Relating Anomaly Correlation to Lead Time: Principal Component Analysis of NMME Forecasts of Summer Precipitation in China

The skill of global climate model (GCM) forecasts is usually indicated by the anomaly correlation between ensemble mean and observation. For GCM forecasts, anomaly correlation does not steadily improve with decreasing lead time but oscillates instead. This paper aims to address the oscillation and illustrate the relationship between anomaly correlation and lead time. We formulate the anomaly correlation of forecasts at different initialization times as a vector and pool anomaly correlation vectors across grid cells in the analysis. We propose two patterns to characterize the spatial and temporal variation of anomaly correlation in the three-dimensional space of latitude, longitude, and initialization time. The first pattern suggests that the anomaly correlation at different initialization times is at a similar level. The second pattern indicates that the anomaly correlation linearly increases with decreasing lead time. These two patterns are tested using the eigenvectors through principal component analysis. They are first illustrated using the GFDL-CM2p1-aer04 forecasts of summer precipitation in China. They are further verified by another nine sets of North-American Multi-Model Ensemble (NMME) forecasts. Overall, the first pattern explains more variation than the second pattern. In total, the two patterns explain 42% of the variation of anomaly correlation for CanCM3, 59% for CanCM4, 42% for COLA-RSMAS-CCSM3), 45% for COLA-RSMAS-CCSM4, 59% for GFDL-CM2p1, 67% for GFDL-CM2p1-aer04, 65% for GFDL-CM2p5-FLOR-A06, 57% for GFDL-CM2p5-FLOR-B01, 48% for NCAR-CESM1, and 60% for NCEP-CFSv2. The percentage of explained variation demonstrates the effectiveness of the two patterns as exploratory tools to analyze the predictive performance of GCM forecasts.