RED DWARF (M-CLASS) STARS OFFER SOME OF THE BEST OPPORTUNITIES TO FIND AND CHARACTERIZE EARTH-LIKE EXOPLANETS IN THE NEAR FUTURE BY EITHER SPACE- OR GROUND-BASED INSTRUMENTATION. HOWEVER THE PROCESSES THAT SHAPE THE ATMOSPHERES OF POTENTIALLY HABITABLE WORLDS AROUND M-STARS ARE STILL VERY POORLY UNDERSTOOD. TO OPTIMIZE MISSION PLANNING AND GAIN THE MAXIMUM INSIGHT FROM FUTURE OBSERVATIONS MORE DETAILED THEORETICAL STUDY IS REQUIRED. MOST POTENTIALLY HABITABLE ROCKY PLANETS AROUND M-STARS WILL HAVE CLOSE ORBITS LEADING TO LOW ORBITAL OBLIQUITIES AND IN MANY CASES TIDAL LOCKING WITH PERMANENT DAY AND NIGHT SIDES. THEY WILL ALSO SUFFER EXTENDED PERIODS OF ATMOSPHERIC AND VOLATILE EROSION EARLY IN THEIR EVOLUTION. IN COMBINATION THESE EFFECTS MAY HAVE DIVERSE CONSEQUENCES FOR CLIMATE AND HABITABILITY INCLUDING EXTREME SURFACE TEMPERATURE VARIATIONS COLLAPSE OF VOLATILE SPECIES INTO COLD TRAP REGIONS AND EXTENSIVE PLANETARY OXIDATION VIA HYDROGEN LOSS. ALL OF THESE PROCESSES HAVE IMPORTANT OBSERVABLE CONSEQUENCES BUT MOST ARE STILL VERY POORLY UNDERSTOOD.HERE WE PROPOSE A NUMERICAL AND THEORETICAL INVESTIGATION OF A KEY PROCESS GOVERNING THE HABITABILITY OF ROCKY PLANETS AROUND M-STARS: ATMOSPHERIC VOLATILE TRANSPORT. WE PLAN TO TAKE A UNIVERSAL APPROACH TREATING TWO KEY VOLATILES (H2O AND CO2) ON AN EQUAL FOOTING THEORETICALLY IN ORDER TO MAXIMIZE THE GENERALITY OF OUR RESULTS. AT EACH STEP OF THE PROJECT ANALYSIS AND BASIC THEORY WILL BE USED TO OBTAIN A DEEP UNDERSTANDING OF THE RESULTS.FIRST WE WILL USE A 3D GENERAL CIRCULATION MODEL WITH ACCURATE MULTIBAND RADIATIVE TRANSFER DEVELOPED BY THE PI TO STUDY ATMOSPHERIC HEAT TRANSPORT AND VOLATILE COLLAPSE ON PLANETS WITH A RANGE OF MASSES ORBITS AND ATMOSPHERIC COMPOSITIONS. GENERAL EMPIRICAL FORMULAE WILL BE CONSTRUCTED FROM THE RESULTS TO AID FUTURE RESEARCH. NEXT WE WILL USE THE 3D MODEL TO STUDY VOLATILE EQUILIBRATION IN THE COLLAPSED CASE. BESIDES ITS FUNDAMENTAL THEORETICAL IMPORTANCE THIS SECOND PHASE OF THE PROJECT WILL HAVE TWO DIRECT IMPLICATIONS FOR UNDERSTANDING PLANETARY HABITABILITY. FIRST IT WILL ALLOW US TO ASSESS THE EXTENT TO WHICH WATER-POOR DESICCATED M-STAR PLANETS MAY LOCALLY HAVE HABITABLE SURFACE CONDITIONS. SECOND IT WILL ALLOW US TO CALCULATE THE LONG-TERM STABILITY OF PLANETARY WATER INVENTORIES AGAINST UPPER ATMOSPHERE H2O PHOTOLYSIS AND HYDROGEN LOSS TO SPACE. BESIDES ITS IMPLICATIONS FOR LONG-TERM HABITABILITY THIS WILL ALLOW ASSESSMENT OF THE POTENTIAL FOR ABIOTIC OXYGEN ATMOSPHERES TO EMERGE ON SUCH PLANETS AN ISSUE OF VITAL IMPORTANCE TO REMOTE BIO SIGNATURE DETECTION.THIS PROPOSAL ADDRESSES THE FACT THAT MOST POTENTIALLY HABITABLE EXOPLANETS WILL NOT BE EARTH-LIKE BY INCLUDING A RANGE OF PLANETARY MASSES ORBITS AND ATMOSPHERIC COMPOSITIONS IN ITS SCOPE. THE UNIVERSALITY OF THE ATMOSPHERIC CONDENSATION PROBLEM MEANS THAT THIS WORK ALSO HAS POTENTIAL TO HELP ADVANCE UNDERSTANDING OF VOLATILE REDISTRIBUTION IN THE SOLAR SYSTEM (E.G. THE CO2 CYCLE ON MARS OR THE N2 CYCLE ON TRITON). THE EMPIRICAL COLLAPSE FORMULAE RESULTING FROM THIS STUDY WILL SERVE AS A VALUABLE RESOURCE FOR FUTURE OBSERVATION/ MISSION PLANNING AND SUBSEQUENT STUDIES OF PLANETARY HABITABILITY MAKING IT IMPORTANT TO NASA'S WIDER GOALS. FINALLY THE WORK WILL HAVE IMPLICATIONS FOR THE SEARCH FOR LIFE AROUND OTHER STARS BY TESTING SCENARIOS UNDER WHICH FALSE POSITIVES FOR LIFE (SUCH AS AN ABIOTIC O2-DOMINATED ATMOSPHERE) MAY ARISE.