If i properly understand your question, you can do it through resample tool in ArcGIS software. Put your lower resolution data in input furthermore in the output you have to assign some 1 km data.
You may convert your low resolution grid to points (centroids), then use any software having interpolation feature, set output grid size 1km and try different number of influence neighbor points (hit and trail). Though not a good solution, but still you will get some better results.