Thanks, I think I found the problem.
My data field was sigma-theta calculated from theta and s, with mask values of 1e20 for land. I had been using the first set of fields to make a mask matrix with values of 1 for land and 0 for water, and using that to set all my 1e20 to 0, then calculating sigmat-theta.
To my dismay, some of the model output fields were careless in applications of land mask -- the mask from the first field did not necessarily match the mask in other fields! So some 1e20 were getting through, turning into 1e18 or 1e19 values of sigma-theta. I had to pipe an ncdump to an output file, then search through the output file for "e" . . . and found these values. These strange values were causing the odd lines. When I re-wrote the code with more checks to hop out of the sigma-theta calculation, the lines went away.