Why during subsidence inversion, upper layer warms more than lower layer? Source : weather.gov




This is mentioned in the book I have been reading regarding stability in atmosphere. 
But I am not able to pin point exact reason behind this.


  "As the layer subsides, it becomes compressed by the weight of the
  atmosphere and shrinks vertically. The upper part of the layer sinks
  farther, and, hence, warms more than the bottom part." (Ahrens et al.,2019)




-Ahrens, C.D., Henson, R. (2019). "Meteorology Today: An Introduction to Weather, Climate, and the Environment". 12th Edition. Chapter 6 ( Stability and Cloud Development), CENGAGE Learning Custom Publishing, page 146-147
I assume that the sentence in the book mainly refers to subsidence as an adiabatic process. This sinking motion has a maximum which is at a height well above the surface, simply for the reason that air flow can not penetrate the earth's surface. Therefore maximum adiabatic heating rates occur well above the surface as well. The precise height where this occurs depends on the height of the planetary boundary layer, which itself depends on many more both adiabatic and diabatic effects.