## 1 Introduction

[2] In its strictest form, the ergodic hypothesis states that ensemble statistics (mean and higher-order moments) at any given time or position are identical to the temporal or spatial statistics. It is a central concept invoked in a wide variety of subjects including chaotic systems [*Eckmann and Ruelle*, 1985], thermodynamics [*Evans and Searles*, 2002; *Brody et al*., 2007], stochastic processes [*Deodatis*, 1996; *Ding et al*., 2011], hydrology [*Benson et al*., 2000; *Veneziano and Tabaei*, 2004], and turbulence [*Stanisic*, 1985]. In atmospheric sciences, ergodicity provides the mathematical underpinnings for *Monin and Obukhov* [1954] similarity theory that is the most common framework for describing the atmospheric surface layer [*Brutsaert*, 1982; *Stull*, 2003]. When considering atmospheric motions, *Monin and Yaglom* [1971, pp. 209–210] noted that the statistical approach to the theory of turbulence “transition from the consideration of a single turbulent flow to the consideration of the statistical ensemble of all similar flows, created by some set of fixed external conditions.” However, in the case of atmospheric turbulence, it is clear that for any given atmospheric observation, the external meteorological and hydrological conditions are not precisely controlled and cannot be repeated as may be the case in laboratory studies. Given that almost all turbulence theories employ ensemble averaging of the equations of motion while almost all atmospheric surface layer (ASL) measurements report time (or space)-averaged statistics, it is logical to ask under what conditions do the two averaging operators converge in light of the difficulties alluded to by *Monin and Yaglom* [1971]. Support for the ergodic hypothesis has been reported via direct numerical simulations of the Navier-Stokes equations for statistically stationary and homogeneous flows [*Da Prato and Debussche*, 2003; *Galanti and Tsinober*, 2004]. In laboratory studies, the ergodic hypothesis has also been tested using velocity time series measurements in a channel with repeated independent yet similar experiments at the Institut de Mecanique de Grenoble [*Lesieur*, 1990, p. 102]. In the ASL, a weaker form of “similar experiments” is implicitly adopted if “similarity” refers to the mean surface heating (*H _{s}*) and friction velocity (

*u*), the two surface boundary conditions that the flow experiences. Support for this weaker version of “similar experiments,” discussed in

_{*}*Monin and Yaglom*[1971], has received much success in the form of the

*Monin and Obukhov*[1954] similarity theory, where changes in the flow statistics scale with the changes in

*H*and

_{s}*u*(i.e., external conditions). While similarity theory provides indirect validation for the use of

_{*}*H*and

_{s}*u*as indices or surrogates for quantifying similarity in “external conditions,” direct testing of the ergodic hypothesis in the ASL has frustrated all experimental efforts and frames the compass of this work. The main novelty here is to demonstrate how Raman lidar (light detection and ranging)-based water vapor concentration (

_{*}*q*) measurements can provide, for the first time, an evaluation of the ergodic hypothesis for ASL flows using the “similar experiments” concept. By using space and time as proxies for multiple experiments performed under the same external forcing, it is shown via a field study that ergodicity may be robust to transitions in the land surface cover when the system is defined by the composite cover bounding the transition.