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

Abstract

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.

Significant spatial patterns from the GCM seasonal forecasts of global precipitation

“…In the meantime, NMME provides precipitation observations corresponding to the forecasts. Specifically, the Climate Prediction Center (CPC)'s merged analysis of precipitation (CMAP; Xie and Arkin, 1997;Xie et al, 2007), which is monthly, has been regridded to 1 • resolution to verify GCM forecasts (Kirtman et al, 2014;Chen et al, 2017;Zhao et al, 2018).…”

“…, and December. The predictive performance of GCM forecasts exhibits seasonality (Zhao et al, 2017a(Zhao et al, , b, 2018. Accordingly, in the analysis, forecasts are selected by fixing m while varying k, e.g.…”

“…In terms of computation, global climate forecasting is as complex as the simulation of the human brain and of the evolution of the early universe (Bauer et al, 2015). Advances in super-computing facilitate the forecasting and make GCM forecasts readily available for hydrological, environmental, and agricultural modelling (Sheffield et al, 2014;Vecchi et al, 2014;Bellprat et al, 2019;Pappenberger et al, 2019;Zhao et al, 2019a).…”

“…Zhao et al: Significant spatial patterns from the GCM seasonal forecasts of global precipitation GCMs generate a vast amount of high-dimensional forecast data, including retrospective forecasts of past climate and real-time forecasts (Kirtman et al, 2014;Saha et al, 2014;Jia et al, 2015). Due to the complexity of atmospheric processes and model physics, the predictive performance of GCM forecasts is not uniform, but varies considerably across the globe (Yuan et al, 2013;Tian et al, 2017;Zhao et al, 2018). Therefore, interpreting and understanding the predictive performance is a critical issue in the applications of GCM forecasts (Doblas-Reyes et al, 2013;Saha et al, 2014;Jia et al, 2015;Hudson et al, 2017;Wang et al, 2019a).…”

“…The fact that forecasts are commonly generated by GCMs as grid-based data makes spatial plotting a particular tool of choice for verification (Merryfield et al, 2013;Saha et al, 2014;Jia et al, 2015). As to anomaly correlation, spatial plotting overcomes tedious eyeball search by grid cell and is effective in locating where there is a good correspondence between forecasts and observations and where the correspondence is not satisfactory (Luo et al, 2013;Saha et al, 2014;Crochemore et al, 2016;Zhao et al, 2018Zhao et al, , 2019b. Similarly, spatial plotting applies to other verification metrics, such as bias and CRPS, and facilitates the examination of forecast attributes (Hersbach, 2000;Gneiting et al, 2007;Kirtman et al, 2014).…”