An Evaluation of the Flux–Gradient Relationship in the Stable Boundary Layer

Data collected during the SHEBA and CASES-99 field programs are employed to examine the flux–gradient relationship for wind speed and temperature in the stably stratified boundary layer. The gradient-based and flux-based similarity functions are assessed in terms of the Richardson number Ri and the stability parameter z/Λ_*, z being height and Λ_* the local Obukhov length. The resulting functions are expressed in an analytical form, which is essentially unaffected by self-correlation, when thermal stratification is strong. Turbulence within the stably stratified boundary layer is classified into four regimes: “nearly-neutral” (0 < z/Λ_* < 0.02), “weakly-stable” (0.02 < z/Λ_* < 0.6), “very-stable” (0.6 < z/Λ_* < 50), and “extremely-stable” (z/Λ_* > 50). The flux-based similarity functions for gradients are constant in “nearly-neutral” conditions. In the “very-stable” regime, the dimensionless gradients are exponential, and proportional to (z/Λ_*)^3/5. The existence of scaling laws in “extremely-stable” conditions is doubtful. The Prandtl number Pr decreases from 0.9 in nearly-neutral conditions and to about 0.7 in the very-stable regime. The necessary condition for the presence of steady-state turbulence is Ri < 0.7.     

Local Scales of Turbulence in the Stable Boundary Layer

Local, gradient-based scales, which contain the vertical velocity and temperature variances, as well as the potential temperature gradient, but do not include fluxes, are tested using data collected during the CASES-99 experiment. The observations show that the scaling based on the temperature variance produces relatively smaller scatter of empirical points. The resulting dimensionless statistical moments approach constant values for sufficiently large values of the Richardson number Ri. This allows one to derive predictions for the Monin–Obukhov similarity functions φ _m and φ _h , the Prandtl number Pr and the flux Richardson number Rf in weak turbulence regime.     

Structure of the stably-stratified boundary layer during the SESAME-1979 experiment

Airplane measurements in the stable boundary layer during the SESAME-1979 experiment (southcentral Oklahoma, U.S.A.) are examined in terms of the local similarity theory. The obtained results are compared with data from the Minnesota (1973) experiment and with data collected previously on towers in Cabauw (Netherlands) and Boulder (Colorado, U.S.A.). The comparison indicates that the SESAME data are strongly influenced by the terrain features of the experimental site.On leave from: Institute of Environmental Engineering, Warsaw Technical University, 00653 Warsaw, Poland.     

A statistical model for spatial inventory data: a case study of N2O emissions in municipalities of southern Norway

In this paper we apply a linear regression with spatial random effect to model geographically distributed emission inventory data. The study presented is on N₂O emission assessments for municipalities of southern Norway and on activities related to emissions (proxy data). Taking advantage of the spatial dimension of the emission process, the method proposed is intended to improve inventory extension beyond its earlier coverage. For this, the proxy data are used. The conditional autoregressive model is used to account for spatial correlation between municipalities. Parameter estimation is based on the maximum likelihood method and the optimal predictor is developed. The results indicate that inclusion of a spatial dependence component lead to improvement in both representation of the observed data set and prediction.     

Structural integrity of cracks in the head of Washington on Mount Rushmore

Summary Preliminary studies of the stability of Mt Rushmore shows a tendency for permanent crack deformation resulting from seasonal opening and closing of cracks in the structure.