如何使用 Bash 递归地创建不存在的子目录？

我正在创建一个快速备份脚本，它将一些数据库转储到一个漂亮/整洁的目录结构中，我意识到我需要在创建目录之前进行测试以确保目录存在。我的代码有效，但有更好的方法吗？

[ -d "$BACKUP_DIR" ] || mkdir "$BACKUP_DIR"[ -d "$BACKUP_DIR/$client" ] || mkdir "$BACKUP_DIR/$client"[ -d "$BACKUP_DIR/$client/$year" ] || mkdir "$BACKUP_DIR/$client/$year"[ -d "$BACKUP_DIR/$client/$year/$month" ] || mkdir "$BACKUP_DIR/$client/$year/$month"[ -d "$BACKUP_DIR/$client/$year/$month/$day" ] || mkdir "$BACKUP_DIR/$client/$year/$month/$day"