The question whether two different scalars have the same behaviour in
the surface layer under stable conditions is investigated. ''Similarit
y'' of two scalars is defined in terms of the equality of their corres
ponding dimensionless Monin-Obukhov similarity functions. Previous the
oretical and experimental results concerning the issue are briefly rev
iewed: they are found to be contradictory. An analytical derivation of
the square of the correlation coefficient between two scalars is obta
ined based on the correlation structure of the turbulent dissipation f
unctions for stable conditions, when it can be assumed that the diverg
ence of the vertical transport of scalar variance/covariance is neglig
ible. The resulting expression elucidates some earlier conflicting res
ults, and helps to establish the equality of the similarity functions
for all scalars in the stable surface layer. A statistical analysis in
the time domain is also performed using temperature and humidity turb
ulence data measured in nocturnal stable conditions during FIFE-89. Ou
r results, both from the analytical derivation and the statistical ana
lysis of turbulence data, confirm that under validity of the Monin-Obu
khov similarity theory assumptions, the corresponding similarity funct
ions for temperature and humidity are equal to within the statistical
uncertainty of the measurements. An important consequence is that the
eddy diffusivities of temperature and humidity are also equal.