We apply CBaM to post-process seasonal temperature and precipitation forecasts from the North American Multi-Model Ensemble (NMME). Prior to its use as an experimental post-processing tool at the NOAA Climate Prediction Center, CBaM was developed and tested by colleagues at Australia's CSIRO, where they found that the method improved seasonal forecast skill and reliability. CBaM is implemented monthly as an experimental guidcance tool for the Climate Prediction Center's 3-month outlook.

The CBaM method consists of three components: Calibration, Bridging, and Merging. Calibration models statistically relate dynamical model reforecasts to observations over some historical period. These statistical relationships are then applied to correct real-time dynamical model forecasts. We develop bridging models similarly to calibratiion models in that we use statistical models to relate dynamical model reforecasts to observations. However, unlike calibration, our bridging models specifically relate dynamical model reforecasts of the Nino3.4 index to observed temperature or precipitation. Thus, a bridged forecast is a temperature or precipitation forecast derived from dynamical model forecasts of ENSO. This is in contrast to a calibrated forecast, which is a temperature or precipitation forecast derived from dynamical model forecasts of temperature or precipitation. We find that bridging helps correct for instances when dynamical models fail to reproduce observed teleconnection patterns related to ENSO (or any other relevant bridging predictor, for that matter). Both the calibration and bridging components rely on Bayesian joint probability (BJP) modeling. For a more detailed description of the BJP models applied to post-process the NMME, please see Strazzo et al. (2019).

Finally, we "merge" the calibrated and bridged forecasts by taking a weighted average. Presently, we apply Bayesian Model Averaging to determine the weights used in the merging process.

1. Three-month seasonal mean (raw) forecasts of temperature, precipitation and Nino3.4 anomalies are calculated for each of the seven NMME member models out to lead 6.
2. BJP models are used to generate calibrated and bridged forecasts of temperature and precipitation for each of the seven NMME member models. Note that BJP models are developed using NMME hindcast data and observed data from GHCN-CAMS (temperature) and CPC-CMAP (precipitation) datasets.
3. Merged forecasts are calculated for each of the seven NMME member models as a weighted average of each model's calibrated and bridged forecast, where the weights are determined using Bayesian model averaging (BMA).
4. The calibrated (bridged) NMME forecast is calculated by taking the equal-weighted average of the seven calibrated (bridged) member model forecasts.
5. The merged NMME forecast is calculated by taking the weighted average of the NMME calibrated and bridged forecasts, where the weights are determined using BMA.