þ 2 ð6þ 2 O i O where O i is the observed streamflow and P i is the modelsimulated streamflow at time i, respectively, O is the mean of the observed streamflow, and N is the total number of the flows over a given period of time Results at Daily Time Step [44] The SCE method is applied to calibrate the six VIC- 3L model parameters and also two routing model parameters for each of the three routing methods (see Table 1) at the 1/8 degree resolution for all three river basins, i.e., the Blue River basin, the Illinois River basin near Watts, and the Elk River basin. For the new and the D8-based routing frameworks, the two routing parameters calibrated are the river width and channel Manning s coefficient (see Table 1). For the IUH method, the two parameters calibrated are the storage coefficient K and the number of reservoirs m (see Table 1). Values of the calibrated parameters are listed in Table 2. Then, the eight model parameters calibrated at the 1/8 degree resolution are applied to the other five different spatial resolutions (i.e., 1/32, 1/16, 1/4, 1/2, and 1 degree resolutions), respectively, to obtain the model-simulated streamflows at the three river basins outlets for each of the five spatial resolutions at the daily time step. 7of16

8 Table 2. A List of the Ranges and Values of the Eight Model Parameters Calibrated at 1/8 Degree Resolution for the VIC-3L Model and Each of the Three Routing Methods at the Three River Watersheds Based on the Daily Observed Streamflow Time Series From 7 May 1993 to 31 May 1999 a Blue River Illinois River Near Watts Elk River Parameters Range New D8 IUH New D8 IUH New D8 IUH b Ds Dmax Ws d1 (m) d2 (m) w (m) (for Blue and Illinois); (for Elk) n K m a The DEM data used here are at the 400 m resolution. [45] The N-S E values for the new and D8-based routing frameworks and for the IUH method are shown in Figure 3 for each of the three watersheds. These results clearly show that at the daily time step, the new routing framework is significantly superior to the D8-based one in reducing the impacts of the spatial resolutions on the simulated streamflows in terms of the N-S E values and that the new routing method is compatible to the IUH method in this regard as well (see Figure 3). In contrast, the N-S E values are significantly reduced from the 1/8 degree resolution to the 1 degree resolution using the D8-based routing scheme. For the Blue River, Illinois River near Watts, and Elk River basins, the maximum reductions of the E values (see Table 3a) at the six different resolutions are 15%, 13% and 15%, respectively, with the new routing framework, while they are 97%, 79% and 70%, respectively, with the D8- based routing scheme (see Table 3b). The large impacts of the different coarse spatial resolutions on the routed streamflow results with the D8-based routing scheme are mainly caused by the over simplifications of the D8 method in generating the flow path network and also in making use of such information. For example, the D8 method only allows the runoff to exit each modeling grid from one direction. Also, the flow paths, lengths, slopes and contributing areas of the flow network used for routing are significantly distorted from reality using the D8 method. These problems become more serious with a decrease of the spatial resolution. That is why there is a dramatic reduction in the N-S E value from the 1/8 degree to 1 degree resolution using the D8-based routing scheme. These weaknesses of the D8 method, however, are overcome in our new routing framework by allowing, for example, the runoff to exit each modeling grid from multiple directions simultaneously and by the use of the tortuosity coefficient introduced by Guo et al. [2004]. In fact, results shown in Figure 3 are consistent with those by Guo et al. [2004] for the Blue River basin, Figure 3. Comparison of the N-S E values based on the daily simulated streamflows and the corresponding observations for the new routing framework, D8-based routing scheme, and IUH method at (a) the Blue River, (b) the Illinois River near Watts, and (c) the Elk River basins, respectively. The three methods are all calibrated separately at the 1/8 degree resolution at a daily time step and are then applied to other resolutions (i.e., 1/32, 1/16, 1/4, 1/2 and 1 degree). The daily calibrated model parameters for each routing method at each watershed are shown in Table 2. The daily simulation period for all of the cases is from 7 May 1993 to 31 May The DEM data used here are at the 400 m resolution. Table 3a. The Daily N-S E Values Between the Observed Streamflows and the Model-Simulated Streamflows at Six Different Spatial Resolutions With the New Routing Framework Using the Parameters Calibrated at Either the 1/8 or 1/4 Degree Resolutions a Calibrated Spatial Resolution Resolution River 1/32 1/16 1/8 1/4 1/2 1 1/8 degree Blue River Illinois River near Watts Elk River /4 degree Blue River Illinois River near Watts Elk River a The DEM data used here are at the 400 m resolution. 8of16

9 Table 3b. The Daily N-S E Values Between the Observed Streamflows and the Model-Simulated Streamflows At Six Different Spatial Resolutions With the D8-Based Routing Scheme Using the Parameters Calibrated at Either the 1/8 or 1/4 Degree Resolutions a Calibrated Spatial Resolution Resolution River 1/32 1/16 1/8 1/4 1/2 1 1/8 degree Blue River Illinois River near Watts Elk River /4 degree Blue River Illinois River near Watts Elk River a The DEM data used here are at the 400 m resolution. confirming the effective reduction of the sensitivity of the routing method to the different coarse spatial resolutions at different watersheds. [46] Comparing to the IUH method, the new method shows comparable sensitivities to the different spatial resolutions as those with the IUH method for all of the three watersheds. The maximum reductions of the N-S E values with the IUH method at the six different resolutions are 25%, 9% and 5%, respectively, for the Blue River, the Illinois River near Watts, and the Elk River basins (see Table 3c). However, the IUH method is a method that has, in principle, the least sensitivity to the spatial resolutions on its routing results. This is because the IUH method does not consider any influences of the spatial distributions of the precipitation and runoff within a watershed, rather it integratively considers their impacts in a lumped sense on the streamflow at the outlet of the watershed. Therefore, the IUH s results would be independent of the spatial distribution of the runoff at different spatial resolutions as long as (1) the total runoff of the entire watershed (i.e., the sum of the runoff of the individual modeling grids within a watershed) is similar to each other at the different spatial resolutions and (2) the IUH routing parameters are adequately calibrated at one spatial resolution. As shown in Figures 4a 4c, the total runoff time series for each entire watershed does not change significantly among the six different spatial resolutions. This is consistent with the aggregated daily precipitation time series Figure 4. Comparison of the N-S E value between the aggregated simulated daily runoff results at 1/8 degree and those at the other five spatial resolutions for each of the three routing methods. All of the aggregated simulated runoff (including both surface and subsurface runoff) values are directly obtained from the VIC-3L model outputs without any routing. Thus, there is one total runoff value for an entire watershed at each time step. (a) The N-S E values for Blue River (b) The N-S E values for Illinois River near Watts. (c) The N-S E values for Elk River. (d) The N-S E value between the aggregated daily precipitation data of an entire watershed (i.e., one value per watershed at each time step) at 1/8 degree and those at the other five spatial resolutions for each of the three watersheds. for each of the three watersheds as shown in Figure 4d, which clearly indicates that the time series of the total amount of precipitation at the watershed scale vary insignificantly across the six different spatial scales for all three watersheds. Figure 5 shows the relationship of the average Table 3c. The Daily N-S E Values Between the Observed Streamflows and the Model-Simulated Streamflows at Six Different Spatial Resolutions With the IUH Method Using the Parameters Calibrated at Either the 1/8 or 1/4 Degree Resolutions a Calibrated Spatial Resolution Resolution River 1/32 1/16 1/8 1/4 1/2 1 1/8 degree Blue River Illinois River near Watts Elk River /4 degree Blue River Illinois River near Watts Elk River a The DEM data used here is at the 400 m resolution. Figure 5. Comparison of the average correlation coefficients between the daily precipitation at 1/32 degree and five other different spatial resolutions for the three watersheds. 9of16

10 Table 4. Same as Table 2 but With Model Parameters Calibrated at the 1/4 Degree Resolution a Parameters Range New D8 IUH New D8 IUH New D8 IUH b Ds Dmax Ws d1 (m) d2 (m) w (m) (for Blue and Illinois); (for Elk) n K m a The DEM data used here are at the 400 m resolution. Blue River Illinois River Near Watts Elk River correlation coefficient (r) for daily precipitation at the six spatial resolutions which is obtained based on the correlation coefficient (r) calculated as follows: N XN y 1 i y 2 i XN r ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0! 1 0 2! 1 2 u t@ N XN y 1 i XN N XN y 2 i XN A y 1 i y 1 i XN y 2 i y 2 i where y i 1 is taken as the ith grid daily precipitation at the 1/32 degree resolution, y i 2 is taken as the ith grid daily precipitation based on the other five coarser spatial resolutions, and N is the total number of grids at the 1/32 degree resolution. Values at the coarser spatial resolutions are disaggregated to the finer resolution in employing the above equation. The overall average correlation coefficient (r) is then calculated as an average of each r from equation (7) over the total number of rainy days between 7 May 1993 to 31 May If r is close to 1, it implies that on average the spatial difference of the precipitation at different spatial resolutions is close to each other. If r is close to 0, it implies that, on average, the spatial difference at the different spatial resolutions is significantly different from each other. Figure 5 clearly indicates that the spatial distributions of the precipitation at the 1/16, 1/8, 1/4, 1/2, and 1 degree resolutions are significantly different from the spatial distribution at the 1/32 degree resolution for all three watersheds, even though the total amount at the watershed scale is similar to each other (see Figure 4d). In this study, the two routing parameters of the IUH method are calibrated in conjunction with the six VIC-3L model parameters at the 1/8 degree resolution (see Table 2). Therefore, the routed streamflows with the IUH method should be insensitive to the different spatial resolutions since the two conditions required above are satisfied. Indeed, our results (see blue lines in Figure 3) do show that the routed streamflows with the IUH method are not affected, as expected, by the different spatial resolutions, which is the strength of the IUH method. However, the IUH method cannot provide any routed flow information at any interior locations of a watershed. In addition, the value of the calibrated routing parameter for the number of reservoirs in the IUH is 1, i.e., m = 1, for all three watersheds in this study, implying that each of the three watersheds only needs ð7þ one reservoir behaving in an exponential decay fashion to route the spatially distributed runoff to the outlet of each watershed in order to have a good match to the observed streamflows. This seems unrealistic. Comparing to the IUH method, our new routing framework does demonstrate its advantages of being able to provide flow information at interior locations of a watershed and at the same time, being able to significantly reduce the impacts of different spatial resolutions on the routed streamflow like the IUH method. [47] We have also calibrated the eight model parameters (six for VIC-3L and two for routing) at the 1/4, and 1/2 degree resolutions, respectively, using the SCE method and applied the calibrated parameter values to the other five resolutions in a similar way as for the case of calibrating the model parameters at the 1/8 degree resolution. Results obtained for the 1/4 degree resolution case are similar, as expected, to those for the 1/8 degree case (see Table 4 and Figure 6). Results (figure not shown) for the 1/2 degree resolution case are also similar to those for the 1/8 degree (i.e., Figure 3) and the 1/4 degree (i.e., Figure 6) cases except that the N-S E values are much lower for the D8-based routing scheme in this case unless very unreasonable parameter value ranges are specified when the SCE method is applied. In addition, our results also show that the calibrated model parameters (e.g., Tables 2 and 4, table for the 1/2 degree case not shown) are similar to each other for the VIC-3L model and the new routing scheme for the three watersheds. Such results are consistent with the findings of Liang et al. [2004] although two of the watersheds and the routing schemes are different. In this study, the routing scheme is our new routing framework while in Liang et al. [2004], it was a one parameter routing scheme. [48] In summary, the comparison results here clearly show that our new routing framework can significantly reduce the impacts of different spatial resolutions on routing, and it is superior to both the D8-based routing scheme and the IUH method. These characteristics of the new routing framework are useful for large-scale land surface model applications where the accuracy of routing can be severely degraded by the use of a coarse spatial resolution unless the routing parameters are calibrated at each spatial resolution Results at Hourly Time Step [49] The new routing framework is applied to route the hourly VIC-3L runoff at an hourly time step as well for the same three watersheds (i.e., the Blue River basin, the Illinois River near Watts basin, and the Elk River basin) to 10 of 16