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Turbulent heat fluxes in urban areas: Observations and a local-scale urban meteorological parameterization.. Grimmond, C. S. B.; Oke, Timothy R. 2002-07-08

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792 VOLUME 41J 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 q 2002 American Meteorological Society Turbulent Heat Fluxes in Urban Areas: Observations and a Local-Scale Urban Meteorological Parameterization Scheme (LUMPS) C. S. B. GRIMMOND Atmospheric Science Program, Department of Geography, Indiana University, Bloomington, Indiana T. R. OKE Department of Geography, University of British Columbia, Vancouver, British Columbia, Canada (Manuscript received 11 November 2001, in final form 2 February 2002) ABSTRACT A linked set of simple equations specifically designed to calculate heat fluxes for the urban environment is presented. This local-scale urban meteorological parameterization scheme (LUMPS), which has similarities to the hybrid plume dispersion model (HPDM) scheme, requires only standard meteorological observations and basic knowledge of surface cover. LUMPS is driven by net all-wave radiation. Heat storage by the urban fabric is parameterized from net all-wave radiation and surface cover information using the objective hysteresis model (OHM). The turbulent sensible and latent heat fluxes are calculated using the available energy and are partitioned using the approach of de Bruin and Holtslag, and Holtslag and van Ulden. A new scheme to define the Holtslag and van Ulden a and b parameters for urban environments is presented; a is empirically related to the plan fraction of the surface that is vegetated or irrigated, and a new urban value of b captures the observed delay in reversal of the sign of the sensible heat flux in the evening. LUMPS is evaluated using field observations collected in seven North American cities (Mexico City, Mexico; Miami, Florida; Tucson, Arizona; Los Angeles and Sacramento, California; Vancouver, British Columbia, Canada; and Chicago, Illinois). Performance is shown to be better than that for the standard HPDM preprocessor scheme. Most improvement derives from the inclusion of the OHM for the storage heat flux and the revised b coefficient. The scheme is expected to have broad utility in models used to calculate air pollution dispersion and the mixing depths of urban areas or to provide surface forcing for mesoscale models of urban regions. 1. Introduction Knowledge of the surface sensible heat flux and at- mospheric stability is a necessary prerequisite of models to calculate air pollution dispersion, urban mixing depth, and mesoscale airflow. On an operational basis, direct observation of these variables in cities is rare; therefore, it is necessary to parameterize the terms using more routinely measured data. Such parameterizations are in- cluded in meteorological preprocessors (e.g., Seibert et al. 2000; de Haan et al. 2001). Here we present a local- scale urban meteorological parameterization scheme (LUMPS), which consists of a series of linked equations that allow the storage (DQS), turbulent sensible (QH), and latent (QE) heat fluxes to be calculated (Fig. 1). The basic premise is that heat fluxes can be modeled using net all-wave radiation, simple information on surface cover (areas of vegetation, buildings, and impervious materials), morphometry (roughness element height and Corresponding author address: Sue Grimmond, Department of Ge- ography, Student Building 104, 701 E. Kirkwood Ave., Indiana Uni- versity, Bloomington, IN 47405-7100. E-mail: grimmon@indiana.edu density), and standard weather observations (air tem- perature, humidity, wind speed, and pressure). The method has relatively limited data requirements yet is sophisticated enough to predict the spatial and temporal variability of heat fluxes known to occur within, and between, urban areas (Grimmond and Oke 2000). In this paper, the nonradiative heat flux submodels of LUMPS are outlined and are evaluated using local-scale meteorological data collected in seven North American cities. These observations constitute a multicity urban hydrometeorological database (MUHD) (described in section 3), which has been generated to document the variability of local-scale surface heat fluxes in urban environments. The ‘‘surface’’ here is the top of a ‘‘box,’’ the height of which extends from a measurement level above the city down to a depth in the ground where the diurnal conductive heat flux ceases. By ‘‘local scale’’ we refer to horizontal areas of approximately 102–104 m on a side and to measurement heights in the inertial sublayer above the urban canopy and its roughness sub- layer (Fig. 2). At this height and scale, we expect the microscale variability of atmospheric effects generated by individual houses and other surfaces to be integrated into a characteristic neighborhood response.JULY 2002 793G R I M M O N D A N D O K E FIG. 1. Flow chart of the structure of LUMPS. Quantities in parentheses are needed only if net all-wave radiation Q* or incoming shortwave radiation K↓ are not measured: Ta is air temperature, ea is actual vapor pressure, cF is cloud fraction, P is pressure, U is wind speed, DQS is storage heat flux, QH is turbulent sensible heat flux density, QE is latent heat flux density, L is Obukhov length, and u* is friction velocity. FIG. 2. Definition of layers involved in the study of urban climates at the local scale (modified after Oke 1997) relative to the box modeled by LUMPS. The lateral (or third) dimension of the box (not shown) is 102–104 m. Within the roughness sublayer (RSL) there is greater spatial variability of temporally averaged fluxes than within the inertial sublayer; i.e., these fluxes are chaotic in the urban canopy layer and RSL but become invariant in the inertial sublayer. The top of the box is within the inertial sublayer, and the bottom is at the depth at which there is no net heat exchange over the time period of interest. The data in MUHD are used to derive parameters for LUMPS and to evaluate the fluxes the scheme predicts. We recognize that in so doing evaluation is not inde- pendent of model development. Further, the range of conditions for which LUMPS is applicable is limited to those in MUHD, particularly in terms of wind, surface moisture, and anthropogenic heat. Here, LUMPS is compared with relevant portions of the hybrid plume dispersion model (HPDM) urban preprocessor of Hanna and Chang (1992, 1993), which possesses several sim- ilarities. 2. The local-scale urban meteorological parameterization scheme A flow chart of the structure of LUMPS (Fig. 1) shows that it is driven by relatively easily obtained me- teorological and surface data. In this section, each sub- model is described briefly. LUMPS is formulated in the framework of the surface energy balance (SEB), Q* 5 Q 1 Q 1 DQ ,H E S (1) where Q* is the net all-wave radiation. Here we are794 VOLUME 41J 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 TABLE 1 (a). Coefficients used to model storage heat flux [(2)]. Surface is divided into three surface types. The complete set of coefficients used for green space/open and paved/impervious surfaces is given in Table 4 of Grimmond and Oke (1999c). (b) Roof coefficients used with the OHM storage heat flux model from Meyn (2000). Surface type Sites where used Basis for values a1 a2 (h) a3 (W m22) (a) Coefficients used in current application Green space/open All Mean of all seven sources in Table 4 (Grimmond and Oke 1999c) 0.34 0.31 231 Paved/impervious All Mean of all five sources in Table 4 (Grimmond and Oke 1999c) 0.70 0.33 238 Rooftop A93, A94 Sg94, S91u, Vs89, Vs92, T90 Mean of 9, 10, 11; see (b) 0.10 0.26 24 C95u Mean of 9, 11; see (b) 0.11 0.30 26 Me93 Mean of 5, 8, 11, 12; see (b) 0.11 0.45 28 Mi95 Mean of 9, 10; see (b) 0.11 0.25 24 C92 Mean of 5, 8, 9, 11; see (b) 0.13 0.45 29 Vl92 Mean of 5, 8; see (b) 0.16 0.60 212 (b) Roof type Code referred to in (a) Source a1 a2 (h) a3 (W m22) Vancouver (tar and gravel) 2 Yap (1973) 0.17 0.10 217 Uppsala 3 Not recommended (Meyn 2000) Kyoto 4 Not recommended (Meyn 2000) Gravel, tar, concrete flat industrial (avg) 5 Meyn (2000) 0.25 0.92 222 Gravel, tar, concrete flat industrial (dry) 6 Meyn (2000) 0.25 0.70 222 Gravel, tar, concrete flat industrial (wet) 7 Meyn (2000) 0.25 0.70 222 Bitumen spread over flat industrial membrane 8 Meyn (2000) 0.06 0.28 23 Asphalt shingle–on-plywood residential roof 9 Meyn (2000) 0.14 0.33 26 High-albedo asphalt shingle residential roof 10 Meyn (2000) 0.09 0.18 21 Ceramic tile 11 Meyn (2000) 0.07 0.26 26 Slate tile 12 Meyn (2000) 0.08 0.32 0 concerned primarily with the right-hand side of the SEB. Of interest are hourly fluxes, representative of the local scale (see section 1). Net all-wave radiation sets the energetic bounds for the other fluxes in the surface energy balance. In the form of LUMPS presented and evaluated here, measured net allwave radiation is used to drive the scheme. In the absence of Q* observations, this term can be obtained from parameterization using measured or modeled solar radiation K↓ or a mixture of parameterization and mod- eling of the individual radiation fluxes (Newton 1999). If cloud is present, observation is greatly preferred. In this paper, we restrict consideration to the energy balance fluxes in Fig. 1. Calculation of the friction ve- locity u* and Obukhov stability length L will be ad- dressed separately. Urban values of the roughness length for momentum and the zero-plane displacement have been addressed in Grimmond and Oke (1999a), and the roughness length for heat has been considered in Voogt and Grimmond (2000). a. Storage heat flux The storage heat flux in this urban SEB refers to the combined heat uptake and release from all substances (air, soil, biomass, and building materials) in the box, referred to as the equivalent surface flux through its top (Fig. 2). To capture the magnitude and diurnal hysteresis pattern of changes of the storage heat flux, the objective hysteresis model (OHM) of Grimmond et al. (1991) is used: n n n ]Q* DQ 5 ( f a )Q* 1 ( f a ) 1 ( f a ). (2) O O OS i 1i i 2i i 3i 1 2 ]ti51 i51 i51 This requires knowledge of the local-scale net all-wave radiation, the fraction f of each of the n surface types within the area of interest, and the corresponding three coefficients (a1–a3; Table 1; see also Table 4 in Grim- mond and Oke 1999c). The fraction of the surface oc- cupied by each surface type can be calculated for a 2D (plan) or 3D (complete) area. Grimmond and Oke (1999c) conclude that incorporating 3D effects does not result in a significant improvement in the performance of OHM. Therefore for LUMPS at this stage, we rec- ommend using the simplest surface description—that is, only the plan area of the impervious surfaces and roof- tops—and combining the remaining green space and bare-ground areas into one category [thus, n 5 3 in (2)]. Meyn (2000) provides new data for a1–a3 coefficients for roofs (Table 1b). These are incorporated into the version of OHM presented here.JULY 2002 795G R I M M O N D A N D O K E TABLE 2. Previously quoted values of the a and b parameters: (a) range listed by Hanna and Chang (1992) based on information in Beljaars and Holtslag (1989, 1991) and (b) values for urban terrain used by Hanna and Chang (1992). a b (W m22) (a) Range of values for all surface types Dry desert with no rain for months 0.0–0.2 20 Arid rural area 0.2–0.4 20 Crops and field, midsummer during periods when rain has not fallen for several days 0.4–0.6 20 Urban environment, some parks 0.5–1.0 20 Crops, fields or forests with sufficient soil moisture 0.8–1.2 20 Large lake or ocean with land more than 10 km distant 1.2–1.4 20 (b) Values selected for specific urban sites St. Louis (site-105 urban commercial, including warehousing and light in- dustrial uses; plan area 25% buildings, 59% paved, 15% grass, 1% trees) 0.5 20 Industrial (‘‘urban-tower’’ site, grassy field adjacent to densely built-up area) 0.5 20 b. Sensible and latent heat flux In formulating their HPDM, Hanna and Chang (1992, 1993) use the parameterizations of the turbulent sensible and latent heat fluxes (QH and QE, respectively) pro- posed by de Bruin and Holtslag (1982). When written in a form appropriate for an urban environment, these are (1 2 a) 1 (g/s)Q 5 (Q* 2 DQ ) 2 b and (3)H S1 1 (g/s) aQ 5 (Q* 2 DQ ) 1 b, (4)E S1 1 (g/s) where s is the slope of the saturation vapor pressure– versus-temperature curve, g is the psychrometric ‘‘con- stant,’’ and a and b are empirical parameters. These parameters are based on a simplification of the Penman– Monteith approach, which takes into account the Priest- ley–Taylor coefficient aPT for extensive wet surfaces but extends it to include nonsaturated areas. To evaluate (3) and (4), the two parameters a and b must be specified. The a parameter accounts for the strong correlation of QH and QE with Q* 2 DQS, whereas b accounts for the uncorrelated portion (Holtslag and van Ulden 1983). As noted, a depends on the surface moisture status, and in the original scheme b was an empirical constant. Table 2, taken from Hanna and Chang (1992), summarizes their default guidance values for these parameters for a range of land cover conditions. Holtslag and van Ulden (1983) outline a method to determine the a and b parameters that involves rewriting (4) as 1Q 5 a (Q* 2 DQ ) 1 b9 , (5)E S[ ]1 1 (g/s) where b9 is the value for which a 5 1, given that b 5 a 5 0 when QE 5 0 W m22, and b 5 b9a. Using (5) and measurements of QE (with Q*, DQS, and temper- ature to determine s and g), the parameters can be de- rived from regression analysis; a then can be related to the moisture status of the surface (Holtslag and van Ulden 1983), and predictive relations can be developed. Holtslag and van Ulden (1983) indicate that a value of b 5 20 W m22 is reasonable, and this value has been used subsequently by others (Table 2). Hanna and Chang (1992) note that the use of a constant b accounts for the observation that QH turns negative before sunset. However, they do not back-calculate values for either of the parameters from their urban data for use in HPDM. Here we investigate both parameters based on our emerging understanding of flux partitioning in urban environments (see section 3c). c. Anthropogenic heat Similar to the energy balance formulation of HPDM, we do not include an anthropogenic heat flux QF. For the range of conditions we consider (see further de- scriptions below) and the approach we adopt, we do not think it is necessary. This is a saving in input require- ments and uncertainty. LUMPS is based on a measured, not a theoretical or modeled, surface energy balance. The instruments used to measure Q*, QH, and QE are likely to sense most of the anthropogenic contributions to the radiative, convective, and conductive fluxes. Pa- rameterized terms based on these measured quantities thus already include the effects of QF. Adding an in- dependent anthropogenic heat term would be ‘‘double counting’’ this heat source. We stress, however, that this approach is only valid for the range of conditions so far encountered in MUHD, the observational base of the parameterization. MUHD is biased toward low-density residential areas in summer. It will be necessary to ex- tend MUHD to include observations from sites at which QF is large or to devise other modifications to the LUMPS relations if it is to be applied at sites at which combustion release is very large (e.g., manufacturing796 VOLUME 41J 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 TA B L E 3. St ud y si te s o rd er ed by de cr ea sin g fr ac tio n o f th e su rf ac e bu ilt (co mb ine d ar ea o f ro o fs an d im pe rv io us su rf ac es ,o r co n v er se ly , in cr ea si ng fr ac tio n gr ee n sp ac e). Co de re fe rs to th e lo ca tio n an d ye ar o f o bs er v at io n, e. g. ,M e9 3 re fe rs to M ex ic o Ci ty in 19 93 .L an d u se : su bu rb an (S ub ), lig ht in du str ia l( LI ), do w nt ow n/ ce nt ra l( D) . U rb an te rr ai n z o n es (U TZ )a cc o rd in g to El le fs en (1 99 0– 91 ). Fr ac tio n pl an ar ea : bu ild in gs (B ld) ,i m pe rv io us (Im p) ,u n m an ag ed o r v ac an t (U M ), tr ee s (T R) ,g ra ss (G R) ,o r w at er (W T) (af ter G rim m on d an d O ke 19 99 b) . Si te Co de O bs pe rio d O rig in al re fe re nc e w ith fu ll de ta ils H ei gh to f bu ild in gs : m ea n an d st d de v La nd /U se an d U TZ La nd co v er (p lan -ar ea fr ac tio n) B ld Im p U M TR G R W T M ex ic o Ci ty M e9 3 D ec 19 93 O ke et al .( 19 99 ) 18 .4 6 6. 6 D /A 2 54 44 2 1 0 0 Va n co u v er , B C V l9 2 A ug 19 92 G rim m on d an d O ke (1 99 9c ) 5. 8 6 0. 1 LI /D o4 51 44 0 3 2 0 Tu cs o n , A Z T9 0u Ju n 19 90 G rim m on d an d O ke (1 99 5) 5. 2 6 0. 8 Su b/ D o3 23 42 17 11 7 0 M ia m i, FL M i9 5 M ay /J un 19 95 N ew to n (1 99 9) 8. 0 6 2. 1 Su b/ D o3 35 29 0 7 27 2 Ch ic ag o, IL C9 5 Ju n/ A ug 19 95 K in g an d G rim m on d (1 99 7) 5. 9 6 1. 3 Su b/ D c3 36 25 0 7 32 0 Sa n G ab rie l, Lo s A ng el es ,C A Sg 94 Ju l1 99 4 G rim m on d et al .( 19 96 ) 4. 7 6 0. 2 Su b/ D o3 29 31 0 12 25 4 Ch ic ag o, IL C9 2 Ju l1 99 2 G rim m on d et al .( 19 94 ) 6. 7 6 0. 5 Su b/ D o3 33 22 1 10 34 0 Va n co u v er , B C V s9 2 Ju l/S ep 19 92 G rim m on d an d O ke (1 99 9c ) 4. 7 6 0. 2 Su b/ D o3 31 23 2 9 35 0 Va n co u v er , B C V s8 9 Ju l1 98 9 R ot h an d O ke (1 99 3) 4. 7 6 0. 2 Su b/ D o3 31 23 2 9 35 0 Sa cr am en to ,C A S9 1u A ug 19 91 G rim m on d et al .( 19 93 ) 4. 8 6 0. 2 Su b/ D o3 36 12 1 13 34 5 A rc ad ia ,L os A ng el es ,C A A 94 Ju l1 99 4 G rim m on d et al .( 19 96 ) 5. 2 6 0. 2 Su b/ D o3 24 19 2 30 23 2 A rc ad ia ,L os A ng el es ,C A A 93 Ju l/A ug 19 93 G rim m on d an d O ke (1 99 5) 5. 2 6 0. 2 Su b/ D o3 22 18 2 32 24 2 areas or high-rise residential or commercial complexes), especially if they are cities located in extremely hot or cold climates with significant space cooling or heating. 3. The multicity urban hydrometeorological database a. The sites This section outlines the methods and results of work we have conducted over the last decade to compile a multicity urban hydrometeorological database. To date we have observed fluxes and climate data at 10 sites in seven North American cities, and at 2 of the sites we have data for two different periods (see Table 3). These data have informed our understanding of flux partition- ing in urban environments and are used here to evaluate parameterizations of the turbulent sensible and latent heat fluxes. The construction of this database is ongoing, and field campaigns are under way and planned at ad- ditional sites to enhance the range of surface and at- mospheric conditions sampled and also to provide in- dependent test sets. Each set of observations in MUHD is identified by its geographic location (one- or two-letter code) and the year in which it was conducted (last two digits). The sites, selected to represent different building styles and climates, range from Vancouver, British Columbia, Can- ada, (Vl92, Vs92) in the northwest of North America to Mexico City, Mexico, (Me93) in the south. There are observations from the dry southwestern region of the United States (Tucson, Arizona, T90; Los Angeles, Cal- ifornia, A93, A94, Sg94; Sacramento, California, S91) and from the more humid Great Lakes (Chicago, Illinois, C95) and subtropical southeastern region (Miami, Flor- ida, Mi95). The data were collected in the summertime, with the exception of Mexico City, for which obser- vations were conducted during the dry season (Decem- ber of 1993). Most of the data were collected in short-campaign (1–8 weeks) field programs. Simultaneous observations were made at two different locations within both Los Angeles (A94 and Sg94) and Vancouver (Vs92 and Vl92). In addition, data were collected at the same site in Los Angeles in two consecutive summers (A93 and A94) and in Vancouver (site Vs) in 1989 and 1992. In Chicago, measurements were made in two closely prox- imate neighborhoods in 1992 and 1995 (C92 and C95). In general, Chicago was windy and moist, Tucson was hot and dry with strong daily wind variations, and Sac- ramento and Los Angeles were dry with a weak wind in the afternoon. Except for Chicago and Miami, the measurement periods were predominantly rain free. For each of the sites, geographic information systems (GIS), spatially georeferenced databases, have been cre- ated to archive data about the surface cover and build- ing/vegetation morphometry surrounding the measure- ment site (Grimmond and Souch 1994). These data pro-JULY 2002 797G R I M M O N D A N D O K E vide information on the average height of the roughness elements (buildings and trees), their horizontal dimen- sions, their spacing, and the fraction of the area they cover. The urban land uses represented include central city (old colonial core of Mexico City, Me93), light industrial (one- and two-story warehouses in Vancouver, Vl92), and low- or medium-density residential housing (the remainder of the sites). The land cover varies from less than 5% vegetated (Me93, Vl92) to a residential area with almost 60% vegetation cover (Los Angeles, A93, A94; Table 3). Across all sites, the buildings vary in height from 5 to 19 m (Table 3). At many of the residential sites, the trees are as tall or taller than the houses. The surface moisture availability at the MUHD sites varied greatly, and this is critical to their characteristic energy partitioning. Given the infrequent rainfall in Tuc- son, Sacramento, and Los Angeles, the vegetation in the neighborhoods surrounding the measurement sites can only be maintained by irrigation. In Los Angeles and Sacramento, plentiful irrigation sustains lush green land- scapes. In Sacramento during the observation period, people living in the vicinity of the site were permitted to irrigate on alternate days of the week depending on their street address (i.e., alternation of odd- and even- numbered houses). Watering was not permitted on Sun- days. In Los Angeles, no regulations were imposed on irrigation, and frequent watering occurred in the early morning and late afternoon (Grimmond et al. 1996). In Tucson, on the other hand, where water conservation is encouraged, the vegetation is xeric. A reasonable amount of biomass is present, but it is adapted to an environment in which water is a limiting factor. Much of the irrigation occurs at night as drip or subsurface irrigation for short periods and in a much more targeted manner than in the other cities. In Vancouver, which experiences mild summer drought, there is normally (e.g., Vs89) considerable sprinkler-type irrigation of gardens and parks. In 1992, however, lack of precipi- tation led to a ban on external irrigation, so the resi- dential area (Vs92) was much drier than normal. b. Atmospheric observations The surface energy balance data contained within MUHD are observations made using instruments mounted on tall towers (18–451 m), usually at heights of at least 2 times the mean height of the roughness elements. This measurement height ensures that the in- struments are above the influence of individual rough- ness elements and that the fluxes observed represent an integrated response at the local scale (Grimmond and Oke 1999a,c; Rotach 2000). At the instrument heights used, the source areas for the radiation measurements are approximately 5–12 3 104 m2 (i.e., circles of radius 125–195 m centered on the tower). The elliptically shaped source areas for the turbulent fluxes, which lie upwind of the tower sites, range from approximately 1.5 3 105 to 5 3 106 m2 depending on stability, rough- ness, and wind speed [for typical shapes, see Schmid (1994)]. At each site, a net radiometer has been used to mea- sure net allwave radiation flux density, a sonic ane- mometer–thermometer system has been used to measure the turbulent sensible heat flux density, and a krypton hygrometer (with the sonic anemometer) has been used to measure the latent heat flux density. Hence, the tur- bulent heat fluxes are directly measured by eddy co- variance, and heat storage change in the urban fabric, expressed as a heat flux density through a horizontal plane (Fig. 2), is found as the residual in the surface energy balance (which therefore accumulates all mea- surement errors and neglected terms). Grimmond and Oke (1999b,c) provide fuller details about the instru- mentation, its exposure, and the postprocessing of data. Results are hourly averages corrected to local apparent time (LAT) to ensure consistency of solar noon. Day- time and nighttime are defined herein as the times during which Q* is positive or negative, respectively, and ‘‘dai- ly’’ means the 24-h period. c. Summary of known flux partitioning in urban environments Detailed descriptions of the fluxes and flux partition- ing measured as part of MUHD are presented elsewhere (see references in Table 3). The turbulent and storage heat fluxes all represent important terms in the surface energy balance of urban environments. Here we sum- marize the most important characteristics of these fluxes, focusing on their magnitude, variability, and diurnal course, and the implications for the parameterizations used in LUMPS. 1) STORAGE HEAT FLUX For the sites and conditions considered in MUHD, the heat added to or removed from the fabric of the buildings, roads, trees, ground, and the air in the layer beneath measurement level is most important at the downtown and light-industrial sites. At such dry and built-over sites, heat storage changes sequester at least 50% of daytime Q*. Here DQS is typically 20%–30% of daytime Q* at residential sites (Grimmond and Oke 1999c). Average peak daily values range from approx- imately 150 to 280 W m22 (Fig. 3), considerably larger than for most natural systems, except water. At night the release of the daytime heat reservoir produces an upward-directed flux that is initially larger than the net radiation. Then, after one or two hours it settles into a remarkably simple pattern in which it is within 65% of the net radiation loss. At the hourly timescale and from day to day, DQS is variable [see examples presented in Grimmond and Oke (1999c)]. Some of this variability can be attributed to differences in radiant loading; however, even on cloud-798 VOLUME 41J 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 FIG. 3. Mean diurnal hysteresis pattern between observed urban heat storage change (DQS) and net all-wave radiation (Q*). Individual hysteresis patterns are shown in Grimmond and Oke (1999c). (Note that Figs. 3–8 contain no Vs89 results because of insufficient data to calculate ensemble means.) free days, when the diurnal pattern of Q* is smooth, hourly variability results from variations in the convec- tive fluxes (see further discussion below). Storage heat flux uptake in urban areas is not sym- metrical around solar noon; rather, there is a distinct tendency for more energy to enter the urban fabric in the morning (Fig. 3). This hysteresis pattern suggests that parameterizing DQS as a fixed fraction of Q* (e.g., as in HPDM) is less appropriate than a scheme that takes this diurnal hysteresis pattern into account (see section 2a). For most of the night, however, it is acceptable to equate DQS approximately to Q*. 2) LATENT HEAT FLUX Figure 4 summarizes the latent heat fluxes for each of the datasets. The average daily maximum latent heat flux in summertime varies between 10 and 235 W m22 (Fig. 4a). It is not a surprise that those areas with little vegetation (downtown Me93 and industrial Vl92) have extremely small latent heat flux values (Grimmond and Oke 1999b). The very low value (;10 W m22) at Me93 is partly due to the low radiation input in winter but is unlikely to be much greater in summer unless the surface is wetted by rain. Of the residential sites, Vancouver (Vs92) has the lowest rates. As mentioned, the 1992 observations for Vancouver are atypical, based on com- parisons with previous work (Cleugh and Oke 1986; Grimmond 1992), because of abnormally dry conditions that summer and a very effective ban on garden irri- gation (Smith 1994). Vegetation that normally receives large amounts of external irrigation supplemented by occasional rainfall (Grimmond and Oke 1986) was wa- ter stressed and had little evaporation. The other residential areas have daytime peaks in evapotranspiration that range from 125 to 235 W m22. On average at the residential sites, QE constitutes an energy sink of 22%–37% of daytime and 28%–46% of daily net all-wave radiation. Those areas receiving greater irrigation or precipitation have greater rates of evapotranspiration on average (Grimmond and Oke 1999b). Figure 4b gives a sense of the hour-to-hour and day- to-day variability of QE at two of the sites, Chicago (C95) and Los Angeles (A94), both of which have high- er-than-average evapotranspiration rates. C95, where water is supplied by frequent rain events and irrigation, has greater variability. At A94, the data are more con- sistent from day to day because of automated irrigation systems, which give a fairly constant supply of water, and the relatively constant synoptic conditions. This consistency also is evident at the site between years (see A93, A94). Despite the surface and soil moisture supplied by gar- den irrigation that helps to maintain these evaporation rates, all of the urban evapotranspiration fluxes fall be- low equilibrium rates {QEeq 5 (Q* 2 DQS)[s/(s 1 g)]} during the daytime (Fig. 4c). This fact is presumably due to the presence of dry surfaces, especially built surfaces, within the flux source areas. Variability is ev- ident between sites in the early morning. This is attrib- utable to differences in the occurrence or abundance of dewfall and nocturnal irrigation. By late afternoon, QE is more similar between the sites [for further discussion, see Grimmond and Oke (1999b)]. As may be anticipated, there are overall relations be- tween measures of surface cover, such as the fraction of green space or area irrigated at each site, and the QE fluxes (when normalized by Q*, or represented as a fraction of the total turbulent transport, the Bowen ratio QH/QE; Fig. 5). 3) SENSIBLE HEAT FLUX The average daily maximum sensible heat flux in the MUHD summertime sets (i.e., excluding Me93) varies between 200 and 300 W m22 (Fig. 6a). Unlike the case of QE, there are no cities with extremely small QH, because heat, unlike water, is available everywhere at the surface. At all the residential sites, the sensible heat flux is numerically the most important heat sink in the surface energy balance, ranging from ;40% to 60% of daytime Q*. At the light-industrial site (Vl92), QH rep- resents approximately 40% of Q*, but at this dry (low QE) site, DQS is a greater heat sink than QH by day. The smallest daytime maximum QH occurs in the driest of all the sites, Mexico City. However, this low con- vective flux is partly explained by the fact these are winter data. It is also consistent to note the significance of the large heat storage by the massive old colonial buildings (Oke et al. 1999). Notice that, when normal- ized by Q*, the role of QH in Me93 is the lowest of all cities (Fig. 6b).JULY 2002 799G R I M M O N D A N D O K E FIG. 4. Diurnal patterns of latent heat flux: (a) ensemble mean patterns in MUHD cities, individual daily data for (b) Chicago (C95) and (c) Arcadia, California, (A94) to illustrate variability from day to day, and (d) average measured QE as a fraction of equilibrium QEeq (modified from Grimmond and Oke 1999b). See Table 3 for time period of observations and surface characteristics of sites. All sites shed more energy as sensible heat than as latent heat, that is, Bowen ratios are greater than 1 (Fig. 5c). Daytime Bowen-ratio values for the residential sites range from approximately 1.2 to 2, except for Vs92 ratios, which climb to ;2.8 during the irrigation ban. The average daytime Bowen ratio at the sparsely veg- etated light-industrial site (Vl92) is ;4.4, and in central Mexico City it reaches ;9.8. In an absolute sense there is not much variability in QH at night anywhere, although the sign of the flux does vary between sites (Fig. 6a). When normalized by Q*, the variability appears greater (Fig. 6b), but this is in part due to creating a ratio from small numbers. Of particular interest, however, is the time in the evening when QH turns negative. At rural sites, this regularly happens before sunset as the radiative inversion be-800 VOLUME 41J 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 FIG. 5. Relations between (a) QE/Q* and fraction of plan area that is vegetated (FV), (b) Bowen ratio (QH/QE) and FV, (c) QE/Q* and fraction of plan area that is irrigated (FIr), and (d) QH/QE and FIr for all MUHD cities. Data plotted are for individual 4-h periods between 1000 and 1400 LAT when there was consistent fetch. comes established. On this basis, Holtslag and van Ul- den, and others since (section 2c), propose the use of a constant b parameter (typically set to 20 W m22; Table 2) in (3) and (4). On the other hand, our data, and that of others from fully urbanized sites (Oke 1988), show a different pattern wherein QH tends to remain positive after sunset, sometimes for several hours, even through- out the night. This behavior suggests that b values for cities may be different from those of rural sites. Figure 7 shows the ensemble mean ratio QH/Q* for each site for the period when Q* is negative (starting at 1 on the time axis until the time when it turns positive the next day, 2 on the x axis). The time axis is normalized so that the effect of different night lengths is removed. At all sites, QH turns negative well after Q*, if at all. This result is thought to be due to the large release of heat storage, the radiative screening and shelter effects of canyon geometry, and the release of QF from traffic and buildings. 4. Parameters for LUMPS based on MUHD As noted, the turbulent sensible and latent heat fluxes can be modeled using the simple approach of de Bruin and Holtslag (1982). Here we back-calculate the a and b coefficients for each of our sites using our measured latent heat fluxes and the other measured data necessary to solve (5). Calculations are conducted on an hourly basis and are restricted to any hour during a day during which the fetch direction and therefore the turbulent source area were steady for the complete hour. Surface cover, notably the plan area (fraction) covered by veg- etation FV and the area irrigated FIr in the source area, is calculated following the procedure outlined in Grim-JULY 2002 801G R I M M O N D A N D O K E FIG. 6. Diurnal patterns of (a) ensemble mean turbulent sensible heat flux density (W m22), (b) ensemble mean QH/Q*, and (c) ensemble mean Bowen ratio (QH/QE) for MUHD cities.802 VOLUME 41J 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 FIG. 7. Variation of nocturnal turbulent sensible heat flux normalized by net all-wave radiation (QH/Q*). Time on the horizontal axis is standardized for all sites so that the time when Q* becomes negative is 1 and it becomes 2 when it turns positive again. TABLE 4. Average b (W m22) and a values for each site ordered by decreasing size of b. Site City b (W m22) a T90 C95 C92 S91 Vs89 Mi95 A93 Vs92 A94 Vl92 Sg94 Me93 Tucson Chicago Chicago Sacramento Vancouver Miami Arcadia, Los Angeles Vancouver Arcadia, Los Angeles Vancouver San Gabriel, Los Angeles Mexico City 8.4 6.6 5.6 2.9 2.3 2.3 2.2 1.5 1.2 0.6 0.3 20.3 0.28 0.58 0.71 0.56 0.43 0.51 0.57 0.35 0.51 0.22 0.43 0.19 Mean 2.8 0.45 mond and Souch (1994). These cover fractions are then correlated with the corresponding a and b coefficients to identify any statistically meaningful relations (Holts- lag and van Ulden 1983). The back-calculated a values range from less than 0.2 to greater than 0.7 for the sites considered here (Table 4). One-half of the a values are lower than those previously suggested as appropriate for urban areas (Ta- ble 2). All of the poorly vegetated sites or those ex- periencing some form of drought have particularly low values. This fact becomes clear when the a values are plotted against the average area of vegetated surfaces in the source area (footprint) of the turbulent heat flux measurements (Fig. 8a). The vegetated fraction (FV, the plan area covered by grass, trees, shrubs, and open wa- ter) is used as a descriptor to be consistent with the objective of keeping model inputs as simple as possible (such data can be generated easily from analysis of aerial photographs). Those sites that lie above the general trend line (Chicago and Miami) are locations with above-average surface water availability, because of fre- quent rainfall and/or extensive irrigation (Grimmond and Oke 1999b) or because of canals (Newton 1999). Those sites that plot below the line tend to be areas in which irrigation is restricted, notably the residential area in Vancouver (Vs92), which was under an irrigation ban. When the plan-area fraction of irrigated cover is used, which is a more direct measure of surface moisture sta- tus, the scatter in the relation is reduced (Fig. 8b and Table 5). In this study, values of FIr were assessed from aerial photographs and field surveys. If infrared surveys or other appropriate remotely sensed data were avail- able, they would help to refine such estimates. For pe- riods of rainfall (not considered here) when the surface is wet, FIr should be set to 1.0. The influence of surface cover on the a parameter can be considered in more detail by extending the anal- ysis to incorporate the complete range of surface cover information contained in the measurements for each site. Variations in surface cover around each site and changes in wind direction, wind speed, and atmospheric stability combine to create a spectrum of different turbulent source areas for the same site. Utilizing these multiple samples increases the range of conditions over which relations between a and FV and FIr can be established and thereby allows us to consider how such relations hold up both within, as well as between, urban areas. Data for each hour for each site were stratified into classes based on the land cover of the sampled turbulent flux source area. In the example reported here, land cover classes of 5% (i.e., 0%–5%, 5%–10%, and 10%– 15% of plan area vegetated or irrigated) were used. For those land cover classes with at least 25 observations, the measured latent heat fluxes were used to back-cal- culate a and b coefficients. These values, in turn, were plotted against the average surface cover (Figs. 8c,d).JULY 2002 803G R I M M O N D A N D O K E FIG. 8. Relation between surface characteristics (FIr and FV) and a coefficients (a), (b) determined as averages for each site and (c), (d) for multiple land cover categories for each site. TABLE 5. Relation between a coefficient and land cover (LC) characteristics: n is the number of points available for developing the relation, rmse (W m22), rmsesy (systematic) and rmseusy (unsystematic), r2 is coefficient of determination, Flr is the fraction of the plan area irrigated, and FV is the fraction of the plan area vegetated. See text for further details. n Slope Intercept r2 Rmse Rmsesy Rmseusy Avg for each site FV Flr 12 12 0.686 0.610 0.189 0.222 0.699 0.863 0.123 0.130 0.091 0.118 0.082 0.056 5% LC class FV Flr 37 37 0.596 0.547 0.220 0.239 0.500 0.715 0.143 0.138 0.087 0.112 0.114 0.081 The relations between a and both measures of surface cover (FV and FIr) are good, but again correlations are much stronger with FIr (Table 5). Urban areas with sim- ilar plan-area vegetated cover are not identical, because they encompass a range of surface moisture conditions. It is interesting to note on Figs. 8c,d that, for all cities, as the fraction vegetated or irrigated in the turbulent source area increases, so too does the a parameter. This result suggests that this is an appropriate approach for assigning variations in the a parameter to simulate spa- tial variability in turbulent heat fluxes across a city as well as between cities.804 VOLUME 41J 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 TABLE 6. Conditions used in runs of LUMPS to evaluate effects of changing a, b, and DQs independently. The rmse (W m22) is presented as a summary of the results. Fuller details of model performance by city for select runs are presented in Figs. 9 (run 7), 10 (run 5), and 11 (run 11). Run 13 represents average conditions for site used in calculation for all hours. The n for each site is given in Fig. 9a. Options Runs 1 2 3 4 5 6 7 8 9 10 11 12 13 Model HPDM HPDM LUMPS LUMPS LUMPS Q* Measured DQs Measured← → 0.3Q*← → Eq. (2)← → a b (W m22 0.5 20 1.0 20 f (Fv) 20 f (Flr) 20 f (FV) 3 f (Flr) 3 0.5 20 1.0 20 f (FV) 3 f (Flr) 3 f (FV) 3 f (Flr) 3 f (FV) 3 Summary results (for 12 sites), observed mean (W m22) QH 5 79, QE 5 51, DQs 5 20 Rmse (W m22) QH QE DQs 30 30 — 88 88 — 26 26 — 24 24 — 20 20 — 19 19 — 57 36 68 94 93 68 51 30 68 49 30 68 41 27 53 39 27 53 42 27 53 Rmsesy (W m22) QH QE DQs 23 24 — 88 80 — 18 19 — 17 18 — 12 12 — 9 10 — 37 19 59 92 69 59 25 16 59 23 15 59 23 16 28 21 15 28 22 16 28 Rmseusy (W m22) QH QE DQs 16 18 — 8 36 — 16 16 — 15 15 — 16 15 — 15 15 — 41 29 32 18 58 32 42 25 32 42 25 32 32 21 43 32 20 43 34 20 43 The back-calculated b values from the analysis of all sites are given in Table 4. The values are significantly smaller than the 20 W m22 figure suggested for rural sites. This is as expected given the diurnal course of QH that includes a delay, or complete failure, to turn neg- ative at night (Fig. 7). Unlike the a coefficients, how- ever, there is no obvious relation between b and mea- sures of surface cover. Tucson and Chicago have the largest b values, but there is little to suggest why they should be similar, nor why downtown Mexico City and residential San Gabriel, California, should share some different ability with respect to the nocturnal transition period. However, it is important to stress that the overall range is small (0–9 W m22). At this stage, in the absence of an objective method to assign b values to different sites, we recommend a constant value of ;3 W m22 be used for urban areas. 5. Evaluation of the model The performance of LUMPS is evaluated using MUHD. Before doing so, we note that this approach contains both strengths and weaknesses. The merits are that the scheme is being tested against a comprehensive, high-quality dataset. Careful attention has been directed to the instrumentation, field methods, and quality con- trol exercised in processing and analyzing the data. The dataset contains many of the essential surface and at- mospheric characteristics of cities. The main weakness is that the same set used to develop some of the param- eterizations (notably the relations for the a and b pa- rameters—although model evaluation is conducted us- ing hourly data while the parameter functions were de- rived using one average value for each site; Fig. 8a) is being used to test the overall operation of the combined scheme. The development of the dataset has been evo- lutionary, over a period of more than a decade; it is not now possible to extricate the data used to develop re- lations from those that were not. In the future, we aim to gather new sets, to use them to test LUMPS more independently, and to refine and extend parameteriza- tions as the range of observational conditions (meteo- rological and surface cover) expands. The evaluation is performed in a stepwise fashion to allow the impact of each modification on the perfor- mance of LUMPS to be considered independently. First, the original HPDM scheme is evaluated using MUHD (with two sets of parameters selected for a and b, re- spectively). Second, DQS is changed from the constant fraction 0.3Q* (as used in HPDM) to the OHM scheme (see Table 1 for the values of coefficients used). Third, the new a relations (based on FV and FIr; see Table 5) are added, and the smaller value of b 5 3 W m22 is assigned. A summary of model runs, the combinations of schemes used, and a summary of the overall perfor- mance of the scheme (measured in terms of average root-mean-square error across all sites) are givenrmse in Table 6. In all cases, the schemes are initialized with measured Q*, and the fluxes are calculated on an hourly basis. In this evaluation (except for run 13), each coefficient in LUMPS that is based on surface characteristics (i.e., a1–a3, a) is calculated for each hour of observation, based on the source area (footprint) of the measured turbulent flux [using the Schmid (1994) source area model]. Note that this is not a requirement of LUMPS;JULY 2002 805G R I M M O N D A N D O K E here it simply ensures the greatest spatial consistency between the measured and modeled domains. The HPDM model is run with fixed values for all sites (Table 6). Run 13 evaluates LUMPS with fixed parameters for each site. To evaluate the HPDM, and to consider the role of the a and b parameters, first the a parameter was changed from 0.5 to 1.0 (runs 1 and 2 in Table 6); these are the lower and higher default limits suggested for urban environments by the originators (Table 2). Mea- sured DQS was used so the effect of the a and b pa- rameters could be assessed independently. When a is increased, the results show a large increase in rmse when applied across all sites (from 30 to 88 W m22 for both QH and QE). The lower value, used by Hanna and Chang (1992) in their analyses of sites in St. Louis, Missouri, and Indianapolis, Indiana, therefore gives much better performance. Using a constant fraction (0.3) of Q* to calculate DQS reduces the performance of the HPDM: when a 5 0.5 (run 7) reductions are ;27 W m22 for QH and ;6 W m22 for QE. When a 5 1.0 (run 8), the model performance already is very poor, and it is de- graded by 5–6 W m22 for QE and QH. Figures 9a (QH) and 9b (QE) are scatterplots showing the performance of HPDM (a 5 0.5, b 5 20 W m22, DQS 5 0.3Q*) for each of the individual cities in MUHD. At all sites, there is considerable scatter in the relation between measured and modeled values. HPDM underestimates the turbulent fluxes. In particular it miss- es QH at night and caps its maximum predicted values, resulting in underestimates during the middle of the day (Fig. 9a). There is a hysteresis pattern in the model discrepancies (most obvious in predictions of QH for Sg94). This is not directly evident to the reader from Fig. 9, but when the time of the points was added during analysis, hysteresis was distinct. The temporal nature of this error is due to the linear nature of the storage heat flux model used in HPDM (see discussion below). Allowing the a parameter to vary dynamically as a function of FV, rather than remaining constant at 0.5 (but with b 5 20 W m22 and measured DQS), results in a reduction of the rmse of 4 W m22 (;7.5%; cf. runs 3 and 1 in Table 6). Modeling a as a function of FIr reduces the rmse by a further 2 W m22 (cf. runs 4 and 3). Greater improvement in the performance of the mod- el is derived by assigning a lower value to b (3 rather than 20 W m22); in response, the rmse drops by ;6 W m22 (cf. runs 5 and 3, 6 and 4). Lowering b has a significant effect at night (contrast Figs. 10 and 11 with Fig. 9). Thus we conclude that the revised methods for assigning a and b parameters presented here represent significant improvements over the use of fixed values for urban environments. The selection of FV or FIr has a marginal effect. As indicated in section 4, the choice of this variable usually depends on data availability for a given site. The approach taken to model DQS has a significant effect on overall model performance. When QH and QE are modeled with a as a function of area vegetated and b 5 3 W m22, significant improvements are apparent with OHM as compared with the model with a constant fraction (DQS 5 0.3Q*; cf. runs 11 and 9); across all cities the rmse drops by 10 W m22 for QH and 3 W m22 for QE. The city for which LUMPS performs least well is Tucson (Fig. 11). We believe this result is related to the fact that the Tucson site is exposed to the highest wind speeds of the cities in the database. Previous work concluded that OHM does least well in simulating DQS at this site (Grimmond and Oke 1999c). To illustrate the effects of OHM errors on QH and QE predictions, the model was rerun with measured DQS (cf. runs 11 and 5, and Figs. 10 and 11). When measured DQS is used, the rmse drops by 21 W m22 for QH and by 7 W m22 for QE, and the scatter for each of the cities (Fig. 11) is much reduced (Fig. 10). This result stresses the need for improvements in heat storage modeling in order to be able to parameterize accurately the turbulent fluxes, particularly in windy environments. LUMPS is also run using fixed surface characteristics for each site (run 13; Table 7). These properties are calculated for circles around the respective sites. The radii of the circles are defined by generalized footprint analysis for the neutral case. The performance of LUMPS changes very little from the runs in which pa- rameters are individually defined by complete flux source area analysis (see the results compared across the mean of the 12 sites in Table 6). The datasets that have the largest changes are the two Chicago sites and Sacramento (cf. Table 7 and Fig. 11). Even with fixed properties, LUMPS continues to show improvement over HPDM (contrast results in Table 7 and Fig. 9). Overall, the results for LUMPS as presented here [a 5 f (FV), b 5 3 W m22, DQS from OHM] show the model performs well at many of the sites and is a sig- nificant improvement over former versions of HPDM. 6. Conclusions Results of our local-scale surface energy balance ob- servations reveal that turbulent sensible, latent, and stor- age heat fluxes all represent important terms in the sur- face energy balance of most cities. Each of the heat fluxes varies both spatially and temporally. Under the low-wind conditions so far studied, storage heat flux is most important at the downtown and light-industrial sites (at least 50% of daytime Q*), and the sensible heat flux is most important at the residential sites (40%–60% of daytime Q*). At the residential sites, latent heat flux, if sustained by garden irrigation and/or frequent rainfall, is also significant (20%–40% of daytime Q*). Surface cover, notably the fraction of the surface vegetated and irrigated, exerts an important control on QE. At all sites, there is distinct hysteresis in the diurnal course of the storage heat flux; much more of the net radiation is used to heat the urban fabric in the morning. In addition, the806 VOLUME 41J 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 FIG. 9. Measured vs modeled (a) QH and (b) QE using HPDM with measured Q*, DQS 5 0.3Q*, a 5 0.5, and b 5 20 W m22 (run 7, Table 6).JULY 2002 807G R I M M O N D A N D O K E FIG. 10. Measured vs modeled (a) QH and (b) QE using measured Q* and DQS with b 5 3 W m 22 and a a function of FV (run 5, Table 6).808 VOLUME 41J 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 FIG. 11. Measured vs modeled (a) QH and (b) QE using LUMPS with measured Q*, DQS from OHM, b 5 3 W m22, and a a function of FV (run 11, Table 6).JULY 2002 809G R I M M O N D A N D O K E TABLE 7. Statistical results for measured vs modeled QH and QE using LUMPS with measured Q*, DQs from OHM, b 5 3 W m22, and a a function of FV (run 13, Table 6). The surface characteristics are assigned fixed values for all time periods for each site. Compare with Fig. 9 (constant conditions for HPDM) and Fig. 11 (LUMPS but surface characteristics vary with source area characteristics for each hour). A93 A94 C95 C92 Me93 Mi95 S91 Sg94 T90 Vl92 Vs89 Vs92 QH Rmse RmseSY RmseUSY r2 21 10 18 0.95 27 14 23 0.94 47 23 41 0.81 38 24 30 0.87 47 28 38 0.79 50 13 48 0.76 36 9 34 0.83 33 17 28 0.90 48 32 37 0.87 49 17 46 0.79 54 42 34 0.86 49 41 26 0.90 QE Rmse RmseSY RmseUSY r2 19 5 18 0.93 20 7 19 0.93 42 35 23 0.87 58 51 26 0.69 14 6 12 0.20 30 17 25 0.77 24 8 23 0.85 16 3 15 0.90 38 33 17 0.77 20 13 15 0.38 21 12 17 0.85 25 5 24 0.67 sensible heat flux remains positive after the net all-wave radiation turns negative at night. LUMPS, a simple local-scale urban meteorological parameterization scheme, is shown to be capable of pre- dicting the 1D spatial and temporal variability in heat fluxes in urban areas. The data requirements for LUMPS are minimal: net radiation (which can be parameterized well from more routinely collected solar radiation), air temperature and humidity, atmospheric pressure, and surface descriptors (notably the plan-area fractions of vegetation, impervious surface, and roofs). The scheme represents an improvement over earlier models, such as HPDM. This improvement results largely from the OHM parameterization of storage heat flux, which takes into account both the magnitude of this flux and its hysteresis pattern, and new coefficients for the de Bruin and Holtslag (1982)/Holtslag and van Ulden (1983) equations, used to partition QH and QE, which now re- flect urban green space and/or surface moisture avail- ability and the positive QH fluxes observed in urban environments after sunset. We readily acknowledge that there is plenty of scope for improvements in LUMPS; however, these likely will come at the expense of additional input requirements. We know that the effects of wind and large sources of anthropogenic heat are inadequately incorporated in the scheme. In situations in which these variables are im- portant, LUMPS in its present form should not be used. In addition, because the observations in MUHD are col- lected by assuming a 1D energy balance, LUMPS is unlikely to perform well in areas of significant spatial variability of land cover and/or morphometry (for ex- ample, at the urban–rural edge, near coasts, or in com- plex terrain). MUHD also needs to incorporate vege- tation phenology and winter conditions, including the effects of snow cover, melting, and freezing. Acknowledgments. This research has been funded by the National Science Foundation, USDA Forest Service, Southern California Edison, Indiana University, the Nat- ural Sciences and Engineering Research Council of Can- ada, and the Canadian Foundation for Climate and At- mospheric Science. 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