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We present observations of the ground state 1$_{0,1}$-0$_{0,0}$ rotationaltransition of HDO at 464.925 GHz and the 1$_{1,0}$-1$_{0,1}$ transition at509.292 GHz toward the three high-mass star forming regions: G34.26+0.15, W49N,and W51e$_{1}$/e$_{2}$, carried out with the Caltech Submillimeter Observatory.The latter transition is observed for the first time from the ground. Thespectra are modeled, together with observations of higher-energy HDOtransitions, as well as submillimeter dust continuum fluxes from theliterature, using a spherically symmetric radiative transfer model to derivethe radial distribution of the HDO abundance in the target sources. Theabundance profile is divided into an inner hot core region, with kinetictemperatures higher than 100~K, and a cold outer envelope with lower kinetictemperatures. The derived HDO abundance with respect to H$_2$ is(0.3-3.7)$\times 10^{-8}$ in the hot inner region ($T > 100 \mathrm{K}$) and(7.0-10.0)$\times 10^{-11}$ in the cold outer envelope. We also used twoH$_{2}^{18}$O fundamental transitions to constrain the H$_{2}$O abundances inthe outer envelopes. The HDO/H$_{2}$O ratios in these cold regions are found tobe (1.8-3.1)$\times 10^{-3}$ and are consequently higher than in the hot innerregions of these sources.

Analysis of Low Excitation HDO Transitions Toward the High-Mass Star-forming Regions G34.26+0.15, W51e$_{1}$/e$_{2}$, and W49N