A Semi-Analytical Approach for Parametrization of the Obukhov Stability Parameter in the Unstable Atmospheric Surface Layer

A semi-analytical scheme is proposed to parametrize the Obukhov stability parameter \(\zeta \) (= \(z/L\) ; \(z\) is the height above the ground and \(L\) is the Obukhov length) in terms of the bulk Richardson number ( \(R_{iB}\) ) in unstable conditions within the framework of Monin–Obukhov similarity (MOS) theory. The scheme involves, (i) a solution of a cubic equation in \(\zeta \) whose coefficients depend on the gradient Richardson number ( \(R_{i}\) ), and (ii) a relationship between \(R_{i}\) and \(R_{iB}\) . The proposed scheme is applicable for a wide range (i) \(-5\le R_{iB}\le 0\) , (ii) \(0\le \hbox {ln}(z_{0}/z_{h})\le 29.0\) , and (iii) \(10\le z/z_{0}\le 10^{5}\) and performs relatively better than all other schemes in terms of accuracy in computation of surface-layer transfer coefficients. The absolute errors in computing the transfer coefficients do not exceed 7 %. The analysis presented here is found to be valid for different \(\gamma _{m}\) and \(\gamma _{h}\) appearing in the expressions of the similarity functions \(\varphi _{m}\) and \(\varphi _{h}\) (representing non-dimensional wind and temperature profiles), so long as the ratio of \(\gamma _{m}\) to \(\gamma _{h} \ge 1\) . The improved scheme can be easily employed in atmospheric modelling for a comprehensive range of \(R_{iB}\) and a variety of surfaces.     

Similarity Relations for C_{T}^2 in the Unstable Atmospheric Surface Layer: Dependence on Regression Approach,Observation Height and Stability Range

A great variety of similarity functions for the structure parameter of temperature ( \(C_{T}^2\) ) have been proposed in the literature. They differ in the way they were derived from the data and in the characteristics of the dataset used for their derivation (surface type, observation level, stability range). In this study, we use one single dataset (CASES-99 experiment) and investigate the impact on the similarity functions of applying various regression approaches, and measuring at different heights and within different stability ranges. We limit ourselves to similarity functions under unstable conditions, and evaluate only the most common shape that describes the relation with two coefficients ( \(f\left( z/L\right) =c_{1} \left( 1-c_{2} {z}/{L}\right) ^{-2/3}\) , where \(z\) is the height, and \(L\) is the Obukhov length and a measure of the stability, and \(c_{1}\) and \(c_{2}\) are the regression coefficients). The results show that applying various regression approaches has an impact on the regression coefficients \(c_{1}\) and \(c_{2}\) . Thus studies should always specify the regression approach when presenting similarity relations. We suggest use of an orthogonal distance regression method such that uncertainties in \(-z/L\) are also taken into account, to apply this to the logarithmic transformation of both dimensionless groups, and to use a weighted dataset such that unreliable data points have a smaller influence on the fit. Dividing the dataset into eight height ( \(z\) ) and eight stability ( \(-{1/L}\)  classes) classes, we show that the observation height and the stability range has an impact on the coefficients too. This implies that variations in \(c_{1}\) and \(c_{2}\) found in the literature may result from variations in the height and stability ranges among the datasets. Furthermore, application of the coefficients on a dataset obtained at a different height or within a different stability range has to be made with care. Finally, the variation in the coefficients between the classes indicates that the Monin–Obukhov similarity function for \(C_{T}^2\) is not sufficiently described by the two-coefficient function used here.     

Multi-Scale Sensible Heat Fluxes in the Suburban Environment from Large-Aperture Scintillometry and Eddy Covariance

Sensible heat fluxes ( \(Q_{H}\) ) are determined using scintillometry and eddy covariance over a suburban area. Two large-aperture scintillometers provide spatially integrated fluxes across path lengths of 2.8 and 5.5 km over Swindon, UK. The shorter scintillometer path spans newly built residential areas and has an approximate source area of 2–4 \(\text {km}^{2}\) , whilst the long path extends from the rural outskirts to the town centre and has a source area of around 5–10 \(\text {km}^{2}\) . These large-scale heat fluxes are compared with local-scale eddy-covariance measurements. Clear seasonal trends are revealed by the long duration of this dataset and variability in monthly \(Q_{H}\) is related to the meteorological conditions. At shorter time scales the response of \(Q_{H}\) to solar radiation often gives rise to close agreement between the measurements, but during times of rapidly changing cloud cover spatial differences in the net radiation ( \(Q^{*}\) ) coincide with greater differences between heat fluxes. For clear days \(Q_{H}\) lags \(Q^{*}\) , thus the ratio of \(Q_{H}\) to \(Q^{*}\) increases throughout the day. In summer the observed energy partitioning is related to the vegetation fraction through use of a footprint model. The results demonstrate the value of scintillometry for integrating surface heterogeneity and offer improved understanding of the influence of anthropogenic materials on surface-atmosphere interactions.     

Impact of Megacity Shanghai on the Urban Heat-Island Effects over the Downstream City Kunshan

The impact of upstream urbanization on the enhanced urban heat-island (UHI) effects between Shanghai and Kunshan is investigated by analyzing seven years of surface observations and results from mesoscale model simulations. The observational analysis indicates that, under easterly and westerly winds, the temperature difference between Shanghai and Kunshan increases with wind speed when the wind speed \(<\) 5 m s \(^{-1}\) . The Weather Research and Forecasting (WRF) numerical model, coupled with a one-layer urban canopy model (UCM), is used to examine the UHI structure and upstream effects by replacing the urban surface of Shanghai and/or Kunshan with cropland. The WRF/UCM modelling system is capable of reproducing the surface temperature and wind field reasonably well. The simulated urban canopy wind speed is a better representation of the near-surface wind speed than is the 10-m wind speed at the centre of Shanghai. Without the urban landscape of Shanghai, the surface air temperature over downstream Kunshan would decrease by 0.2–0.4  \(^{\circ }\) C in the afternoon and 0.4–0.6  \(^{\circ }\) C in the evening. In the simulation with the urban landscape of Shanghai, a shallow cold layer is found above the UHI, with a minimum temperature of about \(-0.2\) to \(-\) 0.5  \(^{\circ }\) C during the afternoon hours. Strong horizontal divergence is found in this cold layer. The easterly breeze over Shanghai is strengthened at the surface by strong UHI effects, but weakened at upper levels. With the appearance of the urban landscape specific humidity decreases by 0.5–1 g kg \(^{-1}\) within the urban area because of the waterproof property of an urban surface. On the other hand, the upper-level specific humidity is increased because of water vapour transferred by the strong upward vertical motions.     

Very-Large-Scale Motions in the Atmospheric Boundary Layer Educed by Snapshot Proper Orthogonal Decomposition

Large-eddy simulations of the atmospheric boundary layer (ABL) under a wide range of stabilities are conducted to educe very-large-scale motions and then to study their dynamics and how they are influenced by buoyancy. Preliminary flow visualizations suggest that smaller-scale motions that resemble hairpins are embedded in much larger scale streamwise meandering rolls. Using simulations that represent more than 150 h of physical time, many snapshots in the \(xy\) -, \(yz\) - and \(xz\) -planes are then collected to perform snapshot proper orthogonal decomposition and further investigate the large structures. These analyses confirm that large streamwise rolls that share several features with the very-large-scale motions observed in laboratory studies arise as the dominant modes under most stabilities, but the effect of the surface kinematic buoyancy flux on the energy content of these dominant modes is very significant. The first two modes in the \(yz\) -plane in the neutral case contain up to 3 % of the total turbulent kinetic energy; they also have a vertical tilt angle in the \(yz\) -plane of about 0 to 30 \(^\circ \) due to the turning effect associated with the Coriolis force. Unstable cases also feature streamwise rolls, but in the convective ABL they are strengthened by rising plumes in between them, with two to four rolls spanning the whole domain in the first few modes; the Coriolis effect is much weaker in the unstable ABL. These rolls are no longer the dominant modes under stable conditions where the first mode is observed to contain sheet-like motions with high turbulent kinetic energy. Using these proper orthogonal decomposition modes, we are also able to extract the vertical velocity fields corresponding to individual modes and then to correlate them with the horizontal velocity or temperature fields to obtain the momentum and heat flux carried by individual modes. Structurally, the fluxes are explained by the topology of their corresponding modes. However, the fraction of the fluxes produced by the modes is invariably smaller than the fraction of energy they contain, particularly under stable conditions where the first modes are found to perform weak counter-gradient fluxes.     

Thermal Stratification Effects on Flow Over a Generic Urban Canopy

The influence of local surface heating and cooling on flow over urban-like roughness is investigated using large-eddy simulations. By adjusting the incoming or outgoing heat flux from the ground surface, various degrees of local thermal stratification, represented by a Richardson number \((Ri_\tau )\) , were attained. Drag and heat transfer coefficients, turbulence structure, integral length scales, and the strength of quadrant events that contribute to momentum and heat fluxes were obtained and are compared with locally stable, neutral and unstable flows. With increasing \(Ri_\tau \) , or equivalently as the flow characteristics change from local thermal instability to stability, a gradual decline in the drag and heat transfer coefficients is observed. These values are found to be fairly independent of the type of thermal boundary condition (constant heat flux or constant temperature) and domain size. The maps of anisotropy invariants showed that for the values of \(Ri_\tau \) considered, turbulence structures are almost the same in shape for neutral and unstable cases but differ slightly from those in the stable case. The degree of anisotropy is found to decrease as \(Ri_\tau \) increases from \(-2\) to 2.5. Compared to the neutral case, the integral length scales are shortened in the streamwise and vertical direction by ground cooling, but enhanced in the vertical direction with ground heating. Quadrant analysis showed that an increase in floor heating increases the strength of ejections above the canopy. However, the contributions of updrafts or downdrafts to the heat flux are found not to be significantly influenced by the type of local thermal stratification for the values of \(Ri_\tau \) considered. From the octant analysis, the transport mechanisms of momentum and heat above the canopy are found to be very similar in both locally unstable and stable flows.     

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 $2.5 h$ .     

Evolution of Stratocumulus Over Land: Comparison of Ground and Aircraft Observations with Numerical Weather Prediction Simulations

Forecasting of low cloud continues to challenge numerical weather prediction. With this in mind, surface and airborne observations were made over East Anglia, UK, during March 2011 to investigate stratus and stratocumulus advecting from the sea over land. Four surface sites were deployed at various distances inland aligned approximately along the flow. In situ data include cloud-droplet measurements from an aircraft operating off the coast and a tethered balloon 100 km inland. Comparisons of thermodynamic and cloud properties are made with Met Office operational model simulations at horizontal resolutions of 4 and 1.5 km. The clouds contained droplet concentrations up to 600 cm \(^{-3}\) within polluted outflow off Europe. These measurements were compared to three different model schemes for predicting droplet concentration: two of them perform well at low to moderate concentrations but asymptote to 375 cm \(^{-3}\) . Microwave radiometers at the ground sites retrieved liquid water paths that reduced with distance inland and were generally below 200 g m \(^{-2}\) . The modelled water path performs well upstream but more erratically far inland. Comparisons of thermodynamic profiles are made within both Lagrangian and Eulerian frameworks and show the model predicted changes in equivalent potential temperature generally within 1 K, with occasional errors of 2 K or more. The modelled cloud-top temperatures were in good agreement with the observations down to \(-\) 7  \(^{\circ }\) C, but the magnitude of the temperature inversion, although good at times, was too small by on average 1.6 K. The different simulations produced different cloud-top water contents due to a combination of resolution and scientific upgrades to the model, but they generally underestimate the amount of cloud water. Major changes, such as the mesoscale temporary cloud breaks on 2 March 2011 and the complete clearance on 4 March, were seemingly predicted by the model for the correct reasons.     

Storm Surges in New York During Hurricane Sandy in 2012: A Verification of the Wind-Stress Tide Relation

In October 2012 Hurricane Sandy devastated New York City and its vicinity caused mainly by the storm surge, which is the water height above normal astronomical tide level. The meteorological conditions were as follows: minimum central pressure, 962 hPa, highest sustained wind speed 27.1 m s $^{-1}$ ? 1 and maximum gust 37.8 m s $^{-1}$ ? 1 . The peak storm surge was at 3.9 m and the peak storm tide at 4.4 m (which is referenced above mean lower low water). The wind-stress tide relation shows that $S=K\,V^{2}$ S = K V 2 , where $S$ S is the storm surge, $V$ V is the wind speed and $K$ K is the coefficient. It is found that with $S$ S in units of m, and $V$ V in  m s $^{-1}$ ? 1 , $K = 0.0051$ K = 0.0051 with $R^{2}= 0.91$ R 2 = 0.91 ( $R$ R is the correlation coefficient) indicating that 91 % of the total variation of the storm surge can be explained by variations in the wind stress, which is proportional to $V^{2}$ V 2 . Similar results were obtained during Hurricane Irene in 2011, which also affected the New York area. Therefore, this simple wind stress-tide relation should be useful in coastal engineering, urban planning, and emergency management.     

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.     

Precipitation response to La Niña and global warming in the Indo-Pacific

Recent studies have highlighted the nonlinear rainfall response to El Niño sea surface temperature (SST) events in the Indo-Pacific region and how this response might change over coming decades. Here we investigate the response to La Niña SST anomalies with and without global warming by performing idealised SST-forced experiments with an atmospheric general circulation model. The La Niña SST anomaly is multiplied by a factor \(1 \le \alpha \le 4\) and added to climatological SSTs. Similar experiments using El Niño SST anomalies were previously performed, in which large nonlinearities in the precipitation response were evident. We find that: (i) Under current climatic conditions, as \(\alpha\) increases, the precipitation responds in three ways: the intertropical convergence zone (ITCZ) dries and moves poleward, the maximum precipitation along the equator moves west, and the South Pacific convergence zone (SPCZ) narrows, intensifies, and elongates. For weak ( \(\alpha = 1\) ) La Niña events, the precipitation anomalies approximately mirror those from the El Niño events along the ITCZ and SPCZ, though there are some marked differences in the central-eastern Pacific. For stronger La Niña events ( \(\alpha > 1\) ), precipitation responds nonlinearly to SST anomalies, though the nonlinearities are smaller and differ spatially from the nonlinearities in the El Niño runs. (ii) The addition of a global warming SST pattern increases rainfall in the western Pacific and SPCZ, enhances the narrowing of the SPCZ, and increases the nonlinear response in the western Pacific. However, large La Niña events reduce the impact of global warming along the central-eastern equatorial Pacific as the global warming and La Niña SST anomalies have opposite signs in that region. (iii) The response to La Niña SST anomalies is driven primarily by changes in the atmospheric circulation, whereas the response to the global warming SST pattern is mainly driven by increases in atmospheric moisture. (iv) Large changes in La Niña-driven rainfall anomalies can occur in response to global warming, even if the La Nina SST anomalies relative to the warmer background state are completely unchanged.     

Evaluation of clouds and radiative fluxes in the EC-Earth general circulation model

Observations, mostly from the International Satellite Cloud Climatology (ISCCP), are used to assess clouds and radiative fluxes in the EC-Earth general circulation model, when forced by prescribed observed sea surface temperatures. An ISCCP instrument simulator is employed to consistently compare model outputs with satellite observations. The use of a satellite simulator is shown to be imperative for model evaluation. EC-Earth exhibits the largest cloud biases in the tropics. It generally underestimates the total cloud cover but overestimates the optically thick clouds, with the net result that clouds exert an overly strong cooling effect in the model. Every cloud type has its own source of bias. The magnitude of the cooling due to the shortwave cloud radiative effect ( \(\mid \hbox {SWCRE}\mid\) ) is underestimated for the stratiform low-clouds, because the model simulates too few of them. In contrast, \(\mid \hbox {SWCRE}\mid\) is overestimated for trade wind cumulus clouds, because in the model these are too thick. The clouds in the deep convection regions also lead to overestimate the \(\mid \hbox {SWCRE}\mid\) . These clouds are generally too thick and there are too few mid and high thin clouds. These biases are consistent with the positive precipitation bias and the overly strong mass flux for deep convective plumes. Potential sources for the various cloud biases in the model are discussed.     

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.     

Derivation of Structure Parameters of Temperature and Humidity in the Convective Boundary Layer from Large-Eddy Simulations and Implications for the Interpretation of Scintillometer Observations

We derive the turbulent structure parameters of temperature $C_{T}^2$ and humidity $C_q^2$ from high-resolution large-eddy simulations (LES) of a homogeneously-heated convective boundary layer. Boundary conditions and model forcing were derived from measurements at Cabauw in The Netherlands. Three different methods to obtain the structure-parameters from LES are investigated. The shape of the vertical structure-parameter profiles from all three methods compare well with former experimental and LES results. Depending on the method, deviations in the magnitude up to a factor of two are found and traced back to the effects of discretization and numerical dissipation of the advection scheme. Furthermore, we validate the LES data with airborne and large-aperture scintillometer (LAS) measurements at Cabauw. Virtual path measurements are used to study the variability of $C_{T}^2$ in the mixed layer and surface layer and its implications for airborne and LAS measurements. A high variability of $C_{T}^2$ along a given horizontal path in the LES data is associated with plumes (high values) and downdrafts (low values). The path average of $C_{T}^2$ varies rapidly in time due to the limited path length. The LES results suggest that measured path averages require sufficient temporal averaging and an adequate ratio of path length to height above the ground for the LAS in order to approach the domain average of $C_{T}^2$ .     

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.     

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.     

Observed and simulated sensitivities of summertime urban surface air temperatures to anthropogenic heat in downtown areas of two Japanese Major Cities,Tokyo and Osaka

In this study, the sensitivities of surface air temperatures to anthropogenic heat (AH) were investigated in downtowns of the two Japanese major cities, Tokyo and Osaka. First, meteorological measurements were made with the simultaneous monitoring of electricity demand in a contrastive couple of a downtown commercial area (C-area) and a residential area (R-area) within each city in summer 2007. From the measurements, the areal-mean surface air temperatures were obtained as \( {\overline{T}}_{\mathrm{C}} \) and \( {\overline{T}}_{\mathrm{R}} \) for each of the C-area and R-area, respectively. Using the actual electricity demand and the estimated motor fuels consumption, their areal total was evaluated as the energy-consumption-basis AH. The estimated C-areas' AH indicated greater values up to 220 W/m² on weekdays and remarkable decrease about by half on weekends, whereas that in the R-areas showed less values of 10–20 W/m² stably. Then, \( {\overline{T}}_{\mathrm{C}}-{\overline{T}}_{\mathrm{R}} \) on calm and fine days were found to be systematically decreased from weekdays to weekends in both cities roughly indicating a proportional relationship with the reductions in the C-areas' AH on weekends. The result suggested a common afternoon sensitivity for both C-areas of around 1.0°C/100 W/m², which indicated an intensity of the AH impact on surface air temperature there. Next, to simulate the observed AH impact, the authors' CM-BEM (a multilayer urban canopy model coupled with a building energy model) was newly implemented in the mesoscale Weather Research and Forecasting (WMF) model. This new system, WRF-CM-BEM, was applied to Tokyo and almost reasonably validated from the aspects of the reproducibility of urban surface air temperature and electricity demand in the observation areas. The simulations also suggested that WRF-CM-BEM underestimated the observed air temperature sensitivity to AH in the Tokyo C-area roughly by half but still in the same order of magnitude.     

Intercomparison of Methods for the Simultaneous Estimation of Zero-Plane Displacement and Aerodynamic Roughness Length from Single-Level Eddy-Covariance Data

We applied three approaches to estimate the zero-plane displacement $d$ through the aerodynamic measurement height $z$ (with $z = z_{m}- d$ and $z_{m}$ being the measurement height above the surface), and the aerodynamic roughness length $z_{0}$ , from single-level eddy covariance data. Two approaches (one iterative and one regression-based) were based on the universal function in the logarithmic wind profile and yielded an inherently simultaneous estimation of both $d$ and $z_{0}$ . The third approach was based on flux–variance similarity, where estimation of $d$ and consecutive estimation of $z_{0}$ are independent steps. Each approach was further divided into two methods differing either with respect to the solution technique (profile approaches) or with respect to the variable (variance of vertical wind and temperature, respectively). All methods were applied to measurements above a large, growing wheat field where a uniform canopy height and its frequent monitoring provided plausibility limits for the resulting estimates of time-variant $d$ and $z_{0}$ . After applying, for each approach, a specific data filtering that accounted for the range of conditions (e.g. stability) for which it is valid, five of the six methods were able to describe the temporal changes of roughness parameters associated with crop growth and harvest, and four of them agreed on $d$ to within 0.3 m most of the time. Application of the same methods to measurements with a more heterogeneous footprint consisting of fully-grown sugarbeet and a varying contribution of adjacent harvested fields exhibited a plausible dependence of the roughness parameters on the sugarbeet fraction. It also revealed that the methods producing the largest outliers can differ between site conditions and stability. We therefore conclude that when determining $d$ for canopies with unknown properties from single-level measurements, as is increasingly done, it is important to compare the results of a number of methods rather than rely on a single one. An ensemble average or median of the results, possibly after elimination of methods that produce outliers, can help to yield more robust estimates. The estimates of $z_{0}$ were almost exclusively physically plausible, although $d$ was considered unknown and estimated simultaneously with the methods and results described above.     

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.     

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.