Elementary effects for models with dimensional inputs of arbitrary type and range: Scaling and trajectory generation

Area of Science:

• Computational science and engineering
• Sensitivity analysis and uncertainty quantification

Background:

• The Elementary Effects method is a global sensitivity analysis technique.
• It has traditionally been limited to models with dimensionless inputs on [0, 1].

Purpose of the Study:

• To extend the Elementary Effects method for models with dimensional, arbitrary interval, or discrete inputs.
• To propose and evaluate new dimensionless sensitivity indices for improved parameter ranking.

Main Methods:

• Developed two novel dimensionless sensitivity indices by normalizing scaled mean/median absolute effects.
• Tested indices using 9 trajectory generation methods across 4 test functions, including the Penman-Monteith equation.
• Evaluated the necessity of input scaling for accurate parameter importance.

Main Results:

• Scaled elementary effects are crucial for correct parameter importance rankings with diverse input types.
• Methods employing smaller step sizes generally yield more accurate sensitivity rankings.
• Comparing both proposed sensitivity indices offers a more robust assessment.
• Simulation point spread and discrepancy are unreliable performance indicators for trajectory methods.

Conclusions:

• The proposed method effectively extends Elementary Effects analysis to broader model input types.
• Input scaling and careful selection of trajectory generation methods are vital for reliable sensitivity analysis.
• The new indices provide a more accurate and versatile approach to identifying key model parameters.