Data assimilation methods in a coupled system, namely coupled data assimilation (CDA), have been attracting researchers’ interests to improve Earth system modeling. The CDA methods are classified into two; weakly coupled data assimilation (wCDA), which considers cross-domain interaction only in a model’s forecast phase, and strongly coupled data assimilation (sCDA), which additionally uses other domain’s information in an analysis phase. Although sCDA can theoretically provide better estimates than wCDA since sCDA fully uses a cross-domain covariance, the effectiveness of sCDA is still in debate. In this paper, we investigated the conditions under which sCDA is effective by applying Local Ensemble Transform Kalman Filter (LETKF) to the joint-Lorenz96 model. By continuously changing the magnitude of the cross-domain interaction of the joint-Lorenz96 model, we found that the superiority of sCDA against wCDA is particularly evident when the cross-domain interaction is large, albeit it does not contribute to increasing the chaoticity of the system. In addition, the performance of sCDA is quite sensitive to the LETKF’s hyperparameters (such as localization and inflation parameters) especially when the ensemble size is small, and the insufficient calibration of these parameters deteriorate the sCDA’s performance. Furthermore, sCDA is more vulnerable to model bias than wCDA; both cross-domain and intra-domain biases degrade the estimation skills.