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Article

Deep Learning with a Multi-Task Convolutional Neural Network to Generate a National-Scale 3D Soil Data Product: The Particle Size Distribution of the German Agricultural Soil Landscape

by
Mareike Ließ
1,2,* and
Ali Sakhaee
3
1
Data Science Division, Department of Agriculture, Food, and Nutrition, University of Applied Sciences, Weihenstephan-Triesdorf, 91746 Weidenbach, Germany
2
Department Soil System Science, Helmholtz Centre for Environmental Research—UFZ, 01620 Halle, Germany
3
Thünen Institute of Climate-Smart Agriculture, 38116 Braunschweig, Germany
*
Author to whom correspondence should be addressed.
Agriculture 2024, 14(8), 1230; https://doi.org/10.3390/agriculture14081230
Submission received: 26 April 2024 / Revised: 1 July 2024 / Accepted: 2 July 2024 / Published: 26 July 2024
(This article belongs to the Special Issue Applications of Remote Sensing and Machine Learning for Digital Soil Mapping)
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Abstract

:
Many soil functions and processes are controlled by the soil particle size distribution. Accordingly, nationwide geoinformation on this soil property is required to enable climate-smart and resilient land management. This study presents a new deep learning approach to simultaneously model the contents of the three particle sizes of sand, silt, and clay and their variations with depth throughout the landscape. The approach allows for the consideration of the natural soil horizon boundaries and the inclusion of the surrounding landscape context of each soil profile to investigate the soil–landscape relation. Applied to the agricultural soil landscape of Germany, the approach generated a three-dimensional continuous data product with a resolution of 100 m in geographic space and a depth resolution of 1 cm. The approach relies on a patch-wise multi-target convolutional neural network (CNN) model. Genetic algorithm optimization was applied for CNN parameter tuning. Overall, the effectiveness of the CNN algorithm in generating multidimensional, multivariate, national-scale soil data products was demonstrated. The predictive performance resulted in a median root mean square error of 17.8 mass-% for the sand, 14.4 mass-% for the silt, and 9.3 mass-% for the clay content in the top ten centimeters. This increased to 20.9, 16.5, and 11.8 mass-% at a 40 cm depth. The generated data product is the first of its kind. However, even though the potential of this deep learning approach to understand and model the complex soil–landscape relation is virtually limitless, its limitations are data driven concerning the approximation of the soil-forming factors and the available soil profile data.

1. Introduction

All decisions made in the management of agricultural land and their effects on soil productivity and environmental impact are ultimately influenced by local soil conditions. As a result, information on the soil parameter space at a spatial resolution that addresses individual agricultural fields is needed for the national-scale evaluation and modeling of the influence of agricultural management and climate change on soils, yields, and the environment [1,2,3]. This relates to the evaluation of the agricultural productivity of soils, as well as the constraints and necessary adjustments brought on by protracted drought periods [4]. Adequate soil information with a high geographic resolution could greatly enhance crop phenology models [5], the evaluation and modeling of soil-related drought, and corresponding irrigation requirements [6,7,8]. The same is true for assessing soils’ capacity to store soil organic carbon [9,10,11], modeling the intricate processes that release greenhouse gases to combat climate change [12], and modeling potential solutions to minimize nitrate pollution [13,14]. Soil particle size distribution drives most soil functions and related processes [15,16].
Examples of recent data products providing soil texture information at a national scale are Chaney et al. [17], Liu et al. [18], Varón-Ramírez et al. [19], and Schulz et al. [20]. Ließ [2], and Gebauer et al. In [21], soil texture data products were generated for the agricultural soil landscape of Germany. The state-of-the-art approach to generating landscape-scale soil data products involves machine learning to relate the soil profile information of a large and well-distributed soil database to gridded proxies of the soil-forming factors such as climate (C), organisms (O), relief (R), parent material (P), and time (A) [22]. McBratney et al. [23] included proxies to soil itself (S) and the spatial position (N) as predictors completing the so-called SCORPAN factors. This overall approach is referred to by “digital soil mapping” (DSM), “predictive soil mapping”, or “pedometric modeling”. Recent reviews are provided by Padarian et al. [24] and Arrouays et al. [25].
In their assessment of DSM investigations over a spatial extent greater than 10,000 km2, Chen et al. [26] discovered that half of the examined publications solely examined topsoil information (less than 30 cm). However, to address the aforementioned needs to model and answer questions related to crop growth and quality and the impacts of prolonged drought, greenhouse gas emissions, and groundwater contamination, three-dimensional (3D) soil data are required. The following succinctly describes various methods for modeling the three-dimensional soil parameter space: the ‘2.5D approach’ involves creating separate models for distinct soil properties at predefined soil depths and then combining the spatial forecasts. Liu et al. [27], Varón-Ramírez et al. [19], and Taghizadeh-Mehrjardi et al. [28] provide recent examples. The ‘depth function approach’ fits a continuous mathematical function over the available horizon data before projecting the parameters of the function into space [29]. Also, ‘3D regression kriging’ simulates the spatial trend and spatial autocorrelation [30]. Last but not least, convolutional neural networks (CNNs) are becoming more and more common for 3D predictions [31,32,33]. Common to all 3D approaches is that they (1) focus on a single target variable and (2) simplify the information on the natural soil horizon boundaries to predefined depth levels.
Soils are intricate systems that vary in 3D. They are identified by a vertical division into soil horizons which vary in quantity, dimensions, and properties throughout the landscape. Due to numerous physical, chemical, and biological processes, many of their features are interconnected both inside and between horizons. Accordingly, the simultaneous modeling of all soil properties and their changes in horizontal space and with depth would be best suited to address this complexity [2,34]. On the contrary, the separate modeling of related properties may lead to inconsistencies. Particle size distribution itself is not a single value target variable, but a composition of the weight proportions of different particle size fractions. Among other methods, their simultaneous modeling has been addressed using Bayesian maximum entropy [35].
CNNs potentially allow for the simultaneous modeling of various soil properties in 3D. Their application for multi-target prediction in the related research field of soil spectroscopy is well-advanced [36,37,38]. Originally, CNNs were developed and are widely applied in the fields of image analysis and computer vision. Please refer to Aloysius and Geetha [39], Zhang et al. [40], and Sakib et al. [41] for a brief history and reviews. For application to soil mapping, the approach was adapted to consider the wider landscape context of the respective soil profiles to establish models for continuous prediction. A landscape section in terms of a squared window surrounding each profile site is clipped from the data cube of gridded predictor data. These patches are analogous to the input images for a CNN image classification task. Therefore, the contextual landscape characteristics at the soil profile locations, including spatial autocorrelation in the predictor space, are used to derive the soil–landscape relationship. Please see Taghizadeh-Mehrjardi et al. [31], Wadoux [33], and Beucher et al. [42] for recent applications. However, like many other machine learning algorithms, CNNs can only develop their full potential by applying an optimization approach for hyperparameter tuning [21]. Still, few researchers have applied optimization to tune the CNN hyperparameters in predictive soil mapping studies, despite recent work showing its importance [31,43,44]. Overall, we are not aware of any application using CNNs for multi-target soil prediction in 3D.
We will demonstrate a CNN-based approach for national-scale 3D soil texture prediction. It advances current approaches to spatial soil modeling in three ways: (1) it simultaneously models multiple target variables in 3D with a single model, (2) it incorporates natural soil horizon boundaries, and (3) genetic algorithm (GA) optimization is applied for hyperparameter tuning. The validity of the approach is demonstrated for the agricultural soil landscape of Germany, predicting the three particle sizes separately in 3D. In addition, a CNN model to generate a topsoil data product (2D) is included to provide a benchmark, since, often, the more complex 3D model training results in a worse performance.

2. Material and Methods

2.1. Landscape Setting

In the 357,386 km2 that make up Germany, 51% of the land is used for agriculture [45] (Figure 1A). From north to south, its landscape is divided into four morphologic areas: the North German Lowland, the Central German Uplands, the Alpine Foreland, and the Alps. The majority of the North German Lowland is located below 100 m a.s.l. (Figure 1B). The northeastern region of Germany has a glacial influence with many lakes and moraines, in contrast to the marshes, peatlands, and marshy terrain around the North Sea Coast. The central German Uplands region’s mountains are generally not much higher than 1000 m above sea level. They developed basin structures with sedimentary deposits under the influence of several periods of upheaval and subsidence and are interspersed with alluvial glacial loess deposits. In addition, many of the mountain ranges show evidence of past volcanism, creating a complex geological structure. The Alpine Foothills region, with elevations between 400 and 750 m above sea level, was shaped by glaciers and exhibits a wide range of geomorphological features, including molasses basins with sedimentary deposits from Alpine erosion and morainic hills and aprons. The Northern Calcareous Alps include the portion of the Alps in Germany. Parent material and topography are the main determinants of soil distribution in Germany. Gebauer et al. and Ließ et al. [21,46] provide further details on the German landscape setting.

2.2. Soil Data

Data on the particle size distributions of 3102 soil profiles were available from the German agricultural soil inventory [49,50]. The data were collected nationwide through systematic sampling along an 8 by 8 km grid. Samples were taken for each of the 0–10, 10–30, 30–50, 50–70, and 70–100 cm depth increments while taking horizon boundaries into account. Accordingly, samples were taken for each horizon fragment occurring within the respective depth increment. The particle size distribution in terms of three particle size fractions—sand (2000—63 μm), silt (63—2 μm), and clay (<2 μm)—was determined by sieving and the sedimentation method according to DIN ISO 11277 [51]. The data of the three particle size fractions were subdivided into 1 cm slices and included as response data in the model training, tuning, and evaluation. This was performed to allow for the inclusion of the actual horizon boundaries in the model approach without the need to (1) agglomerate them into predefined depth layers or (2) fit depth functions, which would both introduce another source of uncertainty to the training data.

2.3. Data to Approximate the Soil-Forming Factors

The covariates used to train the machine learning models for nationwide spatial prediction were grouped according to the SCORPAN factor they represented. Table 1 gives an overview, including references.
The German Weather Service provided seasonal averages of air temperature and drought, as well as the sums of the precipitation for the winter (Dec., Jan., and Feb.) and summer (Jun., Jul., and Aug.) months for SCORPAN C (climate).
The following factors were included to approximate SCORPAN O (organisms including vegetation and land use): Sentinel-2 data composites from the second yearly quartiles of 2018 and 2021 of the bands B01, B02, B03, B04, B05, B06, B07, B08, B8a, B11, and B12, as well as the vegetation indices Enhanced Vegetation Index (EVI), Moisture Index (MSI), Normalized Difference Moisture Index (NDMI), Normalized Difference Vegetation Index (NDVI), Normalized Difference Water Index (NDWI), and Plant Senescence Reflectance Index (PSRI) (details in Table 1). The composites were created using the Sentinel-Hub and the surface reflectance values from the Level 2A product. Before computing the vegetation indices, the composites were downloaded as multiple tiles with a spatial resolution of 20 m, then mosaicked and resampled to the 100 m INSPIRE—Infrastructure for Spatial Information in Europe—grid topology [52]. Furthermore, Copernicus Global Land Service remote sensing products on Dry Matter Productivity (DMP) and the Vegetation Productivity Index (VPI) during the periods of 11–20 June 2016 and 2018 were obtained. All the SCORPAN O variables were selected to reflect the major annual phase of agricultural productivity.
SCORPAN R (relief) was represented by the Geomorphographic Map of Germany and terrain parameters were calculated on behalf of the EU-DEM digital elevation model using a digital terrain analysis with the SAGA—System for Automated Geoscientific Analyses [53].
To approximate SCORPAN P (parent material), a map of “Groups of soil parent material” was incorporated. Hydrogeological maps of Germany’s lithology and stratigraphy were also added.
Proxies to soil (SCORPAN S) can be found in conventional soil polygon maps and remote sensing products related to soil parameters. In the case of the former, a map of German soilscapes was included. Differences in the DMP and VPI between the dry year of 2018 and the fairly wet year of 2016 were incorporated in the latter. They were related to crop phenology and, as a result, to the root zone plant available soil water capacity.
All covariates were resampled at a 100 m resolution to the INSPIRE grid topology [52]. This resolution was chosen as a compromise between the desire to provide soil information for individual agricultural fields and the usage of computational resources in a limited manner. For categorical predictors, the nearest-neighbor approach was utilized, while for numerical predictors, B-spline interpolation was used. INSPIRE latitude and longitude were also included to reflect the geographic location (SCORPAN N) and, in particular, to represent spatial patterns that the other data proxies did not capture. Pedogenesis in Germany has been ongoing for more than 10,000 years, while the data we use to approximate the soil-forming factors relate to the last decades only. Accordingly, there will always be a gap that we seek to fill. The German national boundary and shoreline were obtained using the Federal Agency for Cartography and Geodesy’s digital land model at a map scale of 1:250,000 (version 2.0, GeoBasis-DE/BKG, 2020).
Table 1. Data to approximate the soil-forming factors.
Table 1. Data to approximate the soil-forming factors.
Soil-Forming FactorsAbbreviationDescriptionData Source
ClimatePRESUAverage seasonal precipitation (summer) [raster, 1000 m][54]
PREWIAverage seasonal precipitation (winter) [raster, 1000 m]
TEMSUAverage seasonal temperature (summer) [raster, 1000 m][55]
TEMWIAverage seasonal temperature (winter) [raster, 1000 m]
DINSUAverage seasonal drought index (summer) [raster, 1000 m][56]
DINWIAverage seasonal drought index (winter) [raster, 1000 m]
Organisms/ SoilB0118, 0218, …, B0818, B8A18, B1118, B1218Sentinel-2 spectral bands B1, B2, …, B8, B8A, B11, and B12 composites of the 2nd yearly quartile of the year 2018Sentinel Hub
B0121, 0221, …, B0821, B8A21, B1121, B1221Sentinel-2 spectral bands B1, B2, …, B8, B8A, B11, and B12 composites of the 2nd yearly quartile of the year 2021Sentinel Hub
EVI18, EVI21Enhanced Vegetation Index, calculated from Sentinel 2 band composites of 2nd quartile 2018 and 2021 (S2-Q2-18/21), EVI = G × (B8A − B04)/(B8A + C1 × B04 − C2 × B02 + L), with G = 2.5, C1 = 6, C2 = 7.5 and L = 1
MSI18, MSI21Moisture index: S2-Q2-18/21, MSI = B11/B08
NDM18,
NDM21		Normalized Difference Moisture Index: S2-Q2-18/21, NDMI = (B08 − B11)/(B08 + B11)
NDV18,
NDV21		Normalized Difference Vegetation Index: S2-Q2-18/21, NDVI = (B08 − B04)/(B08 + B04)
NDW18,
NDW21		Normalized Difference Water Index: S2-Q2-18/21, NDWI = (B03 − B08)/(B03 + B08)
PSR18,
PSR21		Plant Senescence Reflectance Index: S2-Q2-18/21, PSRI = (B04 − B02)/B06
DMP16Dry Matter Productivity, June 2016 [raster, 300 m][57]
DMP18Dry Matter Productivity, June 2018 [raster, 300]
VPI16Vegetation Productivity Index, June 2016 [raster, 300 m][58]
VPI18Vegetation Productivity Index, June 2018 [raster, 300 m]
TopographyGMK00Geomorphographic Map of Germany [raster, 250 m resolution, map scale 1:1,000,000][59]
DEM00Digital elevation model [raster, 25 m resolution][48]
SLO01, SLO05, SLO10Slope: calculated from DEM (cfD) with a search radius of 1, 5, 10 cells, using SAGA module Morphometric features
NOR01, NOR05, NOR10Northness: derived from aspect cfD with a search radius of 1, 5, 10 cells, using SAGA module Morphometric features
EAS01, EAS05, EAS10Eastness: derived from aspect cfD with a search radius of 1, 5, 10 cells, using SAGA module Morphometric features
TST01, TST05, TST10Terrain surface texture: cfD with a search radius of 1, 5, 10 cells, using SAGA module Terrain Surface Texture
TSR01, TSR05, TSR10Terrain surface ruggedness: cfD with a search radius of 1, 5, 10 cells, using SAGA module Terrain Ruggedness Index
CON01, CON05, CON10Convergence Index: cfD with a search radius of 1, 5, 10 cells, using SAGA module Convergence Index (Search Radius)
SLH00Slope Height: cfD using SAGA module Relative Heights and Slope Positions
VAD00Valley depth: cfD using SAGA module Relative Heights and Slope Positions
NOH00Normalized Height: cfD using SAGA module Relative Heights and Slope Positions
WIN00Wind Exposure: cfD using SAGA module Wind Effect
NOP00Negative openness: cfD using SAGA module Topographic Openness
POP00Positive openness: cfD using SAGA module Topographic Openness
VOF0SVertical overland flow distance to all river segments: cfD using SAGA module Terrain analysis/Channels
VOF0MVertical overland flow distance to major rivers: cfD using SAGA module Terrain analysis/Channels
HOF0SHorizontal overland flow distance to all river segments: cfD using SAGA module Terrain analysis/Channels
HOFOMHorizontal overland flow distance to major rivers: cfD using SAGA module Terrain analysis/Channels
SWI00SAGA wetness index: cfD using SAGA module SAGA Wetness Index
Parent materialLIT00Lithology, Hydrogeological map of Germany, HÜK [polygon shapefile, map scale 1:250,000][60]
STR00Stratigraphy, Hydrogeological map of Germany, HÜK [polygon shapefile, map scale 1:250,000]
BAG00Groups of soil parent material in Germany [polygon shapefile, map scale 1:5,000,000][61]
SoilBGL00Soilscapes in Germany [map scale 1:5,000,000][62]
DMP86Dry matter productivity, DMP18–DMP16 [raster, 300 m]Copernicus Global Land Service
VPI86Vegetation Productivity Index, VPI18–VPI16 [raster, 300 m]
Geographic locationLAT00INSPIRE Latitude[52]
LON00INSPIRE Longitude

2.4. Convolutional Neural Network

CNNs are feed-forward artificial neural networks (ANNs) trained with back propagation [63,64]. Their architecture comprises multiple layers. Their fundamental building blocks include convolutional layers, pooling layers, and the fully connected layers of ANNs. These fully connected dense layers each consist of a certain number of neurons. A neuron is the basic unit of a neural network. It is connected to all neurons of the previous and all neurons of the subsequent layer and receives inputs from all neurons of the preceding layer. Weights are assigned to the respective connections to give certain inputs a higher importance compared to others. In addition, a bias is assigned to each neuron. Overall, an optimizer is applied to update the weights during the learning process in order to achieve the lowest prediction error; the learning rate determines how fast these weights are updated. The application of an activation function at each neuron transforms the input into the output, and allows for the introduction of non-linearity. A dropout rate is commonly applied for the regularization of the network structure. This means that a certain portion of randomly selected neurons is ignored during training. Accordingly, their contribution is temporarily removed, and weight updates are not applied. Dropout reduces the co-adaptation of neurons.
At the core of CNNs lies the convolution operation, which involves sliding a convolutional filter (also known as a kernel) across the input data and computing element-wise multiplications followed by summation to produce feature maps. This operation enables CNNs to capture local patterns and spatial relationships within the input data, facilitating robust feature learning. All units of a feature map share the same weights. With a subregion size of z × z, a feature map has z² adjustable weight parameters and one bias parameter. A filter is made up of these parameters. Because of the weight sharing, evaluating the activation function of these units is equal to combining the cell values with a kernel made up of the weight parameters [65]. Usually, a convolutional layer consists of multiple feature maps, each with its own set of weight and bias parameters. Pooling layers play a crucial role in down-sampling feature maps, reducing their spatial dimensions while preserving essential information. Max pooling and average pooling are common pooling techniques, selecting the maximum or average value within each pooling region, respectively.
As with other machine learning algorithms building on the concept model of pedogenesis to learn the soil–landscape relation, CNNs relate the input (the values of p covariates at n soil profile sites) to the output (the soil data at the n profile sites). However, in contrast to other algorithms, they allow for the inclusion of a different type of input data. Instead of the n × p covariate matrix, CNNs allow for the inclusion of covariate data arrays X with dimensions of [n, w, w, p]. Each profile site is represented by an array [1, w, w, p], where w is the window size defining the surrounding landscape patch. CNNs consider the information contained in the w × w landscape surrounding in terms of the spatial autocorrelation between the contained raster cell values and their spatial structures to detect higher-order features [66].
Figure 2 displays the CNN structure which was used to train the models to predict the soil texture in 2D (topsoil) and 3D. All data processing and modeling were performed in R 4.1.3 [67] using the ‘keras’ package [68] to connect to the Keras Python API [69]. A high-performance computation cluster with 25 cores was used to allow for paralellization when feasible; a data science server with a high RAM was used to facilitate the processing of the predictor data and apply the model for spatial prediction. Patch sizes of w = 5 × 5 and 10 × 10 cells were tested to incorporate the surrounding landscape context. This was a compromise, as the consideration of the surrounding area for each profile site led to missing values for those sites close to the border of Germany. Accordingly, this led to a reduction in the considered profile sites and a reduction in the predicted area. MaxPooling was applied with a receptive field of 2 × 2. The rectified linear unit (ReLU) activation function was applied and the Adam optimizer [70] was used to update the weights during the learning process to achieve a minimum mean squared error. One hundred epochs were used for training (test runs with a higher number did not improve the results). Due to the prediction of the particle size distribution with three particle size separated in 2D (topsoil) and 3D (continuously from 0 to 100 cm with a resolution of 1 cm), two different data structures for the response Y were used: Y [n, 3] for 2D and Y [n, 100, 3] for 3D. The Softmax activation function was employed at the end of the final layer. It served to map the predictions to non-negative values and fulfill the constraint that the contributions of all particle size fractions needed to sum up to 1 [39]. Hyperparameter tuning by GA optimization was conducted to select the number of filters (p1), the kernel size (p2), the dropout rate (p3), the numbers of units in the first and second subsequent fully connected dense layers (p4 and p5), and the learning rate (p6). Table 2 provides the hyperparameter ranges.

2.5. Model Training, Tuning, and Evaluation

Table 3 indicates the sizes of the datasets used for the CNN model training to predict the soil texture in 2D and 3D while considering smaller and larger landscape patches surrounding each soil profile. The different sizes resulted from excluding predictor arrays with missing data and/or profiles with missing texture data in part of the profile. The latter resulted from organic soils, mineral soils with organic horizons, or soils limited to a depth of <100 cm, while the former mainly corresponded to profile sites close to the national border or the sea, with distances of <250 m (w = 5) and <500 m (w = 10). In general, SCORPAN data proxies are often limited to national borders and not available beyond, which hampers approaches depending on these data. This particularly applies to conventional map products. Accordingly, the dataset for the 2D [5 cells] model development was the largest, while the dataset for 3D [10 cells] was the smallest. The decrease from 2917 to 2740 sites comparing the datasets for the 2D and 3D predictions [5 cells] was due to missing texture data in at least part of the profile. The decrease from 2917 to 2679 [2D] comparing the datasets with 5- and 10-cell patch sizes was due to missing data in the predictor arrays.
Model training and evaluation were conducted by a 5-times repeated stratified 5-fold cross-validation (CV) to obtain robust models [71]. To implement model tuning, the CV was nested. The predictor–response dataset was subdivided into five folds of equal sizes. Of these five folds, one fold was always kept as a test set while the other four were combined to form the model training set, leading to five separate test set evaluations. Each of the outer CV’s training sets was again further subdivided to provide the datasets for hyperparameter tuning in the inner CV cycle. To save time and computational resources, only the first of the five repetitions of the inner CV cycle was used for optimizing the hyperparameters. To avoid autocorrelation effects between the training and test set data, the data were split considering the profile as an entity. This ensured that a sample from an upper horizon would not be used in the validation when evaluating the precision of a lower horizon of that profile and vice versa.
Concerning the categorical predictors, all predictors were recoded into dummy variables. Categories not present in any data subsets were removed before the model training, tuning, and evaluation. To prevent numerical issues and imbalances, all numerical data were scaled to the range of 0–1 using min–max scaling. Table 3 indicates that, altogether, 119 predictor variables remained. The response data were stratified by partitioning around medoids clustering [72] with the R package ‘cluster’ [73]. The Silhouette Index [74] was used to determine the number of clusters ≥4 and ≤10.

2.6. Genetic Algorithm Optimization

CNN hyperparameter tuning was carried out using GA optimization. The operational structure of GAs is inspired by general biological evolution principles, with mutation, crossover, selection, and elitism providing the terminology when describing the algorithm [75].
The parameter space that is searched for the best combination of hyperparameter values must be set by specifying a minimum and maximum value for each parameter. A random number of n parameter vectors, the ‘parent population’, is then evaluated by a problem-specific objective function. Weights are applied to each parameter vector (‘individual’) based on its objective function value before beginning to modify them through selection, mutation, and crossover to create a new population of parameter vectors that is evaluated again. Mutation refers to the adaptation of individual parameter values and their crossover to an exchange of parameter values between vectors. This modification is repeated until either (1) any of the vectors attain an initially defined objective function value, (2) a maximum number of iterations is reached, or (3) the overall best objective function value does not improve for a certain number of iterations. GA optimization was performed in parallel, subdividing the parent population of 500 individuals into subpopulations on so-called ‘islands’ and allowing for a restricted exchange of population members (hyperparameter vectors) between the islands.
A few test runs were performed to select the GA parameters based on recommendations [76]. The population size was set to 500 parameter vectors, and the number of islands for simultaneous search was limited to 25. The migration interval between islands was set to 18 and the migration rate to 0.1. With a probability of 0.8, single-point crossover between parameter vectors was performed, and uniform random mutation with a frequency of 0.1 was observed. Elitism allowed for the best five individuals to survive in each generation. The likelihood of using local search was set to 0.1, and the selection pressure was set to 0.7. The total number of iterations was set to 200, and the number of consecutive generations without an improvement in the best fitness value before the GA was terminated was set to 20. The average squared prediction error over all targets as a loss function was minimized. The procedure was carried out with the R package ‘GA’ [76,77].

2.7. Variable Importance

Each predictor’s importance was determined by permutation-based variable importance (VI), i.e., permuting the predictor in the test set prior to the model application [78]. Any predictor–response association relating to that predictor was, thus, deleted. The resulting relative increase in the predictive root mean square error (RMSE) was then assigned to the respective predictor as VI. This VI estimation was performed for each of the three particle size fractions, as well as for all depth slices (3D prediction). The values from five permutations were averaged. The VI values for the dummy variables were generated by aggregating for each categorical predictor. The VI plots exhibit boxplots of twenty-five VI values for each predictor due to the five-times repeated 5-fold CV procedure (outer CV cycle).

3. Results and Discussion

3.1. Soil Data

Figure 3 indicates a high variability of the soil texture throughout the sampled soils in Germany. In particular, sand contents varied between 0 and 100%. The variability was much lower for the clay content. Overall, the soils under agricultural use mostly had a clay content below 27%, as indicated by the maximum of the upper hinge in Figure 3C. Regarding the 2740 profiles included in the dataset for 3D modeling with a 5 × 5 cell patch size, field data annotations showed that 44.8% of the soil profiles experienced one change in parent material up to a depth of 100 cm, and an additional 14.1% experienced two or more changes. Only 1.8% of the profiles experienced the first change in parent material at a ≤25 cm depth, 25.1% experienced it between 25 and 50 cm, 25.5% experienced it between 50 and 75 cm, and 47.5% experienced it below 75 cm.

3.2. Model Hyperparameters

Table 4 provides the results of the model hyperparameter tuning with GA optimization. The learning rate and kernel size resulted in the overall lowest value for the model training with a 2D and 3D response for both patch sizes, w = 5 and w = 10 cells, with P2 = 2 and P6 = 0.001. The same applies to the dropout rate (P3 = 0.1) for the topsoil models (2D). For the models with the 3D response, the value was slightly higher, but still low. The selected number of filters was between 87 and 91 and was slightly higher for the models considering a w = 5 cells patch size compared to those with a w = 10 cells patch size. The same applies to the number of units, with the exception of the 3D [10 cells] model.
Taghizadeh-Mehrjardi et al. [31] and Wadoux et al. [43] used a more complex CNN structure with more convolutional layers. Wadoux et al. [43] used two, and Taghizadeh-Mehrjardi et al. [31] even used four convolutional layers. We refrained from doing so due to the decision to restrict the maximum patch size for previously mentioned reasons. However, the high number of selected filters (P1, Table 4) could indicate that the models would benefit from an additional convolutional layer. The first convolutional layer’s kernels were built to recognize basic characteristics like edges and curves, whereas the kernels in subsequent layers were trained to recognize more complex features [40]. We could gradually extract higher-level information by stacking many convolutional and pooling layers. The importance of additional convolutional layers and, hence, the necessity for a more complex model structure would have to be tested, though in a setting where predictor information is available beyond the boundary of the research area and an increase in patch size would not reduce the number of profile sites. Taghizadeh-Mehrjardi et al. [31] tested patch sizes from 3 to 29 cells and received the best results for a patch size of 7 cells. Wadoux et al. [43] tested selected patch sizes ranging from 3 to 35 cells and achieved the best results with a patch size of 21 cells. However, this likely depends on the respective landscapes and available predictor information, since patch size and predictor resolution likely affect each other.

3.3. Predictive Performance

Figure 4 displays the predictive model performance in terms of the RMSE. Scatter plots with R² values are included for selected soil depths, as shown in the Supplementary Material (Figure S1). The overall model performance of the topsoil predictions within the top 30 cm (Figure 3A–C) was better when considering a smaller landscape surrounding each profile site. The median RMSE was 17.2 mass-% for the sand, 14.0 mass-% for the silt, and 9.5 mass-% for the clay content. For the 3D predictions, the results were different. For the sand and clay contents, the larger landscape surrounding the 10 cells’ patch provided lower test set RMSE values across depths. The median RMSE was 17.8 mass-% for the sand, 14.4 mass-% for the silt, and 9.3 mass-% for the clay content up to a depth of 10 cm. The average median RMSEs for the top 30 cm of this model were 18.0, 14.5, and 9.5 mass-% respectively.
Below 26 cm, the RMSE increased abruptly; at a 40 cm depth, the RMSE values were 20.9, 16.5, and 11.8 mass-%. A decrease in model performance with depth has often been reported [2,30,31]. One reason could be the frequent changes in parent material. Considering the high percentage of profile sites with changes in parent material, the available data for SCORPAN P likely caused this increase in uncertainty. SCORPAN P was expected to have a higher explanatory power for deeper soil horizons, while the explanatory power of other soil-forming factors (R, O, and C) decreased with depth. However, as a consequence of this, data proxies to SCORPAN P, which may explain the parent material only to a very limited extent, led to a decrease in the predictive model performance with depth. The SCORPAN P proxies consisted of geological maps of different scales and qualities, and there may be some inconsistencies in how depth is represented. These maps may not fully capture the nuances of the underlying parent material. Still, this could possibly be replaced by topographic information to some extent, as has been shown in various studies. Topographical predictors derived from a DEM have the advantage that they contain measured data in contrast to the expert information on parent material.
Gebauer et al. [21] achieved a slightly better model performance for 30 cm topsoil predictions of the agricultural German soil landscape on behalf of the same dataset, with 15.0 mass-% (sand), 11.8 mass-% (silt), and 8.2 mass-% (clay). However, they trained separate models for the three particle sizes separately, leading to a lower soil complexity included in the models. Another important factor leading to the comparatively lower model performance in our case could be the reduced size of the soil dataset, which was a consequence of the consideration of the landscape information surrounding each sampling site. This impact was even stronger when increasing the patch size. We do not see any further reasons, since both studies relied on the data from the German agricultural soil inventory, used powerful algorithms, and applied optimization for parameter tuning.
The SoilGrids 2.0 data product [79] had a slightly higher uncertainty, with 19.3–25.9 mass-% (sand), 16.5–19.6 mass-% (silt), and 11.4–14.3 mass-% (clay), increasing from the top layer of 0–5 cm to the bottom layer of 60–100 cm (evaluated in Ließ [2]). Global-scale models cannot include the same level of detail in their predictor information and often do not have access to the same amount of soil profile data as national approaches. It is still interesting to emphasize the lower performance of the global model, even though our model included more of the soil system’s internal complexity due to training all three particle size fractions and their changes from a 0 to 100 cm depth at once while including the original soil horizon boundaries.
Unfortunately, the national border restrictions on the predictor data did not allow us to test larger patch sizes, which could have further enhanced the predictive performance. This particularly concerns German national-scale conventional map products. Wadoux et al. [43] handled missing data entries by assigning them a value of −1. However, we find it difficult to justify this procedure in our case, as it might have added artifacts to data located close to the border. As mentioned previously, a deeper CNN model structure with a higher number of convolutional layers might also further improve predictive performance.
It must be mentioned, however, that, to the best of our knowledge, all other approaches applying machine learning for 3D texture predictions transform the soil profile data to certain depth intervals prior to model training. The advantage of our approach is that it can use soil profile data as is and does not introduce additional uncertainty to the input data by fitting depth functions, which then propagates through the models. This uncertainty is currently not accounted for in any predictive mapping approach.

3.4. Spatial Predictions

Figure 5 shows the VI of the most important predictors for the two topsoil (2D) models considering landscape patches of 5 × 5 and 10 × 10 cells. Figure 6 indicates the VI of the most important predictors for the models to predict in 3D, respectively. For the topsoil predictions, elevation above sea level (DEM00), terrain surface texture with a 10 cells radius (TST10), valley depth (VAD00), vertical overland flow distance to major rivers (VOF0M), the Geomorphographic Map of Germany (GMK00), the maps of parent material (BAG00) and stratigraphy (STR00), the Soil Scapes in Germany Map (BGL00), latitude (LAT00), and longitude (LON00) were among these predictors (Figure 5). For the 3D predictions, the list includes the same predictors and, additionally, the Dry Matter Productivity of June 2016 and 2018 (DMP16, DMP18). For the topsoil models, the high importance of the categorical predictors GMK00, BAG00, STR00, and BGL00 was clearly visible, with BAG00 indicating the highest VI. Depending on the considered particle size fraction, LAT00 or LON00 were of a higher importance than STR00 and/or GMK00. GMK00 was only of a high importance for predicting the sand fraction. Particularly, the VI values of the categorical predictors also displayed a high variability. This might have been due to the soil profile dataset being too small to capture all categories with sufficient profiles.
For the 3D predictions, BAG00 (Figure 6A8–F8) was also by far the most important predictor (please be aware of the different Y-axis scales). BAG00 and other predictors with high VI values, namely STR00, BGL00, LAT00, and LON00, displayed decreasing VI values with depth, while there was no predictor with increasing VI values. This indicates very well the reason for the increasing model uncertainty with depth. Obviously, important predictor information that could explain soil texture variation in the subsoil was missing and could not be captured by indicators of geographic location (LAT00 and LON00), either. This can likely be attributed to the poor quality of the SCORPAN P proxies in capturing parent material changes within single soil profiles.
The high importance of the included expert information in terms of soil and parent material vector maps was also reported by Taghizadeh-Mehrjardi et al. [80] and Gebauer et al. [21]. However, on the contrary, it could also indicate that the CNN algorithm favors categorical dummy predictors over continuous predictors, since the detection of low-level features such as edges and curves is more straightforward. This aspect is application-specific to the usage of landscape patches as predictors for soil information, but could possibly be compared to favoring sharp edges over blurred image features in image classification tasks. It would have to be tested whether excluding vector maps encoded as dummy variables would lead to a similar model performance or even improve results. Many studies have shown that SORPAN P predictor information could partly be replaced by topographical predictors. Gebauer et al. [21] demonstrated this for German topsoil texture predictions.
However, altogether, the importance of SCORPAN P and SCORPAN R predictors for the prediction of the particle size fractions in 2D and 3D was clearly visible, but the results indicated that the included predictor information was less suited for predicting the soil texture in the subsoil.
Figure 7 displays selected horizontal slices of the 3D prediction of the particle size fractions of sand, silt, and clay. Glacial deposits in the North German Lowland account for the region’s high sand (Figure 7A1–A4) and comparatively low silt (Figure 7B1–B4) and clay contents (Figure 7C1–C4). The predictors BAG00 and BGL00 make an important contribution to this pattern. Glaciers that advanced from Scandinavia during the three Pleistocene ice eras left behind coarse sedimentary deposits. The lower sand contents in northeast Germany correspond to the young moraine area, which is intermixed with Sander and glacial valleys. The high silt and clay contents along the North Sea indicate the marsh border on the tidal coast [81]. Together with the higher silt and clay contents located along the northern German major river valleys due to floodplain sediments, this coincides well with the unit of the Geomorphographic Map of Germany, indicating sink areas at a very low elevation above the depth line with a very high soil moisture index. The high silt contents north of the Central German Uplands and in southern Germany reflect Loess deposits, mostly with a periglacial influence [82]. In between are the escarpment and ridge landscapes with Triassic rocks and larger Loess-covered basins. The BAG00, BGL00, and GMK00 map units help to differentiate the soil texture patterns in this area. Overall, the spatial distribution indicates the strong influence of the soil parent material and topography. The topsoil pattern aligns well with that predicted by Gebauer et al. [21].

4. Conclusions

Soil particle size distribution is responsible for many soil functions and processes. The generated three-dimensional continuous data product of the sand, silt, and clay contents of the agricultural soil landscape of Germany had a spatial resolution of 100 m and a depth resolution of 1 cm. This product is crucial for assessing the soil functionality and various risks, as well as for forecasting the outcomes of agricultural management practices and their capacity to adapt to climate change.
The high potential of the CNN algorithm in generating such multidimensional and multivariate soil data products was demonstrated. The approach introduces numerous possibilities for predictive soil mapping: (1) It allows for the inclusion of the natural soil horizon boundaries without the need to average soil data over user-defined depth layers. (2) A single model can concurrently predict a variety of soil characteristics and how they interact within and between soil horizons. (3) Each soil profile’s surrounding landscape can be taken into account, and numerous landscape features can be automatically retrieved. However, assessing the complexity of the soil system at the national scale with a single model requires many more data compared to training models for a single soil depth or single soil properties.
To sum up, the potential for this deep learning approach to understand and model the complex soil–landscape relation is virtually limitless. The patch-based CNN for 3D multivariate soil modeling has only data-driven limitations. To approximate the soil-forming factors, steadily improving the availability, quality, and resolution of gridded landscape data and access to the vast buried treasure of soil profile data are essential. Furthermore, there is a high demand to test the required complexity and depth of CNN models to produce soil data cubes of a sufficient quality without the excessive use of computing capacities. The same applies to the inclusion of the landscape context surrounding each soil profile, because vicinity size, filter size, and predictor resolution likely affect one another.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/agriculture14081230/s1, Figure S1: Scatter plots of measured versus predicted values for selected soil depths.

Author Contributions

Conceptualization, formal analysis, methodology, software, validation, and writing—original draft preparation were conducted by M.L. Writing—review and editing by M.L. and A.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Data Availability Statement

Data are available from Ließ [83].

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Figure 1. Landscape setting. (A) Land cover [47] and (B) elevation [48] (adapted from Ließ et al. [46]).
Figure 1. Landscape setting. (A) Land cover [47] and (B) elevation [48] (adapted from Ließ et al. [46]).
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Figure 2. CNN input data (X—covariates and Y—response), model structure, and hyperparameters (p1, p2, p3, …, p6).
Figure 2. CNN input data (X—covariates and Y—response), model structure, and hyperparameters (p1, p2, p3, …, p6).
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Figure 3. Distribution of the particle size fractions in the soil profile dataset (2740 profiles). The solid black line indicates the median of the distribution, the shaded area reflects the area between the upper and lower hinge, the dotted lines correspond to the upper and lower whisker, and the blue line corresponds to the mean. (A) Sand content, (B) silt content, and (C) clay content.
Figure 3. Distribution of the particle size fractions in the soil profile dataset (2740 profiles). The solid black line indicates the median of the distribution, the shaded area reflects the area between the upper and lower hinge, the dotted lines correspond to the upper and lower whisker, and the blue line corresponds to the mean. (A) Sand content, (B) silt content, and (C) clay content.
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Figure 4. Predictive model performance. The upper line of figures corresponds to the 2D texture predictions: (A) sand content, (B) silt content, and (C) clay content. Box plots account for the 5 repetitions of the CV. The lower line of figures corresponds to the 3D texture predictions: (D) sand content, (E) silt content, and (F) clay content. The solid line indicates the median, the shaded area reflects the area between the upper and lower hinge, and the dotted lines correspond to the upper and lower whisker. The colors reflect the two patch sizes. Black w = 5 cells and green w = 10 cells.
Figure 4. Predictive model performance. The upper line of figures corresponds to the 2D texture predictions: (A) sand content, (B) silt content, and (C) clay content. Box plots account for the 5 repetitions of the CV. The lower line of figures corresponds to the 3D texture predictions: (D) sand content, (E) silt content, and (F) clay content. The solid line indicates the median, the shaded area reflects the area between the upper and lower hinge, and the dotted lines correspond to the upper and lower whisker. The colors reflect the two patch sizes. Black w = 5 cells and green w = 10 cells.
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Figure 5. Variable importance plots for the topsoil prediction model. Boxplots reflect the 25 values from the 5-times repeated stratified 5-fold CV applied for model training. Only predictors with a VI ≥ 0.5% in at least one of the two models for at least one of the three particle size fractions are displayed. (A) Sand content [w = 5 cells], (B) sand content [w = 10 cells], (C) silt content [w = 5 cells], (D) silt content [w = 10 cells], (E) clay content [w = 5 cells], and (F) clay content [w = 10 cells]. Please refer to Table 1 for the predictor abbreviations.
Figure 5. Variable importance plots for the topsoil prediction model. Boxplots reflect the 25 values from the 5-times repeated stratified 5-fold CV applied for model training. Only predictors with a VI ≥ 0.5% in at least one of the two models for at least one of the three particle size fractions are displayed. (A) Sand content [w = 5 cells], (B) sand content [w = 10 cells], (C) silt content [w = 5 cells], (D) silt content [w = 10 cells], (E) clay content [w = 5 cells], and (F) clay content [w = 10 cells]. Please refer to Table 1 for the predictor abbreviations.
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Figure 6. Variable importance (VI) plots for the 3D prediction models. Boxplot values reflect the 25 values from the 5-times repeated stratified 5-fold CV applied for model training. The solid line indicates the median, the shaded area reflects the area between the upper and lower hinge, and the dotted lines correspond to the upper and lower whisker. Only predictors with a VI ≥ 0.5% in at least one of the two models for at least one of the three particle size fractions are displayed. (A) Sand content [w = 5 cells], (B) sand content [w = 10 cells], (C) silt content [w = 5 cells], (D) silt content [w = 10 cells], (E) clay content [w = 5 cells], and (F) clay content [w = 10 cells]. Figure lines from top to bottom correspond to the predictor variables: 1 = DEM00, 2 = TST10, 3 = VAD00, 4 = VOF0M, 5 = GMK00, 6 = DMP16, 7 = DMP18, 8 = BAG00, 9 = STR00, 10 = BGL00, 11 = LAT00, and 12 = LON00. Please refer to Table 1 for the predictor abbreviations.
Figure 6. Variable importance (VI) plots for the 3D prediction models. Boxplot values reflect the 25 values from the 5-times repeated stratified 5-fold CV applied for model training. The solid line indicates the median, the shaded area reflects the area between the upper and lower hinge, and the dotted lines correspond to the upper and lower whisker. Only predictors with a VI ≥ 0.5% in at least one of the two models for at least one of the three particle size fractions are displayed. (A) Sand content [w = 5 cells], (B) sand content [w = 10 cells], (C) silt content [w = 5 cells], (D) silt content [w = 10 cells], (E) clay content [w = 5 cells], and (F) clay content [w = 10 cells]. Figure lines from top to bottom correspond to the predictor variables: 1 = DEM00, 2 = TST10, 3 = VAD00, 4 = VOF0M, 5 = GMK00, 6 = DMP16, 7 = DMP18, 8 = BAG00, 9 = STR00, 10 = BGL00, 11 = LAT00, and 12 = LON00. Please refer to Table 1 for the predictor abbreviations.
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Figure 7. Spatial predictions from the 3D model of patch size w = 10. Figure lines correspond to the three particle size fractions: (A) sand content, (B) silt content, and (C) clay content. Figure columns display the respective values at 1, 20, 50 and 100 cm depths. Non-agricultural areas were masked out on behalf of the CORINE Land Cover Inventory 2018 [47]. The coordinate reference system used is EPSG: 25832 (ETRS89, UTM zone 32N).
Figure 7. Spatial predictions from the 3D model of patch size w = 10. Figure lines correspond to the three particle size fractions: (A) sand content, (B) silt content, and (C) clay content. Figure columns display the respective values at 1, 20, 50 and 100 cm depths. Non-agricultural areas were masked out on behalf of the CORINE Land Cover Inventory 2018 [47]. The coordinate reference system used is EPSG: 25832 (ETRS89, UTM zone 32N).
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Table 2. Ranges for hyperparameter tuning.
Table 2. Ranges for hyperparameter tuning.
HyperparameterMinimumMaximum
p1Number of filters25100
p2Kernel size in both dimensions24
p3Dropout rate0.10.5
p4Number of units25100
p5Number of units25100
p6Learning rate0.0010.01
Table 3. Sizes of the predictor arrays.
Table 3. Sizes of the predictor arrays.
PredictionswPredictor Array SizeResponse Array Size
2D5 cells[1:2917, 1:5, 1:5, 1:119][1:2917, 1:3]
2D10 cells[1:2679, 1:10, 1:10, 1:119][1:2679, 1:3]
3D5 cells[1:2740, 1:5, 1:5, 1:119][1:2740, 1:100, 1:3]
3D10 cells[1:2510, 1:10, 1:10, 1:119][1:2510, 1:100, 1:3]
Table 4. Selected model hyperparameters.
Table 4. Selected model hyperparameters.
ParametersCNN-Model [Patch Size]
2D [5 cells]2D [10 cells]3D [5 cells]3D [10 cells]
p1Number of filters91879388
p2Kernel size in both dimensions2222
p3Dropout rate0.10.10.10198260.1606008
p4Number of units75597186
p5Number of units75605246
p6Learning rate0.0010.0010.0010.001
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Ließ, M.; Sakhaee, A. Deep Learning with a Multi-Task Convolutional Neural Network to Generate a National-Scale 3D Soil Data Product: The Particle Size Distribution of the German Agricultural Soil Landscape. Agriculture 2024, 14, 1230. https://doi.org/10.3390/agriculture14081230

AMA Style

Ließ M, Sakhaee A. Deep Learning with a Multi-Task Convolutional Neural Network to Generate a National-Scale 3D Soil Data Product: The Particle Size Distribution of the German Agricultural Soil Landscape. Agriculture. 2024; 14(8):1230. https://doi.org/10.3390/agriculture14081230

Chicago/Turabian Style

Ließ, Mareike, and Ali Sakhaee. 2024. "Deep Learning with a Multi-Task Convolutional Neural Network to Generate a National-Scale 3D Soil Data Product: The Particle Size Distribution of the German Agricultural Soil Landscape" Agriculture 14, no. 8: 1230. https://doi.org/10.3390/agriculture14081230

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