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.

[4][5] Koch received, among other honors, the Vega medal of the Swedish Society for Anthropology and Geography.

This ice-free peninsula is bounded by the Greenland Ice Sheet on the west side.

On the north side, J.P. Koch land is bounded by Upernavik Icefjord, in the west and south by Eqaluarssuit Fjord (sv).