To download all objects using wget:

wget -r -H -N --cut-dirs=5 --include-directories="/v1/" "https://swiftbrowser.dkrz.de/public/dkrz_1e33ba3a-9ecb-452f-93b9-583cf4a66e57/ICON-NAWDEX/20160923/images/?show_all"

Name
dei4_NAWDEX_2016092300_ll_DOM01_ML_0072-cape_ml-trim.png
dei4_NAWDEX_2016092300_ll_DOM01_ML_0072-rh_2m-trim.png
dei4_NAWDEX_2016092300_ll_DOM01_ML_0072-selname_prec-prec-trim.png
dei4_NAWDEX_2016092300_ll_DOM01_ML_0072-selname_wspd_10m-wspd_10m-trim.png
dei4_NAWDEX_2016092300_ll_DOM01_ML_0072-td_2m-trim.png
dei4_NAWDEX_2016092300_ll_DOM01_ML_0072-tqc_dia-trim.png
dei4_NAWDEX_2016092300_ll_DOM01_ML_0072-tqi_dia-trim.png
dei4_NAWDEX_2016092300_ll_DOM01_ML_0072-tqv_dia-trim.png