glm-calibration

name	glm-calibration
description	Calibrating General Lake Model (GLM) parameters to match field observations of water temperature. Use this skill whenever you need to adjust light extinction (Kw), mixing coefficients (coef_mix_hyp), or atmospheric bulk transfer factors (wind_factor, lw_factor, ch) to improve model fit. Essential for reducing temperature RMSE and achieving model validation thresholds for lakes.

GLM Parameter Calibration Strategy

Overview

Calibration is the process of systematically adjusting model parameters to minimize error between simulated and observed water temperatures. For GLM on Lake Mendota, five parameters control temperature evolution:

• Kw (light extinction): Controls solar heating penetration depth
• coef_mix_hyp (hypolimnion mixing): Controls deep water turbulent mixing
• wind_factor (wind multiplier): Scales wind-driven surface mixing
• lw_factor (longwave multiplier): Adjusts atmospheric heat exchange
• ch (sensible heat coefficient): Controls air-water heat transfer

Physical Basis for Parameter Effects

Kw (Light Extinction, 0.1 - 0.5)

• Low Kw (0.1): More light penetrates to depth, warms deeper layers
• High Kw (0.5): Light absorbed quickly, heating concentrated at surface
• Effect on RMSE: Affects whole water column, especially sensitive to epilimnion heating
• Tuning: If summer surface temps too high, increase Kw. If deep winter temps too cold, decrease Kw.

coef_mix_hyp (Hypolimnion Mixing, 0.3 - 0.7)

• Low value (0.3): Less deep mixing, sharper thermocline, deeper water stays colder longer
• High value (0.7): More mixing, faster temperature equilibration in hypolimnion
• Effect on RMSE: Primarily affects annual_deep_rmse (deep water temperatures)
• Tuning: If deep water temperatures lag observations, increase coef_mix_hyp. If too warm, decrease.

wind_factor (Wind Speed Multiplier, 0.7 - 1.3)

• Low value (0.7): Less wind-driven mixing, stronger stratification
• High value (1.3): More wind-driven mixing, weaker stratification, mixed layer deepens faster
• Effect on RMSE: Affects thermocline depth, particularly impacts summer_deep_rmse
• Tuning: If summer thermocline too sharp (warm surface, cold deep), increase wind_factor.

lw_factor (Longwave Radiation Multiplier, 0.7 - 1.3)

• Low value (0.7): Less downwelling IR radiation, surface cools faster at night
• High value (1.3): More IR radiation, surface warming enhanced
• Effect on RMSE: Affects diurnal and seasonal surface temperature amplitude
• Tuning: If winter surface temps too cold, increase lw_factor. If too warm, decrease.

ch (Sensible Heat Coefficient, 0.0005 - 0.002)

• Low value (0.0005): Weak air-water heat exchange, slow surface temperature response
• High value (0.002): Strong air-water heat exchange
• Effect on RMSE: Affects spring/fall transition rates and surface temperature amplitude
• Tuning: If surface temps respond too slowly to weather, increase ch. If overly responsive, decrease.

Calibration Workflow

Phase 1: Baseline and Diagnosis (Iteration 1-3)

1. Run GLM with initial parameter set
2. Compute RMSE overall, annual_deep, summer_deep
3. Diagnose which RMSE threshold is violated most
4. Identify spatial/temporal patterns in error (e.g., always too warm at depth)

Phase 2: Targeted Parameter Adjustment (Iteration 4-15)

Target parameters based on error pattern:

If annual_deep_rmse is highest (deep cold bias):

• Decrease coef_mix_hyp (0.05 step)
• OR increase lw_factor (0.05 step)

If summer_deep_rmse is highest (summer stratification too strong):

• Increase wind_factor (0.1 step)
• OR increase coef_mix_hyp (0.05 step)

If overall_rmse is highest from surface temps (warming bias):

• Increase Kw (0.05 step)
• OR decrease lw_factor (0.05 step)
• OR decrease ch (0.0001 step)

Phase 3: Refinement (Iteration 16+)

Once close to thresholds:

• Make smaller adjustments (0.01-0.02 parameter steps)
• Focus on the single RMSE metric furthest from threshold
• Balance trade-offs (e.g., improving annual_deep might slightly worsen summer_deep)

Step Size Guidelines

Large steps (when far from threshold):

• Kw: 0.05
• coef_mix_hyp: 0.1
• wind_factor: 0.1
• lw_factor: 0.1
• ch: 0.0001

Small steps (when within 0.2 of threshold):

• Kw: 0.01
• coef_mix_hyp: 0.02
• wind_factor: 0.05
• lw_factor: 0.05
• ch: 0.00005

Constraints

Always maintain:

• Kw in [0.1, 0.5]
• coef_mix_hyp in [0.3, 0.7]
• wind_factor in [0.7, 1.3]
• lw_factor in [0.7, 1.3]
• ch in [0.0005, 0.002]

DO NOT modify: sw_factor, cd, ce, initial profiles, time period, or forcing data.

Convergence Criteria

Stop tuning when:

1. overall_rmse < 1.60 AND
2. annual_deep_rmse < 1.55 AND
3. summer_deep_rmse < 1.70

If one metric oscillates around threshold after >20 iterations, accept as best feasible solution within constraints.

Documentation

Record for each iteration:

• Parameters tested
• RMSE results (all three metrics)
• Number of matched pairs (overall, annual_deep, summer_deep)
• Reasoning for next parameter adjustment
• Iteration number and date