Interpolation of steady-state concentration data by inverse modeling

Area of Science:

• Environmental Science
• Hydrogeology
• Geostatistics

Background:

• Groundwater concentration measurements are often sparse, necessitating interpolation for comprehensive analysis.
• Existing interpolation methods struggle with the nonlinear relationship between concentration and hydraulic conductivity.
• Uncertainty quantification is crucial for environmental risk assessment in groundwater studies.

Purpose of the Study:

• To develop an improved interpolation technique for sparse groundwater concentration data.
• To address the nonlinearities inherent in groundwater flow and transport processes.
• To provide concentration estimates with reliable uncertainty bounds.

Main Methods:

• A conditional Monte Carlo approach is proposed, conditioning an ensemble of log-conductivity fields on available hydrological data.
• Flow and transport simulations are performed for each conditional field, ensuring consistency with measurements.
• The method utilizes an ensemble of transport simulations to derive conditional statistical concentration distributions.

Main Results:

• The proposed method generates conditional statistical distributions of concentration between observation points.
• It implicitly respects physical bounds (non-negative concentrations) and non-Gaussian distributions.
• The approach accurately captures the nonlinear dynamics of groundwater transport processes.

Conclusions:

• The conditional Monte Carlo method offers a robust alternative to traditional kriging for interpolating groundwater concentration data.
• This technique provides physically realistic and statistically sound concentration estimates with uncertainty bounds.
• It is particularly valuable for environmental risk analysis where accurate spatial concentration prediction is vital.