Urban Energy Balance Obtained from the Comprehensive Outdoor Scale Model Experiment. Part I: Basic Features of the Surface Energy Balance

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1 VOLUME 49 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y JULY 2010 Urban Energy Balance Obtained from the Comprehensive Outdoor Scale Model Experiment. Part I: Basic Features of the Surface Energy Balance TORU KAWAI* Center for Marine Environmental Studies, Ehime University, Matsuyama, Japan MANABU KANDA Department of International Development Engineering, Tokyo Institute of Technology, Tokyo, Japan (Manuscript received 5 March 2008, in final form 20 March 2010) ABSTRACT The objective of this study is to examine the basic features of the surface energy balance (SEB) using the data obtained from the Comprehensive Outdoor Scale Model (COSMO). COSMO is an idealized miniature city that has no vegetation, no human activity, and no heterogeneity of the surface geometry. The basic features of the SEB such as energy balance closure, the ensemble mean of the diurnal variation of the energy balance, and the daytime and daily statistics of the energy balance were investigated. The following were the main findings of the study: 1) A surface energy imbalance was observed. The sum of sensible and latent heat fluxes estimated by the eddy correlation method underestimated the available energy by 1% during the daytime and by 44% during the night. 2) Large heat storage in the daytime and small radiative cooling at night sustained positive sensible heat fluxes throughout the night in all seasons and in all sunshine conditions. 3) The daytime ratio of heat storage DQ S to net radiation Q*, DQ S /Q*, depended on the friction velocity u * and decreased with increasing u *. 4) The values of DQ S /Q* tended to be larger in winter than in summer. The annual averaged value of this ratio was approximately ) The large volumetric heat capacity of the surface materials and the resulting large energetic hysteresis produced nonzero total daily values of heat storage. The total daily values of heat storage largely depended on the weather (i.e., sunshine condition and with or without rainfall) and showed positive and negative values on clear-sky days and rainy days, respectively. 1. Introduction The surface energy balance (SEB) is an essential element of the boundary layer meteorology and climatology. The SEB is strongly related to, for example, the stability formation, dispersion of scalars and momentum, and mixing layer growth within the boundary layer. As is well known, urbanization through erecting buildings and other urban components alters the energy exchange between the surface and the atmosphere from that of the preexisting landscape. This unique urban SEB is considered to be intricately tied with urban climatic phenomena * Current affiliation: Research Center for Environmental Risk, National Institute of Environmental Studies, Tsukuba, Japan. Corresponding author address: Toru Kawai, Research Center for Environmental Risk, National Institute of Environmental Studies, 16-2 Onogawa, Tsukuba, Ibaraki, , Japan. kawai.toru@nies.go.jp such as localized heavy rain and/or urban heat islands. Thus, better understanding and appropriate numerical predictions of the urban SEB are necessary. In recent years, sophisticated urban parameterizations have rapidly evolved (e.g., Masson 2000; Kusaka et al. 2001; Martilli et al. 2002; Kondo et al. 2005; Kanda et al. 2005a,b; Kawai et al. 2007, 2009; Dupont and Mestayer 2006; Dupont et al. 2006). On the other hand, observations of urban SEB are few, especially in highly urbanized areas. Moreover, most of these experimental studies were based on short-term observations (e.g., Oke 1988; Oke et al. 1999; Grimmond and Oke 1999; Grimmond et al. 2004). Only in recent years have some long-term observation programs been conducted. These observation programs include the Kugahara experiment in Japan (Moriwaki and Kanda 2004) and the Basel Urban Boundary Layer Experiment (BUBBLE; Christen and Vogt 2004; Rotach et al. 2005). In addition to the limited datasets, field observations are accompanied by various uncertainties. These uncertainties arise, for example, from the estimates DOI: /2010JAMC Ó 2010 American Meteorological Society 1341

2 1342 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 49 of heat storage based on the energy balance residual, seasonal changes of vegetation and anthropogenic heat, and/or heterogeneity of the surface geometry and material. With such uncertainties, interpretations of the results from field observations may be difficult. A useful alternative to field measurements is an outdoor scale-model experiment (Pearlmutter et al. 2005; Kanda et al. 2005a). In such an experiment, the surface geometry and material can be controlled to produce homogeneous fetch conditions, which reduce the uncertainties associated with the difference in the source areas between the measured radiation and the turbulence fluxes. An experiment also allows detailed measurements within and above the canopy layer, including direct measurements of heat storage, which are extremely difficult to obtain in real cities. Furthermore, systematic datasets from an outdoor scale-model experiment provide ample opportunities for validation studies with numerical models (Kanda et al. 2005a; Kawai et al. 2007). Therefore, this method is useful as long as the model meets the requirements of physical scale similarities (i.e., radiation, flow, and thermal inertia; Kanda 2006). Since December of 2004, the Comprehensive Outdoor Scale Model (COSMO) experiments have been conducted (Kanda et al. 2007; Kawai et al. 2007; Inagaki and Kanda 2008; Nakayoshi et al. 2009; Kanda and Moriizumi 2009) on an ongoing basis. The model has been created by arranging large concrete cubes on a concrete base to ensure thermal inertia similarity with real cities (appendix A). This study is presented in a series of two papers. These papers address the findings on the urban SEB using a one-year dataset obtained from COSMO. The objective of Part I is to investigate the basic features of the SEB of COSMO: the energy balance closure, the ensemble mean of the diurnal variation of the energy balance, and the daytime and daily statistics of the energy balance in terms of the season and weather conditions (i.e., sunshine condition, with or without precipitation, and wind velocity). In Kawai and Kanda (2010, hereinafter referred to as Part II), the results from the COSMO experiments will be compared with those from field observations using a new energy partitioning method. 2. Method The urban SEB is commonly expressed as Q* 1 Q F 5DQ S 1 Q H 1 Q E 1DQ A, (1) where Q* is net radiation, Q F is anthropogenic heat, DQ S is heat storage, Q H is sensible heat, Q E is latent heat, and DQ A is net advective heat flux (Oke 1987). Here, Q* is calculated from upward ([) and downward (Y) shortwave radiation Q K and longwave radiation Q L as Q* 5 Q K Y Q K [ 1 Q L Y Q L [. (2) The units of all terms in Eqs. (1) and (2) are watts per meter squared. In COSMO, Q F and DQ A in Eq. (1) can be neglected because the geometry and material of the model setup are homogeneous and there exist no human activities. In the next part of this section, a brief summary of COSMO will be provided. More detailed information on these experiments is given in Kanda et al. (2007) and Kawai et al. (2007). a. The Comprehensive Outdoor Scale Model experiments The COSMO experimental site was located in the northern side of the Kanto Plain in Japan (398049N, E) and was characterized by temperate climate with a rainy season in June July and a dry season in winter (Table 1). The data analyzed in this study were collected for one year from April 2006 to March The dominant wind directions of the site were northwesterly in winter (October April) and southeasterly in summer (May November). Rice paddies (northwest side) and sparse residences extended at least a few tens of kilometers around the site. Two outdoor scale models of a city that were scaled at 1 /5 and 1 /50 relative to the area of the Kugahara site were deployed (Fig. 1). These models are referred to as the 1 /5 model and the 1 /50 model hereinafter. As described in appendix A, the geometrical scale of the 1 /50 model is considered to be too small to ensure thermal inertia similarity with a city. Therefore, data obtained from the 1 /5 model are mainly used in this study. The 1 /5 model consisted of cubic concrete blocks with 1.5-m height H and 0.1-m wall thickness. The blocks were empty inside. A total of 512 blocks were regularly arranged on a flat concrete base with a surface area of 50 m m and thickness of 0.15 m. One of the two street directions pointed 438 counterclockwise from north. The plan area of roughness elements, defined as the ratio of the roof area to the total horizontal area of the model city, was The same concrete material was used for the blocks and the basement, and all surfaces were painted with a water-pervious dark-gray paint. Therefore, thermal and radiative properties of all surfaces were the same. In the 1 /5 model, a measurement tower with height of 11 m was deployed at the center point of the site. On the tower, four components of radiation (Q K Y, Q K [, Q L Y, and Q L [) were measured using a radiation balance meter [MR40 from Eko Instruments Co, Ltd., with International Organization for Standardization (ISO) secondclass accuracy] at 1 Hz. To estimate turbulence fluxes (Q H and Q E ) by the eddy-correlation method, a sonic anemometer with a 5-cm sensor span (DA 600 from

3 JULY 2010 K A W A I A N D K A N D A 1343 TABLE 1. Summary of monthly averaged values of total daytime (Q* $ 0) energy fluxes (Q*, DQ S, Q H, and Q E ) and flux ratios (Q H /Q E, DQ S /Q*, Q H /Q*, and Q E /Q*) and daytime-averaged u * obtained in three sunshine conditions (DRR , DRR , and DRR ). DRR is the ratio of daytime diffuse to daytime global shortwave radiations as defined in Eq. (3); ND indicates the number of observation days within a month. The total rainfall reported by the Japan Meteorological Agency is also shown (8 km away from the COSMO site). Rain (mm) Energy flux (MJ m 22 ) Ratio Month [days] DRR ND u * (m s 21 ) Q* DQ S Q H Q E Q H /Q E DQ S /Q* Q H /Q* Q E /Q* Apr [12] May [16] Jun [11] Jul [14] Aug [6] Sep [10] Oct [10] Nov [7] Dec [5] Jan [3] Feb [5] Mar [4] Kaijo, Inc.) and an open-path H 2 O/CO 2 analyzer (LI7500 from Li-Cor, Inc.) were operated at 50 and 20 Hz, respectively, on the same tower. Measurement heights of radiation and turbulence fluxes were 3 and 2 times the obstacle height above the ground, respectively. The height at which the sonic anemometer and H 2 O/CO 2 analyzer were installed is located within the internal boundary layer and above the roughness sublayer (1.5 times the obstacle height; Inagaki and Kanda 2008). Heat storage DQ S was also directly measured near the measurement tower using thin (300 mm mm mm in size) and highly accurate (instrumental accuracy within 65%) heat flux plates (HF-300 from Captec Enterprise Co.). To close the energy balance precisely, a total of 164 heat flux plates were attached to a sample unit that consisted of a block and its surrounding streets. The heat flux plates also measured the surface temperature. By measuring the heat storage directly, we were able to close the surface energy balance, which allows us to analyze and discuss the surface energy imbalance (section 3). All of the heat flux plates were operated at 1 Hz. b. Data handling Days with complete datasets (i.e., radiation, turbulence fluxes, heat storage, and surface temperature) were selected for analyses in sections 3 5. The number of selected days for each month (ND) is shown in Tables 1 and 2. In section 6b, all available data of heat storage and

4 1344 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 49 FIG. 1. Photographs of the scale models: (a) 1 /5 model and (b) 1 /50 model. surface temperature were analyzed. The selected days in section 6b, which included rainy days, covered nearly 1 year (351 days). 1) CLASSIFICATION OF OBSERVATION DAYS Observation days were classified according to rainfall, sunshine condition, and season. If there was any precipitation on a day, the day is defined as rainy. Daily data of rainfall were collected from the Japan Meteorological Agency 8 km away from the COSMO site. The rainy days included all sunshine conditions. Days without precipitation were classified according to the diffuse shortwave radiation ratio DRR, defined as DRR 5 ð sunset sunrise ð sunset Q K Y dt Q KT Y dt ð sunset sunrise, (3) Q K Y dt sunrise where Q KT Y is the downward direct shortwave radiation measured at a point a few meters away from the 1 /5 model. Three kinds of sunshine conditions were defined: DRR for clear sky, DRR for occasionally cloudy, and DRR for cloudy. All observation days were also classified into four seasons: winter, spring, summer, and autumn. These four seasons were simply defined by dividing one year into four periods based on the solstice and equinox days. 2) DATA PROCESSING All of the sampled data were averaged over 30 min. Because of the difference in sampling frequencies between the sonic anemometer and the open-path H 2 O/ CO 2 analyzer, data from these instruments were resampled at 10 Hz. Coordinate rotation (McMillen 1988) was applied to the observed three components of the wind velocity (u, y, and w). In the estimation of latent heat flux by the eddy-correlation method, the density effect was corrected (Webb et al. 1980). Based on the discussions to be presented in section 3, the sensible and latent heat fluxes were found to be underestimated with respect to the available energy. Therefore, for the analyses in sections 4 6, the sensible and latent heat fluxes were corrected by the Bowen ratio method; that is, available energy (Q* 2DQ S ) was distributed into these two fluxes using the Bowen ratio estimated by the eddy-correlation method. 3. Energy balance closure A large volume of data observed over various forests has shown that the sum of sensible and latent heat fluxes estimated by the eddy-correlation method, Q ECH 1 Q ECE, often underestimates the available energy, Q* 1 Q F 2 DQ S 2DQ A (e.g., Lee 1998; Wilson et al. 2002). This phenomenon is called surface energy imbalance (SEI). Although organized large-scale turbulence structures are a possible physical mechanism that accounts for the SEI (Kanda et al. 2004), other various factors could contribute to the SEI in field measurements (Mahrt 1998). Offerle et al. (2005) investigated the energy balance closure for qódź, Poland, by estimating the heat storage term DQ S with the use of the element surface temperature method. Nonetheless, research on SEI in urban areas is still rare because of the difficulties in measuring DQ S.InCOSMO, the estimation of SEI is possible with the direct measurements of conductive heat flux. Figure 2a compares Q ECH 1 Q ECE with the available energy Q* 2DQ S. A significant SEI was observed even for the present urbanlike rough surface. In total, Q ECH 1 Q ECE underestimated Q* 2DQ S by 10% (the slope was 0.9). This underestimation is slightly smaller than the commonly observed value for forests of 20% (Wilson et al.

5 JULY 2010 K A W A I A N D K A N D A 1345 TABLE 2. As in Table 1, but for the monthly average values of total daily energy fluxes, flux ratios, and daily averaged values of the friction velocity. Energy flux (MJ m 22 ) Month DRR ND u * (m s 21 ) Q* DQ S Q H Q E Q H /Q E DQ S /Q* Q H /Q* Q E /Q* Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Ratio 2002). The differences between the daytime and nighttime results were evident. At night with weak turbulence, a significant SEI was observed: Q ECH 1 Q ECE underestimated Q* 2DQ S by 44% (the slope was 0.56), with a relatively large scatter (r ). The disagreement between Q ECH 1 Q ECE and Q* 2DQ S was small in the daytime (slope ; r ). A similar result was found by Offerle et al. (2005). Previous research (Wilson et al. 2002; Kanda et al. 2004; Offerle et al. 2005) reported increasing values of SEI with decreasing u * both in daytime and nighttime. Figure 2b illustrates the dependency of SEI on the friction velocity u *, where the SEI is defined as SEI 5 (Q ECH 1 Q ECE ) (Q* DQ S ) Q* DQ S. (4) The values of SEI are larger in calm conditions (u * # 0.2 m s 21 ) than in windy conditions. In strong winds (approximately u * $ 0.6 m s 21 ), the values of SEI are slightly negative. These slightly negative values of SEI might, in part, be attributable to advection below the flux measurement level removing heat. 4. Ensemble mean of the diurnal variation of the energy balance This section will discusses the ensemble mean of the diurnal variation of SEB in four seasons (winter, spring, summer, and autumn) and three sunshine conditions (DRR , , and 0.8 1; Fig. 3). Figure 3 also shows the ensemble mean of the wind velocity U and radiative temperature T R, converted from the upward

6 1346 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 49 FIG. 2. (a) A comparison of the sum of sensible and latent heat fluxes estimated by the eddy correlation method, QECH 1 QECE, with available energy, Q* 2 DQS. Daytime and nighttime are defined as Q* $ 0 and Q*, 0, respectively. A linear regression with a zero intercept was performed individually for the daytime data, nighttime data, and all of the data combined. (b) The relationship between the values of the SEI and the friction velocity u* for the daytime and nighttime. The values of the SEI were calculated from Eq. (4). The figure displays the data only from jq* 2 DQSj $ 50 W m22. longwave radiation assuming a canopy emissivity of 0.95 (Arnfield 1982). The SEB depends on the wind velocity (section 5a), but variations in the ensemble mean of the wind velocity among the four different seasons and sunshine conditions were small (within 1 m s21). This allows us to examine the influence of the seasons and sunshine conditions on the SEB with the current dataset. a. Results for clear-sky days In daytime, the urban SEB is often characterized by large heat storage DQS (e.g., Oke 1988; Arnfield 2003), and DQS becomes larger than turbulence fluxes in highly urbanized areas with little vegetation (Oke et al. 1999; Grimmond and Oke 1999). Such a trend is also clear in

7 JULY 2010 KAWAI AND KANDA FIG. 3. Ensemble mean of diurnal variations of energy balance Q* 5 DQS 1 QH 1 QE, wind velocity U, and radiative temperature TR for three sunshine conditions (clear sky, occasionally cloudy, and cloudy) in four seasons. The total number of days used for the calculation is shown in each panel. 1347

8 1348 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 49 COSMO: the net radiation Q* was predominantly partitioned into DQ S in all seasons. The maximum value of DQ S was roughly 2 times that of the sensible heat flux. The magnitude of the latent heat flux Q E was the smallest of all the components considered, but is nonnegligible. The nonzero value of Q E observed in COSMO suggests that urban evaporation was released not only from vegetation and/or permeable soil but also from the concrete material. Therefore, nonzero evaporation from the urban surface should not automatically be assumed in urban surface parameterizations. In a rainy season (i.e., summer), the values of Q E were larger than those in the other seasons. In the driest season (i.e., winter), the values of Q E were generally nonzero and reached a maximum of W m 22. To examine such nonzero evaporation, an additional experiment was conducted to evaluate the weight change of a sample unit of a block and its surrounding streets in the 1 /50 model (appendix B). This experiment determined that the sample unit absorbed some of the rainwater and continuously released it over a period of several days. In winter, the sample unit also absorbed dew during nighttime and released the absorbed water during daytime. This diurnal cycle, in part, sustained the daytime evaporation; the dew, if it exists, can become a source of urban evaporation. On the other hand, the ensemble means of nighttime Q E showed slightly positive values in this season, suggesting that dewfall did not always occur. Distinct phase differences were observed among the energy fluxes. Heat storage DQ S shows hysteresis in relation to the net radiation throughout the year in COSMO as found in the previous literature (e.g., Grimmond et al. 1991; Grimmond and Oke 1999). The daily maximum value of DQ S occurred approximately 1 h prior to that of Q*. This phase lag produced a phase lag of Q H with respect to Q* (approximately 2 h). The large thermal inertia of the 1 /5 model also produced a phase lag of the radiative temperature T R from Q*. The pattern of the diurnal variation of T R roughly followed that of Q H with only a slight lag. The maximum value of Q E was observed around noon. Throughout the year, the nocturnal values of Q H and Q E were positive while those of DQ S were negative. The positive values of Q H at night are one of the unique features of urban areas and are not common for less evaporative surfaces, such as desert or flat concrete. There are two possible reasons for this observation. First, the energy storage in daytime in urban areas is large (Oke et al. 1999). This is also supported by the 1 /50 model experiments. In the 1 /50 model with a small volumetric heat capacity, the values of Q H at nighttime were nearly zero rather than positive (appendix A). Second, radiative cooling is small in an urban area because of its reduced sky-view factor in the urban canyon (Oke 1981; Oke et al. 1999). It is likely that both of these urban effects contribute to sustain the positive Q H throughout the night. b. Results for various sunshine conditions In daytime, as the diffuse shortwave radiation ratio DRR increased; all fluxes decreased as a result of the reduced radiative energy supply. However, the relative magnitudes of the energy fluxes remained approximately the same in all sunshine conditions. Regardless of the sunshine condition and season, DQ S was the most dominant energy flux and the value of Q E was nonzero. The values of Q H and Q E on occasionally cloudy and cloudy days were always positive throughout the daytime and nighttime; the dominant partition of Q* into DQ S in daytime together with the restrained nocturnal radiative cooling sustained the positive value of Q H throughout the night. These conditions led to unstable stratification above the canopy layer both on occasionally cloudy and cloudy days. On cloudy days, the diurnal variations of Q H were reduced, with the value of Q H being small positive in daytime. The diurnal hysteresis of DQ S in relation to Q* became less evident with increasing DRR. 5. Daytime statistics Energy fluxes are frequently normalized by net radiation Q* to study the surface energy partition. However, Q* is not physically appropriate for the normalization of the energy fluxes because Q* implicitly includes the surface temperature through Q L [. The surface temperature is determined as a result of the energy partitioning process. Therefore, Q* also depends on the energy partitioning process itself and is not appropriate for the normalization of the energy fluxes. Therefore, instead of Q*, an effective incoming energy should be introduced for the normalization. This issue will be discussed in detail in Part II, in which the surface energy partitioning for COSMO and field data will be compared using a new normalization method. In the remainder of this section and section 6a, with the awareness of the limited nature of net radiation Q* for the normalization procedure, the surface energy partition of COSMO will be studied using the conventional method of normalizing by Q*. a. Effects of day-to-day variability of wind velocity on surface energy balance The effects of wind velocity on the urban SEB have not been thoroughly investigated with field data (Grimmond and Oke 1999). Section 5a will investigate the influence of wind conditions on the urban SEB.

9 JULY 2010 K A W A I A N D K A N D A 1349 FIG. 4. The relationship between the daytime (Q* $ 0) ratio of heat storage to net radiation (DQ S /Q*) and the daytime-averaged values of u *. The data were obtained in three sunshine conditions (clear sky, occasionally cloudy, and cloudy) in four seasons. The dependency of the total daytime values of DQ S /Q* on the daytime-averaged values of u * (m s 21 )wasinvestigated for various weather conditions in all four seasons (Fig. 4), and the relationship between these two variables was quantified as the slope of the linear regression line for the variables (Table 3). Here, u * is used instead of the wind velocity because of the height-dependent nature of the wind velocity. On clear-sky days, DQ S /Q* clearly decreased with increasing u *.Forwinterand spring, the linear regression analysis was performed by using data that were collected over a sufficiently large number of days (35 and 36 days, respectively), and these data were characterized by a wide range of u *. In these cases, the slopes of the linear regression lines were distinctly negative (20.35 and 20.31) with relatively high correlation coefficients squared r 2 (0.64 and 0.59; Table 3). This dependency of the daytime values of DQ S /Q* on u * can be explained by the enhancement of turbulence fluxes and the resulting reduction of heat storage with increasing wind speed. On occasionally cloudy and cloudy days, the values of DQ S /Q* were observed within a relatively narrow range of u *, and few data were available for analysis within each season. These factors probably contributed to the small values of r 2 in Table 3. However, in all of the seasons analyzed here, the slopes on occasionally cloudy and cloudy days consistently showed negative values, and these negative values tended to be large in magnitude as compared with those on clear-sky days. b. Seasonal change of the surface energy balance Table 1 shows the monthly averages of the total daytime energy fluxes (Q*, DQ S, Q H, and Q E ) and flux ratios (DQ S /Q*, Q H /Q*, Q E /Q*, and Q H /Q E ). The same flux ratios and the daytime-averaged values of u * are shown in Fig. 5. On clear-sky days, as discussed in section 4, heat storage was dominant and latent heat flux was the smallest. The annual averaged values of DQ S /Q*, Q H /Q*, and Q E /Q* on clear-sky days were 0.61, 0.29, and 0.10, respectively. The value here of DQ S /Q* of0.61islargerthan most of the values of DQ S /Q* previously reported for urban and suburban areas (Grimmond and Oke 1999). Values of DQ S /Q* for cities with little vegetation and/or little water availability tend to be larger than those for suburban areas because of the reduced values of Q E /Q* (Oke et al. 1999; Roth 2007). In the same way, lack of vegetation in COSMO likely accounted for the large TABLE 3. Results of linear regressions of the daytime values of DQ S /Q* onto the daytime u *. The linear regressions were performed separately for three sunshine conditions and four seasons unless the number of observation days (no. day) was less than 10. The maximum (max) and minimum (min) values of u *, slopes, and correlation coefficients (r 2 ) from the individual linear regressions are shown. u * (m s 21 ) Season No. day Max Min Slope (r 2 ) DRR Winter (0.64) Spring (0.59) DRR Winter (0.05) Spring (0.23) Autumn (0.76) DRR Summer (0.20) Autumn (0.13)

10 1350 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 49 FIG. 5. Monthly averaged values of the daytime (Q* $ 0) flux ratios (Q H /Q*, Q E /Q*, DQ S /Q*, and Q H /Q E ) and the daytime-averaged values of u *. The statistics are presented separately for the three sunshine conditions (clear sky, occasionally cloudy, and cloudy). value of DQ S /Q*. In addition, relatively small values of u * in COSMO contributed to the large value of DQ S /Q* (section 5a). Monthly averaged values of u * on clear-sky days were slightly larger in winter than in summer and autumn and reached their peak in April. If the seasonal trend of u * accounted for the seasonal trend of DQ S /Q*, DQ S /Q* would be larger in the months of May July than in October February. Because this result was not observed, the seasonal trend of DQ S /Q* cannot be explained by the seasonal trend of u *. Thus, the seasonal trend of DQ S /Q* would appear even if the values of u * remained the same throughout the year. The seasonal trend of DQ S /Q* originates from that of Q* itself as will be discussed in Part II. The monthly averaged value of the Bowen ratio Q H /Q E on clear-sky days reached its peak in early spring (4.57 in March) and was approximately 2 in other months. The peak of the Bowen ratio in early spring has been also observed in vegetated cities (Moriwaki and Kanda 2004; Christen and Vogt 2004; Kanda 2007). The frequency of rainfall influenced the seasonal variation of the Bowen ratio. The value of Q E /Q* was smaller in the dry season (i.e., in winter) than in other seasons. On occasionally cloudy and cloudy days, the values of u * were slightly larger in summer than in winter, and the seasonal variations of u * were less obvious than those on clear-sky days. The seasonal trend of the SEB from occasionally cloudy and cloudy days did not differ significantly from that from clear-sky days, although the month-to-month variation of the monthly value of each flux ratio increased with increasing DRR. The values of DQ S /Q* were generally larger in winter than in summer both for the occasionally cloudy and cloudy days. The annual averaged values of DQ S /Q* on occasionally cloudy and cloudy days, 0.60 and 0.58, respectively, were similar to that on clear-sky days of Daily total statistics a. Seasonal change of the surface energy balance Table 2 summarizes the monthly averaged values of the total daily energy fluxes (Q*, DQ S, Q H, and Q E ) and flux ratios (DQ S /Q*, Q H /Q*, Q E /Q*, and Q H /Q E ). The flux ratios and daily averaged values of u * are shown in Fig. 6. Unlike for the daytime case, the daily values of DQ S /Q*wereonlyslightlydependentonu * (not shown). Therefore, this dependency is not considered in the following discussions. Regardless of sunshine conditions, similar to what has been observed for most land surfaces, the total daily values of Q* were always positive, although their magnitudes were reduced from the daytime values as a result of the radiative cooling at night. The total daily values of Q H and Q E were larger than the daytime values because

11 JULY 2010 K A W A I A N D K A N D A 1351 FIG. 6. As in Fig. 5, but for the monthly averaged values of the daily flux ratios and the daily averaged values of u *. of the positive values of Q H and Q E at night (see section 4). The values of the Bowen ratios for the daily case were roughly the same as those for the daytime. The most significant difference between the daytime and daily cases was observed in the heat storage: nocturnal cooling of the blocks contributed to a substantial reduction of the total daily values of DQ S from the daytime values. However, the monthly averaged values of DQ S never became 0 but rather were always positive or negative. On clear-sky days, the values of DQ S /Q* were positive in spring and autumn and negative in winter. Such seasonal variations of DQ S /Q* have often been reported for urban areas such as DQ S /Q* for winter in Mexico City, Mexico, and DQ S /Q* for Vancouver, British Columbia, Canada, in summer (Grimmond and Oke 1999). On cloudy days, the seasonal variations of DQ S / Q* were somewhat different from those on clear-sky days. The values of DQ S /Q* became negative even in spring (March and April) and summer (August) and significantly negative in winter (e.g., December) on cloudy days. The significant differences between daytime DQ S and total daily DQ S, and the positive or negative values of the total daily DQ S with nonnegligible magnitudes suggest that heat storage is a key to understanding the daily total of the surface energy partition. The characteristics of the total daily DQ S will be investigated in section 6b. b. The characteristics of the total daily heat storage The total daily heat storage is the sum of the daytime storage and the nighttime loss of energy. Therefore, the total daily heat storage represents the day-to-day energetic hysteresis of a city. The total daily heat storage DQ S can be directly related to the day-to-day temperature change of the urban substrate DT S [5T S j T S j 0000 (K day 21 ), where T S (K) is the average temperature from surface to the hypothetical depth l eff ]. The hypothetical depth l eff (m) is the depth at which energetic contributions to DT S become negligible in a daily cycle. The relationship between DT S and DQ S can be written as DT S 5 1 c S r S l eff DQ S 5 a h DQ S, where a h 5 1 c S r S l eff, (5) with c S r S (MJ m 23 K 21 ) being the average volumetric heat capacity from the surface to the depth l eff and a h being the coefficient of proportionality between DT S and DQ S. In the current study, the complete surface temperature T C (Voogt and Oke 1997), which is a simple area-averaged surface temperature, was used instead of T S. Also, DQ S was related to DT C in an approximately linear fashion (Fig. 7). The slope of the linear relationship a h was approximately constant at 1.2 for all weather

12 1352 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 49 FIG. 7. The relationship between the total daily heat storage DQ S and the change in the complete surface temperature DT C over a day. The plotted data were observed in four weather conditions (clear sky, occasionally cloudy, cloudy, and rainy). Linear regressions with 0 intercept were performed for the relationships separately for each weather condition, where the values of a h are the coefficient of proportionality between DT C and DQ S. conditions (see legend in Fig. 7). This result suggests that the value of l eff was relatively insensitive to the weather condition. For a given DT C, the data of DQ S varied by more than 65 MJm 22 day 21 around the determined linear relationship. Such variations of the total daily values of DQ S were much larger than the variations of the monthly average of the total daily values of DQ S among various seasons and sunshine conditions (Table 2). With these large variations of the total daily values of DQ S, the total daily values of DQ S clearly depended on the weather: they tended to be positive on clear-sky days and occasionally cloudy days and negative on rainy days. This trend suggests that energy tended to be stored on clear-sky days and occasionally cloudy days and that the stored energy tended to be flushed out on rainy days. The total annual values of DQ S were nonzero for all of the weather conditions (Table 4) although the total annual value of DQ S from all the weather conditions combined was relatively small at MJ m 22 yr 21.Insome literature, the value of DQ S accumulated over several days has been assumed to be zero (e.g., Christen and Vogt 2004). However, if the data from rainy days are excluded for this computation, DQ S may be positive and significantly different from zero. Next, the seasonal variations of the total daily values of DQ S were investigated (Fig. 8). In addition to the total daily values, Fig. 8 shows the monthly averaged values (Total) and standard deviations (STD) of the total daily DQ S from all of the weather conditions combined. Similar to the seasonal trend of the surface temperature, the total daily values of DQ S were positive for March August and negative for November February (Fig. 8). The day-today variation of the total daily heat storage was larger than the seasonal variation of the monthly average of the total daily heat storage. The day-to-day variation of the total daily heat storage was smaller in winter than in nonwinter seasons (see STD in Fig. 8). This observation may be related to seasonal weather trends. The winter during the COSMO experiments was characterized by continuous clear-sky days whereas the spring and autumn were characterized by frequent weather changes and the frequent occurrence of rainy days. To investigate the influence of the day-to-day weather change on the total daily heat storage, the total daily heat storage DQ S was compared with the weather condition of the day under consideration and that of the preceding day (Fig. 9). Although the error bars on the ensemble mean values were large because of the data collected under various synoptic conditions, the ensemble mean values showed well-organized trends. The total daily value of heat storage DQ S depended on the weather conditions of both the day under consideration and the preceding day. Pairs of days with similar weather condition yielded DQ S close to zero. This result implies that the day-to-day weather change was an essential factor in producing a significant day-to-day energetic hysteresis of a city. For a given weather condition on the preceding day, the

13 JULY 2010 K A W A I A N D K A N D A 1353 TABLE 4. Summary of total annual heat storages obtained in clearsky, occasionally cloudy, cloudy, and rainy days; N is the number of days for the respective weather conditions. N (MJ m 22 yr 21 ) (MJ m 22 day 21 ) Clear sky Occasionally cloudy Cloudy Rainy All weather conditions ensemble mean value of the total daily heat storage took a larger positive value on clear-sky and occasionally cloudy days than on cloudy days. Also, for a given weather condition on the preceding day, the ensemble mean value of the total daily heat storage on rainy days was negative and smaller than that on no-precipitation days. For a given weather condition on the day under consideration, the ensemble mean value of the total daily heat storage took the largest positive values following a rainy day and the smallest values following a clear-sky or occasionally cloudy day. In general, the urban substrate stored energy most effectively on days after a rainy day and lost energy most effectively on rainy days following a clear-sky day. ð year DQ S dt ð year DQ S dt/n 7. Concluding remarks The Comprehensive Outdoor Scale Model experiments were conducted. The direct measurement of heat storage in COSMO yielded a dataset with closed energy balance for analysis. A one-year dataset from a large outdoor scale model, the 1 /5 model, which is similar in thermal inertia to a real city, was analyzed in this study. The basic features of the surface energy balance of COSMO were investigated, such as the energy balance closure, the ensemble mean of the diurnal variation of the SEB, and the statistics of the daytime and total daily SEB. The following are the five main findings of this study: 1) A surface energy imbalance was observed for the urbanlike rough surface. The magnitudes of the SEI were 1% and 44% for the daytime and nighttime, respectively; thus they differed significantly between the daytime and nighttime. The magnitude of the SEI for both daytime and nighttime combined was 10%, smaller than the typical magnitude for a forest of 20%. 2) A positive sensible heat flux was observed throughout the nighttime in all seasons and for all sunshine conditions. This observation can be explained by the urban effects of large heat storage in the daytime and reduced radiative cooling at nighttime. FIG. 8. Variations of the total daily heat storage with the day of the year. The data from the four weather conditions (clear sky, occasionally cloudy, cloudy, and rainy) are plotted together. The solid line and dotted line indicate the monthly averaged values (Total) and standard deviations (STD), respectively, of the total daily heat storage from all weather conditions.

14 1354 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 49 APPENDIX A Requirements for Physical Scale Similarities FIG. 9. The dependency of the ensemble mean value of the total daily heat storage on weather condition of the day under consideration and of the preceding day. The weather condition of the day under consideration is classified by DRR (see label in upper-left corner of each panel). Based on the weather condition of the preceding day, a set of four ensemble mean values of the total daily heat storage is calculated for each weather condition on the day under consideration. The symbols indicating the weather condition of the preceding day are shown at the bottom of the figure. The error bars indicate the range of the total daily values of heat storage that are included in ensemble averaging. 3) The surface energy balance was dependent on the wind velocity (as represented by the friction velocity). The daytime ratio of heat storage to net radiation (DQ S /Q*) decreased with increasing friction velocity. 4) Seasonal changes of the daytime surface energy balance were confirmed even with no seasonal change of vegetation and no human activities. In COSMO, the values of DQ S /Q* werelargerinwinterthanin summer. 5) A relationship was found between the day-to-day energetic hysteresis (i.e., total daily values of heat storage) and the weather conditions. In general, the urban substrate stored energy on clear-sky and occasionally cloudy days, and the stored energy was flushed out on rainy days. Acknowledgments. This work was supported by the Core Research for Evolutional Science and Technology (CREST) of the Japan Science and Technology Cooperation, by the Ehime University Global COE Programme under the Ministry of Education, Culture, Sports, Science and Technology, the Government of Japan, and by Japan Society for the Promotion of Science Grant-in- Aid for Young Scientists (B) ( ). We gratefully acknowledge Prof. Kenichi Narita of the Nippon Institute of Technology and Prof. Aya Hagishima of Kyushu University. Physical scale similarity requires similarities of radiation, flow, and thermal inertia (Kanda 2006). As discussed in this section, the thermal inertia similarity is not often met in reduced model experiments with respect to a real city. This section mainly examines the validity of the thermal inertia similarity of the 1 /5 model by comparing the results obtained from the 1 /5 and the 1 /50 model experiments (section b of appendix A) as well as those from numerical simulations (section c of appendix A). a. The 1 /50 model experiments A series of 1 /50 model (Fig. 1b) experiments were conducted simultaneously with the 1 /5 model experiments. These two models were separated by 13 m. The objective of this experiment was to investigate the effects of the geometrical scales of the model on the surface energy balance. The experiments were conducted for the periods of November December 2004 and March May Data from 24 and 7 clear-sky days were analyzed from the two periods, respectively. The surface geometry (i.e., the plan area and frontal area of roughness elements) and the material of the 1 /50 model were the same as those of the 1 /5 model. However, the geometrical scale was considerably different: the height of the cubic blocks was 0.15 m in the 1 /50 model 1 /10th that in the 1 /5 model. As in the 1 /5 model experiments, four components of radiation and turbulence fluxes were measured by the same instruments at the same sample frequencies. The radiation and flux measurement heights were also the same in terms of the relative heights to the block height between the 1 /5 and 1 /50 model experiments. Heat storage and the surface temperature were also directly measured using the same heat flux sensors as for the 1 /5 model experiments except for the size ( mm). A total of 72 sensors were attached to a sample unit that consisted of a block and its surrounding streets. All observed data were handled in the same way as in the 1 /5 model experiments (see section b of appendix A). The same meteorological forcing, geometry, and constituent material between the 1 /5 and 1 /50 models made it easy to compare the results obtained from these two models. b. Comparison between the 1 /50 and 1 /5 model experiments The albedo a can be adequately used as an index to examine the radiation similarity because shortwave radiation is free from the influence of the surface temperature unlike longwave radiation. The ensemble means of a observed from the 1 /5 and 1 /50 models showed good

15 JULY 2010 K A W A I A N D K A N D A 1355 FIG. A1. Ensemble mean of the diurnal variation of the surface energy balance (Q* 5DQ S 1 Q H 1 Q E ) obtained from the 1 /5 and 1 /50 model experiments in two seasons (November December 2004 and March May 2005). agreement in the diurnal variations and the daily averaged values, both in winter and in summer (not shown); thus radiation similarity to a real city was met, regardless of the scale, for both models. This is due to the fact that radiation wavelengths were much shorter than the building dimensions. A thorough investigation of the flow similarity was difficult with the current setup because no adequate instruments were available to estimate the detailed turbulence statistics within the canopy layer of the 1 /50 model. Kanda et al. (2007) evaluated the roughness lengths for momentum both for the 1 /5 and 1 /50 models. The values of TABLE A1. Summary of daytime (Q* $ 0)-averaged values of albedo a, daily average (avg), maximum (max), and minimum (min) values of complete surface temperature T C and daytime and total daily energy fluxes (Q*, DQ S, Q H, and Q E ) and flux ratios (Q H /Q E, DQ S /Q*, Q H /Q*, and Q E /Q*) obtained from the 1 /5 and 1 /50 model experiments. Results are from clear-sky days in two seasons (November December 2004 and March May 2005). Model Period ND a T C (K) Energy flux (MJ m 22 day 21 ) Ratio Avg Max Min Q* DQ S Q H Q E DQ S /Q* Q H /Q* Q E /Q* Q E /Q H Daytime (Q*. 0) 1/5 model Nov Dec /50 model Nov Dec /5 model Mar May /50 model Mar May Daily 1/5 model Nov Dec /50 model Nov Dec /5 model Mar May /50 model Mar May

16 1356 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY FIG. A2. The dependency of mc on the wall thickness, where mc is the building mass per unit surface area. REAL refers to a real city investigated by Moriwaki and Kanda (2004). The plane and frontal area aspect ratios of the city are the same as those of COSMO. The building height of the city was 7.3 m. the roughness lengths showed good agreement, which may be considered as indirect evidence of the flow similarity. To examine the thermal inertia similarity, the diurnal variations of the surface energy balance (Fig. A1) and the complete surface temperature TC were evaluated for the 1/ 5 and 1/ 50 models for both winter and summer. Table A1 summarizes Fig. A1 in terms of the daytime and daily statistics of the energy fluxes and flux ratios, and daily average, maximum, and minimum values of TC. In both of the seasons, differences in the results between the 1/ 5 and 1/ 50 model experiments are evident. The volumetric heat capacity of the 1/ 50 model was smaller than VOLUME 49 that of the 1/ 5 model. Therefore, the daytime values of DQS were smaller in the 1/ 50 model than in the 1/ 5 model, and, as a result, the daytime values of the sensible heat flux QH were larger for the 1/ 50 model than for the 1/ 5 model. At night, the values of QH became almost zero for the 1/ 50 model while measurable positive values of Q were H observed for the 1/ 5 model. Furthermore, the diurnal variations of TC in the 1/ 5 model were larger than those in the 1/ 50 model (see the maximum and minimum values of TC in Table A1). These results suggest that the 1/ 50 model, because of its small roughness elements, did not meet the requirements for thermal inertia similarity with a real city. Therefore, the 1/ 50 model is considered not to be useful for studying the energy balance for an urban area. The results above also indicate an essential influence of urbanization on the energy balance; that is, roughness elements with large volumetric heat capacities increase the daytime heat storage, and this, in part, sustains positive sensible heat fluxes at night. An investigation of the thermal inertia similarity between the 1/ 5 model and real cities is not currently feasible experimentally. Therefore, this similarity is investigated with the aid of numerical simulation as described in section c of appendix A. c. Numerical experiments Numerical experiments were conducted using the simple urban energy balance model for mesoscale simulation (SUMM; Kanda et al. 2005a,b; Kawai et al. 2007, 2009). Kawai et al. (2007) confirmed that SUMM simulates the surface energy balance, surface temperature, FIG. A3. (a) Comparisons of simulated heat storage from case 2 (wall thickness m) and case 3 (wall thickness m) with simulated heat storage from case 1 (wall thickness m). As a reference, observed storage is also compared with simulated heat storage from case 1. The plotted data are hourly averaged values. Linear regressions with a 0 intercept were performed for the relationships between each pair of the simulated results. (b) As in (a), but for the difference between the hourly complete surface temperature and the daily average of the complete surface temperature. (c) As in (a), but for the difference between the hourly interior temperature and the daily average of the interior temperature.

17 JULY 2010 K A W A I A N D K A N D A 1357 and interior temperature of the 1 /5 model well for windy conditions (u * $ 0.3 m s 21 ). For the following analyses, a total of 37 windy days from all seasons were selected, and, except for the wall thickness, the simulation settings were the same as those in Kawai et al. (2007). The building mass per unit surface area m c (kg m 22 ) and the thickness of the thermally active building walls (wall thickness hereinafter) can be used as indices for evaluating the thermal inertia similarity (Pearlmutter et al. 2005). Based on a field survey, Tso et al. (1990) reported 700 kg m 22 for a typical value of m c. To study the thermal inertia similarity between the 1 /5 model and a real city, the dependencies of m c on the wall thickness are compared between the 1 /5 model and the actual city (REAL) that was investigated by Moriwaki and Kanda (2004; Fig. A2). In this figure, a building height of 7.3 m is assumed for the city and the plan and frontal areas of roughness elements of the city are assumed to be the same as for COSMO. Lines are drawn on Fig. A2 for the values of the wall thickness for REAL, 0.25 m, and for the 1 /5 model, 0.35 m for m c kg m 22 (Tso et al. 1990). The value of m c of the 1 /5 model is 267kgm 22, which is smaller than the typical value from the field. To examine the influence of such a small value of m c, a series of numerical experiments were conducted for three cases with different wall thicknesses because m c and wall thickness are related as in Fig. A2. The three cases are: case 1 with a wall thickness m and m c kg m 22, case 2 with a wall thickness m and m c kg m 22, and case 3 with a wall thickness m and m c kg m 22. The results of these experiments are shown in Fig. A3. The heat storage DQ S and the surface temperature T c of the three cases generally show good agreement as indicated by high correlation coefficients (Fig. A3a). The heat storage and the surface temperature are underestimated in cases 2 and 3 with respect to those in case 1, because of the increase of volumetric heat capacity of the blocks. However, these underestimations are negligible. Even in case 3 with significantly larger wall thickness and thus with a significantly larger value of m c, the underestimations are 5% for the heat storage and 2% for surface temperature, as indicated by the slopes. On the contrary, the correlations of the interior temperature among the three cases are poor (Fig. A3b) because of the reduced diurnal variation of the interior temperature with increasing wall thickness. The above results may suggest that the influence of the thickness of the thermally active building wall is relatively small on the diurnal variations of the surface energy balance and of the surface temperature. Thus, the wall thickness of 0.1 m in the 1 /5 model may be FIG. B1. Schematic vertical cross section of the electric balance equipment for measuring weight change of a sample unit of the 1 /50 model. considered to be roughly similar in thermal inertia to those of a real city. APPENDIX B Measurement of the Weight Change of a Sample Unit To observe the temporal variations of the latent heat flux from the concrete surface, change in water content within the concrete was monitored using a sample unit of the 1 /50 model. The sample unit consisted of a block and its surrounding streets with a surface area of m 2 and walls that were 0.15 m in thickness. The weight change was measured using an electrical balance meter with 0.1 g instrumental accuracy (IS64EDE-H from Sartorius AG; Fig. B1). The measurements were made during the period between November 2004 and January All observed data were sampled at 1 Hz and averaged over 30 min. Figure B2 shows temporal weight change of the sample unit during five successive days immediately after a rainfall (Fig. B2a; case 1) and that during four successive rainfree days after a 10-day period with no rain (Fig. B2b; case 2). The time series of latent heat fluxes in these figures were calculated from the weight change of the sample unit. Case 1 shows that the sample unit absorbed some of the water supplied by rain and released it over the period of a few days. Such continuous release of absorbed water resulted in a daytime latent heat flux with maximum values of W m 22. The influence of the continuous release of absorbed water on the latent heat flux was present even 2 weeks after rainfall (case 2). In case 2, dew formation was also observed at night. The sample unit absorbed water from dew and released it during the daytime. This diurnal cycle of dew had a significant influence on the value of the daytime latent heat flux in case 2