Assuming you lose 1 foot of over 4 months, thats .1 inches per day. To replace that each day over 10 acres would take 1/12 acre foot of water or 27,166 gallons of water. If you can pump 12 hours a day that would equal 37.73 gallons a minute to stay even for the day.

That sounds like it could work. During the summer, depending on you location, your evaporation will be higher than .1 inches so you will be behind during the hottest times of the year.