Estimating a Lagrangian Length Scale Using Measurements of CO2 in a Plant Canopy

Analytical Lagrangian equations capable of predicting concentration profiles from known source distributions offer the opportunity to calculate source/sink distributions through inverted forms of these equations. Inverse analytical Lagrangian equations provide a practical means of estimating source profiles using concentration and turbulence measurements. Uncertainty concerning estimates of the essentially immeasurable Lagrangian length scale ( ${\mathcal{L}}$ ), a key input, impedes the operational practicality of this method. The present study evaluates ${\mathcal{L}}$ within a corn canopy by using field measurements to constrain an analytical Lagrangian equation. Measurements of net CO₂ flux, soil-to-atmosphere CO₂ flux, and in-canopy profiles of CO₂ concentration provided the information required to solve for ${\mathcal{L}}$ in a global optimization algorithm for 30-min time intervals. For days when the canopy was a strong CO₂ sink, the optimization frequently located ${\mathcal{L}}$ profiles that follow a convex shape. A constrained optimization then fit the profile shape to a smooth sigmoidal equation. Inputting the optimized ${\mathcal{L}}$ profiles in the forward and inverse Lagrangian equations leads to strong correlations between measured and calculated concentrations and fluxes. Coefficients of the sigmoidal equation were specific to each 30-min period and did not scale with any measured variable. Plausible looking ${\mathcal{L}}$ profiles were associated with negative bulk Richardson number values. Once the canopy senesced, a simple eddy diffusivity profile sufficed to relate concentrations and sources in the analytical Lagrangian equations.     

Cross-Validation of Open-Path and Closed-Path Eddy-Covariance Techniques for Observing Methane Fluxes

Methane ( ${\mathrm {CH}}_{4}$ ) fluxes observed with the eddy-covariance technique using an open-path ${\mathrm {CH}}_{4}$ analyzer and a closed-path ${\mathrm {CH}}_{4}$ analyzer in a rice paddy field were evaluated with an emphasis on the flux correction methodology. A comparison of the fluxes obtained by the analyzers revealed that both the open-path and closed-path techniques were reliable, provided that appropriate corrections were applied. For the open-path approach, the influence of fluctuations in air density and the line shape variation in laser absorption spectroscopy (hereafter, spectroscopic effect) was significant, and the relative importance of these corrections would increase when observing small ${\mathrm {CH}}_{4}$ fluxes. A new procedure proposed by Li-Cor Inc. enabled us to accurately adjust for these effects. The high-frequency loss of the open-path ${\mathrm {CH}}_{4}$ analyzer was relatively large (11 % of the uncorrected covariance) at an observation height of 2.5 m above the canopy owing to its longer physical path length, and this correction should be carefully applied before correcting for the influence of fluctuations in air density and the spectroscopic effect. Uncorrected ${\mathrm {CH}}_{4}$ fluxes observed with the closed-path analyzer were substantially underestimated (37 %) due to high-frequency loss because an undersized pump was used in the observation. Both the bandpass and transfer function approaches successfully corrected this flux loss. Careful determination of the bandpass frequency range or the transfer function and the cospectral model is required for the accurate calculation of ${\mathrm {CH}}_{4}$ fluxes with the closed-path technique.     

Impacts of Mixing Processes in Nocturnal Atmospheric Boundary Layer on Urban Ozone Concentrations

A number of open questions remain regarding the role of low-level jets (LLJs) and nocturnal mixing processes in the buildup of tropospheric ozone. The prevalence of southerly winds and LLJs in the U.S. Southern Great Plains during summer makes this region an ideal site for investigating the structure of the nocturnal boundary layer and its impacts on urban air quality. Ozone $(\mathrm{O}_{3})$ and nitrogen oxide concentrations measured at regulatory monitoring sites in the Oklahoma City (OKC) area and simulations with the Weather Research and Forecasting with Chemistry (WRF/Chem) model were analyzed to show how the nocturnal LLJ moderates boundary-layer mixing processes and air quality. Datasets collected during the Joint Urban 2003 campaign, which took place in July 2003 in OKC, provided detailed information about nocturnal boundary-layer structure and dynamics. In general, ${\mathrm{O}_{3}}$ time series show the expected behavior that urban ${\mathrm{O}_{3}}$ concentrations decrease at night due to nitrogen oxide titration reactions, but elevated ${\mathrm{O}_{3}}$ concentrations and secondary ${\mathrm{O}_{3}}$ peaks are also seen quite frequently after sunset. LLJs developed on most nights during the study period and were associated with strong vertical wind shear, which affected the boundary-layer stability and structure. Near-surface ${\mathrm{O}_{3}}$ concentrations are higher during less stable nights when active mixing persists throughout the night. The WRF/Chem model results agree well with the observations and further demonstrate the role of LLJs in moderating nocturnal mixing processes and air quality. The highest nocturnal ${\mathrm{O}_{3}}$ concentrations are linked to a strong LLJ that promotes both nocturnal long-range transport and persistent downward mixing of ${\mathrm{O}_{3}}$ from the residual layer to the surface.     

Variability of the Structure Parameters of Temperature and Humidity Observed in the Atmospheric Surface Layer Under Unstable Conditions

The structure parameters of temperature and humidity are important in scintillometry as they determine the structure parameter of the refractive index of air, the primary atmospheric variable obtained with scintillometers. In this study, we investigate the variability of the logarithm of the Monin-Obukhov-scaled structure parameters (denoted as $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ ) of temperature and humidity. We use observations from eddy-covariance systems operated at three heights (2.5, 50, and 90 m) within the atmospheric surface layer under unstable conditions. The variability of $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ depends on instability and on the size of the averaging window over which $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ is calculated. If instability increases, differences in $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ between upward motions (large $C_{s}^2$ ) and downward motions (small $C_{s}^2$ ) increase. The differences are, however, not sufficiently large to result in a bimodal probability density function. If the averaging window size increases, the variances of $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ decrease. A linear regression of the variances of $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ versus the averaging window size for various stability classes shows an increase of both the offset and slope (in absolute sense) with increasing instability. For temperature, data from the three heights show comparable results. For humidity, in contrast, the offset and slope are larger at 50 and 90 m than at 2.5 m. In the end we discuss how these findings could be used to assess whether observed differences in $C_{s}^2$ along a scintillometer path or aircraft flight leg are just within the range of local variability in $C_{s}^2$ or could be attributed to surface heterogeneity. This is important for the interpretation of data measured above a heterogeneous surface.     

Air–Sea \mathrm{CO}_{2} Gas Transfer Velocity in a Shallow Estuary

The air–sea transfer velocity of $\mathrm{CO}_{2}\, (k_{\mathrm{CO}_{2}})$ was investigated in a shallow estuary in March to July 2012, using eddy-covariance measurements of $\mathrm{CO}_{2}$ fluxes and measured air–sea $\mathrm{CO}_{2}$ partial-pressure differences. A data evaluation method that eliminates data by nine rejection criteria in order to heighten parametrization certainty is proposed. We tested the data evaluation method by comparing two datasets: one derived using quality criteria related solely to the eddy-covariance method, and the other derived using quality criteria based on both eddy-covariance and cospectral peak methods. The best parametrization of transfer velocity normalized to a Schmidt number of 600 $(k_{600})$ was determined to be: $k_{600} = 0.3\,{U_{10}}^{2.5}$ where $U_{10}$ is the wind speed in m $\mathrm{s}^{-1}$ at 10 m; $k_{600}$ is based on $\mathrm{CO}_{2}$ fluxes calculated by the eddy-covariance method and including the cospectral peak method criteria. At low wind speeds, the transfer velocity in the shallow water estuary was lower than in other coastal waters, possibly a symptom of low tidal amplitude leading to low intensity water turbulence. High transfer velocities were recorded above wind speeds of 5 m $\mathrm{s}^{-1}$ , believed to be caused by early-breaking waves and the large fetch (6.5 km) of the estuary. These findings indicate that turbulence in both air and water influences the transfer velocity.     

An Approach to Minimizing Artifacts Caused by Cross-Sensitivity in the Determination of Air–Sea \text{ CO }_{2} Flux Using the Eddy-Covariance Technique

The air–sea $\text{ CO }_{2}$ flux was measured from a research vessel in the North Yellow Sea in October 2007 using an open-path eddy-covariance technique. In 11 out of 64 samples, the normalized spectra of scalars ( $\text{ CO }_{2}$ , water vapour, and temperature) showed similarities. However, in the remaining samples, the normalized $\text{ CO }_{2}$ spectra were observed to be greater than those of water vapour and temperature at low frequencies. In this paper, the noise due to cross-sensitivity was identified through a combination of intercomparisons among the normalized spectra of three scalars and additional analyses. Upon examination, the cross-sensitivity noise appeared to be mainly present at frequencies ${<}0.8\,\text{ Hz }$ . Our analysis also suggested that the high-frequency fluctuations of $\text{ CO }_{2}$ concentration (frequency ${>}0.8\,\text{ Hz }$ ) was probably less affected by the cross-sensitivity. To circumvent the cross-sensitivity issue, the cospectrum in the high-frequency range 0.8–1.5 Hz, instead of the whole range, was used to estimate the $\text{ CO }_{2}$ flux by taking the contribution of the high frequency to the $\text{ CO }_{2}$ flux to be the same as the contribution to the water vapour flux. The estimated air–sea $\text{ CO }_{2}$ flux in the North Yellow Sea was $-0.039\,\pm \,0.048\,\text{ mg } \text{ m }^{-2}\,\text{ s }^{-1},$ a value comparable to the estimates using the inertial dissipation method and Edson’s method (Edson et al., J Geophys Res 116:C00F10, 2011).     

Asymmetric effects of soil moisture on mean daily maximum and minimum temperatures over eastern China

This study statistically investigates the effects of soil moisture on mean daily maximum ( $T_{\rm{max} }$ ) and minimum temperatures ( $T_{\rm{min} }$ ) over eastern China in spring (from March to May), summer (from June to August) and fall (from September to November), using the Global Land Data Assimilation System (GLDAS) soil moisture and observational temperatures. The results show that soil moisture exerts asymmetric effects on $T_{\rm{max} }$ and $T_{\rm{min} }$ , thereby has substantial effects on the diurnal temperature range (DTR) in the three seasons. The soil moisture feedbacks on $T_{\rm{max} }$ , $T_{\rm{min} }$ , and DTR are found to evidently vary with season. In spring and summer, soil moisture exerts stronger negative forcing on $T_{\rm{max} }$ than $T_{\rm{min} }$ , and thus has negative effects on the DTR over many areas of northern China. In fall, soil moisture has much stronger positive effects on $T_{\rm{min} }$ than $T_{\rm{max} }$ , and thus has significant negative effects on the DTR over Northeast China and some areas of the climatic and ecological transition zone of northern China. The uncertainties in the employed data and method should be noted. Therefore, the results need to be further investigated by other data sets and methods in the future.     

Some Statistics of the Temperature Structure Parameter in the Convective Boundary Layer Observed by Sodar

The characteristics of the temporal and height variations of the temperature structure parameter $C_\mathrm{T}^{2}$ in strongly convective situations derived from the sodar echo-signal intensity measurements were analyzed for the first 100 m. It was corroborated that the probability density function (pdf) of the logarithm of $C_\mathrm{T}^{2}$ in the lower convective boundary layer is markedly non-Gaussian, whereas turbulence theory predicts it to be normal. It was also corroborated that the sum of two weighted Gaussians, which characterize the statistics of $C_\mathrm{T}^{2}$ within convective plumes and in their environment and the probability of plume occurrence, well approximates the observed pdfs. It was shown that the height behaviour of the arithmetic mean of $ C_\mathrm{T}^{2}$ (both total and within plumes) follows well a power law $C_\mathrm{T}^{2} (z) \sim z^{-q}$ with the exponent $q$ close to the theoretically predicted value of 4/3. But for the geometrical means of $C_\mathrm{T}^{2}$ (both total and within the plumes), $q$ is close to 1. The difference between arithmetically and geometrically averaged $C_\mathrm{T}^{2}$ profiles was analyzed. The vertical profiles of the standard deviation, skewness and kurtosis of $\hbox {ln}C_\mathrm{T}^{2}$ pdfs were analyzed to show their steady behaviour with height. The standard deviations of the logarithm of $C_\mathrm{T}^{2}$ within the plumes and between them are similar and are 1.5 times less than the total standard deviation. The estimate of the variability index $F_\mathrm{T}$ and its height behaviour were obtained, which can be useful to validate some theoretical and modelling predictions. The vertical profiles of the skewness and kurtosis show the negative asymmetry of pdfs and their flatness, respectively. The spectra of variations in $\hbox {ln}C_\mathrm{T}^{2}$ are shown to be satisfactorily fitted by the power law $f^{-\gamma } $ in the frequency range 0.02 and 0.2 Hz, with the average exponent $\approx $ 1.27  $\pm $  0.22.     

Vertical Distribution of Radiation and Energy Balance Partitioning Within and Above a Lodgepole Pine Stand Recovering from a Recent Insect Attack

The current outbreak of mountain pine beetle (MPB) that started in the late 1990s in British Columbia, Canada, is the largest ever recorded in the north American native habitat of the beetle. The killing of trees is expected to change the vertical distribution of net radiation ( $Q^*$ Q ? ) and the partitioning of latent ( $Q_\mathrm{E}$ Q E ) and sensible ( $Q_\mathrm{H}$ Q H ) heat fluxes in the different layers of an attacked forest canopy. During an intensive observation period in the summer of 2010, eddy-covariance flux and radiation measurements were made at seven heights from ground level up to 1.34 times the canopy height in an MPB-attacked open-canopy forest stand $(\hbox {leaf area index} = 0.55~\mathrm{{m}}^{2}\ \mathrm{{m}}^{-2})$ ( leaf area index = 0.55 m 2 m - 2 ) in the interior of British Columbia, Canada. The lodgepole pine dominated stand with a rich secondary structure (trees and understorey not killed by the beetle) was first attacked by the MPB in 2003 and received no management. In this study, the vertical distribution of the energy balance components and their sources and sinks were analyzed and energy balance closure (EBC) was determined for various levels within the canopy. The low stand density resulted in approximately 60 % of the shortwave irradiance and 50 % of the daily total $Q^*$ Q ? reaching the ground. Flux divergence calculations indicated relatively strong sources of latent heat at the ground and where the secondary structure was located. Only very weak sources of latent heat were found in the upper part of the canopy, which was mainly occupied by dead lodgepole pine trees. $Q_\mathrm{H}$ Q H was the dominant term throughout the canopy, and the Bowen ratio ( $Q_\mathrm{H}/Q_\mathrm{E}$ Q H / Q E ) increased with height in the canopy. Soil heat flux ( $Q_\mathrm{G}$ Q G ) accounted for approximately 4 % of $Q^*$ Q ? . Sensible heat storage in the air ( $\Delta Q_\mathrm{S,H}$ Δ Q S , H ) was the largest of the energy balance storage components in the upper canopy during daytime, while in the lower canopy sensible heat storage in the boles ( $\Delta Q_\mathrm{S,B}$ Δ Q S , B ) and biochemical energy storage ( $\Delta Q_\mathrm{S,C}$ Δ Q S , C ) were the largest terms. $\Delta Q_\mathrm{S,H}$ Δ Q S , H was almost constant from the bottom to above the canopy. $\Delta Q_\mathrm{S,C}$ Δ Q S , C , $\Delta Q_\mathrm{S,B}$ Δ Q S , B and latent heat storage in the air ( $\Delta Q_\mathrm{S,E}$ Δ Q S , E ) varied more than $\Delta Q_\mathrm{S,H}$ Δ Q S , H throughout the canopy. During daytime, energy balance closure was high in and above the upper canopy, and in the lowest canopy level. However, where the secondary structure was most abundant, ${\textit{EBC}} \le 66\,\%$ EBC ≤ 66 % . During nighttime, the storage terms together with $Q_\mathrm{G}$ Q G made up the largest part of the energy balance, while $Q_\mathrm{H}$ Q H and $Q_\mathrm{E}$ Q E were relatively small. These radiation and energy balance measurements in an insect-attacked forest highlight the role of secondary structure in the recovery of attacked stands.     

Characteristics and Mechanisms of Low-Level Jets in the Yangtze River Delta of China

A dataset obtained using a wind-profile radar located at the Yangtze River Delta in China ( $31.14^{\circ }$ N, $121.81^{\circ }$ E) in 2009 was used to investigate the characteristics and evolution of low-level jets (LLJs) along the east China coast. The study investigated the daily and seasonal structures of LLJs as well as several possible causes. A total of 1,407 1-h LLJ periods were detected based on an adaptive definition that enabled determination of four LLJ categories. The majority (77 %) of LLJs were found to have speeds $<$ 14.0 m s $^{-1}$ (maximum of 34.6 m s $^{-1})$ and occur at an average altitude below 600 m (76 % of the observed LLJs). The dominant direction of the LLJs was from the south-south-west, which accounted for nearly 32 %, with the second most common wind direction ranging from $040^{\circ }$ to $100^{\circ }$ , albeit with a number of stronger LLJs from the west-south-west. A comparison of LLJs and South-west Jets revealed that the frequencies of occurrence in summer are totally different. Results also revealed that in spring and summer, most LLJs originate from the south-south-west, whereas in autumn and winter, north-east is the dominant direction of origin. The peak heights of LLJs tended to be higher in winter than in other seasons. The horizontal wind speed and peak height of the LLJs displayed pronounced diurnal cycles. The Hilbert–Huang transform technique was applied to demonstrate that the intrinsic mode functions with a cycle of nearly 23 h at levels below 800 m, and the instantaneous amplitudes of inertial events (0.0417–0.0476 h $^{-1}$ frequencies) have large values at 300–600 m. The variations in the occurrences of LLJs suggested connections between the formation mechanisms of LLJs and the South-west Jet stream, steady occupation of synoptic-scale pressure system, and land–sea temperature contrasts.     

Turbulent Schmidt Numbers Above a Wheat Crop

Measurements of vertical fluxes and concentration differences above a spring wheat crop (height $h=0.9$ – $0.95$  m, row spacing 0.25 m, displacement height $d=0.5$ – $0.6$  m) were analyzed to determine the Schmidt numbers for water vapour ( $S^\mathrm{v}$ ) and carbon dioxide ( $S^\mathrm{c}$ ) based on concentration differences between intakes 2.55 and 3.54 m above the ground. During nearly-neutral stratification $S^\mathrm{v}(0) = 0.68 \pm 0.1$ while $S^\mathrm{c} = 0.78 \pm 0.2$ , implying that the roughness sublayer extended above $2.5 h$ .     

Improvements in Sensible Heat-Flux Parametrization in the High-Resolution Regional Model (HRM) Through the Modified Treatment of the Roughness Length for Heat

We discuss the impact of the differential treatment of the roughness lengths for momentum and heat ( $z_{0\mathrm{m}}$ and $z_{0\mathrm{h}}$ ) in the flux parametrization scheme of the high-resolution regional model (HRM) for a heterogeneous terrain centred around Thiruvananthapuram, India (8.5°N, 76.9°E). The magnitudes of sensible heat flux (H) obtained from HRM simulations using the original parametrization scheme differed drastically from the concurrent in situ observations. With a view to improving the performance of this parametrization scheme, two distinct modifications are incorporated: (1) In the first method, a constant value of 100 is assigned to the $z_{0\mathrm{m}}/z_{0\mathrm{h}}$ ratio; (2) and in the second approach, this ratio is treated as a function of time. Both these modifications in the HRM model showed significant improvements in the H simulations for Thiruvananthapuram and its adjoining regions. Results obtained from the present study provide a first-ever comparison of H simulations using the modified parametrization scheme in the HRM model with in situ observations for the Indian coastal region, and suggest a differential treatment of $z_{0\mathrm{m}}$ and $z_{0\mathrm{h}}$ in the flux parametrization scheme.     

Scalar Flux–Gradient Relationships Under Unstable Conditions over Water in Coastal Regions

The scalar flux–gradient relationships of temperature ( $\phi _{T}$ ? T ) and specific humidity ( $\phi _{q}$ ? q ) under unstable conditions are investigated using eddy-covariance measurements of air–sea turbulent fluxes and vertical profiles of temperature and specific humidity collected from a marine meteorological platform. The gradients of temperature and specific humidity are obtained from measurements at five heights above the sea surface using the log-square fitting method and the simpler first-order approximation method. The two methods yield similar results. The proposed flux–gradient relationships $\phi _{T}$ ? T and $\phi _{q}$ ? q covers a wide range of instability: the stability parameter $\zeta $ ζ ranges from $-$ ? 0.1 to $-$ ? 50. The functional form of the proposed flux–gradient relationships is an interpolation between the Businger–Dyer relation and the free convection relation, which includes the “ $-$ ? 1/2” and “ $-$ ? 1/3” scaling laws at two different stability regimes. The widely used COARE 3.0 algorithm, which is an interpolation between the integrals of the Businger–Dyer and the free convection relations, is also evaluated and compared. The analysis and comparisons show that both schemes generate reasonable values of $\phi _{q}$ ? q in the whole unstable regime. The COARE 3.0 algorithm, however, overestimates $\phi _{T}$ ? T values under very unstable conditions. The errors in the flux–gradient relationships induced by the random errors in the turbulence measurements are assessed. When the random errors are taken into account, the observations agree with predictions of various schemes fairly well, implying that the dominant transport mechanism is adequately captured by the Monin–Obukhov similarity theory. The study also shows that $\phi _{q}$ ? q is significantly ${>}\phi _{T}$ > ? T under unstable conditions and that the ratio $\phi _{q}/\phi _{T}$ ? q / ? T increases with $-\zeta $ ? ζ . The ratio of $\phi _{q}$ ? q to $\phi _{T}$ ? T and the ratio of turbulent transport efficiencies of heat and water vapour ( $R_{wT}/R_{wq}$ R wT / R wq ) suggest that heat is transported more efficiently than water vapour under unstable conditions.     

Towards a Validation of Scintillometer Measurements: The LITFASS-2009 Experiment

Scintillometry has been increasingly used over the last decade for the experimental determination of area-averaged turbulent fluxes at a horizontal scale of a few kilometres. Nevertheless, a number of assumptions in the scintillometer data processing and interpretation still call for a thorough evaluation, in particular over heterogeneous terrain. Moreover, a validation of the path-averaged structure parameters derived from scintillometer data (and forming the basis for the flux calculations) by independent measurements is still missing. To achieve this, the LITFASS-2009 field campaign has been performed around the Meteorological Observatory Lindenberg ?C Richard-A?mann-Observatory of the German Meteorological Service (DWD) in July 2009. The experiment combined tower-based in-situ turbulence measurements, field-scale laser scintillometers, long-range optical (large-aperture) and microwave scintillometers, and airborne turbulence measurements using an automatically operating unmanned aircraft. The paper describes the project design and strategy, and discusses first results. Daytime near-surface values of the temperature structure parameter, ${C_{T}^{2}}$ , over different types of farmland differ by more than one order of magnitude in their dependence on the type and status of the vegetation. Considerable spatial variability in ${C_{T}^{2}}$ was also found along the flight legs at heights between 50 and 100?m. However, it appeared difficult to separate the effects of heterogeneity from the temporal variability of the turbulence fields. Aircraft measurements and scintillometer data agreed in magnitude with respect to the temporal variation of the path-averaged ${C_{T}^{2}}$ values during the diurnal cycle. The decrease of ${C_{T}^{2}}$ with height found from the scintillometer measurements close to the surface and at 43?m under daytime convective conditions corresponds to free-convection scaling, whereas the aircraft measurements at 54 and 83?m suggest a different behaviour.     

The Effect of a New Calibration Procedure on the Measurement Accuracy of Scintec’s Displaced-Beam Laser Scintillometer

We describe a new calibration procedure included in the production process of Scintec’s displaced-beam laser scintillometers (SLS-20/40) and its effect on their measurement accuracy. The calibration procedure determines the factual displacement distances of the laser beams at the receiver and transmitter units, instead of assuming a prescribed displacement distance of 2.70 mm. For this study, four scintillometers operated by Wageningen University and the German Meteorological Service were calibrated by Scintec and their data re-analyzed. The results show that significant discrepancies may exist between the factual and the prescribed displacement distances. Generally, the factual displacement is about 0.1 mm smaller than 2.70 mm, but extremes varied between 0.04 and 0.24 mm. Correspondingly, using non-calibrated scintillometers may result in biases as large as 20 % in the estimates of the inner-scale length, $l_{0}$ , the structure parameter of the refractive index, $C_{n_{_2}}$ , and the friction velocity, $u_{*}$ . The bias in the sensible heat flux was negligible, because biases in $C_{n_{_2}}$ and $u_{*}$ cancel. Hence, the discrepancies explain much of the long observed underestimations of $u_{*}$ determined by these scintillometers. Furthermore, the calibration improves the mutual agreement between the scintillometers for $l_{0}$ , but especially for $C_{n_{_2}}$ . Finally, it is noted that the measurement specifications of the scintillometer do not expire and hence the results of the calibration can be applied retroactively.     

Bulk Mixing and Decoupling of the Nocturnal Stable Boundary Layer Characterized Using a Ubiquitous Natural Tracer

Vertical mixing of the nocturnal stable boundary layer (SBL) over a complex land surface is investigated for a range of stabilities, using a decoupling index ( $0 < D_{rb} < 1$ ) based on the 2–50 m bulk gradient of the ubiquitous natural trace gas radon-222. The relationship between $D_{rb}$ and the bulk Richardson number ( $R_{ib}$ ) exhibits three broad regions: (1) a well-mixed region ( $D_{rb} \approx 0.05$ ) in weakly stable conditions ( $R_{ib} < 0.03$ ); (2) a steeply increasing region ( $0.05 < D_{rb} < 0.9$ ) for “transitional” stabilities ( $0.03 < R_{ib} < 1$ ); and (3) a decoupled region ( $D_{rb} \approx 0.9$ –1.0) in very stable conditions ( $R_{ib} > 1$ ). $D_{rb}$ exhibits a large variability within individual $R_{ib}$ bins, however, due to a range of competing processes influencing bulk mixing under different conditions. To explore these processes in $R_{ib}$ – $D_{rb}$ space, we perform a bivariate analysis of the bulk thermodynamic gradients, various indicators of external influences, and key turbulence quantities at 10 and 50 m. Strong and consistent patterns are found, and five distinct regions in $R_{ib}$ – $D_{rb}$ space are identified and associated with archetypal stable boundary-layer regimes. Results demonstrate that the introduction of a scalar decoupling index yields valuable information about turbulent mixing in the SBL that cannot be gained directly from a single bulk thermodynamic stability parameter. A significant part of the high variability observed in turbulence statistics during very stable conditions is attributable to changes in the degree of decoupling of the SBL from the residual layer above. When examined in $R_{ib}$ – $D_{rb}$ space, it is seen that very different turbulence regimes can occur for the same value of $R_{ib}$ , depending on the particular combination of values for the bulk temperature gradient and wind shear, together with external factors. Extremely low turbulent variances and fluxes are found at 50 m height when $R_{ib} > 1$ and $D_{rb} \approx 1$ (fully decoupled). These “quiescent” cases tend to occur when geostrophic forcing is very weak and subsidence is present, but are not associated with the largest bulk temperature gradients. Humidity and net radiation data indicate the presence of low cloud, patchy fog or dew, any of which may aid decoupling in these cases by preventing temperature gradients from increasing sufficiently to favour gravity wave activity. The largest temperature gradients in our dataset are actually associated with smaller values of the decoupling index ( $D_{rb} < 0.7$ ), indicating the presence of mixing. Strong evidence is seen from enhanced turbulence levels, fluxes and submeso activity at 50 m, as well as high temperature variances and heat flux intermittencies at 10 m, suggesting this region of the $R_{ib}$ – $D_{rb}$ distribution can be identified as a top-down mixing regime. This may indicate an important role for gravity waves and other wave-like phenomena in providing the energy required for sporadic mixing at this complex terrain site.     

Scaling fluctuation analysis and statistical hypothesis testing of anthropogenic warming

Although current global warming may have a large anthropogenic component, its quantification relies primarily on complex General Circulation Models (GCM’s) assumptions and codes; it is desirable to complement this with empirically based methodologies. Previous attempts to use the recent climate record have concentrated on “fingerprinting” or otherwise comparing the record with GCM outputs. By using CO₂ radiative forcings as a linear surrogate for all anthropogenic effects we estimate the total anthropogenic warming and (effective) climate sensitivity finding: ΔT _anth  = 0.87 ± 0.11 K, $\uplambda_{{2{\text{x}}{\text{CO}}_{2} ,{\text{eff}}}} = 3.08 \pm 0.58\,{\text{K}}$ . These are close the IPPC AR5 values ΔT _anth  = 0.85 ± 0.20 K and $\uplambda_{{2{\text{x}}{\text{CO}}_{2} }} = 1.5\!-\!4.5\,{\text{K}}$ (equilibrium) climate sensitivity and are independent of GCM models, radiative transfer calculations and emission histories. We statistically formulate the hypothesis of warming through natural variability by using centennial scale probabilities of natural fluctuations estimated using scaling, fluctuation analysis on multiproxy data. We take into account two nonclassical statistical features—long range statistical dependencies and “fat tailed” probability distributions (both of which greatly amplify the probability of extremes). Even in the most unfavourable cases, we may reject the natural variability hypothesis at confidence levels >99 %.     

Transfer Coefficients of Momentum, Heat and Water Vapour in the Atmospheric Surface Layer of a Large Freshwater Lake

In studies of lake–atmosphere interactions, the fluxes of momentum, water vapour and sensible heat are often parametrized as being proportional to the differences in wind, humidity and air temperature between the water surface and a reference height above the surface. Here, the proportionality via transfer coefficients in these relationships was investigated with the eddy-covariance method at three sites within an eddy-covariance mesonet across Lake Taihu, China. The results indicate that the transfer coefficients decreased with increasing wind speed for weak winds and approached constant values for strong winds. The presence of submerged macrophytes reduced the momentum transfer (drag) coefficient significantly. At the two sites free of submerged macrophytes, the 10-m drag coefficients under neutral stability were 1.8 $(\pm \,0.4) \times \,10^{-3}$ ( ± 0.4 ) × 10 ? 3 and $1.7\,(\pm \,0.3) \times \,10^{-3 }$ 1.7 ( ± 0.3 ) × 10 ? 3 at the wind speed of $9\,\text{ m } \text{ s }^{-1}$ 9 m s ? 1 , which are 38 and 34 % greater than the prediction by the Garratt model for the marine environment.     

Characterization of Oscillatory Motions in the Stable Atmosphere of a Deep Valley

In a valley sheltered from strong synoptic effects, the dynamics of the valley atmosphere at night is dominated by katabatic winds. In a stably stratified atmosphere, these winds undergo temporal oscillations, whose frequency is given by $N \sin {\alpha }$ N sin α for an infinitely long slope of constant slope angle $\alpha $ α , $N$ N being the buoyancy frequency. Such an unsteady flow in a stably stratified atmosphere may also generate internal gravity waves (IGWs). The numerical study by Chemel et al. (Meteorol Atmos Phys 203:187–194, 2009) showed that, in the stable atmosphere of a deep valley, the oscillatory motions associated with the IGWs generated by katabatic winds are distinct from those of the katabatic winds. The IGW frequency was found to be independent of $\alpha $ α and about $0.8N$ 0.8 N . Their study did not consider the effects of the background stratification and valley geometry on these results. The present work extends this study by investigating those effects for a wide range of stratifications and slope angles, through numerical simulations for a deep valley. The two oscillatory systems are reproduced in the simulations. The frequency of the oscillations of the katabatic winds is found to be equal to $N$ N times the sine of the maximum slope angle. Remarkably, the IGW frequency is found to also vary as $C_\mathrm{w}N$ C w N , with $C_\mathrm{w}$ C w in the range $0.7$ 0.7 – $0.95$ 0.95 . These values for $C_\mathrm{w}$ C w are similar to those reported for IGWs radiated by any turbulent field with no dominant frequency component. Results suggest that the IGW wavelength is controlled by the valley depth.