We compare line emission calculated from theoretical disk models with optical to sub-millimeter wavelength observational data of the gas disk surrounding TW Hya and infer the spatial distribution of mass in the gas disk. The model disk that best matches observations has a gas mass ranging from $sim10^{-4}-10^{-5}$ms for $0.06{rm AU} <r<3.5$AU and $sim 0.06$ms for $ 3.5 {rm AU} <r<200$AU. We find that the inner dust hole ($r<3.5$AU) in the disk must be depleted of gas by $sim 1-2$ orders of magnitude compared to the extrapolated surface density distribution of the outer disk. Grain growth alone is therefore not a viable explanation for the dust hole. CO vibrational emission arises within $rsim 0.5$AU from thermal excitation of gas. [OI] 6300AA and 5577AA forbidden lines and OH mid-infrared emission are mainly due to prompt emission following UV photodissociation of OH and water at $rlesssim0.1$AU and at $rsim 4$AU. [NeII] emission is consistent with an origin in X-ray heated neutral gas at $rlesssim 10$AU, and may not require the presence of a significant EUV ($h u>13.6$eV) flux from TW Hya. H$_2$ pure rotational line emission comes primarily from $rsim 1-30$AU. [OI]63$mu$m, HCO$^+$ and CO pure rotational lines all arise from the outer disk at $rsim30-120$AU. We discuss planet formation and photoevaporation as causes for the decrease in surface density of gas and dust inside 4 AU. If a planet is present, our results suggest a planet mass $sim 4-7$M$_J$ situated at $sim 3$AU. Using our photoevaporation models and the best surface density profile match to observations, we estimate a current photoevaporative mass loss rate of $4times10^{-9}$ms yr$^{-1}$ and a remaining disk lifetime of $sim 5$ million years.
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