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The Mars Science Laboratory rover Curiosity, operating on the surface of Mars, is exposed to radiation fluxes from above and below. Galactic Cosmic Rays travel through the Martian atmosphere, producing a modified spectrum consisting of both primary and secondary particles at ground level. These particles produce an upward directed secondary particle spectrum as they interact with the Martian soil. Here we develop a method to distinguish the upward and downward directed particle fluxes in the Radiation Assessment Detector (RAD) instrument, verify it using data taken during the cruise to Mars, and apply it to data taken on the Martian surface. We use a combination of Geant4 and Planetocosmics modeling to find discrimination criteria for the flux directions. After developing models of the cruise phase and surface shielding conditions, we compare model-predicted values for the ratio of upward to downward flux with those found in RAD observation data. Given the quality of available information on Mars Science Laboratory spacecraft and rover composition, we find generally reasonable agreement between our models and RAD observation data. This demonstrates the feasibility of the method developed and tested here. We additionally note that the method can also be used to extend the measurement range and capabilities of the RAD instrument to higher energies.