Spatial variability of turbulent fluxes and roughness lengths in HAPEX-MOBILHY

S P A T I A L V A R I A B I L I T Y OF T U R B U L E N T F L U X E S A N D

R O U G H N E S S L E N G T H S IN H A P E X - M O B I L H Y

L. M A H R T and M. EK

Oceanic and Atmospheric Sciences, Oregon State University, Corvallis OR 97331, USA

(Received in final form 7 January, 1993)

Abstract. Surface-based and aircraft measured fluxes over the heterogeneous surface in HAPEX- MOBILHY are analyzed for the ten flight days when cloud cover above the boundary layer was minimal. The fair-weather climatology of the spatial variation of surface fluxes is estimated to provide an assessment of the generality of previous case studies appearing in the literature. For the 10-day averages, greater heating over the forest generates a forest breeze which leads to rising motion and a modest increase of boundary-layer cloud cover at the forest edge.

The exchange coefficients and effective roughness lengths are computed for local averages (15 km scale) and for regional averages (100 km scale) intended to represent a range of grid sizes in numerical models of the atmosphere. The effective roughness length for momentum over the mixed agricultural region for both scales is on the order of 1 m, apparently due to bluff roughness effects associated with scattered trees, edges of small woods and other obstacles. This roughness length value is an order of magnitude larger than values used in numerical models for the same region, which are based on the dominant vegetation type. The spatially varying effective roughness length for heat is computed for use in those models which use surface radiation temperature to estimate surface heat flux. The effective roughness lengths for heat are found to be smaller than those typically used in numerical models of the atmosphere.

1. Introduction

One of the primary goals of HAPEX-MOBILHY (Andr6 et al., 1988, 1989, 1990) is to study subgrid variability of land surface processes for application to large- scale models. Better understanding of the response of boundary-layer fluxes to surface variability may help improve parameterization of subgrid variability in large-scale models.

The main aircraft flight track in the HAPEX-MOBILHY domain traverses a flat pine forest (leg H-G, Figure 1), relatively flat mixed agricultural land (leg G- F) and hilly agricultural land (leg F-E). The blending height (Mason, 1988; Claussen, 1990; Wood and Mason, 1991) for such heterogeneity would theoretically be above the boundary layer and therefore not relevant. Within each region, additional surface heterogeneity occurs simultaneously on a variety of smaller scales including scales too small to allow adjustment of the flow to local surface conditions. Since the heterogeneity occurs simultaneously on a variety of spatial scales, existing parameterizations of surface fluxes are not formally justified, although alternative modelling possibilities are not available. In fact, the equilibrium concepts of surface layers and roughness or interfacial sublayers (see Brutsaert, 1982) cannot everywhere be defined. However, these conditions are typical of the earth's surface.

Boundary-Layer Meteorology 65: 381-400, 1993. �9 1993 Kluwer Academic Publishers. Printed in the Netherlands.

382 L , M A H R T A N D M , E K

HAPEX-MOBILHY

-1.0

Fig. 1.

-0.5 0.0 LONGITUDE 0.4

0 l0 20 50 i00 km

The observational domain and aircraft flight pattern, the forest tower (+), and irrigated (unirrigated) SAMER stations indicated by solid (open) circles.

The present study will examine the spatial variability of observed surface fluxes by including all of the ten fair-weather days in H A P E X - M O B I L H Y where low- level flights were flown across the three regions and cloud activity was essentially absent above the boundary layer. Most of the previous investigations undertaken within H A P E X - M O B I L H Y have been detailed case studies and model comparisons for 16 June 1986 (see Noilhan et aL, 1991; Bougeault et al., 1991; and references therein) and have mainly emphasized differences of various terms in the surface energy balance between the forest and agricultural regions. The following study will show that conclusions based on these previous case studies also Seem to apply to the 10-day "climatology" of surface fluxes. The present study will also

S P A T I A L V A R I A B I L I T Y OF T U R B U L E N T F L U X E S 383

include estimation of momentum fluxes, surface drag coefficients and surface roughness lengths.

We also analyze six 120 km flights about 125 m above the pine forest flown on each of two fair weather days, 19 and 25 May, 1986 (Mahrt, 1991a,b). These two days provide a large sample size allowing evaluation of the relatively subtle heterogeneity associated with clearings and variable tree height. We briefly analyze these two days first.

2. Pine Forest

The aircraft flight level of 125 m is above the forest roughness sublayer (Mazaudier and Weill, 1989; Parlange and Brutsaert, 1989, 1993). However the flight level is not above the influence of clearings and systematic variations of tree height. To study the influence of this variability, turbulence quantities are "mathematically" defined as high pass values using a 4-pole Tangent Butterworth filter with a 5 km cutoff wavelength. The spatial scale of the clearings varies but is typically on the order of one kilometer.

The clearings exert a modest influence on the atmospheric statistics at 125 m above the pine forest (Mahrt, 1991a). In some cases the aircraft flight traversed too close to the upwind boundary of the clearing for the atmospheric observations to be affected by the clearing. Furthermore, the horizontal scale of the main eddies is about 500 m at the aircraft level and therefore not small compared to the scale of many of the clearings. As a result, the eddies at this level partially integrate influences from the individual clearings and the surrounding forest.

In the following calculations, surface conditions are represented by the aircraft- measured surface radiation temperature and the surface elevation measured by the difference between the pressure altitude and radiometric altitude. This difference gives a measure of the effective surface elevation. High pass variations of this difference are dominated by variation of tree height verified from downward- looking video pictures. Since the downward-looking radio altimeter sees both the trees and ground surface between individual trees, the measured "effective" elevation is somewhere between the canopy height and the ground surface. The aircraft-measured surface temperature appears cooler over the trees compared to over the clearings because the surface radiation temperature measured over the trees is strongly influenced by the canopy top temperature, which is cooler than the bare ground surface in the clearings. However, air temperatures at the forest canopy top are warmer than at the same level over the clearings. On a larger scale, this radiative feature was found in Bougeault et al. (1991) with respect to variations between the forest and outside the forest.

All correlations were weaker on 19 May and are not discussed further. On 25 May, the higher temperature over the mature pine trees compared to that over the clearings leads to a correlation of 0.46 between air temperature and effective surface height. Drier air over the mature pine trees leads to a correlation of -0.54

3 8 4 L. M A H R T A N D M. EK

between specific humidity and effective surface height. Therefore the clearings and variable tree height explain about 25% of the temperature and moisture variances. Since these correlations are based on a total of 720 km of flight path, the correlations are significant even though the clearings are not large enough for the turbulence to reach equilibrium. For reference, the r;m.s, values of the air temperature variation along the flight leg average about 0.25 K while the r.m.s. values of specific humidity average about 0.35 g/kg. The momentum field shows little correlation with the location of the clearings.

Attempts to align the repeated flight legs in order to construct statistics for individual clearings of different sizes largely failed partly due to some shift in the flight path between the flight runs. Future experiments need a more sophisticated ground marker system for execution of the flights along the same exact path.

3. Mixed Surface Regimes

3.1. MEASUREMENT ERRORS

The principal source of data for this study is low-level aircraft fluxes systematically computed by Hildebrand (1988) using a high pass filter with an approximately 15 km wavelength followed by block averaging of overlapping 10 km intervals to produce values every 5 km. Each of the ten days contains three executions of the flight pattern (Figure 1) at about 100 m above mean surface height.

We shall also use fluxes and radiation values measured near the surface on the forest tower described in Gash et al. (1989) and from the HAPEX-MOBILHY surface mesonet (SAMER stations, Andrd et al . , 1988). Errors in the tower-based estimates of latent and sensible heat fluxes are discussed in Shuttleworth et al.

(1988). The SAMER latent heat fluxes are thought to be too large since they were computed as a residual and the soil heat flux is significantly underestimated (Goutorbe, 1991; Ben Mehrez et a t . , 1992). Additional SAMER errors include net radiation discrepancies and problems of estimating vertical gradients for the heat flux due to the influence of the roughness or transition sublayer (Goutorbe, 1991). This study uses recalibrated radiation data. See Andr6 et al. (1990) for a quantitative analysis of the SAMER errors.

Estimation of sampling errors for the aircraft data using the coherent structure method (Mahrt and Gibson, 1992) indicates that turbulence flux errors for a given flight leg are on the order of 10-20% due to inadequate record length. Hildebrand (1991) applied the integral scale method and estimated turbulence flux sampling errors to be typically on the order of 20%. Flux errors at a given point for a given flight leg are larger. The present study composites values over 30 flight legs in which case the compositing reduces the random errors. A formal analysis of this error reduction is not definitive since the flux values come from different situations

S P A T I A L V A R I A B I L I T Y O F T U R B U L E N T F L U X E S 385

on different days. We have found that the flux due to "mesoscale" motions (larger than 15 km) is generally unimportant for these data.

Based on averages over the five fair-weather days on which both aircraft and all of the surface observations are available, aircraft-measured downward solar radiation is approximately 50 W/m z greater than the recalibrated radiation data from the SAMER surface network. Aircraft-measured upward shortwave radiation is about 50 W/m 2 less than that measured at the surface. This difference appears to be at least partly instrumental although some of the difference could be radiative flux convergence below the aircraft level. Fortunately, the spatial variation of aircraft- and surface-based solar radiation qualitatively agree. Andr6 et al. (1990) also found greater downward solar radiation for the aircraft as well as discrepancies between the SAMER and aircraft-measured upward longwave radiation data. The

average of the difference between the aircraft and SAMER-measured upward longwave radiation appears to be small for the data used in this study.

Comparisons of aircraft flux measurements with surface-based measurements over heterogeneous terrain should always yield differences since the aircraft fluxes are based on spatial averages while surface-based fluxes are measured at a point. The aircraft latent heat fluxes are about 50 W]m 2 smaller than those from the forest tower while the aircraft-measured sensible heat fluxes are about 100 W/m 2 smaller than the values for the forest tower (Figure 2). Part of the heat flux difference may be due to the fact that the aircraft fluxes include the influence of clearings, which appear to have weaker heat flux, particularly those which contain irrigated crops. A small part of the difference (about 20 W/m 2) may be due to the usual systematic decrease of the turbulent heat flux with height. This systematic height-dependence does not occur for the moisture flux (Mahrt, 1991b). Andr6 et

al. (1990, their Figure 2), for a different set of days, found that aircraft sensible and latent heat fluxes both averaged about 50 W/m 2 smaller than those obtained from forest tower measurements.

Comparison of the aircraft fluxes with surface SAMER fluxes (Figure 2) shows much smaller moisture fluxes for the aircraft while the aircraft sensible heat fluxes are more comparable to values estimated at the surface. This discrepancy between aircraft and surface fluxes is probably partly due to the fact that the aircraft fluxes encompass a wider variety of surface conditions including deciduous forests and hilltop grasslands (Andr6 et al . , 1990). Some of the SAMER stations are located at irrigated sites (Figures 1-2). The difference between surface-based and aircraft- measured fluxes could also be partly due to horizontal advection in the layer between the aircraft level and the surface although such an effect probably does not explain the large systematic differences. Underestimation of the latent heat fluxes by the aircraft is suspected in Shuttleworth (1991). However, since the aircraft latent heat fluxes compare better with the forest tower measurements and since the SAMER latent heat fluxes are computed as residual values, definite conclusions cannot be made.

386 L . M A H R T A N D M , E K

600

W/m 2

�9 Latent (mean values)

SAMER irrigated uairrigated 400

aircraft

�9 S e n s i b l e ~ (mean values)

SAMER unirrigated 2 0 0 irrigated aircraft

forest tower/ SAMER _~'~

irrigated A �9 unirrigated a o

&

A A & a A

o Latent (aircraft)

Sens ib le (aircraft)

, �9 ~ ~

SAMER station .g

0

I ' ' ' ' l , ' ' '

25 50 75 ~ !25 150 distance (km)

Fig. 2. Comparison between aircraft-measured fluxes and the forest tower data and the SAMER surface data for both irrigated and non-irrigated sites for the 5 fair-weather days on which all sets Of observations are available, Horizontal lines to the left of the graph indicate averaged values for the

aircraft data and respective classes of SAMER station values.

3.2. SPATIAL VARIATION

The aircraft-measured surface elevation plotted in Figure 3 shows the hilly region on the left, the mixed agricultural region in the middle and the flat pine forest on the right. The variables from Hildebrand (1988) are composited from the 30 low- level flights on the 10 fair-weather days. The composited albedo is lower over the pine forest, which appears as a darker surface. The boundaries of the pine forest viewed in terms of the composited variables are smoothed by the spatial averaging intrinsic in the filtering.

The composited downward shortwave radiation exhibits a small local minimum over the southern part of the pine forest (Figure 3), which appears to be associated with increased frequency of clouds. This location is also characterized by rising motion when compositing over the 30 flight legs (Figure 4). While the spatial distribution of vertical motion is noisy, rising motion occurs over the southern part of the forest and/or the northern edge of the forest on most of the individual


900

W / m 2

8OO

downward s h o r t w a v e ~ ation / - - - - - ~

t

700 ~ ~ ~ .0.15

terrain height ")~l

7 o , , , . . . . . ,

0 25 50 75 100 125 150 E F G H

distance (km) Downward solar radiation and albedo for the ten fair-weather days (30 flight runs). The

surface terrain height is digitized at 1 km intervals.

250

200

150 m

100

5O

Fig. 3.

days. However, the small sample of ten days does not allow examination of the relationship of the vertical motion field to the synoptic pattern. We believe that the rising motion over the edges of the forest is associated with convergence associated with the forest breeze. This circulation is generated by greater heating of the air over the forest (Figure 4). This forest breeze circulation is predicted by the numerical simulations of Andr6 et al. (1989), Pinty et al. (1989), Bougeault et

at. (1991) and Bechtold et al. (1993). The forest breeze observed here appears to be stationary and does not propagate with a frontal boundary as occurs in sea breeze flows. Bechtold et al. (1993) suggest that this is because the forest breeze is embedded within a deep turbulent layer in contrast to the sea breeze circulation. Apparently the weak temperature deficit of the forest breeze is quickly eliminated by strong vertical mixing over the forest.

While the spatial pattern of vertical motion is noisy, several additional features are suggested by the composited flow. Weak local sinking motion occurs in the northern part of the forest, perhaps coincidentally near a region of a family of clearings, indicated by smaller symbolic trees in Figure 4 (see Noilhan et al . , 1991 for a more detailed map of the clearings). Rising motion also occurs over the hilly

3 8 8 L . M A H R T A N D M , E K

9.0

g/kg 8.0

31.0

29.0

27.0

C

20.25

20.00

19.75

19.50

T

specific humidity

0 25 125 I50 E H

-+0.04

m/s 0.00

-0.04

50 75 100 F G

distance (km) Fig. 4. Composited potential temperature, surface radiation temperature, specific humidity and lin-

early detrended vertical motion for the ten fair-weather days.

region in the south while significant subsidence occurs as the flow descends down into the Adour river valley (point F, Figure 4).

Since the rising motion occurs primarily at the edge of the forest and the air temperature is a maximum over the interior of the forest, the vertical heat trans- port induced by the forest breeze is small. The forest breeze is probably generated by lower pressure over the forest induced by the warmer air which in turn is associated with greater surface heat flux (Figure 5). The heat flux over the forest is about 50 W / m 2 greater compared to the agricultural lands while the latent heat flux is about the same over the two regions. This qualitatively agrees with the modelling study of Mascart et al. (1991) and is similar to the case study of Noithan et al. (1991). The greater heating over the forest in the present study appears to be due mainly to smaller heat flux into the soil and lower albedo over the forest (Figure 3) and slightly smaller upward longwave radiation. The slightly weaker outgoing longwave radiation is due to the higher mean height of the radiative surface above the ground surface corresponding to cooler temperatures compared to the ground surface and low vegetation outside of the forest (Figure 4). However, due to larger cloud cover over the forest, particularly the southern edge, the net

SPATIAL VARIABILITY OF TURBULENT FLUXES 389

600

W/m 2

400

200

Fig. 5,

Net R a d i a t ~ ~

Latent heat flux

Sensible heat flux

0 , , , 0 25 5 0 75 I 0 0 125 a s 0

E F G H

distance (km) Composi ted net radiation, latent hea t flux and sensible heat flux (W/m 2) for the ten fair-

weather days.

radiation over the forest appears to be, at most, a few tens of W / m 2 greater than outside the forest. This underscores the importance of the smaller heat flux into the forest soil which is partly due to shading of the ground surface by the forest canopy and partly due to smaller thermal conductivity of the drier sandy soil in the pine forest. The heat flux into the soil (not shown) in the forest clearing (Lubbon, unirrigated, no shading affect) averages about one third of the average value for the unirrigated SAMER stations outside the forest. The fact that the Bowen ratio is greater over the forest is presumably related to the stomatal control of the pine trees. One must caution against generalizing the above results to other flow situations. For example, Segal et al. (1989), Segal and Arritt (1992) and Hadfield et al. (1992) show how even weak ambient flow may eliminate circulations driven by surface heterogeneity, particularly on smaller scales.

4. Momentum Flux

The vertical velocity variance is about 40% greater over the forest and hilly region compared to that over the mixed agricultural regions (Figure 6). The momentum

0 m

-100 Obukhov length

-200

1.2

(m/s) 2

1.0

0.8

Fig. 6.

7

390 L, MAHRT AND M. EK

0.03

0.02

0.01

0.4

(m/s) 2

0.2

: 0.0 150 H

i i i

0 25 50 75 100 125 E F G

distance (km) Composited Obukhov length, drag coefficient, surface friction velocity and magnitude of the

momentum flux for the ten fair-weather days.

flux is about 50% greater over the forest compared to that over the agricultural lands. The aircraft momentum fluxes averaged over the 5 aircraft days where tower momentum fluxes were available (not shown), agree within a few percent of the averaged tower momentum fluxes even though the tower does not extend above the forest roughness sublayer. This agreement is also noted in the case study of Noilhan et al. (1991).

In the following analysis, we estimate the drag coefficient and effective roughness length for momentum by substituting the measured momentum fluxes into surface-layer similarity relationships. The intention is not to justify application of similarity theory to heterogeneous terrain but rather to compute that roughness length for which similarity theory would yield the observed area-averaged momentum fluxes. Numerical models of the atmosphere are forced to apply such similarity theory regardless of the complexity of subgrid variations.

The drag coefficient Co is estimated from the observed aircraft momentum fluxes as

C D = u * 2 / U 2 (la)

SPATIAL V A R I A B I L I T Y OF T U R B U L E N T FLUXES 391

and related to the effective roughness length through the usual similarity relationship as

CD = K2[ln((z -- d)/zo, eft) - - t o m ( Z / L ) ] - 2 (lb)

where U is the wind speed determined from the low-pass wind components, u* is the friction velocity and L is the Obukhov length, all computed at level z, the height of the flight level above ground determined from the radio altimeter; d is the displacement height assigned a value of 15 m over the forest and 1 m over the mixed agricultural region (see Mascart et al., 1991 for a more detailed breakdown). Because the aircraft is about 100 m above the surface, the results are not sensitive to the values of the displacement height. As recommended by Fazu and Schwerdt- feger (1989), distinction is not made between displacement heights for heat and momentum. The stability function tOm(Z/L) is from Paulson (1970) based on the Businger-Dyer relationships. The effective roughness length Zo.eff is computed from (lb) after estimating the other variables from the aircraft data. This effective roughness length is not necessarily compatible with specific definitions of the effective roughness in previous papers (Wieringa, 1986; see Claussen, 1990 for a survey). Since the roughness length is computed from momentum fluxes which have been horizontally averaged (by means of the low pass filter), the computed roughness length includes significant form drag or bluff roughness effects from isolated or scattered obstacles as is discussed further below. This is in contrast to aggregated roughness lengths computed from some sort of average of the roughness lengths for the dominant surface types of the averaging area.

In this study, the averaged value of the drag coefficient and the Obukhov length are computed in two ways. First, flux magnitudes and the wind speed at a given spatial location are averaged over all of the flights at that location and then the ratios corresponding to the drag coefficient and the Obukhov length are computed from the averaged values. This method can be physically ambiguous since the averaging incorporates many different situations before computing the ratios. However, this method is statistically more sound because it avoids direct averaging of ratios. The second method computes the Obukhov length and drag coefficient for each flight, at each location, and then averages these quantities over all of the flights at a given location. This second method is physically more meaningful but involves the statistical problem of averaging ratios. The results for the second method are quite noisy due to outlying values of the ratios often associated with small values of the denominator. We therefore report results only from the first method.

In order to examine the dependence of the effective roughness length on the choice of similarity theory, we also compute the roughness length by substituting the values of the measured variables into the Louis (1979) formulation for surface fluxes. This calculation requires iteration and evaluation of the surface-layer Rich- ardson number based on the surface radiation temperature. The resulting values of the roughness length are about a factor of two smaller than those values based

392 L . M A H R T A N D M . E K

In

3.0

2.0

1.0

0.0

roughness length (momentum)

Paulson (1970)

Louis (1979)

0 25 50 75 100 125 150 E F G H

distance (km) Fig. 7. Effective roughness lengths for momentum (15 km scale) composited over the ten fair-weather days using the similarity approaches of Paulson (1970) and Louis (1979); the solid horizontal lines indicate the spatial averages of these values. The dashed horizontal lines are the averages of the values of the roughness lengths based on fluxes averaged over the entire flight leg (100 km scale) and then

composited over the ten fair-weather days.

on Paulson (Figure 7). Considering that the fluxes are related to the logarithm of the roughness length, these differences are not large.

The drag coefficients computed from (1 a) are everywhere large (Figure 6), The drag coefficient over the forest averages about 2.5 • 10 -2, which is about 40%

larger than that computed by Parlange and Brutsaert (1993) from soundings. The

difference could be due to different methods, different spatial coverage and different t ime periods used in the two calculations. The instability over the forest is less (larger negative Obukhov length) because the influence of greater heat flux on the Obukhov length is exceeded by the influence of stronger momen tum flux. The effective roughness length computed from (lb) over the forest averages about

1.5 m based on Louis and about 2.5 m based on Paulson (Figure 7). Model simulations of flow over the pine forest have used roughness values on the order of 1 m; for example, Pinty et al. (1989) use 1.68 m.

The "observed" value of the effective roughness length outside the forest ranges from 0.75 m to more than 2 m, again depending on method of calculation and


exact location (Figure 7). The effective roughness length seems to be slightly larger over the more hilly region (Figure 3). The slopes in the hilly region are generally less than 5%, which according to the theory of neutrally stratified flow over hills proposed by Taylor et al. (1989) would modify the roughness length by 5% or less. The effects of interaction between the heating and the hilly terrain in this region is not known. However, comparison of Figure 7 and Figure 3 suggests that the topography is not the major influence on the spatial variation of the roughness length.

These roughness-length values are significantly larger than the O (10 cm) value typically used in models for such agricultural regions. The O (10 cm) value is based on the dominant vegetation types. The larger observed drag coefficients and effective roughness lengths could be partly due to the influence of form drag at the edges of small deciduous woods, individual scattered trees and other bluff roughness effects in the agricultural region, as can be inferred from Garratt and Hicks (1973), Beljaars and Holtslag (1991) and Claussen (1992). While vegetation is normally classified as a permeable surface (Brutsaert, 1982) the edges of woods and isolated trees still induce a pressure drag on the air flow. Sometimes this pressure drag and that due to small scale topography are formally classified as form drag, which enhances the effective roughness. The pressure drag associated with small individual roughness elements (order of 10 m or less) is then incorpor- ated into the skin drag part of the surface stress (Taylor et al., 1989; Claussen and Klaassen, 1992). With this format, individual scattered trees may contribute to form drag whereas trees within a canopy contribute only to skin drag. From a more quantitative view, the observed roughness length is expected to increase with increasing tree spacing up to a critical spacing as can be deduced from the approximate empirical relationship of the roughness length to the roughness den- sity (see Equation (3) in Raupach, 1992).

The large roughness lengths computed in this study could also be associated with applying the similarity relationship to the relatively large height of 100 m over the mixed agricultural region. At the same time, measurements made at heights much lower than 100 m could lie within the roughness sublayer (Raupach, 1979; Garratt, 1980) over regions of scattered trees in which case the similarity theory would be invalid. For example, if the depth of the roughness sublayer is on the order of 100 zo (Garratt, 1980), the aircraft level may be close to the roughness sublayer in some locations.

Therefore, the area-averaged momentum flux and the effective roughness length for the mixed agricultural region may be disproportionally influenced by locations which occupy a small fraction of the surface area. In contrast, the fluxes and roughness lengths for heat and moisture are determined more by the surface type which occupies the largest area. Excluding the influence of hills in the mixed agricultural region, this region seems closest to the "very rough" classification summarized in Wieringa (1992) where roughness values are predicted to be about 0.5 m. This class is described as "Old cultivated landscape with many rather large

394 L. M A H R T A N D M. E K

obstacle groups (large farms, dumps of forest) separated by open spaces of about 10 obstacle heights". Garratt (1980) suggests a roughness length value of 0.4- 0.9 m for scattered trees. Values at the high end of this range appear appropriate for application of the Louis formulation to the mixed agricultural region of the present study while application of the Paulson formulation requires effective roughness lengths two times larger (Figure 7).

Klaassen (1992) shows that variations of the surface roughness can significantly increase the area-averaged momentum flux due to the net effect of advection of stronger momentum from small into high roughness areas. Such an effect may be related to the observation of a sharp increase of stress from a smooth to rough surface transition. At the transition, the stress may reach a value of twice the equilibrium value for the rougher surface (Bradley, 1968; Garratt. 1992. Section 4.5.2). This enhancement of the momentum flux corresponds to larger effective roughness lengths. From a more general point of view. the large effective roughness length computed here may be related to the variation of the local rou#mess on a scale of i km or smaller in the mixed agricultural region. The surface layer m@ fail to achieve even approximate equilibrium over most of the domain. Then the effective roughness length is a numerical value which allows the similarity theory to predict the correct flux even though the assumptions underlying the derivation of the similarity theory are not valid. The effective roughness length values also include the effect of "extra Reynolds terms" resulting from the spatial correlation of the drag coefficient, wind speed and stability within the averaging area (Mahrt, 1987; Claussen, 1990).

Based on the results of this study and form drag studies cited earlier, we conclude that spatial averaging of local roughness lengths based on the dominant vegetation types underestimates the spatially-averaged momentum flux for the HAPEX-MOBILHY domain. The large "observed" effective roughness length could explain the underestimation of the observed surface stress by the modelling study of Noilhan et al. (1991) for the HAPEX-MOBILHY domain although they noted that general underestimation of winds by the model is a factor.

Consequently, the present study contrasts with weaker or simpler heterogeneity amenable to various methods of spatially averaging the local roughness length (see Taylor, 1987 and Claussen, 1990 for surveys of such methods l or spatially averaging the drag coefficient as recently applied by Grant (1991) to an actual heterogeneous region. As circumstantial support for spatially averaging roughness lengths for some situations, Garratt et al. (1990) find that specified random spatial deviations to the surface roughness have little influence on ensemble averages of model simulations.

If we consider the entire aircraft leg to be representative of conditions over a grid area of approximately 100 km width, we can compute an effective roughness length appropriate for use in large-scale models. Components of the wind and stress vectors and other fluxes are averaged along the aircraft flight and then the wind speed, stress magnitude and Obukhov length are computed for the flight leg.


The effective roughness length is computed for each leg and then these values are averaged over all 30 legs. Since the roughness length computed for each leg represents an estimate of the same roughness length (same flight track), we simply linearly average the roughness length estimates. This effective roughness length is smaller than the horizontal average of the effective roughness length based on 15 km averages (Figure 7) particularly when using the Paulson method. However, differences in roughness lengths obtained by the two averaging procedures are small compared to uncertainties of the roughness-length values themselves.

5. Heat Flux

The exchange coefficient for heat transfer, CH, is estimated from the observed aircraft turbulent heat fluxes as

c H = o)} (2)

where U is the averaged wind speed, 0 is the averaged potential temperature at the aircraft level and [w'O'] is the heat flux. The exchange coefficient C/~ not only depends on stability arid height above ground but also depends on the way in which the surface temperature is measured. In large-scale models, 0sfo is normally the surface potential temperature corresponding to the surface temperature computed from the surface energy budget. This value is essentially the surface radiation temperature. The effective roughness height for heat can be related to the computed exchange coefficient by the similarity expression

C ~ = { K u * / U } [ l n ( ( z - d) /Zoh,ef f ) -- Oh(Z/L)] -1 (3)

where Zoh,eff is the effective roughness length for heat; O h( Z /L ) is again from Paulson (1970).

Equation (2) is often theoretically formulated in terms of the potential temperature of the air at the roughness height 0(Zoh) instead of 0sfc. However, temperature measurements at the roughness height are not available, in which case the corresponding flux relationship is of little practical use. Therefore, the roughness length for heat can be defined to be that length corresponding to use of the surface radiation temperature, as is implicitly defined in numerical models of the atmosphere.

This application is complicated by the fact that the surface radiation temperature over the forest is strongly influenced by the temperature of the canopy top while the surface radiation temperature over the mixed agricultural region is strongly influenced by short vegetation and bare soil. As a result, the surface radiation temperature is coolest where the sensible heat flux is greatest, namely over the forest. As a further consequence, the vertical temperature difference in (2) is less

396 L. M A H R T A N D M. E K

10-3 In

10 .4

10-5

10 -6

roughness length (heat)

Paulson (1970)

10-7 [ , , , . I ~ . ~ 1 i ~ .

o 25 50 75 E F G H

distance (kin) Fig. 8. Effective roughness lengths for heat computed from 15 km fluxes composited over the ten fair-weather days; the solid horizontal line indicates the spatial average of these values. The dashed horizontal line is the average of the values of the roughness length based on fluxes averaged over the

entire flight leg (100 km scale) and then composited over the ten fair-weather days.

over the forest, leading to larger surface roughness for heat (Figure 8) as computed from (2-3). Therefore the spatial variation of the computed roughness length for heat partly represents the spatial variation of the effective height contributing to

surface radiation temperature . The need for models to parameter ize the surface heat flux using the surface radiation tempera ture must contend with this complica- tion. 1 In any event, the present results indicate that the effective roughness length

for momen tum may be orders of magnitude larger than that for heat, as previously concluded by Brutsaert (1982, Section 4,4e) and Beljaars and Holtslag (1991). Therefore this analysis suggests that use of the Louis formulation should be

modified to include the large difference between the roughness lengths for heat and momentum. The very small values of the roughness length for heat might be partly related to the use of surface radiation temperature , which corresponds to

a large estimated vertical difference of tempera ture in (2).

We could not assess the importance of the reduction of the radiative temperatures measured over the forest due to exposure of the sandy soil which has a low emissivity.

S P A T I A L V A R I A B I L I T Y O F T U R B U L E N T F L U X E S 397

The roughness length for heat based on the fluxes averaged over the entire flight leg (100 km) is about three times larger than the spatial average of the roughness lengths computed from the 15 km fluxes (Figure 8). This indicates that the roughness length for heat representative of a grid area may not always be precisely related to the spatial average of the roughness lengths for the different subgrid regions, although the difference between the two averages in Figure 8 may not be significant.

6. Conclusions

The "climatology" of the spatial variation of surface fluxes over the heterogeneous surface in HAPEX-MOBILHY has been analyzed for the ten flight days with no significant cloud cover above the boundary layer. As found in previous case studies, the composite over the ten days indicates greater heating over the forest, which generates a forest breeze and both rising motion and modest increase of cloud c6ver at the forest edge. The greater heat flux over the forest is due mainly to weaker heat flux into the soil, and to a lesser extent, smaller albedo and slighter smaller outgoing longwave radiation. The forest breeze is apparently eliminated by mixing before propagating into the forest interior. The direct vertical flux by the forest breeze and other mesoscale circulations is small.

The exchange coefficients and roughness lengths are computed from fluxes representing local averages (15 km scale) and regional averages (100 km scale). The roughness lengths for momentum computed from the observed fluxes and stability using two different similarity approaches agree within a factor of two. The resulting values of the effective roughness lengths for momentum over the mixed agricultural region are on the order of 1 m. These values are an order of magnitude larger than those used in numerical models for such surfaces where the roughness lengths were estimated by averaging the roughness lengths corresponding to the dominant surface types. The larger observed effective roughness lengths are apparently due to bluff roughness effects associated with scattered trees and edges of small woods. The large observed roughness lengths could also be due to non-equilibrium effects in transition zones where the flow is not adjusted to local surface conditions. The values of the effective roughness length reported here are simply those values for which the similarity theory predicts the correct area- averaged flux. Even though the assumptions underlying similarity theory may not be valid for typical land surfaces, numerical models of the atmosphere will continue to apply similarity relationships to the grid-averaged fluxes; no other method exists.

The roughness length for heat is found to be orders of magnitude smaller than that for momentum. The roughness length for heat is several orders of magnitude larger over the pine forest compared to the mixed agricultural land. This variation is partly related to the fact that the heat flux is greater over the forest while the radiation temperature is slightly cooler over the forest. The radiation temperature

3 9 8 L. M A H R T A N D M. E K

over the forest is part ly de te rmined by the canopy tempera tu re and therefore

cooler than the radiat ion t empera tu re over the mixed agricultural land, which is

domina ted by the t empera tu re of bare g round and low vegetat ion.

The present s tudy suggests that for a typical grid area, such as the H A P E X

domain, large-scale models should use a roughness length for m o m e n t u m on the

order of i m and a roughness length for heat on the o rder of 10 -4 m. Beljaars

and Holts lag (1991, Section 4b) conclude that the effective roughness l eng th for

m o m e n t u m is typically about an order of magni tude larger than the local roughness

length based on dominan t vegeta t ion and that the effective roughness length for

heat is typically 1.5 10 -4 m. These values are, perhaps coincidentally, a reasonable

description of the present data over the forest; over the mixed agricultural land,

the effective roughness for heat is even smaller.

Acknowledgements

The comments of J6el Noi lhan, Jean-Paul G o u t o r b e and Mart in Claussen and the

reviewer are greatly appreciated. This material is based upon work suppor ted by

the Mesoscale Meteoro logy P rog ram of the Nat ional Science Founda t ion under

Gran t ATM-8820090 and the Phillips Labora to ry under Cont rac t F19628-91 -K-

0002.

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Spatial variability of turbulent fluxes and roughness lengths in HAPEX-MOBILHY

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