We have revisited Monte Carlo radiative transfer calculations for clumpy molecular clouds. Instead of introducing a three-dimensional geometry to implement clumpy structure, we have made use of its stochastic properties in a one-dimensional geometry. Taking into account the reduction of spontaneous emission and optical depth due to clumpiness, we have derived the excitation conditions of clumpy clouds and compared them with those of three-dimensional calculations. We found that the proposed approach reproduces the excitation conditions in a way compatible to those from three-dimensional models, and reveals the dependencies of the excitation conditions on the size of clumps. When bulk motions are involved, the applicability of the approach is rather vague, but the one-dimensional approach can be an excellent proxy for more rigorous three-dimensional calculations.

Abstract
1. INTRODUCTION
2. ONE-DIMENSIONAL RADIATIVE TRANSFERMODELS IN CLUMPY CLOUDS
    2.1. Cloud Geometry
    2.2. Molecules
    2.3. Proposed Radiative Transfer Code for ClumpyClouds
    2.4. Verification of Radiative Transfer Code
3. RESULTS
    3.1. Microturbulent Clouds
    3.2. Clouds with Bulk Motions
4. DISCUSSION AND CONCLUSIONS
REFERENCES

• Yong-Sun Park(Department of Physics and Astronomy, Seoul National University) Corresponding author