Satellite-based passive microwave radiometers provide a wealth of information on tropical cyclone (TC) structure and energetics. Over the past three years, the University of Wisconsin-Madison Cooperative Institute for Meteorological Satellite Studies (CIMSS), in conjunction with the USAF and Navy, have developed a method to quantitatively determine and distribute TC intensity estimates using passive microwave radiance data from the NOAA-KLM series Advanced Microwave Sounding Unit (AMSU). Independent test results from 2000 and 2001 demonstrate skill in estimating TC minimum sea level pressure (MSLP), regardless of TC position within the AMSU scan swath, provided that accurate tropical cyclone position and representative eye size information are available at the time of satellite observation. Horizontal resolution limits of the temperature (AMSU-A) and moisture (AMSU-B) sounders, while explicitly treated by the UW-CIMSS technique, continue to pose significant challenges for intense TCs with unusually small or "pin-hole" eyes. UW-CIMSS algorithm access to ancillary TC eye size information, either subjective or quantitative, to this small but vitally important subset of TCs can substantially improve AMSU-based TC intensity estimate skill. Finally, preliminary research results also indicate that the altitude of peak TC upper tropospheric warming can vary considerably over the course of a single TC lifecycle or between storms and will be discussed in Part II of this study.