5. Summary

1. The turbulent distribution of water vapor causes fluctuations in the path length through the atmosphere, with periods ranging from seconds to  hour. These fluctuations interact with the observing process for interferometers in different ways, depending on their period t.
2. Fluctuations with , where is the integration time, reduce the amplitude measured in each integration; those with produce an error in the phase measured for the integration.
3. Phase referencing to a nearby bright calibrator source removes fluctuations with , but adds the fluctuations on the calibrator with , where is the period of the observing cycle. This component is aliased to longer timescales.
4. Water vapor radiometry can be used to correct for the residual fluctuations. There are two levels on which the correction can be applied. Correcting the fluctuations during each on-source period constitues a partial correction, since the aliased component from the calibrator is left intact. The coherence time of the interferometer is increased, and the calibration requirements for the radiometers are modest (%).
5. A full correction also measures the change in the path correction between observations of the target and calibrator. Since there can be a large difference in airmass between the calibrator and the target (at least for existing arrays), measuring this change requires that the radiometers have the same response to a given column of water vapor to within %. This stringent calibration may be possible to achieve by monitoring the average derived correction on timescales longer than the atmospheric fluctuations, or by observing more than one calibrator.
6. For reasonable observing conditions at 230 GHz, the prediction for effective seeing is improved from 0.6'' (phase referencing every 25 minutes) to 0.3'' (phase referencing and partial radiometric correction). The full radiometric correction would, in principle, restore perfect seeing.