An information map is obtained by an agricultural system. The information map maps values of a topographic characteristic to different geographic locations in a field. An in-situ sensor detects values of an environmental characteristic as an agricultural work machine moves through the field. A predictive map generator generates a predictive map that predicts the environmental characteristic at different locations in the field based on a relationship between the values of the topographic characteristic and the values of the environmental characteristic detected by the in-situ sensor. The predictive map can be output and used in automated machine control.