A new heterogeneous ice nucleation parameterization that covers a wide temperature range (-36 to -78 degrees C) is presented. Developing and testing such an ice nucleation parameterization, which is constrained through identical experimental conditions, is important to accurately simulate the ice nucleation processes in cirrus clouds. The ice nucleation active surface-site density (n(s)) of hematite particles, used as a proxy for atmospheric dust particles, were derived from AIDA (Aerosol Interaction and Dynamics in the Atmosphere) cloud chamber measurements under water subsaturated conditions. These conditions were achieved by continuously changing the temperature (T) and relative humidity with respect to ice (RHice) in the chamber. Our measurements showed several different pathways to nucleate ice depending on T and RHice conditions. For instance, almost T-independent freezing was observed at -60 degrees C < T < -50 degrees C, where RHice explicitly controlled ice nucleation efficiency, while both T and RHice played roles in other two T regimes: -78 degrees C < T < -60 degrees C and 50 degrees C < T < 36 degrees C. More specifically, observations at T lower than -60 degrees C revealed that higher RHice was necessary to maintain a constant n(s) whereas T may have played a significant role in ice nucleation at T higher than -50 degrees C. We implemented the new hematite-derived n(s) parameterization, which agrees well with previous AIDA measurements of desert dust, into two conceptual cloud models to investigate their sensitivity to the new parameterization in comparison to existing ice nucleation schemes for simulating cirrus cloud properties. Our results show that the new AIDA-based parameterization leads to an order of magnitude higher ice crystal concentrations and to an inhibition of homogeneous nucleation in lower-temperature regions. Our cloud simulation results suggest that atmospheric dust particles that form ice nuclei at lower temperatures, below -36 degrees C, can potentially have a stronger influence on cloud properties, such as cloud longevity and initiation, compared to previous parameterizations.