Reduction of forecast error for global numerical weather prediction by The Florida State University (FSU) Superensemble

Summary The skill of the FSU Superensemble technique as applied to global numerical weather prediction is evaluated extensively in this paper. The global mass and motion fields for year 2000 and precipitation over the domain 55S to 55N for year 2001, as predicted by the Superensemble, the ensemble member models, and the mean of the ensemble members, are evaluated by standard statistical measures of skill to determine the performance of the Superensemble in relation to the other models. The member models are global forecast models from 5 of the worlds operational forecast centers in addition to the FSU global spectral model. For precipitation 5 additional versions of the FSU global model are utilized in the ensemble, as defined by different initial conditions provided by various physical initialization algorithms. Statistical parameters calculated for the mass and motion fields include root mean square (RMS) error, systematic error (or bias), and anomaly correlation. These are applied to the mean sea level pressure, 500hPa heights, and the wind fields at 850hPa and 200hPa. Statistical parameters that were calculated for precipitation include RMS error, correlation, equitable threat score (ETS), and a special definition of bias appropriate for the precipitation field. For the mass and motion fields the performance of the Superensemble was considered for the annual global case, as well as for each hemisphere (north and south) and for each of the four seasons. For precipitation only the annual case was considered over the domain cited above.For the mass and motion fields the RMS calculations showed the Superensemble to be superior (to have the smallest total forecast error) in all comparisons to the ensemble member models, and to be superior to the ensemble mean in the vast majority of comparisons. Performance in comparison to the other models was generally better in the Southern Hemisphere than in the Northern Hemisphere, and better in the transition seasons of fall and spring than in the extreme seasons of winter and summer. The Superensemble had the best success with mean sea level pressure, followed in order by 500hPa geopotential heights, 850hPa winds, and 200hPa winds.In the calculations of 500hPa geopotential height anomaly correlation the Superensemble had higher scores in all comparisons to the ensemble member models, as well as higher scores in the majority of comparisons to the ensemble mean. As with the RMS error results, the Superensemble performed better in the Southern Hemisphere than in the Northern Hemisphere, and better in fall than in summer, in comparison to the other models. The superior anomaly correlation scores of the Superensemble attest to the ability of the model to forecast daily perturbations from the climatological means, perturbations that are associated with transient synoptic scale features, given the horizontal resolution in the forecast models.In terms of systematic error reduction the Superensemble produces its most impressive results. Annual global mean sea-level pressure systematic errors for day 5 forecasts are generally in the range of ±1hPa (compared to errors as high as 8hPa in other models), and day 2 forecasts of 500hPa geopotential height produced systematic errors generally in the range of ±10 meters (compared to errors as high as 60 meters in other models). The Superensemble was able to reduce systematic errors in forecasts of a variety of important features in the global mass and motion fields: surface equatorial trough, wave amplitude in geopotential heights at 500hPa, trade winds and Somali Jet at 850hPa, mid-latitude westerlies, subtropical jet, and Tropical Easterly Jet (TEJ) at 200hPa.In terms of forecasting precipitation the Superensemble outperforms all ensemble member models and the ensemble mean in terms of RMS error, correlation coefficient, equitable threat score, and bias. The superior correlation scores indicate that the Superensemble is more reliable than the other models in predicting perturbations in the area distribution of precipitation, perturbations that are essentially associated with migrant synoptic scale disturbances, considering the horizontal resolution of the forecast models.The Superensemble is a valuable tool for significantly improving upon the global model forecasts of the worlds operational forecast centers. These forecasts are used daily as important guidance in making weather forecasts in all regions of the world. This paper will demonstrate that the Superensemble improves upon the ensemble member model forecasts: (1) in a statistical sense considering broad areas of the globe, (2) in a synoptic climatology sense through focus on the improved forecasts of climatological features seen in the global mass and motion fields, (3) in a synoptic sense through use of anomaly correlation and correlation coefficient where improvement is demonstrated in the forecasts of perturbations from mean fields which are essentially associated with transient synoptic scale disturbances.     

Influence of foehn winds on air temperature and humdity in the Polish Carpathians

Summary The present study concerns an attempt to determine the influence of foehn winds on air temperature and humidity in the Polish Carpathians. This was carried out using the mean monthly temperature and relative humidity obtained from a number of synoptic stations. Periods with classical foehn conditions and the whole period (1966–1985) of record were analysed.With 3 Figures     

Improving the diagnostic relation for the nocturnal boundary-layer height

A one-dimensional model of the nocturnal boundary layer (NBL) has been used to investigate the time variation of the NBL height for stationary and horizontally homogeneous synoptic conditions. The time variation of the well known quantity = hflu _* has been shown to be related to the wind variation at the top of the NBL. For the simple simulated conditions, this variation depends only on the roughness length and the Coriolis parameter. The value of averaged over the whole night is a function of the friction velocity. An expression is proposed for which is compared with observations. Under stationary external conditions, the new relation improves the determination of the NBL height if compared with the classical relation using a constant value of .     

Ab initio study on carbon Kinetic Isotope Effect (KIE) in the reaction of CH4+Cl•

Recent studies suggest that the destruction of methane by Cl in the marine boundary layer could be accounted for as another major sink besides the methane destruction by OH. High level ab initio molecular orbital calculations have been carried out to study the CH₄+Cl reaction, the carbon Kinetic Isotope Effect (KIE) is calculated using Conventional Transition-State Theory (CTST) plus Wigner and Eckart semiclassical tunneling corrections. The calculated KIE is around 1.026 at 300 K and has a small temperature variation. This is by far the largest KIE among different processes involving atmospheric methane destruction (e.g., OH, soil). A calculated mass balance of atmospheric methane including the KIE for the CH₄+Cl reaction is found to favor those methane budgets with enhanced biological methane sources, which have relatively lighter carbon isotope composition.     

Anomalous gradient winds in the subtropical jet stream and interpretations of forecast failures

Summary Dramatic examples of forecast failures in global models of moderate resolution (i.e., T106) have been shown to occur during periods of the negative phase of the Pacific/North American (PNA) pattern in the Northern Hemisphere winter. Specifically, in these periods forecast skills at 500hPa as measured by the standard anomaly correlation index dropped to rather low values by days 4 and 5 of the forecasts. This paper examines systematically some of the factors that may have contributed to the failure of these model forecasts.In particular, strong winds approaching intensities on the order of 100ms^–1 south of Japan at the 200hPa level were degraded by the initialization and data assimilation procedures of the models. These observed winds were found to be supergradient in nature and representative of the anomalous solution of the gradient wind equation. Procedures such as the multivariate optimum interpolation (with its geostrophic constraints) and the normal-mode initialization including several vertical modes apparently were factors that led to the degradation of these strong winds in the initial model states. In this paper, an analysis of these factors is presented, and it is shown that uninitialized analyses (with no constraints) based on a simple successive correction procedure can retain the strong winds evident in the observations. Forecasts thus performed appear to retain wave trains, a characteristic feature of negative PNA initial states, leading to a significant improvement in forecast skill.     

Equatorial disturbances,monsoons, and 1982–1983 ENSO

Summary Interannual modes are described in terms of three-month running mean anomaly winds (u,v), outgoing longwave radiation (OLR), and sea surface temperature (T _* ). Normal atmospheric monsoon circulations are defined by long-term average winds (u _n,v _n) computed every month from January to December. Daily winds are grouped into three frequency bands, i.e., 30–60 day filtered winds (u _L,v _L); 7–20 day filtered winds (u _M,v _M); and 2–6 day filtered winds (u _S,v _S). Three-month running mean anomaly kinetic energy (signified asK _L , K _M , andK _S , respectively) is then introduced as a measure of interannual variation of equatorial disturbance activity. Interestingly, all of theseK _L , K _M , andK _S perturbations propagate slowly eastward with same phase speed (0.3 ms^–1) as ENSO modes. Associated with this eastward propagation is a positive (negative) correlation between interannual disturbance activity (K _L , K _M , K _S ) and interannualu (OLR) modes. Namely, (K _L , K _M , K _S ) becomes more pronounced than usual nearly simultaneously with the arrival of westerlyu and negativeOLR (above normal convection) perturbutions. In these disturbed areas with (K _L , K _M , K _S >0), upper ocean mixing tends to increase, resulting in decreased sea surface temperature, i.e.T _* 0. Thus, groups (not individual) of equatorial disturbances appear to play an important role in determiningT _* variations on interannual time scales. HighestT _* occurs about 3 months prior to the lowestOLR (convection) due primarily to radiational effects. This favors the eastward propagation of ENSO modes. The interannualT _* variations are also controlled by the prevailing monsoonal zonal windsu _n, as well as the zonal advection of sea surface temperature on interannual time scales. Over the central Pacific, all of the above mentioned physical processes contribute to the intensification of eastward propagating ENSO modes. Over the Indian Ocean, on the other hand, some of the physical processes become insignificant, or even compensated for by other processes. This results in less pronounced ENSO modes over the Indian Ocean.With 10 FiguresContribution No. 89-6, Department of Meteorology, University of Hawaii, Honolulu, Hawaii.     

Turbulence mechanisms at an agricultural site

An extensive set of turbulence data from the 3- and 12-m heights taken over an agricultural site (Marsta, Sweden) are analyzed and compared with data from ideal sites.In unstable air, Monin-Obukhov similarity is found to be valid for the non-dimensional gradients of wind, _m , temperature, _h , and humidity, _e , for (only a few data), for _T /|T _*|,/ _E /|E _*| and for the non-dimensionalized inertial subrange spectra of temperature and humidity. Where comparison is possible, the unstable data also agree with those found in the Kansas study, with one remarkable exception, the inertial subrange constant of the temperature spectrum, ₁, being only 0.39, compared to the value 0.80 found at the Kansas site.On the stable side, most similarity predictions break down, with most of the data differing systematically from the corresponding Kansas results, the only exception being . The inertial subrange constants for temperature, ₁, and for humidity, ₁ are found to have the same values, 0.39 and 0.30, respectively, as they do on the unstable side. Remarkable similarity is found for the shape of the stable u- and - and e-spectra. In addition, this shape is found to be identical with that found in Kansas. The peak wavelength of the stable u-, and -spectra is found to be about four times larger than it is for the corresponding Kansas spectra. This is interpreted to be a result of the increased macro-roughness at the Marsta site as compared with that at the Kansas site. A possible explanation for the low ₁-value is discussed, suggesting that ₁ is not a universal constant, but instead dependent on the turbulent structure.     

Flux-profile Relationships for Wind Speed and Temperature in the Stable Atmospheric Boundary Layer

Wind and temperature profiles in the stable boundary layer were analyzed in the context of MoninObukhov similarity. The measurements were made on a 60-m tower in Kansas during October 1999 (CASES-99). Fluxprofile relationships, obtained from these measurements in their integral forms, were established for wind speed and temperature. Use of the integral forms eliminates the uncertainty and accuracy issues resulting from gradient computations. The corresponding stability functions, which were nearly the same for momentum and virtual sensible heat, were found to exhibit different features under weakly stable conditions compared to those under strongly stable conditions. The gradient stability functions were found to be linear, namely _m = 1+ 5.8 and _h = 1 + 5.4 up to a limit of the MoninObukhov stability parameter = 0.8; this is consistent with earlier findings. However, for stronger stabilities beyond a transition range, both functions were observed gradually to approach a constant, with a value of approximately 7. To link these two distinct regimes, a general but pliable functional form with only two parameters is proposed for the stability functions, covering the entire stability range from neutral to very stable conditions.     

A note on the analogy between momentum transfer across a rough solid surface and the air-sea interface

The aerodynamic classification of the resistance laws above solid surfaces is based on the use of a so-called Reynolds roughness number Re _s =h _s u _*/, whereh _s is the effective roughness height, -viscosity,u _*-friction velocity. The recent experimental studies reported by Toba and Ebuchi (1991), demonstrated that the observed variability of the sea roughness cannot be explained only on the basis of the classification of aerodynamic conditions of the sea surface proposed by Kitaigorodskii and Volkov (1965) and Kitaigorodskii (1968) even though the latter approach gains some support from recent experimental studies (see for example Geernaertet al. 1986). In this paper, an attempt is made to explain some of the recently observed features of the variability of surface roughness (Toba and Ebuchi, 1991; Donelanet al., 1993). The fluctuating regime of the sea surface roughness is also described. It is shown that the contribution from the dissipation subrange to the variability of the sea surface can be very important and by itself can explain Charnock's (1955) regime.     

Measurements of solar radiation and estimation of optical depth in the high Andes of Peru

Summary During an expedition to the high Andes of Southern Peru in June–July 1977, measurements of direct solar radiation in four spectral bands (0.270–0.530–0.630–0.695–2.900 ) were conducted at six sites in elevations ranging from sea level to 5645 m. These measurements were evaluated in Langley plots to determine total optical depths () and irradiances at the top of the atmosphere. In addition, water vapor optical depths (_wv) were calculated from the mean radiosounding over Lima during the expedition, and Rayleigh (_ray) and ozone (_oz) optical depths were obtained from published tabulations. Subtracting _ray, _oz, and _wv from yielded estimates of aerosol optical depth _aer. The components _ray and _oz decrease from the shorter towards the longer wavelength bands and from the lower towards the higher elevation sites; _aer also decreases towards the higher elevations. Particularly pronounced is the decrease of _aer and from the lowlands of the Pacific coast to the highlands of the interior, reflecting the effect of a persistent lower-tropospheric inversion and the contrast from the marine boundary layer to the clear atmosphere of the high Andes.With 4 Figures     

A study of a fair weather boundary layer in TOGA-COARE: Parameterization of surface fluxes in large scale and regional models for light wind conditions

The study focuses on a way to parameterize the effect of subgrid scale convective motions on surface fluxes in large scale and regional models for the case of light surface winds. As previously proposed, these subgrid effects are assumed to scale with the convection intensity through the relationship: where is the mean velocity of the wind, U₀ the velocity of the mean wind, w_* the free convection velocity, and an empirical coefficient to be determined. Both observations and numerical simulation are presently used to determine the free convection coefficient .Large eddy simulation of a fair weather convective boundary layer case observed during TOGA-COARE is performed. Comparisons between observations and the simulation of surface properties and vertical profiles in the planetary boundary layer are presented. The simulated vertical turbulent fluxes of heat, moisture and buoyancy range well within estimates from aircraft measurements.The most important result is that the true free convection coefficient , directly estimated from simulation, leads to a value of 0.65, smaller than the ones estimated from temporal and spatial variances. Using observations and simulation, estimates of from temporal and spatial variances are obtained with similar values 0.8. From both theoretical derivations and numerical computations, it is shown that estimates of the true from variances are possible but only after applying a correction factor equal to 0.8. If this correction is not used, is overestimated by about 25%. The time and space sampling problem is also addressed in using numerical simulations.     

A diagnostic study on the environmental influence of a mesoscale convective system over southern China in Meiyu season

Summary ¶During the Post-TAMEX forecast experiment of Taiwan in 1992, a mesoscale convective system (MCS) developed on June 5–6 over southern China. As this system matured, it produced readily apparent cirrus outflow on satellite imageries while the upper level flow also exhibited a diffluent pattern. The purpose of the current study is to examine the possible changes in its environment associated with the development of this MCS.By using 12-h data from 1200 UTC June 5 to 1200 UTC June 6, objective analyses were performed for a 1°×1° latitude/longitude grid using sounding data and a low-pass filter. To facilitate the diagnosis, a band-pass filter was further applied to separate mesoscale features from macroscale ones, while the apparent heat source and apparent moisture sink defined by Yanai et al (1973) were also calculated.Results suggest that the MCS exerted clearly discernable effects on its environment. The latent heat release led to the development of a warm core and mesoscale high-pressure disturbance at upper levels when the system matured. Ageostrophic winds and diffluent flow patterns together with strong anticyclonic vorticity at 200hPa near the MCS were associated with the mesohigh. After the mature stage, weak cooling occurred above 350hPa, likely due to radiative emission from the cloud top. However, a mid-level cyclonic vortex, often present in MCSs over the North America, was not apparent here due to weak environmental vorticity and small Coriolis parameter f. The level of maximum divergence was initially located at 500hPa, but rose to 200hPa as the MCS matured. In response, the upward motion not only intensified, but the level at which strongest rising occurred also ascended from 700 to 350hPa. Results from the apparent heat source and moisture sink calculation suggest that this slow ascent of maximum heating was partially due to vertical transport of sensible heat by updrafts.During the MCSs mature stage, under the stratiform clouds to the west of the strongest convection, a cold mesohigh formed at the surface due to evaporative cooling in downdrafts, and a gust front appeared along the leading edge of the outflow boundary. A trailing mesolow was also observed, likely due to near-adiabatic warming in drier downdrafts since no precipitation was associated with it.Received April 11, 2002; revised May 27, 2002; accepted July 14, 2002 Published online: April 10, 2003     

An elementary valley wind model

Summary With the typical geometry of a large Alpine valley in mind, a box-type model consisting of only one (Alpine) basin, the forelands, and one valley tube connecting those two has been set up. Using drastically simplified equations of motion, continuity and heat, and supposing weak-gradient synoptic conditions, a periodic solution for the daily wave of the valley wind regime is obtained.Fundamental concepts like the area-height distribution of valley segments, or the role of slope winds and other fast-reacting local circulations in heating or cooling the main valley and larger basins, are being incorporated. The solution has valley wind speeds correct in amplitude and phase, maximum upvalley wind occurring around 16 h local time. Valley winds attempt to equalize horizontal pressure differences, which are caused by the fact that the interior of valleys is being heated and cooled more strongly by a factor of 2 or more than the atmosphere over the adjacent plain = foreland. In this attempt, they reduce the temperature contrast somewhat, but not very much, because friction in the valley is a dominating process. The present model also nicely reproduces observed features of the daily pressure wave, including the existence of a level of pressure equalization (between the valley interior and the plain) at about crest height.

---

Grundzüge eines Talwindmodells

Zusammenfassung Ich habe das typische Relief eines großen Alpentals vor Augen, und konstruiere ein Schachtel-Modell, das drei schematische Regionen umfaßt: ein inneralpines Becken, das Alpenvorland, und eine Talröhre, die diese beiden verbindet. Die Impuls-, Kontinuitäts- und thermodynamische Gleichung werden in stark vereinfachter Form angesetzt, wobei eine gradientschwache Wetterlage vorausgesetzt wird. Wir untersuchen die tagesperiodische Lösung dieses Systems für Talwind, Temperatur, Luftdruck. In diesen Gleichungsansatz wurden grundlegende Konzepte eingearbeitet: z.B. die Flächen-Höhenverteilung des Beckens, oder die Rolle der Hangwinde und anderer kleinräumiger, schnell reagierender thermischer Zirkulationen, die die lokale Erwärmung/Abkühlung dem Haupttal bzw. größeren Talbecken mitteilen. Die vorliegende Lösung zeigt Talwindgeschwindigkeiten, deren Amplitude und Phase mit den Beobachtungen gut übereinstimmen: der Taleinwind hat sein Maximum um ca. 16 Uhr Lokalzeit (MEZ). Die Talwinde sind ein Versuch, horizontale Druckdifferenzen auszugleichen, die wiederum auf Grund der Tatsache entstehen, daß die Erwärmung/Abkühlung des Taiinneren um mehr als den Faktor 2 stärker ist als die der Luftsäule über dem angrenzenden Vorland. Bei diesem Versuch reduzieren die Talwinde den Temperaturkontrast, aber nur um weniges, da die Ausgleichsströmung durch die Talröhre starker Reibung unterliegt. Schließlich reproduziert das vorliegende Modell in zufriedenstellender Weise den tagesperiodischen Druckgang, wie er in verschiedenen Höhen beobachtet wird, vor allem auch das sogenannte Druckausgleichsniveau, das ungefähr in Kammhöhe liegt.

---

---

With 2 Figures     

Hidden information within series of measurements — four examples from atmospheric science

Whether in classical networks such as meteorological networks of in more recent ones of atmospheric chemistry, a wealth of data is at hand. These data have been evaluated in a manner depending on the purpose of the network. However, much more information is hidden in these time series and waits for discovery. Only the imagination of scientists is needed. Four examples are given which lead to new information about the atmospheric aerosol and the behaviour of the atmosphere. These examples are: Atmospheric turbidity from sunshine recordings, Meteorological drainage area from the variance of observations, Location of point sources from air mass trajectories, and Total vertical ozone from turbidity measurements.     

An improved calibration for tethered balloon wind measurements

A previously published technique for using tethered spherical balloons as anemometers for measuring light low-level winds has been further developed. Earlier data on the relationship between the aerodynamic drag coefficient and the Reynolds number of spherical rubber balloons were combined with a large number of new data and re-analysed; and the errors in the relationship were estimated. The results allowed a more accurate calculation of wind speed from the deflection of a tethered balloon from the vertical. When combined with a new technique for calculating the effects of the tether, this enabled light to moderate low-level winds at fixed heights up to 600 m or more to be measured with simple, cheap, and readily mobile equipment; and a slight modification of the technique allowed measurement of winds in and above fog. Wind speeds measured by the ballon technique showed reasonably good agreement with measurements by an anemometer carried beneath the balloon.Glossary of Symbols a, b, c Coefficients in the relationship between lnC _d and lnR - A Quantity under square root in solution for lnV whena0 - C _d Wind drag coefficient for balloon - C _dc Value ofC _d given by calibration curve of Table I - D Dynamic wind pressure force on balloon - F Buoyant free lift of balloon with load - Re Reynold's number of balloon (sphere) - R = Re/10⁵ - r Radius of sphere - T Tension in tether - V Wind speed - ₈₃() =(lnC _dc -lnC _d ) when 83° , or 0 for other - Error in lnC _d - Elevation of tether where attached to balloon - Elevation of balloon from ground tether point - Molecular viscosity of air - Ratio of circumference to diameter of circle - Density of air     

Local Similarity Relationships In The Urban Boundary Layer

To investigate turbulent structures in an urban boundary layer (UBL) with many tallbuildings, a number of non-dimensional variable groups based on turbulent observationsfrom a 325-m meteorological tower in the urban area of Beijing, China, are analyzedin the framework of local similarity. The extension of surface-layer similarity to localsimilarity in the stable and unstable boundary layer is also discussed. According to localsimilarity, dimensionless quantities of variables: e.g., velocity and temperature standarddeviations _i/u_*l (i=u,v,w) and_T/T_*l,correlation coefficients of uw and wT covariance, gradients of wind and temperature_m and _h, and dissipation rates of turbulent kinetic energy (TKE) andtemperature variance and _N can be represented as a functiononly of a local stability parameter z/, where is the local Obukhovlength and z is the height above ground. The average dissipation rates of TKE andtemperature variance are computed by using the u spectrum, and the uw and wTcospectra in the inertial subrange. The functions above were found to be in a goodagreement with observational behaviour of turbulence under unstable conditions, butthere were obvious differences in the stable air.     

Analytical investigations of horizontal meso-scale momentum equations with Newtonian nudging

Summary This study presents an analytical investigation of the local behaviour of the solution to a mesoscale model with Newtonian nudging when observed winds are time varying. The analysis examines each Fourier component of the time series of observed winds. Unlike the case with a constant observed wind, the nudged wind vector does not asymptotically approach the observed wind. In response to sinusoidal oscillation of the observed wind, the nudged wind vector is always on a half circle connecting the vector ends of the observed and un-nudged modelled winds. When nudging parameter 0, the nudged wind vector approaches the un-nudged wind; when , the nudged wind vector approaches the observed wind. For commonly used values of nudging parameter , the modelled wind field always carries errors.A target nudging scheme is devised in this study in order to ensure the model result is identical to observed winds with sinusoidal oscillation. Investigation shows that such a target wind exists for a finite value of , and the magnitude of the target-nudging term is about the same as that of a normal nudging term if f, wheref is the Coriolis parameter and is the frequency of the wind oscillation.With 7 Figures     

Radiometrically determined skin temperature and scalar roughness to estimate surface heat flux part II: Performance of parameterized scalar roughness for the determination of sensible heat

Several formulations and proposals to determine the value of the radiometric scalar roughness for sensible heatz _0h,r are tested with respect to their performance in the estimation of the sensible heat flux by means of the profile equations derived from Monin-Obukhov similarity theory. The equations are applied to the data set of spatially averaged surface skin temperature and profiles of wind speed and temperature observed in a pasture field during a growing season. The use of a physical model developed for a dense canopy to estimate scalar roughness for sensible heatz _0h,r produced sensible heat fluxH with a correlation coefficientr=0.884, the ratio of means being H _s /H=1.19 in a comparison with reference values ofH _s . In comparison, a proposal for a fixed value ofz _0h yieldedr=0.887, H _s /H=0.879. In both cases, the validity ofz _0h =z _0h,r was assumed. All expressions derived to estimatez _0h,r from a multiple linear regression with such predictors as leaf area index, solar radiation and the ratio of solar radiation to extraterrestrial radiation, were found to produce a better result, withr better than 0.90 and H _s /H around 1.0. However, when the constantsc andf of a linear regression equationHs=cH+f are used to evaluate the equations, a marked difference in performance of each formulation appeared. In general, equations with smaller numbers of predictors tend to produce a biased result, i.e., an overestimation ofH at largeH _s . These values ofH are used in conjunction with the energy balance equation to derive values of the latent heat fluxLE, which are shown to be in good agreement with the reference valuesLE _s , withr greater than 0.97.     

Stable boundary layers: Observations,models and variability part I: Modelling and measurements

Selected field measurements of evening stable boundary layers are presented in detail comparable with published Large Eddy Simulation results. Such models appear to match idealized theories more closely than do some boundary-layer observations. Any attempt to compare detailed observations with idealized models therefore highlights the variability of the real boundary layer.Here direct turbulence measurements across the stable boundary layer from a heterogeneous and an ideal site are contrasted. Recommendations are made for the information needed to distinguish heterogeneous and ideal cases.The companion paper (Part II) discusses further the issues of data, analysis in the presence of variability, and the effects of averaging over heterogeneous terrain.Part of UK Meteorological Office Atmospheric Process Research Division.     

Effects of heat and water vapor transport on eddy covariance measurement of CO2 fluxes

Flux densities of carbon dioxide were measured over an arid, vegetation-free surface by eddy covariance techniques and by a heat budget-profile method, in which CO₂ concentration gradients were specified in terms of mixing ratios. This method showed negligible fluxes of CO₂, consistent with the bareness of the experimental site, whereas the eddy covariance measurements indicated large downward fluxes of CO₂. These apparently conflicting observations are in quantitative agreement with the results of a recent theory which predicts that whenever there are vertical fluxes of sensible or latent heat, a mean vertical velocity is developed. This velocity causes a mean vertical convective mass flux (= _cw for CO₂, in standard notation). The eddy covariance technique neglects this mean convective flux and measures only the turbulent flux _c w. Thus, when the net flux of CO₂ is zero, the eddy covariance method indicates an apparent flux which is equal and opposite to the mean convective flux, i.e., _c w = – _c w. Corrections for the mean convective flux are particularly significant for CO₂ because _cw and _c w are often of similar magnitude. The correct measurement of the net CO₂ flux by eddy covariance techniques requires that the fluxes of sensible and latent heat be measured as well.