Earth's terrestrial near-subsurface environment can be divided into relatively porous layers of soil, intact regolith, and sedimentary deposits above unweathered bedrock. Variations in the thicknesses of these layers control the hydrologic and biogeochemical responses of landscapes. Currently, Earth System Models approximate the thickness of these relatively permeable layers above bedrock as uniform globally, despite the fact that their thicknesses vary systematically with topography, climate, and geology. To meet the need for more realistic input data for models, we developed a high-resolution gridded global data set of the average thicknesses of soil, intact regolith, and sedimentary deposits within each 30 arcsec (∼1 km) pixel using the best available data for topography, climate, and geology as input. Our data set partitions the global land surface into upland hillslope, upland valley bottom, and lowland landscape components and uses models optimized for each landform type to estimate the thicknesses of each subsurface layer. On hillslopes, the data set is calibrated and validated using independent data sets of measured soil thicknesses from the U.S. and Europe and on lowlands using depth to bedrock observations from groundwater wells in the U.S. We anticipate that the data set will prove useful as an input to regional and global hydrological and ecosystems models.

Key Points:

We have quantified the thicknesses of permeable layers above bedrock for Earth System Models
We distinguish among uplands and lowlands, using optimal models for each to predict depth to bedrock
The data set honors the geologic, topographic, and climatic controls on permeable layer thicknesses

1 Introduction

1.1 Problem Statement

Moisture within the relatively porous weathered material between Earth's surface and unweathered bedrock plays a central role in the land-atmosphere exchange of energy, water, and carbon fluxes as well as dynamic vegetation [e.g., Zeng et al., 2008]. In particular, moisture availability in the shallow subsurface can provide a critical constraint on the short-term and long-term memory of previous climatic forcing [e.g., Koster et al., 2004]. The depth of the rooting zone also has a significant impact on the time scale of moisture variability [Wang et al., 2006]. Over the tropical forest, the availability of moisture from the deep vadose zone helps to maintain evapotranspiration and vegetation greenness over the dry season [e.g., Zeng et al., 1998; Saleska et al., 2007; Sakaguchi et al., 2011].

Inclusion of data on the thicknesses of the relatively porous subsurface layers above bedrock is essential for accurate land surface modeling of the energy, water, carbon cycle, and dynamic vegetation. In general, a lower boundary condition is needed to solve the governing equation for vadose zone moisture, but no conditions are satisfactory without a depth to bedrock (DTB) estimate [e.g., Zeng and Decker, 2009]. Since constraints on permeable layer thickness are not available at present, land models (for hydrometeorology, climate, and carbon-cycle studies) often assume a globally uniform value. Even the use of an unconfined aquifer in land models implicitly assumes a globally constant bedrock depth [e.g., Lawrence et al., 2011]. In the North American Monsoon region, Gochis et al. [2010] found that assuming a uniform soil or permeable layer thickness can limit land surface model performance at the sites studied; the main impact of accounting for thinner soils is to increase the dynamic range of sensible and latent heat fluxes when compared with simulations using a fixed soil thickness of 2 m. At high latitudes, Lawrence et al. [2008] demonstrated the importance of deep soil layers on the simulation of permafrost.

Existing regional and global soil thickness data sets are remarkable data compilations but are limited as measures of the thicknesses of relatively porous layers above unweathered bedrock. The CONUS-Soil data set of Miller and White [1998], for example, is the best available 30 arcsec pixel⁻¹ gridded soil thickness data set for the conterminous U.S. It is a gridded version of the USDA State Soil Geographic (STATSGO) data for the depth to the paralithic contact based on tens of thousands of field measurements of soil thickness made by soil scientists over many decades. The depth to paralithic contact is the thickness of disaggregated material above material that is consolidated but is often not unweathered bedrock. The CONUS-Soil map is incomplete as a measure of the thickness of porous material above bedrock for two reasons. First, intact regolith (weathered bedrock) is often not included. Intact regolith generally has a lower porosity than the more highly weathered soil layer above it, but its great thickness (often tens of meters) means that it can be a significant storage zone for water despite its typically lower porosity [Graham et al., 2010; Holbrook et al., 2014]. Water storage within the intact regolith layer can be an especially important source of water for deep-rooting plants during droughts [e.g., Arkley, 1981; Jones and Graham, 1993]. Second, the CONUS-Soil data set provides little to no constraint on the thickness of sedimentary deposits above bedrock in lowlands (e.g., depositional areas such as coastal plains). Sedimentary deposits in lowlands generally exceed the 2 m depth limit of most soil surveys. The Harmonized World Soils Dataset [FAO/IIASA/ISRIC/ISSCAS/JRC, 2012] and other regional and global soil maps [e.g., Liu et al., 2013; Shangguan et al., 2014; Hengl et al., 2014] are similarly limited to providing information only on the depth to paralithic contacts if such contacts occur within depths of approximately 2 m.

In the data set described herein, the thicknesses of soil, intact regolith, and sedimentary deposits are mapped up to 50 m in thickness. To do this, we explicitly mapped all the upland hillslopes and valley bottoms resolvable in 3 arcsec (∼90 m) pixel⁻¹ Digital Elevation Models (DEMs) globally, and applied models for estimating soil, intact regolith, and sedimentary deposit thicknesses optimized for each landform type. Our data set estimates the average thickness of soil, intact regolith, and sedimentary deposits on upland hillslopes and valley bottoms separately within each grid cell and provides a measure of the area fraction of hillslopes versus valley bottoms within each grid cell. In this way, the data set honors the variability of permeable layer thicknesses within 30 arcsec pixels and provides the data necessary to treat hillslopes and valley bottoms as separate types with the “tile” method of sub-grid-scale parameterization commonly used in Earth System Models [Avissar and Pielke, 1989; Koster and Suarez, 1992]. For users who prefer a single thickness product that averages over hillslopes and valley bottoms, we have provided an average value of the thickness of unconsolidated material (including soil on upland hillslopes and sedimentary deposits in valley bottoms) within each 30 arcsec pixel, weighted by both the relative areas of each landform type (hillslope versus valley bottom) as well as a measure of the time that surface water comes into contact with each landform type as it is routed through the landscape.

The data set associated with this paper is composed of six self-consistent grids of 43,200 columns × 18,000 rows covering 180°W–180°E and 60°S–90°N. It contains (1) a cover mask that classifies each pixel as predominantly ocean, upland, lowland, lake, or perennial ice, (2) a grid of the fraction of area within each 30 arcsec pixel composed of hillslopes versus valley bottoms, (3) a grid of average upland hillslope soil thickness, (4) a grid of the maximum upland regolith (soil plus intact regolith) thickness, (5) a grid of average upland valley bottom and lowland sedimentary deposit thickness, and (6) a product that averages soil and sedimentary deposit thicknesses for users who want a single thickness value that averages across upland hillslopes and valley bottoms.

1.2 Definitions and Conceptual Model

Our data set quantifies spatial variations in the thickness of relatively high-porosity material above unweathered bedrock. In uplands, this high-porosity material is termed regolith and can be divided into a layer of soil above a layer of intact regolith (Figure 1a). Soil is the material that sustains life and is mobile over geologic time scales (partly because life is an agent of physical transport). Intact regolith refers to the chemically altered but relatively immobile material between soil and unweathered bedrock [Holbrook et al., 2014]. In lowlands, we refer to all unconsolidated material above bedrock as sedimentary deposits. Sedimentary deposits can lithify into sedimentary bedrock over time via burial at depth or via chemical processes close to the surface, but our use of the term sedimentary deposits refers only to unconsolidated deposits.

Details are in the caption following the image — **Figure 1**
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Conceptual diagrams of typical subsurface profiles on upland hillslopes and valley bottoms in (a) transport-limited landscapes and (b) detachment-limited landscapes. (c) Diagram of mathematical formulation used to estimate upland valley bottom deposit thickness, assuming that the side-slopes project to a V shape beneath the valley bottom.

Well-developed soils on uplands often contain sufficient silt and clay that they have a relatively low permeability compared to the intact regolith beneath them despite their generally higher porosity [e.g., Obermeier and Langer, 1986]. Both layers are significant hydrologically. The relatively low permeability of soils (especially the Av and/or B horizons) is often the rate-limiting factor for infiltration [Soil Survey Staff, 1999]. The intact regolith layer is an important storage zone for water in at least some upland landscapes [e.g., Graham et al., 2010; Holbrook et al., 2014]. It should be noted that, in some rare cases (e.g., some volcanic tuffs), unweathered bedrock can be of higher porosity than the soil and intact regolith above it. Most often, however, bedrock is of lower porosity than the material above it.

On uplands, sharp boundaries often do not exist between soil and intact regolith and between intact regolith and unweathered bedrock. However, both soils and intact bedrock have characteristic thicknesses that vary in systematic ways with topography, climate, and bedrock weatherability. It is these characteristic thicknesses of soil, intact regolith, and sedimentary deposits that we constrain in this paper and the associated data set.

In our workflow, we first partition Earth's land surface into uplands and lowlands. Uplands are defined as areas undergoing net erosion over geologic time scales (i.e., ∼10⁵ years and longer), while lowlands are areas undergoing net deposition over similar time scales. Uplands typically have soils that vary in thickness from as little as a few decimeters to as much as a few meters in thickness. Intact regolith typically varies from as little as a few meters to as much as a few tens of meters in thickness. Lowlands typically have sedimentary deposits tens to hundreds of meters thick. Precise estimates of the thicknesses of lowland sedimentary deposits greater than a few tens of meters in thickness require geophysical data and/or dense networks of wells deep enough to penetrate bedrock at depth. Such data are readily available for only a small fraction of Earth's land surface. As such, we limit our data set to estimating soil, intact regolith, and sedimentary deposit thicknesses within the range of 0–50 m. That is, areas predicted to be greater than 50 m based on our methodology are assigned a value of 50 m with the understanding that the actual thickness may be much greater than 50 m. The range of depths from 0–50 is the most critical range for terrestrial ecology applications as all plant roots exist within this range. Uplands and lowlands are distinguished based on geologic criteria in addition to a topographic analysis that identifies depositional areas not resolved in some geologic maps.

We next partition Earth's land surface into hillslopes and valley bottoms. Hillslopes are areas of unconfined surface water flow, while valley bottoms are areas of topographically confined surface water flow. On uplands, the distinction between hillslopes and valley bottoms is important for the purposes of estimating soil, intact regolith, and sedimentary deposit thicknesses because upland valley bottoms, while erosional over long time scales, can be areas of significant deposition over short time scales, which can result in locally thick sedimentary deposits. For example, variations in erosion rates caused by Quaternary climatic changes have led to recent (i.e., ∼10³ to 10⁴ years) deposition in many valley bottoms, even those within mountain ranges that are undergoing net erosion over longer time scales [Bull, 1991; Pelletier, 2014]. The distinction between hillslopes and valley bottoms is usually not significant for estimating sedimentary deposit thicknesses in lowlands because sedimentary deposit thicknesses are most strongly controlled by structural geologic factors (e.g., fault geometries that define the boundaries between mountain ranges and adjacent depositional basins), with surface topography acting as a relatively minor controlling factor. However, the distinction between hillslopes and valley bottoms is significant hydrologically in all land areas because surface water velocities tend to be relatively slow on hillslopes and faster in valley bottoms where flow is topographically confined. For this reason, we provide a raster grid as part of our data set that maps the fraction of area within each pixel composed of hillslopes versus valley bottoms for Earth's entire land surface, even though this distinction is significant only on uplands for the purpose of estimating the thicknesses of soil, intact regolith, and sedimentary deposits. Hillslopes and valley bottoms are distinguished based on topographic criteria.

2 Methods

2.1 Distinguishing Among Lowlands, Upland Hillslopes, and Upland Valley Bottoms

We applied different methods to estimate the soil, intact regolith, and sedimentary deposit thicknesses on upland hillslopes, upland valley bottoms, and lowlands. In this section, we describe the methods we used for partitioning Earth's land surface into these three different landscape components. In section 2.2, we describe the methods for estimating soil, intact regolith, and sedimentary deposit thicknesses within each landform component.

2.1.1 Distinguishing Uplands From Lowlands

We used two types of geologic data, i.e., geologic maps of surficial deposits and geologic maps of the age of the underlying geologic unit, to differentiate between uplands and lowlands. The primary source of global geologic information is the collection of digital geologic maps available from the World Petroleum Assessment (WPA) [2014] project of the U.S. Geological Survey (USGS). These maps are digitized versions of generalized geologic maps produced by the USGS, the United Nation's Educational, Cultural, and Scientific Organization (UNESCO), and other local sources, primarily for the purpose of oil exploration.

The WPA maps (Figure 2a) were converted from shapefiles to 30 arcsec pixel⁻¹ raster grids. Separate geologic maps were downloaded for Africa, the Arabian Peninsula, Australia and surrounding islands, Europe, Northeast Asia, Southeast Asia, South Asia, North America, South America, Iran, and the former Soviet Union. Areas mapped as “sedimentary” and “Miocene” or younger were selected from each map to represent lowlands by rasterizing the appropriate polygons. This age threshold was chosen to discriminate uplands from lowlands because in North America these units usually define the extent of unconsolidated sand and gravel deposits [Soller et al., 2009] (described in section 3.1 and shown in Figures 2b and 2c). Furthermore, sediments of this age are typically too young to have been buried, lithified, and exhumed back to the surface. In addition to these young sediments, we also included undifferentiated Cenozoic deposits as lowlands. The largest such unit is the Andean foreland basin, which in most locations has unconsolidated sediments at least hundreds of meters thick based on seismic surveys and well observations [e.g., Horton and DeCelles, 1997]. Even though maps for different regions are not always consistent (e.g., the geological map of North America is more detailed than for the rest of the world), there is generally continuity between classifications of rock types and age categories across map boundaries, and there are few visible discontinuities in the resulting lowlands mask (Figure 3).

For Canada and the U.S., surficial geologic maps [Fulton, 1995; Soller et al., 2009] were also used to refine the identification of uplands and lowlands. Specifically, areas of continuous surficial deposits were considered lowlands, while areas of discontinuous surficial deposits were considered uplands. In general, this means that areas of unconsolidated sedimentary deposits, glacial, lacustrine, coastal, eolian, and spatially continuous glacial sediments are considered as lowlands and areas with residual materials, colluvium, rock outcrop, and discontinuous glacial deposits are considered uplands. Bringing to bear additional data for these countries is appropriate because they contain large areas of Quaternary glacial deposits (often tens of meters thick) but are underlain in most areas by pre-Miocene geologic units that would classify them as uplands based on age criteria from bedrock geologic maps alone. The Fulton [1995] and Soller et al. [2009] maps differentiate among locations where surficial materials are derived from weathering of the bedrock beneath them (consistent with the definition of uplands) and where they are derived from source regions elsewhere and are transported to where they are deposited by water or wind (i.e., lowlands).

One limitation of the digital geologic map data are their relatively low resolution in many parts of the world. Because the upland versus lowland distinction proves crucial to the accuracy of the data set, we sought to improve the accuracy of this classification using additional criteria besides geologic age and type. Depositional areas often occur at relatively low elevations, so we tried using combinations of elevation and its derivatives (i.e., slope and curvature) to refine the classification. However, we found this approach to be problematic because there were always counterexamples to any rule we tried. For example, many intramontane depositional basins (i.e., lowlands) exist at high elevations and many flat mesas have thin soils above bedrock. As a result, no simple elevation, slope, or curvature thresholds had the effect of improving the uplands versus lowlands classification in some areas without causing misclassifications to appear elsewhere. As an alternative to simple topographic criteria, we used the successive flow-routing algorithm of Pelletier [2008] globally at 30 arcsec pixel⁻¹ resolution to identify lowlands not resolved in the geologic maps. This iterative algorithm accepts a prescribed runoff depth as input and routes that depth of runoff across the landscape to predict a depth of flow using a combination of Manning's equation and conservation of discharge. Then, all areas above a threshold depth of flow (including large valleys and their adjacent floodplains) are classified as lowlands if they are not already classified as such using geologic criteria. The runoff depth for each pixel (10 mm) and the threshold depth for the identification of lowlands (30 m) were chosen because these parameters provided an optimal match with areas of continuous deposits in the U.S. as determined by Soller et al. [2009].

This algorithm, though, does not apply to glacial landscapes. In North America, we identified as lowlands all areas of continuous glacial deposits in the Soller et al. [2009] and Fulton [1995] maps. In Scandinavia, the extent of former glaciation was defined using Ehlers and Gibbard [2008]. We also used a threshold value of the Topographic Ruggedness Index (described in more detail in section 2.4) to map flatter areas of continuous glacial deposits as lowlands and steeper areas of discontinuous glacial deposits as uplands.

Finally, we used a combination of the MODIS-based land cover “climatology” [Broxton et al., 2014] and version 2 of the Global Land Cover by National Mapping Organizations (GLCNMO) land cover map [Tateishi et al., 2014] to mask out areas beneath oceans, lakes, and perennial ice. We modified portions of the GLCNMO v2 map within the Great Salt Lake basin because some areas of saline deposits were misclassified as snow/ice in that data set. The Broxton et al. [2014] land cover climatology data set has a ∼500 m resolution on the MODIS sinusoidal grid. For this project, it was regridded to a 30 arcsec pixel⁻¹ latitude/longitude grid using nearest-neighbor resampling. The GLCNMO v2 land cover map, which has a 15 arcsec pixel⁻¹ resolution, was similarly regridded to 30 arcsec pixel⁻¹.

2.1.2 Distinguishing Hillslopes From Valley Bottoms

The elevation data used in this study is a hybrid of the 3 arcsec pixel⁻¹ GDEM obtained from measurements of the Shuttle Radar Topography Mission (SRTM; Version 3) [Farr et al., 2007], and the 7.5 arcsec pixel⁻¹ version of the Global Multi-resolution Terrain Elevation Data 2010 (GMTED2010) produced by the U.S. Geological Survey (USGS) and the National Geospatial-Intelligence Agency (NGA) [Danielson and Gesch, 2011]. SRTM data were used everywhere they are available (from 56°S to 60°N), while GMTED2010 data were used everywhere else. We used bilinear interpolation to convert the 7.5 arcsec pixel⁻¹ GMTED2010 product to a 3 arcsec pixel⁻¹ product. We experimented with using data from version 2 of the global DEM produced by the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) satellite. However, we found this product to have significant variations in fine-scale roughness among satellite tracks. Such variations produced significant spatial variations in computed terrain slopes and curvatures, even after filtering was performed to minimize this effect. Our merged SRTM-GMTED2010 terrain data set was analyzed as approximately 20,000 1° × 1° tiles (global coverage is 22,702 tiles but we did not include Antarctica).

As noted in section 1.2., hillslopes and valley bottoms differ in terms of the efficiency with which water drains from them. Valley bottoms also tend to have thicker sedimentary deposits, and the thickness of those deposits tends to increase with increasing valley bottom width. As such, it was necessary to distinguish between hillslopes and valley bottoms at high resolution globally.

Most existing methods for distinguishing hillslopes and valley bottoms in DEMs rely to one extent or another on contributing area as a mapping criterion, with areas of larger contributing area classified as valley bottoms and areas of lower contributing area classified as hillslopes. This is problematic because it guarantees that portions of the landscape with large contributing areas will be classified as valleys regardless of their morphology, i.e., whether or not they are portions of the landscape where the flow of water and sediment is localized. To solve this problem, Pelletier [2013] developed a technique for drainage network identification that uses only contour curvature (i.e., the curvature of contour lines) to distinguish hillslopes from valley bottoms. In this method, DEMs are filtered to remove small-scale noise using the Optimal Wiener Filter, the contour curvature is computed at every pixel, and valley heads are identified as the areas closest to the divides where the contour curvature (in units of length⁻¹) exceeds a user-defined threshold value. Once valley heads are identified, a multiple-flow-direction routing algorithm is used to identify the valley bottom downstream from each valley head. In the original paper describing this method, Pelletier [2013] included a second parameter to terminate valley bottoms in areas where flow becomes sufficiently unconfined or distributary. We did not use that component of the method in this study because it is essential only for those areas with discontinuous fluvial networks. Such areas are relatively rare on Earth's surface.

We used the method of Pelletier [2013] to distinguish hillslopes and valley bottoms using a threshold contour curvature of 0.00003 m⁻¹. This value was chosen because it was found, by visual comparison, to lead to an optimal identification of the valley network in two example 1° × 1° tiles as discussed in section 3.1.2. We applied this algorithm in parallel on the University of Arizona High-Performance-Computing cluster to map hillslopes and valley bottoms at 3 arcsec pixel⁻¹ resolution, resulting in a seamless global map of valley bottoms and their contributing areas.

Grids distinguishing hillslopes and valley bottoms at 3 arcsec pixel⁻¹ resolution were used to compute the fraction of area within each 30 arcsec pixel composed of hillslopes. The land area of each 3 arcsec pixel mapped as hillslopes was then summed to estimate the fraction of area within each 30 arcsec pixel composed of hillslopes. However, not all of the areas of 3 arcsec pixels mapped as valley bottoms are actually valley bottoms. Many small drainage basins have valley bottoms that are ∼1–10 m wide that are not resolvable at 3 arcsec pixel⁻¹ scales. To account for this fact, we identified all valley bottoms that were mapped as a single pixel wide at 3 arcsec pixel⁻¹ resolution, and estimated the bottom widths, w, of those valleys using a power-law relationship of contributing area, A, measured in units of km²:

$urn:x-wiley:19422466:media:jame20243:jame20243-math-0001$ (1)

where b = 0.4 and c = 3 m are the most representative values based on analyses of small upland fluvial valleys [Whipple, 2004]. That is, width is assumed to be 3 m for a drainage basin of contributing area 1 km² and increases as the 0.4 power of contributing area. While not perfect, this approach is better than the alternative of assuming that all valley bottoms are greater than or equal to ∼90 m in width globally.

2.2 Estimating Soil and Regolith Thicknesses on Upland Hillslopes

2.2.1 Soil

Mathematical models have been developed that successfully predict the spatial variation of soil thickness in uplands at hillslope-to-watershed scales [Pelletier and Rasmussen, 2009a; Crouvi et al., 2013]. These models quantify soil thickness as the long-term balance between the production of soil by the physical breakdown of bedrock into soil, and the erosion of that soil from the hillslope by sediment transport processes on hillslopes. The transport of soil on hillslopes is, to first order, proportional to the topographic gradient. This assumption, combined with conservation of mass for soil on hillslopes, implies that the erosion rate, E, on hillslopes is proportional to topographic curvature [e.g., Culling, 1963; Pelletier, 2008]:

$urn:x-wiley:19422466:media:jame20243:jame20243-math-0002$ (2)

where z is the local elevation and κ is a coefficient with units of L² T⁻¹. Geomorphologists have also learned over the past 20 years that the rate of soil production from bedrock, P, at a point on a hillslope declines with increasing soil depth, h [e.g., Heimsath et al., 1997]:

$urn:x-wiley:19422466:media:jame20243:jame20243-math-0003$ (3)

where h₀ is a constant approximately equal to 0.5 m. In equation 3, the rate of soil production is a maximum for bare bedrock hillslopes. The maximum rate, P₀, depends on water availability, quantified here as mean annual rainfall. Over geologic time scales, the production and erosion of soils on hillslopes exist in an approximate balance. Assuming this balance, i.e., equating equations 2 and 3 and solving for h, yields an expression for the average soil depth on hillslopes in which soil depth is proportional to the logarithm of the inverse of hillslope curvature:

$urn:x-wiley:19422466:media:jame20243:jame20243-math-0004$ (4)

The argument of the ln function, through P₀, depends on climate [Pelletier and Rasmussen, 2009b].

Equations (2)–(4) provide a basis for using topographic curvature and mean annual rainfall to estimate soil thickness on upland hillslopes. We used the CONUS-Soil data set of Miller and White [1998] to calibrate the relationship among upland hillslope soil thickness, h_uh, mean upland curvature (computed at 3 arcsec pixel⁻¹ resolution but averaged within each 30 arcsec pixel), and mean annual rainfall, R, as

$urn:x-wiley:19422466:media:jame20243:jame20243-math-0005$ (5)

where h₀, a, b, c, and R₀ are constants. A value of b equal to 1 makes equation 5 equivalent to equation 4 in terms of the dependence of soil thickness on topographic curvature. We added the possibility of b not being equal to 1 to provide greater flexibility to the model. The power-law relationship between soil thickness and mean annual rainfall is only one possible relationship between soil thickness and climate. We chose to use mean annual rainfall rather than mean annual precipitation based on the evidence that both increased water availability and increased temperature above freezing drive weathering of bedrock into soil [Rasmussen et al., 2005]. We used the monthly historical mean temperature and precipitation grids of Hijmans et al. [2005] to estimate mean annual rainfall globally at 30 arcsec pixel⁻¹ resolution. Precipitation that fell on months with mean temperatures above zero was assumed to fall as rain. These values were summed for each pixel to derive the grid of R values. Using calibrated values for h₀, a, b, c, and R₀, equation 5 was used predict the mean soil thickness on upland hillslopes globally.

It is important to note that equations (2)–(4) apply to weathering-limited hillslopes as well as the transported-limited hillslope pictured in Figure 1a. To see this, consider the idealized weathering-limited hillslope pictured in Figure 1b. In the transport-limited case of Figure 1a, local soil thickness depends on the local topographic curvature or the Laplacian of elevation [Dietrich et al., 1995; Pelletier and Rasmussen, 2009a]. We know of no general rule regarding whether it is the upper or lower portions of the slope that have thicker soils: it simply depends on the magnitude of the local curvature. In the weathering-limited case, the landscape is often stepwise in form. Weathered material is removed from the steepest portions of the landscape, leaving bedrock exposed (this is the definition of weathering limited). However, these steep slopes are also areas of large negative curvature as gentler slopes suddenly transition to steep (sometimes vertical) slopes. As such, equation 4, which is based on topographic curvature and predicts thin soils where curvature has a large negative value, correctly predicts the absence of soil in the steep, weathering-limited portions of typical arid-region hillslopes. Crouvi et al. [2013] have shown that equation 4 and more general curvature-based equations for predicting the distribution of soil across landscapes apply to weathering-limited landscapes in the Mojave Desert. In short, equation 4 applies to both transport-limited and weathering-limited cases.

High-resolution soil thickness data from the European Soils Database (ESDB) (distributed as part of the Harmonized World Soils Dataset) [FAO/IIASA/ISRIC/ISSCAS/JRC, 2012] were used to validate the upland soil thickness data. Specifically, errors were quantified by computing the percent of successful predictions of soil depth within the specific soil depth ranges of the ESDB for each 30 arcsec pixel. We calibrated equation 5 to conterminous U.S. data and validated to European data because the European Soils Database (ESDB) provides more limited resolution than the CONUS-Soil data. Soil thicknesses in the ESDB are grouped into intervals of 0.0–0.4 m, 0.4–0.8 m, 0.8–1.2 m, and >1.2 m, while CONUS-Soil data have decimeter resolution.

2.2.2 Regolith

Rempe and Dietrich [2014] argued that the thickness of regolith in uplands is equivalent to the depth to the permanent water table because most physical and chemical weathering mechanisms/agents require cycles of wetting and drying. In this study, we used the 30 arcsec pixel⁻¹ equilibrium water table depth raster data set of Fan et al. [2013] to estimate the depth to the permanent water table and hence the thickness of regolith in uplands, following the Rempe and Dietrich [2014] model.

We should state at the outset that we have less confidence in our ability to estimate regolith thickness than we have for any other variable in the data set. Part of this uncertainty stems from the lack of global data sets to leverage for model calibration and validation. There is, however, a growing consensus among critical zone scientists (driven largely by recent shallow seismic refraction and scientific drilling studies) that regolith thicknesses are typically in the range of 10–40 m, with thicker regolith values usually occurring beneath topographic divides and thinner values beneath valley bottoms [Holbrook et al., 2014, Parsekian et al., 2015; St. Clair et al., 2015]. Given the importance of the intact regolith layer as a reservoir for water that plants can tap during droughts, we believe it is more beneficial than not to place what constraints we can on the thickness of regolith (with caveats).

We should also note that the regolith thickness grid we present is an approximate upper bound, one that is likely close to the actual value in semihumid and humid regions but that may be far larger than actual values in semiarid and arid regions. In arid climates where water table depths can reach hundreds of meters and where the water table is generally below the elevations of both hillslopes and valley bottoms, it is likely that properties besides water table depth limit regolith thickness. The Rempe and Dietrich [2014] model is a “bottom-up” control on regolith depth. In arid environments, regolith thickness may be limited by the “top-down” propagation of weathering from the surface to the subsurface. In such cases, landscape age, climate, and bedrock weatherability can all be expected to play a significant role in controlling regolith thickness.

The Fan et al. [2013] data set maps the equilibrium water table globally, not the low or permanent water table observed during the driest months and invoked by the Rempe and Dietrich [2014] model. In the supporting information, we demonstrate the suitability of using the Fan et al. [2013] equilibrium water table map as an estimate for the permanent/low water table. Using mean monthly data from all USGS groundwater wells that tap bedrock and that have at least 3 years of data (204 wells), we show that the median difference between the equilibrium and permanent water table depth is 8% (less if very shallow water tables that likely are lowlands are excluded from the analysis). As such, the equilibrium water table is a reasonable proxy for the permanent water table within the context of our analysis, which seeks to place approximate constraints on regolith thickness.

As a 30 arcsec resolution product, the Fan et al. [2013] data set we used to create the regolith thickness layer generally does not resolve many of the low-order valleys in uplands where water table depths often go to zero. To account for this resolution issue, we divided the water table depths of Fan et al. [2013] by a factor of 2 to reflect the fact that the average water table depths will generally vary within 30 arcsec pixels from a maximum value given by Fan et al. [2013] to zero near valley bottoms. After application of this factor, the range of predicted regolith thickness in uplands is consistent with typical values (10–40 m) inferred from seismic refraction surveys [e.g., Holbrook et al., 2014, Parsekian et al., 2015; St. Clair et al., 2015], except in arid and semiarid upland regions, where values as high as 50 m are common.

2.3 Estimating Sedimentary Deposit Thickness on Upland Valley Bottoms

Upland valley bottoms are areas that have undergone net erosion over geologic time scales but are often infilled with sedimentary deposits as a result of Quaternary climatic changes that have episodically delivered large volumes of sediment from hillslopes to valley bottoms that are not adjusted to transport such high sediment loads [e.g., Bull, 1991; Pelletier, 2014]. As a result, many of these valley bottoms are filled with meters to tens of meters of sediment above bedrock. In the absence of detailed geophysical or well data, a common means of estimating the thickness of sedimentary deposits in valley bottoms is to project the side slopes down below the valley bottom, assuming that the bedrock surface has a U or V shape. The thickness of sedimentary deposits is then estimated as the difference between the topographic surface and the projected bedrock surface beneath it. This approach has been widely used at a variety of spatial scales [e.g., Wheeler, 1984; James, 1996; Schrott et al., 2003; Gartner et al., 2008; Straumann and Korup, 2009].

To estimate the thickness of sedimentary deposits in valley bottoms, we used the curvature of the valley bottom and the gradient of the hillslopes flanking the valley to estimate the average thickness of upland valley bottom sedimentary deposits, h_uv, assuming that the side-slopes project down to a V shape in the subsurface (a V shape was used because of the predominance of fluvial processes globally) (Figure 1b):

$urn:x-wiley:19422466:media:jame20243:jame20243-math-0006$ (6)

where $urn:x-wiley:19422466:media:jame20243:jame20243-math-0007$ is the slope gradient on hillslopes and $urn:x-wiley:19422466:media:jame20243:jame20243-math-0008$ is the valley-bottom curvature (i.e., the Laplacian). Equation 6 was derived from the schematic diagram in Figure 1b. In this figure, the infilled valley bottom is approximated as a parabola defined by the valley-bottom curvature, $urn:x-wiley:19422466:media:jame20243:jame20243-math-0009$ , and the maximum depth of bedrock beneath the valley bottom is computed by solving for the horizontal distance from the valley centerline where the slope of the parabola matches that of the most planar segment of the hillslope. We then approximated the average sedimentary deposit thickness as half of the maximum thickness assuming a triangular geometry for the valley infill. Equation 6 was applied at the 30 arcsec resolution using averages of hillslope gradient and valley-bottom curvature within each pixel computed at 3 arcsec resolution.

In the United States, DTB data are collected by state geological surveys as part of their standard groundwater well data sets. These data sets commonly have tens of thousands of wells per state, many of these wells are located in valley bottoms where soil pits cannot reach bedrock, and many of these wells have driller's logs available in digital form that record DTB. We compiled groundwater well data sets for as much of the conterminous U.S. as a means to validate the predictions of equation 6. This validation procedure is described in more detail in sections 2.4 and 3.3. We defer the discussion to those sections because the water well data also play a central role in calibrating and validating the data for sedimentary deposit thickness in lowlands.

2.4 Estimating Sedimentary Deposit Thickness in Lowlands

To estimate the sedimentary deposit thickness in lowlands, a 30 arcsec pixel⁻¹ grid of Topographic Ruggedness Index (TRI) [Riley et al., 1999] was first generated. TRI is the average elevation difference among a central pixel and its eight neighbors, and thus gives a measure of terrain relief at the pixel scale. To generate the TRI map, the GDEM data was first regridded to 30 arcsec resolution (which is the resolution of our soil and sedimentary deposit thickness product). Then, the utility program gdaldem (part of the Geospatial Data Abstraction Library (GDAL)) was used to generate the map of TRI.

We used DTB observations from groundwater wells to calibrate a predictive model for DTB as a function of TRI. Sedimentary deposit thicknesses measured in wells can be at least an order of magnitude deeper than soil depths given in the STATSGO data set. For example, in New York and Pennsylvania, the median sedimentary deposit thickness measured in 33,000 New York wells and 137,500 Pennsylvania wells are 9.1 and 7.9 m, even though New York is largely covered, and Pennsylvania is almost entirely covered, by STATSGO polygons that show soil depths to be less than 1.5 m. This underscores the need to consider hillslopes and valley bottoms separately in order to accurately estimate soil and sedimentary deposit thickness in these different landscape types.

Two types of well data are used to calibrate and validate the lowland sedimentary deposit thickness data. The first type is high-density well data for New York, Pennsylvania, Kentucky, and Indiana state geological surveys (Figure 4a). These states were chosen for analysis because well data were readily available in digital form and because they represent a variety of topographic and geologic environments. The data combined from these four states contain DTB measurements, and these data were used for calibration of the lowland sedimentary deposit thickness model. We also used the USGS Groundwater Dataset, a sparser but more spatially expansive well data set (Figures 4b and 4c). Specifically, we collected metadata about the wells from the USGS's site Information webpage, which contains information about well depths, and the unit that the well penetrates to. Although DTB is not explicitly recorded in this data set, the well information can be cross-referenced using the aquifer codes to determine the age and type of the deepest unit that the well penetrates. Therefore, we can reasonably conclude which well do or do not penetrate into bedrock, which, along with well depth information, gives estimates of upper or lower bounds of the bedrock surface in different places. For this study, we considered wells that penetrate to geologic units that are Miocene or younger as not penetrating bedrock, and wells that penetrate to geologic units that are older than Miocene age as penetrating into bedrock (consistent with our classification of uplands versus lowlands). Due to the inexact nature of the DTB estimates given by this data set, this data set is only used for validation of the lowland sedimentary deposit thickness data.

2.5 Combining Soil/Sedimentary Deposit Thicknesses Into an Averaged Product

For lowland areas, there is a single estimate of sedimentary deposit thickness for both hillslopes and valley bottoms. For uplands, however, there are two soil/sedimentary deposit thickness values for every pixel: one for hillslopes and one for valley bottoms, plus a fraction of the area of each pixel composed of hillslopes versus valley bottoms. For users who prefer to work with a single thickness value within each 30 arcsec pixel, we combined the soil thickness values estimated for upland hillslopes together with the values estimated for sedimentary deposit thickness on upland valley bottoms to obtain a single weighted-average value for the relatively porous and unconsolidated material. Weighing the hillslope and valley bottom estimates based solely on the fraction of area in each yields a product very similar to the soil thickness map for upland hillslopes because hillslopes comprise the vast majority of upland area (>90% in many areas). However, from a hydrologic or recharge point of view, the sedimentary deposit thickness on valley bottoms may be as relevant as or more relevant than soil thickness on hillslopes because all of the water discharged from a drainage basin is routed through the valley bottoms. That is, the time that each parcel of water interacts with valleys is larger than their area fraction would suggest, because all water that does not infiltrate is routed through valleys. To honor this fact, our average soil/sedimentary deposit thickness on uplands, h_av, was computed by weighing the thickness values on hillslopes and valley bottoms by both the area fraction and the topographic wetness index (TWI) of hillslopes and valley bottoms (defined as the natural logarithm of the unit contributing area divided by the slope gradient):

$urn:x-wiley:19422466:media:jame20243:jame20243-math-0010$ (7)

where f represents the area fraction of hillslopes versus valley bottoms and the subscript h represents the values for hillslopes and v represents the values for valley bottoms.

Figure 5 summarizes the workflow used to create the data set. Tasks are illustrated using rectangles and input and output data sets are illustrated using ovals.

3 Results

3.1 Distinguishing Among Lowlands, Upland Hillslopes, and Upland Valley Bottoms

3.1.1 Distinguishing Uplands From Lowlands

The global distribution of Quaternary, Neogene, Paleogene, and undifferentiated Cenozoic sediments are shown in Figure 2a. The mapped Quaternary sediments are widespread on most of the continents and occur in regions known to have deep sedimentary deposits. There are also widespread areas with sedimentary units that are mapped as Pliocene and Miocene age (in North America) or simply “Neogene” (outside North America), as well as Paleocene-Oligocene age (in North America) or simply “Paleocene” (outside North America). Note that the WPA data do not show any Cenozoic units underlying much of the area covered by ice during Quaternary glaciations, despite the fact that some of these areas have thick till and other glacial sediments.

Within the U.S., and in areas that were not covered by ice during Quaternary glaciations, the sedimentary units that are Quaternary or Neogene in age in the WPA classification do not extend significantly beyond areas that are covered with continuous sedimentary deposit, lacustrine, coastal, or eolian sediments in the higher resolution surficial deposits map of Soller et al. [2009] (Figures 2b and 2c). In fact, only about 10% of the spatial extent of uplands (as suggested by discontinuous surficial deposits of colluvium and residual materials) is collocated with these units. By contrast, if Paleogene sediments in the WPA maps are included, then 25% of the upland area is collocated with these units and there are clear visual discrepancies between Paleogene units and the lowland surficial deposits, suggesting that Paleogene sediments should not be included in our lowland classification.

At the same time, the Quaternary and Neogene units in the WPA map are insufficient to characterize all the lowland deposits in the Soller et al. [2009] map, as these units only cover 63% of the lowland deposits. Visually, there is good agreement between the large expanses of lowlands in the Soller et al. [2009] map and these units (e.g., in the Great Basin, in the high Plains, and along the Gulf Coast). However, upon closer inspection, many smaller-scale features are missing. Notably, along large rivers, the Soller et al. [2009] map shows sedimentary deposits along the river plains that are absent in WPA data. These are especially noticeable in the southern Great Plains, and in other relatively flat regions that are not covered by expansive lowland deposits. The successive-routing algorithm of Pelletier [2008] captures many of these lowland areas. This addition improved the lowland classification, but the resulting map is still somewhat biased toward uplands. Overall, the Quaternary and Neogene units in the WPA map plus the area classified as lowland by the successive-routing algorithm correctly classify ∼70% of lowland deposits, as well as 87% of upland deposits in the Soller et al. [2009] map.

Figure 2d shows the spatial distribution of upland versus lowland deposits in regions that were covered by continental ice sheets. It is harder to distinguish between uplands and lowlands in areas that were covered by ice during Quaternary glaciations. However, an optimal threshold of TRI equal to 11.5 m results in 66% of the lowland deposits being classified as lowland and 66% of upland deposits being classified as upland. There are clear disagreements (e.g., in New England and the interior regions of British Columbia), but there is also broad agreement through much of the center of the continent. As mentioned in section 2.1.1., this threshold is only applied extensively to the glaciated area of Scandinavia, as the Soller et al. [2009] and Fulton [1995] maps are used directly to identify upland versus lowland areas in North America. The resulting global cover map for both glacial and nonglacial terrains is shown in Figure 3.

3.1.2 Distinguishing Hillslopes From Valley Bottoms

Figure 6 shows examples of the classification of hillslopes versus valley bottoms for two of the approximately twenty thousand 1° × 1° land-surface tiles of the global analysis we performed. These example tiles were picked essentially at random but they nicely show the results of the Pelletier [2013] algorithm on different types of landscapes, i.e., a high-relief Basin-and-Range landscape in southern California and a lower-relief landscape of variable dissection/drainage density in the Great Plains. In both cases, the method performs well in classification based on a visual comparison with the shaded relief maps of Figures 6a and 6b. In the basin floor of Figure 6a, the method captures the broad, unconfined nature of flow on distributary alluvial fans.

Figure 7 shows a color map of the fraction of each 30 arcsec pixel composed of hillslope versus valley bottom. Lakes are treated as hillslopes for the purposes of this map (our data set contains a cover map that includes all lakes so it would be straightforward for users to treat lakes in a different way). The fraction hillslope map is nearly 1 in many low-relief landscapes, which tend to have a low drainage density. The hillslope fraction decreases significantly below 1 in areas of large rivers and in mountainous areas, where a larger density of valleys penetrate the landscape.

3.2 Estimating Soil Thickness on Upland Hillslopes

Figure 8 plots the average soil thickness from the CONUS-Soil data set of Miller and White [1998] as a function of the negative of the Laplacian (i.e., the convex curvature) and mean annual rainfall (MAR). To make these plots, all of the soil thickness values for each bin of hillslope curvature and MAR were averaged before plotting. These plots document a systematic decrease in the mean soil thickness with increasing negative curvature, consistent with the process-based modeling that has been successful at predicting spatial variations in soil thickness at watershed scales referenced in section 3.2 [e.g., Pelletier and Rasmussen, 2009a]. At a given value of hillslope curvature, more arid climates tend to have thinner soils or depth to paralithic contact, consistent with the fact that soil production rates are limited by water availability in arid regions. The solid lines in Figure 8 are the predictions of equation 5 with h₀ = 2 m, a = 0.01 m⁻¹, b = 0.1, and R₀ = 1000 mm yr⁻¹, c = 0.2. These values were not obtained from a least squares minimization but instead were adjusted to obtain the best visual match between data and model using trial and error. We used equation 5 with the above mentioned parameter values to predict upland soil thickness globally. Note that mean soil thickness values lose accuracy as they approach 1.5 m because in the CONUS-Soil data set relies on soil surveys that have a limited depth range.

The predicted upland hillslope soil thickness map is presented as a color map in Figure 9. Areas of inland water and perennial ice are assigned values of zero. Following equation 5, soils are generally thicker, i.e., 1–2 m, in areas of more humid climates and/or lower-relief topography and generally thinner, i.e., 0.2–1 m, in mountain ranges where erosion can better keep pace with soil production. Because these data were calibrated based on topographic and climatic criteria, and soil thickness is known also to depend on bedrock properties (e.g., mineralogy and fracture density) at all spatial scales, Figure 9 likely underpredicts the spatial variability in soil thickness values. However, as the validation described in the next paragraph demonstrates, the data illustrated in Figure 9 predict the average soil thicknesses and their variations with topography and climate reasonably well.

Figure 10 illustrates the results of the validation test of the upland hillslope soil thickness predictions against data from the European Soil Database. The model correctly predicts the thickness class (i.e., 0–40, 40–80, 80–120, and >120 cm) of 34% of the upland areas in Figure 10. The model correctly predicts an additional 48% (or a total of 82%) to within a difference of one thickness class. The predicted values differ from observed values by more than one thickness class in 18% of cases. Note that, in cases where the predicted and actual thicknesses differ by one thickness class, the difference between the predicted and actual values might be quite small (e.g., a predicted value of 38 cm versus an actual value of 42 cm, or vice versa).

The supporting information presents a color map of regolith (soil plus intact regolith) thickness obtained using the methods described in section 2.2.2.

3.3 Estimating Soil Thickness Upland Valley Bottoms and Lowlands

Sedimentary deposit thicknesses in lowlands are difficult to predict because they depend on local geologic factors that are poorly constrained on a global basis. However, as in the case of upland valley bottoms, lowland areas of lower relief tend to have thicker sedimentary deposits, on average. To calibrate the relationship among sedimentary deposit thickness and topographic factors, we analyzed hundreds of thousands of groundwater wells from lowland areas in the U.S. We analyzed well data from New York, Pennsylvania, Indiana, and Kentucky (states which represent a range of geologic histories and have readily available digital well data) (Figure 2). Figure 11 shows the inverse relationship between soil thickness (between 0 and 50 m) and curvature (measured via Topographic Ruggedness Index, TRI) at the 1 km scale.

The empirical model used to predict lowland sedimentary deposit thickness or DTB was calibrated using well data from individual U.S. states and validated using well data nationwide using the USGS well data set. Using these well data, we found a significant inverse correlation between DTB and TRI. Figure 11a shows the relationship between TRI and DTB measured in boreholes located in New York, Pennsylvania, Kentucky, and Indiana. Indiana and Kentucky have been divided into two regions since the southwestern corner of Kentucky is underlain by Cenozoic sediments (which range in age from lower Ordovician-Quaternary) and large portions of Indiana are covered in glacial sediments. In Kentucky, the region with Cenozoic bedrock clearly has deeper DTB (>50 m) than virtually all the rest of the state (which in general, has relatively shallow [<5 m] bedrock). In Indiana, the region with glacial deposits generally has large DTB values, in many cases exceeding 50 m. Areas with no glacial deposits have much smaller DTB.

In general, the relationship between DTB and TRI follows a negative exponential curve. The error bars in Figure 11a show the 25th to 75th percentile spread for each data grouping in terms of both DTB and TRI. Figures 11b–11g show that the distribution of DTB for each state that is produced by the model is a reasonable approximation of the actual distribution of DTB from the well data (with the exception of young sediments in western Kentucky). This suggests that this model does an acceptable job of reproducing the statistical properties of upland valley bottom and lowland DTB for these areas. However, the spatial agreement between modeled and measured DTB is less good when comparing individual kilometer grid boxes. Figure 12 shows that the magnitudes of measured and predicted DTB are similar for Kentucky and Pennsylvania, though the exact spatial positioning of variations of predicted DTB can vary between measurements and predictions. For example, along the Kentucky transect shown, the location of deepest modeled DTB occurs a little to the west of the location of deepest measured DTB. These small-scale spatial mismatches are unsurprising because at such scales one would not expect that surface topography perfectly reflects subsurface geologic structure, though there is clearly a relationship at larger scales. Overall, there is a relatively high degree of statistical similarity between the measured and modeled DTB, though a lower degree of point-wise similarity. For example, the interquartile ranges (25th to 75th percentiles) for modeled and measured DTB are 2.6–8.7 and 4.5–11.2 m for Pennsylvania and 2.4–7.0 and 2.5–10.3 m for Kentucky, but the mean absolute error between measured and observed DTB for both states is ∼6 m (which is relatively high compared to the average DTB of 7.8 m in Kentucky and 9.3 m in Pennsylvania) (Table 1).

Table 1. Predicted Versus Observed Median and Interquartile Values (25th and 75th Percentiles) for Upland Valley and Lowland DTB/Sedimentary Deposit Thicknesses (m) for the Four States Analyzed

	New York		Pennsylvania		Kentucky		Indiana
	Obs.	Pred.	Obs.	Pred.	Obs.	Pred.	Obs.	Pred.
Upland valley
Q75	1.8	1.3	4.2	3.5	2.1	1.4	2.4	5.0
Median	7.2	2.7	7.0	6.4	3.3	4.7	4.9	9.0
Q25	19.0	6.1	12.1	11.0	5.8	10.3	8.5	15.4
Lowland
Q75	4.3	4.9	5.2	6.0	3.3	10.0	8.2	19.0
Median	9.1	8.2	9.1	9.2	5.5	18.1	15.5	27.4
Q25	18.6	14.9	16.7	14.7	16.4	32.5	26.2	37.1

The regression model of Figure 11a is also reasonably successful at predicting DTB across the rest of the conterminous U.S. When compared with the upper and lower DTB bounds determined from the USGS well data set, the predicted bedrock surface is below the bottoms of 74.3% of wells that are in Miocene age or younger sediments (condition 1) and is above the bottoms of 70.1% of wells that are in rocks that are older than Miocene age (condition 2). For comparison, a constant DTB that maximizes both conditions 1 and 2 (28 m) only satisfies the first condition 55.8% of the time and it satisfies the second condition 53.3% of the time.

Figure 13 shows a color map of sedimentary deposit thicknesses in upland valley bottoms and lowlands. This map was made using equation 6 (for upland valley bottoms) and the sedimentary deposit thickness/DTB relationship with TRI plotted in Figure 11. In low-relief areas including the Great Plains and lower Mississippi Valley (Figure 13b), sedimentary deposit thickness is generally predicted to be greater than or equal to 50 m. Sedimentary deposit thickness decreases to ∼10 m in more rugged terrain, including the mountain ranges of the Basin and Range, where the narrow upland valley bottoms limit the accommodation space for the sedimentary deposit infilling, and the glaciated regions of New England and upstate New York, where deposition of glacial till was of limited thickness due to the rugged nature of the topography over which glaciers were flowing.

3.4 Combining Soil/Sedimentary Deposit Thicknesses Into an Averaged Product

The thickness of soil and sedimentary deposits varies greatly down to scales of tens to hundreds of meters, i.e., from hillslopes to valley bottoms, within a drainage basin. As such, any single estimate of soil depth at a 30 arcsec (or coarser) resolution will necessarily be highly simplified. The best use of the data set described in this paper is to treat hillslopes and valley bottoms separately within each grid cell using, for example, the tile method approach to sub-grid-scale parametrization [Avissar and Pielke, 1989; Koster and Suarez, 1992]. However, for users who want a single averaged value, we have provided a map that represents our best estimate of the thickness of highly porous material above weathered bedrock at the 30 arcsec scale (Figure 14). We did not include intact regolith in this average product due to the greater uncertainty associated with those data. As such, the upland thickness values in this grid underestimate the full extent of the water storage zone of upland hillslopes. Nevertheless, this grid is expected to be accurate in terms of predicting the partitioning of rainfall into Hortonian runoff and infiltration, since this partitioning is primarily a function of the properties of soil (on uplands) and sedimentary deposits (on lowlands).

4 Discussion

4.1 Limitations of the Data Set

The soil, intact regolith, and sedimentary deposit thicknesses in this data set represent what is, in nature, often a gradual transition. Porosity and/or mechanical strength often vary gradually with depth below the surface and such variation can, in some cases, be approximated by an exponential function [e.g., Saar and Manga, 2004; Jiang et al., 2010]. For this reason, it may be reasonable for some applications of this data set to treat the thickness values we report as the characteristic length scale of a smooth function (e.g., exponential) characterizing the material hydrologic properties. More broadly, additional research is needed to determine how best to use the data presented herein in hydrologic and ecosystem models. The answer to that question may vary among applications or aspects of Earth's critical zone being addressed within a particular application.

Our assumption of V-shaped valleys does not work well in alpine glacial valleys. In such cases, the assumption of a V shape tends to overestimate the thickness of sedimentary deposits on the valley floor. The inaccuracy of the V-shaped valley assumption in formerly glaciated valleys is one reason why we limited the range of thicknesses predicted by the data set to a maximum of 50 m (knowing that in a wide glacial valley with steep side slopes, alluvial thicknesses predicted assuming a V shape will be an overestimate that, in many cases, will be greater than 50 m). Also, it is important to note that alpine glaciers covered only a small percentage of Earth's surface during the Quaternary (landscapes formerly covered with ice sheets are handled as a subclass of lowlands in our approach, so the U-shaped valley assumption for upland valley bottoms is an issue only for mountainous/alpine areas). It is also important to note that, in places where both the land surface and the bedrock surface beneath it are parabolic, there is no way to place any constraints on the thickness of sedimentary deposits using surface morphology. Using a V shape, one can project the side slopes below the valley fill in a unique manner given the surface morphology. Our calibration and validation procedures make use of data primarily from midlatitude regions. As such, it is likely that the dataset described in this paper has limited accuracy at high latitudes and other areas of climate extremes. We will seek to test the dataset against new data as they are made available and we anticipate focusing on high latitudes especially as we improve the dataset for future releases.

4.2 Future Applications of the Data Set

The data set we have constructed provides thickness information without self-consistent estimates of soil hydrologic parameters such as permeability and drainable porosity. We are currently working to provide such estimates via forward modeling. Global maps of soil texture are being used to derive pedon-scale estimates of permeability and drainable porosity via pedotransfer functions [Schaap et al., 2001]. These values are then being scaled with a tunable coefficient to represent the fact that field-scale hydrologic properties (which are controlled, in part, by macroporosity not accounted for in pedotransfer functions) are generally larger than pedon-scale properties. Calibration of the coefficient is being performed via comparison of the model to the observed hydrologic behavior of MOPEX catchments [Duan et al., 2006]. Such estimates of permeability and drainable porosity should complement available global data sets that estimate bedrock permeability [Gleeson et al., 2011].

4.3 Concluding Remarks

Despite the limitations described in section 4.1., the soil, intact regolith, and sedimentary deposit thicknesses presented here can be used to implement variable soil thicknesses in global models. For example, M. A. Brunke et al. (Implementing and evaluating variable soil thickness in the Community Land Model version 4.5 (CLM4.5), submitted to Journal of Climate, 2015) used this data set to determine a variable number of soil layers globally for 0.9° latitude × 1.25° longitude grid boxes in the Community Land Model version 4.5 (CLM4.5). The greatest impact was to grid boxes where the number of soil layers was reduced from the original constant 10 layers. In model experiments, the soil-moisture profiles of these grid boxes changed significantly. Hydrological fluxes such as base flow and surface runoff were impacted as well in those areas.

5 Conclusions

Quantifying the thicknesses of the relatively permeable soil, intact regolith, and sedimentary deposits above unweathered bedrock is important for quantifying the land surface moisture dynamics that strongly affect terrestrial ecosystems and carbon/water/energy cycles. Regional modeling has shown the climate system behavior to be sensitive to the thickness of these high-porosity layers. As such, it is important to quantify the thickness of high-porosity subsurface layers globally in order for Earth System Models to properly model subsurface water storage and ecosystem functioning. In this study, we used geomorphic models, calibrated with available high-resolution data sets for the United States (e.g., gridded versions of STATSGO soil data and sedimentary deposit thicknesses from groundwater wells) to develop a high-resolution (30 arcsec pixel⁻¹, i.e., approximately 1 km pixel⁻¹) global data set of soil, intact regolith, and sedimentary deposit thicknesses. The data set can be obtained upon request from the corresponding author and will be permanently archived at the Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC) for Biogeochemical Dynamics [Pelletier et al., 2016].

Acknowledgments

We thank DOE through award DE-SC0006773 and the NASA Terrestrial Ecology Program through cooperative agreement NNX13AK82A for financial support of this work. We also thank Ying Fan Reinfelder and an anonymous reviewer for helpful comments that improved the manuscript. The data set can be obtained upon request from the corresponding author and will be permanently archived at the Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC) for Biogeochemical Dynamics.

Supporting Information

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Erratum

In the originally published version of this article, the data set reference was not cited in the reference list. The reference list has since been corrected, and this version may be considered the authoritative version of record.

Citing Literature

Volume8, Issue1

March 2016

Pages 41-65

A gridded global data set of soil, intact regolith, and sedimentary deposit thicknesses for regional and global land surface modeling†

Abstract

Key Points:

1 Introduction

1.1 Problem Statement

1.2 Definitions and Conceptual Model

2 Methods

2.1 Distinguishing Among Lowlands, Upland Hillslopes, and Upland Valley Bottoms

2.1.1 Distinguishing Uplands From Lowlands

2.1.2 Distinguishing Hillslopes From Valley Bottoms

2.2 Estimating Soil and Regolith Thicknesses on Upland Hillslopes

2.2.1 Soil

2.2.2 Regolith

2.3 Estimating Sedimentary Deposit Thickness on Upland Valley Bottoms

2.4 Estimating Sedimentary Deposit Thickness in Lowlands

2.5 Combining Soil/Sedimentary Deposit Thicknesses Into an Averaged Product

3 Results

3.1 Distinguishing Among Lowlands, Upland Hillslopes, and Upland Valley Bottoms

3.1.1 Distinguishing Uplands From Lowlands

3.1.2 Distinguishing Hillslopes From Valley Bottoms

3.2 Estimating Soil Thickness on Upland Hillslopes

3.3 Estimating Soil Thickness Upland Valley Bottoms and Lowlands

3.4 Combining Soil/Sedimentary Deposit Thicknesses Into an Averaged Product

4 Discussion

4.1 Limitations of the Data Set

4.2 Future Applications of the Data Set

4.3 Concluding Remarks

5 Conclusions

Acknowledgments

Supporting Information

References

Citing Literature

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A gridded global data set of soil, intact regolith, and sedimentary deposit thicknesses for regional and global land surface modeling^†