Can Deep Learning Extract Useful Information about Energy Dissipation and Effective Hydraulic Conductivity from Gridded Conductivity Fields?

We confirm that energy dissipation weighting provides the most accurate approach to determining the effective hydraulic conductivity (Keff) of a binary K grid. A deep learning algorithm (UNET) can infer Keff with extremely high accuracy (R2 > 0.99). The UNET architecture could be trained to infer the energy dissipation weighting pattern from an image of the K distribution, although it was less accurate for cases with highly localized structures that controlled flow. Furthermore, the UNET architecture learned to infer the energy dissipation weighting even if it was not trained directly on this information. However, the weights were represented within the UNET in a way that was not immediately interpretable by a human user. This reiterates the idea that even if ML/DL algorithms are trained to make some hydrologic predictions accurately, they must be designed and trained to provide each user-required output if their results are to be used to improve our understanding of hydrologic systems.

Can Deep Learning Extract Useful Information about Energy Dissipation and Effective Hydraulic Conductivity from Gridded Conductivity Fields?

We confirm that energy dissipation weighting provides the most accurate approach to determining the effective hydraulic conductivity (Keff) of a binary K grid. A deep learning algorithm (UNET) can infer Keff with extremely high accuracy (R2 > 0.99). The UNET architecture could be trained to infer the energy dissipation weighting pattern from an image of the K distribution with high fidelity, although it was less accurate for cases with highly localized structures that controlled flow. Furthermore, the UNET architecture learned to infer the energy dissipation weighting even if it was not trained on this information directly. However, the weights were represented within the UNET in a way that was not immediately interpretable by a human user. This reiterates the idea that even if ML/DL algorithms are trained to make some hydrologic predictions accurately, they must be designed and trained to provide each user-required output if their results are to be used to improve our understanding of hydrologic systems most effectively.

A physical based model to describe effective hydraulic conductivity of the soil mixtures

<p>There is a long-lasting interest in obtaining the effective hydraulic conductivity functions of soil mixtures. The few available models to obtain hydraulic conductivity of mixtures are mostly empirical and applicable for saturated conditions. We propose a simple physical model based on the effective medium theory to calculate the effective hydraulic conductivity of soil mixtures with two or more components. The model incorporates the volumetric content of each mixture component and their hydraulic conductivity to calculate the effective conductivity of the mixture. The results of the model were compared with the measured hydraulic conductivity data obtained from the simplified evaporation method using the Hyprop device. Samples were prepared by packing homogeneous mixtures of different soil textures in cylinders with a volume of 250 cm<sup>3</sup>. Packed soil mixtures were saturated and exposed to evaporation in a climate controlled laboratory with constant air temperature and humidity. The results show an acceptable match between the measured and modeled hydraulic conductivity of the tested soil mixtures. The model can be used as a physical way to describe the effective hydraulic conductivity of mixtures in a wide range of moisture.</p>

Laboratory device to investigate the heterogeneity’s influence on the effective hydraulic conductivity

<p>Groundwater flow and contaminant transport are strongly influenced by the aquifer’s heterogeneity (Chao et al., 2000; Fernàndez-Garcia et al., 2004). Generally, the flow (and transport) variables, such as the effective conductivity K<sub>eff</sub>, can be modelled as random space functions (RSFs) and determined by means of a self-consistent approximation (Severino, 2018). In particular, we aim at estimating the effective conductivity K<sub>eff</sub> of a highly heterogeneous aquifer made of 12 different porous materials, whose K-values were experimentally measured.</p><p>A heterogeneous phreatic aquifer was built in the GMI Laboratory of the Department of Civil Engineering of the University of Calabria, inside a metal box (2 m x 2 m x 1 m). The thickness (0.35 m) of the aquifer was built by overlapping 7 different layers of 0.05 m, each consisting of 361 cells (19 x 19), with dimensions equal to 0.1 m x 0.1 m x 0.05 m. For each layer, each cell was filled with one of the 12 porous materials previously characterized in the lab, making the choice randomly. A central (pumping) well and 37 piezometers were located at different distances from the first according to a radial configuration.</p><p>A pumping test was carried out by a constant flow rate of 70 L/hour. The hydraulic head data, evaluated by using the Neuman method and verified in compliance with the boundary conditions, allowed an effective hydraulic conductivity value K<sub>eff</sub> to be obtained.</p><p>Afterwards, this value was compared with K values measured in laboratory by permeameter for each of the 12 porous media used to build the heterogeneous aquifer considered here and with the main statistical parameters related to them. We found the K<sub>eff</sub> value in a very good agreement with the expression obtained by the self-consistent approximation (Severino, 2018).</p><p> </p><p><strong>References</strong></p><p>Chao C.-H., Rajaram H. and Illangasekare T. H. (2000). Intermediatescale experiments and numerical simulations of transport under radial flow in a two-dimensional heterogeneous porous medium, Water Resour. Res., 36(10), 2869– 2884.</p><p>Fernàndez-Garcia D., Illangasekare T. H. and Rajaram H. (2004). Conservative and sorptive forced-gradient and uniform flow tracer tests in a three-dimensional laboratory test aquifer. Water Resour. Res., Vol. 40, W10103, doi:10.1029/2004WR003112.</p><p>Severino G., 2018. Effective conductivity in steady well-type flows through porous formations. Stochastic Environmental Research and Risk Assessment, Vol. 5, https://doi.org/10.1007/s00477-018-1639-5.</p>

Effective hydraulic conductivity and its relationship with the other attributes of Cerrado soils

ABSTRACT The objective of this study was to determine the effective hydraulic conductivity of six areas located in the Cerrado region of Mato Grosso, Brazil, and to identify physical attributes of soils with potential for predicting effective hydraulic conductivity. The tests to determine the effective hydraulic conductivity were carried out in six areas, covering the textural classes sand, sandy loam and clay, and the following uses: pasture, Cerrado and agriculture. Particle size, sand fractionation, total carbon content, degree of clay flocculation, bulk density, macroporosity, microporosity, mean weight diameter, mean geometric diameter and aggregate stability index were determined. From the data, statistical analyses of contrasts were performed by the Kruskal - Wallis test, and simple Pearson’s correlation coefficient was determined between variables. The average values of effective hydraulic conductivity for the pasture, agriculture and Cerrado areas were 95.73, 27.83 and 48.31 mm h-1, respectively. Higher value of effective hydraulic conductivity was observed in the Pasture area point 2 when compared to the Agriculture area point 2, because the amount of clay determined in Agriculture area was approximately 16 times greater than that of the area Pasture point 2, conditioning lower water infiltration in the soil profile of the area Agriculture point 2. Among the physical attributes analyzed, those with the highest potential for Ke prediction were: clay, silt, sand (coarse, medium and fine), total carbon and aggregate stability index.