The turbulent heat flux from arctic leads

The turbulent transfer of heat from Arctic leads in winter is one of the largest terms in the Arctic heat budget. Results from the AIDJEX Lead Experiment (ALEX) suggest that the sensible component of this turbulent heat flux can be predicted from bulk quantities. Both the exponential relation N = 0.14R _x ^0.72 and the linear relation N = 1.6 × 10^–3 R _x+ 1400 fit our data well. In these, N is the Nusselt number formed with the integrated surface heat flux, and R _x is the Reynolds number based on fetch across the lead. Because of the similarity between heat and moisture transfer, these equations also predict the latent heat flux. Over leads in winter, the sensible heat flux is two to four times larger than the latent heat flux.The internal boundary layer (IBL) that develops when cold air encounters the relatively warm lead is most evident in the modified downwind temperature profiles. The height of this boundary layer, , depends on the fetch, x, on the surface roughness of the lead, z ₀ and on both downwind and upwind stability. A tentative, empirical model for boundary layer growth is % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaaiabes% 7aKbqaaiaadQhadaWgaaWcbaGaaGimaaqabaaaaOGaeyypa0JaeqOS% di2aaeWaaeaacqGHsisldaWcaaqaaiaadQhadaWgaaWcbaGaaGimaa% qabaaakeaacaWGmbaaaaGaayjkaiaawMcaamaaCaaaleqabaGaaGim% aiaac6cacaaI4aaaaOWaaeWaaeaadaWcaaqaaiaadIhaaeaacaWG6b% WaaSbaaSqaaiaaicdaaeqaaaaaaOGaayjkaiaawMcaamaaCaaaleqa% baGaaGimaiaac6cacaaI0aaaaaaa!472D!\[\frac{\delta }{{z_0 }} = \beta \left( { - \frac{{z_0 }}{L}} \right)^{0.8} \left( {\frac{x}{{z_0 }}} \right)^{0.4} \] where L is the Obukhov length based on the values of the momentum and sensible heat fluxes at the surface of the lead, and is a constant reflecting upwind stability.Velocity profiles over leads are also affected by the surface nonhomogeneity. Besides being warmer than the upwind ice, the surface of the lead is usually somewhat rougher. The velocity profiles therefore tend to decelerate near the surface, accelerate in the mid-region of the IBL because of the intense mixing driven by the upward heat flux, and rejoin the upwind profiles above the boundary layer. The profiles thus have distinctly different shapes for stable and unstable upwind conditions.     

Methoxy formation in the reaction of CH3O2 radicals with NO

Formation of methoxy (CH₃O) radicals in the reaction (1) CH₃O₂+NOCH₃O+NO₂ at 298 K has been observed directly using time resolved LIF. The branching ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdyMaae% 4qaiaabIeadaWgaaWcbaGaae4maaqabaGccaqGpbGaaeiiaiaabIca% ieqacaWF9aGaa8hiaiaa-nbicaWFGaGaeuiLdqKaai4waiaaboeaca% qGibWaaSbaaSqaaiaabodaaeqaaOGaae4taiaac2facaWFVaGaeuiL% dqKaai4waiaaboeacaqGibWaaSbaaSqaaiaabodaaeqaaOGaae4tam% aaBaaaleaacaqGYaaabeaakiaac2facaqGPaaaaa!4E31!\[\phi {\rm{CH}}_{\rm{3}} {\rm{O (}} = -- \Delta [{\rm{CH}}_{\rm{3}} {\rm{O}}]/\Delta [{\rm{CH}}_{\rm{3}} {\rm{O}}_{\rm{2}} ]{\rm{)}}\] has been determined by quantitative cw-UV-laser absorption at 257 nm of CH₃O₂ and CH₃ONO, the product of the consecutive methoxy trapping reaction (2) % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4qaiaabI% eadaWgaaWcbaGaae4maaqabaGccaqGpbacbeGaa83kaiaa-bcaieaa% caGFobGaa43taiaa+bcacaGFOaGaa83kaiaa+1eacaGFPaGaa4hiai% abgkziUkaabccacaqGdbGaaeisamaaBaaaleaacaqGZaaabeaakiaa% b+eacaqGGaGaaeOtaiaab+eacaqGGaGaa4hkaiaa-TcacaGFnbGaa4% xkaiaa+5cacaGFGaGaa4hiaiabeA8aMnaaBaaajqwaacqaaiaaboea% caqGibWaaSbaaKazcaiabaGaae4maaqabaqcKfaGaiaab+eaaSqaba% aaaa!55AC!\[{\rm{CH}}_{\rm{3}} {\rm{O}} + NO ( + M) \to {\rm{ CH}}_{\rm{3}} {\rm{O NO }}( + M). \phi _{{\rm{CH}}_{\rm{3}} {\rm{O}}} \] is found to be (1.0±0.2). The rate constant k ₁ is (7±2) 10^-12 cm³/molecule · s in good agreement with previous results.     

An analytic similarity theory for the planetary boundary layer stabilized by surface buoyancy

An analytic solution for a steady, horizontally homogeneous boundary layer with rotation, % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadAgaaaa!38AA! \[ f \] , and surface friction velocity, û_*, subjected to surface buoyancy characterized by Obukhov length L, is proposed as follows. Nondimensional variables are % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeA7a6jabg2 % da9iaadAgacaWG6bGaai4laiabeE7aOnaaBaaaleaacqGHxiIkaeqa % aOGaamyDamaaBaaaleaacqGHxiIkaeqaaOGaaiilaiqadwhagaqcai % abg2da9iabeE7aOnaaBaaaleaacqGHxiIkaeqaaOGabmyvayaajaGa % ai4laiqadwhagaqcamaaBaaaleaacqGHxiIkaeqaaOGaaiilaiqads % fagaqcaiabg2da9iqbes8a0zaajaGaai4laiaadwhadaWgaaWcbaGa % ey4fIOcabeaakiqadwhagaqcamaaBaaaleaacqGHxiIkcaGGSaaabe % aaaaa!5587! \[ \zeta = fz/\eta _ * u_ * ,\hat u = \eta _ * \hat U/\hat u_ * ,\hat T = \hat \tau /u_ * \hat u_{ * ,} \] , where carets denote complex (vector) quantities; Û is the mean velocity; % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiqbes8a0zaaja% aaaa!3994!\[\hat \tau \]is the kinematic turbulent stress; and % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeE7aOnaaBa % aaleaacqGHxiIkaeqaaOGaeyypa0JaaiikaiaaigdacqGHRaWkcqaH % +oaEdaWgaaWcbaGaamOtaaqabaGccaWG1bWaaSbaaSqaaiabgEHiQa % qabaGccaGGVaGaamOuamaaBaaaleaacaWGJbaabeaakiaadAgacaWG % mbGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaiaac+cacaaIYaaaaa % aa!4B1F! \[ \eta _ * = (1 + \xi _N u_ * /R_c fL)^{ - 1/2} \]is a stability parameter. The constant % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabe67a4naaBa % aaleaacaWGobaabeaaaaa!3A81! \[\xi _N \] is the ratio of the maximum mixing length(% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaaBaaaleaaca% WGTbaabeaaaaa!38DD!\[_m \]) to the PBL depth, % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadwhadaWgaa % WcbaGaey4fIOcabeaakiaac+cacaWGMbaaaa!3B7C! \[ u_ * /f \] , for neutrally stable conditions; and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadkfadaWgaa% WcbaGaam4yaaqabaaaaa!39AA!\[R_c\](the critical flux Richardson number) is the ratio % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadYgadaWgaa % WcbaGaamyBaaqabaGccaGGVaGaamitaaaa!3B5C! \[ l_m /L \] under highly stable conditions. Profiles of stress and velocity in the ocean (<0) are given by % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaaxacabaGabm % yDayaajaGaeyypa0ZaaiqaaqaabeqaaiabgkHiTiaadMgacqaH0oaz % caWGLbWaaWbaaSqabeaacqaH0oazcqaH2oGEaaGccaqGGaGaaeiiai % aabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGa % aeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca % qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa % bccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaae % iiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqG % GaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc % cacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeii % aiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGa % GaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabcca % caqGGaGaaeiiaiaabccacaqGGaGaeqOTdONaeyizImQaeyOeI0Iaeq % OVdG3aaSbaaSqaaiaad6eaaeqaaaGcbaGaeyOeI0IaamyAaiabes7a % KjaadwgadaahaaWcbeqaaiabes7aKjabe67a4naaBaaameaacaWGob % aabeaaaaGccqGHsisldaWcaaqaaiabeE7aOnaaBaaaleaacaGGQaaa % beaaaOqaaiaadUgaaaWaamWaaeaaciGGSbGaaiOBamaalaaabaWaaq % WaaeaacqaH2oGEaiaawEa7caGLiWoaaeaacqaH+oaEdaWgaaWcbaGa % amOtaaqabaaaaOGaey4kaSIaaiikaiabes7aKjabgkHiTiaadggaca % GGPaGaaiikaiabeA7a6jabgUcaRiabe67a4naaBaaaleaacaWGobaa % beaakiaacMcacqGHsisldaWcaaqaaiaadggaaeaacaaIYaaaaiabes % 7aKjaacIcacqaH2oGEdaahaaWcbeqaaiaaikdaaaGccqGHsislcqaH % +oaEdaqhaaWcbaGaamOtaaqaaiaaikdaaaGccaGGPaaacaGLBbGaay % zxaaGaaeiiaiaabccacaqGGaGaaeiiaiabeA7a6naaBaaaleaacaaI % WaaabeaakiabgwMiZkabeA7a6jabg6da+iabgkHiTiabe67a4naaBa % aaleaacaWGobaabeaaaaGccaGL7baaaSqabKazbaiabaGabmivayaa % jaGaeyypa0JaamyzamaaCaaajqMaacqabeaacaWGPbGaeqiTdqMaeq % OTdOhaaaaaaaa!C5AA! \[ \mathop {\hat u = \left\{ \begin{array}{l} - i\delta e^{\delta \zeta } {\rm{ }}\zeta \le - \xi _N \\ - i\delta e^{\delta \xi _N } - \frac{{\eta _* }}{k}\left[ {\ln \frac{{\left| \zeta \right|}}{{\xi _N }} + (\delta - a)(\zeta + \xi _N ) - \frac{a}{2}\delta \end{array} \right.}\limits^{\hat T = e^{i\delta \zeta } } \] where % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabes7aKjabg2 % da9maabmaabaGaamyAaiaac+cacaWGRbGaeqOVdG3aaSbaaSqaaiaa % d6eaaeqaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaaIXaGaai4lai % aaikdaaaGccaGG7aGaamyyaiabg2da9iabeE7aOnaaBaaaleaacqGH % xiIkaeqaaOGaaiikaiaaigdacaGGVaGaeqOVdG3aaSbaaSqaaiaad6 % eaaeqaaOGaey4kaSIaamyDamaaBaaaleaacqGHxiIkaeqaaOGaai4l % aiaadAgacaWGmbGaamOuamaaBaaaleaacaWGJbaabeaakiaacMcaca % GGOaGaaGymaiabgkHiTiabeE7aOnaaBaaaleaacqGHxiIkaeqaaOGa % aiykaiaacUdaaaa!5CB6! \[ \delta = \left( {i/k\xi _N } \right)^{1/2} ;a = \eta _ * (1/\xi _N + u_ * /fLR_c )(1 - \eta _ * ); \] and ₀ is the nondimensional surface roughness. The constants are% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadkfadaWgaa% WcbaGaam4yaaqabaaaaa!39AA!\[R_c \]= 0.2 and% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabe67a4naaBa% aaleaacaWGobaabeaaaaa!3A81!\[\xi _N \]= 0.052. The solutions for the atmosphere are similar except û is the nondimensional velocity The model produces satisfactory predictions of geostrophic drag and near-surface current (wind) profiles under stable stratification.     

Kinetics of the reaction of nitrogen dioxide with ozone

The kinetics of the reaction of NO₂ with O₃ have been investigated at 296 K, using UV absorption spectroscopy to monitor decay of NO₂ or O₃ and infrared laser absorption spectroscopy to monitor formation of the reaction product N₂O₅. The results both for the rate coefficient at 296 K (k ₁=3.5×10^-17 cm³ molecule^-1 s^-1) and the reaction stoichiometry (NO₂/O₃=1.85±0.09) are in good agreement with previous studies, confirming that the two step mechanism involving formation of symmetrical NO₃ as an intermediate is predominant.% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOtaiaab+% eadaWgaaWcbaGaaeOmaaqabaGccqGHRaWkcaqGpbWaaSbaaSqaaiaa% bodaaeqaaOWaa4ajaSqaaaqabOGaayPKHaGaaeOtaiaab+eadaWgaa% WcbaGaae4maaqabaGccqGHRaWkcaqGpbWaaSbaaSqaaiaabkdaaeqa% aaaa!41D7!\[{\text{NO}}_{\text{2}} + {\text{O}}_{\text{3}} \xrightarrow{{}}{\text{NO}}_{\text{3}} + {\text{O}}_{\text{2}} \]% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOtaiaab+% eadaWgaaWcbaGaae4maaqabaGccqGHRaWkcaqGobGaae4tamaaBaaa% leaacaqGYaaabeaakiabgUcaRiaab2eadaGdKaWcbaaabeGccaGLsg% cacaqGobWaaSbaaSqaaiaabkdaaeqaaOGaae4tamaaBaaaleaacaqG% 1aaabeaakiabgUcaRiaab2eaaaa!4464!\[{\text{NO}}_{\text{3}} + {\text{NO}}_{\text{2}} + {\text{M}}\xrightarrow{{}}{\text{N}}_{\text{2}} {\text{O}}_{\text{5}} + {\text{M}}\]A possible minor role for the unsymmetrical ONOO species is suggested to account for the lower-than-expected stoichiometry factor. The importance of this reaction in the oxidation of atmospheric NO₂ is discussed.     

An analytical-empirical method for determining the roughness length and zero-plane displacement

A method based on the principle of the Method of Weighted Residuals for evaluating the roughness-length (z ₀) and zero-plane displacement (d) is presented. This method not only can minimize errors involved during the calculation process but can also smooth and re-distribute the already minimized error in a most favourable manner via using appropriate weighting functions. With the inclusion of d in addition to z ₀, formulae for wind and temperature profiles in the surface layer are presented by:% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGvbGaeyypa0% ZaaSaaaeaacaWG1bWaaSbaaSqaaiaacQcaaeqaaaGcbaGaam4Aaaaa% daWadaqaaiGacYgacaGGUbWaaeWaaeaadaWcaaqaaiaadQhacqGHsi% slcaWGKbaabaGaamOEamaaBaaaleaacaaIWaaabeaaaaaakiaawIca% caGLPaaacqGHRaWkcqaHipqEaiaawUfacaGLDbaaaaa!43FC!\[U = \frac{{u_* }}{k}\left[ {\ln \left( {\frac{{z - d}}{{z_0 }}} \right) + \psi } \right]\]and% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH4oqCcqGHsi% slcqaH4oqCdaWgaaWcbaGaaGimaaqabaGccqGH9aqpcqaH4oqCdaWa% daqaaiGacYgacaGGUbWaaeWaaeaadaWcaaqaaiaadQhacqGHsislca% WGKbaabaGaamOEamaaBaaaleaacaaIWaaabeaaaaaakiaawIcacaGL% PaaacqGHRaWkcqaHipqEdaWgaaWcbaacbmGaa8hvaaqabaaakiaawU% facaGLDbaaaaa!485A!\[\theta - \theta _0 = \theta \left[ {\ln \left( {\frac{{z - d}}{{z_0 }}} \right) + \psi _T } \right]\]where and _T are the integrated diabetic influence functions' for velocity and temperature profiles respectively.Analytical expressions for both and _T as functions of wind shear or, implicitly in terms of the Richardson number have been derived.Presented at the 10th Annual Congress of the Canadian Meteorological Society, Quebec City, Canada, May 26–28, 1976.     

The NO2-O3 system at sub-ppm concentrations: Influence of temperature and relative humidity

The stoichiometry and kinetics of the reaction of NO₂ with O₃ at sub-ppm concentration level have been investigated as a function of temperature and relative humidity. The experiments were performed in a continuous flow reactor using chemiluminescent and wet chemical methods of analysis.The rate constant found can be described by the Arrhenius expression: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaaik% dacaGGUaGaaGyoaiaaiEdacqGHXcqScaaIWaGaaiOlaiaaigdacaaI% 0aGaaiykaiabgEna0kaaigdacaaIWaWaaWbaaSqabeaacqGHsislca% aIXaGaaG4maaaakiaabwgacaqG4bGaaeiCaiaacIcadaWcgaqaaiaa% cIcacqGHsislcaaIYaGaaGOnaiaaikdacaaIWaGaeyySaeRaaGyoai% aaicdacaGGPaaabaGaamivaiaacMcacaqGGaGaae4yaiaab2gadaah% aaWcbeqaaiaabodaaaGccaqGGaWaaSGbaeaacaqGTbGaae4BaiaabY% gacaqGLbGaae4yaiaabwhacaqGSbGaaeyzamaaCaaaleqabaGaaeyl% aiaabgdaaaaakeaacaqGZbWaaWbaaSqabeaacaqGTaGaaeymaaaaaa% aaaaaa!62A3!\[(2.97 \pm 0.14) \times 10^{ - 13} {\text{exp}}({{( - 2620 \pm 90)} \mathord{\left/ {\vphantom {{( - 2620 \pm 90)} {T){\text{ cm}}^{\text{3}} {\text{ }}{{{\text{molecule}}^{{\text{ - 1}}} } \mathord{\left/ {\vphantom {{{\text{molecule}}^{{\text{ - 1}}} } {{\text{s}}^{{\text{ - 1}}} }}} \right. \kern-\nulldelimiterspace} {{\text{s}}^{{\text{ - 1}}} }}}}} \right. \kern-\nulldelimiterspace} {T){\text{ cm}}^{\text{3}} {\text{ }}{{{\text{molecule}}^{{\text{ - 1}}} } \mathord{\left/ {\vphantom {{{\text{molecule}}^{{\text{ - 1}}} } {{\text{s}}^{{\text{ - 1}}} }}} \right. \kern-\nulldelimiterspace} {{\text{s}}^{{\text{ - 1}}} }}}}\] and are independent of the relative humidity. As commonly encountered in previous studies a lower-than-two reaction stoichiometry is observed.Heterogeneous reactions occurring at the reactor wall seem to be essential in the reaction mechanism. The NO₃ wall conversion to NO₂ and the N₂O₅ wall scavenging in the presence of H₂O are suggested to account for the observed stoichiometric factors.     

Absolute OH quantum yields in the laser photolysis of nitrate,nitrite and dissolved H2O2 at 308 and 351 nm in the temperature range 278–353 K

Absolute quantum yields for the formation of OH radicals in the laser photolysis of aqueous solutions of NO₃ ^-, NO₂ ^- and H₂O₂ at 308 and 351 nm and as a function of pH and temperature have been measured. A scavenging technique involving the reaction between OH and SCN^- ions and the time resolved detection by visible absorption of the (SCN)₂ ^- radical ion was used to determine the absolute OH yields. The following results were obtained:

1. NO ₃ ^- -photolysis:% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaIWa% GaaGioaGGaaiab-bcaGiaab6gacaqGTbGaaeOoaiab-bcaGiabfA6a% gnaaBaaaleaacqWFFoWtcqWFxoasaeqaaOGaaiikaiaaikdacaaI5a% GaaGioaiab-bcaGiab-P5aljaacMcacqGH9aqpcqWFGaaicqWFWaam% cqWFUaGlcqWFWaamcqWFXaqmcqWF3aWncqWFGaaicqGHXcqScqWFGa% aicqWFWaamcqWFUaGlcqWFWaamcqWFWaamcqWFZaWmcqWFGaaicaqG% MbGaae4BaiaabkhacaqGGaGaaeinaiaabccacqGHKjYOcaqGGaGaam% iCaiaabIeacaqGGaGaeyizImQaaeiiaiaabMdaaeaacqWFGaaicqWF% GaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicq% WFGaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicqqHMoGr% daWgaaWcbaGae83Nd8Kae83LdGeabeaakiaacIcacaWGubGaaiykai% abg2da9iabfA6agnaaBaaaleaacqWFFoWtcqWFxoasaeqaaOGaaiik% aiaaikdacaaI5aGaaGioaiab-bcaGiab-P5aljaacMcacqWFGaaica% qGLbGaaeiEaiaabchacaqGGaWaamWaaeaacaqGOaGaaeymaiaabIda% caqGWaGaaeimaiaabccacqGHXcqScaaI0aGaaGioaiaaicdacaqGPa% GaaeikamaalaaabaGaaeymaaqaaiaabkdacaqG5aGaaeioaaaacaqG% GaGaeyOeI0IaaeiiamaalaaabaGaaeymaaqaaiaadsfaaaGaaeykaa% Gaay5waiaaw2faaiaac6caaaaa!9673!\[\begin{gathered}08 {\text{nm:}} \Phi _{{\rm O}{\rm H}} (298 {\rm K}) = 0.017 \pm 0.003 {\text{for 4 }} \leqslant {\text{ }}p{\text{H }} \leqslant {\text{ 9}} \hfill \\\Phi _{{\rm O}{\rm H}} (T) = \Phi _{{\rm O}{\rm H}} (298 {\rm K}) {\text{exp }}\left[ {{\text{(1800 }} \pm 480{\text{)(}}\frac{{\text{1}}}{{{\text{298}}}}{\text{ }} - {\text{ }}\frac{{\text{1}}}{T}{\text{)}}} \right]. \hfill \\\end{gathered}\] Selected experiments at 351 nm indicate that these results are essentially unchanged.
2. NO ₂ ^- -photolysis:% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaIWa% GaaGioaGGaaiab-bcaGiaab6gacaqGTbGaaeOoaiab-bcaGiabfA6a% gnaaBaaaleaacqWFFoWtcqWFxoasaeqaaOGaaiikaiaaikdacaaI5a% GaaGioaiab-bcaGiab-P5aljaacMcacqGH9aqpcqWFGaaicqWFOaak% cqWFWaamcqWFUaGlcqWFWaamcqWFXaqmcqWF3aWncqWFGaaicqGHXc% qScqWFGaaicqWFWaamcqWFUaGlcqWFWaamcqWFWaamcqWFXaqmcqWF% PaqkcqWFGaaicaqGMbGaae4BaiaabkhacaqGGaGaaeinaiaabccacq% GHKjYOcaqGGaGaamiCaiaabIeacaqGGaGaeyizImQaaeiiaiaabMda% caqGSaaabaGae8hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaaIae8% hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaaIa% e8hiaaIae8hiaaIaeuOPdy0aaSbaaSqaaiab-95apjab-D5aibqaba% GccaGGOaGaamivaiaacMcacqGH9aqpcqqHMoGrdaWgaaWcbaGae83N% d8Kae83LdGeabeaakiaacIcacaaIYaGaaGyoaiaaiIdacqWFGaaicq% WFAoWscaGGPaGae8hiaaIaaeyzaiaabIhacaqGWbGaaeiiamaadmaa% baGaaeikaiaabgdacaqG1aGaaeOnaiaabcdacaqGGaGaeyySaeRaae% iiaiaabodacaqG2aGaaeimaiaabMcacaqGOaWaaSaaaeaacaqGXaaa% baGaaeOmaiaabMdacaqG4aaaaiaabccacqGHsislcaqGGaWaaSaaae% aacaqGXaaabaGaamivaaaacaqGPaaacaGLBbGaayzxaaGaaiilaaqa% aiaaiodacaaI1aGaaGymaiaabccacaqGUbGaaeyBaiaabQdacqWFGa% aicqqHMoGrdaWgaaWcbaGae83Nd8Kae83LdGeabeaakiaacIcacaaI% YaGaaGyoaiaaiIdacqWFGaaicqWFAoWscaGGPaGaeyypa0Jae8hiaa% Iae8hkaGIae8hmaaJae8Nla4Iae8hmaaJae8hnaqJae8NnayJae8hi% aaIaeyySaeRae8hiaaIae8hmaaJae8Nla4Iae8hmaaJae8hmaaJae8% xoaKJae8xkaKIae8hiaaIaaeOzaiaab+gacaqGYbGaaeiiaiaabsda% caqGGaGaeyizImQaaeiiaiaadchacaqGibGaaeiiaiaab2dacaqGGa% GaaeioaiaabYcaaeaacqWFGaaicqWFGaaicqWFGaaicqWFGaaicqWF% GaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicqWFGaaicq% WFGaaicqWFGaaicqWFGaaicqqHMoGrdaWgaaWcbaGae83Nd8Kae83L% dGeabeaakiaacIcacaWGubGaaiykaiabg2da9iabfA6agnaaBaaale% aacqWFFoWtcqWFxoasaeqaaOGaaiikaiaaikdacaaI5aGaaGioaiab% -bcaGiab-P5aljaacMcacqWFGaaicaqGLbGaaeiEaiaabchacaqGGa% WaamWaaeaacaqGOaGaaeymaiaabIdacaqGWaGaaeimaiaabccacqGH% XcqScaqGGaGaaeinaiaabcdacaqGWaGaaeykaiaabIcadaWcaaqaai% aabgdaaeaacaqGYaGaaeyoaiaabIdaaaGaaeiiaiabgkHiTiaabcca% daWcaaqaaiaabgdaaeaacaWGubaaaiaabMcaaiaawUfacaGLDbaaca% GGUaaaaaa!FC61!\[\begin{gathered}08 {\text{nm:}} \Phi _{{\rm O}{\rm H}} (298 {\rm K}) = (0.017 \pm 0.001) {\text{for 4 }} \leqslant {\text{ }}p{\text{H }} \leqslant {\text{ 9,}} \hfill \\\Phi _{{\rm O}{\rm H}} (T) = \Phi _{{\rm O}{\rm H}} (298 {\rm K}) {\text{exp }}\left[ {{\text{(1560 }} \pm {\text{ 360)(}}\frac{{\text{1}}}{{{\text{298}}}}{\text{ }} - {\text{ }}\frac{{\text{1}}}{T}{\text{)}}} \right], \hfill \\351{\text{ nm:}} \Phi _{{\rm O}{\rm H}} (298 {\rm K}) = (0.046 \pm 0.009) {\text{for 4 }} \leqslant {\text{ }}p{\text{H = 8,}} \hfill \\\Phi _{{\rm O}{\rm H}} (T) = \Phi _{{\rm O}{\rm H}} (298 {\rm K}) {\text{exp }}\left[ {{\text{(1800 }} \pm {\text{ 400)(}}\frac{{\text{1}}}{{{\text{298}}}}{\text{ }} - {\text{ }}\frac{{\text{1}}}{T}{\text{)}}} \right]. \hfill \\\end{gathered}\]
3. H₂O₂-photolysis:% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaIWa% GaaGioaGGaaiab-bcaGiaab6gacaqGTbGaaeOoaiab-bcaGiabfA6a% gnaaBaaaleaacqWFFoWtcqWFxoasaeqaaOGaaiikaiaaikdacaaI5a% GaaGioaiab-bcaGiab-P5aljaacMcacqGH9aqpcqWFGaaicqWFOaak% cqWFWaamcqWFUaGlcqWF5aqocqWF4aaocqWFGaaicqGHXcqScqWFGa% aicqWFWaamcqWFUaGlcqWFWaamcqWFZaWmcqWFPaqkcqWFGaaicaqG% MbGaae4BaiaabkhacaqGGaGaamiCaiaabIeacaqGGaGaeyizImQaae% iiaiaabEdacaqGSaaabaGae8hiaaIae8hiaaIae8hiaaIae8hiaaIa% e8hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaaIae8hiaa% Iae8hiaaIae8hiaaIae8hiaaIaeuOPdy0aaSbaaSqaaiab-95apjab% -D5aibqabaGccaGGOaGaamivaiaacMcacqGH9aqpcqqHMoGrdaWgaa% WcbaGae83Nd8Kae83LdGeabeaakiaacIcacaaIYaGaaGyoaiaaiIda% cqWFGaaicqWFAoWscaGGPaGae8hiaaIaaeyzaiaabIhacaqGWbGaae% iiamaadmaabaGaaeikaiaabAdacaqG2aGaaeimaiaabccacqGHXcqS% caqGGaGaaeymaiaabMdacaqGWaGaaeykaiaabIcadaWcaaqaaiaabg% daaeaacaqGYaGaaeyoaiaabIdaaaGaaeiiaiabgkHiTiaabccadaWc% aaqaaiaabgdaaeaacaWGubaaaiaabMcaaiaawUfacaGLDbaacaGGSa% aabaGaaG4maiaaiwdacaaIXaGaaeiiaiaab6gacaqGTbGaaeOoaiab% -bcaGiabfA6agnaaBaaaleaacqWFFoWtcqWFxoasaeqaaOGaaiikai% aaikdacaaI5aGaaGioaiab-bcaGiab-P5aljaacMcacqGH9aqpcqWF% GaaicqWFOaakcqWFWaamcqWFUaGlcqWF5aqocqWF2aGncqWFGaaicq% GHXcqScqWFGaaicqWFWaamcqWFUaGlcqWFWaamcqWF0aancqWFPaqk% cqWFGaaicaqGMbGaae4BaiaabkhacaqGGaGaaeinaiaabccacqGHKj% YOcaqGGaGaamiCaiaabIeacaqGGaGaaeypaiaabccacaqG3aGaaeil% aaqaaiab-bcaGiab-bcaGiab-bcaGiab-bcaGiab-bcaGiab-bcaGi% ab-bcaGiab-bcaGiab-bcaGiab-bcaGiab-bcaGiab-bcaGiab-bca% Giab-bcaGiabfA6agnaaBaaaleaacqWFFoWtcqWFxoasaeqaaOGaai% ikaiaadsfacaGGPaGaeyypa0JaeuOPdy0aaSbaaSqaaiab-95apjab% -D5aibqabaGccaGGOaGaaGOmaiaaiMdacaaI4aGae8hiaaIae8NMdS% Kaaiykaiab-bcaGiaabwgacaqG4bGaaeiCaiaabccadaWadaqaaiaa% bIcacaqG1aGaaeioaiaabcdacaqGGaGaeyySaeRaaeiiaiaabgdaca% qG2aGaaeimaiaabMcacaqGOaWaaSaaaeaacaqGXaaabaGaaeOmaiaa% bMdacaqG4aaaaiaabccacqGHsislcaqGGaWaaSaaaeaacaqGXaaaba% GaamivaaaacaqGPaaacaGLBbGaayzxaaGaaiOlaaaaaa!F3D0!\[\begin{gathered}08 {\text{nm:}} \Phi _{{\rm O}{\rm H}} (298 {\rm K}) = (0.98 \pm 0.03) {\text{for }}p{\text{H }} \leqslant {\text{ 7,}} \hfill \\\Phi _{{\rm O}{\rm H}} (T) = \Phi _{{\rm O}{\rm H}} (298 {\rm K}) {\text{exp }}\left[ {{\text{(660 }} \pm {\text{ 190)(}}\frac{{\text{1}}}{{{\text{298}}}}{\text{ }} - {\text{ }}\frac{{\text{1}}}{T}{\text{)}}} \right], \hfill \\351{\text{ nm:}} \Phi _{{\rm O}{\rm H}} (298 {\rm K}) = (0.96 \pm 0.04) {\text{for 4 }} \leqslant {\text{ }}p{\text{H = 7,}} \hfill \\\Phi _{{\rm O}{\rm H}} (T) = \Phi _{{\rm O}{\rm H}} (298 {\rm K}) {\text{exp }}\left[ {{\text{(580 }} \pm {\text{ 160)(}}\frac{{\text{1}}}{{{\text{298}}}}{\text{ }} - {\text{ }}\frac{{\text{1}}}{T}{\text{)}}} \right]. \hfill \\\end{gathered}\] Together with the absorption coefficients and an assumed actinic flux within atmospheric droplets of twice the clear air value, the partial photolytic lifetimes (τ_OH) of these molecules at 298 K are estimated as 10.5 d, 5.4 h and 30.3 h for NO₃ ^-, NO₂ ^- and H₂O₂, respectively. These lifetimes will increase by a factor of two (NO₃ ^-, NO₂ ^-) and by 15% (H₂O₂) at T=278 K. Using average ambient concentrations in tropospheric aqueous droplets, the photolytic OH source strengths from these species are calculated to be 2.8×10^-11, 1.3×10^-11 and 1.4×10^-11 mol 1^-1 s^-1 for NO₃ ^-, NO₂ ^- and H₂O₂ respectively.

     

Prediction of the Monin-Obukhov similarity functions from a second-order-closure model

The atmospheric surface layer model of Lewellen and Teske (1973) is extended. Obvious discrepancies between model results and empirical data suggest the use of improved closure schemes for the non-diffusive parts of the pressure-velocity correlations in the Reynolds stress equations. Subsequently a time scale for the surface layer, which is based on vertical velocity fluctuations, is tested by means of the extended model. Finally the extended model is optimized by variation of the diffusion parameters, and an additional equation is introduced for the dissipation rate of Reynolds stresses. Investigations show that the normalized mean velocity and temperature gradients are verified by all model versions favorably, whereas the other turbulence variables % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaanaaabaGaam% yDaGqaciaa-DcacaWFGaGaamyDaiaa-DcaaaGaaiilaiaabccadaqd% aaqaaiabew8a1jaa-DcacaWFGaGaeqyXduNaa83jaaaacaqGSaGaae% iiamaanaaabaGaae4Daiaa-DcajaaqcaWFGaGccaqG3bGaa83jaaaa% caqGSaGaaeiiamaanaaabaGaamyDaiaa-DcajaaqcaWFGaGccaWFub% Gaa83jaaaaaaa!4DB4!\[\overline {u' u'} ,{\rm{ }}\overline {\upsilon ' \upsilon '} {\rm{, }}\overline {{\rm{w}}' {\rm{w}}'} {\rm{, }}\overline {u' T'} \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaGqaciaa-rfaca% WFNaqcaaKaa8hiaOGaa8hvaiaa-Dcaaaa!3BB8!\[T' T'\] cannot be simulated so easily. Complications especially arise in unstable temperature stratification.     

Review of some basic characteristics of the atmospheric surface layer

Some of the fundamental issues of surface layer meteorology are critically reviewed. For the von Karman constant (k), values covering the range from 0.32 to 0.65 have been reported. Most of the data are, however, found in a rather narrow range between 0.39 and 0.41. Plotting all available atmospheric data against the so-called roughness Reynolds number, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOuaiaabw% gadaWgaaWcbaGaaeimaaqabaGccqGH9aqpcaWG1bWaaSbaaSqaaiaa% cQcaaeqaaOGaamOEamaaBaaaleaacaaIWaaabeaakiaac+cacqaH9o% GBaaa!3FD0!\[{\rm{Re}}_{\rm{0}} = u_* z_0 /\nu \] or against the surface Rossby number, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOuaiaab+% gadaWgaaWcbaGaaeimaaqabaGccqGH9aqpcaWGhbGaai4laiaadAga% caWG6bWaaSbaaSqaaiaaicdaaeqaaaaa!3DF1!\[{\rm{Ro}}_{\rm{0}} = G/fz_0 \] gives no clear indication of systematic trend. It is concluded that k is indeed constant in atmospheric surface-layer flow and that its value is the same as that found for laboratory flows, i.e. about 0.40.Various published formulae for non-dimensional wind and temperature profiles, _m and _h respectively, are compared after adjusting the fluxes so as to give % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaiabg2% da9iaaicdacaGGUaGaaGinaiaaicdaaaa!3AC6!\[k = 0.40\] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWabeaaii% GacqWFgpGzdaWgaaWcbaGaamiAaaqabaGccaGGVaGae8NXdy2aaSba% aSqaaiaad2gaaeqaaaGccaGLOaGaayzkaaWaaSbaaSqaaiaadQhaca% GGVaGaamitaiabg2da9iaaicdaaeqaaOGaeyypa0JaaGimaiaac6ca% caaI5aGaaGynaaaa!4655!\[\left( {\phi _h /\phi _m } \right)_{z/L = 0} = 0.95\]. It is found that for % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWabeaaca% WG6bGaai4laiaadYeaaiaawEa7caGLiWoacqGHKjYOcaaIWaGaaiOl% aiaaiwdaaaa!3F72!\[\left| {z/L} \right| \le 0.5\] the various formulae agree to within 10–20%. For unstable stratification the various formulations for _h continue to agree within this degree of accuracy up to at least % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEaiaac+% cacaWGmbGaeyisISRaeyOeI0IaaGOmaaaa!3BC9!\[z/L \approx - 2\]. For _m in very unstable conditions results are still conflicting. Several recent data sets agree that for unstable stratification % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOuaiaabM% gacqGHijYUcaaIXaGaaiOlaiaaiwdacaWG6bGaai4laiaadYeaaaa!3E0D!\[{\rm{Ri}} \approx 1.5z/L\] up to at least % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaam% OEaiaac+cacaWGmbGaeyypa0JaaGimaiaac6cacaaI1aaaaa!3C8D!\[ - z/L = 0.5\] and possibly well beyond.For the Kolmogorov streamwise inertial subrange constant, _u , it is concluded from an extensive data set that % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS% baaSqaaiaadwhaaeqaaOGaeyypa0JaaGimaiaac6cacaaI1aGaaGOm% aiabgglaXkaaicdacaGGUaGaaGimaiaaikdaaaa!4178!\[\alpha _u = 0.52 \pm 0.02\]. The corresponding constant for temperature is much more uncertain, its most probable value being, however, about 0.80, which is also the most likely value for the corresponding constant for humidity.The turbulence kinetic energy budget is reviewed. It is concluded that different data sets give conflicting results in important respects, particularly so in neutral conditions.It is demonstrated that the inertial-subrange method can give quite accurate estimates of the fluxes of momentum, sensible heat and water vapour from high frequency measurements of wind, temperature and specific humidity alone, provided apparent values of the corresponding Kolmogorov constants are used. For temperature and humidity, the corresponding values turn out to be equal to the true constants, so % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdi2aaS% baaSqaaiaadgeaaeqaaOGaeyisISRaeqOSdiMaeyisISRaaGimaiaa% c6cacaaI4aGaaGimaaaa!4074!\[\beta _A \approx \beta \approx 0.80\]. For momentum, however, the apparent constant % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS% baaSqaaiaadwhacaWGbbaabeaakiabgIKi7kaaicdacaGGUaGaaGOn% aiaaicdaaaa!3E18!\[\alpha _{uA} \approx 0.60\].Based on an invited paper presented at the EGS Workshop Instrumental and Methodical Problems of Land Surface Flux Measurements, Grenoble 22–26 April, 1994.     

Minimum friction velocity and heat transfer in the rough surface layer of a convective boundary layer

A simple model is deduced for the surface layer of a convective boundary layer for zero mean wind velocity over homogeneous rough ground. The model assumes large-scale convective circulation driven by surface heat flux with a flow pattern as it would be obtained by conditional ensemble averages. The surface layer is defined here such that in this layer horizontal motions dominate relative to vertical components. The model is derived from momentum and heat balances for the surface layer together with closures based on the Monin-Obukhov theory. The motion in the surface layer is driven by horizontal gradients of hydrostatic pressure. The balances account for turbulent fluxes at the surface and fluxes by convective motions to the mixed layer. The latter are the dominant ones. The model contains effectively two empirical coefficients which are determined such that the model's predictions agree with previous experimental results for the horizontal turbulent velocity fluctuations and the temperature fluctuations. The model quantitatively predicts the decrease of the minimum friction velocity and the increase of the temperature difference between the mixed layer and the ground with increasing values of the boundary layer/roughness height ratio. The heat transfer relationship can be expressed in terms of the common Nusselt and Rayleigh numbers, Nu and Ra, as Nu ~ Ra^{% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaaGOmaaaaaaa!3779!\[{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\]}. Previous results of the form Nu ~ Ra^{% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaaG4maaaaaaa!377A!\[{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}\]} are shown to be restricted to Rayleigh-numbers less than a certain value which depends on the boundary layer/roughness height ratio.     

Measuring C T 2 , C Q 2 , and C TQ in the unstable surface layer,and relations to the vertical fluxes of heat and moisture

The structure parameters of temperature (C _T ² ), humidity (C _Q ² ) and temperature-humidity (C _TQ ) were observed at a height of 4 m in the unstable surface layer using thin platinum wires and two Ly- hygrometers. Two ways of measuring structure parameters were employed: one using spaced sensors, the other using time-delayed observations at one location. It is found that the three structure parameters follow free-convection scaling down to -z/L 0.02. The scaling functions % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₁ (of C _T ² ), % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₂ (of C _TO ) and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₃ (of C _Q ² ) are found to be related through % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₂/% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₁ 0.69 and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₃/% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₁ 0.84. The usefulness of the structure parameters for inferring the fluxes of heat and water vapor, as well as the Bowen ratio, is demonstrated. The scatter is about 30% on either side of the mean.This work was done while the author was a visiting scientist at the Wave Propagation Laboratory, NOAA, ERL, Boulder, U.S.A. He received support from the Netherlands Minister for Science Policy and the U.S. Army Research Office.     

The source area influencing a measurement in the Planetary Boundary Layer: The “footprint” and the “distribution of contact distance”

This paper considers the ground area which affects the properties of fluid parcels observed at a given spot in the Planetary Boundary Layer (PBL). We examine two source-area functions; the footprint, giving the source area for a measurement of vertical flux: and the distribution of contact distance, the distance since a particle observed aloft last made contact with the surface. We explain why the distribution of contact distance extends vastly farther upwind than the footprint, and suggest for the extent of the footprint the inequalities: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOabaeqabaGaamyvam% aalaaabaGaamiAaaqaaiabeo8aZnaaBaaaleaacaWGxbaabeaakiaa% cIcacaWGObGaaiykaaaacqGH8aapcaWG4bGaeyipaWJaamyvaKazaa% iadaGabaqaamaaDaaajqwaacqaaiaadIgacaGGVaGabmOEayaacaGa% aiilaiaabccacaGGVbGaaiiDaiaacIgacaGGLbGaaiOCaiaacEhaca% GGPbGaai4CaiaacwgaaeaacaWGubWaaSbaaKazcaiabaGaamitaaqa% baqcKfaGaiaacIcacaWGObGaaiykaiaabYcacaqGGaGaaeiAaiaabc% cacaGGHbGaaiOyaiaac+gacaGG2bGaaiyzaiaabccacaGGZbGaaiyD% aiaackhacaGGMbGaaiyyaiaacogacaGGLbGaeyOeI0IaaiiBaiaacg% gacaGG5bGaaiyzaiaackhaaaaajqgaacGaay5EaaaakeaaaeaacaGG% 8bGaamyEaiaacYhacqGH8aapcqaHdpWCdaWgaaWcbaGaamODaaqaba% GccaGGOaGaamiAaiaacMcadaWcaaqaaiaadIhaaeaacaWGvbaaaaaa% aa!7877!\[\begin{array}{l} U\frac{h}{{\sigma _W (h)}} < x < U\left\{ {_{h/\dot z,{\rm{ }}otherwise}^{T_L (h){\rm{, h }}above{\rm{ }}surface - layer} } \right. \\ \\ |y| < \sigma _v (h)\frac{x}{U} \\ \end{array}\] where U is the mean streamwise (x) velocity, h is the observation height, _L is the Lagrangian timescale, _v and _w are the standard deviations of the cross-stream horizontal (y) and vertical (z) velocity fluctuations, and is the Lagrangian Similarity prediction for the rate of rise of the centre of gravity of a puff released at ground.Simple analytical solutions for the contact-time and the footprint are derived, by treating the PBL as consisting of two sub-layers. The contact-time solutions agree very well with the predictions of a Lagrangian stochastic model, which we adopt in the absence of measurements as our best estimate of reality, but the footprint solution offers no improvement over the above inequality.     

Macro- and micro-scale mixing in chemical reactive plumes

The average dispersion of a plume in the atmospheric boundary layer is strongly influenced by atmospheric turbulence. Atmospheric turbulence determines also concentration fluctuations due to turbulent meandering by large scale turbulent eddies and in-plume fluctuations, due to smaller scale eddies. Conversion of NO to NO₂ in a plume is influenced by micro-scale mixing, due to the concentration fluctuation correlation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% qGobGaae4tamaaCaaaleqabaGaaeymaaaakiaab+eadaqhaaWcbaGa% ae4maaqaaiaabgdaaaaaaaaa!3AF4!\[\overline {{\rm{NO}}^{\rm{1}} {\rm{O}}_{\rm{3}}^{\rm{1}} } \] and macro-scale mixing, the mixing in of ambient air containing O₃ into the plume.The study of turbulent meandering, in-plume fluctuations, microscale and macro-scale mixing will contribute to a better understanding of concentration fluctuations in general.     

An examination of turbulence statistics in the surface boundary layer

Simulated data derived from random numbers are used to show that the process of relating % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG3baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baaaaa!3D7C!\[\sigma _w /u_ * \]and similar properties to the stability parameter % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadQhacaGGVa% Gaamitaaaa!3A42!\[z/L\]is highly susceptible to error. An alternative method, making use of Ri as a stability index, is not affected in this way and is used to re-examine the data obtained in the 1968 Kansas micrometeorological experiment. The relationship % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG3baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baGccqWIdjYocaaIXaGaaiOlaiaaikdacaaI1aaaaa!419F!\[\sigma _w /u_ * \simeq 1.25\] % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaabmaabaGaaG% ymaiabgkHiTiaaikdacaWG6bGaai4laiaadYeaaiaawIcacaGLPaaa% daahaaWcbeqaaiaaigdacaGGVaGaaG4maaaaaaa!4087!\[\left( {1 - 2z/L} \right)^{1/3} \]is found to provide a good fit to the unstable data, but it is unclear as to whether a small peak observed in stable conditions is real (perhaps associated with gravity waves) or not (possibly a consequence of measurement errors).The properties % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG1baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baaaaa!3D7A!\[\sigma _u /u_ * \]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG1baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baaaaa!3D7A!\[\sigma _u /u_ * \] are found to attain a relatively constant value ( 3) in conditions more unstable than about Ri = -0.4. The shape ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG1baabeaakiaac+cacqaHdpWCdaWgaaWcbaGaamODaaqa% baaaaa!3E4F!\[\sigma _u /\sigma _v \] is found to decrease to less than unity in very unstable conditions, possibly as a consequence of some undetected error in measurement of _u . In the case of temperature fluctuations, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacqaHepaDaeqaaOGaai4laiaadsfadaWgaaWcbaGaey4fIOca% beaakiabg2da9iaaicdacaGGUaGaaGyoaiaaiwdacaGGOaGaeyOeI0% IaamOEaiaac+cacaWGmbGaaiykamaaCaaaleqabaGaeyOeI0IaaGym% aiaac+cacaaIZaaaaaaa!4A30!\[\sigma _\tau /T_ * = 0.95( - z/L)^{ - 1/3} \] is found to provide an excellent fit in unstable conditions (Ri < -0.1), even though this form also agrees well with random behavior.Now With: Atmospheric Turbulence and Diffusion Laboratory, NOAA, P. O. Box E, Oak Ridge Tenn., 37830, U.S.A.     

Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy

This paper argues that the active turbulence and coherent motions near the top of a vegetation canopy are patterned on a plane mixing layer, because of instabilities associated with the characteristic strong inflection in the mean velocity profile. Mixing-layer turbulence, formed around the inflectional mean velocity profile which develops between two coflowing streams of different velocities, differs in several ways from turbulence in a surface layer. Through these differences, the mixing-layer analogy provides an explanation for many of the observed distinctive features of canopy turbulence. These include: (a) ratios between components of the Reynolds stress tensor; (b) the ratio K _H/K _M of the eddy diffusivities for heat and momentum; (c) the relative roles of ejections and sweeps; (d) the behaviour of the turbulent energy balance, particularly the major role of turbulent transport; and (e) the behaviour of the turbulent length scales of the active coherent motions (the dominant eddies responsible for vertical transfer near the top of the canopy). It is predicted that these length scales are controlled by the shear length scale % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa% aaleaacaWGtbaabeaakiabg2da9iaadwfacaGGOaGaamiAaiaacMca% caGGVaGabmyvayaafaGaaiikaiaadIgacaGGPaaaaa!3FD0!\[L_S = U(h)/U'(h)\] (where h is canopy height, U(z) is mean velocity as a function of height z, and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaafa% Gaeyypa0JaaeizaiaadwfacaGGVaGaaeizaiaadQhaaaa!3C32!\[U' = {\rm{d}}U/{\rm{d}}z\]). In particular, the streamwise spacing of the dominant canopy eddies is _x = mL _s, with m = 8.1. These predictions are tested against many sets of field and wind-tunnel data. We propose a picture of canopy turbulence in which eddies associated with inflectional instabilities are modulated by larger-scale, inactive turbulence, which is quasi-horizontal on the scale of the canopy.     

Etude experimentale d'une relation entre le coefficient de frottement et le facteur de rafales en regime de vent faible et au-dessus d'une surface d'eau

In usual aerodynamic bulk formulas, the drag coefficient C _d has been best estimated in the 5 to 16 m s^–1 range of mean wind velocity; a value of 1.3 × 10^–3 is often considered for operational use. However, in the 0 to 5 m s^–1 range of mean wind velocity, corresponding to meteorological conditions of very light wind, experimental results have not resulted in any convincing agreement between various authors (Hicks et al., 1974; Wu, 1969; Kondo and Fujinawa, 1972; Mitsuta, 1973; Brocks and Krugermeyer, 1970).In the present paper, the drag coefficient is experimentally determined in conditions of very light wind and limited fetch (about 250 m). Due to this limited fetch, we have to be cautious in the extrapolation of our results to other sites. Nevertheless, some of experimental results are worth describing, considering the paucity of data in light wind conditions.Mean value and standard deviation (respectively 1.84 × 10^–3 and 1.24 × 10^–3) are obtained from 70 runs of 10-min duration. Mean wind velocities observed at 2 m above water surface are found to lie between 1.2 and 3.6 m s^–1. Whereas this mean value is in fair agreement with C _{d 10} = 1.3 × 10^–3, usually given for the 5 to 16 m s^–1 range (Kraus, 1972), the above value for the standard deviation seems too large to be left without further analysis.A more exhaustive analysis of the 70 values obtained for C _d shows that it depends on a parameter characteristic of longitudinal fluctuations of the wind velocity. A similar idea was put forward earlier by Kraus (1972). Relations between the drag coefficient and wind fluctuations may be tentatively given by: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa% aaleaacaWGKbGaaGOmaaqabaGccqGH9aqpdaqadaqaaiabgkHiTiaa% igdacaGGUaGaaGimaiaaiEdacqGHRaWkcaaIXaGaaGinaiaac6caca% aIZaGaaGinamaalaaabaGaeq4Wdm3aaSbaaSqaaiaadwhacaGGNaaa% beaaaOqaaaaaaiaawIcacaGLPaaaruqqYLwySbacfaGaa8hEaiaa-b% cacaaIXaGaaGimamaaCaaaleqabaGaeyOeI0IaaG4maaaakiaabcca% caqGGaGaaeiiaiaabccacaqGXaGaaeOlaiaabAdacaqGGaGaaeyBai% aabccacaqGZbWaaWbaaSqabeaacaqGTaGaaeymaaaakiabgsMiJkqa% dwhagaqeamaaBaaaleaacaaIYaaabeaakiabgsMiJkaaiodacaGGUa% GaaGOnaiaab2gacaqGGaGaae4CamaaCaaaleqabaGaaeylaiaabgda% aaaaaa!634E!\[C_{d2} = \left( { - 1.07 + 14.34\frac{{\sigma _{u'} }}{{}}} \right)x 10^{ - 3} {\text{ 1}}{\text{.6 m s}}^{{\text{ - 1}}} \leqslant \bar u_2 \leqslant 3.6{\text{m s}}^{{\text{ - 1}}} \] and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa% aaleaacaWGKbGaaGOmaaqabaGccqGH9aqpdaqadaqaaiabgkHiTiaa% iodacaGGUaGaaGioaiaaiAdacqGHRaWkcaaIZaGaaiOlaiaaiodaca% aI2aGaam4raaGaayjkaiaawMcaaerbbjxAHXgaiuaacaWF4bGaa8hi% aiaaigdacaaIWaWaaWbaaSqabeaacqGHsislcaaIZaaaaOGaaeilaa% aa!4B42!\[C_{d2} = \left( { - 3.86 + 3.36G} \right)x 10^{ - 3} {\text{,}}\] where _u/\-u ₂ and G, respectively, represent the standard deviation of u normalized with \-u ₂ and the longitudinal gust factor quoted in Smith (1974).We have established a relationship between these fluctuation parameters and the stability as given by a bulk layer Richardson number (between 0 and 2 m). These relations are given by: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq% aHdpWCdaWgaaWcbaGaamyDaiaacEcaaeqaaaGcbaGabmyDayaaraWa% aSbaaSqaaiaaikdaaeqaaaaakiabg2da9iaaicdacaGGUaGaaGymai% aaikdacqGHRaWkcaaIZaGaaiOlaiaaiIdacaaI1aGaaeiiaiaabkfa% caqGPbWaaSbaaSqaaiaabcdacaqGTaGaaeOmaaqabaaaaa!4802!\[\frac{{\sigma _{u'} }}{{\bar u_2 }} = 0.12 + 3.85{\text{ Ri}}_{{\text{0 - 2}}} \] and G=1.35+14.56 Ri_0–2. The increase in gustiness with stability is in qualitative agreement with Goptarev (1957)'s experimental results.In spite of the high-level correlation between C _d and _u/\-u ₂(G) on the one hand and between _u/\-u ₂(G) and Ri_0–2on the other hand, we found a poor relationship between C _d and Ri_0–2. It is worth noting too that the trend observed here for C _d to increase with stability is in complete disagreement with the usual theoretical expectation for C _d to decrease with increasing layer stability above water.

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E.R.A. du C.N.R.S. n 259.     

Impact of density fluctuations on flux measurements of trace gases: Implications for the relaxed eddy accumulation technique

A simple and fast approach to determine when density fluctuations are non-negligible in the calculation of the flux of trace gases (F _c ) is proposed. The correction (F _c – F _c (raw)), when expressed as the percentage of the flux, is dependent on the ratio of background concentration of the trace gas over its flux (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeikaiabeg% 8aYnaaBaaaleaacaWGJbaabeaakiaab+cacaWGgbWaaSbaaSqaaiaa% dogaaeqaaOGaaeykaaaa!3CBC!\[{\rm{(}}\rho _c {\rm{/}}F_c {\rm{)}}\], on the partitioning of available energy between sensible (F _T ) and latent (F _v ) heat fluxes, and on the flux measuring system. An increase from 100 to 200 W m^-2 in available energy and from 0 to 20% in F _T /(F _T + F _v ) led to a threefold reduction in the required value of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaacq% aHbpGCdaWgaaWcbaGaam4yaaqabaaaaOGaai4laiaadAeadaWgaaWc% baGaam4yaaqabaaaaa!3B6D!\[\overline {\rho _c } /F_c \] to have a density correction of 10%. A trace gas with a % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaceaaca% WGgbWaaSbaaSqaaiaadogaaeqaaaGccaGLhWUaayjcSdGaai4lamaa% naaabaGaeqyWdi3aaSbaaSqaaiaadogaaeqaaaaaaaa!3E91!\[\left| {F_c } \right|/\overline {\rho _c } \] value above 0.014 m s^-1 has a density correction on flux of less than 10%, for even the worst case scenario. Values of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa% aaleaacaWGJbaabeaakiaac+cadaqdaaqaaiabeg8aYnaaBaaaleaa% caWGJbaabeaaaaaaaa!3B6D!\[F_c /\overline {\rho _c } \] for several trace gases computed from typical situations show that the fluxes of N₂O, NO, CO₂, CH₄ and O₃ need to be corrected, while those of pesticides and volatile organic compounds, for example, do not. The corrections required with the newly developed relaxed eddy accumulation technique are discussed and equation development is shown for two sampling systems.Land Resource Research Centre Contribution No 91-61.     

Latitudinal variation of measured O3 photolysis frequencies J(O1D) and primary OH production rates over the Atlantic Ocean between 50° N and 30° S

The latitudinal variation of the photolysis frequency of ozone to O(¹D) atoms, J(O¹D), was measured using a filter radiometer during the cruise ANT VII/1 of the research vessel Polarstern in September/October 1988. The J(O¹D) noon values exhibited a maximum of 3.6×10^-5 s^-1 (2 sr) at the equator and decreased strongly towards higher latitudes. J(O¹D) reached highest values for clean marine background air with low aerosol load and almost cloudless sky. The J(O¹D) data, measured under these conditions and a temperature of 295 K, can be expressed by: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsaiaacI% cacaqGpbWaaWbaaSqabeaaiiaacqWF8baFaaGccaqGebGaaeykaiaa% bccacqWF9aqpcaqGGaGaaeyzaiaabIhacaqGWbGaaeiiaiaabUhacq% GHsislcaaI4aGaaiOlaiaaicdacaaIYaGaeyOeI0IaaGioaiaac6ca% caaI4aGaaiiEaiaaigdacaaIWaWaaWbaaSqabeaacqGHsislcaaIZa% aaaOGaaeiiaiaabIhacaqGGaGaam4uaiabgUcaRiaaiodacaGGUaGa% aGinaiaacIhacaaIXaGaaGimamaaCaaaleqabaGaeyOeI0IaaGOnaa% aakiaadofadaahaaWcbeqaaiaaikdaaaGccaGG9bGaaeikaiaaboha% daahaaWcbeqaaiabgkHiTiaaigdaaaGccaGGPaaaaa!5EE9!\[J({\text{O}}^| {\text{D) }} = {\text{ exp \{ }} - 8.02 - 8.8x10^{ - 3} {\text{ x }}S + 3.4x10^{ - 6} S^2 \} {\text{(s}}^{ - 1} )\] where S represents the product of the overhead ozone column (DU) and the secant of the solar zenith angle. The meridional profile of the primary OH radical production rate P(OH) was calculated from the J(O¹D) measurements and simultaneously recorded O₃ and H₂O mixing ratios. While the latitudinal distribution of J(O¹D) and water vapour was nearly symmetric to the equator, high tropospheric ozone levels up to 40 ppb were observed in the Southern Hemisphere, SH, resulting in higher P(OH) in the SH.     

Models and observations of the growth of the atmospheric boundary layer

The evolution of the mixed layer during a clear day can be described with a slab model. The model equations have to be closed by a parameterization of the turbulent kinetic energy budget. Several possibilities for this parameterization have been proposed. In order to assess the practical applicability of these models for the atmosphere, field experiments were carried out on ten clear days in 1977 and 1978. Within the accuracy of the measurements the mixed-layer height in fully convective conditions (at noon on clear days) is well predicted taking a constant heat flux ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Yaa0% aaaeaacqaH4oqCcaWG3bWaaSbaaSqaaiaadIgaaeqaaaaakiabg2da% 9iaaicdacaGGUaGaaGOmamaanaaabaGaeqiUdeNaam4DamaaBaaale% aacaWGZbaabeaaaaaaaa!41D4!\[ - \overline {\theta w_h } = 0.2\overline {\theta w_s } \]. In the early morning hours mechanical entrainment is also important. Good overall results are obtained with the entrainment formulation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Yaa0% aaaeaacqaH4oqCcaWG3bWaaSbaaSqaaiaadIgaaeqaaaaakiabg2da% 9iaaicdacaGGUaGaaGOmamaanaaabaGaeqiUdeNaam4DamaaBaaale% aacaWGZbaabeaaaaGccqGHRaWkcaaI1aGaamyDamaaDaaaleaacqGH% xiIkaeaacaaIZaaaaOGaamivaiaac+cacaWGNbGaamiAaaaa!49C1!\[ - \overline {\theta w_h } = 0.2\overline {\theta w_s } + 5u_ * ^3 T/gh\].Only large differences in the entrainment coefficients lead to significantly different results. Making the entrainment model more complex does not lead to substantial improvement.The mean potential temperature in the mixed layer is reproduced within 0.5 °C. This temperature is insensitive to the choice of a particular entrainment formulation and depends more on the surface heat input and the temperature gradient in the stable air aloft.     

A comparison between observed and predicted values for the entrainment coefficient in the planetary boundary layer

A new method is presented for determining experimentally the entrainment coefficient % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyqaiabg2% da9iabgkHiTiaacIcadaqdaaqaaiabeI7aXjaacEcacaWG3bGaai4j% aaaacaGGPaGaamyAaiabg+caViaacIcadaqdaaqaaiabeI7aXjaacE% cacaWG3bGaai4jaaaacaGGPaWaaSbaaSqaaiaaicdaaeqaaaaa!4646!\[{\text{A}} = - (\overline {\theta 'w'} )i/(\overline {\theta 'w'} )_0 \] characteristic of a convective, planetary boundary layer. This method, which makes use of sodar records together with simultaneous meteorological observations, can be applied to morning convection situations (i.e. shallow mixed layer capped by a marked temperature inversion). Data from the Voves experiment (France, summer 1977) yield A values between 0 and 1, thus departing from the 0.2 ± 0.1 interval which is the range of commonly accepted values.A comparison between these results and theoretical predictions using models developed by Stull (1976) and Zeman and Tennekes (1977) indicates a fair amount of agreement; the importance of mechanically driven turbulence in the entrainment process, especially for the early morning hours, is therefore confirmed.

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Résumé Une méthode de détermination expérimentale du coefficient d'entraînement % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyqaiabg2% da9iabgkHiTiaacIcadaqdaaqaaiabeI7aXjaacEcacaWG3bGaai4j% aaaacaGGPaGaamyAaiabg+caViaacIcadaqdaaqaaiabeI7aXjaacE% cacaWG3bGaai4jaaaacaGGPaWaaSbaaSqaaiaaicdaaeqaaaaa!4646!\[{\text{A}} = - (\overline {\theta 'w'} )i/(\overline {\theta 'w'} )_0 \] dans une couche limite planétaire convective est proposée. Cette méthode, qui combine les données enregistrées par un sodar à des mesures météorologiques in situ, s'applique aux cas de convection matinale (couche de mélange assez peu développée surmontée par une inversion de température marquée.) Dans le cas des observations recueillies lors de la campagne de Voves (1977) elle fournit des valeurs de A qui s'écartent parfois de 0.2 ± 0.1 (gamme des valeurs souvent adoptées) et couvrent la totalité de l'intervalle 0-1.La comparaison entre les valeurs de A déterminées par cette méthode et celles prédites à partir des modèles de Stull (1976) et Zeman (1977) conduit à un accord satisfaisant, ce qui confirme le rôle joué par la turbulence mécanique dans le processus d'entraînement durant les premières heures de la convection matinale.