A new multiscale routing framework and its ... - Wiley Online Library

WATER RESOURCES RESEARCH, VOL. 48, W08528, doi:10.1029/2011WR011337, 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 Yang1 Received 29 August 2011; revised 18 April 2012; accepted 24 June 2012; published 31 August 2012.

[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, W08528, doi:10.1029/2011WR011337.

1. 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. 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. 2

Corresponding author: X. Liang, Department of Civil and Environmental Engineering, University of Pittsburgh, 941 Benedum Hall, 3700 O’Hara St., Pittsburgh, PA 15261, USA. ([email protected]) ©2012. American Geophysical Union. All Rights Reserved. 0043-1397/12/2011WR011337

[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 0.1 0.1 (10 10 km2) to 5 5 (500 500 km2). 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]

W08528

1 of 16

W08528

WEN ET AL.: A NEW MULTISCALE ROUTING FRAMEWORK AND ITS EVALUATION

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

W08528

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.

2 of 16

W08528


[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]. 2.1. 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., ArcGIS). 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.

W08528

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. 2.2. 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: v¼

1 2 12 R3 S0 n

ð1Þ

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 S0 is the slope of the overland flow or the channel flow. For the overland flow, the Manning’s coefficient is determined based on land

3 of 16

W08528


W08528

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 t¼

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, R¼

hw hw ≈ ¼h 2h þ w w

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, R¼

h ′ w′ 2h′ þ w′

ð3Þ

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 2 1 2 1 1 h′ w′ 3 12 Q ¼ A v ¼ A R3 S02 ¼ h′ w′ S0 n n 2h′ þ w′

ð4Þ

where Q (m3) is the discharge in the channel and A (m2) is the cross section area of the channel. Through Newton’s

L v

ð5Þ

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

4 of 16

W08528


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., 100 100 km2) 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., 400 400 m2 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

W08528

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]. 3.2. 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 km2) and the Illinois River near Watts basin (1231 km2) in Oklahoma, and the Elk River basin (2212 km2) 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 (http://www.weather.gov/oh/hrl/dmip/). 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

5 of 16

W08528


W08528

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 VIC3L 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 VIC-3L

Routing

Parameters b d1 (m) d2 (m) Dmax Ds Ws w′ (m) n K m

Meaning The exponent (b) of the VIC-3L soil moisture capacity curve which describes the spatial subgrid variability of the soil moisture capacity The depth of the upper soil layer The depth of the lower soil layer The maximum velocity of the base flow The fraction of Dmax at which nonlinear base flow occurs The fraction of maximum soil moisture where nonlinear base flow occurs The width of the channel used in the new or the D8-based routing methods The channel’s Manning coefficient used in the new or the D8-based routing methods The storage delay time parameter used in the IUH routing method The number of reservoirs used in the IUH routing method

6 of 16

W08528


(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 VIC3L 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.

W08528

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] N X

E ¼ 1:0

ðOi Pi Þ2

i¼1 N X

Oi O

2

ð6Þ

i¼1

where Oi is the observed streamflow and Pi 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. 4.1. Results at Daily Time Step [44] The SCE method is applied to calibrate the six VIC3L 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.

7 of 16

W08528


W08528

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 1999a 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)

0.0001–0.4 0.0001–1 1–30 0.0001–1 0.1–3 0.3–4.5 20–45 (for Blue and Illinois); 20–60 (for Elk) 0.02–0.03 1–10 1–10

0.18 0.071 1.14 0.96 0.14 0.46 42.46

0.19 0.003 1.02 0.98 0.19 0.45 20.19

0.087 0.001 1.49 0.97 0.25 0.60

0.39 0.0003 21.97 0.20 0.44 2.53 43.99

0.39 0.0001 23.13 0.19 0.48 2.83 25.28

0.22 0.001 29.03 0.21 0.39 1.99

0.32 0.68 26.53 0.0066 0.65 4.48 59.44

0.34 0.84 15.74 0.38 0.65 4.49 27.83

0.11 0.93 11.16 0.53 0.37 1.72

0.029

0.02

0.028

0.029

0.029

0.024

n K m

2.56 1

2.79 1

3.22 1

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

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 1999. The DEM data used here are at the 400 m resolution.

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 D8based 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,

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 Resolutionsa Calibrated Resolution

Spatial Resolution River

1/32 1/16 1/8

1/8 degree Blue River 0.61 Illinois River near Watts 0.60 Elk River 0.46 1/4 degree Blue River 0.62 Illinois River near Watts 0.55 Elk River 0.46 a

8 of 16

0.62 0.59 0.49 0.62 0.57 0.48

0.62 0.59 0.49 0.62 0.59 0.49


1/4

1/2

1

0.59 0.59 0.49 0.60 0.60 0.49

0.56 0.58 0.47 0.56 0.58 0.48

0.53 0.51 0.42 0.51 0.51 0.43

W08528


W08528

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 Resolutionsa Calibrated Resolution 1/8 degree

1/4 degree


1/32

1/16

1/8

1/4

1/2

1

Blue River Illinois River near Watts Elk River Blue River Illinois River near Watts Elk River

0.60 0.58

0.57 0.56

0.60 0.57

0.49 0.38

0.12 0.22

0.02 0.12

0.48 0.57 0.58

0.48 0.54 0.56

0.50 0.59 0.56

0.40 0.52 0.41

0.25 0.13 0.24

0.15 0.01 0.13

0.46

0.46

0.47

0.43

0.27

0.16

a


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 Resolutionsa Calibrated Resolution 1/8 degree

1/4 degree

a


1/32

1/16

1/8

1/4

1/2

1

Blue River Illinois River near Watts Elk River Blue River Illinois River near Watts Elk River

0.59 0.58

0.59 0.58

0.59 0.58

0.59 0.58

0.54 0.57

0.44 0.52

0.38 0.56 0.58

0.40 0.59 0.58

0.44 0.59 0.58

0.44 0.59 0.58

0.43 0.54 0.57

0.41 0.44 0.52

0.39

0.41

0.44

0.44

0.43

0.41

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.

9 of 16


W08528

W08528

Table 4. Same as Table 2 but With Model Parameters Calibrated at the 1/4 Degree Resolutiona Blue River


Elk River

Parameters

Range

New

D8

IUH

New

D8

IUH

New

D8

IUH



0.19 0.002 1.00 0.98 0.17 0.47 24.12

0.07 0.10 1.00 0.96 0.14 0.51 20.08

0.09 0.0001 1.50 0.97 0.25 0.59

0.40 0.0002 21.09 0.19 0.44 2.44 43.76

0.40 0.0001 13.80 0.18 0.40 2.02 20.07

0.23 0.0001 29.99 0.20 0.40 2.03

0.25 0.82 25.38 0.01 0.64 4.44 59.87

0.40 0.76 21.25 0.50 0.52 4.50 20.44

0.11 0.40 17.73 0.38 0.36 1.62

0.028

0.02

0.029

0.02

0.03

0.021

n K m

2.55 1

2.81 1

3.24 1

a


correlation coefficient (r) for daily precipitation at the six spatial resolutions which is obtained based on the correlation coefficient (r) calculated as follows: N

N X

y1i y2i

N X

y1i

N X

y2i

i¼1 i¼1 i¼1 ffi r ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u0 !2 1 0 !2 1 u N N N N X X X X u@ y1i y1i A @N y2i y2i A t N i¼1

i¼1

i¼1

i¼1

ð7Þ

where y1i is taken as the ith grid daily precipitation at the 1/32 degree resolution, y2i 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 1999. 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

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. 4.2. 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

W08528


W08528

Table 6. Comparison of the Hourly and Daily N-S E Values Between the Observed and the Model-Simulated Streamflows for the Old [Guo et al., 2004] and New Routing Methods Over the Three River Basins New Routing Method

Old Routing Method River

Hourlya

Daily 1b Daily 2c

Blue River Illinois River near Watts Elk River

2.05 5.50

0.34 0.48

16.68

6.04

Hourlyd

Hourlye

Dailyf

0.47 0.59

1.15 2.73

0.60 0.56

0.61 0.67

0.52

9.61

0.68

0.74

a

Figure 6. Same as Figure 3 but for the case in which the model parameters are all calibrated separately at the 1/4 degree resolution at a daily time step and are then applied to other resolutions (i.e., 1/32, 1/16, 1/8, 1/2 and 1 degree). The daily calibrated model parameters for each routing method at each watershed are shown in Table 4.

investigate impacts of the temporal resolutions on the routed flows. Again, six VIC-3L model parameters and two routing parameters are calibrated using the SCE method for all three watersheds based on the hourly observed streamflow data from 1 January 1996 to 31 December 1996. Since it is computationally expensive to calibrate the eight model parameters at the hourly time step, we only use a short period of time in the calibration process. Values of the eight calibrated parameters conducted at the 1/8 degree resolution are listed in Table 5 for the VIC-3L model and each of the three routing methods associated with the three watersheds. [50] When applying the routing method of Guo et al. [2004] (i.e., the old method) to the three test basins at an hourly time step, the hydrographs at the outlets become very spiky even with the calibrated model parameters. In fact, large negative N-S E values were obtained through the SCE calibration process when the Guo et al. [2004] method was

N-S E values are calculated based on the hourly time series obtained by applying the eight model parameters calibrated at the daily time step with the old routing method. b N-S E values are calculated by aggregating the corresponding hourly time series of column 2. c N-S E values are calculated based on the daily time series with which the eight model parameters are calibrated with the old routing method. d N-S E values are calculated based on the hourly time series obtained by applying the eight model parameters calibrated at the hourly time step with the old routing method. e N-S E values are calculated based on the hourly time series with which the eight model parameters are calibrated with the new routing method. f N-S E values are calculated by aggregating the corresponding hourly time series.

applied at an hourly time step due to its corresponding very spiky hydrographs. Therefore, the eight model parameters were calibrated at the daily time step with the Guo et al. [2004] method, whose N-S E values are shown in column 4 in Table 6, and were applied to the hourly simulations to obtain the hourly routed streamflow time series (see Figure 7), whose N-S E values are shown in column 2 in Table 6. These spiky hydrographs are mainly caused by the use of an averaged overland flow length for each overland flow portion when route the runoff. That is, when such an average flow path length is employed, a large amount of runoff generated by a LSM would get into the next river reach within a short period of time (i.e., a short time step) at the same time and, thus, add a large amount of water to the river flow. Such a large amount added would, therefore, cause a large spike in a hydrograph. However, such an impact could be significantly reduced, as expected, if the time step becomes large. As shown in Figure 8, much less spiky results are obtained at the hourly time step with our

Table 5. A List of the Ranges and Values of the Eight Calibrated Model Parameters for the VIC-3L Model and Each of the Three Routing Methods At The Three River Watersheds Based on the Hourly Time Step From 1 January 1996 to 31 December 1996a Blue River


Elk River

Parameters

Range

New

D8

IUH

New

D8

IUH

New

D8

IUH



0.005 0.003 1.00 0.98 0.21 1.35 28.69

0.0002 0.001 2.21 0.54 0.11 1.83 43.93

0.0009 0.001 1.00 0.9 0.34 1.40

0.082 0.004 1.01 0.98 0.15 0.30 28.68

0.39 0.24 11.02 0.64 0.23 1.67 32.94

0.07 0.24 1.28 0.88 0.23 0.31

0.0001 0.077 3.14 0.94 0.22 0.41 59.03

0.02 0.002 1.72 0.41 0.17 0.79 20.91

0.018 0.004 1.45 0.32 0.24 0.68

0.029

0.03

0.023

0.028

0.03

0.03

n K m

16.9 2

a


11 of 16

15.49 2

16.7 3

W08528


W08528

Figure 7. Comparison of the hourly streamflow time series between the old routing method [i.e., Guo et al., 2004] and the observations at (a) the Blue River, (b) the Illinois River near Watts, and (c) the Elk River basins, respectively, based on the eight model parameters calibrated at the daily time step at the 1/8 degree resolution for the old routing method. In the old routing method, an average routing length of each portion [i.e., Guo et al., 2004] is used. The DEM data used here are at the 400 m resolution.

new routing method in which a histogram (i.e., statistical distribution), rather than an average overland flow length, is used to represent the highly heterogeneous overland flow lengths within each portion. The reason for obtaining much less spiky hydrographs in Figure 8 as opposed to those in Figure 7 is that the amount of runoff generated at the current time step is routed to the next routing unit (i.e., next river reach) according to the distributions of the overland flow length histograms as illustrated in Figure 1. Figure 9 shows the daily discharge results that are aggregated directly from the hourly simulations using the old and new methods, respectively. The relatively better performance of the old method at the daily time step than that at the hourly time step is due to the calibration of the eight model parameters at the daily time step. But as can be seen, the daily discharges aggregated directly from the hourly simulations with the new method have lower peaks than those with the old method as expected. Moreover, the different temporal resolutions (i.e., hourly versus daily) clearly have much less impacts on the routed runoff obtained from the new routing method, whose N-S E values are shown in Table 6, than that from the old method (see Figures 7–9). Figure 10 shows the comparisons of the N-S E values based on the hourly simulated streamflows and the corresponding observations for the new routing method, D8-based routing scheme, and IUH method, respectively, at the three watersheds. The maximum reductions of the N-S E values using the new method at the six different resolutions are 47%, 15% and 8%, respectively,

for the Blue River, the Illinois River near Watts, and the Elk River basins. The corresponding reductions for the Blue River, the Illinois River near Watts, and the Elk River basins are 47%, 3%, and 10% with the IUH method and are 87%, 87%, and 50% with the D8-based routing scheme, respectively. Figure 11, similar to Figure 4 but for the hourly case, shows that the total amount of the hourly discharge (see Figures 11a–11c) and the total amount of the hourly precipitation (see Figure 11d) at the watershed scale are similar to each other except for the 1 degree resolution case which shows some difference. Figure 12, similar to Figure 5 but for the hourly precipitation case, shows that the spatial distributions of the hourly precipitation at the 1/16, 1/8, 1/4, 1/2, and 1 degree resolutions are also significantly different from the hourly precipitation spatial distribution at the 1/32 degree resolution for all three watersheds. From Figures 10–12, we can see clearly that at the hourly time step the impacts of the different spatial scales on the routed streamflows with the new routing method are much smaller, similar to the daily time step case (i.e., Figures 3–5), than those with the D8based routing scheme. Also similar to the daily time step case (i.e., Figure 3), the impacts of the spatial scales with the new routing method at the hourly time step are similar to those with the IUH method as well. This feature of the new method in reducing the impacts of both of the different temporal scales (i.e., hourly and daily time scales) and spatial scales on the routed hydrographs using the same calibrated model parameters (i.e., at the hourly time step associated with the

12 of 16

W08528


Figure 8. Comparison of the hourly streamflow time series between the new routing method and the observations at (a) the Blue River, (b) the Illinois River near Watts, and (c) the Elk River basins, respectively, based on the eight model parameters calibrated at the 1/8 degree resolution. In the new routing method, a histogram of the overland flow path lengths for each portion is used. The DEM data used here are at the 400 m resolution. Note the different vertical scale from that in Figure 7.

Figure 9. Comparison of the daily streamflow time series among the new routing method, the old routing method [i.e., Guo et al., 2004], and the observations at (a) the Blue River, (b) the Illinois River near Watts, and (c) the Elk River basins, respectively, based on the eight model parameters calibrated at the 1/8 degree resolution at the hourly time step. The daily time series of the simulated flows are aggregated from the hourly simulated flows for the new routing method, the old routing method, and observations. The DEM data used here are at the 400 m resolution. 13 of 16

W08528

W08528


Figure 10. Comparison of the N-S E values based on the hourly simulated streamflows and the corresponding observations for the new routing framework, D8-based routing scheme, and IUH method at (a) Blue River, (b) Illinois River near Watts, and (c) Elk River, respectively. The three methods are all calibrated separately at the 1/8 degree resolution at an hourly time step and are then applied to other resolutions (i.e., 1/32, 1/16, 1/4, 1/2 and 1 degree). The hourly calibrated model parameters for each routing method at each watershed are shown in Table 5. The hourly simulation period for all of the cases is from 1 January 1996 to 31 December 1996. The DEM data used here are at the 400 m resolution.

1/8 degree resolution in this case) makes this new approach suitable and attractive for large-scale land surface model simulations in which multiple temporal and spatial scales are often needed for different applications. In other words, significant amount of work can be reduced in employing our new routing framework with which one does not need to calibrate his/her land surface model and routing model parameters at different temporal and spatial scales but rather just to calibrate the model parameters at one spatial and one temporal scale, and yet one is still able to obtain reasonable results across different temporal and spatial scales. 4.3. Sensitivity Analysis of DEM Resolution [51] A sensitivity analysis is conducted to investigate impacts of DEM resolutions on the routing parameters and the routing results. Two types of experiments are carried out: (1) applying the same eight model parameters calibrated based on the 400 m resolution of DEM data with the VIC-3L model resolution of 1/8 degree, as listed in Table 2, to the cases of using the 30 m and 100 m resolutions of the DEM data, respectively; and (2) calibrating the eight model parameters (i.e., six VIC-3L parameters and two routing parameters) based on the 30 m and 100 m DEM data, respectively, and the VIC-3L model resolution of 1/8 degree. Sensitivity of the DEM data resolutions on the routing results is listed in Table 7 in terms of the N-S E values. Table 8 lists all the parameters calibrated at each of the DEM data resolution. Comparing Table 7 with Table 3a and Table 8 with Table 2, one can clearly see that both the model

W08528

Figure 11. Comparison of the N-S E value between the aggregated simulated hourly 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 hourly 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.

parameters and the N-S E values are not sensitive to the three different DEM data resolutions (i.e., 30 m, 100 m, and 400 m) investigated. This is because different resolutions of the DEM data do not affect the identifications of the multiple

Figure 12. Comparison of the average correlation coefficients between the hourly precipitation at 1/32 degree and five other different spatial resolutions for the three watersheds.

14 of 16


W08528

Table 7. Sensitivity Results for the Three River Basins at the Daily Time Stepa Blue River


W08528

by the LSM model as discussed in sections 1–3. Therefore, only one set of routing parameters needs to be determined.

5. Conclusions

Elk River

DEM Resolution (m)

N-S E Value 1

N-S E Value 2

N-S E Value 1

N-S E Value 2

N-S E Value 1

N-S E Value 2

400 100 30

0.625 0.619 0.615

0.625 0.619 0.615

0.586 0.571 0.561

0.586 0.588 0.587

0.491 0.485 0.482

0.491 0.488 0.488

a

For each river basin, different DEM resolutions are used for the new routing framework. The model parameters are calibrated at the 1/8 degree resolution. Values 1 are calculated using the same parameters (calibrated at 400 m DEM resolution, see Table 2) to each DEM resolution. Values 2 are calculated using parameters calibrated at each DEM resolution (see Table 8).

flow directions, and the estimations of the contributing areas, slopes, flow network lengths, histograms of the overland flow path lengths, and a few other associated hydrologic characteristics in a significant way if the DEM data is fine enough. These sensitivity results show that not only are the routing parameters of our new routing scheme insensitive to the different spatial resolutions used by the LSMs (e.g., VIC-3L), but also they are insensitive to the different resolutions of the DEM data used as long as the DEM data is fine enough, e.g., at 400 m resolution given by the DMIP project in this case. [52] It is important to point out that in principle, the finer the DEM data, the better it would be, in general, for a routing scheme. Although our sensitivity study here shows that our new routing scheme is not sensitive to the resolution of the DEM data as long as it is fine enough, we recommend using high-resolution DEM data where appropriate and available. For example, use higher resolution DEM data for a hilly watershed than that for a flatter watershed. The use of highresolution DEM data does not add much more processing time to our routing framework since such a data processing task only needs to be conducted once to extract certain information. Then, our routing framework can be applied to any spatial resolutions used by a LSM to determine its routing parameters easily. The routing parameters thus determined are not sensitive to the spatial resolutions used

[53] This paper presents a new multiscale routing framework to transport model-simulated runoff to the outlet of a river basin for hydrological and/or land surface models. This new routing framework is featured with multiscale (both in space and time) characteristics by using multidirections, tortuosity coefficients, and histograms for overland flow path lengths. The strengths of our new routing framework have been demonstrated through its applications to the Blue River basin, the Illinois River near Watts basin, and the Elk River basin at six different spatial resolutions and two temporal resolutions. Our results show that the new routing framework is significantly less affected by both the spatial and temporal resolutions than the typical D8-based routing scheme. Comparing the streamflow results at the basins’ outlets to those obtained from the instantaneous unit hydrograph (IUH) routing method which is, in principle, has the least spatial resolution impacts on the routing results, the new routing framework provides almost the same results as those by the IUH method regarding the impacts of spatial resolutions. However, the new routing framework has an advantage over the IUH method of being able to provide the routing information along the channels and within the interior locations of a basin. The interior routing information being able to be provided by this new routing framework, as opposed to the IUH method, is particularly useful when applying the routing method to a fate and transport model. The new routing framework also reduces the impacts of different temporal resolutions on the routing results. For example, the problem of spiky hydrographs caused by a typical routing method, due to the impacts of different temporal resolutions, can be significantly reduced with our new routing framework. The sensitivity analysis (e.g., Tables 7 and 8) also shows that our new routing framework is not sensitive to the resolutions of the DEM data (e.g., 30 m, 100 m, and 400 m) used. These good features and characteristics of our new multiscale routing framework make it particularly suitable and attractive for large-scale land surface model applications used in conjunction with climate studies where the accuracy of the flow routing results can be significantly affected by the different spatial and temporal resolutions.

Table 8. A List of Values of the Eight Model Parameters (i.e., Six for the VIC-3L Parameters and Two for the New Flow Routing Parameters) Calibrated at the 1/8 Degree Resolution for the VIC-3L Model at the Three Watersheds Based on the Daily Observed Streamflow Time Series From 7 May 1993 to 31 May 1999a Blue River

Illinois River near Watts

Elk River

Parameters

Range

100 m

30 m

100 m

30 m

100 m

30 m


0.0001–0.4 0.0001–1 1–30 0.0001–1 0.1–3 0.3–4.5 20–45 (for Blue and Illinois); 20–60 (for Elk) 0.02–0.03

0.16 0.0005 1.03 0.97 0.11 0.47 41.70

0.16 0.012 1.02 0.97 0.13 0.49 37.45

0.40 0.0003 28.64 0.20 0.51 3.11 44.64

0.40 0.0003 29.20 0.20 0.51 3.09 44.67

0.28 0.90 27.76 0.0046 0.64 4.46 59.77

0.27 0.82 27.49 0.0051 0.65 4.50 59.94

0.021

0.029

0.030

0.030

0.030

0.030

n a

The DEM data used here are at the 30 m and 100 m resolutions, respectively, as indicated for 30 m and 100 m.

15 of 16

W08528


[54] Acknowledgments. The authors are thankful to the anonymous reviewers for their valuable suggestions which helped us improve the presentation of the materials. This work was partially supported by the NOAA grant of NA06DAR4310130 to the University of Pittsburgh. Partial support to the first and third authors from the China Scholarship Council, the Ministry of Science and Technology of China (grant 2012BAB02B00), the Ministry of Water Resources of China (grant 200901022-01), and the Fundamental Research Funds for the Central Universities of China is also appreciated.

References Arora, V., F. Seglenieks, N. Kouwen, and E. Soulis (2001), Scaling aspects of river flow routing, Hydrol. Process., 15(3), 461–477, doi:10.1002/ hyp.161. Cherkauer, K. A., and D. P. Lettenmaier (1999), Hydrologic effects of frozen soils in the upper Mississippi River basin, J. Geophys. Res., 104(D16), 19,599–19,610, doi:10.1029/1999JD900337. Cherkauer, K. A., and D. P. Lettenmaier (2003), Simulation of spatial variability in snow and frozen soil, J. Geophys. Res., 108(D22), 8858, doi:10.1029/2003JD003575. Du, J. K., H. Xie, Y. J. Hu, Y. P. Xu, and C. Y. Xu (2009), Development and testing of a new storm runoff routing approach based on time variant spatially distributed travel time method, J. Hydrol., 369(1–2), 44–54, doi:10.1016/j.jhydrol.2009.02.033. Duan, Q. Y., S. Sorooshian, and V. K. Gupta (1994), Optimal use of the SCE-UA global optimization method for calibrating watershed models, J. Hydrol., 158(3–4), 265–284, doi:10.1016/0022-1694(94)90057-4. Ducharne, A., C. Golaz, E. Leblois, K. Laval, J. Polcher, E. Ledoux, and G. de Marsily (2003), Development of a high resolution runoff routing model, calibration and application to assess runoff from the LMD GCM, J. Hydrol., 280(1–4), 207–228, doi:10.1016/S0022-1694(03)00230-0. Eidenshink, J. C., and J. L. Faundeen (1994), The 1 km AVHRR global land data set: First stages in implementation, Int. J. Remote Sens., 15(17), 3443–3462, doi:10.1080/01431169408954339. Gong, L., E. Widen-Nilsson, S. Halldin, and C. Y. Xu (2009), Large-scale runoff routing with an aggregated network-response function, J. Hydrol., 368(1–4), 237–250, doi:10.1016/j.jhydrol.2009.02.007. Goteti, G., J. S. Famiglietti, and K. Asante (2008), A catchment-based hydrologic and routing modeling system with explicit river channels, J. Geophys. Res., 113, D14116, doi:10.1029/2007JD009691. Graham, S. T., J. S. Famiglietti, and D. R. Maidment (1999), Five-minute, 1/2 degrees, and 1 degrees data sets of continental watersheds and river networks for use in regional and global hydrologic and climate system modeling studies, Water Resour. Res., 35(2), 583–587, doi:10.1029/ 1998WR900068. Guo, J. (2006), Impacts of physical processes across scales on water budgets in hydrological modeling, PhD thesis, Univ. of Calif., Berkeley. Guo, J., X. Liang, and L. R. Leung (2004), A new multiscale flow network generation scheme for land surface models, Geophys. Res. Lett., 31, L23502, doi:10.1029/2004GL021381. Koren, V., S. Reed, M. Smith, Z. Zhang, and D. J. Seo (2004), Hydrology Laboratory Research Modeling System (HL-RMS) of the US National Weather Service, J. Hydrol., 291(3–4), 297–318, doi:10.1016/j.jhydrol. 2003.12.039. Leung, L. R., A. F. Hamlet, D. P. Lettenmaier, and A. Kumar (1999), Simulations of the ENSO hydroclimate signals in the Pacific Northwest Columbia River basin, B. Am. Meteorol. Soc., 80(11), 2313–2329. Leung, L. R., M. Y. Huang, Y. Qian, and X. Liang (2011), Climate-soilvegetation control on groundwater table dynamics and its feedbacks in a climate model, Clim. Dyn., 36(1–2), 57–81, doi:10.1007/s00382-0100746-x. Li, H., M. Huang, M. S. Wigmosta, Y. Ke, A. M. Coleman, F. W. Leung, A. Wang, and D. M. Ricciuto (2011), Evaluating runoff simulations from the Community Land Model 4.0 using observations from flux towers and a mountainous watershed, J. Geophys. Res., 116, D24120, doi:10.1029/ 2011JD016276. Liang, X., and Z. H. Xie (2001), A new surface runoff parameterization with subgrid-scale soil heterogeneity for land surface models, Adv. Water Resour., 24(9–10), 1173–1193, doi:10.1016/S0309-1708(01)00032-X. Liang, X., D. P. Lettenmaier, E. F. Wood, and S. J. Burges (1994), A simple hydrologically based model of land surface water and energy fluxes for general circulation models, J. Geophys. Res., 99(D7), 14,415–14,428, doi:10.1029/94JD00483. Liang, X., D. P. Lettenmaier, and E. F. Wood (1996a), One-dimensional statistical dynamic representation of subgrid spatial variability of

W08528

precipitation in the two-layer variable infiltration capacity model, J. Geophys. Res., 101(D16), 21,403–21,422, doi:10.1029/96JD01448. Liang, X., E. F. Wood, and D. P. Lettenmaier (1996b), Surface soil moisture parameterization of the VIC-2 L model: Evaluation and modification, Global Planet. Change, 13(1–4), 195–206, doi:10.1016/0921-8181(95) 00046-1. Liang, X., et al. (1998), The Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) phase 2(c) Red-Arkansas River basin experiment: 2. Spatial and temporal analysis of energy fluxes, Global Planet. Change, 19(1–4), 137–159, doi:10.1016/S0921-8181(98)00045-9. Liang, X., E. F. Wood, and D. P. Lettenmaier (1999), Modeling ground heat flux in land surface parameterization schemes, J. Geophys. Res., 104(D8), 9581–9600, doi:10.1029/98JD02307. Liang, X., Z. H. Xie, and M. Y. Huang (2003), A new parameterization for surface and groundwater interactions and its impact on water budgets with the variable infiltration capacity (VIC) land surface model, J. Geophys. Res., 108(D16), 8613, doi:10.1029/2002JD003090. Liang, X., J. Z. Guo, and L. R. Leung (2004), Assessment of the effects of spatial resolutions on daily water flux simulations, J. Hydrol., 298(1–4), 287–310, doi:10.1016/j.jhydrol.2003.07.007. Lohmann, D., R. Nolte-Holube, and E. Raschke (1996), A large-scale horizontal routing model to be coupled to land surface parametrization schemes, Tellus, Ser. A, 48(5), 708–721, doi:10.1034/j.1600-0870.1996. t01-3-00009.x. Lohmann, D., E. Raschke, B. Nijssen, and D. P. Lettenmaier (1998), Regional scale hydrology: II. Application of the VIC-2 L model to the Weser River, Germany, Hydrol. Sci. J., 43(1), 143–158, doi:10.1080/ 02626669809492108. Mao, D. Z., and K. A. Cherkauer (2009), Impacts of land-use change on hydrologic responses in the Great Lakes region, J. Hydrol., 374(1–2), 71–82, doi:10.1016/j.jhydrol.2009.06.016. Maurer, E. P., A. W. Wood, J. C. Adam, D. P. Lettenmaier, and B. Nijssen (2002), A long-term hydrologically based dataset of land surface fluxes and states for the conterminous United States, J. Clim., 15(22), 3237–3251, doi:10.1175/1520-0442(2002)0152.0.CO;2. Naden, P. S. (1992), Spatial variability in flood estimation for large catchments: The exploitation of channel network structure, Hydrol. Sci. J., 37, 53–71, doi:10.1080/02626669209492561. Nash, J. (1957), The form of the instantaneous unit hydrograph, IAHS Publ., 45(3), 114–121. Nash, J. E., and J. V. Sutcliffe (1970), River flow forecasting through conceptual models. Part I: a discussion of principles, J. Hydrol., 10, 282–290, doi:10.1016/0022-1694(70)90255-6. Nijssen, B., D. P. Lettenmaier, X. Liang, S. W. Wetzel, and E. F. Wood (1997), Streamflow simulation for continental-scale river basins, Water Resour. Res., 33(4), 711–724, doi:10.1029/96WR03517. Nijssen, B., G. M. O’Donnell, A. F. Hamlet, and D. P. Lettenmaier (2001a), Hydrologic sensitivity of global rivers to climate change, Clim. Change, 50(1/2), 143–175, doi:10.1023/A:1010616428763. Nijssen, B., G. M. O’Donnell, D. P. Lettenmaier, D. Lohmann, and E. F. Wood (2001b), Predicting the discharge of global rivers, J. Clim., 14(15), 3307–3323, doi:10.1175/1520-0442(2001)0142.0.CO;2. Oki, T., and Y. C. Sud (1998), Design of total runoff integrating pathways (TRIP)—A global river channel network, Earth Interact., 2, 1–37, doi:10.1175/1087-3562(1998)0022.3.CO;2. Olivera, F., and D. Maidment (1999), Geographic information systems (GIS)-based spatially distributed model for runoff routing, Water Resour. Res., 35(4), 1155–1164, doi:10.1029/1998WR900104. Pitman, A. J., A. Henderson-Sellers, and Z. L. Yang (1990), Sensitivity of regional climates to localized precipitation in global models, Nature, 346(6286), 734–737, doi:10.1038/346734a0. Price, R. K. (2009), An optimized routing model for flood forecasting, Water Resour. Res., 45, W02426, doi:10.1029/2008WR007103. Smith, M. B., K. P. Georgakakos, and X. Liang (2004), The distributed model intercomparison project (DMIP), J. Hydrol., 298(1–4), 1–3, doi:10.1016/j.jhydrol.2004.05.001. U.S. Department of Agriculture, Natural Resources Conservation Service (1992), State Soil Geographic Database (STATSGO) Data User’s Guide, Publ. 1492, U.S. Govt. Print. Off., Washington, D. C. Wang, M. H., A. T. Hjelmfelt, and J. Garbrecht (2000), DEM aggregation for watershed modeling, J. Am. Water Resour. Assoc., 36(3), 579–584, doi:10.1111/j.1752-1688.2000.tb04288.x. Wu, H. A., J. S. Kimball, N. Mantua, and J. Stanford (2011), Automated upscaling of river networks for macroscale hydrological modeling, Water Resour. Res., 47, W03517, doi:10.1029/2009WR008871.

16 of 16

A new multiscale routing framework and its ... - Wiley Online Library

A new multiscale routing framework and its ... - Wiley Online Library

Suggest Documents

A multiscale framework for the origin and ... - Wiley Online Library

Multiscale derivative analysis: A new tool to ... - Wiley Online Library

Spatial regression and multiscale ... - Wiley Online Library

A new framework for estimating englacial water ... - Wiley Online Library

A new pressure ulcer conceptual framework - Wiley Online Library

Space Weather Modeling Framework: A new ... - Wiley Online Library

A New Framework to Assess Relative ... - Wiley Online Library

A new regulatory framework for extrajudicial ... - Wiley Online Library

A fast algorithm for multiscale electromagnetic ... - Wiley Online Library

FADD and its Phosphorylation - Wiley Online Library

Multiscale Characterization of a Heterogeneous ... - Wiley Online Library

Multiscale Modeling Reveals Inhibitory and ... - Wiley Online Library

Multiscale finite element analyses for stress and ... - Wiley Online Library

Multiscale error analysis, correction, and ... - Wiley Online Library

HOMEOPATHY A Theoretical Framework and ... - Wiley Online Library

A framework for aligning needs, abilities and ... - Wiley Online Library

Open access and online publishing: a new ... - Wiley Online Library

A framework for aligning needs, abilities and ... - Wiley Online Library

A modeling framework for the establishment and ... - Wiley Online Library

CD248 and its cytoplasmic domain: A ... - Wiley Online Library

Mlange and its seismogenic roof dcollement: A ... - Wiley Online Library

Derivatization of bisphenol A and its analogues ... - Wiley Online Library

Its Incidence and a Possible Relationship with ... - Wiley Online Library

DNA barcode library and its efficacy for ... - Wiley Online Library