 In 1906–1908 he was a member of the ill-fated Denmark expedition led by Ludvig Mylius-Erichsen, which mapped the last pieces of the northeastern coast of Greenland.On the death of Mylius-Erichsen and two others on a long sled voyage from Danmarkshavn to Peary Land, Koch along with the Greenlander Tobias Gabrielsen searched for the lost party, and found only the Greenlander Jørgen Brønlund on whose body were recovered the charts hand drawn by Niels Peter Høeg Hagen which completed the map of Greenland.In 1907 Koch, together with Aage Bertelsen, was reported to have first seen Fata Morgana Land (), a phantom island supposedly lying between NE Greenland and Svalbard.