On The Temperature-Humidity Correlation And Similarity

The correlation coefficient between temperature and specific humidity (r_Tq) is considered. A brief literature review as well as experimental data reveals that there is evidence that the eddy diffusivities for heat and water vapour are not equal if |r_Tq| 1. Several conditions under which this can occur are discussed. It is concluded that if non-local effects are of the same order as local effects T and q will behave in a non-similar fashion. Moreover, it is shown that if |r_Tq| = 1, temperature and specific humidity both will obey Monin–Obukhov similarity. In addition, based on that derivation, a new method is presented to determine the Bowen ratio from the T - q correlation. A first test of this new Bowen ratio regression method is presented. It is recommended to use r_Tq as a diagnostic tool to judge whether T-q similarity holds.     

Relaxed Eddy Accumulation Simulations of Aerosol Number Fluxes and Potential Proxy Scalars

Direct eddy-covariance measurements of aerosol number fluxes obtained during the 2007 CHATS field experiment in Dixon, California, USA are compared with relaxed eddy accumulation simulations using temperature and water vapour concentration as proxy scalars. After a brief discussion of the limited time response of the aerosol measurement, the applicability of temperature and water vapour concentration as proxy scalars for aerosol number concentration is investigated by evaluating scalar and spectral correlation coefficients as simple measures of scalar similarity. In addition, the proportionality factor b, which compensates for the use of a constant sampling flow in relaxed eddy accumulation, is derived from the time series of aerosol number, temperature and water vapour, and its variability is analyzed. The reduction of the b factor due to application of a deadband, i.e. the rejection of data when the vertical wind speed is close to zero, is evaluated for all three studied scalars, and compared with published functional relationships. In this study, using temperature or water vapour as proxy scalars for aerosol number shows no advantage over the use of a constant b factor. Thus, it is suggested to apply a deadband H _REA  = w′/σ _w  = 0.6 to 0.8 (where w′ is the vertical velocity fluctuation and σ _w is its standard deviation), to use a theoretical b factor based on a parameterization that includes a stability dependence, and to calculate the deadband effect according to a derived relation for aerosol relaxed eddy accumulation.     

Turbulent Flow at 190 m Height Above London During 2006–2008: A Climatology and the Applicability of Similarity Theory

Flow and turbulence above urban terrain is more complex than above rural terrain, due to the different momentum and heat transfer characteristics that are affected by the presence of buildings (e.g. pressure variations around buildings). The applicability of similarity theory (as developed over rural terrain) is tested using observations of flow from a sonic anemometer located at 190.3 m height in London, U.K. using about 6500 h of data. Turbulence statistics—dimensionless wind speed and temperature, standard deviations and correlation coefficients for momentum and heat transfer—were analysed in three ways. First, turbulence statistics were plotted as a function only of a local stability parameter z/Λ (where Λ is the local Obukhov length and z is the height above ground); the σ _i /u _* values (i = u, v, w) for neutral conditions are 2.3, 1.85 and 1.35 respectively, similar to canonical values. Second, analysis of urban mixed-layer formulations during daytime convective conditions over London was undertaken, showing that atmospheric turbulence at high altitude over large cities might not behave dissimilarly from that over rural terrain. Third, correlation coefficients for heat and momentum were analyzed with respect to local stability. The results give confidence in using the framework of local similarity for turbulence measured over London, and perhaps other cities. However, the following caveats for our data are worth noting: (i) the terrain is reasonably flat, (ii) building heights vary little over a large area, and (iii) the sensor height is above the mean roughness sublayer depth.     

Local and Global Similarity in Turbulent Transfer of Heat, Water Vapour, And CO 2 in the Dynamic Convective Sublayer Over a Suburban Area

We investigated the ‘local’ and ‘global’ similarity of vertical turbulent transfer of heat, water vapour, and CO₂ within an urban surface layer. The results were derived from field measurements in a residential area of Tokyo, Japan during midday on fair-weather days in July 2001. In this study, correlation coefficients and quadrant analysis were used for the evaluation of ‘global’ similarity and wavelet analysis was employed for investigating ‘local’ similarity. The correlation coefficients indicated that the transfer efficiencies of water vapour and CO₂ were generally smaller than that of heat. Using wavelet analysis, we found that heat is always efficiently transferred by thermal and organized motions. In contrast, water vapour and CO₂, which are passive quantities, were not transferred as efficiently as heat. The quadrant analyses showed that the heat transfer by ejection exceeded that by sweep, and the ratios of ejection to sweep for water vapour and CO₂ transfer were less than that for heat. This indicated that heat is more efficiently transferred by upward motions and supported the findings from wavelet analysis. The differences of turbulent transfer between heat and both CO₂ and water vapour were probably caused both by the active role of temperature and the heterogeneity in the source distribution of scalars     

A Study in Search of Interconnection between Surface Parameters and Surrounding Synoptic And Subsynoptic Features

The paper reveals that the variations in parameters like u*, the scaling velocity and θ*. The scaling tempera-ture during the various phases of monsoon might be linked with subsynoptic features. The rise in u* is mainly connected with the presence of lower tropospheric cyclonic vorticity over a subsynoptic scale of the site. However the variations in θ* is mainly linked with the various phases of monsoon and θ* shows a sharp rise in presence of low level convective cloud.Besides the correlation studies of u and u*, θv and θv* , θv-θv0 and θv* are undertaken. The correlation be?tween θv and θv* is poor. In other two cases correlations are good. Besides u/u* , has shown good coefficient of variation values within the ζ range.     

A bulk similarity approach in the atmospheric boundary layer using radiometric skin temperature to determine regional surface fluxes

Profiles of wind velocity and temperature in the outer region of the atmospheric boundary layer (ABL) were used together with surface temperature measurements, to determine regional shear stress and sensible heat flux by means of transfer parameterizations on the basis of bulk similarity. The profiles were measured by means of radiosondes and the surface temperatures by infrared radiation thermometry over hilly prairie terrain in northeastern Kansas during the First ISLSCP Field Experiment (FIFE). In the analysis, the needed similarity functions were determined and tested; the main scaling variables used for the ABL were h _i , the height of the convectively mixed layer, and V _a and _a, the wind speed and potential temperature averaged over the mixed layer. Good agreement (r = 0.80) was obtained between values of friction velocity u _* determined by this ABL bulk similarity approach and those obtained by Monin-Obukhov similarity in the surface sublayer. Similarly, values of surface flux of sensible heat H determined by this method compared well (r = 0.90) with the regional means measured at six ground stations. The corresponding regional evaporation values, determined with the energy budget equation, also compared favorably (r = 0.94).     

Vertical Structure of Selected Turbulence Characteristics above an Urban Canopy

Summary In this paper the results of an urban measurement campaign are presented. The experiment took place from July 1995 to February 1996 in Basel, Switzerland. A total of more than 2000 undisturbed 30-minute runs of simultaneous measurements of the fluctuations of the wind vector u′, v′, w′ and the sonic temperature θ _s ′ at three different heights (z=36, 50 and 76 m a.g.l.) are analysed with respect to the integral statistics and their spectral behaviour. Estimates of the zero plane displacement height d calculated by the temperature variance method yield a value of 22 m for the two lower levels, which corresponds to 0.92 h (the mean height of the roughness elements). At all three measurement heights the dimensionless standard deviation σ _w /u _* is systematically smaller than the Monin-Obukhov similarity function for the inertial sublayer, however, deviations are smaller compared to other urban turbulence studies. The σ_θ/θ_* values follow the inertial sublayer prediction very close for the two lowest levels, while at the uppermost level significant deviations are observed. Profiles of normalized velocity and temperature variances show a clear dependence on stability. The profile of friction velocity u _* is similar to the profiles reported in other urban studies with a maximum around z/h=2.1. Spectral characteristics of the wind components in general show a clear dependence on stability and dimensionless measurement height z/h with a shift of the spectral peak to lower frequencies as thermal stability changes from stable to unstable conditions and as z/h decreases. Velocity spectra follow the −2/3 slope in the inertial subrange region and the ratios of spectral energy densities S _w (f)/S _u (f) approach the value of 4/3 required for local isotropy in the inertial subrange. Velocity spectra and spectral peaks fit best to the well established surface layer spectra from Kaimal et al. (1972) at the uppermost level at z/h=3.2. Received September 26, 1997 Revised February 15, 1998     

Large-Eddy Simulation of Flow and Pollutant Transports in and Above Two-Dimensional Idealized Street Canyons

A large-eddy simulation (LES) model, using the one-equation subgrid-scale (SGS) parametrization, was developed to study the flow and pollutant transport in and above urban street canyons. Three identical two-dimensional (2D) street canyons of unity aspect ratio, each consisting of a ground-level area source of constant pollutant concentration, are evenly aligned in a cross-flow in the streamwise direction x. The flow falls into the skimming flow regime. A larger computational domain is adopted to accurately resolve the turbulence above roof level and its influence on the flow characteristics in the street canyons. The LES calculated statistics of wind and pollutant transports agree well with other field, laboratory and modelling results available in the literature. The maximum wind velocity standard deviations σ _i in the streamwise (σ _u ), spanwise (σ _v ) and vertical (σ _w ) directions are located near the roof-level windward corners. Moreover, a second σ _w peak is found at z ≈ 1.5h (h is the building height) over the street canyons. Normalizing σ _i by the local friction velocity u _*, it is found that σ _u /u _* ≈ 1.8, σ _v /u _* ≈ 1.3 and σ _w /u _* ≈ 1.25 exhibiting rather uniform values in the urban roughness sublayer. Quadrant analysis of the vertical momentum flux u′′w′′ shows that, while the inward and outward interactions are small, the sweeps and ejections dominate the momentum transport over the street canyons. In the x direction, the two-point correlations of velocity R _v,x and R _w,x drop to zero at a separation larger than h but R _u,x (= 0.2) persists even at a separation of half the domain size. Partitioning the convective transfer coefficient Ω _T of pollutant into its removal and re-entry components, an increasing pollutant re-entrainment from 26.3 to 43.3% in the x direction is revealed, suggesting the impact of background pollutant on the air quality in street canyons.     

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.     

Discrepancy and Applicability of Various Similarity Functions in Flux Calculations Under Stable Conditions

Based on data obtained during the Hualhe River Basin Experiment （HUBEX） in 1999, this study intends to detect the quantitative discrepancies in the momentum （τ0）, sensible heat （H0） and latent heat （E0） fluxes among six sets of similarity functions with the aerodynamic method. It also aims to clarify the applicability of the functions under stable conditions. The relative discrepancy was studied with the normalized transfer coefficients for τ0, H0 and E0, namely CD, CH and CQ, respectively. Except for one set of functions that adopted a rather small von Kármán＇s constant （0.365）, the relative discrepancy in τ0 among the other functions was less than 10%, while that in H0（E0） sometimes reached 25% when the bulk Richardson number （R/B） was less than 0.07. The absolute discrepancy in the fluxes was studied with statistical computations. Among the six sets of functions, the discrepancy in τ0, H0 and E0 sometimes reached 0.03 kg m^-1 s^-2, 4 W m^-2 and 10 W m^-2, respectively, and the discrepancy in the energy balance ratio sometimes exceeded 0.1. Furthermore, when RiB exceeded the critical value （Ric） for a specific set of functions, no fluxes could be derived with the functions. It is therefore suggested that RiB be compared with Ric before computing the fluxes if RiB is less than Ric. Finally, two sets of nonlinear similarity functions are recommended, due to their unlimited applicability in terms of RiB.     

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.     

A Measurement Based Sensitivity Analysis of the Penman-Monteith Actual Evapotranspiration Model for Crops of Different Height and in Contrasting Water Status

Summary This paper presents a study of the sensibility of the Penman-Monteith evapotranspiration model to climatic (available energy and vapour pressure deficit) and parametric (aerodynamic and canopy resistances, r _a and r _c respectively) factors in a semi-arid climate, for crops in contrasting water status (well irrigated and under water stress) and of different heights. Three experiments were carried out in southern Italy on reference grass (≈ 0.1 m), grain sorghum (≈ 1 m) and sweet sorghum (≈ 3 m). For this analysis the sensitivity coefficients, taken as hourly means, were evaluated during the growth season when the crops completely covered the soil. The relative errors on evapotranspiration were also evaluated for r _a and r _c . The results showed that, for reference grass, available energy and aerodynamic resistance play a major role. For crops under water stress the most important term to evaluate is canopy resistance. For a tall crop, as sweet sorghum, the role of the vapour pressure deficit is fundamental, both when the crop is in good water status and under water stress. Received July 14, 1997 Revised February 5, 1998     

Local Similarity in the Stable Boundary Layer and Mixing-Length Approaches: Consistency of Concepts

In stably stratified flows vertical movement of eddies is limited by the fact that kinetic energy is converted into potential energy, leading to a buoyancy displacement scale z _B . Our new mixing-length concept for turbulent transport in the stable boundary layer follows a rigid-wall analogy, in the sense that we assume that the buoyancy length scale is similar to neutral length scaling. This implies that the buoyancy length scale is: ℓ _B  = κ _B z _B , with κ _B ≈ κ, the von Karman constant. With this concept it is shown that the physical relevance of the local scaling parameter z/Λ naturally appears, and that the α coefficient of the log-linear similarity functions is equal to c/κ ², where c is a constant close to unity. The predicted value α ≈ 1/κ ² = 6.25 lies within the range found in observational studies. Finally, it is shown that the traditionally used inverse linear interpolation between the mixing length in the neutral and buoyancy limits is inconsistent with the classical log-linear stability functions. As an alternative, a log-linear consistent interpolation method is proposed.     

A comparison of airborne eddy correlation and bulk aerodynamic methods for ocean-air turbulent fluxes during cold-air outbreaks

Four bulk schemes (LKB, FG, D and DB), with the flux-profile relationships of Liuet al. (1979), Francey and Garratt (1981), Dyer (1974), and Dyer and Bradley (1982), are derived from the viscous interfacial-sublayer model of Liuet al. These schemes, with stability-dependent transfer coefficients, are then tested against the eddy-correlation fluxes measured at the 50 m flight level above the western Atlantic Ocean during cold-air outbreaks. The bulk fluxes of momentum (), sensible heat (H), and latent heat (E) are found to increase with various von Kármán constants (k _M for k _H forH, andk _E forE). Except that the LKB scheme overestimates by 28% (46Wm^–2), on the average, the fluxes estimated by the four bulk schemes appear to be in fairly good agreement with those of the eddy correlation method (magnitudes of biases within 10% for , 17% forH, and 13% forE). The results suggest that the overall fluxes and surface-layer scaling parameters are best estimated by FG and thatk _H <k _E . On the average, the FG scheme underestimates by 10% (0.032N m^–2) andE by 4% (12Wm^–2), and overestimatesH by 0.3% (0.5W m^–2). The equivalent neutral transfer coefficients at 10 m height of the FG scheme compare well with some schemes of those tested by Blanc (1985).The relative importance of various von Kármán constants, dimensionless gradients and roughness lengths to the oceanic transfer coefficients is assessed. The dependence of transfer coefficients on wind speeds and roughness lengths is discussed. The transfer coefficients for andE agree excellently between LKB and FG. However, the ratio of the coefficient forH of LKB to that of FG, increasing with decreasing stability, is very sensitive to stability at low winds, but approaches the neutral value of 1.25 at high winds.     

On the Scaling Laws of the Velocity-Scalar Cospectra in the Canopy Sublayer Above Tall Forests

The scaling laws of the vertical (F _wc ) and longitudinal (F _uc ) velocity-scalar cospectra within the inertial subrange are explored using dimensional arguments and a simplified cospectral budget in the canopy sublayer above three distinct forested ecosystems. The cospectral budget was shown to be consistent with plausible scaling laws originating from dimensional considerations. Using the analytical solution to the novel cospectral budget, it was shown that F _wc (k) and F _uc (k) are governed by the linear superposition of two terms that scale as k ^−2/3−α and k ^−β , where k is the wavenumber, −α is the exponent of the velocity spectrum, and β( ≥ 7/3) depends on the ratio of the similarity constants for the pressure-scalar covariance and the flux transport terms. It was also demonstrated that, when the magnitude of the mean scalar concentration gradient is large, the k ^−2/3−α term dominates the velocity-scalar cospectral budget. For such a case, correcting for biases emerging from high frequency losses in eddy-covariance scalar flux measurements can be readily formulated by using the measured velocity spectral exponent in the inertial subrange.     

珠海凤凰山森林下垫面干季和湿季气象要素的对比分析与动量和感热交换系数的参数化研究

利用珠海凤凰山陆气相互作用观测塔站2014年11月至2016年5月的观测数据,对比分析了干湿季森林下垫面能量通量和气象要素的变化特征,分析了在不同稳定度下3个风向范围（315°～45°、45°～135°和135°～225°）的动量和感热交换系数随冠层表面风速的变化特征,并对动量和感热交换系数进行了参数化研究。结果表明:干季感热和潜热通量值相当,湿季潜热远大于感热。干季和湿季的夜晚都出现负感热现象,感热从大气向森林输送。相对湿度的变化幅度大,与该地气象状况密切相关,相对湿度的垂直梯度夜晚较大,白天较小。干季的气温垂直梯度比湿季的明显。风速在冬季变化平缓,夏季变化剧烈,低层风速随高度变化梯度明显,高层较紊乱。各高度风向差异不大。中性和近中性状态下,在风向为315°～45°、45°～135°和135°～225°时,动量交换系数C_dn分别为0.05、0.0055和0.022,感热交换系数C_hn分别为0.0055、0.003和0.004。在稳定和不稳定状态下,动量交换系数C_d、感热交换系数C_h随冠层表面风速v明显发生变化,稳定条件下,C_d、C_h随v的增大而增大;不稳定条件下,C_d、C_h随v的增大而减小。分不同风向对森林冠层C_d、C_h在稳定和不稳定条件下与v的关系进行了拟合,得到了参数化公式。     

Daily reference evapotranspiration estimates by the Penman-Monteith equation in Southern Italy. Constant vs. variable canopy resistance

Summary ?The performance of the Penman-Monteith (PM) equation to estimate daily reference evapotranspiration (ET_O) was investigated by attributing three distinct features to the canopy resistance (r _c): (i) r _c constant at 70 s m⁻¹ (Allen et al., 1998; FAO Irrigation and Drainage Paper n. 56), (ii) r _c variable as linear function of a critical resistance r _c, depending on weather variables and empirical parameters relating r _c to r ^* (Katerji and Perrier, 1983; Agronomie, 3[6]: 513–521) and (iii) r _c variable as a mechanistic function of weather variables only (Todorovic, 1999; J. Irrig. Drainage Eng., ASCE, 125[5]: 235–245). Daily weather and grass lysimeter data, measured for a period of seven years at Policoro (Southern Italy), were used. The results confirmed the relative robustness of the PM method with constant r _c while better estimates were obtained only when variable r _c was used. The mechanistic approach of Todorovic (1999) provided the best estimates, while the approach of Katerji and Perrier (1983), with empirically derived parameters, has shown to be not conservative enough to be extended to different locations without calibration. Received January 2, 2002; revised October 31, 2002; accepted December 7, 2002     

A Note on Two-Equation Closure Modelling of Canopy Flow

The note presents a rational approach to modelling the source/sink due to vegetation or buoyancy effects that appear in the turbulent kinetic energy, E, equation and a supplementary equation for a length-scale determining variable, φ, when two-equation closure is applied to canopy and atmospheric boundary-layer flows. The approach implements only standard model coefficients C _φ1 and C _φ2 in the production and destruction terms of the φ equation, respectively. Numerical tests illustrate the practical applicability of the method, where, for example, simulations with the E–ω model (where is the specific dissipation and is the dissipation rate of E) properly reproduce both the surface-layer wind profile estimated from the Monin-Obukhov similarity theory and the mixing-height evolution observed above forested terrain in Southern Finland.     

Atmospheric inorganic nitrogen in marine aerosol and precipitation and its deposition to the North and South Pacific Oceans

Aerosol and rain samples were collected between 48°N and 55°S during the KH-08-2 and MR08-06 cruises conducted over the North and South Pacific Ocean in 2008 and 2009, to estimate dry and wet deposition fluxes of atmospheric inorganic nitrogen (N). Inorganic N in aerosols was composed of ~68% NH₄⁺ and ~32% NO₃^– (median values for all data), with ~81% and ~45% of each species being present on fine mode aerosol, respectively. Concentrations of NH₄⁺ and NO₃⁻ in rainwater ranged from 1.7–55 μmol L⁻¹ and 0.16–18 μmol L⁻¹, respectively, accounting for ~87% by NH₄⁺ and ~13% by NO₃⁻ of total inorganic N (median values for all data). A significant correlation (r = 0.74, p < 0.05, n = 10) between NH₄⁺ and methanesulfonic acid (MSA) was found in rainwater samples collected over the South Pacific, whereas no significant correlations were found between NH₄⁺ and MSA in rainwater collected over the subarctic (r = 0.42, p > 0.1, n = 6) and subtropical (r = 0.33, p > 0.5, n = 6) western North Pacific, suggesting that emissions of ammonia (NH₃) by marine biological activity from the ocean could become a significant source of NH₄⁺ over the South Pacific. While NO₃⁻ was the dominant inorganic N species in dry deposition, inorganic N supplied to surface waters by wet deposition was predominantly by NH₄⁺ (42–99% of the wet deposition fluxes for total inorganic N). We estimated mean total (dry + wet) deposition fluxes of atmospheric total inorganic N in the Pacific Ocean to be 32–64 μmol m⁻² d⁻¹, with 66–99% of this by wet deposition, indicating that wet deposition plays a more important role in the supply of atmospheric inorganic N than dry deposition.     

Along-wind dispersion of puffs released in a built-up urban area

The SF₆ gas tracer observations for puffs released near the ground during the Joint Urban 2003 (JU2003) urban dispersion experiment in Oklahoma City have been analysed. The JU2003 observations, at distances of about 100–1,100 m from the source, show that, at small times, when the puff is still within the built-up downtown domain, the standard deviation of the concentration time series, σ_t, is influenced by the initial puff spread due to buildings near the source and by hold-up in the wakes of large buildings at the sampler locations. This effect is parameterised by assuming an initial σ_to of about 42 s, leading to a comprehensive similarity formula: σ_t = 42 + 0.1t. The second term, 0.1t, is consistent with an earlier similarity relation, σ_t = 0.1t, derived from puff observations in many experiments over rural terrain. The along-wind dispersion coefficient, σ_x, is assumed to equal σ_t u, in which u is the puff speed calculated as the distance from the source to the sampler, x, divided by the time after the release that the maximum concentration is observed at the sampler. σ_x can be expressed as σ_x = σ_xo + 0.14x, with the initial σ_xo of 45 m. This initial σ_xo agrees with the suggestion of an initial plume spread of about 40 m, made by McElroy and Pooler from analysis of the 1960s’ St. Louis urban dispersion experiment. The puff speeds, u, are initially only about 20% of the observed wind speed, averaged over about 80 street-level and rooftop anemometers in the city, but approach the mean observed wind speed as the puffs grow vertically. The scatter in the σ_t data is about ± a factor of two or three at any given travel time. The maximum σ_t is about 250 s, and the maximum duration of the puff over the sampler, Dt, sometimes called the retention time, is about 1,100 s or 18 min for these puffs and distances.