To improve the quality of scalar-flux measurements, the two-point covariance between the vertical velocity w̃ and a scalar s̃, separated in space both horizontally and vertically, is studied. The measurements of such two-point covariances between vertical velocity and temperature with horizontal and vertical separations show good agreement with a symmetric turbulence model when the displacement is horizontal. However, a similar model does not work for vertical displacements because up–down asymmetry exists; that is, there is a lack of reflection symmetry of the covariance function. The second-order equation for conservation of two-point covariance of w̃ and s̃ reveals the reason for this up–down asymmetry and determines its character. On the basis of our measurements, the “loss of flux” for a given lateral displacement decreases with increasing height of the sensors. For example, at a height of z = 10 m with a sensor displacement of D = 0.2 m, less than 1% of the flux is lost, whereas at z = 1 m ... Abstract To improve the quality of scalar-flux measurements, the two-point covariance between the vertical velocity w̃ and a scalar s̃, separated in space both horizontally and vertically, is studied. The measurements of such two-point covariances between vertical velocity and temperature with horizontal and vertical separations show good agreement with a symmetric turbulence model when the displacement is horizontal. However, a similar model does not work for vertical displacements because up–down asymmetry exists; that is, there is a lack of reflection symmetry of the covariance function. The second-order equation for conservation of two-point covariance of w̃ and s̃ reveals the reason for this up–down asymmetry and determines its character. On the basis of our measurements, the “loss of flux” for a given lateral displacement decreases with increasing height of the sensors. For example, at a height of z = 10 m with a sensor displacement of D = 0.2 m, less than 1% of the flux is lost, whereas at z = 1 m ...