We present millimeter- and submillimeter-wave phase characteristics measured between 2012 and 2014 of Atacama Large Millimeter/submillimeter Array ( ALMA ) long baseline campaigns .
This paper presents the first detailed investigation of the characteristics of phase fluctuation and phase correction methods obtained with baseline lengths up to \sim 15 km .
The basic phase fluctuation characteristics can be expressed with the spatial structure function ( SSF ) .
Most of the SSFs show that the phase fluctuation increases as a function of baseline length , with a power-law slope of \sim 0.6 .
In many cases , we find that the slope becomes shallower ( average of \sim 0.2 - 0.3 ) at baseline lengths longer than \sim 1 km , namely showing a turn-over in SSF .
These power law slopes do not change with the amount of precipitable water vapor ( PWV ) , but the fitted constants have a weak correlation with PWV , so that the phase fluctuation at a baseline length of 10 km also increases as a function of PWV .
The phase correction method using water vapor radiometers ( WVRs ) works well , especially for the cases where PWV > 1 mm , which reduces the degree of phase fluctuations by a factor of two in many cases .
However , phase fluctuations still remain after the WVR phase correction , suggesting the existence of other turbulent constituent that cause the phase fluctuation .
This is supported by occasional SSFs that do not exhibit any turn-over ; these are only seen when the PWV is low ( i.e. , when the WVR phase correction works less effectively ) or after WVR phase correction .
This means that the phase fluctuation caused by this turbulent constituent is inherently smaller than that caused by water vapor .
Since in these rare cases there is no turn-over in the SSF up to the maximum baseline length of \sim 15 km , this turbulent constituent must have scale height of 10 km or more , and thus can not be water vapor , whose scale height is around 1 km .
Based on the characteristics , this large scale height turbulent constituent is likely to be water ice or a dry component .
Excess path length fluctuation after the WVR phase correction at a baseline length of 10 km is large ( \gtrsim 200 ~ { } \mu m ) , which is significant for high frequency ( > 450 GHz or < 700 ~ { } \mu m ) observations .
These results suggest the need for an additional phase correction method to reduce the degree of phase fluctuation , such as fast switching , in addition to the WVR phase correction .
We simulated the fast switching phase correction method using observations of single quasars , and the result suggests that it works well , with shorter cycle times linearly improving the coherence .