Why is Mode C helpful for ASDE-X systems? Airports that operate an ASDE-X system require aircraft to operate transponders in mode C while moving on the surface. 

While I understand the general purpose of operating the transponder to correlate with the other information ingested by the ASDE-X system, why is altitude (encoded in mode C) important for tracking surface movement? 

Wouldn't mode A suffice?
Without knowing the altitude, it is very difficult (or impossible) to accurately calculate the position of a transponder by using multilateration (which is what ASDE-X uses). In addition, without knowing the altitude, ASDE-X would be unable to determine whether an aircraft is on the airport's surface, or passing overhead.