We have performed carbon monoxide line radiative transfer computations for spherically symmetric clumps that are irradiated by FUV radiation of intermediate strength (10(2...3) G0, G0 = 1.6 10(-3) erg cm-2 s-1). The clumps are assumed to have sizes of about 1 pc, a radially varying density n is-proportional-to r-3/2, and a temperature and chemical distribution, including fractionation of (CO)-C-12 and (CO)-C-13, according to photodissociation region (PDR) models. The model reproduces successfully the (CO)-C-12 and (CO)-C-13 J = 1 --> 0 and J = 2 --> 1 intensities observed in the Orion A molecular cloud (Castets et al. 1990) and other sources, that cannot be accounted for in simple, single component radiative transfer calculations. The (CO)-C-12 lines are shown to emerge from the almost-equal-to 30 K warm layer at the bottom of the PDR, whereas the (CO)-C-13 lines exhibit additionally a substantial contribution from the cold (10 K) isothermal clump core. Different beamfilling of the (CO)-C-12 and (CO)-C-13 lines plays a minor role for the intensity ratios.