Just out of curiosity, were any measurements taken across the full 15 km from the first marker to the last?
No, at that distance too much light refraction would have rendered the experiment null and void. The purpose of measuring one segment at a time and summing the total was to avoid any dispute about what might be attributed to light refraction. Since the effects of refraction are nonlinear, the summation of each segment will result in significantly less refraction than a single measurement across the entire survey would.
This is a very sneaky claim. You are right when you say the effects of refraction are non-linear. But you forget to say that the non-linearity is not increasingly worse with distance, but the exact opposite. No matter what you do, the maximum temperature differential you might get between any two places in the whole 15 km stretch is less than 5 degrees centigrade, and this is the equivalent of making a prism out of a material with refractive index of 1.00026666 and putting it in air with refractive index of 1.000271373. (you can use the calculator at
http://emtoolbox.nist.gov/Wavelength/Ciddor.asp). And this is true no matter what distance you are looking through.
So, even in the perfect situation in which the air suddenly changes 5 degrees Celsius at the perfect height above the lake, producing the maximum refraction possible with such a small change in refractive index, the total refraction would be 0.2 degrees. (this comes from n2/n1*arcsin(Theta)=1). In fact, you would see more a mirage than a subtle refraction. And even if you had a lake of several hundreds of kilometers, you would not be able to get more than 0.2 degrees of refraction.
On the other hand, the size of the curvature that you can measure increases in an approximately exponential scale. While there is nothing measurable in 2 km, you have some 20 meters at 15 km (enough to see a clear appearance of a sinking boat).
In conclusion, the whole argument for the design of this experiment is totally wrong. Measuring stretches of 2 km, no matter how many of them, is totally useless as a method to calculate the circumference of the Earth.