Modeling Soil Volumetric Water Content Based on Climatic Factors in the Tripoli Region (Libya) Using Multiple Linear Regression

Technical Summary: Modeling Soil Volumetric Water Content in Tripoli, Libya

Problem Statement
Soil moisture is a critical component of the Earth's water and energy cycles, influencing agricultural productivity, water resource management, and the frequency of extreme weather events such as droughts and floods. In Libya, a country characterized by semi-arid to arid climates, understanding soil water dynamics is essential for food security and disaster risk mitigation. However, long-term global monitoring of soil moisture via field measurements is limited. While remote sensing offers an alternative, there is a specific need to quantitatively model the relationship between local climatic factors and soil volumetric water content (VWC) using statistical methods. This study addresses the gap in quantitative analysis regarding how specific climatic variables influence soil moisture in the Tripoli region, particularly in the context of climate change projections indicating decreased precipitation and increased temperatures for North Africa.

Methodology
The study utilized monthly data spanning 297 readings from 2001 to 2024, sourced from the ERA5 dataset (European Centre for Medium-Range Weather Forecasts). The analysis was conducted using R statistical software.

• Variables:
  • Dependent Variable ($Y$): Mean volumetric soil water content across four soil depths.
  • Initial Independent Variables: Relative humidity, precipitation, mean soil temperature (across four depths), air temperature, wind speed, potential evaporation, and groundwater depth.
• Statistical Approach:
  1. Descriptive Analysis: Examined the distribution and central tendency of all variables.
  2. Multicollinearity Assessment: A correlation matrix and Variance Inflation Factor (VIF) analysis were performed. Initial analysis revealed severe multicollinearity among several variables (e.g., air temperature, soil temperature, and potential evaporation had VIF values exceeding 12, far above the acceptable threshold of 5).
  3. Variable Selection: To ensure model stability, variables with high VIF values were excluded. The final model retained three independent variables with acceptable VIF scores: Relative Humidity ($X_1$), Precipitation ($X_2$), and Mean Soil Temperature ($X_3$).
  4. Model Construction: A Multiple Linear Regression (MLR) model was developed to predict soil VWC based on the selected climatic factors.
  5. Model Validation: Assumptions were verified using residual plots (Residuals vs. Fitted) and Q-Q plots to check for homoscedasticity and normality of residuals.

Key Results

• Descriptive Statistics: The mean volumetric soil water content was 0.02 with low standard deviation, indicating consistency. Precipitation showed high variability (mean 0.92 mm), while relative humidity averaged 44.10%.
• Correlation Analysis:
  • A strong positive correlation was found between soil VWC and Relative Humidity ($r = 0.638$).
  • A moderate positive correlation existed between soil VWC and Precipitation ($r = 0.528$).
  • A moderate negative correlation was observed between soil VWC and Mean Soil Temperature ($r = -0.559$).
• Regression Model Performance:
  • The final model equation is: $\hat{Y} = 0.01378 + (7.0 \times 10^{-5} \times X_1) + (4.22 \times 10^{-4} \times X_2) - (9.8 \times 10^{-5} \times X_3)$.
  • Significance: All three predictors were statistically significant ($p < 0.001$).
    • Precipitation: Identified as the most influential factor ($\beta = 4.22 \times 10^{-4}$). An increase of 1 mm in precipitation results in a direct increase of 0.000422 in average soil moisture.
    • Relative Humidity: Shows a positive effect ($\beta = 7.0 \times 10^{-5}$), attributed to reduced evaporation.
    • Soil Temperature: Shows a significant negative effect ($\beta = -9.8 \times 10^{-5}$), attributed to increased evaporation and seepage.
  • Explanatory Power: The adjusted $R^2$ value is 0.477, indicating that the model explains approximately 48% of the variation in soil volumetric water content.
  • Overall Fit: The F-test confirmed the model's overall statistical significance ($F \approx 91$, $p < 0.001$). Diagnostic plots confirmed that residuals were randomly distributed and followed a normal distribution, validating the model's assumptions.

Significance and Claims
The paper claims that the study successfully establishes a statistically significant relationship between selected climatic factors and soil volumetric water content in the Tripoli region. By isolating precipitation, relative humidity, and soil temperature as the primary drivers, the research provides a predictive tool for understanding soil moisture dynamics in a semi-arid environment.

The authors assert that this modeling approach supports water resource management and agricultural planning, which is critical given climate projections for North Africa predicting a 10–20% decrease in precipitation and a 2–3°C temperature rise by 2050. The study concludes that while the model explains nearly half of the variance (a value considered good for environmental studies), it effectively highlights the direct impact of precipitation and the inverse impact of temperature on soil moisture. The authors recommend the use of these key variables for future assessments in arid regions and suggest that more advanced models (e.g., time series or nonlinear) could further improve predictive accuracy.