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Impact of Soil Hydraulic Parameter Variability on Soil Moisture: An Empirical Orthogonal Function Analysis

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Understanding soil moisture variability is essential for addressing major global challenges in climate modeling, agriculture, hydrology, and water resource management. Land surface models (LSMs) simulate the exchange of water, energy, and momentum between the land and atmosphere, but the complexities and uncertainties that are inherent in soil hydraulic parameters make it difficult for these models to accurately represent soil moisture. Critical parameters such as porosity, field capacity, and hydraulic conductivity exhibit significant spatial and temporal variability, which further complicates the simulation of soil processes [10].

To address these obstacles, we investigated the effect of soil parameter variations on soil moisture simulations across the contiguous U.S. (CONUS). We employed a statistical technique called empirical orthogonal function (EOF) analysis to identify dominant modes of soil moisture variability and assess these modes’ responses to changes in soil parameterization. This methodological approach provides novel insights into soil moisture dynamics and highlights areas for improvement in LSMs.

Addressing the Core Challenge

<strong>Figure 1.</strong> Application of the truncated singular value decomposition (tSVD) to climate data. The matrix \(\mathbf{Y}_w\) of dimensions \(n \times m\) represents the original climate data. Using tSVD, we decompose this matrix into the \(n \times \rho\) matrix \(\hat{\mathbf{U}}\) of left singular vectors, i.e., empirical orthogonal function (EOF) vectors; the \(\rho \times \rho\) diagonal matrix \(\hat{\mathbf{\Gamma}}\) that contains the top \(\rho\) singular values; and the \(\rho \times m\) matrix \(\hat{\mathbf{V}}^T\) with right singular vectors, i.e., principal component (PC) vectors. The truncation level \(\rho\) is such that \(\rho \le \min(n,m)\). Figure courtesy of the author.
Figure 1. Application of the truncated singular value decomposition (tSVD) to climate data. The matrix \(\mathbf{Y}_w\) of dimensions \(n \times m\) represents the original climate data. Using tSVD, we decompose this matrix into the \(n \times \rho\) matrix \(\hat{\mathbf{U}}\) of left singular vectors, i.e., empirical orthogonal function (EOF) vectors; the \(\rho \times \rho\) diagonal matrix \(\hat{\mathbf{\Gamma}}\) that contains the top \(\rho\) singular values; and the \(\rho \times m\) matrix \(\hat{\mathbf{V}}^T\) with right singular vectors, i.e., principal component (PC) vectors. The truncation level \(\rho\) is such that \(\rho \le \min(n,m)\). Figure courtesy of the author.

Soil moisture is a critical variable in the hydrological cycle that influences drought prediction, irrigation management, and regional climate patterns. It plays an important role in water storage regulation and exchange processes within the soil, making it a pivotal component of both natural ecosystems and human activities. However, uncertainties in soil hydraulic properties—which are typically estimated via pedotransfer functions (PTFs)—impose obstacles for soil moisture modeling. PTFs can infer hydraulic properties from easily measurable soil texture data, but their reliance on generalized assumptions often introduces inaccuracies that can propagate through LSMs and cause errors in the simulation of water and energy fluxes [11].

Furthermore, the variability of soil hydraulic properties across spatial and temporal scales complicates efforts to capture soil moisture dynamics — an issue that is exacerbated by the mismatch between the scale of PTF development and the resolution of LSMs. Improving the representation of soil hydraulic parameters is thus critical to advance the predictive accuracy of hydrological models [8]. Our study confronts these challenges with three experimental setups that examine the impact of different soil parameterization schemes on simulated soil moisture.

Experimental Methodology

We utilized four experimental configurations within the Community Land Model version 5 (CLM5) framework [6] to explore the relationship between soil parameterization and soil moisture dynamics. The first experiment (EXP1) used globally standardized soil hydraulic parameters from the Soil Parameter Model Intercomparison Project [4] to establish a baseline for the assessment of inter-model variability. EXP2 then employed PTFs to derive parameters from common soil texture properties, allowing us to evaluate the effects of these parameter estimation methods. EXP3 served as the reference case and used the default soil hydraulic settings of CLM5, while EXP4 tested spatially uniform soil parameter configurations for specific textures—such as loamy sand, loam, clay, and silt—to assess soil texture’s effect on moisture retention and distribution [4, 7].

We ran each configuration over a 30-year period from 1980 to 2010, focusing on the root zone (up to 1 meter of depth) across the CONUS, then used EOF decomposition to extract and analyze soil moisture anomalies [2, 5]. Figure 1 summarizes the EOF decomposition, which relies on truncated singular value decomposition; the spatial components are EOF vectors and the temporal components are principal component vectors.

<strong>Figure 2.</strong> Spatial patterns of the first three empirical orthogonal functions (EOFs) of soil moisture for the contiguous U.S., derived from the ERA5-Land reanalysis dataset and three different experimental model runs (EXP1, EXP2, and EXP3). The color shading indicates the correlation coefficient; blue represents negative correlations and red represents positive correlations. <strong>2a.</strong> First mode (EOF-1). <strong>2b.</strong> Second mode (EOF-2). <strong>2c.</strong> Third mode (EOC-3). Figure courtesy of the author.
Figure 2. Spatial patterns of the first three empirical orthogonal functions (EOFs) of soil moisture for the contiguous U.S., derived from the ERA5-Land reanalysis dataset and three different experimental model runs (EXP1, EXP2, and EXP3). The color shading indicates the correlation coefficient; blue represents negative correlations and red represents positive correlations. 2a. First mode (EOF-1). 2b. Second mode (EOF-2). 2c. Third mode (EOC-3). Figure courtesy of the author.

Dominant Variability Patterns Via EOF Analysis

EOF analysis provides a powerful lens for understanding soil moisture dynamics and uncovering dominant spatial and temporal variability patterns across the CONUS. The first mode (EOF-1) captures the most significant variance in soil moisture, with positive correlations in humid regions like the southeast and negative correlations in arid regions like the southwest (see Figure 2a). This pattern reflects large-scale climatic influences, including precipitation gradients and evaporation rates. The second mode (EOF-2) highlights regional contrasts, particularly in the Great Plains, where both hydrological and topographical factors cause disparities in soil moisture (see Figure 2b). These findings underscore the utility of EOF analysis to diagnose critical drivers of soil moisture variability.

<strong>Figure 3.</strong> Temporal variability of corresponding empirical orthogonal functions from 1980-2010 that display the amplitude of the first four principal components. The results of each experiment—EXP1 in blue, EXP2 in green, and EXP3 in orange—are derived from each simulation’s soil moisture decomposition. Figure courtesy of the author.
Figure 3. Temporal variability of corresponding empirical orthogonal functions from 1980-2010 that display the amplitude of the first four principal components. The results of each experiment—EXP1 in blue, EXP2 in green, and EXP3 in orange—are derived from each simulation’s soil moisture decomposition. Figure courtesy of the author.

Temporal EOF patterns further elucidate seasonal and interannual variations (see Figure 3). The principal components that are associated with EOF-1 and EOF-2 reveal recurring cycles that align with climatic phenomena, such as the El Niño-Southern Oscillation (ENSO) and North American Monsoon. Meanwhile, the third mode (EOF-3) emphasizes localized interactions — particularly in regions such as the Pacific Northwest, where the complex relationship between precipitation, soil properties, and vegetation impacts soil moisture dynamics (see Figure 2c).

Discrepancies With Reanalysis Data

After comparing the computed Euclidean distance between the ERA5-Land dataset and CLM5 experiment (see Figure 4), we observed notable discrepancies in the model experiment — particularly in the central Great Plains. This region consistently exhibits higher variability and poorer alignment with observed data across all configurations, showcasing the difficulty of accurately parameterizing soil properties in areas with complex hydrological dynamics. In contrast, western CONUS regions demonstrate better agreement with reanalysis data, suggesting that parameterization strategies may be more effective for arid climates.

Broader Implications and Future Directions

Our findings have significant implications for hydrological modeling and resource management, as accurate soil moisture simulations are critical for drought monitoring, agricultural planning, and a variety of other tasks. By identifying the dominant modes of variability via EOF analysis, we have provided a roadmap for the improvement of LSM calibration and performance. Moreover, researchers could extend our methodological framework to other geophysical variables—such as temperature and vegetation dynamics—to foster interdisciplinary applications in Earth systems science.

<strong>Figure 4.</strong> Euclidean distance between the empirical orthogonal function (EOF) modes for the Soil Parameter Model Intercomparison Project experiments and the EOF modes for the ERA5-Land benchmark dataset. The hatch lines indicate regions where the distance between data points is below the threshold distance of 5. Figure courtesy of the author.
Figure 4. Euclidean distance between the empirical orthogonal function (EOF) modes for the Soil Parameter Model Intercomparison Project experiments and the EOF modes for the ERA5-Land benchmark dataset. The hatch lines indicate regions where the distance between data points is below the threshold distance of 5. Figure courtesy of the author.

To build upon these findings and better account for soil heterogeneity, future research should explore adaptive parameterization techniques that are tailored to specific regions with complex climatic and hydrological interactions [9]. The integration of in situ measurements and remote sensing data into the calibration process could further enhance the accuracy of soil hydraulic parameters [3], and linking EOF patterns with broader climatic phenomena—such as ENSO or the North American Monsoon—might provide deeper insights into the drivers of soil moisture variability [1]. Such advancements will support sustainable resource management and resilience to climatic changes.

Acknowledgments: This study was supervised by Alejandro Flores of Boise State University (BSU) and research scientist Irene Cionni of BSU’s Lab for Ecohydrology and Alternative Futuring.

References
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About the Author

Kachinga Silwimba

Ph.D. candidate, Boise State University

Kachinga Silwimba is a Ph.D. candidate in computing with a data science emphasis at Boise State University. His research focuses on machine learning and artificial intelligence techniques for climate and hydrological modeling, with a focus on uncertainty estimation and interpretability.