Forecast Generation¶

Weather Forecast Uncertainty Model Development¶

The emulator models uncertainty in forecasts of dry-bulb temperature (ambient temperature) and global horizontal irradiation (GHI) using a first-order autoregressive model (AR(1)). The model was trained using historical forecast and measurement data from four locations with varying climates and forecast sources: Berkeley, Berlin, Oslo, and Leuven. Forecast errors were calculated over a 48-hour prediction horizon at one-hour intervals.

Dry-Bulb Forecast Uncertainty Model

The forecast error for ambient temperature is modeled using a first-order autoregressive process AR(1):

The synthetic forecast is computed by adding the forecast error to the measured value:

Where:

• \(\phi\) is the autoregressive coefficient.

• \(\mu\) and \(\sigma\) are the mean and standard deviation of the residual noise.

• \(X_{k+\tau}\) is the measured value at timestep \(k + \tau\).

• \(\tau \in [1, 48]\) is the forecast horizon in hours.

The initial error is generated separately as:

GHI Forecast Uncertainty Model

The forecast error for global horizontal irradiation (GHI) uses the same AR(1) structure, but with Laplace-distributed residuals to better match the peaked and heavy-tailed nature of the real GHI forecast errors:

The synthetic GHI forecast is similarly constructed:

Special handling is applied to GHI data:

• Nighttime conditions: When the measured GHI is zero, no error is added (\(\hat{X}_{\tau|k} = 0\)).

• Post-processing: A moving average filter with a 3-sample window is applied

to smooth synthetic GHI forecasts and reduce unrealistic high-frequency noise.

The model calibration process, including error extraction, statistical analysis, and model fitting, was performed separately from the BOPTEST framework within Zheng et al. (2025). The resulting model parameters (AR coefficients and distribution properties) are the only components carried forward into BOPTEST.

Weather Forecast Uncertainty Scenarios Definition¶

BOPTEST supports four different uncertainty scenarios:

1. Deterministic (no uncertainty included in the forecasts).

2. Low uncertainty.

3. Medium uncertainty.

4. High uncertainty.

Each uncertainty scenario corresponds to a predefined set of AR(1) model parameters. These include the autoregressive coefficient (F), gain on the noise term (K), and the mean of the noise distribution (μ). An initial error condition is also defined using F₀ and K₀.

For GHI, the parameters are derived directly from the behavior observed at three cities analyzed in Zheng et al. (2025) (Berkeley, Leuven, and Berlin). Each city dataset was mapped to one of the scenarios based on the observed error distributions.

For ambient temperature, the scenario parameters were not taken from a single site, but rather derived through a combination and aggregation of data across five locations (Berkeley, Leuven, Berlin, Oslo, and Milan). This allowed for a broader representation of forecast variability. The statistical targets, mean error and standard deviation evolution over the forecast horizon, were established based on real data, and an optimization routine was used to calibrate the AR(1) model parameters accordingly. These models were tuned to approximate real-world behaviors such as variance growth over time and location-specific biases. For example, the high uncertainty scenario includes a nonzero mean to reflect systematic bias observed in some forecast datasets.

Configuration of Uncertainty in BOPTEST by Users¶

The forecast uncertainty can be configured by users in the following ways:

• Whether uncertainty is enabled: Users can choose whether they want deterministic or stochastic forecasts.

• Which forecast variables are affected: Uncertainty may be applied to ambient temperature, global horizontal irradiation (GHI), or both.

• The uncertainty scenario: Forecasts may follow low, medium, or high uncertainty levels, representing varying degrees of forecast error.

• The seed for randomization: Users can define a fixed seed value to ensure reproducibility of stochastic forecast realizations across simulation runs.

Users use the BOPTEST API to configure forecast uncertainty. Specifically, scenario parameters are available in the /scenario request for temperature_uncertainty and solar_uncertainty, which can each take values of None (default), for deterministic, or low, medium, or high if a user wants to enable uncertainty. A user can also define a seed parameter with any integer value, which allows for repeatable results of the underlying random processes, and therefore, sequence of uncertain forecasts for a given test set up.

When obtaining forecasts with the /forecast request, if a scenario with uncertainty has been configured, and the forecast request includes ambient temperature (TDryBul) or GHI (HGloHor), the horizon parameter is limited to less-than-or-equal to 48 hours. In addition, the forecast and associated error with these variables will only be updated at the start of each hour of simulation time. Use of the interval parameter will interpolate the forecasts to the specified interval, but for forecast variables with uncertainty, the interpolation will be linear based on an underlying uncertain forecast with interval of one hour, consistent with the validation of the error models as described above.

Code Integration and Related Files¶

The forecast uncertainty emulator is integrated into the BOPTEST framework through the following core modules and configuration files:

• forecast/error_emulator.py

This is the core module implementing the forecast uncertainty model (previously referred to as uncertainty_emulator.py). It includes the AR(1) model logic and error sampling functionality for temperature and GHI.

• forecast_uncertainty_params.json

A JSON file storing the pre-calibrated parameters (AR coefficients, noise distributions, etc.) for each uncertainty scenario. This file is loaded and read-in by BOPTEST at runtime upon deployment.

• tests/test_forecast_uncertainty.py

Contains specific unit tests for verifying emulator functionality. Additional unit tests are also present in the API unit test module.

References¶

Zheng, W., Zabala, L., Febres, J., Blum, D., & Wang, Z. (2025). Quantifying and simulating the weather forecast uncertainty for advanced building control. Journal of Building Performance Simulation, 1–16. https://doi.org/10.1080/19401493.2025.2453537.