12.1 Calibration techniques and objective functions

Calibration techniques and objective functions are crucial for fine-tuning hydrological models. They help adjust parameters to match simulated results with real-world data, improving model accuracy and reliability. This process is key to making models useful for predicting water behavior and managing resources.

Choosing the right calibration method and objective function is essential for model success. From manual tweaks to advanced algorithms, these tools help modelers find the best parameter sets. The goal? To create models that can tackle real-world water challenges with confidence.

Model Calibration in Hydrology

Purpose and Importance

• Model calibration adjusts model parameters to improve agreement between simulated and observed hydrological variables (streamflow, groundwater levels, soil moisture)
• Calibration necessary because hydrological models contain parameters that cannot be directly measured or estimated from field data
  • These parameters need optimization to ensure model accurately represents real-world system
• Calibration reduces model uncertainty, improves model reliability, and increases model's ability to predict future hydrological behavior under different scenarios (climate change, land use change)
• Iterative process involving running model multiple times with different parameter sets
  • Compares simulated outputs with observed data
  • Adjusts parameters until satisfactory level of agreement achieved
• Enhances model's predictive capabilities crucial for various applications
  • Water resource management
  • Flood forecasting
  • Environmental impact assessment

Calibration Techniques for Model Optimization

Manual and Automatic Calibration

• Manual calibration involves manually adjusting model parameters based on:
  • Expert knowledge
  • Visual inspection of simulated and observed hydrographs
  • Trial-and-error approaches
• Automatic calibration uses optimization algorithms to systematically search for best parameter sets
  • Minimizes differences between simulated and observed hydrological variables
• Optimization algorithms for automatic calibration include:
  • Local search methods (Nelder-Mead simplex, pattern search)
  • Global search methods (genetic algorithms, particle swarm optimization, shuffled complex evolution)

Advanced Calibration Techniques

• Multi-objective calibration considers multiple objective functions simultaneously
  • Minimizes error in streamflow and groundwater levels
  • Finds set of Pareto-optimal solutions representing trade-offs between different objectives
• Sensitivity analysis performed before or during calibration
  • Identifies most influential parameters on model outputs
  • Focuses calibration efforts on most important parameters
  • Reduces computational time

Objective Functions for Hydrological Models

Common Objective Functions

• Objective functions quantify difference between simulated and observed hydrological variables
  • Guide calibration process to find optimal parameter sets
• Mean squared error (MSE) and root mean squared error (RMSE)
  • Measure average squared difference between simulated and observed values
  • RMSE is square root of MSE
• Nash-Sutcliffe efficiency (NSE)
  • Compares model performance to mean of observed data
  • Values range from -∞ to 1 (1 indicates perfect fit)
• Percent bias (PBIAS)
  • Measures average tendency of simulated values to be larger or smaller than observed values
  • Expressed as percentage

Selecting Appropriate Objective Functions

• Kling-Gupta efficiency (KGE)
  • Multi-component objective function considering correlation, bias, and variability between simulated and observed values
  • Provides more balanced evaluation of model performance compared to NSE
• Choice of objective function depends on:
  • Model's purpose
  • Type of hydrological variable being simulated
  • Desired emphasis on different aspects of model performance (high flows, low flows, overall water balance)

Model Performance Evaluation

Goodness-of-Fit Measures

• Goodness-of-fit measures assess agreement between simulated and observed hydrological variables
  • Provide quantitative evaluation of calibrated model's performance
• In addition to objective functions used during calibration (MSE, RMSE, NSE, PBIAS, KGE), other measures can be employed:
  • Coefficient of determination (R²)
    • Measures proportion of variance in observed data explained by model
    • Values range from 0 to 1 (1 indicates perfect fit)
  • Volumetric efficiency (VE)
    • Assesses agreement between simulated and observed total water volume over specified period
    • Values range from -∞ to 1 (1 indicates perfect fit)

Graphical Techniques and Model Validation

• Graphical techniques visually compare simulated and observed values
  • Scatterplots
  • Hydrographs
  • Flow duration curves
  • Identify systematic biases or discrepancies in model's performance
• Model validation using independent dataset (data not used during calibration)
  • Assesses model's ability to generalize and predict hydrological behavior under different conditions
• Goodness-of-fit measures should be interpreted in context of:
  • Model's purpose
  • Specific hydrological system being studied
  • Limitations and uncertainties associated with input data and model structure