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Use of Synthetic Data to Test Flight Patterns for a Boundary Layer Field Experiment. Santoso, Edi; Stull, Roland B. 1999

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VOLUME 16 SEPTEMBER 1999JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGYq 1999 American Meteorological Society 1157Use of Synthetic Data to Test Flight Patterns for a Boundary Layer Field ExperimentEDI SANTOSO AND ROLAND STULLAtmospheric Science Programme, Department of Geography, University of British Columbia, Vancouver,British Columbia, Canada(Manuscript received 13 July 1998, in final form 28 October 1998)ABSTRACTA virtual research aircraft was flown through a synthetic atmospheric boundary layer to help design a realflight plan that would allow robust turbulence statistics to be obtained in a heterogeneous, evolving, convectiveboundary layer. The synthetic boundary layer data consisted of a field of coherent, large-diameter, thermalupdraft/downdraft structures, superimposed in random smaller-scale turbulence having a Gaussian distribution.These large and small eddy perturbations, with scales set from published empirical relationships, were super-imposed on the expected mean profiles of wind and potential temperature. The goal was to determine whethersufficiently robust line-averaged statistics could be gathered to study a new similarity theory for the radix layer,the bottom fifth of the convective boundary layer, where mean profiles are not uniform with height.After testing a variety of flight patterns with the synthetic data, a vertical zigzag pattern of slant ascent/descentlegs was selected as the best compromise, given typical aircraft flight and safety constraints. This flight patternwas then successfully flown with the University of Wyoming King Air aircraft in the real atmosphere duringBoundary Layer Experiment 1996 (BLX96) over Oklahoma and Kansas. Postexperiment comparison revealedthat the synthetic data exhibited less scatter than the actual data, perhaps caused by a heterogeneous surfaceand a nonstationary boundary layer. Based on this comparison, some practical recommendations are given forfuture use of synthetic boundary layer data.1. IntroductionSome meteorological instrument systems are so ex-pensive, or their deployment so complex, that it is wiseto first test the feasibility of the experimental plan usingvirtual instruments or synthetic data. This allows prob-lems to be detected and remedied at relatively low cost,before the physical instrument is constructed, launched,or deployed. Also, alternative experimental procedurescan be tested and compared to find the optimum pro-cedure.Synthetic experiments have been used in the past totest new instruments for weather satellites (Atlas et al.1985; Bell 1987; Hedin 1991; Green 1983; Liou andOu 1979; Meneghini et al. 1986). The monetary costand scientific loss of launching an inadequate satelliteinstrument is so prohibitive that it makes sense to tryto simulate instrument performance as much as possiblebefore construction and launch.The synthetic data approach is a powerful tool thatcan also be applied to other types of instrument systemsand meteorological field experiments, including thoseCorresponding author address: Roland Stull, Atmospheric ScienceProgramme, Department of Geography, University of British Colum-bia, 1984 West Mall, Vancouver, BC V6T 1Z2, Canada.E-mail: rstull@geog.ubc.cain the boundary layer (BL). For example, we needed insitu observations of wind and temperature profiles hav-ing very high vertical and temporal resolution, made ina region of the BL where one must average over a largenumber of coherent thermal structures to get robust sta-tistics. Given the trade-offs of various instruments thatwere available for the variety of sites needed, it wasconcluded that airborne measurements would be themost feasible.However, with a finite aircraft speed of order 100 ms21and the need for long flight legs of order 70 km toget robust turbulence statistics, there was concernwhether nonstationarity and horizontal heterogeneity inthe BL would create mutually exclusive requirementsfor the flight. Namely, if a horizontal flight leg werelong enough to average over sufficient thermals risingfrom a heterogeneous surface, then would the durationbe so long that the BL would change during the flight?For this reason, we realized that it would be wise tofirst test alternative flight patterns using synthetic data.We created a synthetic dataset having the same statisticalcharacteristics as a field of large coherent thermal struc-tures superimposed on quasi-random smaller-scale tur-bulence, all embedded within a BL having typical meanwind and temperature profiles. Then we ‘‘flew’’ a hy-pothetical aircraft through this synthetic BL, where theaircraft speed and data sampling rate mimicked those1158 VOLUME 16JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGYof the real aircraft. We analyzed the resulting time seriesof synthetic data as if it were real data, using our existingaircraft data analysis package to find the best fit meanwind and temperature profiles, and corresponding var-iances and covariances.We found that the traditional flight pattern of hori-zontal flight legs stacked at different altitudes was in-adequate for our needs because of BL nonstationarityand heterogeneity. We then tested a variety of alternativeflight patterns using the synthetic data, finally settlingon a vertical zigzag pattern that gave reasonably robustturbulence statistics. Our numerical simulations came tofruition when we later adopted this as one of our flightpatterns for the real field experiment flown using theUniversity of Wyoming (UW) King Air aircraft overKansas and Oklahoma in summer 1996.The purpose of this paper is to describe how syntheticdata can be used to good advantage in planning bound-ary layer field campaigns, using our particular appli-cation as an example. We review in section 2 the BLtheory that motivated this work and that set the require-ments (section 3) for the synthetic flights. Section 4describes the procedures we used to construct the syn-thetic data field, while section 5 describes how we col-lected the synthetic time series by flying a virtual aircraftfor a variety of case studies. Analysis of the resultingtime series to yield wind and temperature profiles andstatistics is described in section 6, and comparisons withactual flight data are discussed in section 7.2. Radix layer reviewDuring convective conditions with statically unstableair, one can identify subdomains of the convectivemixed layer (ML) having different similarity scalings.Using wind speed as an example, winds are zero nearthe ground and smoothly increase until finally becomingtangent to the vertically uniform winds in the mid-ML(Santoso and Stull 1998). In this middle layer, calledthe uniform layer (UL), wind speed and direction arenearly uniform, but subgeostrophic, with height. Abovethat is the entrainment zone, a transition layer betweenthe subgeostrophic UL below and the nearly geostrophicfree atmosphere above. At the bottom of the ML is thesurface layer (SL), the nearly constant flux region whereMonin–Obukhov (MO) similarity theory applies. In thislayer, the wind profile is nearly logarithmic, caused bymechanically generated turbulence within the wall shearflow (Stull 1996).There is a region or gap between the top of the SLand the bottom of the UL where some researchers feelthat SL similarity theories fail. To better explain thisportion of the ML, Santoso and Stull (1998) analyzeddata from the 1973 Minnesota field experiment (Izumiand Caughey 1979) and were able to define a radix layer(RxL) as the region between the surface and the bottomof the UL that obeys a similarity different than MO.The classic SL is a subdomain within the bottom of theRxL. The Latin word ‘‘radix,’’ meaning ‘‘origin’’ or‘‘root,’’ was used to name this layer because it is theroot of convective thermals. Within the RxL the windand temperature profiles are influenced by both SL andML scales. Typical depths of the RxL are on the orderof hundreds of meters for wind profiles and tens ofmeters for temperature profiles. Not all researchers areyet convinced of the need for a radix layer similaritytheory, nor of the suitability of the radix layer to succeedas a framework for such a new similarity theory. Oneof the motivations for a field experiment was to furtherexplore these issues.Based on these Minnesota data, the following em-pirical relations (Santoso 1993; Santoso and Stull 1998)were found to describe the vertical profiles of mean windspeed M and potential temperature u within and abovethe radix layer: A1zzM exp A 1 2 for z # zUL 1 rm12 2M 5 []rm rm(1)M for z . z , UL rm A2zz(u 2 u )12 exp A 1 2 for z # z0UL 2 rt5 12 1 26[]u 2 u 5 ULrt rt(2)0 for z . z , rtwhere MULand uULare mean wind speed and potentialtemperature in the uniform layer; u0is mean potentialtemperature at the height of the roughness length fortemperature; zrmand zrtare the depths of the RxL forwind and temperature; z is height above the surface;overbars represent a horizontal-average ergodic approx-imation to the ensemble average; and A1and A2areempirical constants of 0.096 and 0.101 respectively.SEPTEMBER 1999 1159SANTOSO AND STULL3. Need for special dataField experiment data for the RxL are very limited.As was shown by Santoso and Stull (1998), it is im-possible to use SL tower data at low altitudes with ra-winsonde data aloft, because there is usually an artificialgap between the two profiles at altitudes where accurateRxL data are needed most. The first system gives goodtime averages while the second system gives snapshotswith large sampling error. This experimental artifact ofa discontinuity between the two segments of wind ortemperature profiles would give large errors if used toanalyze the RxL. A new field experiment with consistenttime or space averages at all heights was needed to getbetter understanding of this region.Other sensing platforms such as wind profilers or ra-dio acoustic sounding systems were inadequate for thisresearch because of the low-altitude data void associatedwith receiver–transmitter ringing feedback and other in-strument characteristics. One possible source of datawould be very tall (200–300 m) instrumented towers,although their measurements would be for a small-foot-print quasi-homogeneous plot of land, rather than theaverage over typical heterogeneous landscapes that wedesired. Also, we wanted to investigate whether the RxLprofiles depended on surface roughness length, whichmeant that we needed to make similar measurementsover different landscapes.Based on these factors, we concluded that an instru-mented aircraft would be most likely to give us theneeded data. As stated in section 1, conventional hor-izontal flight legs were found to be inadequate. For thisreason we proposed using a rarely used pattern, namely,a vertical zigzag. Lenschow et al. (1988a,b) had usedit in the nocturnal BL, but to our knowledge it had notbeen used during daytime convective conditions whenthere are 1–2-km diameter coherent thermal structuresand a full spectrum of turbulence. It was unknownwhether such a vertical zigzag would be able to collectsufficiently high vertical resolution profile data of windsand potential temperature with sufficiently robust sta-tistics needed to test the radix profile equations. Thiswas the motivation for the synthetic sampling study re-ported here.4. Synthetic data-generation proceduresTo generate the synthetic turbulence data, we super-impose the effects of three components: 1) backgroundprofiles of mean variables, 2) perturbations associatedwith coherent thermal updrafts and downdrafts, and 3)perturbations from random Gaussian fluctuations rep-resenting medium- and small-scale turbulence. For thefirst component (mean profiles) we used the RxL sim-ilarity equations (1) and (2) described in section 2.For the second component (coherent structures), pub-lished empirical formulations of Stull (1990) and Young(1988b) were used for horizontal wind speed andM9upotential temperature perturbations within thermalu9uupdrafts:1/2zM95u* 21.5 1 0.5 (3)u12[]zi0.2 z20.5 1 212 0.9 2 2 ))zu95 i zu1 2 100 0.9 2 12[]ziw9u9ys3 ,w*(4)where ziis ML depth, u*is friction velocity, w*isDeardorff velocity [(g/Ty)ziw9 ]1/3, g is gravitationalu9ysacceleration, Tyis average absolute virtual temperature,w9 is the surface eddy covariance value of kinematicu9ysvertical virtual potential temperature flux (a measure ofbuoyancy flux), and subscript u denotes updraft. Duringfree convection, thermal updrafts usually contain slowerhorizontal wind and warmer potential temperature thanthe surrounding air.In the downdraft environment, wind and potentialM9dtemperature perturbations are set to counterbalanceu9dthe updrafts, in order to conserve mass, heat, and mo-mentum:fuM952 M9, (5)dufdfuu952 u9, (6)dufdwhere fuand fdare fractional cross sections of updraftand downdraft areas, and subscript d denotes downdraft.The minus sign indicates the opposite direction. As re-ported by Greenhut and Khalsa (1982, 1987), Khalsaand Greenhut (1985, 1987), Godowitch (1986), andYoung (1988a,b), we also assumed for some of our casestudies that there can be background air that is neitherin coherent updrafts or downdrafts. The velocity andpotential temperature excesses of this background airare zero.For the quasi-random third component, we used arandom number generator to pick wind and potentialtemperature perturbations from a Gaussian distributionhaving standard deviations based on the published em-pirical results of Panofsky et al. (1977), Caughey andPalmer (1979), and Sorbjan (1986). These standard de-viations are 1/3ziu* 12 2 0.5 for z # 0.1zis 5LM(7)0.6w* for 0.1z , z # z , ii21/3 2/3zzw9u9ss 5 1.4 1 2 1.2 , (8)u12 1 2*ii1160 VOLUME 16JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGYwhere sMand suare wind and potential temperaturestandard deviations, L is Obukhov length, and w9 isu9sturbulent kinematic heat flux near the surface.Combining these three components gives the totalsynthetic wind and temperature for thermal updrafts:M 5 M 1 M91Gs (9a)uuMu 5 u 1 u91Gs , (9b)uuubackground air (subscript b):M 5 M 1 Gs (10a)bMu 5 u 1 Gs , (10b)b uand environmental downdrafts:M 5 M 1 M91Gs (11a)ddMu 5 u 1 u91Gs , (11b)dduwhere G is a dimensionless random number with Gauss-ian distribution of unit standard deviation (Press et al.1992).All of the equations (9)–(11) are functions of height.There is no need, however, to use these equations tocreate a full 2D or 3D field of turbulent ML quantitiesthrough which we fly the virtual aircraft. The reason isthat we need the synthetic data at only those locationswhere the virtual aircraft will fly. Thus, our approachis to first define the track of the virtual aircraft through2D or 3D space, and then solve (9)–(11) ‘‘on the fly’’at the virtual aircraft locations, to create a synthetic timeseries of sampled data as would be measured at theaircraft. This process is described in more detail in sec-tions 5 and 6, and is efficient in computational time andmemory requirements.When flying a virtual aircraft through this syntheticdata, it is assumed that a sequences of data points willbe in an updraft, the next sequence will be in backgroundair if any exists, and the next sequence will be in down-draft air. The duration of each sequence is set to cor-respond to typical updraft and downdraft diameters,which are reported in the literature to be proportionalto the ML depth. A full flight track would include manysuch sequences. Based on conditional sampling of air-craft data, Greenhut and Khalsa (1982, 1987), Khalsaand Greenhut (1985, 1987), Godowitch (1986), andYoung (1988a,b) suggest that well-defined thermal up-drafts cover 15%–43% of horizontal area, while well-defined downdrafts cover about 20%–55%. The re-maining percentage is categorized as background air.The next section describes how time series of syntheticdata are created by flying virtual aircraft through theboundary layer just defined.5. Synthetic data case study definitionTo synthesize data using the previous equations, wemust specify information such as convective BL depthzi, RxL depths zrmand zrt, turbulent kinematic heat fluxat the surface w9 , friction velocity u*, Deardorff ve-u9slocity w*, average wind speed and potential temperaturein the uniform layer MULand uUL, potential temperatureat (near) the surface u0, and Obukhov length L. Thevertical zigzag flight pattern is designed to span the SL,the RxL, and the bottom of UL. For typical ML depthsof about 1 km, we thus want to generate vertical profilesof mean wind and potential temperature between alti-tudes of about 10 and 600 m above ground level (AGL).One of the goals of our synthetic experiments is to testa variety of zigzag options, such as the number of ascent/descent pairs (A/D).In this study we consider two cases of horizontaldistribution of thermals: one where thermals are evenlydistributed, and the other for random distributions. Inthe real atmosphere, thermals have been observed tohave quasiperiodic spacing, such as across horizontalroll vortices. Our simulations with both regularly spacedand random locations are designed to give us infor-mation that brackets the characteristics of the real at-mosphere, thereby allowing us to determine optimumflight distances for worse-case thermal spacings.In the evenly distributed case, thermals are assumedto have uniform cross-section diameter of order zi, andany two neighboring thermals are separated by down-drafts (and in some experiments by both downdrafts andbackground air) that are also evenly distributed. Forexample, for a case where the thermals cover one-thirdof the flight path and downdrafts cover two-thirds ofthe flight path, this means that the synthetic aircraft willpass through a sequence of pairs of 1-km cross-sectionthermal updraft and 2-km downdraft. For these evenlyspaced cases, the virtual flights are designed to passthrough the middle of all the thermals.For the randomly distributed cases, thermal positionsand diameters are chosen randomly. The diameter isdistributed normally about a mean value of zi, with theGaussian tails cut off at 0.1ziand 1.9zi. The two nearestthermals are separated by downdrafts that are set to beno less than 1.1 times the average of their diameters.Although as reported here we used a Gaussian distri-bution of thermal characteristics for our synthetic workprior to the actual field experiment in 1996, we realizenow that a lognormal distribution might have been moreappropriate. Lognormal distributions are also easy tocreate in synthetic data, and we recommend that otherresearchers consider using such distributions if they cre-ate their own synthetic datasets for the mixed layer.For simplicity in this study we will assume that thesurface is flat, and the virtual flights are always cross-wind. We use a horizontal aircraft speed component of100ms21regardless of ascent or descent, a verticalspeed of 5 m s21during the A/D, and a data samplingrate of 50 Hz, which are typical for the UW King Airaircraft that was to be used later in real life. It is alsoassumed that the lowest safe altitude is 10 m, while thehighest altitude is dependent on the horizontal distanceSEPTEMBER 1999 1161SANTOSO AND STULLTABLE 1. Meteorological sets used for evenly distributed synthetic thermals (see text for notation).Setindexzi(m)zrm(m)zrt(m)w9u9s(K m s21)u*(m s21)w*(m s21)MUL(m s21)uUL(K)u0(K)L(m)AB2000100018513032250.200.100.250.252.351.507.56.0292.5285.5302.5290.525.9211.4TABLE 2. Thermal distribution cases for evenly distributed thermals. A/D represents one ascent/descent pair of flight legs.CaseindexFraction of area covered byupdraft downdraft backgroundHorizontaldistance perA/D (km)Total numberof A/DsTotalhorizontaldist. (km)Verticaldistance (m)(above 10 m)0102030405061/31/31/41/41/51/52/31/23/41/24/51/201/601/403/1020202222242433445560608888120120500500550550600600covered by each A/D pair, using an aircraft vertical ve-locity that is constant for all virtual flights.To capture some of the variability of the real atmo-sphere, we ran simulated flights for various combina-tions of meteorology and thermal distributions. The me-teorological options are identified below as ‘‘sets,’’ andthe thermal distributions as ‘‘cases.’’ Results will beidentified by their set and case indices.a. Evenly distributed thermal casesFor each of the BL meteorology sets listed in Table1, we collect synthetic flight data for the evenly dis-tributed thermal cases of Table 2. Included are trialswhere the convective BL consists of thermal updraftsand downdrafts only, and other trials with updrafts anddowndrafts embedded within background environmentair. For some cases the thermal updrafts occupy one-third, one-quarter, or one-fifth of the flight paths, andthe rest is occupied by downdrafts. For the other cases,thermals fill one-third, one-quarter, or one-fifth of flightpaths, downdrafts occupy one-half, and the rest is back-ground air.Based on the thermal/downdraft geometry, one cancalculate the minimum-required horizontal flight dis-tance per A/D, total number of A/Ds per horizontaltrack, and total flight path distance needed to get at leasttwo samples in thermals at any point in the verticaldomain. For example, in case 1 where one-third of theflight path is covered by thermals and the remaindercovered by downdraft, one would need a total horizontalflight distance of 60 km consisting of three A/Ds of 20-km horizontal distance each in order to get two or moredata samples in each 2-m vertical increment. Verticaldistance is simply calculated using ratio of vertical tohorizontal speeds of the aircraft, multiplied by horizon-tal distance. Therefore, for case 1 the vertical distanceis 500 m above the lowest height (10 m), giving a max-imum altitude of 510 m AGL at the top of the A/Dpattern.For those cases that include ambient background airin addition to thermal updrafts and downdrafts, althoughthe downdraft and background air vary, they neitherinfluence the total flight distance nor the total A/D pat-terns individually, because total flight distance is de-termined by relative comparison of the percentage ofthe thermals and of the percentage of the remainder. Forexample, in case 2, the total fight distance needed alsohappens to be 60 km, which consists of three up–downpatterns of 20-km horizontal distance each, with a max-imum altitude of 510 m AGL. Total horizontal distanceslisted in Table 2 are only minimum distances requiredfor uniformly distributed thermals. For variable diam-eters, one would need longer total horizontal flight dis-tances than those listed in Table 2.Simulating the six flight path/thermal cases of Table2 for each of the two sets of BL meteorology of Table1 yields 12 trials that were performed. Figures 1–3 showonly a subset of these, to save space. The outcome re-garding optimal experimental design is discussed in alater section.b. Randomly distributed thermalsTo more faithfully represent the range of meteoro-logical conditions expected over Kansas–Oklahomawhere the real Boundary Layer Experiment 1996(BLX96) field program was to take place, three addi-tional sets of synthetic meteorological data were created,listed in Table 3.The creating of randomly distributed synthetic ther-mals is a bit more complicated than for the even dis-tribution. Here, we consider a 100 km 3 100 km hor-izontal domain, within which thermal diameters and po-sitions are distributed randomly. The distance betweenthe centers of any two neighboring thermals is set to be1162 VOLUME 16JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGYFIG. 1. Top: Vertical zigzag flight pattern for synthetic data trialA01, for which thermals are evenly distributed. Dark lines indicatethe portion of the flight track in updrafts, while medium gray linesindicate downdrafts. Middle left: Wind speed (M) raw synthetic datapoints obtained during the virtual zigzag flight, conditional sampledto include only the updraft data (UP). Middle right: Same, but fordowndrafts (DN). Bottom: same as middle but for potential temper-ature (th). The total number of synthetic data points is 30 000.greater than 1.1 of the average of their diameters. Increating randomly distributed thermals we assume that,on average, the thermals cover one-third of the area.Within the 100 km 3 100 km domain, we randomlypick five points as starting locations for five flight tracks.Thus, for any one realization (i.e., flight track) it ispossible that the line-averaged thermal coverage will beless or greater than the one-third overall area average,as shown in Table 4. Table 4 also lists the coordinatesof the starting points of each virtual flight track.Because the distribution is random, we realized thatflight distances needed to be longer than for the evenlydistributed cases, in order to get robust statistics. Ourchoice of synthetic flight distance is 72 km (20% longerthan for the evenly distributed thermals), consisting ofthree A/D patterns of 24 km each. Horizontal and ver-tical speeds of the aircraft are the same as those forevenly distributed cases, as is the lowest altitude theaircraft could reach. Again, of the 15 trial simulationsthat were performed, only a few are plotted here (Figs.4–6) for illustration.6. Mean wind and potential temperature verticalprofilesAn example of the time series of synthetic data isplotted in Fig. 7. Such synthetic data are used here asinput to our data analysis packages as if it were froma real aircraft, both to test the adequacy of our analysisalgorithms and to confirm whether the number of A/Dpairs is optimal for the BLX96 field program.First, the data are sorted by altitude into nonoverlap-ping bins of 2-m vertical depth. Because several slantA/D legs were flown, each bin will contain data pointsfrom different horizontal locations along the flight path.The average of each bin is assigned to a height at thebin center.The resulting bin averages plotted in Figs. 8 and 9(only some are shown here to save space) still havescatter associated with sampling error. The reason isthat, by chance, some bins might have sampled moreupdrafts than downdrafts, while other bins might havesampled different portions of the two or three idealizedair types (up, down, background).Next, as if this were real data, nonlinear regressionis used to fit (1) and (2) to the profile data. These best-fit curves are plotted in Figs. 8 and 9, as solid lines(again only some are shown here). The input mean pro-files that were used to generate the synthetic data arenot plotted here because they virtually coincide with thebest fit results. Tables 5 and 6 compare the RxL param-eters that were input to those found from analyzing thesynthetic data. If our synthetic data were sufficientlyrealistic, then the difference between the analyzed andinput parameters is a measure of the expected differencebetween aircraft-measured and true atmospheric param-eters. Namely, it is one measure of expected experi-mental error, which includes the effects of samplingerror by the aircraft and analysis error by our analysisalgorithms. In a real field experiment the number of slantA/D legs is constrained by nonstationarity of the BL,and mesoscale heterogeneity, as previously discussed.Based on these competing factors, and utilizing whatwe learned from the synthetic data, our proposed designfor the flight pattern of the real aircraft was to havethree A/D pairs while flying in one direction over a 72-km horizontal ground track. As will be mentioned later,we had to modify this flight design during the real fieldexperiment because of limitations of the instruments anddata system on the King Air aircraft. A comparison withthe actual flight results is given in the next section.For the evenly distributed cases (see examples in Fig.8), the synthetic wind data were more scattered thanwas temperature. Nevertheless, the synthetic data ofmean wind and potential temperature were distributedaround the input mean profiles (not plotted in Fig. 8)SEPTEMBER 1999 1163SANTOSO AND STULLFIG. 2. Same as Fig. 1, but for trial B02. Light gray indicates background (BG) data points thatare in neither up- nor downdrafts. In the top figure the very light gray (or white in some printings)portions of the vertical zigzag indicate background (BG) data points that are neither updrafts nordowndrafts. The data collected along these portions of the flights are printed in medium gray inthe bottom center two figures labeled BG.and represented them very well. It can be seen in Table5 that zrm, zrt, MUL, uUL, and u0found from the best fitare close to their input values. For the evenly distributedcases, the sampled data captured the thermals and down-drafts (and background air) very well for the wholevertical and horizontal domain. The thermals were coun-terbalanced precisely by the downdrafts (and back-ground air). Theoretically the conservation of mass,heat, and momentum was satisfied not only in the wholevertical and horizontal domains, but also in almost everyvertical bin.For the randomly distributed cases (see examples inFig. 9), the mean wind and temperature data were morescattered. The data were still distributed around the inputmean profiles (not plotted in Fig. 9) quite well, but notas well as for the evenly distributed cases. This couldbe explained as follows. Though in the whole verticaland horizontal domain, the conservation of mass, heat,and momentum was satisfied, such conservation was notalways true in every bin. For randomly distributed ther-mals, it is likely that in most bins the sampled datarepresenting thermals and downdrafts were not coun-terbalanced. Those were shown in Fig. 9 for both windand potential temperature, where the vertical plots werequite wiggly. This amount of scatter was anticipated tobe more representative of the real BL.7. Comparison with actual flight dataa. Field site characteristicsDuring 15 July–13 August 1996 the University ofBritish Columbia conducted Boundary Layer Experi-ment 1996 over Oklahoma and Kansas (Stull et al.1164 VOLUME 16JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGYFIG. 3. Same as Fig. 1, but for trial B03. The total number of syn-thetic data points is 44 000.TABLE 3. Meteorological sets for randomly distributed thermals.Setindexzi(m)zrm(m)zrt(m)w9u9s(K m s21)u*(m s21)w*(m s21)MUL(m s21)uUL(K)u0(K)L(m)CDE2200160012002002451503450280.200.200.100.250.450.252.452.201.607.511.86.0292.5296.5285.5302.5304.5290.525.9234.5211.41997). The topography gently sloped up toward thewest-northwest, with a mean gradient of 1/900. Landuse was heterogeneous, and the land varied from mostlyflat to some very small, rolling hills. Mean winds weregenerally from the south, so we flew crosswind flighttracks that were oriented roughly east–west. These KingAir aircraft tracks were flown over three different siteshaving different land use and roughness. These siteswere named after nearby villages: Lamont, Winfield,and Meeker.The Lamont track, in Oklahoma, was primarily overcrop land. Terrain under the track was quite flat butgently rising to the west, with elevations ranging from320 to 425 m. Land use consisted of 60%–80% wheatfields, 40%–20% pasture, and a small number of treesless than 10 m tall. About 40% of the cultivated fieldswere recently plowed at the time of the experiment,leaving the reddish-brown soil bare under portions ofthe track. The average aerodynamic roughness based onaveraged direct calculations and the table classifications(Smedman-Ho¨gstro¨m and Ho¨gstro¨m 1978; Stull 1988;Wieringa 1980, 1986) was z05 0.1 m.The Winfield track, in Kansas, was over predomi-nantly pasture land, but with a small quarry near themiddle of the track. Small hills near the center of thetrack ranged from 70 to 100 m above local ground level.Terrain was rising to the west, with elevations rangingfrom 250 to 400 m. Land use consisted of 30%–60%pasture, 50%–10% forested areas mostly at the west sideof the track, with trees less than 10 m tall, and the restwas cultivated. The average aerodynamic roughness wasz05 0.9 m.The Meeker track, in Oklahoma, had greater forestcoverage. It had more small rolling hills ranging from40 to 60 m above local ground level. Terrain was risingto the west, with elevations from 250 to 280 m. Landuse consisted of 40%–50% pasture, 60%–40% woodedareas with trees less than 10 m tall, and 10%–30% crop-land primarily near the west end of the track. A 5 km2lake was just beyond the east end of the track. Theaverage aerodynamic roughness was z05 1.4 m.b. Flight patternsTo investigate the RxL, the vertical zigzag pattern asdesigned in the previous section was originally to beflown crosswind over each ground track to get verticalprofiles of mean wind and potential temperature be-tween altitudes of about 10 and 700 m AGL. Based onlast-minute recommendations of the UW King Air pro-ject manager (G. Gordon 1996, personal communica-tion), aircraft vertical velocity during climbs and de-scents was reduced by roughly half to 2.54 m s21inorder to improve the accuracy of the turbulence mea-surements. To accommodate this, only one and a halfA/D legs could be flown in one direction along the 72-km horizontal track. In order to get sufficient sampling,we decided to immediately reverse course and fly theremaining one and a half A/D legs. This yielded thethree total A/Ds that we had determined were necessaryusing the synthetic data and remained within the samehorizontal domain of 72 km; however, the sacrifice camein total time duration, which was now roughly doubledto complete the flight pattern. This compromise flightSEPTEMBER 1999 1165SANTOSO AND STULLTABLE 4. Thermal distribution cases for randomly distributedthermals.SetindexCaseindexStart x(km)Start y(km)Thermalcoverage(%)CCCCCDDDDDEEEEE10111213141516171819202122232413.0408.7229.37010.48519.5335.53410.69011.66418.24613.24211.09115.3717.01611.7796.49169.99313.23033.53486.34857.02357.67075.45486.36223.7038.06958.33462.63081.64732.16110.90336.9845.5134.5736.7025.3435.2441.5632.9534.0834.8729.2941.1432.5737.4234.88FIG. 5. Same as Fig. 4, but for trial D18.FIG. 4. Same as Fig. 1, but for the randomly distributed thermalsof trial C10. The total number of synthetic data points is 36 000.pattern could be flown in 24–26 min, which we felt wasstill sufficiently short to yield a quasi-stationary, earlyafternoon BL during the three A/D pairs. Figure 10shows the total flight track, of which only the verticalzigzag portions were associated with this RxL subex-periment.There were 12 successful research flights, each ofabout 4.5-h duration for all subexperiments (see Berget al. 1997 for the airborne scientist flight logs). In everyflight two sets of zigzag measurements of horizontalwind and temperature were collected. After quality con-trolling the data, there were only 10 flights that wereadequate for analysis. As for the synthetic data, meanwind and potential temperature were calculated by av-eraging wind and temperature within nonoverlappingbins of 2-m depth and assigned to altitudes at the bincenters. The altitude AGL was measured by two radaraltimeters. The actual lowest altitudes of the slant A/Dlegs varied from 6 to 28 m AGL, depending on flightobstructions near the surface.c. Field resultsA subset of results for Lamont, Winfield, and Meekeris shown in Figs. 11–13. The BLX96 mean wind dataexhibit more scatter than temperature over the wholevertical domain (in the SL, the RxL, and the UL). ForUL winds less than 3 m s21, the data do not show con-sistent profile forms. For faster UL winds, the observed1166 VOLUME 16JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGYFIG. 6. Same as Fig. 4, but for trial E21.FIG. 8. Wind (M) and potential temperature (th) profiles computedafter sorting the raw data into height bins of 2-m depth, and averagingto yield the data points plotted here. Solid lines are the best-fit non-linear regression of the radix layer curves 1 and 2 to the data points.These best-fit lines are so close to the desired (input) profiles thatthey cannot be distinguished. (a) and (b) Trial A01, (c) and (d) A04,and (e) and (f) A05.FIG. 7. An example of the time series of synthetic data as wouldhave been measured at 50 Hz by a virtual aircraft flying a verticalzigzag flight through randomly distributed thermals at horizontalspeed 100 m s21, for trial D19.profiles showed the expected patterns of slower windsnear the surface that smoothly increase until becomingtangent to uniform winds in the mid-ML. For temper-ature profiles, the data exhibited an RxL merging intoa UL and was quite well defined within the UL. Com-paring plotted data from all sites, the Lamont track,which was the flattest and smoothest, had slightly lessscatter.Based on our analysis of the synthetic data, we ex-pected the BLX96 vertical zigzag flights to reach suf-ficiently low altitude to yield a robust sample of theprofile curvature near the bottom of RxL. However, ac-tual terrain conditions and obstructions near the surfaceprecluded measurement at sufficiently low altitude, forsafety reasons. Occasionally at the bottom of some A/Dflights we reached altitudes lower than 10 m, but mostflights were unable to get that low. Measured RxL char-acteristics for BLX96 will be discussed in a separatepaper.Other types of difficulties were found in the BLX96data. For some flights we found that mean values ofSEPTEMBER 1999 1167SANTOSO AND STULLFIG. 9. Same as Fig. 8, except for the randomly distributed thermals.The increased scatter in these data is more representative of the scatterexpected from measurements in the real atmosphere. (a) and (b) TrialD10, (c) and (d) D12, and (e) and (f) D14.TABLE 5. Best fit radix layer parameters to the synthetic data, forevenly distributed thermals. The rows labeled ‘‘input’’ are the desiredparameters for each meteorological set. If there were no samplingerrors, and if the data analysis algorithms contain no errors, then theparameters analyzed from each of the trials should be identical to theinput parameter values for that same meteorological set. The spreadof trial values about the desired input value indicates the experimentalerror that could be expected if this synthetic experiment were repeatedin the real atmosphere, except as recommended in the conclusionssection.Trialzrm(m)zrt(m)MUL(m s21)uUL(K)u0(K)A inputA01A02A03A04A05A06185.0178.0188.0176.0176.1193.0193.032.032.732.432.532.631.831.57.507.517.507.497.497.517.51292.50292.50292.50292.50292.50292.50292.50302.50302.50302.50302.50302.50302.50302.50B inputB01B02B03B04B05B06130.0135.0123.5122.8126.2139.3128.825.023.924.123.825.825.023.76.006.005.996.006.006.016.00285.50285.50285.50285.50285.50285.50285.50290.50290.50290.50290.50290.50290.50290.50TABLE 6. Same as Table 5, but for randomly distributed thermals.Trialzrm(m)zrt(m)MUL(m s21)uUL(K)u0(K)C inputC10C11C12C13C14200.0214.9260.2226.9223.2201.634.038.141.933.639.937.57.507.507.487.517.507.55292.50292.51292.51292.51292.51292.49302.50302.50302.50302.50302.50302.50D inputD15D16D-17D-18D-19245.0177.5214.5279.2222.7314.450.047.654.754.952.262.611.8011.7311.7011.8311.7411.84296.50296.50296.51296.50296.50296.50304.50304.50304.50304.50304.50304.50E inputE20E21E22E23E24150.0149.6115.6113.4155.2124.528.029.122.525.726.825.96.006.025.955.985.985.98285.50285.49285.51285.50285.50285.50290.50290.50290.50290.50290.50290.50wind in the RxL were faster than in the UL, due toeither baroclinicity or sampling error. Analogous errorsof potential temperature being cooler in the RxL thanin the UL were also found. This could have been causedby the fact that the lowest point in the A/D legs were,by chance, over a surface feature that did not have aland use near the median of land uses for that track.Compared to mean wind and potential temperatureprofiles from the synthetic data, the actual values ofmean wind have more scatter, while those for temper-ature have roughly equivalent scatter. Nonetheless, theactual values were sufficiently robust to allow a goodanalysis, considering that some of the real conditionswere far from perfect compared to those of the syntheticcases. As explained previously, in the synthetic casesthe conditions were all ideal, including factors such asa flat homogeneous surface; conservation of mass, heat,and momentum within the horizontal and vertical flightdistances; stationarity during any one flight leg; and noacceleration or deceleration in virtual aircraft’s speed,pitch, and roll. That the real data did not exhibit theseidealized traits suggests that more sophisticated syn-thetic experiments could be developed in the future.d. DiscussionIn the real atmosphere, thermals are distributed some-what randomly, their diameters vary from several hun-1168 VOLUME 16JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGYFIG. 10. (a) Sketch of typical east–west flight pattern during the BLX96 field experiment inOklahoma and Kansas. Solid lines indicate measurement of ML scaling variables, and the dashedlines indicated the vertical zigzag pattern designed for measurement of the radix layer. The long–short dash line was for other subexperiments, and dotted lines represent ascent/descent turnsmade outside the measurement domain. (b) A continuation of (a), which together yield two fullradix layer patterns flown during each aircraft flight. Letters index key points during the flight;for example, a zigzag pattern that travels through points ACDEDCA would be indexed usingtheir starting and ending points as AA. During each flight the key points were encountered inthe following order: S, A, B, A, C, D, E, D, C, A, F, G, H, I, A, S, J, S, K, R, L, R, K, S, N,O, P, Q, S, A, end.dreds of meters to order 1 or 2 km, and they are notuniform in diameter from bottom to top. For randomlydistributed, variable diameter, nonuniform thermals, itwas possible that conservation of mass, heat, and mo-mentum was not satisfied within our finite-length flightlegs. At the time of the experiment it was also possiblethat the thermal coverages were less than those assumed;therefore our modified flight pattern might not have beenlong enough to sample data representatively. Conse-quently, when we calculated averaged mean values inevery bin, the results still contained some scatter, be-cause of the imbalance between the thermal up- anddowndrafts and background air.Also, while the actual flight conditions for any oneflight leg appeared quasi stationary based on visual ex-amination of the real time series, the amount of non-stationarity remaining was nonetheless important com-pared to the stationary synthetic data. However, it shouldbe possible to simulate nonstationary MLs by applyinga time-varying ziin (9)–(11) before sampling with thevirtual aircraft, something worth considering by futureinvestigators.For the real flights, it was difficult to maintain con-stant speed, pitch, and roll, especially in the zigzag flightor when avoiding obstacles such as hills, power trans-mission poles, radio towers, or oil derricks. ThoughSEPTEMBER 1999 1169SANTOSO AND STULLFIG. 11. Same as Fig. 9, but using real wind speed (M) and potentialtemperature (th) data from the BLX96 field program from flights overthe Lamont site. (a) and (b) From 27 July 1996 track SS, (c) and (d)4 Aug 1996 track AA, and (e) and (f) 13 Aug 1996 track SS.FIG. 12. Same as Fig. 11 but for the Winfield site. (a) and (b) From15 July 1996 track SS, (c) and (d) 25 July 1996 track AA, and (e)and (f) 31 July 1996 track AA.most of the intervals of acceleration, deceleration, andmaneuvers have been excluded from our data duringquality control, some errors cannot be excluded totally.Sometimes the aircraft temporarily followed locallysloping terrain, as it descended and ascended in valleysor elevated areas. In this kind of flight, though the air-craft was ascending or descending, the radar altitudemeasurements were not parallel to pressure heights,thereby possibly causing more scatter in the averagedvalues.Comparing the real observations of Figs. 11–13 withthe synthetic observations of Fig. 9, the real data exhibitroughly twice as much spread as the synthetic. The mainreason is that the empirical relationships in the literaturethat were used to generate the synthetic data were basedon observations either at a fixed point (in the case oftower data), or over a surface that was much more hor-izontally homogeneous than was actually observed dur-ing BLX96. Because the BLX96 field experiment wasspecifically designed to gather data over heterogeneoussurfaces, we should have anticipated larger standard de-viations of wind and potential temperature associatedboth with the random small–medium eddies and withthe larger coherent thermal structures.8. Conclusions and recommendationsWe flew a virtual aircraft through synthetic data tohelp design a boundary layer field campaign and to help1170 VOLUME 16JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGYFIG. 13. Same as Fig. 11, but for the Meeker site. (a) and (b) From16 July 1996 track SS, (c) and (d) 28 July 1996 track SS, and (e)and (f) 2 Aug 1996 track SS.test our data analysis algorithms. Our first synthetic ex-periments used evenly spaced thermals and did not ex-hibit the complexity and sampling error that we antic-ipated in real life. A second set of synthetic experimentsincluded more realistic quasi-random spacing and di-ameters of thermals, which we used to design the flightpatterns of the real field program. Perhaps a lognormaldistribution would have been an even better represen-tation of thermal characteristics, and we thus recom-mend its use in future simulations by other investigators.When the real field program BLX96 was flown overOklahoma and Kansas, there were many additional com-plications beyond those anticipated in our simulations,including a heterogeneous surface and a nonstationaryboundary layer. As such complications would probablydiffer from field experiment to field experiment, it isdifficult to make specific recommendations on how toproduce more realistic synthetic experiments. In fact,no matter what level of sophistication is included in thegeneration of synthetic data, there will always be ad-ditional unanticipated complications in real life.Instead, we recommend that a common engineeringapproach be used. We observe that the published tur-bulence standard deviations of (7) and (8) and the max-imum thermal updraft and downdraft perturbations of(3)–(6) are too small by a factor of roughly 2. If in-vestigators wish to simulate a heterogeneous land usesimilar to that under our flight tracks in Oklahoma andKansas, then we recommend that the literature valuesof standard deviation and the thermal perturbations bemultiplied by a factor of 2 before being used to generatesynthetic data.If investigators want a conservative estimate that willlikely work for a wider variety of heterogeneous landuse, then we recommend that a scaling factor of 3 or 4be used instead. This should increase the sampling errorwithin the synthetic time series to hopefully be slightlyworse than real life. Data analysis algorithms that provesuccessful with these degraded data would have a great-er chance of succeeding with actual data.From BLX96 we did gain new insight into the work-ings of the radix layer. These new results will soon bepublished. So in that sense, while our simulation wasfar from perfect, it successfully served its purpose byallowing us to design a useful flight track for real life.In a broader sense perhaps there is more that can belearned, as suggested by one of the paper’s referees:‘‘The authors eventually found that nature tends to con-found the simulator of observational data. While theengineering approach . . . is a practical method for solv-ing a particular problem, I would urge the authors andanyone else . . . to consider the inherent value of theprocess of doing the observation simulations. There maybe useful insights gained by comparing simulated ob-servation behavior with that obtained from real data.Ideally, the process of observation simulation shouldevolve with our improved understanding of atmosphericprocesses.’’Acknowledgments. This research was funded by theU.S. National Science Foundation (NSF) under GrantATM-9411467. The University of Wyoming King Airaircraft is also sponsored by NSF. The Canadian NaturalScience and Engineering Research Council (NSERC)and the Environment Canada Atmospheric EnvironmentService (AES) also provided grant support. The U.S.Department of Energy is gratefully acknowledged fortheir Grant DE-FG02-92ER61361, as well as for theirdata and field support at the Southern Great Plains At-mospheric Radiation Measurement (ARM) program.Josh Hacker provided excellent daily forecasts that wereused for flight planning and served as an airborne sci-SEPTEMBER 1999 1171SANTOSO AND STULLentist, and Larry Berg also served as one of the airbornescientists.REFERENCESAtlas, R., E. Kalnay, W. E. Baker, J. Susskind, D. Reuter, and M.Halem, 1985: Simulation studies of the impact of future ob-serving system on weather prediction. Preprints, Seventh Conf.on Numerical Weather Prediction, Montreal, PQ, Canada, Amer.Meteor. Soc., 145–151.Bell, T. 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