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tokens: sources HD 100546 and TW Hya. 2. For both disks, we fitted fully parametric physical models to the spectral energy distribution, spatially resolved CO emission, and a range of far-infrared emission lines. The most important difference from past physical models is that spatially resolved CO line emission is also reproduced. 3. We confirm earlier findings that the HD 100546 disk atmosphere has either an interstellar gas-phase carbon abundance ([C]/[H] , if = 10) or is moderately depleted ([C]/[H], if = 100); and that the TW Hya disk atmosphere is two orders of magnitude deficient in gas-phase volatiles ([C]/[H], [O]/[H], and ). 4. Upper limits on HD emission for HD 100546 put an upper limit of on the gas to dust ratio in the disk. 5. The star HD 100546 has solar-like photospheric abundances of volatile elements (C, N, O) but a strong depletion of rock-forming elements (e.g. Fe, Mg, Si). 6. Most carbon atoms in the HD 100546 disk gas have not passed through a hydrocarbon more complex than CH during the lifetime of the system. 7. An underabundance of volatile elements in the disk atmosphere can develop when gas is mixed through the midplane and the temperature there allows freeze-out of major carrier species onto settled grains. An analytical formulation of this process is presented in Sect. 6.2 . 8. The volatiles return to the gas in the inner disk, as evidenced by their enhanced abundance relative to refractory elements in the gas accreting onto both stars. Appendix A: HD 100546 photospheric abundances Table A.1 Photospheric abundances derived for HD 100546. Notes. Number of lines used in the abundance fitting is shown in Col. 4. Asterisks denote very uncertain results. Solar abundances are from Asplund et al. (2009) . The photospheric properties of HD 100546 were derived through directly fitting synthetic spectra to the optical spectrum of the star. This process gives a measurements of , , , and chemical abundances. The synthetic spectra were calculated using the Z eeman spectrum synthesis program ( Landstreet 1988 ; Wade et al. 2001 ), using model stellar atmospheres from ATLAS9 ( Kurucz 1993 ), and atomic data from the Vienna Atomic Line Data Base (VALD; Kupka et al. 1999 ). The best-fit stellar parameters were derived using and automatic minimization routine, in which all parameters were fitted simultaneously ( Folsom et al. 2012 ). This fitting process was performed on none independent spectral windows (416427, 440460, 460480, 490510, 510520, 520540, 540560, 620650, and 710750 nm). The final best fit parameters are the averages of the individual windows, and the uncertainties are the standard deviations. In cases where a chemical abundance for an element was derived in only three or fewer windows, the uncertainties were increased to account for the full window-to-window variation, as well as any potential uncertainties due to line blending and continuum normalization. Great care was taken to avoid any lines contaminated by emission. Weak