Parameter estimation of hydrologic models using a likelihood function for censored and binary observations.

Area of Science:

• Hydrology and Environmental Modeling
• Statistical Inference in Environmental Science

Background:

• Accurate hydrologic modeling requires extensive observational data, which is often costly and difficult to obtain.
• Simpler sensors provide frequent but censored data (e.g., binary observations), posing challenges for parameter estimation.
• Existing methods struggle to effectively utilize censored observations for learning model parameters.

Purpose of the Study:

• To develop a formal likelihood function for incorporating censored observations into hydrologic model parameter inference.
• To implement a Bayesian framework for parameter estimation using censored data, accounting for model deficits and input uncertainty.
• To demonstrate the methodology's effectiveness using binary observations from an urban catchment's combined sewer overflows.

Main Methods:

• Developed a novel likelihood function designed to handle censored data, including binary observations.
• Employed a Bayesian inference framework to estimate parameters of a hydrodynamic rainfall-runoff model.
• Applied the method to a case study involving an urban catchment and combined sewer overflow data.

Main Results:

• Censored observations significantly improve parameter learning, reducing parameter standard deviation by an average of 45%.
• The inference process substantially enhances model predictive performance, indicated by higher Nash-Sutcliffe efficiency.
• The value of censored data for inference is highly dependent on the experimental design, particularly sensor placement.

Conclusions:

• Censored observations are valuable for hydrologic model parameter estimation within a Bayesian framework.
• The proposed methodology offers a cost-effective way to improve hydrologic model accuracy using readily available sensor data.
• Future advancements in Internet of Things technology can leverage this approach for widespread environmental monitoring and modeling.