A pump apparatus has a downhole pump disposed in a wellbore and has motor at a surface of the wellbore, and the downhole pump is reciprocated in the wellbore by a rod string operatively moved by the motor. A card indicative of load and position of the downhole pump is generated using surface measurements and a wave equation model having a damping factor or two damping factors. Actual fluid load lines are determined from the downhole card for upstroke and downstroke of the downhole pump, and calculated fluid load lines from the load distribution of the downhole data. The actual fluid load lines are compared to the calculated fluid load lines so that at least one parameter of the pump apparatus can be modified based on the comparison. For example, the damping of the wave equation model can be adjusted so that another downhole card can be generated.