Thermal-Memory Lake Temperature Model

Research prototype. Recommended workflow: Calibration → Independent validation → Final model → Reconstruction & prediction.

01 Load calibration dataset

02 Validate input

03 Calibrate & reconstruct

04 Independent validation

05 Final model

06 Reconstruction & prediction

Configure and load calibration dataset

Temporal resolution

Daily Monthly Yearly

Use one row for every selected timestep. Sparse observed LST is allowed; sparse atmospheric forcing is not.

Choose or drop a calibration CSV file Required columns are checked automatically

Calibration CSV columns date air_temp_c shortwave_w_m2 wind_speed_m_s observed_lst_c

No calibration dataset loaded

Select a temporal resolution and load a CSV to begin.

Validate calibration input

Date	Air temp (°C)	Shortwave (W m⁻²)	Wind (m s⁻¹)	Observed LST (°C)

Calibration results

Parameter estimates

Parameter	Estimate	Meaning

Model equation

T_L(t) = e^−Δt/τ T_L(t−Δt)

(1 − e^−Δt/τ) [β₀ + β_TT_a(t) + β_SS_↓(t) + β_UU(t)]

M = e^−1/τ

03A

Historical reconstruction

Observed and reconstructed LST

Hover or move across the plot to inspect individual timesteps.

Reconstructed / projected LST Observed LST

Select timestep

Independent validation

✓

Chronological hold-out validation

Observed LST values are ordered by date. The earlier observations are used to calibrate a separate validation model, while the later observations are withheld and used only for testing.

Calibration share of observed LST

70%

Default: 70% calibration / 30% held-out validation. The split is based only on observed LST dates, not on all daily rows.

Temporal validation

Free-running prediction from the calibration period compared with held-out LST observations.

Validation-model prediction Calibration observations Held-out observations

Observed vs predicted

Held-out observations only; the diagonal line represents perfect agreement.

Held-out validation observations

Date	Observed LST (°C)	Predicted LST (°C)	Residual (°C)

Final model using all observations

After validation, rebuild the final lake-specific model using all reliable observed LST values. These final parameters are then carried into the reconstruction and prediction stage.

Final parameter estimates

Parameter	Estimate	Meaning

Final model state

Reconstruction & prediction

Use the final calibrated parameters for gap-filling, hindcast reconstruction, remote-access / sparse-observation periods, or forecast / future prediction.

1. Load application-period forcing

Choose or drop an application CSV file Observed LST can be blank or partly available

No application dataset loaded

Load an application dataset after building the final model.

2. Choose application settings

Initial state

For direct continuation beyond the historical record, the first option is usually appropriate.

Use observed LST in the application file as state re-anchors whenever available

Application mode

Application-period LST

Reconstructed / predicted application series

The chart uses the final lake-specific parameters estimated in Step 05.

Modeled LST Observed LST in application file

Select application timestep

Application-period preview

Date	Observed LST (°C)	Modeled LST (°C)	State source

Scientific interpretation and limitations

This is a reduced-order, physically motivated, semi-empirical model. It is not a complete lake heat-budget or hydrodynamic model.

The model explicitly represents thermal memory through τ, but does not explicitly simulate bathymetry, mixed-layer depth, longwave radiation, humidity, inflow heat, sediment heat flux, ice processes, or vertical stratification.

Step 05 provides the final parameters that are carried into Step 06. Application quality depends on the representativeness of the calibration observations and the availability of continuous atmospheric forcing.