In a high tunnel, you manage the water supply.  You can do it by hand or with fully automated systems or with various methods in between.  Regardless how you do it, it is imperative that it is done.  

One of the best resources for Alaska High Tunnel management is the document "Controlling the High Tunnel Environment" found on the USDA/NRCS Alaska publications webpage.  The fourth page of this document gets into the details and considerations of irrigation.

There are many other resources you can find easily on the internet.  This list is not intended to endorse purchasing from any specific site, but you can get plenty of information witout purchasing. Some of the many useful sites include:

• YouTube video webinar on drip irrigation 
• Farm Tek Irrigation Buyer's Guide 
• Rain Catchment from a High Tunnel