A two-concentric-loop iterative method in estimation of displacement height and roughness length for momentum and sensible heat

ORIGINAL PAPER

A two-concentric-loop iterative method in estimationof displacement height and roughness length for momentumand sensible heat

Wenguang Zhao & Russell J. Qualls & Pedro R. Berliner

Received: 5 January 2008 /Revised: 16 August 2008 /Accepted: 17 August 2008# ISB 2008

Abstract A two-concentric-loop iterative (TCLI) methodis proposed to estimate the displacement height androughness length for momentum and sensible heat by usingthe measurements of wind speed and air temperature at twoheights, sensible heat flux above the crop canopy, and thesurface temperature of the canopy. This method is deducedtheoretically from existing formulae and equations. Themain advantage of this method is that data measured notonly under near neutral conditions, but also under unstableand slightly stable conditions can be used to calculate thescaling parameters. Based on the data measured above anAcacia Saligna agroforestry system, the displacementheight (d0) calculated by the TCLI method and by aconventional method are compared. Under strict neutralconditions, the two methods give almost the same results.Under unstable conditions, d0 values calculated by theconventional method are systematically lower than thosecalculated by the TCLI method, with the latter exhibitingonly slightly lower values than those seen under strictly

neutral conditions. Computation of the average values ofthe scaling parameters for the agroforestry system showedthat the displacement height and roughness length formomentum are 68% and 9.4% of the average height of thetree canopy, respectively, which are similar to percentagesfound in the literature. The calculated roughness length forsensible heat is 6.4% of the average height of the treecanopy, a little higher than the percentages documented inthe literature. When wind direction was aligned within 5 °of the row direction of the trees, the average displacementheight calculated was about 0.6 m lower than when thewind blew across the row direction. This difference wasstatistically significant at the 0.0005 probability level. Thisimplies that when the wind blows parallel to the rowdirection, the logarithmic profile of wind speed is shiftedlower to the ground, so that, at a given height, the windspeeds are faster than when the wind blows perpendicularto the row direction.

Keywords Displacement height . Momentum .

Roughness length . Scaling parameters . Sensible heat .

Two-concentric-loop iterative method

Introduction

The Penman-Monteith equation (Monteith 1963, 1965) hasbeen a very popular equation used in estimation of theevapotranspiration from various vegetation types from crops(Slabbers 1977) to forests (Calder 1977). In order to applythe Penman-Monteith equation, the atmospheric resistancemust be computed (Matejka et al. 2003; R. Crago, R.J.Qualls and W. Zhao, manuscript submitted). In order tocalculate atmospheric resistance, the displacement height andthe roughness lengths for momentum and sensible heat of an

Int J BiometeorolDOI 10.1007/s00484-008-0181-4

The field experiment of this study was carried out during the seniorauthor’s sojourn at the Blaustein Institute for Desert Research, BenGurion University, Israel.

Mentioning of brand names and companies is for the convenience ofreaders only, and does not imply any affiliation or endorsementbetween the authors and that company.

W. Zhao : P. R. BerlinerJacob Blaustein Institute for Desert Research,Ben-Gurion University of the Negev,Sede Boker Campus,84990 Midreshet Ben-Gurion, Israel

W. Zhao (*) :R. J. QuallsDepartment of Biological & Agricultural Engineering,University of Idaho,P. O. Box 440904, Moscow, ID 83844, USAe-mail: [email protected]

underlying surface are required (Mölder et al. 1999; Chenget al. 1999; Dong et al. 2001; Crago et al. 2005; Lin et al.2007). The displacement height and roughness lengths arealso fundamental concepts presented in numerous textbookson fluid mechanics, dynamic meteorology, biometeorologyand physical oceanography (Zilitinkevich et al. 2008). Theyare used widely in aerodynamic modeling of momentum,sensible heat, vapor and flux transfer of carbon dioxide, etc.(Cahill et al. 1997; Song et al. 2000; Mölder and Lindroth2001; Katul and Siqueirab 2002; Aiken et al. 2003; Mahrtand Vickers 2004; Crago et al. 2005; Patel et al. 2006).

The displacement height (d0) and the roughness lengthsfor momentum (z0m) and sensible heat (z0h) can beestimated from wind and air temperature profile measure-ment data. Robinson (1962) and Stearns (1970) describedleast-squares fit methods for estimating d0 and z0m. Lo(1977) proposed an analytical-empirical method for deter-mining these parameters. Kanemasu et al. (1979) suggestedthat the roughness length could be evaluated from theintercept of a plot of logarithm of height [ln(z)] versus windspeed (u).

Most researchers estimate d0, z0m and z0h from datameasured under “near neutral stability” conditions andassume that the estimated d0, z0m and z0h values are validunder both stable and unstable conditions (e.g., Hatfield1989; Kustas et al. 1989; Matthias et al. 1990; Jacovides et al.1992; Tolk et al. 1995; Sauer et al. 1996; Driese and Reiners1997; Suzuki et al. 2002). However, the applicability of thisassumption has seldom been validated or questioned.

In the natural environment, atmospheric stability is mostfrequently either unstable or stable and appears neutral onlyduring transitional periods. Therefore, the quantity of datameasured under real “neutral” conditions is very limited. Inorder to be able to estimate d0 and z0m from a relatively largenumber of data sets, data measured under “near neutralstability” conditions have been used (Matthias et al. 1990;Jacovides et al. 1992; Tolk et al. 1995; Sauer et al. 1996).

The criteria for defining “near neutral stability” is generallybased on stability parameters, such as the Bulk RichardsonNumber (Ri), which is calculated from (Thom 1975):

Ri ¼ g Ta2 � Ta1ð Þ z2 � z1ð ÞT u2 � u1ð Þ2 ð1Þ

where Ta1, Ta2 and u1, u2 are the air temperature (K) andwind speed (m s−1), respectively, at heights z1 and z2 (m); gis the acceleration due to gravity (m s−2); and T is theaverage temperature of the two levels (K).

Although quantifying the magnitude of stability isstraightforward, defining the limits that distinguish “nearneutral stability” from stable and unstable conditions israther subjective. Different researchers have used differentcriteria for defining this limit. Thom (1975) suggests that

neutral stability (fully forced convection) exists only when|Ri|≤0.01. Some researchers use |Ri|≤0.015 as the criterionfor neutral stability (Kustas et al. 1989; Matthias et al.1990). A more relaxed limit of |Ri|≤0.1 was used byHatfield et al. (1985) and Driese and Reiners (1997) fordefining “near neutral stability”.

In this paper, a two-concentric-loop iterative (TCLI)method will be proposed to determine d0, z0m and z0h ofa vegetation canopy by using measurements of windspeed and air temperature at two heights, sensible heatflux above the canopy, and the canopy temperature (Tc).Using this method, d0, z0m and z0h can be estimated notonly for near neutral conditions but also for unstable andmoderate stable conditions. The method will be illustratedwith data measured above an Acacia Saligna forestrysystem. The d0 estimated under near neutral conditionswill be compared with that estimated under unstableconditions.

Theory

The displacement height, roughness lengths for momentumand sensible heat, as well as the stability correction termsand the scaling parameters can be determined through theTCLI method by using the measurements of wind speedand air temperature at two heights, sensible heat flux abovethe crop canopy, and the surface temperature of the cropcanopy.

The wind speed at a certain height above the canopy canbe expressed as:

u ¼ u�k

lnðz� d0z0m

Þ �<m

� �ð2Þ

where, d0 is the displacement height (m), z0m is theroughness length for momentum (m); u and Ψm are the windspeed (m s−1) and the dimensionless stability correction termfor momentum at height z (m), respectively; u* is frictionvelocity (m s−1) and k is von Karman’s constant.

Using the wind speed and stability correction terms formomentum at two heights, we can express the frictionvelocity, from Eq. 2, as:

u� ¼ kðu2 � u1Þln ð z2�d0

z1�d0Þ þ<m1 �<m2

ð3Þ

The Monin-Obukhov length L in the layer between z1and z2 can be expressed as:

L ¼ � raCp u3� Ta1 þ Ta2ð Þ2kgH

ð4Þ

where, ρa is the density of air (kg m−3), Cp is the specificheat of air at constant pressure, and H is the sensible heat

Int J Biometeorol

flux above the canopy. Following Brutsaert (1982), H istaken as positive when the direction of the sensible heatflux is from the surface to the atmosphere. Thus, L ispositive for stable, negative for unstable, and infinitelylarge in absolute value for neutral conditions.

A non-dimensional variable, ζ, is introduced to describethe stability stratification, as:

z ¼ z� d0L

ð5Þ

Therefore, ζ is positive for stable, negative for unstable, andzero for neutral conditions.

The stability correction terms are expressed differentlyaccording to the stability stratifications (see e.g., Garratt1978a, b; Choudhury et al. 1986). For stable and neutralconditions, when ζ ≥ 0, the stability correction terms areoften written as:

< ¼ <m ¼ <h ¼ �5z ð6ÞFor unstable conditions, when ζ<0, they are often writtenas:

<m ¼ 2 lnð1þ X Þ þ lnð1þ X 2Þ � 2 arctanðX Þ þ p2

� 3 ln 2 ð7Þand

<h ¼ 2 lnð1þ X 2Þ � 2 ln 2 ð8Þwhere,

X ¼ ½1� 16z�14 ð9Þ

Therefore, given a displacement height d0, the otherterms u*, L, ζ, X and Ψm, can be calculated iterativelythrough Eqs. 2, 4, 5 and either 6 or 7 and 9 depending onthe value of ζ, until they converge to a constant value,given measurements of u1, u2, Ta1, Ta2 and H. This is theinner loop of the TCLI method.

When the inner loop converges, (i.e., the differencebetween two consecutive values is less than a prescribedvalue), Ψh1 and Ψh2 can be calculated by Eq. 6 or Eq. 8,depending on the atmospheric stability condition, parame-terized either by L or ζ values. The temperature differencebetween the surface of the canopy and the air layer atheights z1 and z2 can be expressed as:

Tc � Ta ¼ T �k

lnz� d0z0h

� ��<h

� �ð10Þ

where, Tc is the canopy temperature of the crops, andT � ¼ H

raCpu�

is the temperature scaling parameter (K).

Using the air temperature and stability correction termsfor sensible heat at two heights, we can express thetemperature scaling parameter, T*, from Eq. 10 as:

T� ¼ � k Ta2 � Ta1ð Þln z2�d0

z1�d0

� �þ<h1 �<h2

ð11Þ

Substituting for T* with HraCpu�

in Eq. 10, and eliminating u*with Eq. 3, we can obtain:

H ¼ � k2raCp u2 � u1ð Þ Ta2 � Ta1ð Þln

z2�d0z1�d0

� �þ<m1�<m2

iln

z2�d0z1�d0

� �þ<h1 �<h2

ihhð12Þ

Rearranging Eq. 12, we obtain:

ln2z2�d0z1�d0

� �þ <m1 �<m2 þ<h1 �<h2ð Þ ln z2�d0

z1�d0

� �

þ <m1 �<m2ð Þ <h1 �<h2ð Þ þ k2raCpu2 � u1ð Þ Ta2 � Ta1ð Þ

H¼ 0

ð13ÞTherefore, when z2>z1, which is our case,

lnz2 � d0z1 � d0

� �¼ �Bþ B2 � 4Cð Þ1=2

2ð14Þ

(Note that when z1>z2, lnz2�d0z1�d0

� �¼

�B� B2�4Cð Þ1=22

should be used). Where,

B ¼ <m1 �<m2 þ<h1 �<h2 ð15Þand

C ¼ <m1 �<m2ð Þ <h1 �<h2ð Þ

þ k2raCpu2 � u1ð Þ Ta2 � Ta1ð Þ

Hð16Þ

It should be mentioned that the other root ln z2�d0z1�d0

� �¼

�B� B2�4Cð Þ1=22

is ignored because it is a negative value and

leads to d0>z2>z1. Similarly, when z1>z2, the other root

ln z2�d0z1�d0

� �¼

�Bþ B2�4Cð Þ1=22

also needs to be ignored

because it is a positive value and leads to d0>z1>z2.

Rearranging Eq. 14, d0 can be expressed as:

d0 ¼z2 � z1 � exp

�Bþ B2�4Cð Þ1=22

" #

1� exp�Bþ B2�4Cð Þ1=2

2

� � ð17Þ

Therefore, a new value of d0 can be calculated by meansof the measured sensible heat flux (H), wind speed (u1, u2)and air temperature (Ta1, Ta2) at two heights above the

Int J Biometeorol

canopy, and the values of the stability correction terms(Ψm1, Ψm2, Ψh1, Ψh2) obtained from the inner loop. Thisprocess is the outer loop of the TCLI method.

Once the new d0 is obtained, it will be used to replacethe old one, and another round of the inner loop starts. Thisprocess is repeated a few times until d0 converges to astable value. By using this TCLI method, Ψm, Ψh, u*, T*, L,ζ, X and d0 can be estimated.

Thereafter, from Eq. 2 we can obtain:

z0m ¼ z� d0

exp k uu�

þ<m

� � ð18Þ

and from Eq. 10, we can obtain

z0h ¼ z� d0

expk Tc�Tað Þ

T�þ<h

h i ð19Þ

By using this TCLI method, d0, z0m and z0h can beestimated not only from data measured under near neutralstability conditions but also from data measured underunstable and moderately stable conditions. Under verystable conditions, e.g., ζ>0.02, this method may be invalid,as the solution does not converge.

Materials and methods

The data used to verify the TCLI method were obtainedfrom a field trial in Israel. The field trial was conductedfrom 11 May to 25 August 1995 at the MashashExperimental Farm, Jacob Blaustein Institute for DesertResearch. The farm is located in the north of the NegevDesert, with an annual precipitation of 96 mm (1971–1990average) distributed mainly in winter from November toFebruary. The experiment was carried out in an AcaciaSaligna agroforestry system in which the trees were plantedin 1990 with a 4 m separation between rows and a 1 mspacing between trees within a row. The row direction was165° clockwise from the north. The average height of thetrees during the experimental period was 5.7 m. The AcaciaSaligna plot was 65 m wide and 200 m long. The long axisis 75° clockwise from the north.

A 7-m-high tower was set up near the southeasterncorner of the plot downstream of the dominant winddirection, and about 5 m from the edge. Therefore, thefetch along the dominant wind direction was at least 60 m.

The air temperature and the vapor pressure gradientsabove the tree canopy were measured using two home-made psychrometers installed in a Bowen ratio system.

The psychrometer was lined with polyurethane boardsinside a plastic frame. The polyurethane board has a verylow sensible heat transfer coefficient so that the sensible

heat load on the sensors can be minimized. Both the outsideand the inside of the psychrometer were covered withaluminum foil with a very high reflectivity and a very lowthermal inertia in order to minimize the radiative heat loadon the sensors. A 12 V, 2.6 W fan was used to ventilate thepsychrometer. A rough check with smoke showed that thewind speed within the psychrometer exceed 4 m s−1. Thedry and wet bulb temperatures were measured using twopairs of copper-constantan thermocouples in the psychrom-eters, one pair of which was wrapped with a wick. A smallreservoir was attached to a Mariotte bottle of water tomaintain a constant water level inside the reservoir. TheMariotte bottle was situated inside the psychrometerbetween the thermocouples and the fan in order to keepthe water away from solar radiation and to block anypossible thermal radiation from the fan to the sensors. Thewet thermocouples were positioned 1 cm above the waterlevel in order to make sure that they could get enough waterthrough the wick without flooding it. The dry thermocou-ples were situated about 4 cm upwind from the wet ones.The thermocouples were calibrated against the averagereadings of 12 pairs of copper-constantan thermocouples.

The Bowen ratio system was composed of two psy-chrometers and a relay controlled mechanism to switchpositions. The positions of the psychrometers wereswitched every 5 min. During the first minute, no measure-ments were made; while during the remaining 4 min, thetemperatures of the dry and wet bulbs were sampled every5 s and averaged over 4 min. The height of the Bowen ratiosystem was changed every week so that the lowerpsychrometer was maintained at 0.3 m above the treecanopy and the upper one 0.6 m above the lower one.

An eddy correlation system (Campbell Scientific Inc.,Logan, UT), composed of a 1-dimensional sonic anemom-eter (CA27) to measure vertical wind speed and a0.0127 mm fine wire Chromel-Constantan thermocouple(127) to measure temperature, was used to measure sensibleheat flux.

Wind profiles were measured using two three-cupanemometers and a wind vane (model 014A and 024Arespectively, Met One Instruments Inc., Grants Pass, OR).The anemometers were mounted at the same heights as thetwo psychrometers in the Bowen ratio system. The winddirection information was used to expunge data from theatmospheric resistance calculation when the fetch was lessthan 60 m.

Leaf surface temperature was measured with eight pairsof fine-wire Copper-Constantan thermocouples attached tothe leaf surface by transparent tape at different locationswithin the canopy. These measurements were averaged intoa single representation of canopy temperature. The mea-surement results were calibrated with an infrared thermom-eter (IRT) for 1 day during the experiment period. The IRT

Int J Biometeorol

measured the average radiative temperature of leaves withinits view angle that aimed at the thermocouples.

An AM416 multiplexer and a CR10 micrologger (bothfrom Campbell Scientific) were used to switch and recordthe signals from the instruments described above. Thesampling rate for the eddy correlation system was 5 Hz(five times per second) and for the other instruments was5 s. The output data were the half-hour averages.

From the above experiment data, good sets of 30-min-average data were selected in which the eddy correlationsystem, the Bowen ratio system, the cup-anemometers andthe fine-wire thermocouples attached to the leaf surfaceswere working properly. The following criteria were alsoused to reject the data:

1 When the wind direction was out of the range between255° and 345° clockwise from north due to insufficientfetch.

2 When the average wind speed in the lower measurementheight (6.0 m height) was less than 1 m s−1 (thethreshold of the 014 A Met-One cup anemometers was0.447 m s−1).

Results and discussion

The displacement height d0, roughness length for momen-tum z0m and sensible heat z0h were calculated from the goodsets of data using the TCLI method. As calculation of thez0m and z0h via conventional methods requires extensivemeasurement of wind speed profiles, air temperatureprofiles and other parameters, we will discuss displacementheight d0 in detail in this research, while the roughness formomentum and sensible heat will be compared with valuespublished in the literature.

The calculated displacement height d0 is plotted againstthe Bulk Richardson Number, Ri (open circles in Fig. 1).The average value of d0 is 3.86 m (with a standarddeviation of 0.41 m), which is 68% of the average treeheight (5.7 m). The maximum and minimum value of d0 are5.23 m and 2.64 m, respectively.

A stricter criterion than is typically cited in the literature,−0.005≤Ri≤0.005, was used in this analysis to ensure thatthe data represented neutral stability. A total of 104 datapoints satisfied this criterion. Each point was used tocalculate d0 by both the TCLI method and the conventionalmethod. The results are depicted in Fig. 2. From Fig. 2, wecan see that, under strictly neutral conditions, the d0 valuescalculated by the TCLI method and the conventionalmethod are very close to one another, with averages of4.13 m and 4.10 m, respectively, and standard deviations of0.58 m and 0.59 m, respectively. A two-sample t-testperformed between the d0 values calculated by the TCLI

and conventional method showed no significant differencebetween their means at a significance level of 0.25.

Figure 3 depicts the comparison of d0 values calculatedby the TCLI method and by the conventional method fromdata obtained under near neutral conditions (−0.015≤Ri<−0.005). There were 133 data points in this group. Themean values of d0 calculated by the TCLI method and theconventional method were 3.87 m and 3.74 m, respectively.Their standard deviations were 0.42 m and 0.45 m,respectively. A two-sample t-test performed between thed0 values calculated by the TCLI and conventional methodsrevealed a significant difference between their means evenat the 0.0005 significance level. It can also been seen fromFig. 3 that d0 calculated by the conventional methodbecomes systematically lower than d0 calculated by theTCLI method as atmospheric stability moves further awayfrom neutral conditions. This difference is most pronouncedunder unstable conditions, e.g., Ri<−0.015, (see Fig. 4),where the conventional method was applied as if under nearneutral conditions. There were 313 data points measuredunder this category. The d0 means calculated by the TCLImethod and the conventional method were 3.77 m and3.04 m, respectively. Their standard deviations were 0.29 mand 0.55 m, respectively. The large difference between theTCLI method and the conventional method is expectedbecause, theoretically, the latter method is not applicableunder unstable conditions.

It can been seen from Fig. 4 that |Ri|≤0.1, used byHatfield et al. (1985) and Driese and Reiners (1997) fordefining near neutral conditions, is not a good criterion, atleast under unstable conditions. When Ri=−0.1, the d0values calculated by the conventional method are lower, bymore than 1 m, than those calculated by the TCLI methodor the d0 values calculated under strict neutral conditions. Incontrast, the TCLI method showed only a small variationbetween the d0 values calculated under neutral and unstableconditions.

Only three data points were successfully calculated viathe TCLI method under stable conditions (e.g., Ri>0.005).Two reasons may be given for this data scarcity. The first—and main—reason was that most of the measurement dataunder stable conditions were eliminated because the half-hour-average wind speeds at the first level were less than1 m s−1. The second reason was that the TCLI methoddiverged when used to calculate data measured under stableconditions. The d0 means calculated by the TCLI methodand the conventional method for these three data pointswere 3.69 m and 3.77 m, respectively. Their standarddeviations were 0.34 m and 0.33 m, respectively.

Comparing the d0 means calculated under strictly neutral(−0.005≤Ri≤0.005), near neutral (−0.015≤Ri<−0.005) andunstable (Ri<−0.015) conditions, it seemed that the d0means decreased as the atmospheric stability changed from

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neutral to unstable. Two-sample t-tests were performedbetween any combination of d0 means calculated under thethree atmospheric stability conditions, and differencesbetween any two means were significant (at the 0.005significance level). This may imply that d0 values may varywith atmospheric stability conditions. If this is true, theassumption made by numerous researchers that d0 valuescalculated under neutral conditions may be used in unstableconditions, may not be valid.

The roughness length for momentum (z0m) and sensibleheat (z0h) were also calculated from the data measuredabove the agroforestry system. The average value of z0m is0.534 m, which is 9.4% of the average tree height. The

maximum and minimum value of z0m are 0.222 m and1.423 m, respectively, with a standard deviation of 0.190 m.The average value of z0h is 0.366 m, which is 6.4% of theaverage tree height. The maximum and minimum value ofz0h are 0.004 m and 0.817 m, respectively, with a standarddeviation of 0.200 m. The z0h value, as an average, is about2/3 of the z0m value.

It is interesting to examine the influence of the winddirection on the displacement height d0 values calculatedvia the TCLI method. Figure 5 shows their generalrelationship. In Fig. 5, the horizontal axis is the anglebetween the direction of wind and the direction of row inthe agroforestry system, and the vertical axis is d0. On the

0

1

2

3

4

5

6

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1

Richardson Number (Ri)

Dis

plac

emen

t H

eigh

t (m

)

d0 calculated with TCLI method

Fig. 1 The displacement height d0 plotted against the Bulk Richardson number (Ri)

0

1

2

3

4

5

6

7

-0.005 -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004 0.005

Richardson Number (Ri)

Dis

plac

emen

t Hei

ght (

m)

d0 calculated with TCLI method

d0 calculated with conventional method

Fig. 2 Comparison of d0 calcu-lated by the two-concentric-loopiterative (TCLI) method and theconventional method underneutral conditions

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horizontal axis, 0° means that the wind blew parallel to therow direction, i.e., 345° clockwise from the north, and 90°means that the wind blew perpendicular to the rowdirection, i.e., 255° clockwise from the north. Actually, allwind speeds measured with the lower cup anemometerfrom 255° to 275° clockwise from the North, were less than1 m s−1 and were expunged from the data set. From Fig. 5,we can see that when the wind direction deviates less than5° from the row direction, the d0 values calculated via theTCLI method were smaller compared to the d0 valuescalculated at other wind directions.

In order to analyze the difference more quantitatively,the angles between the wind direction and the direction of

row were divided into 14 groups, in successive 5°increments. The number of samples, average values,standard deviation, and maximum and minimum values ofd0 in each group are reported in Table 1. It can be seen fromTable 1 that when the wind direction was within 5° of therow direction of the trees, the d0 average calculated via theTCLI method was about 0.6 m lower than the overall meand0 shown in the last row. A t-test showed that the averagevalue of d0 for wind-row angle differences in the 0–5°group, which was equal to 3.30 m, was significantly smallerthan the overall mean value of d0, which was equal to3.86 m, at the 0.0005 significance level. None of the otherwind–row angle groups had d0 values that were statistically

0

1

2

3

4

5

6

7

-0.515 -0.415 -0.315 -0.215 -0.115 -0.015

Richardson Number (Ri)

Dis

plac

emen

t Hei

ght (

m)

d0 calculated with TCLI methodd0 calculated with conventional method Ri=-0.1

Fig. 4 Comparison of d0 calculated by the TCLI method and the conventional method under unstable conditions

0

1

2

3

4

5

6

7

-0.015 -0.014 -0.013 -0.012 -0.011 -0.01 -0.009 -0.008 -0.007 -0.006 -0.005

Richardson Number (Ri)

Dis

pla

cem

ent

Heig

ht

(m)

d0 calculated with TCLI methodd0 calculated with conventional method

Fig. 3 Comparison of d0 calculated by the TCLI method and the conventional method under near neutral conditions

Int J Biometeorol

different from the overall mean, even at the 0.01 signifi-cance level. This makes sense because when wind blowsalong the row direction, more air flows between the rows oftrees. Conversely, when the wind blows across the rowdirection, the crowns of the trees act as a windbreak andshift the wind profile upward, away from the canopy.

Comparison with the literature

For the sake of simplicity in sensible and latent heat fluxmodels, and when only limited or no profile data exist, thedisplacement height and roughness lengths are oftenestimated as fixed fractions of the average vegetation height(h). Choudhury et al. (1986) calculated the fraction forwheat as:

d0 ¼ 0:56h and z0m ¼ 0:13h

while Brutsaert (1982) gave nearly the same fraction forz0m (=1/8 h), but a larger fraction for d0 (=2/3 h). Theseproportions are thought to be satisfactory for a broad rangeof vegetation types (Kustas et al. 1989). Monteith (1973)presented the relationship as d0=0.63 h, and the same valueas Choudhury et al. (1986) for z0m (=0.13 h). Kanemasu etal. (1979) suggested that the surface roughness length z0mfor dense plant canopies is 0.12–0.14 of the average cropheight, and the zero displacement height d0 is about 70% ofthe average crop height. From a review of the literature,Matthias et al. (1990) reported rough estimates of d0 as0.66 h and z0m as 0.1 h. Garratt (1992) noted that 0.66 h isprobably a reasonable estimate of d0 for crops and forests,although the value may approach zero for sparse vegeta-tions and 1 h for dense smooth canopies. He also stated that0.1 h could be a rough estimate of z0m although, based on

an extensive review of the literature (Garratt 1992), itsrange can vary from 0.02 h to 0.2 h for natural surfaces.The d0 and z0m values calculated by the TCLI methodpresented here from our experimental data are 0.68 h and0.094 h, respectively, which are compatible with valuesfound in the literature.

The roughness length for sensible heat z0h is lessdocumented than z0m and is usually estimated as a fractionof z0m, especially for forests. Brutsaert (1982) noted that theratio (z0h/z0m) displays less change for most grassy or tree-

Table 1 Statistical results for displacement height calculated fordifferent angles between wind and rows (unit: m)

Windrowangle(degrees)

Numberofsamples

Mean Standarddeviation

Maximumvalue

Minimumvalue

0–5 36 3.30 0.39 4.08 2.645–10 24 3.82 0.40 4.58 3.0210–15 24 3.92 0.32 4.68 3.2015–20 20 3.73 0.32 4.51 3.2420–25 21 3.84 0.27 4.44 3.3825–30 46 3.90 0.38 5.21 3.1630–35 66 3.75 0.32 5.14 2.9635–40 77 3.87 0.38 4.97 3.0840–45 87 3.94 0.38 5.08 3.3045–50 75 4.03 0.43 5.23 3.1950–55 42 4.04 0.41 5.11 3.3555–60 16 3.97 0.41 5.11 3.3360–65 15 3.85 0.47 4.99 3.2565–70 4 3.85 0.30 4.22 3.510–70 553 3.86 0.41 5.23 2.64

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80 90

Angle between wind and row direction (Degrees)

Dis

plac

emen

t hei

ght (

m)

Fig. 5 The relationship of d0 calculated by the TCLI method and the angle between the wind direction and the direction of rows

Int J Biometeorol

covered surfaces than it does for surfaces with bluffroughness. He suggested that the ratio for tall trees is onthe order of 1:3 to 1:2 (Brutsaert 1982). From the z0h andz0m values obtained with our experimental data, the averageratio is close to 2:3.

Conclusions

The TCLI method proposed in this study uses measure-ments of wind speed and air temperature at two heights,sensible heat flux above a crop canopy and the surfacetemperature of the canopy to estimate the displacementheight and roughness lengths for momentum and sensibleheat. The TCLI method was developed on the basis ofexisting formulae and was validated for the computation ofthe scaling parameters for an Acacia Saligna agroforestrysystem. The main advantage of this method is that not onlydata measured under near neutral conditions, but also datameasured under unstable and slightly stable conditions canbe used to calculate the scaling parameters.

Comparison of the calculation results of displacementheight d0 using the TCLI method and the conversionalmethod showed that:

1 Under strict neutral conditions (−0.005≤Ri≤0.005), thed0 values calculated by the TCLI method and theconventional method are practically the same.

2 Under near neutral but slightly unstable conditions(−0.015≤Ri<−0.005), the d0 values calculated by theconventional method are systematically lower than thatcalculated by the TCLI method, although the differencecan be quite small.

3 When Ri<−0.015, the d0 values calculated by theconventional method are much lower than thosecalculated by the TCLI method or those calculated fromthe strict neutral data. |Ri|≤0.1 is not a good criterion fordefining “near neutral conditions” in calculation of thescaling parameters.

4 The d0 means seemed to decrease as the atmosphericstability changed from neutral to unstable. This mightimply that d0 values vary with atmospheric stabilityconditions and that the assumption used by numerousresearchers, that the d0 calculated under neutral con-ditions can be extended for use under unstable con-ditions, may not be valid.

When wind direction was within 5° of the row directionof the trees, the average value of d0 was about 0.6 m smallerthan when wind blew across the row direction. This impliesthat when the wind blows parallel to the row direction, thelogarithmic profile of wind speed is shifted lower to theground, so that, at a given height, wind speeds are fasterthan when the wind blows transverse to the row direction.

Acknowledgments This research was partially supported by theGerman–Israeli Science agreements [Project Number: 01314 (GR)DISUM 00028 (MG)] and partially supported through the NSF-IdahoEPSCoR Program. We wish to thank the late Arieh Rogel and YossiGoldstein (Mashash Farm, Ben-Gurion University of the Negev,Israel) for their technical support.

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