Prediction of Topsoil Texture Through Regression Trees and Multiple Linear Regressions

Pinheiro, Helena Saraiva Koenow; Carvalho Junior, Waldir de; Chagas, César da Silva; Anjos, Lúcia Helena Cunha dos; Owens, Phillip Ray

doi:10.1590/18069657rbcs20170167

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Division 1 – Soil in Space and Time, Commission – Pedometry • Rev. Bras. Ciênc. Solo 42 • 2018 • https://doi.org/10.1590/18069657rbcs20170167 linkcopy

Prediction of Topsoil Texture Through Regression Trees and Multiple Linear Regressions

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Users of soil survey products are mostly interested in understanding how soil properties vary in space and time. The aim of digital soil mapping (DSM) is to represent the spatial variability of soil properties quantitatively to support decision-making. The goal of this study is to evaluate DSM techniques (Regression Trees - RT and Multiple Linear Regressions - MLR) and the ability of these tools to predict mineral fraction content under a wide variability of landscapes. The study site was the entire Guapi-Macacu watershed (1,250.78 km²) in the state of Rio de Janeiro in the Southeast region of Brazil. Terrain attributes and remote sensing data (with 30 m of spatial resolution) were used to represent landscape co-variables selected as an input in predictive models in order to develop the explanatory variables. The selection of sampling sites was based on the Latin Hypercube algorithm. A representative set of one hundred points with feasible field access was chosen. Different input databases were tested for prediction of mineral fraction content (harmonized and original data). The Spline algorithm was used to harmonize data according to the GlobalSoil. Net consortium standards. The results showed better performance from the RT models, using input from an average of six covariates; the simplest MLR model used twice as many input variables, creating more complex models without gaining precision. Furthermore, better R² values were obtained using RT models, irrespective of harmonization of soil data. The harmonized dataset from the 0.00-0.05 and 0.05-0.15 m layers, in general, presented better results for the clay and silt, with R² values of 0.52 (0.00-0.05 m) and 0.69 (0.05-0.15 m), respectively. Prediction of sand content showed better results when the original depth data was used as an input, although all regression tree models had R² values greater than 0.52. The RT models provided a better statistical index than MLR for all predicted properties; however, the variance between models suggests similarity of performance. Regarding harmonization of soil data, both input databases (harmonized or not) can be used to predict soil properties, since the variance of model performance was low and generalization of the soil maps showed similar trends. The products obtained from the digital soil mapping approach make it possible to integrate the factor of uncertainties, providing easier interpretation for soil management and land use decisions.

Keywords:
terrain attributes; soil depth functions; digital soil mapping; regression models

Covariates	Description	References	Original data		0.00-0.05 m		0.05-0.15 m
Covariates	Description	References	MLR	RT	MLR	RT	MLR	RT
Landsat data (band 1 to 5, 7, and indexes)	Six multispectral bands from Landsat 5 TM; derived indexes: NDVI (band 4 - band 3)/(band 4 + band 3); clay minerals (band 5/band 7); Iron Oxide (band 3/band 1)	Yang et al. (1997), Sabins (1997, 1999), Chagas et al. (2013), Pinheiro et al. (2013)	(1,2,3)	(1,2,3)	(1,2,3)	(1,2,3)	(1,2,3)	(1,2,3)
Geology map	Simplified map from lithology units (Brazilian Department of Mineral Resources, at a 1:50,000 scale)	Pinheiro et al. (2013)	(1,2)	N	(1,2)	N	(1,2)	N
Landform map	Landform map (Geomorphon classification) with the ten most common landforms (flat, peak, ridge, shoulder, spur, slope, hollow, footslope, valley, and pit), considering a broad range of scales according to the search radius distance (predefined as 45 cells) and flatness threshold (1°)	Jasiewicz and Stepinski (2013)	0	0	0	0	0	0
Elevation	DEM from interpolation of primary elevation data, described by Pinheiro et al. (2012)	Hutchinson and Gallant (2000), Moore et al. (1991)	0	0	0	0	0	0
Slope	Slope gradient, first derivative from the DEM (%)	Thompson et al. (2001), Wilson and Gallant (2000)	0	(1,2)	0	(1,2)	0	(1)
Curvature classification	Classification of surface curvature based on the combination of profile and plan curvatures. Negative values correspond to concave surfaces, positive to convex, and planar surfaces between −0.01 and 0.01	Hall and Olson, (1991), Gessler et al. (1995), Figueiredo (2006)	(1,2,3)	0	(1,3)	0	(1,2)	0
Euclidean distance	Linear distance of the nearest stream network feature (m)	Pinheiro (2012), Cunha (2013)	(1)	(1)	(1)	(1)	(1)	(1,2)
Compound topographic index - CTI	Topographic wetness index calculated according to slope and catchment area [CTI = ln (As/tan ß)], where As is the catchment, and ß represents slope in radians	Böhner and Selige (2006), Moore et al. (1993), Gessler et al. (1995)	0	0	0	0	0	0
Mass balance index	Represent areas of soil loss and accumulation. Negative values correspond to depressions, and positive values are related to convex steep and erosional slopes. Values near zero represent balance between soil loss and accumulation	Moller and Volk (2015), Moller et al. (2008)	0	0	0	0	0	0
Mid-slope position	Relative vertical distance to the mid-slope valley or crest directions	Böhner and Antonic (2009), Häring et al. (2012)	(3)	0	(3)	0	(3)	0
Modified catchment area	Flow accumulation in pixels as a sum of precedent flow in catchment area (pixels or square meters)	Lea (1992), Costa-Cabral and Burges (1994)	0	0	0	0	0	(1)
Multiresolution index of ridge top flatness - MrRTF	Indicate flat positions on high elevation areas	Gallant and Dowling (2003)	(1,2)	(2)	(1,2)	(2)	(1,2)	(2)
Multiresolution index of valley bottom flatness -MrVBF	Indicate flat surfaces on valley bottom	Gallant and Dowling (2003)	(1)	0	(1,2)	0	(1)	0
Normalized height	Relative topographic position (%) used for modeling relative heights and slope positions	Böhner and Conrad (2007), Nguyen et al. (2006)	(3)	0	(3)	(1)	0	(3)
Protection index	Maximum angle of zenith or at nadir relating a point to surrounding relief	Yokoyama (2002), Bruna et al. (2013), Yokoyama (2002)	(3)	(1)	(3)	(1)	(3)	(1,3)
Sky view factor and Sky view factor (simplified)	Represents the fraction of visible sky viewed from the ground up. Varies from 0 to 1 from the location center	Böhner and Antonic (2009), Zakšek et al. (2011)	(1,2,3)	(1)	(1,2,3)	0	(1,2,3)	(1,2)
Slope height	Vertical distance from the base of the slope to the crest, or line of intersection of the two slope planes	Böhner and Conrad (2007), Gökceoglu and Aksoy(1996)	(1,2)	0	(1,2)	0	(1,2)	0
Solar radiation	Potential incoming solar radiation (insolation) or amount of incoming solar energy (KWH m⁻² yr⁻¹)	Böhner and Antonic (2009), Thompson et al. (2012)	(2,3)	0	(2,3)	0	(2,3)	0
Total insolation	Sum of direct and diffuse incoming solar radiation (KWH m⁻² yr⁻¹)	Böhner and Antonic (2009), Wilson and Gallant (2000)	(1,3)	0	(1,3)	0	(1,3)	0
Terrain view factor	Factor of terrain obstruction to incoming radiation	Böhner and Antonic (2009), Sandmeier and Itten (1997)	(1,2,3)	(3)	(1,2,3)	(2,3)	(1,2,3)	0
Valley depth	Vertical distance of a base level channel network (m)	Conrad (2012)	(3)	0	(3)	0	(3)	0
Altitude above the channel	Vertical distance of stream network (m)	Prates et al. (2012), Brenning (2009)	0	0	0	(2)	0	0
Vertical overland flow distance	Vertical distance projected of mean runoff length (m)	Freeman (1991), Quinn et al. (1991), Gomi et al. (2008)	(3)	0	(2,3)	0	0	(2,3)
SAGA wetness index	Similar to the ‘Topographic Wetness Index’ (TWI); however, it is based on a modified catchment area	Böhner et al. (2002), Moore et al. (1993)	(3)	0	(3)	0	0	(3)
Wind effect	Climatic factor (m s⁻¹)	Böhner and Antonic (2009), Ließ et al. (2014)	0	0	0	0	0	0
Hillshading	The angle between the surface and the incoming radiation (radians)	Tarini et al. (2006)	0	(2)	0	(2)	0	0
Channel network base level	Difference between the DEM and a surface interpolated from the channel network (m)	Grimaldi et al. (2007)	(1,2,3)	(3)	(1,2,3)	(3)	(1,2,3)	0
Diffuse insolation	Incoming solar radiation reflected by atmospheric components (KWH m⁻² yr⁻¹)	Böhner and Antonic (2009), Wilson and Gallant (2000)	(3)	0	(3)	(1,2)	(3)	(1)
Direct insolation	Incoming solar insolation perpendicular to surface, excluding diffuse insolation (KWH m⁻² yr⁻¹)	Böhner and Antonic (2009), Wilson and Gallant (2000)	0	0	0	0	0	0
Duration of insolation	Mean time of incoming insolation by day (h day⁻¹)	Böhner and Antonic (2009), Wilson and Gallant (2000)	0	0	0	0	0	0

Soil particle size(1)	Original Data			0.00-0.05 m			0.05-0.15 m
Soil particle size(1)	Min	Avg	Max	Min	Avg	Max	Min	Avg	Max
	-------------------------- g kg⁻¹ -------------------------------
Clay	60	279.5	655	51.1	272.4	645.4	57.6	281.3	656.7
Total sand	43	554	906	45.1	557.5	927.2	42.7	551.9	911.7
Silt	34	166.5	575	21.7	170.1	569.1	30.7	166.8	573.4

Soil property	Predictive model	Original data			0.00-0.05 m			0.05-0.15 m			Variance(1)
Soil property	Predictive model	R²	Adj R²	N	R²	Adj R²	N	R²	Adj R²	N	R²	Adj R²
Clay	MLR	0.42	0.32	15	0.47	0.16	15	0.40	0.30	15	0.0013	0.0076
Clay	RT	0.48	0.47	6	0.52	0.51	7	0.46	0.13	7	0.0009	0.0436
Sand	MLR	0.38	0.28	13	0.34	0.25	12	0.39	0.29	13	0.0007	0.0004
Sand	RT	0.58	0.57	5	0.56	0.56	7	0.52	0.52	6	0.0009	0.0007
Silt	MLR	0.51	0.39	19	0.47	0.36	17	0.51	0.40	18	0.0005	0.0004
Silt	RT	0.66	0.66	5	0.65	0.64	5	0.69	0.68	3	0.0004	0.0004

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[TFN1] MLR = Multiple Linear Regression; RT = Regression Tree; NDVI = Normalized Difference Vegetation Index. (1) = Clay; (2) = Sand, (3) = Silt; 0 = not used.