model-calibration

Model Calibration Skill

Overview

Model calibration involves adjusting parameters to minimize differences between simulations and observations. RMSE (Root Mean Squared Error) is a standard metric for measuring model performance.

RMSE Calculation

Basic Formula

RMSE = sqrt(mean((simulated - observed)^2))

Implementation

import numpy as np
import pandas as pd

def calculate_rmse(simulated, observed):
    """Calculate RMSE between matched pairs"""
    if len(simulated) == 0:
        return np.nan
    residuals = simulated - observed
    rmse = np.sqrt(np.mean(residuals**2))
    return rmse

def calculate_metrics(sim_temps, obs_temps, depths=None, dates=None):
    """
    Calculate multiple RMSE metrics

    Parameters:
    - sim_temps: matched simulated temperatures
    - obs_temps: matched observed temperatures
    - depths: depth of each match (for deep water filtering)
    - dates: datetime of each match (for seasonal filtering)

    Returns:
    - overall_rmse: RMSE of all matched pairs
    - annual_deep_rmse: RMSE of pairs at depths >= 13m
    - summer_deep_rmse: RMSE of summer (Jun-Sep) pairs at depths >= 13m
    """

    overall_rmse = calculate_rmse(sim_temps, obs_temps)

    # Annual deep water (depths >= 13m)
    if depths is not None:
        deep_mask = np.array(depths) >= 13
        annual_deep_rmse = calculate_rmse(
            sim_temps[deep_mask],
            obs_temps[deep_mask]
        )
    else:
        annual_deep_rmse = np.nan

    # Summer deep water (Jun-Sep, depths >= 13m)
    if dates is not None and depths is not None:
        summer_mask = (np.array([d.month for d in dates]) >= 6) & \
                     (np.array([d.month for d in dates]) <= 9)
        deep_mask = np.array(depths) >= 13
        combined_mask = summer_mask & deep_mask
        summer_deep_rmse = calculate_rmse(
            sim_temps[combined_mask],
            obs_temps[combined_mask]
        )
    else:
        summer_deep_rmse = np.nan

    return {
        'overall_rmse': overall_rmse,
        'annual_deep_rmse': annual_deep_rmse,
        'summer_deep_rmse': summer_deep_rmse
    }