Decomposition of the mean absolute error (MAE) into systematic and unsystematic components

Area of Science:

• Hydrology
• Quantitative Modeling
• Error Analysis

Background:

• Quantitative model performance is often evaluated using sums-of-squares error metrics like Mean Squared Error (MSE) and Root Mean Squared Error (RMSE).
• While MSE/RMSE are mathematically tractable for decomposition, Mean Absolute Error (MAE) offers superior interpretability for quantifying average error.
• Existing MSE decompositions provide insights into systematic and unsystematic error components.

Purpose of the Study:

• To develop and demonstrate a novel decomposition of MAE into three distinct error submeasures.
• To provide a more interpretable alternative to MSE-based error decompositions for quantitative models.
• To enhance the understanding of model-error distributions.

Main Methods:

• Developed a three-part decomposition for MAE, comprising bias error, proportionality error, and unsystematic error.
• Applied this decomposition to a long-term streamflow reconstruction dataset.
• Illustrated the properties and benefits of the new MAE decomposition.

Main Results:

• The proposed MAE decomposition effectively separates model error into bias, proportionality, and unsystematic components.
• This method offers clearer insights into the nature of model-error distributions than MSE-based decompositions.
• The decomposition was successfully illustrated using streamflow data from the Upper Colorado River.

Conclusions:

• The three-part MAE decomposition provides a more intuitive and informative assessment of quantitative model performance.
• This approach enhances the interpretability of model errors, aiding in model improvement.
• The method is broadly applicable to various quantitative modeling applications, particularly in hydrology.