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 Upscaling fine resolution river networks in a realistic manner is a cumbersome process and manual corrections are difficult to avoid. A modified algorithm is presented that offers improvement over the existing approaches and requires comparatively fewer manual corrections. The algorithm uses fine resolution flow directions to find the adjacent coarse resolution grid cell in which the majority of water drains and then corrects for increased occurrences of river flow through the sides of the grid cells. Visual comparison remains an acceptable way to assess the success of various upscaling algorithms given the complex nature of rivers and in the absence of a method for comprehensive quantitative comparison. Here, the fraction of ordinal river flow directions (a measure of side-to-corner preference) and the fraction of grid cells that only drain themselves (a measure of connectivity of low order river segments) are used to provide information about the nature of upscaled coarse resolution river networks in comparison to the fine resolution networks. For both visual evaluation and these more quantitative measures, the modified algorithm presented here yields the best comparison with the 0.5° resolution river networks on which the upscaled coarse resolution networks are based.
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 Fresh water flow from the land surface to the oceans is an important component of the climate system and affects ocean salinity and the thermohaline circulation [Mysak et al., 1990; Wijffels et al., 1992; Wang et al., 1999]. The routing of river runoff from the land to the oceans closes the hydrologic cycle and climate models generally use river networks derived at the model resolution to route runoff generated by their land surface schemes [Miller et al., 1994; Hagemann and Dümenil, 1998; Arora and Boer, 1999]. Routing of runoff also allows evaluation of a climate model's estimates of streamflow against observation-based hydrograph data. Land surface schemes partition incoming precipitation into evapotranspiration and runoff, and incoming radiation into latent and sensible heat fluxes [Pitman, 2003]. Since observation-based gridded estimates of runoff are generally not available, model generated runoff can best be evaluated by comparing routed runoff against observation-based estimates of streamflow. Provided that model values of precipitation and other climate variables are realistic, simulated streamflow can be used to assess the adequacy of its land surface scheme [Liston et al., 1994; Arora, 2001]. Finally, the routed runoff yields streamflow (or river discharge) which also provides the means to assess the impact of climate change on the hydrology of river basins and the availability of water resources at the regional scale [Miller and Russell, 1992; Arora and Boer, 2001].
 Flow routing algorithms used in macroscale hydrology and climate models receive runoff from upstream grid cells and route it to downstream grid cells based on the cardinal (North, East, West and South) and ordinal (Northeast, Southeast, Southwest and Northwest) directions and require river networks at coarse resolution [Miller et al., 1994; Nijssen et al., 1997; Hagemann and Dümenil, 1998; Lohmann et al., 1998; Arora and Boer, 1999]. The process of scaling river flow networks from the fine to coarse resolution is referred to as upscaling.
 River networks at coarse model resolution are obtained by upscaling fine resolution river networks possibly with the use of digital elevation models (DEMs). Olivera et al. , Fekete et al. , and O'Donnell et al. , for example, use DEMs to first determine fine resolution river flow networks and then use these data to upscale river flow networks to the desired coarser resolution. Arora and Boer , however, use existing 1° river flow networks from Oki and Sud  directly to upscale to river flow networks at 2.8° and 3.75° resolutions for the Canadian Centre for Climate Modelling and Analysis (CCCma) global climate model. River networks derived from DEMs are typically fragmented due to spurious local depressions. Several automated algorithms exist to correct digital elevation data and DEM derived river networks [Jenson and Domingue, 1988; Band, 1993]. The use of digital elevation data to obtain river networks inevitably requires creating a depression-free DEM [e.g., O'Donnell et al., 1999]. Döll and Lehner  discuss the limitations of deriving river flow networks on the basis of DEMs. The use of existing 1° and 0.5° resolution flow networks such as that of Oki and Sud  (see also http://hydro.iis.u-tokyo.ac.jp/∼taikan/TRIPDATA/TRIPDATA.html) offers the advantage that they, in addition to digital elevation data, are also based on real-world river networks obtained from atlases.
 Upscaling algorithms for river flow networks can be divided broadly into two groups. The first group of algorithms [Olivera et al., 2002; Fekete et al., 2001; O'Donnell et al., 1999] uses the number of upstream cells draining through a given grid cell (also referred to as the flow accumulation matrix) at fine resolution to aid in the derivation of coarse resolution flow networks. The basic premise is that the flow accumulation matrix (FAM) is used in a manner similar to a DEM, but in contrast to the use of a DEM which uses a maximum downhill (decreasing) elevation search, the FAM instead defines flow directions on the basis of maximum uphill (increasing) drainage area gradients [Fekete et al., 2001]. These algorithms are referred here as FAM-based algorithms.
 The second group of algorithms derives coarse resolution flow networks by upscaling fine resolution river directions that lie inside a coarse resolution grid cell. Arora and Boer  first implemented this algorithm and used fine resolution flow directions (FRDs) to find the adjacent coarse resolution grid cell in which the majority of water drains assuming a unit amount of runoff is generated over the entire coarse resolution grid cell of interest. Döll and Lehner  improved upon the Arora and Boer  algorithm by additionally taking flow accumulation matrix information into account. They thus use the runoff that enters a grid cell from upstream fine resolution grid cells, combined with runoff generated within the current coarse resolution grid cell, to estimate to which adjacent coarse resolution grid cell the majority of water drains. We refer to this as the FRD algorithm. Döll and Lehner  used the FRD algorithm to upscale river networks from 10′ to 30′ resolution. They did not, however, compare the performance of the FRD algorithm with an FAM-based algorithm. As pointed out by Olivera et al.  the Arora and Boer  algorithm, and consequently the Döll and Lehner  algorithm, suffer from the limitation that they yield a higher side-to-corner ratio and the upscaled rivers preferentially flow along the cardinal directions compared to the ordinal directions. This yields upscaled river networks exhibiting a stair-like pattern rather than flowing diagonally. This is a result of a coarse grid cell being assigned a diagonal flow direction considerably less often than a horizontal or vertical flow direction (as discussed in section 2).
 In this paper, we first argue that upscaled river networks derived using the FRD algorithm are more realistic than those derived using a FAM algorithm which results in several false river segments as well as excludes real river segments. The FRD algorithm yields realistic river networks but prefers cardinal flow directions and there are more occurrences of river flow through the sides as opposed to corners of the grid cells. We then modify the FRD algorithm to overcome its preference for cardinal directions. The resulting upscaled flow networks compare reasonably well with the original fine resolution flow networks and require minimal manual correction. We test the performance of these three algorithms at the global scale and focus here on the results for the South American continent and four major Russian river basins.
 We use the 0.5° TRIP (Total River Integrated Pathways) river flow directions and basin delineations [Oki and Sud, 1998] as our input data to obtain upscaled river networks at T95 (∼1.88°) and T127 (∼1.41°) resolutions for use in CCCma global climate model. These upscaled flow networks are to be used in conjunction with the Arora and Boer  variable velocity river flow algorithm to estimate fresh water flux at the continental edges.
 The 0.5° TRIP basin delineations are first used to discretize river basins at the T95 and T127 resolutions of the climate model. The discretization procedure ensures that areas of the major river basins at the coarser resolutions are as close as possible to their areas at 0.5° resolution. Next, upscaled flow networks are derived at both T95 and T127 resolutions using 1) the FAM algorithm, 2) the FRD algorithm and 3) the modified FRD algorithm developed here. The FAM algorithm is described in detail by Fekete et al.  and illustrated in Figure 1a. In this algorithm, the fine resolution flow network is used to generate a FAM that corresponds to number of grid cells that drain through a given cell. FAM contains value of one for grid cells that only drain themselves and the value at the mouth of the river is equal to the total number of grid cells in a river basin (see Figure 1a). The coarse resolution grid is then overlaid on the fine resolution FAM and the maximum FAM value (FAMmax) in each coarse resolution grid cell is found (shown in bold in Figure 1a). The FAMmax values for coarse resolution grid cells are then used to upscale the river network. A flow direction is assigned to each coarse resolution grid cell such that water always flows towards the neighbouring grid cell with the highest FAMmax value. The FRD algorithm uses the flow accumulation matrix in conjunction with the fine resolution flow directions (see Figure 1b). Based on the fine resolution flow directions that lie within a coarse resolution grid cell it finds the neighbouring grid cell in which the majority of grid cells drains [Arora and Boer, 1999; Döll and Lehner, 2002]. The sum of numbers shown in bold in every coarse resolution grid cell in Figure 1b is the number of fine resolution grid cells that drain into the neighboring coarse resolution grid cell based on the direction assigned by the FRD algorithm. Figures 1a and 1b illustrate how the differences in the FAM and FRD algorithms yield differences in upscaled river networks. Finally, the estimated coarse resolution river flow directions are checked and corrected automatically to ensure that water does not flow into adjacent river basins and it does not circulate within a basin.
 Owing to its design, the FRD algorithm results in a coarse resolution river network with a higher fraction of rivers flowing through the sides of the grid cells as opposed to the corners than the fine resolution river network. Figure 1c illustrates this aspect for a simple case. If there are nine (3 × 3) fine resolution grid cells inside a coarse resolution grid cell then out of the eight surrounding cells (numbered 1 to 8) only the four corner fine resolution grid cells (numbered 1, 3, 5 and 7) can yield an assignment of diagonal direction for the coarse resolution grid cell. In addition, in this case, the coarse resolution grid cell in Figure 1a will be assigned a northeast (↗) direction only if the corner fine resolution grid cell (shown as shaded) has a northeast flow direction. All other directions for the shaded corner grid cell will result in an assignment of non-diagonal flow direction. This bias in the FRD algorithm yields a stair-like pattern for the rivers flowing along ordinal directions. The modified FRD algorithm attempts to rectify this by tracking the river after it leaves a coarse resolution grid cell. As shown in Figure 1d, for example, if after leaving the grid cell A the river meanders to the diagonally located grid cell C through the adjacent quadrant of grid cell B then a diagonal flow direction is assigned to the coarse resolution grid cell A.
 In contrast to the FRD algorithm, the FAM algorithm leads to a higher fraction of grid cells draining through their corners (as seen in Figure 1a) and thus include a higher fraction of ordinal flow directions than in the original fine resolution data. This is because the FAM algorithm always assigns a flow direction towards a neighbouring grid cell with a highest value of the flow accumulation matrix which results in rivers flowing through the shortest (diagonal) path rather than the two sides.
Figure 2 shows the 0.5° river flow networks (shown in light orange) overlaid on the derived coarse resolution river networks (shown in black) using the three algorithms for the South American continent at T127 (∼1.41°) resolution. The thickness of river channels is made proportional to the number of upstream grid cells they drain. The different colours correspond to the different river basins including the Amazon, the Parana, and the Tocantins. Figure 3 shows the results for Russian river basins including the Yenisey, the Lena, the Ob and the Amur at T95 (∼1.88°) resolution. No manual corrections are performed on the results shown here. High resolution plots showing the performance of the three algorithms at the global scale at T127 resolution are available at http://www.cccma.ec.gc.ca/∼varora/rivers/. Visually, Figures 2 and 3 illustrate that the FAM algorithm performs less well than the FRD algorithm which in turn performs less well than its modified version. The FAM algorithm yields a number of false segments and also fails to represent several real river segments. The FRD algorithm captures primary river segments more realistically but displays an unrealistic stair-like pattern (see Figure 3b) which is avoided in the modified FRD algorithm. In Figure 2, the FAM algorithm combines the two separate nearly parallel flowing branches of the Tocantins River into one while this distinction is preserved in the two FRD-based algorithms. For the Parana River basin, the FAM approach yields two parallel branches of the rivers flowing together where there is only one branch in the TRIP 0.5° resolution network. The FAM algorithm yields higher fraction of diagonal flow directions that leads to a fish-bone like pattern as seen in Figures 1a and 2a. In Figure 3, the FAM approach yields unrealistic parallel river segments for both the Yenisey and the Lena River basins. Fekete et al.  suggest that the FAM algorithm can be improved by limiting the search for maximum uphill drainage area gradients within sub-basins and the search is extended outside sub-basins when no other outlet is found.
Table 1 shows that the higher occurrences of diagonal river segments in the upscaled river network produced by the FAM algorithm leads to a higher fraction of diagonal segments than is found in the original 0.5° resolution networks for the Amazon, the Parana, the Tocantins, the Ob, the Yenisey, the Lena and the Amur River basins. Similarly, due to its preference for rivers exiting through the sides of the grid cells, the FRD algorithm leads to lower fraction of diagonal segments than in the 0.5° resolution networks. The modified FRD algorithm avoids both these biases and largely preserves the fraction of diagonal flow directions. Another related measure of comparison between the fine and coarse resolution river networks is the fraction of grid cells that drain only themselves and thus have a flow accumulation matrix value of one. If derived coarse resolution river networks lack (have increased) connectivity of low order river segments, compared to the fine resolution network, then the fraction of grid cells with a FAM value of one increases (decreases). Table 1 shows that compared to the 0.5° resolution river network, the FAM algorithm always yields a higher fraction of grid cells that drain only themselves. This is the result of the fish-bone type implementation of river networks that leads to rivers flowing through the shortest path trying to join the next higher order river segment as soon as possible. In the process each low order coarse resolution river segment tends to behave separately from its neighbouring segments, despite being joined by river segments at the fine resolution. The fraction of grid cells that drain only themselves for the FRD algorithm is lower compared to the 0.5° resolution river networks because of its tendency to yield stair-like pattern that yields increased connectivity of low order river segments and forces the grid cells to flow through their adjacently located side (as opposed to diagonally located) grid cells. The modified FRD algorithm preserves the fraction of grid cells that drain only themselves reasonably well and again yields the best comparison with the 0.5° resolution river networks.
Table 1. Comparison of the Fraction of Ordinal (Diagonal) Flow Directions and the Fraction of Grid Cells That Drain Only Themselves at the T95 (∼1.88°) and T127 (∼1.41°) Resolutions With Values at 0.5° Resolution River Networks for the Three Upscaling Algorithms Investigated Here
 Upscaling fine resolution river networks in a realistic manner is difficult. Several algorithms exist and they can be broadly divided into two groups: 1) those based on FAM and 2) those that use FRDs to calculate the adjacent grid cell in which the majority of water drains. The modified FRD developed here offers improvement over the traditional FAM algorithm and corrects the FRD algorithm that preferentially yields cardinal flow directions. Results show that the FRD based algorithms, in general, perform better than the FAM based approach which yields false river segments and also inadequately represents several real river segments. Given the complex nature of rivers, comprehensive quantitative comparison of fine and coarse resolution river networks is difficult. The fraction of diagonal river flow directions (a measure of side-to-corner preference) and the fraction of grid cells that drain only themselves (a measure of connectivity of low order river segments) nevertheless provide some information about the nature of upscaled coarse resolution river networks in comparison to the fine resolution networks. For both the visual evaluation and values of these quantitative measures, the modified algorithm presented here yields the best comparison with the 0.5° resolution river networks. Although not tested here for resolutions finer than 0.5°, the modified FRD algorithm developed here can, in principle, be used for upscaling river networks at any resolution. Newer fine resolution river direction data sets, such as the 3″ HydroSHEDS data set (hydrosheds.cr.usgs.gov), are becoming available and will likely form the basis for future upscaled river networks.
 We would like to thank George Boer, Greg Flato, and Steve Lambert for providing comments on an earlier version of this manuscript and Balazs Fekete and an anonymous reviewer, who provided useful comments that improved this paper.