ALL PLANETARY ATMOSPHERES CONTINUALLY LOSE HYDROGEN TO SPACE. FOR VENUS AND MARS H LOSS HAS BEEN PARTICULARLY IMPORTANT IN DEPLETING THEIR PRIMORDIAL WATER INVENTORY BUT KEY QUESTIONS REMAIN ABOUT HOW H IS LOST AND HOW MUCH HAS BEEN REMOVED. IN PARTICULAR THE RELATIVE IMPORTANCE OF THERMAL AND HOT H ESCAPE HAS YET TO BE DEFINITIVELY ESTABLISHED AT MARS OR EXPLORED THROUGHOUT SOLAR SYSTEM HISTORY. EVEN AT VENUS WHERE HOT H ESCAPE IS UNAMBIGUOUS DISCREPANCIES BETWEEN MEASUREMENTS OF HOT H AND THE MOST RECENT MODELS (MORE THAN FIFTEEN YEARS OLD) MOTIVATE A REASSESSMENT OF H LOSS. AT MARS IT HAS BEEN MORE THAN TWENTY YEARS SINCE A COMPREHENSIVE STUDY OF NONTHERMAL H ESCAPE WAS UNDERTAKEN; IN THE MEANTIME UPDATES IN KNOWLEDGE OF KEY PROCESSES AND CIRCUMSTANTIAL EVIDENCE FOR SIGNIFICANT NONTHERMAL HYDROGEN ESCAPE NECESSITATE A FOLLOWUP STUDY. FINALLY THE RELATIVE IMPORTANCE OF HOT AND THERMAL H ESCAPE OVER SOLAR SYSTEM HISTORY HAS YET TO BE ESTABLISHED WITH THE RESULT THAT WE REMAIN FUNDAMENTALLY IGNORANT ABOUT THE MECHANISM OF H (AND THEREFORE WATER) ESCAPE IN THE EARLY SOLAR SYSTEM. OUR WORK WILL COUPLE THREE MODELS ALREADY DEVELOPED BY PROPOSAL CO-INVESTIGATORS OVER THE COURSE OF THREE YEARS TO ADDRESS THESE THREE INADEQUACIES IN CURRENT MODELS AND WILL: 1. COMPUTE EXPECTED THERMAL AND HOT H ESCAPE RATES FOR VENUS AND MARS; 2. IDENTIFY SIGNATURES OF HOT H ESCAPE AT MARS; AND 3. DETERMINE THE CIRCUMSTANCES UNDER WHICH HOT H ESCAPE DOMINATES THERMAL H ESCAPE. THE RESULT WILL BE A NEW UNDERSTANDING OF HOW NONTHERMAL ESCAPE HAS INFLUENCED THE EVOLUTION OF VENUS AND MARS OVER SOLAR SYSTEM HISTORY. THE WORK WE PROPOSE IS A HIGH PRIORITY: NEW PHYSICAL INPUT PARAMETERS SUCH AS CROSS SECTIONS AND NEW SPACECRAFT DATASETS SUCH AS THOSE FROM VENUS EXPRESS AND MARS ATMOSPHERE AND VOLATILE EVOLUTION (MAVEN) MISSION REQUIRE A RE-EVALUATION OF THE RELATIVE IMPORTANCE OF NONTHERMAL ESCAPE FROM VENUS AND MARS. BECAUSE OUR WORK IS MOSTLY MODELING AND BECAUSE WE ADOPT AN APPROACH THAT EMBRACES BOTH VENUS AND MARS OUR WORK CAN ONLY BE FUNDED BY SSW.