Valley bottoms function as hydrological buffers that significantly affect runoff behavior. Distinguishing valley bottoms from hillslopes is an important first step in identifying and characterizing sediment deposits for hydrologic and geomorphic purposes. Valley bottoms occur at a range of scales from a few meters to hundreds of kilometers in extent. This paper describes an algorithm for using digital elevation models to identify valley bottoms based on their topographic signature as flat low-lying areas. The algorithm operates at a range of scales and combines the results at different scales into a single multiresolution index. This index classifies degrees of valley bottom flatness, which may be related to depth of deposit. The index can also be used to identify groundwater constrictions and to delineate hydrologic and geomorphic units.
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 Valley bottoms are important hydrologic and geomorphic features. Distinguishing between hillslopes and valley bottoms is necessary because of the substantial difference in hydrological processes in the two landforms [Flügel, 1995; Band, 1999]. Soils on hillslopes are generally shallower than in valleys and are dominated by erosion and transportation regimes, whereas valley bottoms are generally depositional environments where material accumulates over time. Valley bottom sediment deposits in the form of floodplains or fans function as hydrologic buffers and affect catchment connectivity [Herron and Wilson, 2001] to substantially modify the runoff response of a catchment. Soil hydraulic conductivity can also vary systematically between floodplains, fans, and colluvial zones [Butterworth et al., 2000].
 Hillslope flow paths are primarily driven by surface topography, and this connection is used extensively in distributed hydrological modeling [Vertessy et al., 1993; Wigmosta et al., 1994] and semidistributed approaches such as TOPMODEL [Beven and Kirkby, 1979; Quinn et al., 1991]. The connection between topography and water flow is less clear in valley bottoms where low gradients and depressions make delineation of flow paths from surface topography more difficult. This difficulty is compounded by the relative sparseness of contours in flat valley bottoms, which creates considerable uncertainty in the shape of the topography in those areas. Furthermore, water flow in valley bottoms does not faithfully follow surface topography particularly in high flow conditions.
 There are therefore clear reasons why mapping sediment deposits would be valuable for hydrologists, geomorphologists, and others. A useful, perhaps necessary, first step is mapping valley bottoms where sediment deposits may have accumulated. The obvious characteristics of valley bottoms are that they are relatively flat and low compared to the surrounding landscape, making them readily identifiable in the field or from aerial photographs and contour maps. Digital terrain analysis methods [Wilson and Gallant, 2000] can be used to implement automated identification of well-defined features using digital elevation models (DEMs). This follows extensive previous work developing methods for identifying landscape features by explicit computer-based algorithms [Chorley, 1972; Dikau, 1992; Fels and Matson, 1996; Band, 1999; Ventura and Irvin, 2000; Miliaresis, 2001]. These methods assume that landscape function (sediment deposit in this case) can be inferred from landform, an assumption that must be treated with some caution. Correlations between form and function sometimes have a clear basis through physical processes. Frequently, however, the links are empirical, and inferences concerning modes of geomorphic activity and materials constituting a landform require field sampling and correlation. Nevertheless, explicit, consistent, and repeatable methods for describing landforms are an essential first step in developing an understanding of landscape processes.
 There are no published methods for mapping valley bottoms by automated algorithms although a number of methods exist that are designed to map floodplains. Williams et al.  defined floodplains as terrain surrounding the channel network that is less than 15 m above the stream surface, based on cross sections constructed perpendicular to the channel. They note inherent problems with the alignment of perpendicular cross sections where channels meander in the floodplain. They also note the importance of multiscale classification and characterization, but their method does not explicitly address multiple scales of valley bottoms. Pickup and Marks  also used channels and cross sections but adopted a hydrodynamic approach to identifying inundated areas. Noman et al.  review methods for mapping inundation areas based on water level measurements and a DEM. None of these methods are applicable to the mapping of valley bottoms outside floodplains, such as perched swamps, terraces, stagnant alluvial plains, and steeper valleys.
 The multiresolution valley bottom flatness (MRVBF) algorithm identifies valley bottoms using the following assumptions: (1) Valley bottoms are low and flat relative to their surroundings. (2) Valley bottoms occur at a range of scales. (3) Large valley bottoms are flatter than smaller ones.
 MRVBF identifies valley bottoms using a slope classification constrained to convergent areas. The classification algorithm is applied at multiple scales by progressive generalization of the DEM combined with progressive reduction of the slope class threshold. The results at different scales are then combined into a single index. This follows earlier work on the role of scale in landform analysis by Wood , Gallant and Hutchinson , and Gallant .
 The MRVBF index utilises the flatness and lowness characteristics of valley bottoms. Flatness is measured by the inverse of slope, and lowness is measured by a ranking of elevation with respect to a circular surrounding area. The two measures, both scaled to the range 0 to 1, are combined by multiplication and could be interpreted as membership functions of fuzzy sets [Kaufmann, 1975]. The method draws on ideas in the Fuzzy Landscape Analysis GIS (FLAG) method for fuzzy landscape indices [Roberts et al., 1997; Dowling et al., 2003].
 The identification of valley bottoms is carried out at a range of scales in order to identify different scales of valley bottoms. The measures of flatness (from slope) and valley bottom flatness (flatness and lowness) are carried through the series of scales separately. This allows broad scale valley bottom flatness to override the finer scale and thus represent broad-scale features without unnecessary detail, while preventing small steep areas from being overlooked in the generalised data. A location is considered to have valley bottom flatness at a given scale if it is sufficiently low and flat at that scale and is sufficiently flat (but not necessarily low) at all finer scales.
 The different index values correspond to different resolutions and different slope thresholds. At each step in scale, the DEM cell size increases by a factor of 3, and the slope threshold reduces by a factor of 2. A useful side effect of progressively generalising the DEM is that computation time reduces at each successive step. If the same resolution was used for all scales, the computation time would increase at each step as the scope of the lowness calculations grew.
2.2. Components of the Algorithm
 Two terrain attributes are used in the analysis, slope and elevation percentile. Slope is computed using standard finite difference techniques [Gallant and Wilson, 2000; Environmental Systems Research Institute, Redlands, California, Arc/Info Geographic Information System, version 8.1, available at http://www.esri.com, 2000] using the ArcInfo GRID module. Slope is computed as a percentage or 100 times the tangent of the slope angle.
 Elevation percentile is computed using a stand-alone program (PCTL) based on the ElevResidGrid program [Gallant and Wilson, 2000]. Elevation percentile is a ranking of the elevation of a grid point with respect to the surrounding cells in a circular region of user-specified radius. It is calculated as the ratio of the number of points of lower elevation to the total number of points in the surrounding region. Low values indicate the point is low in the local landscape since most of the surrounding points are higher.
 At several points in the algorithm a nonlinear transformation is required to map an input value x > 0 onto the range 0 to 1. The function chosen to achieve this has two parameters, a threshold t and shape parameter p:
This function decreases with increasing x, having the value 1 when x = 0 and 0.5 when x = t. Larger values of p give more abrupt transitions between 1 (for x ≪ t) and 0 (for x ≫ t). A number of parameters are required in the algorithm, and the methods by which they were chosen are described in section 2.8.
2.3. Finest-Scale Step
 Slope for the first step S1 is calculated, then transformed to flatness F1 (0 to 1) using the nonlinear function (1) with p = 4:
where ts,1 is the slope threshold for the first step. For the 25 m DEMs used to develop the index, this first slope threshold is set to 16%.
 Elevation percentile for the first step (PCTL1) is calculated with a radius of three DEM cells (half the number of cells used for the remainder of the steps). Elevation percentile is transformed to a local lowness value using equation (1) with t = 0.4 and p = 3, and then combined with flatness F1 to produce the preliminary valley flatness index (PVF1) for the first step:
F1 and the transformed elevation percentile behave as membership functions with values greater than 0.5 signifying sufficient flatness or lowness to be considered a valley bottom. The product of the two should therefore be considered as indicating a valley bottom when it is greater than about 0.25. PVF1 is transformed using equation (1) to compensate for this bias:
Larger values of VF1 indicate increasing valley bottom character, with values less than 0.5 considered to be not in valley bottoms, being too steep or too high.
2.4. Second Step
 The second step commences the same way with the original DEM at its base resolution, using a slope threshold ts,2 half of ts,1:
The elevation percentile calculation uses a radius of six cells and the valley flatness index for this step is computed as for the first step:
The VF2 index has the same interpretation as VF1 but at a broader scale (due to the change in elevation percentile radius) and for a lower slope threshold. The results from steps one and two are combined to form MRVBF2, such that areas identified as valley bottom by VF2 take values from approximately 1.5 to 2.0, and areas excluded by VF2 but included by VF1 take values from about 0.5 to 1.0. This result is achieved by a weighted combination of VF1 (range 0 to 1) and 1 + VF2 (range 1 to 2):
The parameters t and p2 are chosen to give a reasonably rapid transition from near 0 for VF2 < 0.3 to near 1 for VF2 > 0.6 and to ensure that MRVBF2 = 1.5 when VF2 = 0.6 and VF1 = 0. Choosing t = 0.4 gives p2 = 6.68.
 A combined flatness index CF2 is also computed for use in subsequent steps:
2.5. Remaining Steps
 The remaining steps are similar to the second step. The main differences are that the DEM is smoothed, the resolution becomes coarser at each step, and the combined flatness from previous steps is included to prevent fine-scale nonflat areas being lost in the coarser-scale analysis.
 The level of generalization (scale) and the working cell size (resolution) of the DEM are manipulated independently in the algorithm. In the following description, the scale and resolution of each layer are identified by two subscripts, in that order. The original scale and the base resolution are both denoted as 1, so the original DEM is denoted DEM1,1. The second step involves no smoothing or resolution change so DEM2,2 is identical to the original DEM1,1.
 The processing at each step (L) uses three layers of information from the previous step (L − 1): the DEM (DEML−1,L−1), a cumulative flatness index (CFL−1,1) and the accumulated valley bottom flatness index (MRVBFL−1,1).
 First, a smoothed DEM (DEML,L−1) is derived without changing resolution. The smoothing is performed with the Arc/Info focal mean function using an 11 × 11 Gaussian smoothing kernel g(r) with an effective radius of three cells (to correspond with the factor of 3 resolution change):
where r is the distance (in cells) from the center of the kernel. From the smoothed DEM, the slope SL,L−1 is derived then resampled (refined) to the base resolution (SL,1) using bilinear interpolation. The smoothed DEM is then resampled (coarsened) to the resolution of the current processing step (DEML,L) and the elevation percentile (PCTLL,L) calculated from this DEM using a window size of six cells. Elevation percentile is then resampled (refined) to the base resolution (PCTLL,1). Elevation percentile is computed after coarsening of the DEM because the computation is much more efficient with fewer cells in the window, and it is not significantly affected by the coarsening due to the substantial number of cells in the window.
 The flatness FL,1 is computed at the base resolution using the slope threshold for step L:
This is multiplied by combined flatness from the previous step to give the accumulated combined flatness CFL,1 to this step:
Note that CF carries the effect of flatness from all previous scales, so low flatness (excessive slope) at any scale will reduce CF for all coarser scales as well. This combined flatness prevents small steep areas from being considered flat when the DEM is generalised.
 The preliminary valley flatness index is the product of combined flatness with elevation percentile transformed to lowness:
and final valley flatness index is
The MRVBFL,1 index is computed from VFL,1 and MRVBFL−1,1 using the weighting described in the second step:
The value of t is kept at 0.4, and pL is varied so that the contribution from VFL,1 is always L − 0.5 at VFL,1 = 0.6. Thus
2.6. Complementary Ridge Top Flatness Index
 A multiresolution ridge top flatness index (MRRTF) is a separate index derived in a very similar manner, except that the upper parts of the landscape are identified from PCTL. This is achieved by replacing the nonlinear function part of equations (3), (6), and (14) by
In most grid cells at least one of MRVBF and MRRTF is less than 0.5, unequivocally identifying that location as a ridge top or valley bottom, or a hillslope if both are less than 0.5. Areas where they overlap are to some degree ambiguous, but the dominant character, ridge-like or valley-like, can be inferred from the index with the larger value. This is described in more detail in sections 4 and 5.
2.7. Application With Different Resolution DEMs
 The MRVBF algorithm was developed using 25 m resolution DEMs but can be applied at any resolution provided appropriate adjustments are made. The link between size and flatness of valley bottoms is incorporated into the algorithm by reducing the slope threshold by a factor of 2 at each step, and it is assumed that the relationship between slope threshold, resolution, and MRVBF value does not vary between landscapes or with different resolution DEMs. If the DEM resolution is substantially different from 25 m, the initial slope threshold must be adjusted to retain the relationship between slope and resolution. An initial resolution of 75 m, one resolution step larger than the base 25 m resolution, would use a slope threshold of 8% instead of 16% for the first step, while an initial resolution of 8 m, one step smaller than the base, would use a slope threshold of 32% for the first step.
 The other adjustment is an offset of the MRVBF value itself. The MRVBF values derived from a 75 m DEM in the first processing step correspond to those derived in the second step when using a base 25 m resolution, so the MRVBF index values must be increased by one to compensate for the change in resolution.
 The algorithm was applied using the Australian DEM at 9″ resolution or approximately 250 m, which is about two resolution steps coarser than a 25 m DEM. The first slope threshold was therefore set to 4%, and the MRVBF values increased by 2. Values less than 0.5 are preserved as nonvalley bottom areas by setting to 0 any adjusted values less than 2.5.
 The Arc/Info AML developed to implement the MRVBF algorithm automatically picks the appropriate slope threshold for the starting resolution and optionally applies the offset to the computed MRVBF values. The use of the algorithm at fine DEM resolutions is still under investigation. The resolution-dependent alterations to the slope threshold described above suggest that at a resolution of 3 m the first threshold should be 64%, and at 1 m it should be 128%. It seems unlikely that land with a slope of over 100% could be described as valley bottom or a depositional site, so some consideration of physical processes may be required to define suitable slope thresholds at such fine resolutions.
2.8. Parameter Selection
 Some aspects of the algorithm involve arbitrary choices, and the reasons for these choices are described below.
2.8.1. Slope Thresholds
 The slope thresholds change by a ratio of 2 at each step. Experimentation with the slope thresholds showed that a smaller ratio divided the landscape into too many classes. The geometric, as opposed to arithmetic, sequence is consistent with traditional slope mapping [Speight, 1990], and using multiples of 2 makes for simple interpretation. A different choice of slope thresholds would result in shifted class boundaries with similar spatial patterns.
 The resolution ratio of 3 was established by trial and error. For the landforms studied so far, a resolution ratio of 2 was found to be too small to capture the broad-scale nature of very flat features, and a ratio of 6 was too large. In the Kyeamba Creek study area, the frequency of slope classes corresponding to the MRVBF thresholds was analyzed, and the area in each class was found to increase by about a factor of 3 for successive classes.
2.8.3. Nonlinear Function and Parameters
 The shape of the nonlinear function (1) is arbitrary and could be replaced by any function that decreases smoothly from 1 to 0. The function chosen is simple, the parameters are readily interpretable, and the exact shape of the function is not expected to have a substantial impact on the results.
 The threshold t of 0.4 for elevation percentile provided best separation of uplands and lowlands based on visual analysis of contours. A value of 0.35 was found to be too small, resulting in fragmentation of valley bottom regions that did not match field observations. Larger values have not been tested but are expected to overestimate valley bottom areas.
 The shape parameter p of 4 for the slope transformation and 3 for the elevation percentile transformation were chosen based on their effect on the plotted transformation curve. Maps produced using various values of p for both slope and elevation percentile were tested in the field, and the selected values produced maps that best corresponded with field interpretations of the landscape. Similarly for MRRTF, t = 0.35 was selected because 0.4 caused clear overestimation of the extent of flat ridge tops while 0.3 was too restrictive.
2.8.4. Modifications for Finest-Scale Step
 The first step, with steeper slope threshold and smaller elevation percentile radius, was included to account for the loss of fine detail incurred in the original mapping and subsequent interpolation of the DEM. The landscape structure at the resolution of contour-derived DEMs is not captured well, with small valley bottoms tending to be steeper and less convergent in the DEM than in reality. Omitting the nonstandard first step resulted in a map that missed small valley features that were observed in the field. Attempts to remedy this by shifting the slope thresholds so that the first step still used 16% resulted in a substantial reduction of the 8% class, and some important transitions in valley bottom form were missed.
3. Study Sites
 Results from two Australian sites are presented. The first site at Illalong covers approximately 2 × 2 km (within a larger DEM), located at 34°44′S 148°42′E about 100 km NW of Canberra, Australian Capital Territory. The second site, Kyeamba Creek catchment, covers approximately 20 × 50 km, centered around 35°20′S 147°30′E about 50 km SE of Wagga Wagga, New South Wales.
 The Illalong site is underlain by Ordovician metasediments and contains rolling hills and some valleys with sediment deposits. Kyeamba Creek catchment contains Ordovician metasediments with granite intrusions and has relatively steep uplands in the rim of the catchment with wide floodplains in the lower catchment.
 DEMs at both sites are at 25 m resolution, produced by New South Wales Land and Property Information using ANUDEM [Hutchinson, 1989, 1996] from 1:25,000 scale contours and streamlines. The 9″ DEM of Australia [Australian Surveying and Land Information Group, 2002], also produced using ANUDEM, with a resolution of about 250 m was used to derive a coarser-scale result. For the Kyeamba site, a 1:100,000 scale soil-landscape map based on aerial photographs and field observations [Chen and McKane, 1997] was obtained to compare with the MRVBF results.
 While MRVBF is a continuous measure, it naturally divides into classes corresponding to the different resolutions and slope thresholds. Values less than 0.5 are not valley bottom areas. Values from 0.5 to 1.5 are considered to be the steepest and smallest resolvable valley bottoms for 25 m DEMs. Flatter and larger valley bottoms are represented by values from 1.5 to 2.5, 2.5 to 3.5, and so on.
4.1. Illalong Creek
Figure 1a shows the Illalong Creek study area with an aerial orthophotograph draped over the DEM; heights are exaggerated by a factor of 2. Figure 1b includes the MRVBF index and depicts the relationship between topography and the index values. The upper catchment areas, marked (i) in Figure 1, are occupied by the first two classes (orange and pink) corresponding to the steepest and narrowest valley bottoms. The larger valleys have higher index values (green) indicating flatter terrain in the valley bottoms and relative lowness at a broader scale. Figure 1c shows the MRRTF ridge top index (with the same color scheme) for comparison, and Figure 1d shows the combined valley and ridge index using hue and intensity to represent valley or ridge character and scale, respectively.
 Of particular interest is the valley bottom (ii) associated with the main creek that flows from upper right to lower left in Figure 1. There is a constriction (iii) between two hills near the lower left corner that shows up in the MRVBF map both as a narrowing of the valley bottom feature and a disconnection of the flatter and broader class. Field observations indicate that the valley bottom (ii) is formed by sediment deposited behind this constriction. Similar deposits behind lesser constrictions correspond to green areas farther up the valley.
 Saddles (iv) are sometimes, but not always, identified as valley bottom features in the MRVBF map and sometimes identified as ridge top features in the MRRTF map. In either case they connect the convergent or divergent features on either side of the saddle.
Figure 1d depicts the combined MRVBF and MRRTF values, using red for ridges and blue for valleys, with increasing color intensity corresponding to increasing index values (broader and flatter features). Intermediate features are colored green (MRVBF is greater than MRRTF, ridges within larger valleys) to yellow (MRVBF equals MRRTF, ambiguous areas) to orange (MRVBF is less than MRRTF, valleys within larger ridges). The hue and saturation are defined as
Hue is red for 0° and 360°, green at 120°, and blue at 240°. Areas that are neither ridge tops nor valley bottoms are depicted using grey hill shading.
 Most of the saddles in this area (iv) are depicted as red to orange indicating a ridge-like character. A small ridge (v) within the broader valley is visible as a green area.
4.2. Kyeamba Creek
Figure 2 shows the MRVBF map for the Kyeamba Creek catchment derived from the 25 m DEM. The map shows the long narrow floodplain of the main Kyeamba Creek channel on the eastern side of the catchment and the broader floodplain areas in O'Briens Creek in the western arm of the catchment. Important features in this catchment include the following: A narrowing in the floodplain near the outlet of the catchment caused by a bedrock constriction is depicted by (i). Constrictions along both Kyeamba and O'Briens Creek floodplains with flatter areas behind them are depicted by (ii). These constrictions play an important role in the development of surface salinity in this catchment, with high groundwater levels upstream of the constrictions. Mount Flakney, a granite intrusion with steep slopes and a general absence of valley fill areas, is depicted by (iii). Livingstone Creek, a densely dissected area with an abundance of narrow valley fills, is depicted by (iv). Tooles Creek, an area with deep valley fill that has been reincised in recent times producing extensive erosion gullies several meters deep, is depicted by (v). These gullies fall within the MRVBF range 2.5–3.5 indicating a moderately sized valley bottom and are shown on the 1:25,000 topographic maps. Big Springs, a groundwater discharge area where spring water is collected commercially, is depicted by (vi). This site is also behind a constriction but is fed by fresh water from the steeper forested slopes of Mount Flakney (iii) and Livingstone State Forest (viii). Tywong Creek where the drainage network is poorly defined in a large depositional area is depicted by (vii). Livingstone State Forest on steeper hills is depicted by (viii).
 The MRVBF map effectively identifies dominant landforms in the Kyeamba Creek catchment. There is a marked contrast between the steeper areas with few flat valley bottoms such as Mount Flakney (iii), the low slopes with narrow valley bottoms, and the broad flat alluvial areas. The distinct character of the upper Livingstone Creek area (iv) is also readily apparent.
Figure 3 shows an area around the junction of Tooles Creek and Kyeamba Creek as portrayed by the slope and MRVBF maps. Each map is overlain with the 1:100,000 scale soil-landscape polygons; the units in downslope sequence are colluvial, erosional, transferral, and alluvial (a higher residual unit is also mapped but does not appear in this area). Figure 3b shows good agreement between the mapped landscape units and the patterns of MRVBF: Hilltop polygons are predominantly white; alluvial units are predominantly black; lower slope units are mostly grey with some white, while upper slope units are mostly white with some grey.
4.3. MRVBF at Different Resolutions
Figure 4 shows the Kyeamba Creek results derived using the algorithm applied to the 9″ (250 m) resolution DEM (Figure 4a) and from the 25 m DEM (Figure 4b); the finer-resolution results have been generalized and projected to the 9″ resolution (using bilinear interpolation), and values less than 2.5 have been set to 0 to facilitate the comparison.
 This comparison shows that the information extracted from the coarser DEM is similar to the corresponding information from the finer DEM, without any modification to the algorithm other than the adjustment of the starting slope threshold based on the resolution. This is a direct result of the multiresolution nature of the method and is a very useful property of the algorithm that contrasts with the scale dependence of many other terrain attributes [Moore et al., 1993; Zhang and Montgomery, 1994; Gallant, 1997].
 Some important features are generalized in the coarser analysis. Fine detail associated with small valleys is lost, and there is a tendency for larger valleys to broaden. Some distinct constrictions identified in the 25 m results are also lost.
5.1. Validation of the MRVBF Algorithm
 The MRVBF algorithm is designed to identify valley bottoms as areas that are flat and low relative to their surroundings. The motivation for developing this index is the need to discriminate between depositional regions (assumed to correspond to valley bottoms) and erosional regions (areas other than valley bottoms) and to estimate storage volumes for hydrological applications.
 The validation of the algorithm can therefore be considered in three steps. First, does the MRVBF index map valley bottoms? Second, does the index discriminate between erosional and depositional areas? Third, does it provide a reliable estimate of storage volume via the depth of deposit?
 The first step and some of the second step are considered in detail here. The third step requires acquisition and analysis of quantitative regolith depth data and will be addressed in a subsequent paper.
 The results of Figure 1 indicate that MRVBF is correctly identifying both the location and scale of valley bottoms. The comparison of MRVBF classes and soil-landscape polygons in Figure 3b provides strong evidence that the MRVBF index is identifying the same valley bottom areas as those delineated by a field surveyor mapping soil-landscape associations. The high MRVBF values within the main mapped alluvial unit confirm that MRVBF is identifying broad flat valley bottoms. The smaller branch of the same alluvial unit in the upper part of Figure 3b has smaller MRVBF values due to the narrower valley bottom. The sequence of soil-landscape units from valley bottom to ridge top is closely matched by progressively lighter shades (finer and steeper valley bottoms) and an increasing proportion of white area (sites other than valley bottoms) on the MRVBF map. While there is also a clear relationship between landform units and slope (Figure 3a), the discrimination between upper and lower landscape positions and the more connected nature of the broader valley units as mapped by MRVBF results in a better representation of the landform patterns mapped by the soil surveyor.
 More definitive validation of the relationship between MRVBF and valley bottoms is difficult, largely because there are no direct measurements of “valley bottomness.” Possible validation methods include manual delineation of valley bottoms of various sizes from contour maps and field observations of valley bottom shape and extent.
 The development of the method was partly inspired by the variety of scales of valley bottoms that could be identified on a contour map, and the quality of early developments were assessed against contours. However, the contour map is also the basis for the DEM from which MRVBF is derived and cannot be considered an independent data source.
 One flaw in the MRVBF map is the identification of some flatter saddles as valley bottoms, as noted in the Illalong results. The interpretation of these areas is assisted by the MRRTF map, and further developments of the algorithm may improve the ability to discriminate between valley bottoms and broad saddles.
 There are several applications for the MRVBF index. At the simplest level it provides a tool in support of landform interpretation. The index discriminates between uplands (hilltops, ridges, and slopes) and lowlands (convergent areas and valley bottoms), as well as separating degrees of valley bottom flatness. In contrast to a slope map, which typically suffers from fine-grained variability even in broad flat areas, MRVBF represents valley bottoms as contiguous regions more in keeping with conventional geomorphic mapping.
 MRVBF also highlights valley bottom constrictions and sediment deposition behind them that can act as storages with restricted outlets. A useful visualization of landscapes has been developed using a color classification of MRVBF in lowland areas and grey hill shading or other contextual background in upland areas (MRVBF < 0.5).
5.2.1. Hydrologic Applications
 A key application of the MRVBF index is providing information for hydrologic models at the catchment scale, both in the form of hydrologic units and, potentially, regolith properties. MRVBF should prove particularly useful for delineating hydrologic units in low relief terrain. An important component of hydrologic analysis is an appropriate choice of width of a flow path, particularly for subsurface flow. Hydrologic units for analysis and modeling are usually based on channel junctions, with the contributing area for each channel reach identified. This is problematic in low relief areas where drainage divides between channels are indistinct, the channel network relates poorly to catchment geometry, and the surface topography is an unreliable indicator of subsurface flow pathways. We argue that in these areas valley bottoms are the key hydrologic features rather than channels and provide a suitable basis for estimates of subsurface flow path width.
Figure 5 shows a prototype hierarchical delineation of hydrologic units in the upper reaches of O'Briens Creek in the Kyeamba Creek catchment. The MRVBF map has first been divided at selected class boundaries into valley bottom and hillslopes at broad scale. The valley bottom unit has been segmented at constrictions (i) and then catchment divide lines (ii) constructed along ridges to the catchment boundary. In the uppermost segment (iii), nine subsidiary valley bottom elements have been defined; for the uppermost of these (iv), two additional areas are defined; for one of those elements, four additional valley bottom units are delineated. These are the smallest resolvable valley bottom units at this scale of mapping, but the hillslope above these units could be subdivided to capture the spatial variability of the hillslope hydrological processes. This approach contrasts with the units that would be derived based on channel junctions and contours. The ability to construct the delineation across a range of scales is attractive and suggests approaches to hydrological modeling that could operate at different scales. An automated version of this method is under investigation.
 While no attempt has yet been made to systematically study the relationship between MRVBF and regolith properties, it is reasonable to postulate that quantitative relationships with depth can be established since deeper deposition leads to broad flat valleys (although other processes can lead to the same result). Regolith texture can also be related to the depositional environment. There are thus good prospects for enhanced prediction of hydrologic response of catchments using information derived from MRVBF.
 Another approach for characterizing the hydrologic behavior of catchments is by computing the proportion of catchment area in each MRVBF class, similar to the proportions of landscape types used by Dowling et al. . Comparison of catchments using such indices can lead to additional knowledge for determining similarities and differences between catchments.
5.2.2. Applications in Soil-Landscape Mapping
 The close connection between landform units identified by soil-landscape mapping and the patterns of MRVBF is demonstrated in Figure 3b. This suggests that the MRVBF map could provide an additional source of information to improve the quality of soil-landscape maps.
 Conventionally derived soil landscape units do not attempt to account for variation between ridge and valley positions. The detail provided by MRVBF can be used to infer finer spatial variation in pedogenic processes and hence patterns of soil properties within mapped units [McKenzie et al., 2003].
5.3. Interpretation of MRVBF Maps
 When interpreting the results and particularly when comparing the maps with field observations, the composite nature of the index must be kept in mind. The MRVBF values do not directly correspond to either slope or size, so the value at a particular site cannot be used as a measure of the slope at that point nor of the size of the valley bottom. MRVBF essentially corresponds to the lesser of flatness and extent at any particular point. A common example at our field sites is a valley bottom of 2–3% slope that is about 100 m wide being assigned an index value of 1 or 2. The fact that the site does not have a value of 3 (corresponding to a slope less than 4%) indicates that the landscape is not sufficiently locally low at the 75 m resolution.
 A contrasting example is where a valley bottom only a few hundred meters across is assigned an MRVBF value of 5 or more, a much higher value than expected from its extent. This situation occurs where the land surface is very flat at all scales (satisfying the cumulative flatness criterion) and is low relative to the surrounding broad-scale landscape (satisfying the lowness criterion). The broad-scale lowness is manifested as the convergence of a number of valley systems toward the flat site, suggesting a potentially large sediment supply for building a flat valley bottom.
 The combination of multiple resolutions can produce misleading results in some instances. For example, a small hilltop can be given an MRVBF index value of around 1, which usually indicates an area sufficiently low and flat at the DEM base resolution. In fact, the area is locally high at the finest resolution, and the value is derived from a coarser resolution stage of the analysis with a low valley flatness VFL giving a low weighting WL multiplied by L − 1 + VFL rather larger than 1 to give an MRVBF near 1 (see equation (13)). This behavior is a side effect of the weighted combination of values and cannot be easily avoided. Areas such as small hilltops are identified as such in the ridge top index, and the combined ridge-valley index can be used to identify these fine-scale features nested within broader-scale features of the opposite type.
 The same effect is responsible for the identification of some saddles as valley bottoms: the flatness of the saddles is correctly identified, but its relatively high position in the landscape is either lost in the generalization or is not sufficiently strong to override the flatness. Many saddles are classified as both valley bottom and ridge top features, and the combined ridge-valley representation used in Figure 1d differentiates between saddles that are dominated by the ridge characteristic and those that are more valley-like. This distinction may reflect a real difference in hydrologic and geomorphic processes in these saddles that could be revealed by measurements of soil depth in contrasting saddle types.
 In some areas the MRVBF index increases gradually from values near 0 through the various classes, indicating a gentle reduction in slope and broadening of the valley. In other areas, particularly along the larger floodplains, the index increases abruptly. The former tends to occur along the profile from hillslope to first-order catchment area and down to the larger valley, while the latter occurs where hillslopes connect directly with the larger valley. This distinction may indicate a difference in the mode of sediment supply, with the gradual transition indicating that most of the sediment is transported from the local uphill sources, while the abrupt transition indicates that the sediment has been transported along the larger valley from farther up the catchment.
5.4. Consistency and Future Evolution of the Algorithm
 The thresholds, resolution steps, and other parameters could, in principle, be adjusted to match the different characteristics of different landscapes. For example, the resolution step could be altered to fit the typical sizes of valley bottoms at successive slope thresholds. However, our experience is that such a typical size is difficult to assess, or there is no consistent typical size. The adjustment of the algorithm to suit different landscapes could result in a proliferation of slightly different algorithms. The authors believe that there is more value in adopting a single set of parameters so that results from different areas can be reliably compared. There is considerable value, however, in testing variations of the algorithm in pursuit of improved representation of valley bottom features. The existing algorithm is not considered final: Testing and validation are ongoing and the algorithm will be modified if demanded by field evidence.
 A new algorithm for representing the characteristics of flat valley bottom terrain has been presented. The algorithm relies on a set of geometrically spaced slope thresholds and a combination of local lowness and flatness indices computed at a range of scales. Compared with floodplain mapping the MRVBF index provides a richer characterization of the landscape by identifying valley bottoms at a range of sizes and slopes. MRVBF does not rely on prior identification of channels and can depict unchanneled valley areas including perched swamps.
 The multiresolution nature of the algorithm effectively discriminates between different scales and flatness of valley bottoms. The index is reasonably insensitive to changes in DEM source resolution as demonstrated by comparison between 25 and 250 m resolution results. The valley bottom flatness index is complemented by a similar ridge top flatness index that separately identifies the flat upper parts of the landscape. This provides a means of identifying where the generalization at coarse scales has overlooked minor hills and identified them as valley bottoms. It also allows identification of nested features, where a broad-scale valley bottom contains a finer-scale ridge or vice versa.
 The index clearly identifies depositional parts of the landscape and corresponds with field observations of valley bottom areas. It provides a valuable visual portrayal of low relief areas and identification of valley bottom constrictions and the deposits that build up behind them.
 The index has potential applications in the delineation of hydrologic and geomorphic units and for quantitative comparison of catchments. If a relationship with deposit depth can be established, it will provide quantitative estimates of storage capacity for use in hydrological modeling. The algorithm, composed of the mrvbf.aml Arc/Info AML and a Unix or Windows PCTL executable, is available from the authors on request.
 The authors gratefully acknowledge the valuable discussions and assistance with field validation provided by Peter Richardson of CSIRO Land and Water and the insightful and helpful suggestions on the first draft of this manuscript provided by Neil McKenzie and Ian Prosser of CSIRO Land and Water. This work was partly funded by the Cooperative Research Centre for Catchment Hydrology Project 1.2 and 2.3 and by the Catchment Categorisation Project (Murray Darling Basin Commission projects D9004/D2013).