I've used WOS before and it's pretty accurate IF you feed in the correct temp and IF you fly close to the pickup.
With Doppler measurements you need to think of your sound waves as ripples on a pond. If these ripples were made by a bucket with a drip in it and the bucket was standing still, you'd have a bunch of rings with a center where the drip hits the pond. But now move the bucket. The next drip from the bucket hits the water closer to one side of the last ring and farther from the other. The difference in this distance is dependent on the speed of the bucket. The pitch you here from a horn on a train changes as the train goes by you. This is the reason, the sound of the horn (which is just ripples of compressed air) is compressed on approach side (raising the pitch) and stretched on the retreating side (lower pitch). WOS shows you the high pitch, the low pitch and then figures out the speed (based on the difference of the pitch). Because we're measuring sound the speed of which varies mostly with the temperature of the air, you feed the air temps into WOS.
Think a little more. IF you record your plane going past with a recorder which is quite a bit away from the airplane, you are essentially measuring the flatter part of those rings where as if the recorder is directly under you get pretty much the whole effect. So try to fly right over the recorder which is easy because you can put that out on the field somewhere and get out of the flight path.