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El Niño induces an anomalous lower-tropospheric anticyclone over the tropical Northwest Pacific (NWP), accompanied by suppressed local convection and rainfall. The tropical NWP anomalies persist until the following summer, with major effects on the Asian summer monsoons. Based on the phase 5 of the Coupled Model Intercomparison Project (CMIP5) multi-model ensemble, this study finds that climate models commonly underestimate this El Niño-NWP teleconnection with too weak tropical NWP anticyclone and rainfall anomalies in post-El Niño summers, potentially limiting the models' skill in seasonal prediction of the Asian summer monsoons. The analyses show that such underestimated NWP anomalies in post-El Niño summers in CMIP5 models can be traced back to the well-known excessive equatorial Pacific cold tongue error in the mean. Models with an excessive westward extension of Pacific cold tongue tend to displace westward the simulated pattern of El Niño-related warm SST anomalies along the equator. The warm SST biases over the western Pacific in CMIP5 models would enhance the local atmospheric convection/rainfall and induce low-level cyclonic circulation anomalies over the tropical NWP with a Gill-type Rossby wave response, resulting in the commonly underestimated NWP anticyclone and rainfall anomalies during post-El Niño summers. The present results, along with our previous finding that the equatorial cold tongue bias would distort the projections of tropical Pacific warming pattern under increased greenhouse gas scenario, imply that reducing equatorial cold tongue bias in models can substantially improve climate simulation and prediction/projection for the tropical Pacific and Asian monsoons. [ABSTRACT FROM AUTHOR]