Where does all the energy go? Surface energy partitioning in ...

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Surface energy partitioning in suburban Christchurch under stable wintertime conditions. Authors; Authors and affiliations. R. A. Spronken-Smith; M. Kossmann ...
Theor. Appl. Climatol. 84, 137–149 (2006) DOI 10.1007/s00704-005-0151-2

1

Current affiliation: Higher Education Development Centre, University of Otago, Dunedin, New Zealand 2 University of Canterbury, Christchurch, New Zealand 3 Current affiliation: Deutscher Wetterdienst, Offenbach a. M., Germany

Where does all the energy go? Surface energy partitioning in suburban Christchurch under stable wintertime conditions R. A. Spronken-Smith1;2 , M. Kossmann2;3 , and P. Zawar-Reza2 With 7 Figures Received March 24, 2004; revised August 23, 2004; accepted February 5, 2005 Published online July 19, 2005 # Springer-Verlag 2005

Summary

1. Introduction

Typical observations of surface energy fluxes in urban areas usually employ the eddy covariance approach with measurements from a tower at a height well above the roughness elements. Net radiation and the turbulent fluxes are directly measured, the anthropogenic flux may be estimated and the storage flux is calculated as an energy balance residual. This paper reports both measurement and modelling of energy fluxes during wintertime in suburban areas of Christchurch, New Zealand. Under settled anticyclonic conditions, a strong inversion can occur over the city which severely restricts turbulent mixing. Even after sunrise the turbulent fluxes are small, and if one assumes advection is negligible, this means the storage flux increases in importance to very high levels. This paper suggests that these high storage rates are physically unrealistic for this environment. Rather, it is likely that some energy, which is assumed to be dissipated as heat storage, is more likely lost through mesoscale advection or attributed to errors caused by unsuitable measurement techniques under conditions with low friction velocity. However, even these two processes cannot fully account for flux loss. A full study is recommended to resolve this issue and meanwhile, caution is advised when applying current research methodology to estimate storage fluxes in urban areas in stable wintertime conditions.

The energy balance of an urban area is expressed by Oke (1988) as: Q þ QF ¼ QH þ QE þ DQS þ DQA

½W m2  ð1:1Þ

where the flux densities are: Q net all-wave radiation, QF anthropogenic heat, QH turbulent sensible heat, QE turbulent latent heat (or evaporation), DQS sensible heat storage, and DQA heat advection (representing the net gain or loss due to transport associated with the spatial gradients in temperature, humidity and wind as well as heat advection associated with local and mesoscale circulations such as country or sea breezes and foehn winds). Conceptually, this formulation applies to a notional control volume that extends vertically, from the underlying soil to above the roughness elements, and horizontally over many roughness element heights (see Oke, 1988). The assumptions associated with this volume approach are given by Finnigan et al. (2003). Typically, for urban energy balance research in

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recent years, flux measurements are taken from a tower at a height well above the roughness elements, in the constant flux layer. The location of the tower is carefully chosen so that measurements are representative of a specific urban landuse (such as residential). This requires an extensive fetch of similar landuse so that advective effects can be assumed to be negligible. Net all-wave radiation is measured using a net radiometer, the eddy covariance approach is used to measure the turbulent fluxes and advection is neglected (since sites are carefully chosen to avoid advective effects). The storage flux is then calculated as a residual: ¼ Q  Q  Q ð1:2Þ DQ S res

H

E

which is the common method for many urban applications (e.g. see Grimmond and Oke, 1995, 1999; Roth and Oke, 1994). Recent work by Spronken-Smith (2002) found that in very stable wintertime conditions in Christchurch, New Zealand, the turbulent fluxes were slow to increase after sunrise. During this ‘morning transition period,’ which is defined as the period between sunrise and the time at which the nocturnal inversion has been eroded (Stull, 1988), the turbulent fluxes often do not increase for 2–3 hours after sunrise, despite a substantial increase in Q . During these strongly stable conditions, and because DQS was calculated as a residual, this resulted in an anomalously high storage flux after sunrise. For example, Spronken-Smith (2002) showed that although Q increased at sunrise (about 730 h) QH only became positive at 1000 h and since QE was also close to zero until this time, DQS rose to about 150 W m2 by 1000 h and peaked at about 200 W m2 at solar noon (at a time when Q was typically about 300 W m2 ). Due to a highly non-stationary time during the morning transition in stable conditions, the use of the eddy covariance approach appears to be problematic. If the residual approach is used to calculate DQS , then on a daytime basis DQS =Q could be as high as 0.74–0.98. There is a paucity of wintertime measurements of surface energetics in mid-latitude urban areas with which to compare the findings of Spronken-Smith (2002). Grimmond (1992) reported wintertime energy fluxes for Vancouver, British Columbia. She used a similar methodol-

ogy to Spronken-Smith (2002), and found an average of only 19% of Q being channelled into DQS on a daytime basis. While the surface characteristics in these two studies were broadly similar (i.e. residential landuse), the synoptic conditions were very different. Kerschgens and Drauschke (1985) estimated urban fluxes over two winter days in Bonn, Germany. While they were taking measurements in stable wintertime conditions, they used a different approach which makes direct comparison difficult. Because of the cold climate and the anthropogenic heat input, they observed continuous addition of heat into the urban boundary layer so that the turbulent fluxes exceeded Q . Grimmond and Oke (1999) studied heat storage in seven cities and the highest reported daytime fraction of DQS =Q was 0.58 which was for the downtown heavily built Mexico City during the dry, ‘cooler’ season. Certainly, there is an issue with the high storage rates observed by Spronken-Smith (2002). Given that the residential neighbourhoods in Christchurch are predominantly one or two storey dwellings with much green space, it is unlikely that the urban fabric could be storing such large amounts of energy1. So the overriding question is: are these wintertime storage rates realistic, or is there a problem with the research methodology? Other researchers studying surface energetics in mainly non-urban environments have noted the problem with flux loss under stable conditions (e.g. Massman and Lee, 2002; Mahrt et al., 2001; Mahrt, 1998; Goulden et al., 1996). However, in these non-urban environments, there is usually a better understanding of heat storage in the ground and=or canopy and thus the flux loss usually arises from difficulties noted in trying to achieve closure. Furthermore, the reported problems are usually a nocturnal phenomenon, rather than continuing during the morning transition period. Massman and Lee (2002) point out that the eddy covariance approach is limited during stable conditions. This is because of both instrumental and meteorological problems. The 1 In summer, Spronken-Smith (2002) found that heat storage accounted for about 32% of Q on a daytime basis, which is similar to other summer time studies in mid-latitude residential areas (e.g. Grimmond and Oke, 1995).

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instrument problems result because the eddy covariance instruments are best suited to daytime convective conditions when turbulent motions are frequent and large so that sensor limitations are insignificant. However, during stable atmospheric conditions, turbulent motions shift to relatively higher frequencies and become more intermittent. Thus the finite instrument response time, path-length averaging, and sensor separation can result in severe limitations. While large corrections can be made for poor instrument response, Massman and Lee (2002) suggest that this is still unlikely to account for flux loss since there are remaining meteorological problems: *

*

*

*

As the air becomes increasingly stratified, the eddy covariance footprint (or source area) expands rapidly and thus the tower must be surrounded by an extensive area of similar fetch. Shear-generated gravity waves can transport both momentum and heat, which results in flux loss. They are beyond the scope of traditional micrometeorology because of their horizontal scales and three dimensional nature. The irregularity of the canopy top or terrain has been found to induce gravity waves (Mahrt, 1998) and thus they may be a concern in urban areas. Cold air drainage flows can be significant in transporting flux. At low values of friction velocity (u ), turbulence decreases and thus restricts the applicability of the eddy covariance methodology. The minimum friction velocity, below which there is systematic underestimation of tur-

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bulent fluxes, is termed the critical friction velocity u c. Massman and Lee (2002) suggest that u c may be site specific, and report a range of values from 0 to 0.6 m s1 for forest canopies. As a result of their review, Massman and Lee (2002) suggest that the difficulties of making flux measurements in stable conditions are largely meteorological in nature, rather than instrumental. Further, they emphasise the need for an experimental study that can measure all terms of the mass conservation equations. This paper aims to further investigate suburban energy partitioning under stable wintertime conditions to try and determine where all the energy goes, particularly in the morning transition period. The observations presented here were made as part of the Christchurch Air Pollution Study (CAPS) (Spronken-Smith et al., 2002). Christchurch, a city of about 330,000 inhabitants, is located on the east coast of New Zealand’s South Island. Under settled anti-cyclonic weather conditions in winter, Christchurch frequently experiences onshore flows from the north-east during daytime, and nocturnal drainage winds from the Port Hills in the south and from the foothills of the Southern Alps in the west (Gimson, 1998). The focus of CAPS at the time was not to resolve the issue of urban surface energy partitioning. However, due to a fairly comprehensive dataset gathered during CAPS, and the repeated occurrence of high storage fluxes during the morning transition (Fig. 1), it was possible to explore some hypotheses for the

Fig. 1. Energy balance measurements at the Bishopdale tower during CAPS for selected case study days in winter 2000. Note that heavy dew caused sensors to go off-line in the early morning of July 11. The net all-wave radiation flux density is Q , QH is the turbulent sensible heat flux density, QE is the latent heat flux density, and DQS res is the heat storage flux density calculated by residual

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high storage fluxes. Unfortunately during CAPS, high frequency turbulence data were not stored, so many of the potential instrument and sampling problems identified by Massman and Lee (2002) or Mahrt (1998) could not be explored. However, Massman and Lee (2002) did suggest that the meteorological issues were more of a concern than instrumentation problems. So the focus of this paper is to investigate aspects of the meteorology that might influence flux loss and hence result in an anomalously high heat storage flux. The possible roles of (a) mesoscale horizontal advection and (b) the slow increase in mixing depth during morning transition in stable conditions, are explored since these could result in high heat storage. The hypotheses that are considered here are: 1. that low level advection is occurring which is causing horizontal flux divergence in the control volume; 2. that under strongly stable conditions it takes time for the mixing depth to grow to mea-

surement height, hence the delay in turbulent fluxes increasing at the tower height, in the morning transition period.

2. Methods 2.1 Measurement of energy balance fluxes Observations were made during the CAPS in winter 2000 from June 29 (YD181) to July 31 (YD213) and from this study period three case study days were chosen to further explore flux loss and heat storage issues. The measurements were made in the mainly residential suburb (with predominantly single-storey dwellings) of Bishopdale (Fig. 2). This suburb is well vegetated with 64% of plan area greenspace, 18% buildings and 18% roads (Table 1). Measurements of the energy balance were made at 28.4 m on an instrumented tower in a small horse paddock surrounded by houses and a small power substation (Fig. 2). Given that the focus of CAPS

Fig. 2. Map of the study area (a), the instrumented Bishopdale tower (b), and characteristics of the neighbourhood (c). This map also shows the location of the instrumented tower and the automatic weather stations (Airport, Bottle Lake, Coles Place, Belfast and University), which were used to estimate advection (see Section 2.2.2 for details)

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Table 1. Surface characteristics and coefficients used for objective hysteresis modelling of the heat storage flux

Buildings=rooftops Roads Greenspace

Surface cover  % plan area

Coefficients for OHM1

Bishopdale

St Albans

a1

a2

a3

17.6 18.3 64.1

21.7 21.8 56.4

0.44 0.82 0.22

0.57 0.68 0.33

28.9 20.1 19.85

1

Derived from test of OHM in summer conditions at St Albans on a dataset reported in Spronken-Smith (2002) using coefficients suggested in Grimmond and Oke (1999)

was on air pollution, and that the energy flux measurements were supplementary, the surface characteristics of the neighbourhood adjacent to the tower, were not fully documented (i.e. building dimensions were not ascertained). However, given the similarity of the neighbourhood to nearby St Albans, where Spronken-Smith (2002) estimated the aerodynamic roughness length and zero-plane displacement using the method of Raupach (1994), these values (0.4 m and 2.4 m respectively) were deemed to be useful estimates for Bishopdale. The aerodynamic roughness length was also estimated using the eddy correlation stress method (Grimmond et al., 1998), with a zero-plane displacement assumed to be 2.4 m (as at St Albans). This method requires neutral conditions, which limited the analysis to only 12 observations, which reduced to 9 after fetch considerations. These roughness length estimates ranged from 0.15–0.75 m, with an average of 0.34 m and a median of 0.24 m. Given this variability and the small dataset, the aerodynamic roughness length of 0.4 m from nearby St Albans, was used in flux source area calculations. Net all-wave radiation Q was measured with a Radiation Energy Balance System Q 7.1 net radiometer and the eddy covariance technique was used to measure the turbulent heat fluxes. The anthropogenic heat flux was neglected but has been estimated previously to be low. Tapper et al. (1981) estimated QF to be about 4 W m2 in winter, while the Canterbury Regional Council (1997) suggested an average of about 6 W m2 . A Campbell Scientific (CSI) CSAT 3-D sonic anemometer measured fluctuations in vertical velocity and temperature and a CSI krypton hygrometer measured fluctuations in water vapour. A second lower level (at 16.9 m) of eddy covariance instrumentation (CSI 1D sonic anemometer and CSI krypton hygrometer) ran from

July 11–17 (YD 193–199). The vertical velocity, air temperature and humidity measurements were sampled at 10 Hz and covariances determined over 30 min periods. Standard flux corrections were made for air density and oxygen absorption (Webb et al., 1980; Tanner and Greene, 1989). Given the height of measurement, there were no corrections for sensor separation, and there were no coordinate rotations. In hindsight it would have been useful to have the high frequency data and readers are referred to a discussion of averaging and coordinate rotation for eddy covariance measurements by Finnigan et al. (2003). The storage flux was calculated as a residual, assuming no advection, using Eq. 1.2. Flux source areas were estimated using the flux source area model of Schmid (1994) but this model is limited in its applicability to stable conditions. Measurements of air temperature and relative humidity (Vaisala HMP35D probe in a radiation shield) were made at 32 m with a further set of air temperature measurements at 4 m intervals down the tower (HOBO temperature loggers in radiation shields, Whiteman et al. (2000)). Wind speed and direction (Vector instruments) were measured at both 32 m and 16 m.

2.2 Measurements, modelling and calculations to test hypotheses about high storage rates 2.2.1 Estimating heat storage by the residual approach (DQS res ) The heat storage flux was estimated using the residual approach as given by Eq. 1.2. An important consideration is that the source areas for net radiation and turbulent fluxes are the same. However, the nature of the urban fabric, with substantial microscale variation, means that source areas

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for these fluxes may have different characteristics. This is of concern in this study where the source area for the net radiometer is primarily over a paddock, while the flux source areas originate mainly from a residential neighbourhood and an adjacent power substation (see Fig. 2c). Fortunately, research has shown that in urban areas the net radiative flux has relatively conservative behaviour with little spatial variability (e.g. Schmid et al., 1991; White et al., 1978) although some caution is advised where there is a mismatch between radiation and turbulent flux source areas (Schmid, 1997). The predominant wind directions during the three case study days were daytime winds from the east to northeasterly direction and nighttime northerly or northwesterly drainage flow. The source areas for the turbulent fluxes were thus mainly from the residential surrounds, rather than from the paddock (Fig. 2). During the morning transition period, as the nocturnal inversion was being eroded, the source areas for the turbulent fluxes stretched as far as 1.8 km from the tower, but were still over residential areas. At solar noon, with a more unstable surface layer, these source areas contracted to about 150– 200 m from the tower. 2.2.2 Calculation of the mesoscale advective flux (DQA ) The first hypothesis requires the investigation of whether there is horizontal flux divergence in the control volume. Ideally advection should be estimated at both the local scale, since changes in landuse characteristics surrounding the tower might lead to advection, and at the mesoscale, where thermo-topographic flows might result in advection through the control volume. However, the network of automatic weather stations (AWS) during CAPS was such that only the mesoscale advective flux (DQA ) could be estimated. Air temperatures (at heights of 2–5 m) from 5 AWS (see locations in Fig. 2) and wind speed and direction measurements (at a height of 15 m on the Bishopdale tower) were used to give an estimation of DQA . Vertically integrated advection of heat was then estimated using:   DT DT v cp Dz ð2:1Þ DQA ¼ u Dx Dy

where u and v are wind speeds in the west–east and north–south directions; DT is the temperature change over the distances (Dx in the west– east direction and Dy in the north–south direction (Fig. 2));  is air density, cp is the specific heat of air at constant pressure and Dz is the height to the measurement sensors. 2.2.3 Links between stability, surface mixing, turbulent heat fluxes and heat storage To test the second hypothesis that the delay in the increase in turbulent fluxes was due to the time it takes for the mixing to grow to measurement height, the eddy covariance data from both tower levels were examined in conjunction with the bulk Richardson’s number which was calculated from temperature and wind speed gradients for both tower levels (16 and 32 m) using Oke’s (1987) formula. The friction velocity, u , which was calculated by the 3D sonic anemometer at 28.4 m, was also analysed, especially to determine periods where u was below the critical value of 0.3 m s1 identified by Goulden et al. (1996). Furthermore, the temperature profiles during the morning transition period were analysed to estimate heat storage within the column of air below the sensors, DQS air , using: DT cp Dz ð2:2Þ Dt where DT=Dt is the vertically averaged temperature change over the time interval. Since the lowest measured air temperature was at 4 m, the air temperatures were extrapolated to the surface assuming that the same gradient from 8 to 4 m continued down to ground level. This formulation will give a first approximation of DQS air that is likely to be slightly underestimated.

DQS air ¼

2.2.4 Modelling heat storage with OHM The objective hysteresis model (OHM) of Grimmond et al. (1991) calculates the heat storage flux (DQS OHM ) as a function of net all-wave radiation and suface properties: DQ ð2:3Þ DQS OHM ¼ a1 Q þ a2 þ a3 Dt   Q =Dt with Dt ¼ where DQ =Dt ¼ ½Qtþ1 t1 3600 s and a1, a2 and a3 empirical coefficients

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Fig. 3. Modelling of the heat storage flux with OHM (DQS OHM ) for the nearby suburb of St Albans in summer 1996 using dataset reported in Spronken-Smith (2002). An ensemble average of five days is shown. The net all-wave radiation flux is Q and DQS res is the storage flux calculated by residual

that depend on surface type. This model accounts for heat storage in the air, as well as heat storage in the ground and canopy. Application of this model involves i) conducting an inventory of building dimensions and areal coverage of different surface types, ii) compiling a list of the coefficients for the different surface types in the study area, iii) calculating site specific coefficients for the OHM by weighting those for individual surface types according to the proportion of total area of each surface and iv) estimating the modelled storage flux from measured Q by summing the contributions by each surface over all types (Grimmond and Oke, 1999). The OHM was first run for summertime conditions on an energy balance dataset for the nearby suburb of St Albans (reported in Spronken-Smith, 2002). From iteration of coefficients provided by Grimmond and Oke (1999), a selection was made for values that gave the best fit to the residual storage flux. The chosen coefficients together with surface characteristics for the two suburbs, are given in Table 1. It must be stressed that the suburb of St Albans, although mainly residential like Bishopdale, has some difference in surface characteristics (Table 1). For example, in St Albans the plan areal coverage by greenspace is 56.4% while for Bishopdale it is higher at 64.1%. Further, crude estimates were made of the breakdown of greenspace into grass and treed areas (50% of each was assumed). Thus the results of the OHM should be interpreted with caution and really only give a first approximation of the likely magnitude of the modelled storage heat flux. Despite the crude

assumptions, the modelling for summer (Fig. 3) shows very good agreement in terms of magnitude but DQS OHM is lagged about an hour behind DQS res . 3. Results Figure 1 shows observational data from the case study days to further examine high storage fluxes. These days were selected because of early morning inversions and more complete datasets. Note the slow increase of the turbulent fluxes after sunrise and the consequently high heat storage rates. On a daytime (Q >0) basis DQS res ranged from 1.94 to 3.24 MJ m2 dy1, which is similar to magnitudes observed by SpronkenSmith (2002) for other residential suburbs in Christchurch during winter (DQS res ranged from 2.24 to 3.99 MJ m2 dy1 ). The daytime ratios of DQS res =Q for these case study days ranged from 0.55 to 0.65, which is about mid-range for those reported by Spronken-Smith (2002) (where daytime storage ratios ranged from 0.39 to 0.98). 3.1 Mesoscale advection During the northerly nocturnal drainage flows, cold air advection was evident, while during the daytime there was warm air advection associated with east-northeasterly onshore flow (Fig. 4). It is unlikely that this on-shore flow is an initiation of a sea breeze, since sea surface temperatures were warmer than near surface air temperatures over land for most of the daytime. The onset of the east-northeasterly winds is thought to be

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Fig. 4. The mesoscale advective flux (DQA ) and wind direction (WD) for the case study days. The wind direction is measured at 32 m on the Bishopdale tower

Fig. 5. Analysis of heat storage fluxes from 600 to 1300 h (with sunrise at about 720 h). The net all-wave radiation flux is Q , DQS res is the storage flux calculated by residual, DQS OHM is the storage flux modeled using the objective hysteresis model, DQA is the mesoscale advective flux, DQS air is heat storage in the air column from 28.4 m to ground level, and DQS sum ¼ ðDQS OHM þ DQA Þ

due to the down-mixing of larger scale winds. McKendry et al. (1986) have documented the many origins of this onshore flow, including sea breezes, which are common in summer, synoptic easterly winds and lee-trough induced northeasterlies. For the three case study days, the synoptic charts indicated that the origin of the flow was lee-trough induced northeasterlies. It is significant that the morning transition period coincides with a reversal in local airflow from off-shore to on-shore flow. However, the magnitude of the mesoscale advective flux, DQA , is still small (less than 30 W m2 ), compared to the ‘‘excess’’ energy, and cannot account for the discrepancy in the residual storage flux (Fig. 5). 3.2 Stability, surface mixing, and turbulent fluxes There was a limited (two day) dataset to examine the timing of the onset of the turbulent fluxes

after sunrise (about 720 h) at the two tower heights (16.9 m and 28.4 m) (Fig. 6). The temperature profiles showed significant low-level warming between 900 h and 1000 h on both days (Fig. 7) and it was not until 1000 to 1100 h that a lapse profile was established, leading to an increase in the turbulent fluxes. These case study days are examined in more detail to explore the links between stability, mixing and turbulent fluxes. 3.2.1 July 11 Prior to sunrise, there were light winds (2–3 m s1 at 32 m height), with a low friction velocity (about 0.15 m s1 ), and the mesoscale advective flux, DQA was about 35 W m2 , indicating cold air advection associated with nocturnal drainage flow (Fig. 4). The nocturnal temperature inversion was present (Fig. 7a) and the surface layer was strongly stable (Rib >0:25)

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Fig. 6. Case study days (a) July 11 and (b) July 12, 2000, to examine links between stability (estimated by the bulk Richardson number, Rib) and the sensible heat flux, QH, at both tower levels (top and bottom (bot)). Net allwave radiation (Q ) is also shown. The fluxes are 30 minute averages while Rib is calculated for 10 minute averages. Sunrise occurred about 720 h

with downward directed QH (Fig. 6a). Figure 6a shows that Q became positive at 830 h, about an hour after sunrise. At this time the surface layer became less stable (decreasing Rib at both levels). Although the temperature profiles indicate substantial warming between 900 and 1000 h (Fig. 7a), which resulted in decreasing stability, wind speeds were low (during transition from nocturnal drainage flow to onshore flow), the friction velocity was very low (average of 0.08 m s1 between 830–1000 h) and thus the turbulent fluxes remained close to zero. Despite the considerable warming in the air column between 900 and 1000 h, DQS air was still relatively small, peaking at about 30–40 W m2 (Fig. 5). However, this is probably an underestimate as the surface temperatures were estimated. By 1000 h the mesoscale flow regime had switched to onshore flow and at 1100 h DQA was 15 W m2 , indicating warm air advection (Fig. 4). This resulted in increasing wind speeds with the friction velocity increasing to 0.37 ms1

at 1130 h. The behaviour of both Rib and QH at the two tower levels indicated that convective activity first occurred at the top level, followed soon after by the lower level (Fig. 6a). Instability first occurred at 1020 h at the top level with QH becoming positive (upward) at 1030 h, while at the lower level Rib indicated a fairly neutral layer until convective activity was established at 1050 h after which QH at the lower level also became positive (for average of 1100–1130 h). This sequence suggests that there is rapid coupling of the surface to the atmospheric boundary layer following the onset of onshore flow, which serves to initiate mixing through a deeper layer. Thus, in this instance, it is not convective warming from below that is mainly driving the mixing. 3.2.2 July 12 On this day, although the temperature profiles are similar to July 11, the sequence of processes

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occurring in the surface layer, is quite different. Prior to sunrise, the surface layer is much less stable than the preceding day, but there was a substantial downward directed QE, indicating dewfall (Fig. 1). Consequently, DQS res was high for this period (Fig. 5). Air temperatures were much warmer than the previous night and the nocturnal inversion was much weaker (Fig. 7b). Therefore, not surprisingly, mesoscale advection was small (DQA from 12 to 13 W m2 during the morning transition) and indeed there was no evidence of the nocturnal drainage flows that had occurred the night before (Fig. 4). Because of the weaker nocturnal inversion, it took less time for convective activity to initiate at the tower levels. Between 900 and 1000 h, heat storage in the air column below 28.4 m was only 16 W m2 , which was half the magnitude of the previous day (Fig. 5). Although the lower level was less stable, convective instability did not occur until 950 h, while at the top level, Rib turned negative earlier at 920 h (Fig. 6b). Both levels of sensible heat flux became positive at 1000 h but more so at the lower level. This convective activity also coincided with a slight increase in u , from 0.16 m s1 at 900 h to 0.22 m s1 at 930 h. This day was characterised by very low u, which did not increase above 0.30 m s1 until near midnight. Therefore, on this day, mesoscale advection played a more minor role initiating mixing in the surface layer. Rather it appears that warming of the surface layer came from both below and above. 3.3 Comparison of storage flux components Using the DQS OHM as a first approximation of the storage flux, and adding in the mesoscale advective component, DQS sum (DQS sum ¼ DQS OHM þ DQA ) is still much lower than the residual storage flux (DQS res ) (Fig. 5). Given the comparatively high amount of heat storage in the air (DQS air ), it is perhaps not surprising that OHM has underestimated the heat storage flux. In stable conditions it is possible that, due to high heat storage in the air, there should be a 1

Fig. 7. Morning temperature profiles for (a) July 11 and (b) July 12, 2000. Note that the surface temperature was estimated by assuming the gradient from 8–4 m continued to ground level (see Section 2.2.3 for details). Sunrise occurred about 720 h

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correction made to OHM. Although both mesoscale horizontal advection and heat storage in the air can account for some of the excess energy, there is still a considerable (up to 90 W m2 ) amount of energy unaccounted for ðDQS res  ðDQS sum þ DQS air ÞÞ. Thus there is still a problem of flux loss which probably results from the aerodynamic issue of trying to apply eddy covariance methodology during conditions of low friction velocity. 4. Discussion Given a useful but incomplete dataset from CAPS, this paper aimed to explore two hypotheses to explain where all the energy goes during the morning transition period. The first hypothesis was that advection was causing horizontal flux divergence in the control volume, while the second was that during stable conditions it takes time for mixing to grow to measurement height and hence the delay in the increase in turbulent fluxes. The results show that mesoscale circulations such as nocturnal drainage flow and onshore flow, complicate the meteorology of this urban area. The complexity of airflow over Christchurch during clear-sky winter nights has been noted by previous research (e.g. Gimson, 1998; Spronken-Smith et al., 2002) and has indicated a very shallow near-surface layer with very light airflow. Although the magnitude of the mesoscale advective flux was generally small, it could reach 30–40 W m2 and therefore should not be neglected in future studies. Nevertheless, advection cannot fully account for the excess of energy during the morning transition period. Ideally local scale advective effects should also be explored since these may be of greater importance than mesoscale effects in an urban setting. However, the available data from CAPS for calculating advective fluxes was at the mesoscale, hence the focus of the analysis. Future investigations should however, explore advection at both the mesoscale and the local scale. It appears that in very stable conditions, flow at the surface may become decoupled from the airflow aloft. The breakdown of the nocturnal inversion may not occur until several hours after sunrise. On July 11, as the surface warmed the surface layer became less stable, but wind speeds (and u ) remained low especially while the

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mesoscale flow regime was in transition between nocturnal drainage flow and onshore flow. The establishment of onshore flow resulted in increased wind speeds which then led to an increase in u and deeper mixing through the surface layer, finally causing the turbulent heat flux to increase first at the top and then at the lower level. The timing and sequence of events suggests that in this instance, the morning convective warming of the surface is not enough to couple the surface to the atmospheric boundary layer. Rather, the coupling is initiated by the arrival of a mesoscale onshore flow, which results in mixing through a deeper layer. On July 12 the nocturnal inversion was not as strong and consequently the drainage flow was not established. Thus on this occasion, mesoscale advection was of minor importance in instigating mixing in the surface layer. Rather it is thought that there was warming of the surface layer from both above and below, that resulted in convective instability. The friction velocity was very low for settled anticyclonic conditions – typically less than 0.35 m s1 throughout most of the day and could be below 0.15 m s1 during strong inversion conditions overnight and into the morning, not increasing substantially until about 1130 h. Indeed for July 12, u was below 0.30 m s1 all day except near midnight. For this suburban site in winter, a critical friction velocity of 0.20 m s1 is suggested to determine periods when the turbulent fluxes will be underestimated by the eddy covariance methodology. This uc is the same as that suggested by Goulden et al. (1997) for a black spruce forest. Thus the aerodynamic issue, as discussed by Massman and Lee (2002) is pertinent for this setting. However, it is not only nighttime fluxes that are affected, but also fluxes in the morning transition period and indeed possibly through the daytime as well. This presents a real difficulty for the measurement of wintertime fluxes in urban areas where conditions can be stable. This is because errors associated with the approach accumulate in the heat storage flux if it is estimated as a residual. Other possibilities for flux loss include instrumentation and sampling error and gravity waves. Flux source area issues are not thought to be an issue at this site although the mismatch of radiative and flux source areas deserves more investigation.

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During the morning transition period the turbulent fluxes are consequently very slow to increase, resulting in high rates of sensible heat storage. Kerschgens and Drauschke (1985), in their short study of wintertime fluxes in Bonn, also experienced very stable conditions. They found that during these stable conditions, the high input of QF and DQS (energy always flowed from the canopy layer into the atmosphere due to anthropogenic heat release) enabled the sum of the turbulent fluxes (QH þ QE) to exceed Q . They also noted the turbulent fluxes in the boundary layer were small due to the stable stratification of the atmosphere. However, in contrast to this study, they suggested that the mainly horizontal advection of cooler air was eliminating the excess heat of the urban boundary layer. Modelling of the storage heat flux gave insight into the likely magnitude of this flux for wintertime conditions. The objective hysteresis model of Grimmond and Oke (1999), which showed good agreement for summertime conditions in a similar neighbourhood, suggested that DQS OHM peaked between 50 and 90 W m2 in the morning transition period in winter. However, estimates of heat storage in the air were considerable (up to 37 W m2 ) and it is possible that in winter, the OHM (which theoretically includes this component as well as heat storage from ground and built surfaces) is underestimating the actual heat storage flux. 5. Conclusions Analysis of the CAPS dataset has given insight into the issue of high storage fluxes during stable wintertime conditions. During strong inversions, which occur frequently in Christchurch during the winter months, the near-surface flow may become decoupled from airflow aloft. After sunrise as Q becomes positive there is a delay of a couple of hours until the turbulent fluxes start to increase at measurement height. Complex meteorology complicates the situation during the morning transition period. If there are mesoscale circulations operating, these may serve to initiate mixing in the surface layer which leads to coupling with the atmospheric boundary layer. Otherwise, the coupling probably results from a combination of warming from below and above the surface layer. It seems likely that neither

mesoscale advection alone, nor heat storage in the surface layer can account for the excess energy. The low friction velocities that persist well into the morning (or even for the day) mean that the eddy covariance approach is problematic in this setting. In order to fully resolve these issues, a carefully designed observation programme is required. Ideally this should involve eddy covariance measurements of turbulent fluxes at several measurement heights, including one near to the surface (within 2–3 m). The high frequency data should be captured and stored in such a study. Furthermore, to fully explore possibilities of heat and moisture advection at the local and mesoscale, there should be measurements of air temperature and humidity at sites surrounding the tower, and if possible, vertical soundings of the atmosphere to help resolve air flow, temperature and humidity structure of the atmosphere. Until the issue is resolved, caution is advised when applying current research methodology to estimate storage fluxes in urban areas during stable wintertime conditions.

Acknowledgements Thanks are due to Dr. Helen Cleugh and a second anonymous referee for helpful comments on the manuscript, as well as to Marney Brosnan for preparation of the figures. This research was funded by the Public Good Science Fund under contract C01X0011 ‘Urban Air Quality Processes’, and the Department of Geography at the University of Canterbury.

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