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Regional surface fluxes over the Nopex area
Journal of Hydrology 212–213 (1998) 155–171
Regional surface fluxes over the Nopex area M. Frech a,*, P. Samuelsson b, M. Tjernstro¨m b, A.M. Jochum a a
Institut fu¨r Physik der Atmospha¨re, DLR Oberpfaffenhofen, D-82234 Wessling, Germany b Department of Meteorology, Uppsala University, S-75220 Uppsala, Sweden Received 8 November 1995; accepted 28 October 1996
Abstract The regional surface fluxes of sensible heat and moisture are estimated for two days during Nopex ’94 by means of aircraft measurements. A box flight pattern is analysed for 13 June (a weak wind case) and 14 June (a strong wind case), both with cold air advection. We perform a scale analysis in order to identify the main transporting scales of the turbulent fluxes and to investigate the mesoscale variability of the sensible heat and moisture flux. The example of a mesoscale moisture front indicates the importance of subgrid mesoscale variability. The turbulent fluxes of sensible heat and moisture are affected significantly by this mesoscale variability. This mesoscale variability is usually subgrid in numerical models and therefore must be parameterized. The source of the mesoscale moisture variability appears to be related to a cold front. Mesoscale flux divergence is explicitly included into the budget of sensible heat and moisture. The average vertical mesoscale flux divergence is small compared to the turbulent flux for the two cases investigated. However, the vertical mesoscale flux can be large locally. The budgets indicate the importance of horizontal advection for the Nopex region. The time evolution of sensible heat and moisture during 14 June appears to be dominated by large scale horizontal advection. A comparison between the area-averaged surface flux from aircraft data and surface flux stations for the 13 June is not conclusive because of fractional cloud cover. For the strong wind case on 14 June, the surface fluxes obtained from aircraft data and from surface flux stations disagree, which appears to be related with the pronounced mesoscale moisture variability. 䉷 1998 Elsevier Science B.V. All rights reserved. Keywords: Heat and moisture flux; Regional surface fluxes; Turbulent flux
1. Introduction The northern hemisphere land surface climate processes experiment (Nopex), is devoted to study land-surface–atmosphere interactions in a northern European forest-dominated landscape (Halldin et al., 1998). The Nopex main study region is selected to represent the southern part of the boreal zone. It is the goal of Nopex to investigate fluxes of energy, momentum, water, CO2 and the associated interaction
* Corresponding author.
between soil, vegetation and atmosphere, between lakes and the atmosphere, as well as within the soil and the atmosphere on local to regional scales ranging from centimeters to tens of kilometers. Aircraft based measurements provide a tool to estimate the integration of energy fluxes over heterogeneous terrain and to estimate area averaged surface fluxes. Furthermore, a budget analysis based on aircraft measurements can be used to study the basic processes contributing to the boundary-layer time variation of potential temperature, u, and specific humidity, q. A better understanding of spatial and temporal variations of energy fluxes is necessary in order to improve existing
0022-1694/98/$ - see front matter 䉷 1998 Elsevier Science B.V. All rights reserved. PII: S0022-169 4(98)00207-8
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aggregation methods of surface fluxes for use in regional and global climate models. The variability of surface fluxes is controlled by a number of factors. A permanent controlling factor would be the landscape characterized by its topography and soil type. Furthermore, underground hydrology, vegetation and land use (e.g. grazing, burning, crop selection), atmospheric forcing (e.g. the synoptic situation, cloud cover, mesoscale dynamics) impose additional factors which contribute to the variability of surface fluxes within a grid box. Therefore, considerable variability of surface fluxes is even found over fairly homogeneous surfaces as it was observed during Fife (first international satellite land surface climatology project field experiment, Smith et al., 1992). On an appropriate scale of heterogeneity ( ⬇ 10 km) mesoscale circulations may evolve due to contrasts in surface temperature in weak ambient background flow. For example, the soil moisture field and organized vegetation patterns can organize boundary layer circulation patterns (Segal and Arritt, 1992; Smith et al., 1994). Mesoscale circulations can modulate ‘small scale’ turbulence or directly contribute to the flux (e.g. Dalu and Pielke, 1993; Mahrt et al., 1994; Doran et al., 1995). The mesoscale flux contribution appears to be significant in the surface energy balance with weak large scale flow and strong surface heterogeneity (Sun and Mahrt, 1994). In their study, inclusion of mesoscale flux leads to an approximate closure of the energy balance at the surface. Modeling studies indicate the importance of mesoscale circulations induced by landscape heterogeneities of energy fluxes (Avissar and Chen, 1993). These studies suggest that it is necessary to parameterize mesoscale circulations which are usually subgrid scale in global models (Lynn et al., 1995). The Fife atmospheric boundary layer budget studies (Betts et al., 1992, Betts, 1992, Grossman, 1992a) show that simple mixed-layer models were applicable and also indicate the importance of accurate horizontal advection estimates to balance the budget of sensible heat and moisture. These budget studies revealed that entrainment fluxes in mixed layer models are underestimated (the entrainment coefficient was found to be of the order of 0.4 compared to the usual value of 0.2). It is unknown if
this result can be generalized. Entrainment coefficients on the order of 0.4 are commonly found in the unstably stratified marine boundary layer (Tjernstro¨m and Smedman, 1993). There is often a disagreement between surface flux estimates from aircraft data and measurements from surface flux stations. The disagreement is sometimes larger for the latent heat flux as compared to the sensible heat flux (Betts et al., 1992). This is usually attributed to the under-sampling of larger scale flux contributions by the aircraft because of short flight legs and sometimes to data processing (Grossman, 1992b). Part of this under-sampling might be inherent in aircraft measurements because of the quasi-1D sampling of 3D boundary layer turbulence. A direct comparison between tower measurements or measurements at the surface and surface fluxes derived from aircraft is difficult since we are comparing point measurements with a measurement in space. A comparison is even more difficult if we make measurements over a heterogeneous landscape. A complicating aspect is that mixing of moisture can be different to mixing of sensible heat. This can be related to different source areas for temperature and moisture fluctuations (Roth and Oke, 1995) and mesoscale heterogeneity in the surface energy balance (Mahrt, 1991a, 1991b). In this study we will analyse aircraft data from two flight missions during the first concentrated field effort (CFE) of Nopex in June 1994. As a first step we investigate the dominant scales in the flux estimates and the variability of these fluxes over the Nopex domain. Then, the budget components of sensible heat and moisture are estimated. The estimated surface flux from aircraft data is compared to weighted area-averaged surface fluxes based on representative measurement sites (i.e. forest, lake, farmland) within the Nopex domain.
2. Data 2.1. The flight mission The Nopex area and the experiment is described in detail by Halldin et al., 1998. Forests dominate the area as a whole, with agricultural fields concentrated towards the south and a increasingly larger fraction of
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Fig. 1. The location of surface flux stations. The dashed line denotes the Nopex area, the solid line the shape of the box flight pattern.
the ground covered with forests towards the north. The forest is mainly spruce and pine, with a small fraction (15%) of deciduous trees, primarily in the south. The forests occupy approximately 54%, farmland 38%, wetlands and lakes 4% of the Nopex area. The land use distribution below the aircraft for the box flight pattern (including a nominal fetch of 600 m to the left and right of the flight track) indicates 56% coverage by forest, 36% by farmland, 4% by wetlands and lakes, and 4% by populated area. This distribution is later used to calculate a weighted area average from
the surface flux stations as an estimate for the regional latent and sensible heat flux. There are a number of surface flux stations (see Fig. 1) in the Nopex area, one for each main surface type. Available is data from two towers within a forest with eddy correlation measurements at different heights (near 33 m at the Siggefora and near 35, 70 and 100 m at the Norunda tower). The trees are about 20–25 m high consisting of mature mixed spruce and pine stands of different age. Flux data from two agricultural sites (Lo¨vsta and Tisby) and from one
Fig. 2. The non-orthogonal albedo wavelet variance spectra along the box flight pattern during Nopex 1994.
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Fig. 3. The composited radiosonde profiles of u (⬚C) and q (g kg ⫺1) for the 13 (a,b) and 14 (c,d) June. T indicates the period of the ‘turbulence’ flights; B the time period of the box flights. The bold dashed line indicates the boundary layer height.
lake station (Ta¨mnaren; 37 km 2, average depth 1.2 m) are available (this flux data is also based on eddy correlation measurements). Aircraft measurements were performed during the experiment in order to sample the mean and turbulent boundary layer structure over the Nopex area. There are also radiation measurements (upward and downward long/short wave radiation) available from these flights. We are analysing the box flight pattern shown in Fig. 1. The flight paths (legs) have the shape of a rectangle and were flown at two levels during each box flight mission. The legs are approximately 45 and 90 km long. In the text legs 1, 2, 3 and 4 correspond to the lower flight level, and legs 5, 6, 7 and 8 to the upper flight level.
It takes approximately 90 min to fly this pattern. Each flight pattern started at about 2000 m above ground with a profiling descent. This box flight pattern is used to derive the components of the budget of sensible heat and moisture and to estimate area-averaged surface energy fluxes on a regional scale. The aircraft is the Sabreliner 40A operated by the Defence Material Administration (FMV) of Sweden. The instrumentation of the aircraft is described in detail by Tjernstro¨m and Friehe (1991). More information about the flight missions during the Nopex CFE 1994 are summarized by Samuelsson and Tjernstro¨m (1997). The radiation measurements from the aircraft
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Fig. 4. The time tendency of u and q at different height levels for June 13 (a,b) and 14 (c,d) based on radiosonde soundings. The time tendency is given for different height levels. T indicates the period of the ‘turbulence’ flights; B the time period of the box flights. Bold solid line 100 m, bold dashed line 500 m, bold dash-dotted line 900 m, dotted line 1300 and dashed line 1700 m.
characterize the surface heterogeneity of the Nopex area. A spectral analysis of albedo using the Haar wavelet spectra (Mahrt, 1991a) serves as a tool to obtain an expression about the surface heterogeneity that is sampled by the aircraft (Fig. 2). The peaks of albedo variance are found near 5 km for leg 1, near 2 and 35 km for leg 2, near 3 and 15 km for leg 3 and near 4 and 20 km for leg 4. These values indicate the spatial variability within the Nopex domain. Small scale patches are intermixed into larger scale patches which is reflected by the albedo variance where, for example, leg 2 is dominated by patches of 2 km scale which are embedded into albedo variations on a 35 km scale. The mean albedo derived from aircraft data shows a weak north–south gradient (0.12 in the northern section, 0.14 in the southern section).
2.2. The boundary layer evolution and the mean structure On June 13 the wind was weak to moderate from north-east. Boundary layer cloudiness was small with 1/8–2/8 of shallow cumulus clouds at the top of the ABL around 1500 m. However there was a 6/8 of cirrus stratus during the flight. On June 14, the winds were significantly stronger with wind on the order of 12 m s ⫺1 from south-west. A few boundary layer cumulus clouds were observed (1/8). There were radio sondes launched at the Marsta site every hour on June 13 and 14 (Bergstro¨m, personal communication). A time–height composite from these soundings show the temporal evolution of potential temperature and specific humidity (Fig. 3). The boundary layer height
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Fig. 5. The moisture variability during the flight mission: 13 June (top figure 100 m). The dashed area sketched in the xy plane indicates the Nopex domain and the box the flight pattern projected onto the xy plane. The circle at the z-axis denotes the mean specific humidity of the box flight at the level.
is estimated from the potential temperature profile. The evolution of the boundary layer depth is marked by the bold dashed line in the graph. June 13 shows a classical boundary layer growth from the morning hours to about noon, asymptotically approaching a
constant height near 1500 m. In contrast, on June 14 the boundary layer growth seems to be inhibited during the morning hours and shows an almost linear increase in height up to about 1700 m until 14 LST. The reason for this linear increase is unknown. The
Fig. 6. 14 June (z 100 m). See Fig. 5.
M. Frech et al. / Journal of Hydrology 212–213 (1998) 155–171 Table 1 General flight conditions for 13 and 14 June
Mean height of the legs (m) Length of the legs Flight time Boundary layer height estimated from radio sonde soundings Cloud cover Mean wind speed and wind direction Sampling rate of the mean data Sampling rate of the turbulence data
13.6 flight 350
14.6 flight 352
192, 728
100, 1700
80 and 45 km 80 and 45 km 13:57–15:52 (SST) 14:33–16:28 (SST) 1600 m 1850 m
2/8 Cu, 6/8–8/8 Ci 1/8 Cu 5.5 m s ⫺1, 320⬚ 12 m s ⫺1, 230⬚ 6.1 Hz
6.1 Hz
48.8 Hz
48.8 Hz
atmosphere aloft seems significantly more stably stratified during the first day. The specific humidity is well mixed on June 13 during the box flight. There is a weak negative gradient on June 14. The temporal development of potential temperature within the boundary layer is nearly linear for both days as is seen from the time evolution for different height levels (Fig. 4). In the upper levels potential temperature slightly decreases for the first day and is quasi constant for the second day. In the boundary layer moisture increases weakly on the first day and
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decreases on the second day. From the upper levels we can see that very dry air mass is replaced by more humid air on June 13, presumably by large scale horizontal advection. In contrast, specific humidity is quasi constant and slowly decreases in the afternoon on June 14. To give an impression about the spatial and temporal variability of specific humidity over the Nopex domain, Fig. 5 and Fig. 6 show the specific humidity signal along the box flight pattern. We observe a fairly smooth north-west to south-east gradient in specific humidity on June 13. The decrease in specific humidity along this gradient is about 1 g kg ⫺1. There is a strong spatial variability in specific humidity on the mesoscale during the box flight on June 14 (Fig. 6) with higher moisture content in the south-west corner of the area. We can observe a decrease in specific humidity by 1 g kg ⫺1 within one day. 3. The turbulent structure Covariances are calculated from high-pass filtered data (40 km cutoff) by means of the eddy correlation technique. We first investigate the most energetic length scales of the vertical fluxes by performing a spectral analysis. After the spectral analysis we estimate the flux sampling uncertainty and discuss the spatial variability of the fluxes.
Fig. 7. The non-orthogonal Haar spectra of sensible heat and moisture flux: Legs 2 (z 192 m) and 6 (z 728 m), 13 June. Dilation is a direct measure of the structure size.
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Fig. 8. See Fig. 7: Legs 2 (z 100 m) and 6 (z 1700 m), 14 June.
3.1. The covariance spectra The scale dependence of the heat and moisture flux is studied with non-orthogonal wavelet spectra based on the Haar-wavelet (Mahrt, 1991a, 1991b; Howell and Mahrt, 1994). Spectral peaks are better isolated by this local transform since main transporting scales of the flux are local phenomena. The spectra are based on high pass filtered data (40 km cutoff). The general flight conditions are given in Table 1. The covariance spectra of the vertical heat and moisture flux are shown for leg 2 and 6 (Fig. 7 and Fig. 8). Leg 2 and 6 are a pair of legs at different heights over the same segment within the flight pattern (June 13: leg 2 z 192 m, leg 6 z 728 m; June 14: leg 2 z 100 m, leg 6 z 1700 m). The
approximate maxima in the covariance spectra for both days are summarized in Table 2. The length scales in the turbulent regime is typical for a convective boundary layer. We expect smaller turbulent scales in the lower part of the boundary layer. The larger scales in the upper part of the boundary layer can be explained by smaller scale eddies which merge on their ascent forming large thermals. This can be seen in from Fig. 7. The upper flight leg on June 14 was near the boundary layer top. Here we observe negative entrainment fluxes. From this analysis we find that most of the turbulent flux in the boundary layer occurs on the scale of 1– 2 km which corresponds roughly to the scale of the depth of the boundary layer for these days. Different peaks in the covariance spectra of
Table 2 Identified length scales of the most energetic flux contributions based on wavelet covariance spectra. The spectra are based on high pass filtered data (40 km cutoff) 13 June
Leg Leg Leg Leg Leg Leg Leg Leg
1 5 2 6 3 7 4 8
wu 1000 m, 15 km 800 m, 6 km 500 m 1.2 km, 10 km 1 km 2 km, 12 km 900 m, 11 km 1.7 km, 15 km
14 June wq 900 m, 15 km 800 m, 3 km, 15 km 500 m 1.2 km, 30 km 700 m 2 km, 12 km 800 m, 10 km 1.7 km, 10 km
wu 400 m 2 km, 7 km 500 m, 6 km 2 km, 7 km 800 m, 4.5 km 2 km, 10 km 1 km, 17 km 2 km
wq 300 m 1 km, 7 km 400 m, 6 km 1.3 km, 6 km, 22 km 500 m, 6 km 900 m, 10 km 1 km, 18 km 6 km
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sensible heat and moisture flux may point to different source areas for heat and specific humidity fluctuations. For example, a significant part of a positive moisture flux in the lower part of the boundary layer can be caused by entrainment fluxes whereas a positive heat flux may be primarily forced by buoyancy generated turbulence at the heated land surface (e.g. Roth and Oke, 1995). From the covariance spectra shown in Figs 7 and 8 and Table 2 we find that there are always flux contributions present in the boundary layer at a larger scale of 4–5 km for the two days investigated in this study. The source of this covariance can be surface driven or of transient nature. For the strong wind conditions found for 14 June we would not expect the evolution of mesoscale circulation due to differential surface heating. Based on this scaling behavior we will refer to a ‘mesoscale regime’ for the covariance at scales larger than 5 km. The spectral peaks in the mesoscale regime (2) scatter a lot between legs and seem point to the transient nature of these features. 3.2. The mesoscale flux From data mesoscale fluctuations and fluxes are calculated the following way: We decompose the time series c of a particular leg in
c c ⫹ cⴱ ⫹ c 0
1
where c can be u or q. c is the mean along the flight, c * the ‘mesoscale’ deviation from the mean and c 0 the turbulent fluctuation. The turbulent fluctuation can be defined as the deviation from a local average [c]. The local average is written as the sum of the total leg average and the mesoscale deviation (e.g. Mahrt et al., 1994).
c c ⫺ c ⴱ
2
The turbulent part is just the deviation from the local average. Note that when averaging eqn (2) over the flight leg the mesoscale part becomes zero. From a modeling point of view, the total average c represents the GCM grid box mean, the second term in eqn (1) is the subgrid mesoscale signal due to subgrid heterogeneity and the last term is the turbulent deviation from the mesoscale signal which is defined by the scale of surface heterogeneity (e.g. Avissar and Chen, 1993). The separation into mesoscale and turbulent
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fluctuations from actual data can be reached in different ways. One is to define a cutoff wavelength or structure length for the turbulence and define every flux contribution above a certain scale to be a mesoscale flux. The cutoff wavelength can be determined from covariance spectra based on the total flight leg. We use non-orthogonal wavelet spectra based on the Haar wavelet to determine the length scales. The resulting scale (5 km) defines a window which is translated sequentially through the time series. The mesoscale and the turbulent signal is calculated for each location along the leg. If the surface heterogeneity is distinct enough (scale of the order of 10 km) the decomposition of the flow can be posed in terms of the underlying surface (Mahrt et al., 1994). Albedo, surface radiation temperatures or greenness index can be used for partitioning if the flight level is close enough to the surface. However, the surface heterogeneity of the Nopex area is not well defined so that it is not possible to perform a decomposition of the data in terms of the surface heterogeneity. After the decomposition of the data we can write the total leg averaged covariance as (here for the heat flux; the mean is removed from the time series): wu wⴱ ⫹ w 0 uⴱ ⫹ u 0
3
The overline represent a spatial average over the whole leg. The covariance between mesoscale and turbulent fluctuation average to zero with the given decomposition. The average covariance reduces to wu wⴱ uⴱ ⫹ w 0 u 0
4
3.3. The uncertainty of the turbulent flux The uncertainty of the turbulent fluxes is estimated by choosing samples of approximately 8 km length. The turbulent flux is calculated for each segment. We then assume a Gaussian distribution of these flux samples and apply the central limit theorem in order to estimate the sampling uncertainty (Mahrt and Gibson, 1992). We find uncertainties in latent and sensible heat flux on the order of 20%–25% for the low level legs and 25%–50% for the legs at the higher flight level for 13 June (Table 3). The flux uncertainties for the low level data on 14 June are on the order of 10%–20%. Fractional cloud cover seems to be the reason for larger flux sampling uncertainties during 13
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Table 3 The flux sampling uncertainty (in %) for individual legs Leg
1
2
3
4
5
6
7
8
13 June w 0 u 0 13 June w 0 q 0 14 June w 0 u 0 14 June w 0 q 0
22 18 10 23
21 17 31 21
31 19 10 28
17 15 13 24
62 34 77 58
32 13 146 88
29 22 37 56
36 21 55 67
June which causes a larger variability of the turbulent fluxes over the Nopex domain. The flight legs near 1700 m for 14 June are characterized by large sampling uncertainties. We compared the expected uncertainty of the flux estimate with Ogives which were calculated for each leg (Desjardins et al., 1989). The fluxes are accumulated along the wavelength as shown in Fig. 9 for the 13 June. This method gives us more confidence that we actually capture most of the flux at wavelengths smaller than 20 km. For all legs located well in the boundary layer the curves tends to level out for wavelengths larger than 20 km. There are indications that the latent heat flux contains more energy at shorter wavelengths compared to the sensible heat flux (9). For the flight
legs in the entrainment zone near 1700 m there are still significant contributions to the fluxes at scales larger 20 km (not shown here). 3.4. Spatial variability of turbulent and mesoscale fluxes The variation in specific humidity along leg 4 will be investigated briefly in order to investigate its influence on the vertical turbulent flux through the boundary layer. In this particular case the variability in the moisture field appears to be related to a cold front which passed the Nopex domain 2.5 h after this observation. A more detailed analysis may be found in Frech (1998). The moisture variation seen in leg 4 (see Fig. 6) is shown in Fig. 10. We find a very sharp drop in specific humidity by Dq ⬇ 1.6 g kg ⫺1. This moisture variation is referred to as a moisture front. The most striking feature in these time series is that there is no equivalent drop in temperature as one might expect. Here the moisture field appears decoupled from the temperature field. This moisture front is characterized by a large momentum deficit in the presence of a strong
Fig. 9. Cumulative integral of the cospectrum for sensible and latent heat for 13 June. All curves are normalized with the flux value at the cut-off wavelength, approximately 40 km. The lines represent: Full line, sensible heat flux for leg 4. Dashed line, latent heat flux for leg 4. Dash-dotted line, sensible heat flux for leg 8. Dotted line, latent heat flux for leg 8.
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Fig. 10. The observed moisture front 14 June, NOPEX 1994, leg 4. The turbulent fluctuations of w, u and q are shown for a 18 km segment which includes the moisture front. In addition, the associated wind speed is plotted.
updraft region. This indicates the transport of low momentum and warm air from regions near the surface. To investigate this phenomena we select two segments to the left and right of the sudden change in q. The segments chosen are 8 and 10 km long and specific humidity is quasi constant within these segments. The statistics of these segments are summarized in Table 4. The ‘dry’ segment shows reduction in latent heat flux by 60% compared to the moist section. Sensible heat flux is less affected by the moisture variation which seems consistent with the undisturbed temperature time series. A large vertical flux divergence is implied when we compare sensible and latent heat flux with net radiation in both segments. The air within the ‘dry’ segment is less unstable which can explain the reduced sensible
heat flux. The variation of the turbulent flux and specific humidity cannot be explained by the land surface characteristics. There is no significant change in surface temperature and albedo. In addition the landuse characteristics do not change within 600 m upstream to the flight leg which is approximately the footprint of the turbulent flux at flight level. The maximum upwind source area of influence can be estimated from x Uh/sw (using sw ⬇ 2 m s ⫺1 and ¯ ⬇ 13 m s ⫺1; Weil and Horst, 1992). U The mesoscale variation of specific humidity seems advected. From the data we cannot determine the depth of this disturbance. The variation of the turbulent and mesoscale latent heat flux along leg 2 for 14 June is shown in order to illustrate the flux variability (Fig. 11). The fluxes
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Fig. 11. The spatial variability of the turbulent and mesoscale latent heat flux along leg 2 for 14 June 1994. Also shown is the albedo variation along this flight leg (the block averages are based on the results of the ‘variable block averaging’ (VBA) algorithm, Howell, 1995.
shown are based on the decomposition given in eqn (1) using a window width of 4 km. There is a weak correlation of the flux intensity with the surface conditions (characterized by albedo) below the flight leg between kilometer 7 and 22. In this segment we observe relatively weak fluxes. The albedo below the flight leg is characteristic for the upstream area where we expect the source area for part of the turbulent flux. For other parts of the leg there is no obvious correlation between albedo and the measured flux. The segment between 50 and 60 km is influenced by Table 4 The statistics of two segments near a sudden change of q for Leg 4, 14 June, flight 352. Standard notation is used. Tsfc radiative surface temperature, u v virtual potential temperature, L Obukhov length, z observation level, Rnet net radiation
q¯ (g kg ⫺1) u (⬚C) T¯ (⬚C) T¯sfc (⬚C) ¯ (m s ⫺1) U dir (⬚) L (m) z/L u* (m s ⫺1) H (W m ⫺2) LE (W m ⫺2) Rnet (W m ⫺2)
Segment a (‘moist’)
Segment b (‘dry’)
4.9 23.7 22.6 23.9 12.8 232 ⫺ 72.5 ⫺ 1.52 1.16 139 247 416
3.3 23.8 22.6 23.8 13.1 236 ⫺ 116.4 ⫺ 0.94 1.18 95 91 444
Lake Ta¨mnaren which is in the upstream region to the flight leg. This segment is characterized by large mesoscale fluxes.
4. The budget We consider the box flight pattern as a hypothetical grid box in a numerical model. It is one objective to investigate which processes contribute to trends (in time) of potential temperature and specific humidity within this grid box. The budget for any scalar c can be written as: X 2c 2c ⫹ ui S 2t 2x i
5
where ui are the velocity components (u, v, w) and xi denotes the coordinate system (x,y,z). The terms on the left hand side are the local time rate of change and advection of c. S represents sources and sinks of c which can be, for example, radiative flux divergence for the budget of u or evaporation of condensate for the budget of q. The only souce and sink term we keep in our study is the longwave radiative flux divergence which proved non-negligible. The decomposition of the velocity components ui follows eqn (1). Substituting the variables into the budget eqn (5), rearranging
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and applying Reynolds averaging rules, we obtain: X 2c 2c 2u 0i c 0 2uⴱ c ⴱ ⫹ ui ⫹ ⫹ i S 2x i 2x i 2t 2x i
6
In eqn (6), the third and fourth term on the left hand side represent the components of turbulent and mesoscale flux divergence of c, respectively. The overbar represents the grid average. 4.1. The budget terms The components of the budget are estimated using aircraft, radiosonde and surface data. We first identify the dominating terms in the budgets. A first idea on the boundary layer time trend of u and q¯ can be obtained from composited radiosonde soundings. On June 13 the moisture trend seems nonlinear for the time period of the box flight (4). On June 14 there is essentially no trend in potential temperature during the flight. A significant linear decrease of specific humidity in time is found at the same time. However, radio soundings may have considerable sampling errors so that this is a rather qualitative observation. A method to derive the trend of a scalar solely from aircraft data is described in Betts et al. (1992). The composite of leg averaged mean data is determined. A linear fit over this composite yields the trend. Estimating the time tendency for our control volume by applying this method is not possible because of the heterogeneity of the Nopex area. Boundary layers of different history are sampled by the flight pattern and are partly characterized by the underlying surface and the upstream conditions. Therefore the time tendency is based on a pair of flight legs over the same area. It takes approximately 45 min before the aircraft flies over the same area within the flight pattern. The four estimates are averaged to obtain a regional estimate and the standard deviation yields a measure of its uncertainty. We also calculated the time tendency from surface stations: Siggefora, Tisby and Lake Ta¨mnaren. These tendencies are weighted according to the fractional area of each surface type within the Nopex area. The situation on 14 June is more complicated. Here the specific humidity is not well mixed. So we cannot determine the time tendency from aircraft data. The time tendency of moisture from the individual surface
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stations partially show opposing trends. This can be explained by the strong spatial variability of the moisture field. We, therefore, estimate the time tendency in that case with radiosonde soundings (4). Since potential temperature is approximately well mixed its time tendency is calculated from aircraft data. The horizontal advection terms are based on linear trends from single flight legs. These estimates are corrected by the time tendency in order to separate trends in time and space. This procedure assumes that the time tendency is constant for a flight leg. The standard error of the slope of the linear trend defines the error estimate of the advection term. An estimate of the large scale vertical velocity can be derived from the horizontal divergence of the wind field. The uncertainty in w turned out to be large for 14 June. The vertical advection term is therefore not included. For this day vertical advection of q could be non-negligible since q is not well mixed. The vertical flux divergence is calculated for each pair of legs over the same segment. This method assumes that the vertical flux divergence is constant for the time period between the legs (45 min). The four estimates are averaged to obtain a regional flux divergence value for the Nopex control volume. The assumption of linearity is made for both the turbulent and mesoscale vertical flux divergence. This is probably not always appropriate for the mesoscale flux divergence as is suggested in the modeling studies of Lynn et al. (1995). The uncertainty in the estimated flux divergence values can be quite large since the flux divergence values depend only on two flux values. The uncertainty of the flux divergence will be based on the uncertainty of the flux estimate. Both the turbulent and mesoscale horizontal flux divergence are found to be negligible. Longwave radiative flux divergence is estimated from a profile flight which was part of the flight mission. Because fluxes from the upper flight level on June 14 have a large sampling error no reliable vertical flux divergence can be estimated for this flight. 4.2. Results The situation on 13 June is characterized by weak winds and cold air advection. The negative vertical turbulent heat flux divergence indicates the usual
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Table 5 The budget of sensible heat, 13 June and 14 June 1994 in W m ⫺3 Flight
2u 2t
u
2u 2x
13 June 14 June
0.03 8 ^ 0. 017 ⫺0.066 ^ 0.015
⫺0.01 3 ^ 0.003 0.203 ^ 0.002
v
2u 2y
0.075 ^ 0.003 ⫺0.078 ^ 0.004
daytime heating of the boundary layer. The vertical mesoscale heat flux divergence is small and adds to the heating of the boundary layer (Tables 5 and 6). The positive time tendency of sensible heat is about a factor of two smaller compared to the flux divergence which indicates the importance of cold air advection on the time evolution of u. The longwave radiative flux divergence is not negligible in the budget. The relative large residual in the budget for sensible heat may point to flux sampling uncertainties and errors due to the nonlinearity of the time tendency term. We find moist air advection in the budget of moisture. The negative vertical turbulent moisture flux divergence indicates a moistening of the boundary layer. The vertical mesoscale flux divergence indicates a drying tendency at larger scales. The mesoscale flux divergence improves the budget and is more important compared to that for sensible heat. The budget indicates the importance of advection which is on the same order of magnitude as the turbulent flux divergence. The residual in the budget of specific humidity is acceptable when we use the time tendency based on the surface flux stations. However, it is difficult to assess how representative a regional time tendency from point measurements can be. To summarize, the time tendencies of the budgets of sensible heat and moisture are not balanced by the vertical flux divergence. This implies that a simple one dimensional mixed layer model will not work. Advection is important for the time tendency of heat
2 w 0 u 0 2z
2 wⴱ uⴱ 2z
2Fnet 2z
Residual
⫺0.083 ^ 0.025 —
⫺0.002 —
⫺0.02 ⫺0.034
⫺0.035 —
and moisture. There seems to be a tendency that the mesoscale flux divergence is more important for the budget of moisture. However, we cannot determine the uncertainty of the estimated vertical mesoscale flux divergence. On 14 June the advection terms are large. Cool air is advected which leads to a cooling trend. Again, the longwave radiative flux divergence cannot be neglected. The budget of specific humidity is dominated by dry air advection which leads to a negative moisture tendency.
5. Area-averaged flux If reliable estimates of the budget terms exist, we can derive the regional surface flux as a residual (Grossman, 1992a). Since the residual is quite large on June 13, we refrain from inverting the budget to estimate a surface flux. All errors from individual budget terms would accumulate in the surface flux estimate. Therefore the vertical flux divergence is used to extrapolate to the surface on June 13. In addition we can assume a linear profile for the heat flux and estimate the surface flux with w 0 u 0s w 0 u 0 z=1 ⫺ 1:2 z=zi (Stull, 1988). For the 14 June case, we will use the lowest flight level as an estimate for the regional surface flux. A second surface heat flux estimate will be based on the assumption of a linear profile. The surface flux estimates are compared with flux
Table 6 The budget of latent heat, 13 June and 14 June 1994 in Wm ⫺3. On June 13, the time tendency of q based on aircraft data and surface stations is included. The first time tendency of specific humidity on June 13 is based on surface measurements. Flight
2q 2t
u
2q 2x
13 June 13 June 14 June
0.185 ^ 0.029 0.093 ^ 0.019 ⫺0.829 ^ 0.178
⫺0.088 ^ 0.003 ⫺0.088 ^ 0.003 0.256 ^ 0.007
v
2q 2y
⫺0.072 ^ 0.007 ⫺0.072 ^ 0.007 0.563 ^ 0.056
2 w 0 q 0 2z ⫺0.109 ^ 0.033 ⫺0.109 ^ 0.033 —
2 wⴱ qⴱ 2z
Residual
0.027 0.027 —
⫺0.057 ⫺0.149 —
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169
Table 7 The average latent and sensible heat flux for the NOPEX area. The average flux for different land surface characteristics is given including fluxes at 100 m from the Norunda tower. The average surface flux of the surface flux stations are weighted by the area they occupy in the NOPEX area (‘Mean’). The Norunda data at 100 m is used for this estimate. ‘Div’ denotes the flux at 100 m height which is derived by extrapolating to this level using the estimated vertical flux divergence of the turbulent flux. ‘Level’ denotes the average turbulent and mesoscale (in brackets) flux at the lower flight level. ‘Profile’ denotes the surface heat flux derived by assuming a linear profile. The fluxes are in W m ⫺2 Flight 13 June 13 June 14 June 14 June
14:00–16:00 LST 14:00–16:00 LST 14:30–15:30 LST 14:30–15:30 LST
Flux
Agricultural
Forest
Norunda (100 m)
Ta¨mnaren
Mean
Div
Level
w 0 u 0 w 0 q 0 w 0 u 0 w 0 q 0
64 154 128 252
246 121 474 143
171 119 281 191
⫺ 11 71 ⫺ 99 246
118 125 200 208
78 131
64 (6) 113 (2) 118 (9) 172 (13)
measurements at the surface. The area-averaged surface flux derived from surface measurements is weighted by the fractional coverage of the respective surface types below the flight path. the results are summarized in Table 7. We take the flux from the Norunda tower at 100 m as an effective flux value for the forest within the Nopex area. The flux values at 35 m from the forest sites seem not representative especially for the 14 June which is the strong wind case. This is highlighted by the fact these fluxes do not balance with the measured net radiation (ground heat flux and storage terms are on the order of 40 W m 2). The flux values at the 35 m level presumably have a smaller footprint and therefore are more vulnerable to specific surface features. In addition, net radiation as derived from aircraft radiometers and from surface measurements is used to see whether the surface energy budget is closed (Table 8). On June 13 there is a disagreement between aircraft and surface measured net radiation. This is likely to be due to fractional cloud cover. The agreement of both measurements is good on June 14. On June 13 the flight levels where well in the boundary layer (192 and 728 m and zi 1600 m). We estimate an area-averaged surface flux using the estimated flux divergence and extrapolate to a height of 30 m above ground, about 8 m above the tree tops. The disagreement in the estimated surface flux
Profile 75 126
values between aircraft and surface flux data for the 13 June appears to be due to fractional cloud cover. The surface stations indicate larger net radiation values during this flight mission (8). From surface data we find that ground heat flux and the storage term are on the order of 50 W m 2. The surface energy balance closes approximately using the aircraft measured net radiation and energy fluxes. There is no significant disagreement between surface heat flux derived from the flux divergence and from the assumed flux profile. In this case the profile method is not very sensitive to errors in zi. For June 14 (zi 1850) we assume that the flux estimate at the lower flight level (z 100 m) is a good estimate for the regional flux (therefore results from the period 14:30–15:30 LST are shown which is approximately the time it takes to perform the lowest flight level). The surface heat flux from the profile method does not differ much from the heat flux at z 100 m. The comparison of aircraft data with surface flux measurements for the 14 June is difficult. As discussed earlier there is significant mesoscale variability in the moisture field which affects the turbulent fluxes heavily (see the section on the mesoscale moisture front). Since the agreement between the net radiation values from the surface and aircraft data is good for this day, the large difference between low-level aircraft flux
Table 8 The net radiation (in W m ⫺2) for the agricultural, forest and lake sites during the flight mission. Also listed is the weighted mean net radiation and the value derived from aircraft data Flight
Agricultural
Forest
Lake
Mean
Aircraft
13 June 14:00–16:00 LST 14 June 14:30–15:30 LST
300 430
363 528
315 364
325 467
250 456
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and the surface flux data cannot be explained by flux sampling problems. Flux sampling uncertainties for the latent and sensible heat flux are on the order of 10%–20%. We suspect that the mesoscale variability of the moisture field and the associated large scale and mesoscale advection processes are the reason for the disagreement between surface flux stations and aircraft data. The surface flux stations apparently do not ‘see’ this type of mesoscale variability. A large vertical flux divergence is implied for the lowest 100 m of the boundary layer.
6. Discussion and summary Regional fluxes over a heterogeneous landscape were investigated using Nopex aircraft data. On June 13 a comparison of regional fluxes from aircraft data with an area-averaged surface flux from surface data proved difficult because of fractional cloud cover. However in this case, regional fluxes based on aircraft data are consistent with aircraft measured net radiation. On June 14 there is a large disagreement between regional fluxes from aircraft and surface based flux. In this case, net radiation measurements agree and sampling uncertainties of aircraft measured fluxes are not significant. This implies a strong vertical flux divergence in the surface layer. This seems due to the strong advective conditions during this day. We find strong mesoscale moisture variability especially for 14 June which significantly affects the energy fluxes through the boundary layer. The mesoscale moisture variability is more pronounced compared to the temperature field. In this particular case, the moisture variability is related to a cold front. Mesoscale fluxes were defined from covariance spectra. In general we found flux contributions at scales larger than 5 km which was referred to as a mesoscale regime. The mesoscale features are believed to be transient features since landuse characteristics and background flow probably do not support surface driven (e.g. due to temperature difference) mesoscale circulations. On average these mesoscale fluxes are small, but locally they can be large. The boundary layer budgets terms of heat and moisture were estimated for two days of Nopex ’94. Advection terms are important for the regional energy
budget on both days. Including mesoscale vertical flux divergence in the budget on June 13 reduces the residual, but the results are more of a exploratory nature. The mesoscale fluxes may contain large sampling uncertainties. There seems a tendency that the mesoscale flux contribution to the budget of moisture is more important than that for heat. The advective conditions indicate that simple 1D boundary-layer models will not work for the two days we have analyzed if they do not account for large scale horizontal advection. However, even if large (or synoptic) scale horizontal advection is included, mesoscale subgrid advection appears to have an significant impact on the energy exchange in the planetary boundary layer. This has been shown in context with the mesoscale moisture front in Section 4. This subgrid phenomena must be parameterized. In addition, the observed subgrid moisture variability is likely to have an impact on the subgrid relative humidity variation which is an important parameter for boundary layer cloud schemes. The results might point to some limits of existing boundary layer schemes for heterogeneous land surfaces which are used in regional and global climate models. For example, the mosaic approach (e.g. Koster and Suarez, 1992, Seth et al., 1994) cannot be used to model the boundary layer energy fluxes over the Nopex area. The mosaic approach assumes geographically distinct tiles which make up a grid square mosaic within the grid box. It is assumed that each tile interacts independently with the atmosphere. In our case part of the spatial variability of the surface fluxes and the energy transfer through the boundary layer is not related to the surface heterogeneity on 14 June.
Acknowledgements Acknowledgement We thank Sven-Erik Gryning, Martti Heikinheimo and Anders Lindroth for providing the surface flux data. Thanks also to Hans Bergstro¨m for providing the radiosonde data. The helpful discussions with Anders Lindroth and Achim Grelle are appreciated. M. Frech is funded by BMBF through the ‘Wasserkreislauf’ program under contract 07 VWK 01/6. P. Samuelsson and M. Tjernstro¨m are funded under contracts G-GU 02684-314 and G-GU 02684-312 of the Swedish Natural Research Council.
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The aircraft was operated and instrumentation installed by personnel from Testing Directorate of the Swedish Defence Material Administration. The authors are grateful to technicians as well as to the pilots. References Avissar, R., Chen, F., 1993. Development and analysis of prognostic equations for mesoscale (subgrid scale) fluxes for largescale atmospheric models. J. Atmos. Sci. 50, 3751–3773. Betts, A.K., 1992. Fife atmospheric boundary layer budget methods. J. Geophys. Res. 97 (18), 523–531. Betts, A.K., Desjardins, R.L., MacPherson, J.I., 1992. Budget analysis of the boundary layer grid flights during Fife 1987. J. Geophys. Res. 97 (18), 533–546. Dalu, G.A., Pielke, R.A., 1993. Vertical heat fluxes generated by mesoscale atmospheric flow induced by thermal inhomogeneities in the PBL. J. Atmos. Sci. 50, 919–926. Desjardins, R.L., MacPherson, J., Schuepp, P., Karanjia, F., 1989. An evaluation of aircraft measurements of CO2, water vapour and sensible heat. Bound.-Layer Met. 47, 55–69. Doran, W.J., Shaw, W.J., Hubbe, J.M., 1995. Boundary layer characteristics over areas of inhomogeneous surface fluxes. J. Appl. Met. 34, 559–571. Frech, M., 1998. Mesoscale moisture variability and its impact on energy transfer through the boundary layer. Bound.-Layer Met. 87, 41–68. Grossman, R.L., 1992. Convective boundary layer budgets of moisture and sensible heat over an unstressed prairie. J. Geophys. Res. 97 (18), 425–438. Grossman, R.L., 1992. Sampling errors in the vertical fluxes of potential temperature and moisture measured by aircraft during Fife. J. Geophys. Res. 97 (18), 439–443. Halldin, S., Gottshalk, L., van de Griend, A.A., Gryning, S.-E., Heikinheimo, M., Ho¨gstro¨m, U., Jochum, A., Lundin, L.-C., 1998. NOPEX—a northern hemisphere climate processes land surface experiment. J. Hydrol. 212–213, 172–187. Howell, J.F., 1995. Identifying sudden changes in data. Mon. Weather Rev. 123, 1207–1212. Howell, J.F., Mahrt, L., 1994. An adaptive decomposition: application to turbulence. In: Foufoula-Georgiou, E., Kumar, P. (Eds.), Wavelets in Geophysics. Academic Press, New York. Koster, R.D., Suarez, M.J., 1992. A comparative analysis of two land-surface heterogeneity representations. J. Clim. 5, 1379– 1390. Lynn, B.H., Abramopoulos, F., Avissar, R., 1995. Using similarity theory to parameterize mesoscale heat fluxes generated by
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subgrid-scale landscape discontinuities in GCMs. J. Clim. 8, 932–951. Mahrt, L., 1991. Boundary-layer moisture regimes. Quart. J. Roy. Met. Soc. 117, 151–176. Mahrt, L., 1991. Eddy asymmetry in the sheared heated boundary layer. J. Atmos. Sci. 48, 472–492. Mahrt, L., Gibson, W., 1992. Flux decomposition into coherent structures. Bound.-Layer Met. 60, 143–168. Mahrt, I., MacPherson, J.I., Desjardins, R., 1994. Observations of fluxes over heterogeneous surfaces. Bound.-Layer Met. 67, 345–367. Roth, M., Oke, T.R., 1995. Relative efficiencies of turbulent transfer of heat, mass and momentum over a patchy urban surface. J. Atmos. Sci. 52, 1863–1874. Samuelsson, P., Tjernstro¨m, M., 1997. In-situ airborne meteorological measurements in Nopex: part I: the experiment and some average conditions. Agric. For. Met. 00, 000–000 Submitted. Segal, M., Arritt, R.W., 1992. Nonclassical mesoscale circulations caused by surface sensible heat-flux gradients. Bull. Am. Met. Soc. 73, 1593–1604. Seth, A., Giorgi, F., Dickinson, R., 1994. Simulating fluxes from heterogeneous land surfaces: Explicit subgrid method employing the biosphere-atmosphere transfer scheme (BATS). J. Geophys. Res. 99 (18), 651–667. Smith, E.A., Hsu, A.H., Crosson, W.L., Field, R.T., Fritschen, L.J., Gurney, R.J., Kanemasu, E.T., Kustas, W.P., Nie, D., Shuttleworth, W.J., Stewart, J.B., Verma, S.B., Weaver, H.L., Wesely, M.L., 1992. Area-averaged surface fluxes and their time-space variability over the Fife experimental domain. J. Geophys. Res. 97, 599–622. Smith, E.A., Wai, M.M.-K., Cooper, H.J., Rubes, M.T., 1994. Linking boundary-layer circulations and surface processes during Fife 89 part I: observational analysis. J. Atmos. Sci. 51, 1497–1529. Stull, R.B., 1988. An Introduction to Boundary Layer Meteorology. Kluwer Academic, Norwell, MA. Sun, J., Mahrt, L., 1994. Spatial distribution of surface fluxes estimated from remotely sensed variables. J. Appl. Met. 33, 1341– 1353. Tjernstro¨m, M., Friehe, C.A., 1991. Analysis of radome air motion system on a twin-jet aircraft for boundary-layer research. J. Atmos. Oceanic Technol. 8, 19–41. Tjernstro¨m, M., Smedman, A.-S., 1993. The vertical turbulence structure of the coastal marine atmospheric boundary layer. J. Geophys. Res. 98, 4809–4826. Weil, J.C., Horst, T.W., 1992. Footprint estimates for atmospheric flux measurements in the convective boundary layer. In: Schwartz, S.E., Slinn, W.G.N. (Eds.), Precipitation Scavenging and Atmosphere-Surface Exchange, vol. 2. Hemisphere, New York. pp. 717–728.
Regional surface fluxes over the Nopex area M. Frech a,*, P. Samuelsson b, M. Tjernstro¨m b, A.M. Jochum a a
Institut fu¨r Physik der Atmospha¨re, DLR Oberpfaffenhofen, D-82234 Wessling, Germany b Department of Meteorology, Uppsala University, S-75220 Uppsala, Sweden Received 8 November 1995; accepted 28 October 1996
Abstract The regional surface fluxes of sensible heat and moisture are estimated for two days during Nopex ’94 by means of aircraft measurements. A box flight pattern is analysed for 13 June (a weak wind case) and 14 June (a strong wind case), both with cold air advection. We perform a scale analysis in order to identify the main transporting scales of the turbulent fluxes and to investigate the mesoscale variability of the sensible heat and moisture flux. The example of a mesoscale moisture front indicates the importance of subgrid mesoscale variability. The turbulent fluxes of sensible heat and moisture are affected significantly by this mesoscale variability. This mesoscale variability is usually subgrid in numerical models and therefore must be parameterized. The source of the mesoscale moisture variability appears to be related to a cold front. Mesoscale flux divergence is explicitly included into the budget of sensible heat and moisture. The average vertical mesoscale flux divergence is small compared to the turbulent flux for the two cases investigated. However, the vertical mesoscale flux can be large locally. The budgets indicate the importance of horizontal advection for the Nopex region. The time evolution of sensible heat and moisture during 14 June appears to be dominated by large scale horizontal advection. A comparison between the area-averaged surface flux from aircraft data and surface flux stations for the 13 June is not conclusive because of fractional cloud cover. For the strong wind case on 14 June, the surface fluxes obtained from aircraft data and from surface flux stations disagree, which appears to be related with the pronounced mesoscale moisture variability. 䉷 1998 Elsevier Science B.V. All rights reserved. Keywords: Heat and moisture flux; Regional surface fluxes; Turbulent flux
1. Introduction The northern hemisphere land surface climate processes experiment (Nopex), is devoted to study land-surface–atmosphere interactions in a northern European forest-dominated landscape (Halldin et al., 1998). The Nopex main study region is selected to represent the southern part of the boreal zone. It is the goal of Nopex to investigate fluxes of energy, momentum, water, CO2 and the associated interaction
* Corresponding author.
between soil, vegetation and atmosphere, between lakes and the atmosphere, as well as within the soil and the atmosphere on local to regional scales ranging from centimeters to tens of kilometers. Aircraft based measurements provide a tool to estimate the integration of energy fluxes over heterogeneous terrain and to estimate area averaged surface fluxes. Furthermore, a budget analysis based on aircraft measurements can be used to study the basic processes contributing to the boundary-layer time variation of potential temperature, u, and specific humidity, q. A better understanding of spatial and temporal variations of energy fluxes is necessary in order to improve existing
0022-1694/98/$ - see front matter 䉷 1998 Elsevier Science B.V. All rights reserved. PII: S0022-169 4(98)00207-8
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aggregation methods of surface fluxes for use in regional and global climate models. The variability of surface fluxes is controlled by a number of factors. A permanent controlling factor would be the landscape characterized by its topography and soil type. Furthermore, underground hydrology, vegetation and land use (e.g. grazing, burning, crop selection), atmospheric forcing (e.g. the synoptic situation, cloud cover, mesoscale dynamics) impose additional factors which contribute to the variability of surface fluxes within a grid box. Therefore, considerable variability of surface fluxes is even found over fairly homogeneous surfaces as it was observed during Fife (first international satellite land surface climatology project field experiment, Smith et al., 1992). On an appropriate scale of heterogeneity ( ⬇ 10 km) mesoscale circulations may evolve due to contrasts in surface temperature in weak ambient background flow. For example, the soil moisture field and organized vegetation patterns can organize boundary layer circulation patterns (Segal and Arritt, 1992; Smith et al., 1994). Mesoscale circulations can modulate ‘small scale’ turbulence or directly contribute to the flux (e.g. Dalu and Pielke, 1993; Mahrt et al., 1994; Doran et al., 1995). The mesoscale flux contribution appears to be significant in the surface energy balance with weak large scale flow and strong surface heterogeneity (Sun and Mahrt, 1994). In their study, inclusion of mesoscale flux leads to an approximate closure of the energy balance at the surface. Modeling studies indicate the importance of mesoscale circulations induced by landscape heterogeneities of energy fluxes (Avissar and Chen, 1993). These studies suggest that it is necessary to parameterize mesoscale circulations which are usually subgrid scale in global models (Lynn et al., 1995). The Fife atmospheric boundary layer budget studies (Betts et al., 1992, Betts, 1992, Grossman, 1992a) show that simple mixed-layer models were applicable and also indicate the importance of accurate horizontal advection estimates to balance the budget of sensible heat and moisture. These budget studies revealed that entrainment fluxes in mixed layer models are underestimated (the entrainment coefficient was found to be of the order of 0.4 compared to the usual value of 0.2). It is unknown if
this result can be generalized. Entrainment coefficients on the order of 0.4 are commonly found in the unstably stratified marine boundary layer (Tjernstro¨m and Smedman, 1993). There is often a disagreement between surface flux estimates from aircraft data and measurements from surface flux stations. The disagreement is sometimes larger for the latent heat flux as compared to the sensible heat flux (Betts et al., 1992). This is usually attributed to the under-sampling of larger scale flux contributions by the aircraft because of short flight legs and sometimes to data processing (Grossman, 1992b). Part of this under-sampling might be inherent in aircraft measurements because of the quasi-1D sampling of 3D boundary layer turbulence. A direct comparison between tower measurements or measurements at the surface and surface fluxes derived from aircraft is difficult since we are comparing point measurements with a measurement in space. A comparison is even more difficult if we make measurements over a heterogeneous landscape. A complicating aspect is that mixing of moisture can be different to mixing of sensible heat. This can be related to different source areas for temperature and moisture fluctuations (Roth and Oke, 1995) and mesoscale heterogeneity in the surface energy balance (Mahrt, 1991a, 1991b). In this study we will analyse aircraft data from two flight missions during the first concentrated field effort (CFE) of Nopex in June 1994. As a first step we investigate the dominant scales in the flux estimates and the variability of these fluxes over the Nopex domain. Then, the budget components of sensible heat and moisture are estimated. The estimated surface flux from aircraft data is compared to weighted area-averaged surface fluxes based on representative measurement sites (i.e. forest, lake, farmland) within the Nopex domain.
2. Data 2.1. The flight mission The Nopex area and the experiment is described in detail by Halldin et al., 1998. Forests dominate the area as a whole, with agricultural fields concentrated towards the south and a increasingly larger fraction of
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Fig. 1. The location of surface flux stations. The dashed line denotes the Nopex area, the solid line the shape of the box flight pattern.
the ground covered with forests towards the north. The forest is mainly spruce and pine, with a small fraction (15%) of deciduous trees, primarily in the south. The forests occupy approximately 54%, farmland 38%, wetlands and lakes 4% of the Nopex area. The land use distribution below the aircraft for the box flight pattern (including a nominal fetch of 600 m to the left and right of the flight track) indicates 56% coverage by forest, 36% by farmland, 4% by wetlands and lakes, and 4% by populated area. This distribution is later used to calculate a weighted area average from
the surface flux stations as an estimate for the regional latent and sensible heat flux. There are a number of surface flux stations (see Fig. 1) in the Nopex area, one for each main surface type. Available is data from two towers within a forest with eddy correlation measurements at different heights (near 33 m at the Siggefora and near 35, 70 and 100 m at the Norunda tower). The trees are about 20–25 m high consisting of mature mixed spruce and pine stands of different age. Flux data from two agricultural sites (Lo¨vsta and Tisby) and from one
Fig. 2. The non-orthogonal albedo wavelet variance spectra along the box flight pattern during Nopex 1994.
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Fig. 3. The composited radiosonde profiles of u (⬚C) and q (g kg ⫺1) for the 13 (a,b) and 14 (c,d) June. T indicates the period of the ‘turbulence’ flights; B the time period of the box flights. The bold dashed line indicates the boundary layer height.
lake station (Ta¨mnaren; 37 km 2, average depth 1.2 m) are available (this flux data is also based on eddy correlation measurements). Aircraft measurements were performed during the experiment in order to sample the mean and turbulent boundary layer structure over the Nopex area. There are also radiation measurements (upward and downward long/short wave radiation) available from these flights. We are analysing the box flight pattern shown in Fig. 1. The flight paths (legs) have the shape of a rectangle and were flown at two levels during each box flight mission. The legs are approximately 45 and 90 km long. In the text legs 1, 2, 3 and 4 correspond to the lower flight level, and legs 5, 6, 7 and 8 to the upper flight level.
It takes approximately 90 min to fly this pattern. Each flight pattern started at about 2000 m above ground with a profiling descent. This box flight pattern is used to derive the components of the budget of sensible heat and moisture and to estimate area-averaged surface energy fluxes on a regional scale. The aircraft is the Sabreliner 40A operated by the Defence Material Administration (FMV) of Sweden. The instrumentation of the aircraft is described in detail by Tjernstro¨m and Friehe (1991). More information about the flight missions during the Nopex CFE 1994 are summarized by Samuelsson and Tjernstro¨m (1997). The radiation measurements from the aircraft
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Fig. 4. The time tendency of u and q at different height levels for June 13 (a,b) and 14 (c,d) based on radiosonde soundings. The time tendency is given for different height levels. T indicates the period of the ‘turbulence’ flights; B the time period of the box flights. Bold solid line 100 m, bold dashed line 500 m, bold dash-dotted line 900 m, dotted line 1300 and dashed line 1700 m.
characterize the surface heterogeneity of the Nopex area. A spectral analysis of albedo using the Haar wavelet spectra (Mahrt, 1991a) serves as a tool to obtain an expression about the surface heterogeneity that is sampled by the aircraft (Fig. 2). The peaks of albedo variance are found near 5 km for leg 1, near 2 and 35 km for leg 2, near 3 and 15 km for leg 3 and near 4 and 20 km for leg 4. These values indicate the spatial variability within the Nopex domain. Small scale patches are intermixed into larger scale patches which is reflected by the albedo variance where, for example, leg 2 is dominated by patches of 2 km scale which are embedded into albedo variations on a 35 km scale. The mean albedo derived from aircraft data shows a weak north–south gradient (0.12 in the northern section, 0.14 in the southern section).
2.2. The boundary layer evolution and the mean structure On June 13 the wind was weak to moderate from north-east. Boundary layer cloudiness was small with 1/8–2/8 of shallow cumulus clouds at the top of the ABL around 1500 m. However there was a 6/8 of cirrus stratus during the flight. On June 14, the winds were significantly stronger with wind on the order of 12 m s ⫺1 from south-west. A few boundary layer cumulus clouds were observed (1/8). There were radio sondes launched at the Marsta site every hour on June 13 and 14 (Bergstro¨m, personal communication). A time–height composite from these soundings show the temporal evolution of potential temperature and specific humidity (Fig. 3). The boundary layer height
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Fig. 5. The moisture variability during the flight mission: 13 June (top figure 100 m). The dashed area sketched in the xy plane indicates the Nopex domain and the box the flight pattern projected onto the xy plane. The circle at the z-axis denotes the mean specific humidity of the box flight at the level.
is estimated from the potential temperature profile. The evolution of the boundary layer depth is marked by the bold dashed line in the graph. June 13 shows a classical boundary layer growth from the morning hours to about noon, asymptotically approaching a
constant height near 1500 m. In contrast, on June 14 the boundary layer growth seems to be inhibited during the morning hours and shows an almost linear increase in height up to about 1700 m until 14 LST. The reason for this linear increase is unknown. The
Fig. 6. 14 June (z 100 m). See Fig. 5.
M. Frech et al. / Journal of Hydrology 212–213 (1998) 155–171 Table 1 General flight conditions for 13 and 14 June
Mean height of the legs (m) Length of the legs Flight time Boundary layer height estimated from radio sonde soundings Cloud cover Mean wind speed and wind direction Sampling rate of the mean data Sampling rate of the turbulence data
13.6 flight 350
14.6 flight 352
192, 728
100, 1700
80 and 45 km 80 and 45 km 13:57–15:52 (SST) 14:33–16:28 (SST) 1600 m 1850 m
2/8 Cu, 6/8–8/8 Ci 1/8 Cu 5.5 m s ⫺1, 320⬚ 12 m s ⫺1, 230⬚ 6.1 Hz
6.1 Hz
48.8 Hz
48.8 Hz
atmosphere aloft seems significantly more stably stratified during the first day. The specific humidity is well mixed on June 13 during the box flight. There is a weak negative gradient on June 14. The temporal development of potential temperature within the boundary layer is nearly linear for both days as is seen from the time evolution for different height levels (Fig. 4). In the upper levels potential temperature slightly decreases for the first day and is quasi constant for the second day. In the boundary layer moisture increases weakly on the first day and
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decreases on the second day. From the upper levels we can see that very dry air mass is replaced by more humid air on June 13, presumably by large scale horizontal advection. In contrast, specific humidity is quasi constant and slowly decreases in the afternoon on June 14. To give an impression about the spatial and temporal variability of specific humidity over the Nopex domain, Fig. 5 and Fig. 6 show the specific humidity signal along the box flight pattern. We observe a fairly smooth north-west to south-east gradient in specific humidity on June 13. The decrease in specific humidity along this gradient is about 1 g kg ⫺1. There is a strong spatial variability in specific humidity on the mesoscale during the box flight on June 14 (Fig. 6) with higher moisture content in the south-west corner of the area. We can observe a decrease in specific humidity by 1 g kg ⫺1 within one day. 3. The turbulent structure Covariances are calculated from high-pass filtered data (40 km cutoff) by means of the eddy correlation technique. We first investigate the most energetic length scales of the vertical fluxes by performing a spectral analysis. After the spectral analysis we estimate the flux sampling uncertainty and discuss the spatial variability of the fluxes.
Fig. 7. The non-orthogonal Haar spectra of sensible heat and moisture flux: Legs 2 (z 192 m) and 6 (z 728 m), 13 June. Dilation is a direct measure of the structure size.
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Fig. 8. See Fig. 7: Legs 2 (z 100 m) and 6 (z 1700 m), 14 June.
3.1. The covariance spectra The scale dependence of the heat and moisture flux is studied with non-orthogonal wavelet spectra based on the Haar-wavelet (Mahrt, 1991a, 1991b; Howell and Mahrt, 1994). Spectral peaks are better isolated by this local transform since main transporting scales of the flux are local phenomena. The spectra are based on high pass filtered data (40 km cutoff). The general flight conditions are given in Table 1. The covariance spectra of the vertical heat and moisture flux are shown for leg 2 and 6 (Fig. 7 and Fig. 8). Leg 2 and 6 are a pair of legs at different heights over the same segment within the flight pattern (June 13: leg 2 z 192 m, leg 6 z 728 m; June 14: leg 2 z 100 m, leg 6 z 1700 m). The
approximate maxima in the covariance spectra for both days are summarized in Table 2. The length scales in the turbulent regime is typical for a convective boundary layer. We expect smaller turbulent scales in the lower part of the boundary layer. The larger scales in the upper part of the boundary layer can be explained by smaller scale eddies which merge on their ascent forming large thermals. This can be seen in from Fig. 7. The upper flight leg on June 14 was near the boundary layer top. Here we observe negative entrainment fluxes. From this analysis we find that most of the turbulent flux in the boundary layer occurs on the scale of 1– 2 km which corresponds roughly to the scale of the depth of the boundary layer for these days. Different peaks in the covariance spectra of
Table 2 Identified length scales of the most energetic flux contributions based on wavelet covariance spectra. The spectra are based on high pass filtered data (40 km cutoff) 13 June
Leg Leg Leg Leg Leg Leg Leg Leg
1 5 2 6 3 7 4 8
wu 1000 m, 15 km 800 m, 6 km 500 m 1.2 km, 10 km 1 km 2 km, 12 km 900 m, 11 km 1.7 km, 15 km
14 June wq 900 m, 15 km 800 m, 3 km, 15 km 500 m 1.2 km, 30 km 700 m 2 km, 12 km 800 m, 10 km 1.7 km, 10 km
wu 400 m 2 km, 7 km 500 m, 6 km 2 km, 7 km 800 m, 4.5 km 2 km, 10 km 1 km, 17 km 2 km
wq 300 m 1 km, 7 km 400 m, 6 km 1.3 km, 6 km, 22 km 500 m, 6 km 900 m, 10 km 1 km, 18 km 6 km
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sensible heat and moisture flux may point to different source areas for heat and specific humidity fluctuations. For example, a significant part of a positive moisture flux in the lower part of the boundary layer can be caused by entrainment fluxes whereas a positive heat flux may be primarily forced by buoyancy generated turbulence at the heated land surface (e.g. Roth and Oke, 1995). From the covariance spectra shown in Figs 7 and 8 and Table 2 we find that there are always flux contributions present in the boundary layer at a larger scale of 4–5 km for the two days investigated in this study. The source of this covariance can be surface driven or of transient nature. For the strong wind conditions found for 14 June we would not expect the evolution of mesoscale circulation due to differential surface heating. Based on this scaling behavior we will refer to a ‘mesoscale regime’ for the covariance at scales larger than 5 km. The spectral peaks in the mesoscale regime (2) scatter a lot between legs and seem point to the transient nature of these features. 3.2. The mesoscale flux From data mesoscale fluctuations and fluxes are calculated the following way: We decompose the time series c of a particular leg in
c c ⫹ cⴱ ⫹ c 0
1
where c can be u or q. c is the mean along the flight, c * the ‘mesoscale’ deviation from the mean and c 0 the turbulent fluctuation. The turbulent fluctuation can be defined as the deviation from a local average [c]. The local average is written as the sum of the total leg average and the mesoscale deviation (e.g. Mahrt et al., 1994).
c c ⫺ c ⴱ
2
The turbulent part is just the deviation from the local average. Note that when averaging eqn (2) over the flight leg the mesoscale part becomes zero. From a modeling point of view, the total average c represents the GCM grid box mean, the second term in eqn (1) is the subgrid mesoscale signal due to subgrid heterogeneity and the last term is the turbulent deviation from the mesoscale signal which is defined by the scale of surface heterogeneity (e.g. Avissar and Chen, 1993). The separation into mesoscale and turbulent
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fluctuations from actual data can be reached in different ways. One is to define a cutoff wavelength or structure length for the turbulence and define every flux contribution above a certain scale to be a mesoscale flux. The cutoff wavelength can be determined from covariance spectra based on the total flight leg. We use non-orthogonal wavelet spectra based on the Haar wavelet to determine the length scales. The resulting scale (5 km) defines a window which is translated sequentially through the time series. The mesoscale and the turbulent signal is calculated for each location along the leg. If the surface heterogeneity is distinct enough (scale of the order of 10 km) the decomposition of the flow can be posed in terms of the underlying surface (Mahrt et al., 1994). Albedo, surface radiation temperatures or greenness index can be used for partitioning if the flight level is close enough to the surface. However, the surface heterogeneity of the Nopex area is not well defined so that it is not possible to perform a decomposition of the data in terms of the surface heterogeneity. After the decomposition of the data we can write the total leg averaged covariance as (here for the heat flux; the mean is removed from the time series): wu wⴱ ⫹ w 0 uⴱ ⫹ u 0
3
The overline represent a spatial average over the whole leg. The covariance between mesoscale and turbulent fluctuation average to zero with the given decomposition. The average covariance reduces to wu wⴱ uⴱ ⫹ w 0 u 0
4
3.3. The uncertainty of the turbulent flux The uncertainty of the turbulent fluxes is estimated by choosing samples of approximately 8 km length. The turbulent flux is calculated for each segment. We then assume a Gaussian distribution of these flux samples and apply the central limit theorem in order to estimate the sampling uncertainty (Mahrt and Gibson, 1992). We find uncertainties in latent and sensible heat flux on the order of 20%–25% for the low level legs and 25%–50% for the legs at the higher flight level for 13 June (Table 3). The flux uncertainties for the low level data on 14 June are on the order of 10%–20%. Fractional cloud cover seems to be the reason for larger flux sampling uncertainties during 13
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Table 3 The flux sampling uncertainty (in %) for individual legs Leg
1
2
3
4
5
6
7
8
13 June w 0 u 0 13 June w 0 q 0 14 June w 0 u 0 14 June w 0 q 0
22 18 10 23
21 17 31 21
31 19 10 28
17 15 13 24
62 34 77 58
32 13 146 88
29 22 37 56
36 21 55 67
June which causes a larger variability of the turbulent fluxes over the Nopex domain. The flight legs near 1700 m for 14 June are characterized by large sampling uncertainties. We compared the expected uncertainty of the flux estimate with Ogives which were calculated for each leg (Desjardins et al., 1989). The fluxes are accumulated along the wavelength as shown in Fig. 9 for the 13 June. This method gives us more confidence that we actually capture most of the flux at wavelengths smaller than 20 km. For all legs located well in the boundary layer the curves tends to level out for wavelengths larger than 20 km. There are indications that the latent heat flux contains more energy at shorter wavelengths compared to the sensible heat flux (9). For the flight
legs in the entrainment zone near 1700 m there are still significant contributions to the fluxes at scales larger 20 km (not shown here). 3.4. Spatial variability of turbulent and mesoscale fluxes The variation in specific humidity along leg 4 will be investigated briefly in order to investigate its influence on the vertical turbulent flux through the boundary layer. In this particular case the variability in the moisture field appears to be related to a cold front which passed the Nopex domain 2.5 h after this observation. A more detailed analysis may be found in Frech (1998). The moisture variation seen in leg 4 (see Fig. 6) is shown in Fig. 10. We find a very sharp drop in specific humidity by Dq ⬇ 1.6 g kg ⫺1. This moisture variation is referred to as a moisture front. The most striking feature in these time series is that there is no equivalent drop in temperature as one might expect. Here the moisture field appears decoupled from the temperature field. This moisture front is characterized by a large momentum deficit in the presence of a strong
Fig. 9. Cumulative integral of the cospectrum for sensible and latent heat for 13 June. All curves are normalized with the flux value at the cut-off wavelength, approximately 40 km. The lines represent: Full line, sensible heat flux for leg 4. Dashed line, latent heat flux for leg 4. Dash-dotted line, sensible heat flux for leg 8. Dotted line, latent heat flux for leg 8.
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Fig. 10. The observed moisture front 14 June, NOPEX 1994, leg 4. The turbulent fluctuations of w, u and q are shown for a 18 km segment which includes the moisture front. In addition, the associated wind speed is plotted.
updraft region. This indicates the transport of low momentum and warm air from regions near the surface. To investigate this phenomena we select two segments to the left and right of the sudden change in q. The segments chosen are 8 and 10 km long and specific humidity is quasi constant within these segments. The statistics of these segments are summarized in Table 4. The ‘dry’ segment shows reduction in latent heat flux by 60% compared to the moist section. Sensible heat flux is less affected by the moisture variation which seems consistent with the undisturbed temperature time series. A large vertical flux divergence is implied when we compare sensible and latent heat flux with net radiation in both segments. The air within the ‘dry’ segment is less unstable which can explain the reduced sensible
heat flux. The variation of the turbulent flux and specific humidity cannot be explained by the land surface characteristics. There is no significant change in surface temperature and albedo. In addition the landuse characteristics do not change within 600 m upstream to the flight leg which is approximately the footprint of the turbulent flux at flight level. The maximum upwind source area of influence can be estimated from x Uh/sw (using sw ⬇ 2 m s ⫺1 and ¯ ⬇ 13 m s ⫺1; Weil and Horst, 1992). U The mesoscale variation of specific humidity seems advected. From the data we cannot determine the depth of this disturbance. The variation of the turbulent and mesoscale latent heat flux along leg 2 for 14 June is shown in order to illustrate the flux variability (Fig. 11). The fluxes
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Fig. 11. The spatial variability of the turbulent and mesoscale latent heat flux along leg 2 for 14 June 1994. Also shown is the albedo variation along this flight leg (the block averages are based on the results of the ‘variable block averaging’ (VBA) algorithm, Howell, 1995.
shown are based on the decomposition given in eqn (1) using a window width of 4 km. There is a weak correlation of the flux intensity with the surface conditions (characterized by albedo) below the flight leg between kilometer 7 and 22. In this segment we observe relatively weak fluxes. The albedo below the flight leg is characteristic for the upstream area where we expect the source area for part of the turbulent flux. For other parts of the leg there is no obvious correlation between albedo and the measured flux. The segment between 50 and 60 km is influenced by Table 4 The statistics of two segments near a sudden change of q for Leg 4, 14 June, flight 352. Standard notation is used. Tsfc radiative surface temperature, u v virtual potential temperature, L Obukhov length, z observation level, Rnet net radiation
q¯ (g kg ⫺1) u (⬚C) T¯ (⬚C) T¯sfc (⬚C) ¯ (m s ⫺1) U dir (⬚) L (m) z/L u* (m s ⫺1) H (W m ⫺2) LE (W m ⫺2) Rnet (W m ⫺2)
Segment a (‘moist’)
Segment b (‘dry’)
4.9 23.7 22.6 23.9 12.8 232 ⫺ 72.5 ⫺ 1.52 1.16 139 247 416
3.3 23.8 22.6 23.8 13.1 236 ⫺ 116.4 ⫺ 0.94 1.18 95 91 444
Lake Ta¨mnaren which is in the upstream region to the flight leg. This segment is characterized by large mesoscale fluxes.
4. The budget We consider the box flight pattern as a hypothetical grid box in a numerical model. It is one objective to investigate which processes contribute to trends (in time) of potential temperature and specific humidity within this grid box. The budget for any scalar c can be written as: X 2c 2c ⫹ ui S 2t 2x i
5
where ui are the velocity components (u, v, w) and xi denotes the coordinate system (x,y,z). The terms on the left hand side are the local time rate of change and advection of c. S represents sources and sinks of c which can be, for example, radiative flux divergence for the budget of u or evaporation of condensate for the budget of q. The only souce and sink term we keep in our study is the longwave radiative flux divergence which proved non-negligible. The decomposition of the velocity components ui follows eqn (1). Substituting the variables into the budget eqn (5), rearranging
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and applying Reynolds averaging rules, we obtain: X 2c 2c 2u 0i c 0 2uⴱ c ⴱ ⫹ ui ⫹ ⫹ i S 2x i 2x i 2t 2x i
6
In eqn (6), the third and fourth term on the left hand side represent the components of turbulent and mesoscale flux divergence of c, respectively. The overbar represents the grid average. 4.1. The budget terms The components of the budget are estimated using aircraft, radiosonde and surface data. We first identify the dominating terms in the budgets. A first idea on the boundary layer time trend of u and q¯ can be obtained from composited radiosonde soundings. On June 13 the moisture trend seems nonlinear for the time period of the box flight (4). On June 14 there is essentially no trend in potential temperature during the flight. A significant linear decrease of specific humidity in time is found at the same time. However, radio soundings may have considerable sampling errors so that this is a rather qualitative observation. A method to derive the trend of a scalar solely from aircraft data is described in Betts et al. (1992). The composite of leg averaged mean data is determined. A linear fit over this composite yields the trend. Estimating the time tendency for our control volume by applying this method is not possible because of the heterogeneity of the Nopex area. Boundary layers of different history are sampled by the flight pattern and are partly characterized by the underlying surface and the upstream conditions. Therefore the time tendency is based on a pair of flight legs over the same area. It takes approximately 45 min before the aircraft flies over the same area within the flight pattern. The four estimates are averaged to obtain a regional estimate and the standard deviation yields a measure of its uncertainty. We also calculated the time tendency from surface stations: Siggefora, Tisby and Lake Ta¨mnaren. These tendencies are weighted according to the fractional area of each surface type within the Nopex area. The situation on 14 June is more complicated. Here the specific humidity is not well mixed. So we cannot determine the time tendency from aircraft data. The time tendency of moisture from the individual surface
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stations partially show opposing trends. This can be explained by the strong spatial variability of the moisture field. We, therefore, estimate the time tendency in that case with radiosonde soundings (4). Since potential temperature is approximately well mixed its time tendency is calculated from aircraft data. The horizontal advection terms are based on linear trends from single flight legs. These estimates are corrected by the time tendency in order to separate trends in time and space. This procedure assumes that the time tendency is constant for a flight leg. The standard error of the slope of the linear trend defines the error estimate of the advection term. An estimate of the large scale vertical velocity can be derived from the horizontal divergence of the wind field. The uncertainty in w turned out to be large for 14 June. The vertical advection term is therefore not included. For this day vertical advection of q could be non-negligible since q is not well mixed. The vertical flux divergence is calculated for each pair of legs over the same segment. This method assumes that the vertical flux divergence is constant for the time period between the legs (45 min). The four estimates are averaged to obtain a regional flux divergence value for the Nopex control volume. The assumption of linearity is made for both the turbulent and mesoscale vertical flux divergence. This is probably not always appropriate for the mesoscale flux divergence as is suggested in the modeling studies of Lynn et al. (1995). The uncertainty in the estimated flux divergence values can be quite large since the flux divergence values depend only on two flux values. The uncertainty of the flux divergence will be based on the uncertainty of the flux estimate. Both the turbulent and mesoscale horizontal flux divergence are found to be negligible. Longwave radiative flux divergence is estimated from a profile flight which was part of the flight mission. Because fluxes from the upper flight level on June 14 have a large sampling error no reliable vertical flux divergence can be estimated for this flight. 4.2. Results The situation on 13 June is characterized by weak winds and cold air advection. The negative vertical turbulent heat flux divergence indicates the usual
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Table 5 The budget of sensible heat, 13 June and 14 June 1994 in W m ⫺3 Flight
2u 2t
u
2u 2x
13 June 14 June
0.03 8 ^ 0. 017 ⫺0.066 ^ 0.015
⫺0.01 3 ^ 0.003 0.203 ^ 0.002
v
2u 2y
0.075 ^ 0.003 ⫺0.078 ^ 0.004
daytime heating of the boundary layer. The vertical mesoscale heat flux divergence is small and adds to the heating of the boundary layer (Tables 5 and 6). The positive time tendency of sensible heat is about a factor of two smaller compared to the flux divergence which indicates the importance of cold air advection on the time evolution of u. The longwave radiative flux divergence is not negligible in the budget. The relative large residual in the budget for sensible heat may point to flux sampling uncertainties and errors due to the nonlinearity of the time tendency term. We find moist air advection in the budget of moisture. The negative vertical turbulent moisture flux divergence indicates a moistening of the boundary layer. The vertical mesoscale flux divergence indicates a drying tendency at larger scales. The mesoscale flux divergence improves the budget and is more important compared to that for sensible heat. The budget indicates the importance of advection which is on the same order of magnitude as the turbulent flux divergence. The residual in the budget of specific humidity is acceptable when we use the time tendency based on the surface flux stations. However, it is difficult to assess how representative a regional time tendency from point measurements can be. To summarize, the time tendencies of the budgets of sensible heat and moisture are not balanced by the vertical flux divergence. This implies that a simple one dimensional mixed layer model will not work. Advection is important for the time tendency of heat
2 w 0 u 0 2z
2 wⴱ uⴱ 2z
2Fnet 2z
Residual
⫺0.083 ^ 0.025 —
⫺0.002 —
⫺0.02 ⫺0.034
⫺0.035 —
and moisture. There seems to be a tendency that the mesoscale flux divergence is more important for the budget of moisture. However, we cannot determine the uncertainty of the estimated vertical mesoscale flux divergence. On 14 June the advection terms are large. Cool air is advected which leads to a cooling trend. Again, the longwave radiative flux divergence cannot be neglected. The budget of specific humidity is dominated by dry air advection which leads to a negative moisture tendency.
5. Area-averaged flux If reliable estimates of the budget terms exist, we can derive the regional surface flux as a residual (Grossman, 1992a). Since the residual is quite large on June 13, we refrain from inverting the budget to estimate a surface flux. All errors from individual budget terms would accumulate in the surface flux estimate. Therefore the vertical flux divergence is used to extrapolate to the surface on June 13. In addition we can assume a linear profile for the heat flux and estimate the surface flux with w 0 u 0s w 0 u 0 z=1 ⫺ 1:2 z=zi (Stull, 1988). For the 14 June case, we will use the lowest flight level as an estimate for the regional surface flux. A second surface heat flux estimate will be based on the assumption of a linear profile. The surface flux estimates are compared with flux
Table 6 The budget of latent heat, 13 June and 14 June 1994 in Wm ⫺3. On June 13, the time tendency of q based on aircraft data and surface stations is included. The first time tendency of specific humidity on June 13 is based on surface measurements. Flight
2q 2t
u
2q 2x
13 June 13 June 14 June
0.185 ^ 0.029 0.093 ^ 0.019 ⫺0.829 ^ 0.178
⫺0.088 ^ 0.003 ⫺0.088 ^ 0.003 0.256 ^ 0.007
v
2q 2y
⫺0.072 ^ 0.007 ⫺0.072 ^ 0.007 0.563 ^ 0.056
2 w 0 q 0 2z ⫺0.109 ^ 0.033 ⫺0.109 ^ 0.033 —
2 wⴱ qⴱ 2z
Residual
0.027 0.027 —
⫺0.057 ⫺0.149 —
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Table 7 The average latent and sensible heat flux for the NOPEX area. The average flux for different land surface characteristics is given including fluxes at 100 m from the Norunda tower. The average surface flux of the surface flux stations are weighted by the area they occupy in the NOPEX area (‘Mean’). The Norunda data at 100 m is used for this estimate. ‘Div’ denotes the flux at 100 m height which is derived by extrapolating to this level using the estimated vertical flux divergence of the turbulent flux. ‘Level’ denotes the average turbulent and mesoscale (in brackets) flux at the lower flight level. ‘Profile’ denotes the surface heat flux derived by assuming a linear profile. The fluxes are in W m ⫺2 Flight 13 June 13 June 14 June 14 June
14:00–16:00 LST 14:00–16:00 LST 14:30–15:30 LST 14:30–15:30 LST
Flux
Agricultural
Forest
Norunda (100 m)
Ta¨mnaren
Mean
Div
Level
w 0 u 0 w 0 q 0 w 0 u 0 w 0 q 0
64 154 128 252
246 121 474 143
171 119 281 191
⫺ 11 71 ⫺ 99 246
118 125 200 208
78 131
64 (6) 113 (2) 118 (9) 172 (13)
measurements at the surface. The area-averaged surface flux derived from surface measurements is weighted by the fractional coverage of the respective surface types below the flight path. the results are summarized in Table 7. We take the flux from the Norunda tower at 100 m as an effective flux value for the forest within the Nopex area. The flux values at 35 m from the forest sites seem not representative especially for the 14 June which is the strong wind case. This is highlighted by the fact these fluxes do not balance with the measured net radiation (ground heat flux and storage terms are on the order of 40 W m 2). The flux values at the 35 m level presumably have a smaller footprint and therefore are more vulnerable to specific surface features. In addition, net radiation as derived from aircraft radiometers and from surface measurements is used to see whether the surface energy budget is closed (Table 8). On June 13 there is a disagreement between aircraft and surface measured net radiation. This is likely to be due to fractional cloud cover. The agreement of both measurements is good on June 14. On June 13 the flight levels where well in the boundary layer (192 and 728 m and zi 1600 m). We estimate an area-averaged surface flux using the estimated flux divergence and extrapolate to a height of 30 m above ground, about 8 m above the tree tops. The disagreement in the estimated surface flux
Profile 75 126
values between aircraft and surface flux data for the 13 June appears to be due to fractional cloud cover. The surface stations indicate larger net radiation values during this flight mission (8). From surface data we find that ground heat flux and the storage term are on the order of 50 W m 2. The surface energy balance closes approximately using the aircraft measured net radiation and energy fluxes. There is no significant disagreement between surface heat flux derived from the flux divergence and from the assumed flux profile. In this case the profile method is not very sensitive to errors in zi. For June 14 (zi 1850) we assume that the flux estimate at the lower flight level (z 100 m) is a good estimate for the regional flux (therefore results from the period 14:30–15:30 LST are shown which is approximately the time it takes to perform the lowest flight level). The surface heat flux from the profile method does not differ much from the heat flux at z 100 m. The comparison of aircraft data with surface flux measurements for the 14 June is difficult. As discussed earlier there is significant mesoscale variability in the moisture field which affects the turbulent fluxes heavily (see the section on the mesoscale moisture front). Since the agreement between the net radiation values from the surface and aircraft data is good for this day, the large difference between low-level aircraft flux
Table 8 The net radiation (in W m ⫺2) for the agricultural, forest and lake sites during the flight mission. Also listed is the weighted mean net radiation and the value derived from aircraft data Flight
Agricultural
Forest
Lake
Mean
Aircraft
13 June 14:00–16:00 LST 14 June 14:30–15:30 LST
300 430
363 528
315 364
325 467
250 456
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and the surface flux data cannot be explained by flux sampling problems. Flux sampling uncertainties for the latent and sensible heat flux are on the order of 10%–20%. We suspect that the mesoscale variability of the moisture field and the associated large scale and mesoscale advection processes are the reason for the disagreement between surface flux stations and aircraft data. The surface flux stations apparently do not ‘see’ this type of mesoscale variability. A large vertical flux divergence is implied for the lowest 100 m of the boundary layer.
6. Discussion and summary Regional fluxes over a heterogeneous landscape were investigated using Nopex aircraft data. On June 13 a comparison of regional fluxes from aircraft data with an area-averaged surface flux from surface data proved difficult because of fractional cloud cover. However in this case, regional fluxes based on aircraft data are consistent with aircraft measured net radiation. On June 14 there is a large disagreement between regional fluxes from aircraft and surface based flux. In this case, net radiation measurements agree and sampling uncertainties of aircraft measured fluxes are not significant. This implies a strong vertical flux divergence in the surface layer. This seems due to the strong advective conditions during this day. We find strong mesoscale moisture variability especially for 14 June which significantly affects the energy fluxes through the boundary layer. The mesoscale moisture variability is more pronounced compared to the temperature field. In this particular case, the moisture variability is related to a cold front. Mesoscale fluxes were defined from covariance spectra. In general we found flux contributions at scales larger than 5 km which was referred to as a mesoscale regime. The mesoscale features are believed to be transient features since landuse characteristics and background flow probably do not support surface driven (e.g. due to temperature difference) mesoscale circulations. On average these mesoscale fluxes are small, but locally they can be large. The boundary layer budgets terms of heat and moisture were estimated for two days of Nopex ’94. Advection terms are important for the regional energy
budget on both days. Including mesoscale vertical flux divergence in the budget on June 13 reduces the residual, but the results are more of a exploratory nature. The mesoscale fluxes may contain large sampling uncertainties. There seems a tendency that the mesoscale flux contribution to the budget of moisture is more important than that for heat. The advective conditions indicate that simple 1D boundary-layer models will not work for the two days we have analyzed if they do not account for large scale horizontal advection. However, even if large (or synoptic) scale horizontal advection is included, mesoscale subgrid advection appears to have an significant impact on the energy exchange in the planetary boundary layer. This has been shown in context with the mesoscale moisture front in Section 4. This subgrid phenomena must be parameterized. In addition, the observed subgrid moisture variability is likely to have an impact on the subgrid relative humidity variation which is an important parameter for boundary layer cloud schemes. The results might point to some limits of existing boundary layer schemes for heterogeneous land surfaces which are used in regional and global climate models. For example, the mosaic approach (e.g. Koster and Suarez, 1992, Seth et al., 1994) cannot be used to model the boundary layer energy fluxes over the Nopex area. The mosaic approach assumes geographically distinct tiles which make up a grid square mosaic within the grid box. It is assumed that each tile interacts independently with the atmosphere. In our case part of the spatial variability of the surface fluxes and the energy transfer through the boundary layer is not related to the surface heterogeneity on 14 June.
Acknowledgements Acknowledgement We thank Sven-Erik Gryning, Martti Heikinheimo and Anders Lindroth for providing the surface flux data. Thanks also to Hans Bergstro¨m for providing the radiosonde data. The helpful discussions with Anders Lindroth and Achim Grelle are appreciated. M. Frech is funded by BMBF through the ‘Wasserkreislauf’ program under contract 07 VWK 01/6. P. Samuelsson and M. Tjernstro¨m are funded under contracts G-GU 02684-314 and G-GU 02684-312 of the Swedish Natural Research Council.
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