If you use the search possible at FamilySearch.org you'll find that there is a family in Barron Co. WI (location of Rice Lake??) with a son Arnold Knutson born ca. 1912 in Wisconsin, mother Sofia and father listed as J. Ole. Arnold and Sofia both born in Wisconsin but the father listed as born Norway and four younger siblings to Arnold that you might recognize. Perhaps you can find a quicker way to determine at least approximate birth years and an emigration year for the father.

Ole Knutson or J. Ole Knutson (and the expected spelling variations you should expect to find in Norwegian records) will be a very common name there. Gather as much information about this man in the US as you possibly can.