An Approximate Analytical Solution Of Flux-Profile Relationships For The Atmospheric Surface Layer With Different Momentum And Heat Roughness Lengths

An approximate method for calculating the relationship between z/L(z = reference height, L = Obukhov length) and the bulk Richardsonnumber is presented. If this relationship is known, the momentum andheat fluxes can be computed easily without any iteration. The avoidance of iteration can speed up computationsin large-scale models considerably (up to 10 times) and cases which do not converge or converge very slowly cannot occur. The proposed formulae take into account the difference between momentum (z_0M) and heat roughnesslengths (z_0H). Because the roughness lengths are not neglected at any step of the derivation, the resulting analytical formulae can be used not only between the surface and the reference height but also between two finite levels z₁ andz₂ (by replacing z_0M and z_0H by z₁ and z by z₂). Theequations remain correct even in the limit z₁ z₂.The formulae are based upon the (partially modified) Businger–Dyer flux–profile relationships and,consequently, they are restricted to predominantly homogeneous terrain.These new approximations are an improvement over the existing solutions because they are simpler than most of the formulae in the literature and are able to match the numerical exact solution for different parameter sets (Businger, Dyer, Högström) with an maximum error of about 2% for a wide range of z/L, z/z_0M and z_0M/z_0H.Furthermore, in stable conditions, schemes with and without a finitecritical bulk Richardson number can be approximated. The possibleambiguity of the exact solution =f(RI_B) in (moderately) stable conditions is discussed briefly. The performance of the new formulae is compared to the exact numerical solution and to different formulae proposed in the literature.     

Derivation of the relationship between the Obukhov stability parameter and the bulk Richardson number for flux-profile studies

Using the relationship between the bulk Richardson numberR _z and the Obukhov stability parameterz/L (L is the Obukhov length), formally obtained from the flux-profile relationships, methods to estimatez/L are discussed. Generally,z/L can not be uniquely solved analytically from flux-profile relationships, and it may be defined using routine observations only by iteration. In this paper, relationships ofz/L in terms ofR _z obtained semianalytically were corrected for variable aerodynamic roughnessz ₀ and for aerodynamic-to-temperature roughness ratiosz ₀/z _T, using the flux-profile iteration procedure. Assuming the so-called log-linear profiles to be valid for the nearneutral and moderately stable region (z/L<1), a simple relationship is obtained. For the extension to strong stability, a simple series expansion, based on utilisation of specified universal functions, is derived.For the unstable region, a simple form based on utilisation of the Businger-Dyer type universal functions, is derived. The formulae yield good estimates for surfaces having an aerodynamic roughness of 10^–5 to 10^–1 m, and an aerodynamic-to-temperature roughness ratio ofz ₀/z _T=0.5 to 7.3. When applied to the universal functions, the formulae yield transfer coefficients and fluxes which are almost identical with those from the iteration procedure.     

Surface influence upon vertical profiles in the nocturnal boundary layer

Near-surface wind profiles in the nocturnal boundary layer, depth h, above relatively flat, tree-covered terrain are described in the context of the analysis of Garratt (1980) for the unstable atmospheric boundary layer. The observations at two sites imply a surface-based transition layer, of depth z _*, within which the observed non-dimensional profiles Φ _M ⁰ are a modified form of the inertial sub-layer relation \(\Phi _M \left( {{z \mathord{\left/ {\vphantom {z L}} \right. \kern-0em} L}} \right) = \left( {{{1 + 5_Z } \mathord{\left/ {\vphantom {{1 + 5_Z } L}} \right. \kern-0em} L}} \right)\) according to $$\Phi _M^{\text{0}} \simeq \left( {{{1 + 5z} \mathord{\left/ {\vphantom {{1 + 5z} L}} \right. \kern-\nulldelimiterspace} L}} \right)\exp \left[ { - 0.7\left( {{{1 - z} \mathord{\left/ {\vphantom {{1 - z} z}} \right. \kern-\nulldelimiterspace} z}_ * } \right)} \right]$$ , where z is height above the zero-plane displacement and L is the Monin-Obukhov length. At both sites the depth z _* is significantly smaller than the appropriate neutral value (z _*N ) found from the previous analysis, as might be expected in the presence of a buoyant sink for turbulent kinetic energy.     

Turbulent dispersion in the atmospheric surface layer

By non-dimensionalizing a trajectory-simulation (TS) model of turbulent dispersion, it is shown that the dimensionless concentration z ₀cu_*/kQ (cu _*/kQ) due to a continuous line (area) source of strength Q in the atmospheric surface layer depends only on z/z ₀, x/z ₀, z ₀/L and z _s/z₀, where z _s is the source height. The TS model is used to tabulate concentration profiles due to ground-level line and area sources. Concentration profiles generated by the TS model for elevated sources are shown to be inconsistent with the Reciprocal Theorems of Smith (1957) and it is suggested that this is because the flux-mean gradient closure scheme inherent in the Reciprocal Theorem is invalid for an elevated source.     

A comparison of turbulence statistics in the surface layer over plant canopies with those over several other surfaces

Turbulence statistics, including higher order moments, in the surface layer over plant canopies were compared with those observed over several different surfaces, using a nondimensional height (z – d)/z ₀: The values of (z – d)/z ₀extend over a very wide range from 10 over plant canopies to 10⁷ over the ocean. Several properties such as intensities of turbulence and skewness factors show a remarkable height-dependency in the air layer below (z – d)/z ₀ = 10², which is supposed to be much influenced by the underlying surface. In that layer, some peculiar phenomena, such as a downward energy transport and positive flux of shear stress, are frequently observed.     

Turbulence Characteristics of the Stable Boundary Layer Over a Mid-Latitude Glacier. Part I: A Combination of Katabatic and Large-Scale Forcing

Profile and eddy-correlation (heights of 4 and 10 m) measurements performed on the Pasterze glacier (Austria) are used to study the characteristics of the stable boundary layer under conditions of katabatic and large-scale forcing. We consider cases where large-scale forcing results in a downslope (or following) ambient wind. The analysis of averaged spectra and cospectra reveals low frequency perturbations that have a large influence on the variances of temperature and horizontal wind components and also alter the cospectra of momentum and sensible heat flux. Only the spectrum of the vertical wind speed is comparable to universal spectra. The low frequency perturbations occur as brief intermittent events and result in downward entrainment of ambient air thereby producing enhanced downward sensible heat fluxes and downward as well as upward momentum fluxes with various magnitudes and timescales. After the variances were high pass filtered, the normalised standard deviations of wind speed and temperature compare favourably to findings in the literature within the range 0>z/L>0.5. For larger z/L they deviate as a result of an increased influence from low frequency perturbations and thus non-stationarity. In line with this, the turbulent kinetic energy budget (at 4 m height) indicates that production (shear) is in balance with destruction (buoyancy and dissipation) within the range 0>z/L>0.3. Non-dimensional gradients of wind speed within the range 0>z/L>0.3 have a slope of about 3.5. The scatter for the dimensionless temperature gradient is quite large, and the slope is comparable to that for wind speed gradients. For z/L>0.3 the imbalance in the turbulent kinetic energy budget grows and non-dimensional gradients for wind speed and temperature deviate considerably from accepted values as a result of increased non-stationarity. Average roughness lengths for momentum and sensible heat flux derived from wind speed and temperature profiles are respectively 1 × 10^-3 m and 6 × 10^-5 m, consistent with the literature. The ratio (z_0h/z_0m) compares to those predicted by surface renewal models. A variation of this ratio with the roughness Reynolds number is not indicated by our data.     

A Case Study Of An On-Ice Air Flow Over The Arctic Marginal Sea-Ice Zone

A case study of warm air advection over the Arctic marginalsea-ice zone is presented, based on aircraft observations with direct flux measurements carriedout in early spring, 1998. A shallow atmospheric boundary layer (ABL) was observed, which wasgradually cooling with distance downwind of the ice edge. This process was mainly connected with astrong stable stratification and downward turbulent heat fluxes of about 10–20 W m^-2, but wasalso due to radiative cooling. Two mesoscale models, one hydrostatic and the other non-hydrostatic,having different turbulence closures, were applied. Despite these fundamental differences betweenthe models, the results of both agreed well with the observed data. Various closure assumptions had amore crucial influence on the results than the differences between the models.Such an assumption was, for example,the parameterization of the surface roughness for momentum (z₀) and heat (z_T). This stronglyaffected the wind and temperature fields not only close to the surface but also within and abovethe temperature inversion layer. The best results were achieved using a formulation for z₀ that took intoaccount the form drag effect of sea-ice ridges together withz_T = 0.1z₀. The stability within theelevated inversion strongly depended on the minimum eddy diffusivity K_min. A simple ad hocparameterization seems applicable, where K_min is calculated as 0.005 timesthe neutral eddy diffusivity. Although the longwave radiative cooling was largest within the ABL, theapplication of a radiation scheme was less important there than above the ABL. This was related to theinteraction of the turbulent and radiative fluxes. To reproduce the strong inversion, it wasnecessary to use vertical and horizontal resolutions higher than those applied in most regional andlarge-scale atmospheric models.     

Variance Method to Determine Turbulent Fluxes of Momentum And Sensible Heat in The Stable Atmospheric Surface Layer

Evidence is presented that in the stable atmospheric surface layer turbulent fluxes of heat and momentum can be determined from the standard deviations of longitudinal wind velocity and temperature, σ _u and σ _T respectively, measured at a single level. An attractive aspect of this method is that it yields fluxes from measurements that can be obtained with two-dimensional sonic anemometers. These instruments are increasingly being used at official weather stations, where they replace the standard cup anemometer–wind vane system. With methods such as the one described in this note, a widespread, good quality, flux network can be established, which would greatly benefit the modelling community. It is shown that a ‘variance’ dimensionless height (ζ _σ) defined from σ _u and σ _T is highly related to the ‘conventional’ dimensionless stability parameter ζ=z/L, where z is height and L is the Obukhov length. Empirical functions for ζ _σ are proposed that allow direct calculation of heat and momentum fluxes from σ _u and σ _T. The method performs fairly well also during a night of intermittent turbulence.     

Numerical Studies with a Regional Atmospheric Climate Model Based on Changes in the Roughness Length for Momentum and Heat Over Antarctica

A regional atmospheric climate model is used toexamine the effect of changes in the roughnesslengths of momentum (_z0m) and heat (_z0h)on the structure of the lower atmosphere and on thesurface energy fluxes over Antarctica. Fourexperiments were carried out in which _z0mand/or _z0h were altered with respect to acontrol experiment. The changes consisted of (1) alowering of _z0m from a field aggregated froma vegetation map with an orographic correction basedon the European Centre for Medium-Range WeatherForecasts _z0m field, to a constant value of10^-3 m; and (2) a lowering of _z0h from a valueequal to _z0m to a constant value of 10^-3 mor a value dependent on the wind speed via a surfacerenewal model. A reduction of _z0m results in theexpected increase in near-surface wind speed. It alsoresults in an increase in the depth of the layer in whichsouth-easterly near-surface winds prevail, and in adecrease in the strength of the large-scale flow overthe continent, in particular in summer. In theescarpment region a decrease of _z0m is foundto result in too high wind speeds. Surface temperatureson average decrease while atmospheric temperaturesincrease, resulting in an increase of near-surfacestatic stability. Changes in roughness lengths donot significantly change the temperature profiles.The surface fluxes, on average found reduced, aremodelled best by using the _z0h based on thesurface renewal method.     

Momentum- and Heat-Flux Parametrization at Dome C,Antarctica: A Sensitivity Study

An extensive meteorological observational dataset at Dome C, East Antarctic Plateau, enabled estimation of the sensitivity of surface momentum and sensible heat fluxes to aerodynamic roughness length and atmospheric stability in this region. Our study reveals that (1) because of the preferential orientation of snow micro-reliefs (sastrugi), the aerodynamic roughness length \(z_{0}\) varies by more than two orders of magnitude depending on the wind direction; consequently, estimating the turbulent fluxes with a realistic but constant \(z_{0}\) of 1 mm leads to a mean friction velocity bias of \(24\,\%\) in near-neutral conditions; (2) the dependence of the ratio of the roughness length for heat \(z_{0t}\) to \(z_{0}\) on the roughness Reynolds number is shown to be in reasonable agreement with previous models; (3) the wide range of atmospheric stability at Dome C makes the flux very sensitive to the choice of the stability functions; stability function models presumed to be suitable for stable conditions were evaluated and shown to generally underestimate the dimensionless vertical temperature gradient; as these models differ increasingly with increases in the stability parameter z / L, heat flux and friction velocity relative differences reached \(100\,\%\) when \(z/L > 1\); (4) the shallowness of the stable boundary layer is responsible for significant sensitivity to the height of the observed temperature and wind data used to estimate the fluxes. Consistent flux results were obtained with atmospheric measurements at heights up to 2 m. Our sensitivity study revealed the need to include a dynamical parametrization of roughness length over Antarctica in climate models and to develop new parametrizations of the surface fluxes in very stable conditions, accounting, for instance, for the divergence in both radiative and turbulent fluxes in the first few metres of the boundary layer.     

Parameterizing turbulent exchange over sea ice: the ice station weddell results

A 4-month deployment on Ice Station Weddell (ISW) in the western Weddell Sea yielded over 2000 h of nearly continuous surface-level meteorological data, including eddy-covariance measurements of the turbulent surface fluxes of momentum, and sensible and latent heat. Those data lead to a new parameterization for the roughness length for wind speed, z₀, for snow-covered sea ice that combines three regimes: an aerodynamically smooth regime, a high-wind saltation regime, and an intermediate regime between these two extremes where the macroscale or `permanent' roughness of the snow and ice determines z₀. Roughness lengths for temperature, z_T, computed from this data set corroborate the theoretical model that Andreas published in 1987. Roughness lengths for humidity,z_Q, do not support this model as conclusively but are all, on average, within an order of magnitude of its predictions. Only rarely arez_Tand z_Q equal to z₀. These parameterizations have implications for models that treat the atmosphere-ice-ocean system.     

On the bulk parameterization of surface fluxes for various conditions and parameter ranges

A comparison between various parameterizations for the bulk transfercoefficient for heat and momentum is carried out for a wide range ofatmospheric stability and values of the roughness lengths for momentum and heat,z_0m and z_0h respectively.It is confirmed that the parameterization of Launiainen compares wellto a numerical iterative solution for the Obukhov length L as function of the gradients of wind speed and temperatureover a limited range of z_0m/z_0h and stability conditions.For _0m/z_0h > 500, an alternativeinterpolation formulation of Holtslag and Ek,in combination with the formulation of Launiainen, provides a better approximation.     

The extent of the unstable Monin-Obukhov layer for temperature and humidity above complex hilly grassland

Potential temperature, specific humidity and wind profiles measured by radiosondes under unstable but windy conditions during FIFE in northeastern Kansas were analyzed within the framework of Monin-Obukhov similarity. Around 86% of these profiles were found to have a height range over which the similarity, formulated in terms of the Businger-Dyer functions, is valid and for which the resulting surface fluxes are in good agreement with independent measurements at ground stations. When scaled with the surface roughness z ₀ = 1.05 m and the displacement height d ₀ = 26.9 m, for the potential temperature this height range was 45 (±31) (z – d ₀ )/z ₀ 104 (±54) and the comparison of the profile-derived surface fluxes with the independent measurements gave a correlation coefficient of r = 0.96. For the specific humidity these values are 42 (±29) (z – d ₀ )/z ₀ 96 (±38) and r = 0.94. In terms of the height of the bottom of the inversion H _i , in the morning hours the upper limit of (z – d ₀ ) in the Monin-Obukhov layer is approximately 0.3H _i , whereas for a fully developed ABL it is closer to 0.1H _i . Probably, as a result of the short sampling times and perhaps also of the small gradients under the windy conditions, the exact height range of validity was difficult to establish from a mere inspection of these profiles.     

The Influences of Thermodynamic Characteristics on Aerodynamic Roughness Length over Land Surface

It has previously been shown that aerodynamic roughness length changes significantly along with nearsurface atmospheric thermodynamic state; however, at present, this phenomenon remains poorly understood, and very little research concerning this topic has been conducted. In this paper, by using the data of different underlying surfaces provided by the Experimental Co-observation and Integral Research in Semi-arid and Arid Regions over North China, aerodynamic roughness length (z₀) values in stable, neutral, and unstable atmospheric stratifications are compared with one another, and the relationship between z₀ and atmospheric thermodynamic stability (ζ) is analyzed. It is found that z₀ shows great differences among the stable, neutral, and unstable atmospheric thermodynamic states, with the difference in z₀ values between the fully thermodynamic stable condition and the neutral condition reaching 60% of the mean z₀. Furthermore, for the wind speed range in which the wind data are less sensitive to z₀, the surface z₀ changes more significantly with ζ, and is highly correlated with both the Monin-Obukhov stability (ζ₀) and the overall Richardson number (R_ib), with both of their correlation coefficients greater than 0.71 and 0.47 in the stable and unstable atmospheric stratification, respectively. The empirical relation fitted with the experimental observations is quite consistent with the Zilitinkevich theoretical relation in the stable atmosphere, but the two are quite distinct and even show opposite variation tendencies in the unstable atmosphere. In application, however, verification of the empirical fitted relations by using the experimental data finds that the fitted relation is slightly more applicable than the Zilitinkevich theoretical relation in stable atmospheric stratification, but it is much more suitable than the Zilitinkevich relation in unstable atmospheric stratification.     

Numerical simulation of particle trajectories in inhomogeneous turbulence,III: Comparison of predictions with experimental data for the atmospheric surface layer

It is shown that predictions of a numerical trajectory-simulation method agree closely with the Project Prairie Grass observations of the concentrations 100 m downwind of a continuous point source of sulphur dioxide if the height (z) dependence of the Lagrangian length scale Λ _L is chosen as: whereL is the Monin-Obukhov length. The value of 0.5 for Λ _L /z in neutral conditions is consistent with the findings of Reid (1979) for the Porton experiment, and is also shown to be the best choice for simulation of an experiment in which concentration profiles were measured a short distance (< 40 m) downwind of an elevated point source of glass beads (40 μn diameter). $$\begin{gathered} \Lambda _L = 0.5z\left( {1 - 6\frac{z}{L}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} L< 0 \hfill \\ \Lambda _L = 0.5z/\left( {1 + 5\frac{z}{L}} \right)L > 0 \hfill \\ \end{gathered} $$      

Estimation of Scalar Source/Sink Distributions in Plant Canopies Using Lagrangian Dispersion Analysis: Corrections for Atmospheric Stability and Comparison with a Multilayer Canopy Model

Source/sink distributions of heat, water vapour andCO₂ within a rice canopy were inferred using aninverse Lagrangian dispersion analysis and measuredmean profiles of temperature, specific humidity andCO₂ mixing ratio. Monin–Obukhov similarity theorywas used to account for the effects of atmosphericstability on _w(z), the standard deviation ofvertical velocity and _L(z), the Lagrangian timescale of the turbulence. Classical surface layer scaling was applied in the inertial sublayer (z > z_ruf)using the similarity parameter = (z - d)/L, where z is height above ground, d is the zero plane displacementheight for momentum, L is the Obukhov length,and z_ruf 2.3h_c, where h_c iscanopy height. A single length scale h_c, was usedfor the stability parameter 3 = h_c/L in the height range 0.25 < z/h_c < 2.5. This choice is justified by mixing layer theory, which shows that within the roughness sublayer there is one dominant turbulence length scaledetermined by the degree of inflection in the windprofile at the canopy top. In the absence of theoretical or experimental evidence for guidance,standard Monin–Obukhov similarity functions, with = h_c/L, were used to calculate the stabilitydependence of _w(z) and _L(z) in the roughness sublayer. For z/h_c < 0.25 the turbulence length and time scales are influenced by the presence of the lowersurface, and stability effects are minimal. With theseassumptions there was excellent agreement between eddycovariance flux measurements and deductions from theinverse Lagrangian analysis. Stability correctionswere particularly necessary for night time fluxes whenthe atmosphere was stably stratified.The inverse Lagrangian analysis provides a useful toolfor testing and refining multilayer canopy models usedto predict radiation absorption, energy partitioningand CO₂ exchanges within the canopy and at thesoil surface. Comparison of model predictions withsource strengths deduced from the inverse analysisgave good results. Observed discrepancies may be dueto incorrect specification of the turbulent timescales and vertical velocity fluctuations close to theground. Further investigation of turbulencecharacteristics within plant canopies is required toresolve these issues.     

Modelling surface energy fluxes and temperatures in dry and wet bare soils

Abstract

A physically‐based numerical model was developed to estimate the temporal course of the surface energy flux densities and the soil temperatures in dry and wet bare soils. Aerodynamic heat, vapour and momentum transfer theory was used to calculate the sensible and latent heat flux densities at the surface under diabatic and adiabatic conditions. A finite‐difference solution of the differential equation describing one‐dimensional heat transfer was used to calculate the surface soil heat flux density and soil profile temperatures. The surface temperature was determined iteratively by the simultaneous solution of equations describing radiative, heat and momentum transfer at the surface. The model was tested with measurements from energy balance studies conducted on a dry, sandy soil and a wet, silt loam soil, and was found to predict accurately the surface energy fluxes and soil temperatures over three‐day periods under conditions of potential and negligible evaporation. The sensitivity of the model to uncertainties in the aerodynamic roughness lengths for momentum (z₀) and heat (z_T) is reported. Values for z₀ and Z₀/Z_T of 0.5 mm and 3.0, respectively, resulted in the best agreement between modelled and measured values of the fluxes and temperatures for both soils.     

Eddy Covariance Measurements On Mountain Slopes: The Advantage Of Surface-Normal Sensor Orientation Over A Vertical Set-Up

The measurement of scalar fluxes employing the eddy covariance method is a widely used experimental approach,for which the flow distortion due to obstacles (e.g., sensor mounts and mast)is a well-known but not fully solved problem. In order to reduce flow distortion we installed a sonic anemometer in a surface-normal orientationrelative to the terrain slope, and a second instrument in a verticalposition at a horizontal distance of 1.54 m from the first instrumentWe found a significant reduction in the rotation angle necessary for the coordinaterotation procedure in the x-z plane whencomputing 30-minute flux averages with the surface-normal orientation. In 91% of all cases this rotation angleremained within the angle of incidence of ±10° recommended bythe manufacturer. In contrast, only 24% of the measurements taken with the vertically mounted anemometer were obtained at an angle of incidencewithin ±10°, and 3% were outside the ±30° range specified for an acceptable operation.A data quality test based on the variance of vertical windspeed normalized with friction velocity (_w/u_*) revealed problems for application under stable conditions due to large uncertainties in the determination of the Monin–Obukhov stability parameter z/L. An alternative test using the bulk drag coefficient C_D revealed other problems related to the dependence of C_D on z/z₀, the measuring height normalized by the roughness length, which do not appear to be constantin complex terrain. With both tests, a tendency for a slightly improved dataquality was found for the surface normal set-up, which, however, proved statistically insignificant.It is concluded that the surface-normal set-up of a sonic anemometer significantly reduces flow distortion by thesensor head. Although the surface-normal mounting position therefore appears to be the preferred one, with decreased flow distortion and a slightly improved data quality, no significant differences in turbulent quantities were found between the two set-uppositions. Hence, the consequences for short-term measurements of massand energy fluxes with a surface-normal set-up in complex terrain appearto be relevant only if single flux events are to be inspected, while for long-term measurements of integrated fluxes both the surface-normaland vertical installation of the sonic anemometer are adequate,indicating that eddy covariance measurements in complex terrain are lessdelicate than expected.     

Influence of the boundary layer height on the global air–sea surface fluxes

Results from large-eddy simulations and field measurements have previously shown that the velocity field is influenced by the boundary layer height, z _i , during close to neutral, slightly unstable, atmospheric stratification. During such conditions the non-dimensional wind profile, φ _m , has been found to be a function of both z/L and z _i /L. At constant z/L, φ _m decreases with decreasing boundary layer height. Since φ _m is directly related to the parameterizations of the air–sea surface fluxes, these results will have an influence when calculating the surface fluxes in weather and climate models. The global impact of this was estimated using re-analysis data from 1979 to 2001 and bulk parameterizations. The results show that the sum of the global latent and sensible mean heat fluxes increase by 0.77 W m⁻² or about 1% and the mean surface stress increase by 1.4 mN m⁻² or 1.8% when including the effects of the boundary layer height in the parameterizations. However, some regions show a larger response. The greatest impact is found over the tropical oceans between 30°S and 30°N. In this region the boundary layer height influences the non-dimensional wind profile during extended periods of time. In the mid Indian Ocean this results in an increase of the mean annual heat fluxes by 2.0 W m⁻² and an increase of the mean annual surface stress by 2.6 mN m⁻².     

Performance of various similarity functions for nondimensional wind and temperature profiles in the surface layer in stable conditions

The linear functions for non-dimensional wind and temperature profiles are commonly used to describe the surface layer fluxes in atmospheric models. However, their applicability is limited to smaller values of the stability parameter z/L (where z is the height above ground and L is the Obukhov length) i.e. z/L < 1.0. These linear functions have been modified (Webb 1970, Quart. J. Roy. Meteor. Soc. 96, 67–90; Clarke 1970, Quart. J. Roy. Meteor. Soc. 96, 91–114; Hicks 1976, Quart. J. Roy. Meteor. Soc. 102, 535–551; Beljaars and Holtslag 1991, J. Appl. Meteorol. 30, 327–341; Cheng and Brutsaert 2005, Boundary-Layer Meteorol. 114, 519–538) over the years for calculating fluxes when z/L > 1.0 under strongly stable conditions. In view of this, the objective of the present study is to analyze the performance of these similarity functions to compute surface fluxes in stable conditions.The meteorological observations from the Cooperative Atmosphere-Surface Exchange Study (CASES-99) experiment are utilized for computing the surface fluxes in stable conditions. The computed fluxes are found to be reasonably close to those observed. The ratio of observed to computed fluxes reveals that the computed fluxes are close to the observations for all the similarity functions for z/L < 1.0 whereas the computed values show relatively a large scatter from observations for z/L > 1.0. The computed values of u and heat flux do not show significant differences from those observed at 99% confidence limit. The performance of all the similarity functions considered here is found to be comparable to each other in strongly stable conditions.