To download all objects using wget:

wget -r -H -N --cut-dirs=4 --include-directories="/v1/" "https://swiftbrowser.dkrz.de/public/dkrz_1e33ba3a-9ecb-452f-93b9-583cf4a66e57/ICON-HErZ/20160728/?show_all"

Name
MODIS_Aqua_CorrectedReflectance_TrueColor-TIME_20160728-DOM01-Res_1000m.jpeg
MODIS_Terra_CorrectedReflectance_TrueColor-TIME_20160728-DOM01-Res_1000m.jpeg
dei4_NARVALII_2016072800_ll_DOM01_ML-cape_ml.gif
dei4_NARVALII_2016072800_ll_DOM01_ML-rh_2m.gif
dei4_NARVALII_2016072800_ll_DOM01_ML-td_2m.gif
dei4_NARVALII_2016072800_ll_DOM01_ML-tqc_dia.gif
dei4_NARVALII_2016072800_ll_DOM01_ML-tqi_dia.gif
dei4_NARVALII_2016072800_ll_DOM01_ML-tqv_dia.gif
dei4_NARVALII_2016072800_ll_DOM01_ML-wspd_10m.gif
narval_bt062_20160728.ogv
narval_bt073_20160728.ogv
narval_bt108_20160728_colenh.ogv
narval_bt108_20160728_surface.ogv