In this paper , we analyse the upper limit fluxes of sub-millimeter ortho-H _ { 2 } ^ { 16 } O 321 GHz , para-H _ { 2 } ^ { 18 } O 322 GHz , and HDO 335 GHz lines from the protoplanetary disk around the Herbig Ae star HD 163296 , using the Atacama Large Millimeter/Submillimeter Array ( ALMA ) .
These water lines are considered to be the best candidate sub-millimeter lines to locate the position of the \mathrm { H _ { 2 } O } snowline , on the basis of our previous model calculations .
We compare the upper limit fluxes with the values calculated by our models with dust emission included , and we constrain the line emitting region and the dust opacity from the observations .
We conclude that , if the outer edge of the region with high water vapor abundance and if the position of the water snowline are beyond 8 au also , the mm dust opacity \kappa _ { \mathrm { mm } } will have a value larger than 2.0 cm ^ { 2 } g ^ { -1 } .
In addition , the position of the water snowline will be inside 20 au , if the mm dust opacity \kappa _ { \mathrm { mm } } is 2.0 cm ^ { 2 } g ^ { -1 } .
Future observations of the dust continuum emission at higher angular resolution and sub-millimeter water lines with longer observation time are required to clarify the detailed structures and the position of the \mathrm { H _ { 2 } O } snowline in the disk midplane .