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Parameterization of net all-wave radiation for urban areas. Offerle, B.; Grimmond, C. S. B.; Oke, Timothy R. 2003

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AUGUST 2003 1157O F F E R L E E T A L . q 2003 American Meteorological Society Parameterization of Net All-Wave Radiation for Urban Areas B. OFFERLE AND C. S. B. GRIMMOND Indiana University, Bloomington, Indiana T. R. OKE University of British Columbia, Vancouver, British Columbia, Canada (Manuscript received 26 September 2002, in final form 24 January 2003) ABSTRACT A simple scheme to estimate net all-wave radiation (Q*) is evaluated using annual datasets in three urban settings (Chicago, Illinois; Los Angeles, California; and Łódź, Poland). Results are compared with a regression model based on incoming solar radiation and with an urban canopy-layer model incorporating a canyon geometry radiation scheme that requires a larger set of meteorological and surface property inputs. This net all-wave radiation parameterization (NARP) is most sensitive to albedo and the effects of clouds on incoming longwave radiation. Although omitting the diurnal variation of albedo has little impact on overall model fit, its seasonal variability needs to be considered in some cases. For incoming longwave radiation, even clear-sky estimates show a large degree of scatter, and results degrade substantially if cloudy periods are included. NARP shows improvement over the regression approach. If observations of downwelling longwave radiation are included, NARP and the more complex canopy scheme show similar results, near or within the range of instrument error, depending of time of year. 1. Introduction Net all-wave radiation (Q*) is a fundamental com- ponent of surface–atmosphere energy exchange; indeed, it almost always provides most of the energy that drives evaporation and sensible heat fluxes. Despite its impor- tance to these processes, it is rarely observed. Although ostensibly an input to parameterizations of surface layer fluxes, it is more commonly computed from other mea- sured and modeled components of the radiation balance. At the surface Q* can be calculated from incoming short- wave and longwave components provided by an atmo- spheric radiative transfer scheme as part of a large-scale atmospheric model (Niemelä et al. 2001a,b). Alterna- tively, without resorting to such numerically intensive methods or requiring vertical profiles of atmospheric properties (for the radiative transfer scheme), Q* may be modeled simply based on near-surface observations of these fields. Representing the radiation exchange within the urban canopy volume of the surface layer presents a greater challenge because of the vertical structure and the range of materials present. Cities have complex surfaces with a wide variety of Corresponding author address: Brian Offerle, Atmospheric Sci- ence Program, Department of Geography, Indiana University, 120 Student Building, 701 E. Kirkwood Ave., Bloomington, IN 47405- 7100. E-mail: bofferle@indiana.edu materials covering a range of albedo, emissivity, and thermal inertia values. The convoluted nature of the urban surface affects radiation exchange by causing multiple reflections of shortwave radiation and intere- lement emissions and reflection of longwave radiation, and the increased surface area in comparison with a horizontal plane aids storage of sensible and latent heat. Urban canyons are, therefore, more effective in captur- ing energy than horizontal surfaces made of the same materials. Modeling these effects has been accom- plished by employing a generalized canyon to represent the whole city (averaged characteristics over the urban domain, e.g., urban tile of a grid cell in a mesoscale model) or a distinct urban surface area (at the local or neighborhood scale) (Arnfield 1982; Masson 2000). One difficulty in objectively evaluating such models is how to determine the appropriate surface characteristics of such an inherently inhomogeneous environment. De- pending on the model requirements, extensive data col- lection and/or some adjustment of surface characteris- tics may be needed to ensure that the model yields re- sults that converge with reality. Though representation of this vertical structure is necessary if the target of interest lies within the urban canyon, above a certain height we may assume that bulk surface characteristics can be applied with nearly the same accuracy. These bulk or effective values define the aggregate response of the conglomeration of materials and geometry over 1158 VOLUME 42J 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. 1. (a) Single building–space unit. (b) Source area fraction (P) for upwelling radiation at height H originating from an area of two building units over urban arrays with various aspect ratios (H/W). (c) Same as (b), but for various numbers of building units with fixed H/W 5 1. See text for definitions. the scale, grid, or tile in question. This approach as- sumes that the response of individual materials or sur- faces (e.g., walls) is not of interest. It also defines the ‘‘surface’’ as the top of a hypothetical volume at a level usually less than 4 times the mean element height or interelement spacing (see Grimmond and Oke 2002). This definition is consistent with surface layer fluxes at this reference height, which should be distinguished from the true surface flux, although in practice the area- averaged fluxes may not be significantly different. In the present application, we define the scale of anal- ysis to be the local scale (102–104 m), such that effective characteristics of the type discussed above are applicable. To ensure that observations are consistent with the model scale, we need to consider the field of view of the mea- suring instrument for the effective surface of interest. Schmid et al. (1991) give the source-area fraction (view factor) P of an inverted flat-plate radiometer as 2 2P 5 1/(1 1 z /r ),m (1) where r is the radius defining the source-area fraction and zm is the measurement height. We can specify (1) in terms of identifiable units, for example, buildings or urban canyons with mean height (H) and spacing or width (W) (Fig. 1a) in order to determine whether the view factor of the instrument adequately captures the effects of multiple buildings. The fraction of net radi- ation received from an area of Nb building units, P(Nb), assuming they are square with their width equal to the spacing (i.e., assuming in Fig. 1a, Wx 5 Wy 5 Lx 5 Ly), is given by replacing r2 in (1) by Nb 4W 2/p, and substituting zm/H 3 H for zm: 2P(N ) 5 1/[1 1 p(z /H 3 H/W ) /(4N )]. (2)b m b This is only an approximation because it does not in- corporate radiation from within the canopy or the effects of variation in building heights or arrangement. Figure 1b shows the relation (2) for a range of aspect ratios in terms of nondimensional height (zm/H) at level H with Nb 5 2. With low aspect ratios (e.g., single- family residential areas), a higher measurement height is required relative to H to incorporate the effects of the same number of building units. However, in these cases building heights are typically lower, and so the absolute height required may not be great. For more closely spaced buildings, the height requirement is relaxed; however, the absolute height could be greater relative to ground level. The height requirement for 50% rep- resentation from two building units given H/W 5 1 is zm 5 2.75H. This is greater than the minimum height requirement (2H) for eddy covariance (EC) flux mea- surements to be representative at the local scale in urban areas (Grimmond and Oke 1999; Roth 2000). Figure 1c shows the radiative contribution made by a specific number of buildings for an aspect ratio of 1. For ex- ample, to achieve 50% representation from five building units requires zm 5 3.5H. Thus, Q* measurements may have more stringent siting requirements than EC. A mit- igating factor, however, may be that within the same urban land-cover type, Q* has been shown to be spa- tially conservative (Oke 1988; Schmid et al. 1991). Direct measurements of Q* are even more uncommon over urban areas than other surfaces. For example, the Atmospheric Radiation Measurement Program (ARM) intentionally excludes urban sites as being ‘‘outside of primary interest’’ (Barr and Sisterson 2000). Conse- quently, there have been few evaluations of parameter- izations over a range of seasonal, climatological, and surface conditions in cities. Interest here is in the evaluation of a parameterization scheme for Q* that requires only a minimal set of easily AUGUST 2003 1159O F F E R L E E T A L . available measured inputs (meteorological and surface characteristics). This offers the advantage of ease of integration into models that do not include radiative transfer schemes and application to different urban sites, without requiring additional measurements or substan- tial increases in computation time. Such models have application in predicting surface layer fluxes (Grim- mond and Oke 2002) or a meteorological preprocessor for use in the urban boundary layer. The objectives of this paper are to present the net all- wave radiation parameterization (NARP), which is a modification of earlier work over nonurban surfaces (Holtslag and van Ulden 1983; Crawford and Duchon 1999), and to evaluate NARP using observations from cities with contrasting surface characteristics and cli- mates over the full annual period. The results of NARP are compared with those from a regression model based solely on the availability of incoming solar radiation observations, and from an urban canyon mesoscale sur- face scheme/tile representation [Town Energy Balance (TEB) Interactions between Soil, Biosphere, and At- mosphere (ISBA)] that uses a more extensive set of inputs. The observations used in the evaluation are from three very different urban sites in Chicago, Illinois; Los Angeles, California; and Łódź, Poland. 2. Parameterization and modeling a. Regression approach The radiation budget for a horizontal surface is Q* 5 K* 1 L* 5 K 2 K 1 L 2 L ,↓ ↑ ↓ ↑ (3) where K and L represent the short- and longwave com- ponents, respectively, the arrows give the direction of the flux, and * is a net flux. Although the preference in developing a simple parameterization scheme of Q* is to minimize data requirements to only the most com- monly available meteorological fields, we find that ob- servations of incoming solar radiation are almost man- datory. While there are many simple relations for K↓, based on latitude and average atmospheric conditions (e.g. Sozzi et al. 1999; Niemelä et al. 2001b), error estimates for hourly intervals or shorter can be large. Niemelä et al. (2001b) used hourly data over 1997 from two sites in Finland. They found root-mean-square er- rors (rmse) ranging from 12 to 49 W m22 (3.2%–13.7%) for simple models and 11 to 19 W m22 (3.2%–6.0%) for more sophisticated radiation transfer schemes under clear-sky conditions (N 5 26 and 27 for the two sites). Badescu (1997) examined actinographic data from two sites in Romania during January and July over 10-yr periods. The rmse ranged from 11% to 17% in July (N 5 258 and 175) and from 15% to 24% in January (N 5 147 and 94). For all-sky conditions, using total cloud- cover estimates, performance is much poorer with rmse ranging from 30% to 45% (Badescu 1997; Niemelä et al. 2001b). The availability of measured K↓ has the ad- ditional advantage of allowing estimation of cloud cover and its effects on L↓. Simple linear regression models of Q*, based on mea- sured K↓, can generate impressive results, with rmse , 30 W m22 (relative values not reported) (Kaminsky and Dubayah 1997). The general form of such models is Q* 5 b 1 b K ,0 1 ↓ (4) with the b coefficients estimated using ordinary least squares (OLS) regression. Where there is large seasonal variability in terms of external forcing (higher latitudes) and atmospheric effects (transmissivity and emissivity), or surface changes (snow cover, leaf cover, surface moisture), seasonally determined coefficients may im- prove results (Kaminsky and Dubayah 1997; Iziomon et al. 2000). Implicit inclusion of albedo in (4), by re- placing K↓ with K*, produces mixed results (Kaminsky and Dubayah 1997). Iziomon et al. (2000) found that the inclusion of additional parameters in the regression model had significant effects on model performance only in the case of a mountainous site. Here, the OLS model (4) is compared with NARP. b. NARP The model forwarded here is applicable in urban areas where access to other than standard weather observa- tions is limited or zero. To estimate Q*, the scheme requires air temperature (Ta), relative humidity (RH), and K↓ to estimate Q*. It is assumed that the measure- ment height of the instruments corresponds to the ref- erence height for the modeled Q*. The implication of input bias, due to different instrument placements or larger than normal measurement errors, is addressed with a sensitivity analysis. 1) NET SHORTWAVE RADIATION The net shortwave term is a function of incoming solar radiation and the bulk surface albedo a0, K* 5 K (1 2 a ),↓ 0 (5) with no distinction made between direct and diffuse radiation. Measured values of a0 for urban areas typi- cally range from 0.10 to 0.27, with a mean near 0.15 (Oke 1987); K↓ is likely to dominate the daytime ra- diation budget (Q*) during summertime, at low lati- tudes, and if there is no significant cloud cover. The albedo of a surface varies in response to solar angle and changes in surface characteristics; a0 gen- erally increases with increasing zenith angle over hor- izontally homogeneous surfaces (Paltridge and Platt 1976). While other empirical relations have been used (De Rooy and Holtslag 1999; Iziomon et al. 2000), the form a (c) 5 a 1 (1 2 a) exp[20.1c 2 (1 2 a)/2],0 (6) where a is the albedo at maximum solar elevation and 1160 VOLUME 42J 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 c is elevation angle in degrees (USEPA 1999), is ex- plored in section 4b. In cities, because of the vertical structure and spatial differences in material properties within the source area of the model or measurement domain, this diurnal effect is not just a simple function of solar angle. Sailor and Fan (2002), using a numerical simulation, found that using typical albedo values es- timated at nadir, rather than a diurnally varying effective albedo, caused an underestimate of the daily absorbed energy. The decrease was as large as 19% averaged over residential areas, although this value depends on as- sumptions about the albedos of the roof, wall, and road surfaces. When observing urban albedo, the radiation received by the sensor from the surface may emanate from a different mix of materials, each with different shading by buildings and trees, through the course of a day. Thus, the albedo may exhibit anisotropy with re- spect to solar angle. In addition to solar angles and localized changes in shading, albedo can be affected by seasonal changes in surface cover, such as with extensive deciduous vege- tation, or due to the effects of snow cover or rain wet- ting. Brest (1987) found the magnitude of seasonal changes in urban albedo to be inversely correlated with the density of buildings. Although vegetation amounts were not given, presumably the correlation is positive. The impact of snow cover and rain is limited in cities by the vertical surfaces, the albedos of which do not change substantially (Arnfield 1982; Brest 1987). The implications of time-varying albedos can be evaluated by comparing the response using constant albedo with that using a more correctly specified daily albedo (a0,d), computed from the direct measurements (a0,d 5 K↑/K↓), or that obtained as the residual of the radiation balance (3) (Sozzi et al. 1999), a 5 (K 1 L 2 L 2 Q*)/K ,0,d ↓ ↓ ↑ ↓ (7) where Q* and K↓ are observed quantities and the long- wave components are estimated. 2) INCOMING LONGWAVE One could make an argument similar to that presented for K↓ to include measurements of L↓ in a parameteri- zation for Q*, because the variability of cloud cover makes estimation of L↓ difficult. Even under clear-sky conditions, estimates of L↓ for cities may be different from measurements because of variability in atmospher- ic aerosols. When comparing six emissivity formula- tions for all-sky conditions, Crawford and Duchon (1999, hereinafter CD99) found unsystematic rmse ranging from 10 to 22 W m22 over 4-month periods at nonurban sites. For clear-sky conditions over a wider range of sites, Prata (1996) also compared six formu- lations (four the same as in CD99) and found rmse of 10–20 W m22. Because L↓ is less commonly observed than K↓, in the absence of output from a radiative trans- fer scheme, surface estimation is needed. To keep the parameterization simple, a single-layer atmosphere model can be used, such that 4L 5 « sT ,↓ sky sky (8) where Tsky is the bulk atmospheric temperature (K) ap- proximated by Ta near the surface, s is Stefan’s constant, and «sky is an estimated broadband atmospheric emis- sivity. Surface-level schemes for clear-sky emissivity («clear) have been reviewed in detail elsewhere (Sugita and Brutsaert 1993; Prata 1996; CD99; Niemelä et al. 2001a). The Prata (1996) formulation, 0.5« 5 1 2 (1 1 w) exp[2(1.2 1 3.0w) ],clear (9) has been found to perform best (Prata 1996; Niemelä et al. 2001a), including tests at an urban site (Newton 1999). In (9), w is the precipitable water content (g cm22) approximated by mean atmospheric values of va- por pressure (ea) and Ta at the reference height in the surface layer: w 5 46.5 e /T .a a Cloud effects on L↓ are harder to generalize because rather than just cloud fraction, both cloud height (es- pecially cloud-base temperature) and type have radiative impacts. In general, «sky should increase toward unity as total cloud cover, depth, and cloud-base temperatures increase. The ratio of measured K↓ to that predicted under clear-sky conditions (K↓,clear) can give an objective estimate of daytime cloud effects related to cover amount and depth; K↓,clear is estimated by (CD99) K 5 I cos(Z)t t t t ,↓,clear Ex R pg w aer (10) where IEx is extraterrestrial solar insolation, Z is the solar zenith angle, and tRtpgtwtaer is the product of transmis- sivities for Rayleigh scattering (R), absorption by per- manent gases (pg) and water vapor (w), and absorption and scattering by aerosols (aer). The transmissivities are a function of time of year, zenith angle, latitude, surface dewpoint (computed from Ta and RH), and surface pres- sure. Although incorporating an observation of local pressure adds an additional input requirement, this mea- surement is routinely available and varies gradually spa- tially, such that values from the nearest station after correction for elevation can be used. The Smith (1966) data used in the formulation of CD99 were interpolated to an array of 18 latitude for each day of the year to facilitate application to the model developed here. The daytime cloud fraction (FCLD) is then given by (CD99) F 5 1 2 K /K .CLD ↓ ↓,clear (11) This method of determining FCLD becomes unreliable at large zenith angles because of the cosine response of pyranometers, and especially to the small magnitude of K↓. A similar situation is encountered using the clearness index (CI 5 K↓/Iex); hence, Sugita and Brutsaert (1993) limited their analysis to observations where K↓ . 30 W m22. Battles et al. (2000) also found that clear-sky solar AUGUST 2003 1161O F F E R L E E T A L . irradiance parameterizations performed less well at high zenith angles. Here, we take note of these errors by lim- iting transmissivity computations to zenith angles ,808. This results in an overestimate of cloud cover at higher zenith angles, which, in turn, biases estimates of L↓ at these times. This is an issue at night when no cloud estimate with (11) is possible and the choice is either no adjustment or basing the cloud estimate on the sunset value, which may well be biased. Here, the latter is pre- ferred as long as the error remains small. Clear-sky emissivity is then adjusted for the effects of cloud cover: 2« 5 « 1 (1 2 « )F .sky clear clear CLD (12) The squared term is intended to minimize the effect of the biased cloud cover while still allowing for «sky 5 1. The performance of this, or other parameterizations of longwave cloud effects, depends on site cloud clima- tology. The above approach does not account for the effects of cloud type (height of cloud base) on emission. Sugita and Brutsaert (1993) find that including cloud type improves the emissivity estimation, because lower clouds have a much greater impact. It may be useful to incorporate this, but for the purposes of the present study the additional input requirement was deemed undesir- able. 3) OUTGOING LONGWAVE Outgoing longwave radiation from the surface, 4L 5 « sT 1 (1 2 « )L ,↑ 0 0 0 ↓ (13) is primarily driven by the effective radiative surface temperature T0; only a small fraction is due to the re- flection of L↓ from the surface (the second term). For a large area, T0 is difficult to determine directly, and it is almost never available from routine observations. This makes it necessary to substitute an approximation of T0 by near-surface Ta in (13). However, this tends to introduce a systematic diurnal bias because surface tem- peratures are greater (less) than near-surface air tem- peratures by day (night). The estimate is particularly biased during the daytime. Traditionally (Sellers 1965; Holtslag and van Ulden 1983), this bias is corrected by using 4 4 3« sT ø « sT 1 4« sT (T 2 T ).0 0 0 a 0 a 0 a (14) For the daytime case, the last term can be based on either Q* or K↓. Here, we use K↓ to develop a correction, because K↓ is an observed quantity in the parameteri- zation. The magnitude of this correction is estimated by 34« sT (T 2 T ) 5 cK (1 2 a ),0 a 0 a ↓ 0 (15) which is a modification of the form given by Holtslag and van Ulden (1983) that did not incorporate a0. Note that van Ulden and Holtslag (1985) revised their original formulation to incorporate a0 and the slope of the sat- uration enthalpy curve but used Q*. As formulated here, with a0 5 0.15, K↓ 5 1000 W m22, Ta 5 300 K, and using c 5 0.08 [approximated from Holtslag and van Ulden (1983)], the correction is equivalent to T0 2 Ta 5 11 K. This seems appropriate for a dry surface. How- ever, this approach does not account for any hysteresis in T0 2 Ta, and at night it results in no correction at all. In practice, T0 should peak after K↓, approach Ta near sunset, and may become cooler than Ta at night under stable conditions. However, these differences are likely to be small relative to the overall correction. Fur- ther, the lack of a nocturnal correction may be more acceptable in urban areas, especially city centers. This is because the nocturnal release of stored heat from the urban fabric is substantial, sufficient enough to produce upward-directed convective sensible heat fluxes (Grim- mond and Oke 2002) and temperature profiles that tend toward neutral (Oke 1995). The lack of a nighttime T0 2 Ta correction is likely to have little impact relative to the errors associated with cloud cover and «sky de- terminations. However, by integrating this parameteri- zation with a surface heat-flux model, stability could be calculated and a better estimate of T0 might be made (van Ulden and Holtslag 1985; De Rooy and Holtslag 1999). Also in question is the time constant of the ef- fective surface temperature, which determines the most appropriate averaging interval over which to implement this correction. To minimize the impact of short-term variations in K↓ due to clouds, the correction is imple- mented using values from the previous hourly average. The complete L↑ specification can be written: 4L 5 « sT 1 0.08K (1 2 a ) 1 (1 2 « )L . (16)↑ 0 a ↓ 0 0 ↓ The complete parameterization scheme is specified by Eq. (5) for the shortwave balances, Eqs. (8)–(12) for incoming longwave, and Eq. (16) for outgoing longwave. 4) RADIATION SCHEME OF THE TEB ISBA MODEL The radiation scheme from the TEB urban canopy- layer parameterization of Masson (2000), coupled with the ISBA model (Noilhan and Planton 1989) is also used to evaluate the effectiveness of NARP. Since the original publication of TEB there have been several modifica- tions to the code and the latest version was used for this evaluation (V. Masson 2003, personal communication). TEB divides the urban canopy into three distinct sur- faces: roofs, walls, and roads. Radiative characteristics (a, «) must be specified for all surfaces, as well as the thermal characteristics of multiple layers within the roofs, walls, and roads to allow for heat diffusion and computation of the surface temperature. Within the ur- ban canyon, constant view factor geometry and no pre- ferred orientation of the streets are used to determine the radiation balance for the walls and roads. Surface temperatures are calculated from thermal characteristics and the energy balance at each time step. Given the input demands of TEB ISBA in terms of surface char- 1162 VOLUME 42J 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 1. Si te in fo rm at io n, m o de lp ar am et er s, an d da ta se tc ha ra ct er is tic s. M ea n Q* v al ue s ar e fo r al l-s ky co n di tio ns re st ric te d to tim e pe rio ds av ai la bl e at al ls ite s; N b w as id en tifi ed u si ng ae ria lp ho to gr ap hs . Si te La tit ud e, lo ng itu de O bs er v at io n pe rio d (y ea r/d ay o f ye ar ) In st ru m en t z m (m ) z m /H N b (9 0% ) a 0 « 0 Cl ea r-s ky da ys M ea n Q* (W m 2 2 ) D ay N ig ht Ch ic ag o Lo s A ng el es (A 94 ) Łó dź 41 85 79 N ;8 78 48 9W 34 80 89 N ;1 18 80 39 W 51 84 69 N ;1 98 27 9E 19 92 /1 98 –1 99 3/ 15 8 19 93 /2 25 –1 99 4/ 20 6 20 01 /0 01 –3 65 Q* 6 Q* 6 CN R1 25 30 37 3. 0 2. 8 2. 2 3 14 14 0. 18 0. 21 0. 08 0. 93 0. 94 0. 92 25 79 20 15 8 25 5 13 7 2 31 2 48 2 38 acteristics, and because it requires L↓ observations as input, this model was only run for one site (Łódź). 3. Site and measurement characteristics a. Instrumentation NARP is evaluated using observations from three sites: Chicago (1992–93), Los Angeles (LA) (1993–94), and Łódź (2001) (Table 1). These research sites were established to make energy balance flux observations and were situated in areas suitable for eddy covariance flux measurements (Grimmond and Oke 1999; Roth 2000). While these observations were not designed pri- marily as radiation studies, they happen to represent three very different urban surface systems. Hence, if a scheme performs well using these datasets, it is likely to indicate more general applicability. In Chicago and Los Angeles, Radiation and Energy Balance Systems (REBS) Q*6 net radiometers measured Q*, and LI-COR pyranometers (LI-200) monitored K↓. In Łódź, a Kipp and Zonen CNR1 measured the four component fluxes of the radiation budget. No snow-cover observations were made at either the Chicago or Łódź sites. In Chi- cago and Los Angeles, the Ta and RH sensors were housed in aspirated shields, whereas in Łódź an unas- pirated Gill shield was used. In all cases the Ta and RH sensors were located close to the net radiometers. The measurement height was at least 2 times the mean can- opy height for all sites (Table 1). All data were recorded as 15-min averages. Greater details about site charac- teristics and operational information may be found in Grimmond et al. (1994, 1996) and Offerle et al. (2002). The accuracy of the Q*6 sensor is subject to some debate. Hodges and Smith (1997) report that the Q*6 underestimates nighttime flux densities by approxi- mately 45% (when compared with individually cali- brated Eppley pyrgeometers). They also reported day- time underestimation of 5%. Duchon and Wilk (1994) also note similar nighttime discrepancies. The manu- facturer examined this issue in controlled field and chamber tests and reached a different conclusion (C. Fritschen 2002, personal communication). Because of the lack of agreement between published results and the manufacturer’s recommendation, we applied no correc- tion. Assuming this results in a systematic bias, the ef- fect should be similar in both Chicago and Los Angeles. The results of Hodges and Smith (1997) suggest that this bias will be negative when compared with the CNR1. The LI-200 sensor used for K↓ has an absolute error of 5% (LI-COR 1991). The expected CNR1 accuracy for daily totals of Q* is 610% (Kipp and Zonen 2001). Oncley et al. (2002) found that the CNR1 performed well for Q*, although individual component fluxes were more in error. Long- wave measurements are known to be affected by dome or window heating, particularly at times of low wind speed. In the CNR1, the body temperature of the in- AUGUST 2003 1163O F F E R L E E T A L . FIG. 2. Daily average Q* (W m22) measured at (top) Łódź, (middle) Los Angeles, and (bottom) Chicago, in the daytime (Q* . 0) and at night (Q* , 0). Thicker lines are 15-day block averages. Note periods of missing data for Los Angeles and Chicago. strument is used to correct for this effect. To avoid con- densation on the domes and windows (receiving plates) of the CNR1, the instrument was heated, but only at night. Heating typically affects shortwave more strongly than longwave readings; hence, restricting it to the night should reduce the potential for errors (Kipp and Zonen 2001). The radiometer domes of the sensors in Chicago and Los Angeles were not heated and, thus, may have been affected by condensation. The radiation instru- ments were calibrated by the manufacturers prior to use in these measurement campaigns. Although all data were subjected to strict data limits to prevent unrea- sonable values, these errors would be biased toward zero and, as such, were probably not detected. With the ex- ception of known periods of instrument malfunction, no other data were rejected. Clear-sky days were identified by visual inspection of the curves for incoming solar radiation (numbers noted in Table 1). Los Angeles rou- tinely experiences early morning low-level cloud cover that typically dissipates by late morning. This has been observed at the study site (Grimmond et al. 1996). Be- cause of this early morning cloudiness, the Los Angeles clear-sky data are restricted to times later than 1100 (local time). The daily mean Q* over the datasets for the three sites is shown in Fig. 2. All sites exhibit day-to-day variability throughout the year because of changes in the local cloud cover. Because of the incomplete data for Chicago and Los Angeles (LA), only the time pe- riods when data are available for all sites are used for the means reported in Table 1. This aids comparison; however, these are not true annual means. b. Estimated parameters Measured values for albedo and emissivity are not available for most urban locations. To evaluate the effect of using general tabulated values on model performance, the surface albedo and emissivity for Chicago and LA were estimated using only general site characteristics and values taken from the literature. In Chicago, the instrument tower (approximately 4 km southeast of O’Hare International Airport) is surrounded by short commercial and institutional buildings with mixed veg- etation (trees and grass). The LA tower is located in the residential neighborhood of Arcadia with mixed vege- tation (trees, shrubs, and bare sandy soil). The Łódź site, located near the urban core, is surrounded by 15– 20-m-tall buildings. For Chicago and LA, the 50% and 50%–90% radi- ative source-area fractions were determined using (1). The dominant surfaces in Chicago were asphalt paving (36%) and short grass (29%), with roofs making up 16% of the weighted source-area fraction. In Los Angeles, trees (deciduous and evergreen) contributed 33% of the surface cover, with roofs and asphalt paving contrib- uting only 15%. Effective a0 and «0 (Table 1) were calculated from weighted averages of surface-cover types, as found in published tables (Arnfield 1982; Oke 1988). Because it was available for Łódź, the annual median measured albedo (0.08) was used, and «0 was set equal to the weighted average (0.92) of the TEB input emissivities (Table 2). This value is lower than the 0.94–0.96 calculated by Arnfield (1982). The TEB ISBA scheme was only evaluated for Łódź, 1164 VOLUME 42J 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 2. Input parameters used in the TEB model calculations for Łódź. Urban surface Plan area fractiona ab «c Layer Depth (m) Heat capacityd (MJ m23 K21) Thermal conductivityd (W m21 K21) Roof 0.32 0.06 0.92 1 tar and gravel 0.01 1.95 0.90 (H 5 17 m) 2 tar and gravel 0.05 1.95 0.90 (H/W 5 1.0) 3 concrete 0.05 1.50 0.93 Wall — 0.15 0.90 4 cement 1 cement/windows 0.01 0.02 1.30 1.45 0.37 0.53 Road 0.38 0.11 0.94 2 brick 3 brick 4 cement 1 asphalt/concrete 0.20 0.20 0.02 0.02 1.60 1.60 1.30 1.83 0.70 0.70 0.37 0.79 2 asphalt/concrete 3 gravel/sandy clay 4 gravel/sandy clay 0.08 0.50 0.50 1.83 1.40 1.40 0.79 0.40 0.40 Sources: a K. Klysik (2001, personal communication); b K. Fortuniak (2002, personal communication); c Oke (1987); d ASHRAE (1981); Meyn (2000); Masson et al. (2002). because it requires both fairly detailed surface charac- teristics and an observed value for L↓ (not directly mea- sured in Chicago and LA). The ISBA portion of the scheme is used for the vegetated fraction, which was 30%, as determined from a surface database. The ra- diative properties of roofs, walls, and roads were based on measurements made at the site for albedos (K. For- tuniak 2002, personal communication) and tabulated values for emissivities. The effective albedo calculated from the scheme was higher than the observed value (0.09 versus 0.08), so it is expected that the results will be biased. The choice of thermal characteristics for roof, wall, and road layers were compiled from observations made at the site and from published data (Table 2). 4. Results The three models (OLS, NARP, and TEB ISBA) are evaluated using the observed data. As a basis for model comparison, we use the mean bias error [MBE 5 1/N S(P 2 O)] and the rmse {5[(1/N ) S (P 2 O)2]1/2}. a. Regression model results The coefficients b0 and b1, of the OLS model (4) relating net all-wave radiation to incoming solar radi- ation, are given in Table 3. The input data represent 30% of the observed data selected randomly. In Chicago and Łódź, only snow-free observations were used. For Chicago, determination of snow cover was based on gridded data (Climate Prediction Center 1999), and for Łódź snow cover was assumed when surface wetness was present and Ta , 08C. The slope value (b1) is an expression of how effective the surface is in converting the radiative exchanges into net (or absorbed) all-wave radiation. Because this ef- ficiency relates not only to both solar and infrared ra- diation exchanges, but also to those of sensible and latent heat leading to surface temperature change, no simple surface or atmospheric control on the slope is to be anticipated (Idso et al. 1969). However, in general, we might hypothesize that, ceteris paribus, a site with lower albedo, lower emissivity, higher surface moisture availability, higher surface thermal admittance, and greater roughness should result in greater absorption (larger slope). The slope coefficients for the three cities (Table 3) are higher than those for grassland sites, which average around 0.6, and lie within the range of forests (Kaminsky and Dubayah 1997; Iziomon et al. 2000). Łódź, the site with the lowest albedo, lowest emissivity, and probably the highest thermal admittance, has the greatest slope. It is not obvious why the other two sites are ordered the way they are; however, the radiometer source areas for these sites contain considerably more vegetation (grass in Chicago and trees at the LA site with the area receiving frequent irrigation). The R2 val- ues and standard errors for the urban sites are similar to results over natural vegetation (Kaminsky and Du- bayah 1997; Iziomon et al. 2000). When these coefficients derived from 30% of the data are used to estimate the net all-wave radiation over the remainder of the dataset, rmse range from 25 to 31 W m22 in the daytime and from 22 to 34 W m22 at night (Table 3). The major disadvantage of using the OLS method is that the coefficients are likely to be place spe- cific. In the absence of data for a given city and knowl- edge of how to select values for b0 and b1 objectively, one can presume that Q* estimates based on an OLS equation will give greater errors than those in Table 3. b. Evaluation of NARP subcomponents Several modifications have been made to existing component models in NARP, notably diurnal and daily albedos, clear-sky solar irradiance, and corrections to outgoing longwave radiation. Because these have not been evaluated for urban surfaces, the effect of each AUGUST 2003 1165O F F E R L E E T A L . TA B L E 3. O LS es tim at es o fQ * fr om m ea su re d K ↓. M od el de ve lo pm en t: st at is tic s de riv ed u si ng 30 % o fa v ai la bl e Q* an d K ↓ da ta se le ct ed ra n do m ly . Ev al ua tio n: pe rf or m an ce st at is tic su si ng th e de riv ed O LS m o de lo n th e re m ai nd er o ft he da ta .V al ue s fo r Q* ar e m ea n o fo bs er v at io ns .O nl y sn o w -f re e da ta ar e u se d, an d N is th e n u m be ro f1 5- m in da ta po in ts u se d in th e an al ys is . M od el de ve lo pm en t Ev al ua tio n Si te N b 0 (W m 2 2 ) b 1 R 2 St an da rd er ro r (W m 2 2 ) N D ay N ig ht Q* (W m 2 2 ) D ay N ig ht R m se (W m 2 2 ) D ay N ig ht Łó dź Lo s A ng el es Ch ic ag o 10 16 7 93 44 73 24 2 38 .8 2 47 .1 2 31 .6 0. 80 0. 72 0. 67 0. 96 0. 98 0. 97 32 .0 29 .6 25 .0 11 43 8 10 55 3 83 60 12 40 9 11 11 4 86 85 15 3 23 6 16 1 2 42 2 47 2 35 30 .8 35 .3 25 .1 33 .5 22 .1 25 .0 change is considered prior to evaluation of the complete Q* scheme. The diurnal albedo parameterization (6) was reesti- mated for Łódź, using clear-sky observations (N 5 997), to yield a (c) 5 a 1 (1 2 a) exp[20.2c 2 (1 2 a)/2]. (17)0 The coefficient for elevation decreased from that given in (6) (20.2 versus 20.1), thereby reducing dependence on elevation angle. Figure 3a shows reflected solar ra- diation flux densities for Łódź, determined with a con- stant albedo, while Fig. 3b shows results with the diurnal variation of albedo modeled using (17) and observations not used in the derivation. Comparing Figs. 3a and 3b, it is evident that the effect of including the diurnal var- iation of albedo is relatively small, less than 20 W m22 in all cases. Although the observations follow the func- tional form of the model (Fig. 3c), other factors (e.g., snow cover) limit the overall improvement in rmse to 0.6 W m22. For purposes of general application to urban sites, incorporating diurnal variation of albedo is un- likely to significantly improve the model accuracy and, hence, it is not included in the final form of NARP. For all sites, the varying daily albedo a0,d was cal- culated (7) by averaging incoming and outgoing solar fluxes over the period from 1000 to 1400 h local time, during predominately cloud-free periods [FCLD , 0.2, (11)], creating a single value for each day. This time period was selected so that the error in modeled L* is small relative to Q*. The availability of measured albedo in Łódź allows the estimate, using (7), to be evaluated (Fig. 4). Linear regression analysis of results for 179 days gives a fit with R2 5 0.77, a slope of 0.96, an intercept of 0.02, and an rmse of 0.025 or 26% of the mean observed value. Although the relative error is large, the correlation between the observed and modeled a0,d for Łódź demonstrates that the method is not overly sensitive to errors in estimation of L*. When averaged over longer periods (the lines on Fig. 4 are 10-day block averages) the performance improves (R2 5 0.90, rmse 5 0.019). Because we are interested in estimating lon- ger-term variations in albedo, a 15-day moving average a0,d is used in subsequent analyses. Figure 4 also shows a weak seasonality in albedo in Łódź and that there are differences among the three sites. The albedo in Łódź, which is characterized by a higher density of buildings and greater amount of vertical sur- face area than the other two sites, exhibits little change from day 90 to day 270, with the 10-day average ranging from 0.09 to 0.07. The 10-day average albedo at the Los Angeles site ranges from 0.20 to 0.13, and at the Chicago site ranges from 0.23 to 0.16. The large peaks in Fig. 4 for Chicago and Łódź are due to snow cover. Even with snow cover, the albedo remains generally lower in Łódź (0.20–0.35) than in Chicago (0.25–0.45). This may be due to the fact that in Chicago, buildings are shorter and more widely spaced. This agrees with the trend in results computed by Arnfield (1982), but is 1166 VOLUME 42J 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. (a) Comparison of modeled vs observed K↓ for Łódź, using a constant albedo (a0). Dashed line denotes one-to-one correspondence. (b) Same as (a), but using modeled diurnal albedo [a0(c)] that includes diurnal variation calculated from (17). (c) Measured and modeled albedo [a0(c)] plotted with respect to solar zenith angle. Data shown were not used in model estimation. not conclusive because sensor bias would affect the re- sults. Excluding snow cover, the curves do not seem to follow those developed by Brest (1987), who calculated slightly lower wintertime albedos from Landsat imagery for New York. Arnfield (1982) suggests that the low solar elevations in winter in high-latitude cities allow less direct solar radiation to penetrate canyons. The re- duced trapping results in higher wintertime albedos. The annual median albedos estimated from (7) were 0.08, 0.17, and 0.21 for Łódź, Los Angeles, and Chi- cago, respectively. These values agree with those mod- eled by Arnfield (1982) for commercial and residential areas similar to the real-world sites used here. The me- dian albedos for Los Angeles and Chicago differ from those determined by surface cover analysis (Table 1) by 10.04 and 20.03, respectively. The calculated cloud fraction (Fig. 5) shows a strong dependence on zenith angle. This results in an overes- timation of L↓ at high zenith angles (Fig. 5). Despite the nonzero values for FCLD at all zenith angles, the effect on L↓ is relatively small because FCLD is a squared term in the adjusted emissivity formulation (12). Until the zenith angle reaches approximately 758 the L↓ error is within 5%. In part this may be due to increased sensor error at higher zenith angles, but, more probably, it is a limitation of the method used to estimate K↓,clear. Be- cause L↓ is actually underestimated at lower zenith an- gles, it could be argued that cloud effects on emissivity should be increased. However, until the problem at high zenith angles is corrected, this would lead to large errors at sunrise, sunset, and nighttime. Unfortunately, limitations in accurately estimating L↓ are not restricted to high zenith angles. Figure 6 shows modeled versus observed L↓ for (a) clear-sky days (day- time only), (b) all-sky data, both using «clear, and (c) all data using the cloud-corrected emissivity [«sky, Eq. (12)]. In (a), results using the Prata «clear formulation agree fairly well with observations on occasions when clear skies are visually identified. For this case there is little bias, which is consistent with earlier results (Prata 1996; Newton 1999). On the other hand, in (b), under cloudy skies with no correction, the distribution is bi- modal. The group on the one-to-one line represents oc- casions with high or no clouds; hence, incoming long- AUGUST 2003 1167O F F E R L E E T A L . FIG. 4. Daily albedo (a0,d) for (top) Łódź, (middle) Los Angeles, and (bottom) Chicago. Directly measured values for Łódź (obs), and those calculated from Eq. (7) for all sites. Lines represent 10-day block averages. FIG. 5. (bottom) Model average FCLD estimates for clear-sky days vs solar zenith angle. As the zenith angle increases, FCLD increases as an artifact of the model. (top) The impact on modeled sky emis- sivity causes the modeled L↓Prata to exceed the observed value at large zenith angles (shown for Łódź only). wave radiation is unaffected. The second group is offset by approximately 75 W m22, suggesting consistent cloud climatology. In (c), with the cloud correction, the bimodality is removed and the result is largely unbiased (MBE 5 3.5 W m22), but considerable scatter remains. As can be seen in the time series plot (Fig. 6d) this error is not restricted to nighttime, but is often greater at that time because of the limitations in estimating nighttime cloudiness. Simply replacing T0 with Ta in the formulation for L↑ leads to large bias errors during the daytime at these urban sites (Fig. 7a). Although the simplified correction (13)–(14) has the shortcomings noted in section 2b(3), the daytime errors are greatly reduced (Fig. 7b). Under clear-sky conditions, when errors attributable to (T0 2 Ta) may be expected to be greatest, peak values are still somewhat underestimated but nighttime errors are typ- ically small (Fig. 7c). The correction also captures short- term changes in effective surface temperature even though air temperatures vary little (e.g., see days 186 and 187; Fig. 7c). Nighttime errors are larger when in- versions are present as might be the case on the night 190, following a cloudy day. c. Evaluation of NARP To test the performance of NARP, two cases were examined for each site: • case 1, using the specified parameter values from Ta- ble 1; and • case 2, replacing a0 with the 15-day moving average of a0,d. Analysis is divided into daytime (K↓ . 5 W m22) 1168 VOLUME 42J 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. 6. Modeled vs observed L↓ for Łódź. (a) Visually identified clear-sky days. (b) All observations with no emissivity correction. (c) Same as in (b), but emissivity corrected for cloud cover using (12). (d) Partial time series of estimated cloud fraction and L↓ (including observed, calculated using no emissivity correction for clouds, and using cloud corrected). For clarity in (b) and (c) not all points are shown. versus nighttime, and ‘‘summer’’ (121 , day of year , 244) (when K↓ is relatively larger) versus ‘‘winter’’ cases. This criterion for day–night separation was se- lected in lieu of zenith angle or Q* because K↓ is an observed quantity, and also because it reduces the chance of positive sensor offset causing miscategori- zation. The distinction between summer and winter does not correspond to the true seasonality at the sites but was fixed at dates ensuring no snow cover occurred in the summer period. 1) DAYTIME RESULTS The base case specification for all sites shows im- provement over the OLS model (Tables 3 and 4). The only exception is the case of Los Angeles in summer. It can be seen from Fig. 4 that this is due to having misspecified the albedo for this period. For Chicago and Łódź, daytime values have low bias errors ( | MBE | , 5% of Q*), indicating that the albedo estimated for Chi- cago was appropriate for an annual mean, and that the model is essentially unbiased for the measured albedo in Łódź. Using the daily computed values for albedo (case 2) leads to improvement at all sites and times (Table 4), particularly for Los Angeles, but also for Chicago because this accounts for the albedo of snow cover better than the estimates of snow cover and the fixed albedo. Use of the daily computed value for Łódź changes results little. This is to be expected because the albedo of Łódź is low and nearly constant throughout the year (Fig. 4), resulting in only small changes in reflected shortwave radiation. The bias errors for case 2 are all negative, and in some cases more so than for case 1. If we attribute this to the longwave portion of the model, either L↑ is over- estimated or L↓ is underestimated. The first is unlikely because L↑ is seen to be underestimated for Łódź, while L↓ is also underestimated (section 5b and Figs. 5 and 7). The choice of function in the cloud model is the probable cause of this bias. In all cases the bias error is within the presumed range of instrument error. The daytime results are characterized by small bias errors and relatively little scatter. As can be seen in the results for case 2 (Fig. 8), there few obvious differences in model fit. Figure 9 shows histograms of errors (pre- dicted 2 observed) for both NARP and the OLS AUGUST 2003 1169O F F E R L E E T A L . FIG. 7. Similar to Fig. 6 but for L↑. No data were used for function estimation. In (c) partial time series of observations, L↑ with no emissivity correction for cloud, that is, based on (13), and L↑ with emissivity correction for clouds based on (14). In (a) and (b) not all points are shown. TABLE 4. Performance of NARP (W m22). Values for Q* are mean of observations. See text for definition of case 1 and case 2. Day Site Period N Q* Case 1 MBE Rmse Case 2 MBE Rmse Night N Q* MBE Rmse Łódź Los Angeles Chicago Summer Winter Summer Winter Summer Winter 7515 9289 5341 9782 4418 9987 218 92 292 205 204 122 21.1 21.4 231.0 212.2 4.9 2.8 19.5 22.0 41.0 22.1 18.5 29.9 20.8 24.3 26.1 24.4 22.0 23.9 19.5 21.6 17.2 15.6 16.0 21.8 4388 13 847 3930 11 185 3174 12 730 256 234 243 249 242 230 17.2 2.1 3.4 26.3 3.5 25.4 25.2 28.0 20.8 20.1 15.0 19.6 scheme, using all the daytime observations at the three sites. The errors in NARP are predominantly ,25 W m22 at each site. The OLS model has a flatter but skewed distribution, so that NARP has the advantage of a greater number of smaller errors. 2) NIGHTTIME RESULTS In general, errors in the nighttime results are expected to be larger than by day, relative to the magnitude of Q*, especially because the model is given no infor- 1170 VOLUME 42J 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. 8. Modeled (case 2) vs observed Q* for (top) Łódź, (middle) Los Angeles, and (bottom) Chicago. mation on cloud cover or surface temperature. Because albedo changes affect the nighttime results only very slightly (because of how night is specified), only case 1 is shown in Table 4. The rmse range from 15 to 28 W m22, approximately the same range as daytime errors, but are quite large relative to Q* (81% for Łódź winter). This is attributable mainly to the lack of a good nocturnal cloud estimate. Because of the bias in FCLD at sunset, the MBE is expected to be positive. This is true for Łódź, both for summer and winter, though less pronounced in winter, but only during summer for Chicago and Los Angeles. As noted in section 3a, the Chicago and Los Angeles sites can be expected to have more negative MBE relative to Łódź, and the results are consistent with this expectation. For all sites, the winter period MBE becomes more negative. This can be attributed to fewer clear nights over the winter period (reducing the FCLD- induced bias) and to more neutral (less stable) surface layers. Thus, it seems that even for the less urbanized site, assuming Ta 5 T0 at night has only a small impact. Although cloud-bias effects could possibly be corrected by making empirical changes to the FCLD formulation, the rmse is largely unsystematic (Fig. 8). Accounting for the nighttime variability in L↓, based on commonly avail- able surface meteorological observations, presents a con- siderable challenge. 3) TEB ISBA RESULTS The results from the TEB ISBA scheme were not substantially biased by the chosen site parameters, as was suggested by the difference between estimated and observed albedo (section 3b). The model results (rmse; Table 5) are good when compared with NARP results, as calculated above (Table 4). However, most of this improvement in performance comes from the use of observed L↓ in TEB ISBA (L↓ is the term with greatest error in NARP). When observed values for L↓ are ap- plied to NARP, there is little difference in the perfor- mance of the two models (see rmse; Table 5). Although it seems that NARP does slightly better overall, this only points to the difficulties in constructing correct parameterizations; it does not necessarily sug- gest that the simpler NARP will perform better in all circumstances. Several factors here are important. First, the treatment of multiple reflections in the generalized urban canyon submodel in TEB allow for a physically based computation of effective albedo and emissivity. NARP used measured albedo, and the same effective emissivity as TEB, so that overall they were probably better estimates. Second, TEB computes the surface en- ergy balance and, therefore, could be expected to pro- duce better estimates of outgoing longwave radiation given the best-case parameterization. However, the smaller errors for NARP at night suggest that air tem- perature is nearly in equilibrium with the effective sur- face temperature at this site, also mitigating this advan- tage. As noted in section 2b(3), highly urbanized set- AUGUST 2003 1171O F F E R L E E T A L . FIG. 9. Histograms of errors (in 10 W m22 bins) incurred by the NARP and OLS models in calculating Q* for (left) Łódź, (middle) Los Angeles, and (right) Chicago (daytime only). TABLE 5. Comparison of Q* estimates for Łódź using TEB ISBA and NARP. Note that in this comparison both models are forced using observed L↓ and K↓. All units are watts per meter squared. Mean N Q* TEB ISBA MBE Rmse NARP MBE Rmse Summer, day Summer, night Winter, day Winter, night All 7515 4388 9289 13 847 35 039 218 256 92 234 51 21.6 7.4 3.5 1.6 2.2 8.4 7.9 14.1 5.4 9.4 8.1 6.4 4.7 3.5 5.2 10.2 7.1 12.6 5.0 9.0 tings have significant nocturnal heat islands that tend to maintain close to a neutral profile through much of the evening and night. Thus, for highly urbanized settings, trying to estimate surface layer outgoing longwave ra- diation from modeled surface temperatures is inherently more difficult and possibly less accurate in the long run. d. Sensitivity to inputs and instrument errors This study raises a number of issues with respect to measuring and modeling Q* near the urban surface. These concerns can be examined by considering the sensitivity of results to potential bias in the inputs, whether due to location or measurement errors. For ex- ample, the inputs may not be observed at the same lo- cation as the intended value for Q*. There may be a vertical, but more frequently horizontal, displacement in space. The following ranges of instrument/location error were considered: Ta, 638C; RH, 610%; K↓, 65%. These were applied to each input variable in separate runs of the model using the same constraints as case 1. The results in terms of MBE are shown in Fig. 10. The model is not strongly affected within this range of Ta or RH, which only affect the longwave results. For a 5% change in K↓, however, the resulting change in MBE is greater than 5%, and this does not consider the like- lihood that a horizontally displaced K↓ observation is also likely to be affected by spatial differences in cloud cover. Perhaps more instructive are the changes in rmse resulting from these changes in inputs shown in Fig. 11. Also shown in Fig. 11 are the results of having a bias of 65% in the measurement of Q* (note that a negative change is an improvement). Because the Los Angeles site had the worst daytime results for case 1, the effects are larger. Clearly the effects of a bias in either K↓ or Q* have large effects on the model results, up to 32% in the case of Los Angeles. However, because the chang- es in Q* are similar to the opposite change in K↓, this could be accounted for by a change in albedo. Thus, though sensitive to accuracy in K↓ and Q*, assuming unbiased measurements and accurate estimates of al- bedo, the range of errors for case 2, should be valid for other sites. 5. Conclusions The performance of a parameterization scheme for net all-wave radiation (NARP) is evaluated using year- long datasets for three urban sites. The parameterization models Q* using as inputs commonly available mete- orological fields and basic information about the albedo and emissivity of the surface. Median annual albedo 1172 VOLUME 42J 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. 10. Sensitivity of NARP Q* to changes in meteorological inputs for the three sites. Change in input fields are denoted in pa- rentheses. FIG. 11. Sensitivity of NARP rmse to changes in all fields for the three sites. Note that a negative change is an improvement. Change in fields are denoted in parentheses. across sites ranged from 0.08 to 0.21, with the lowest value corresponding to the most densely built site. Sea- sonal variations were about 20% of the median value, not including snow effects. At the highly urbanized site, seasonal variations were not as important. Thus, choos- ing a single albedo for all urban sites (i.e., irrespective of degree of urban development) at all times of the year leads to inaccuracies, particularly when substantial amounts of above-building vegetation are present. In comparison with the seasonal changes, incorporating the diurnal variability in albedo has little overall effect. In- sufficient data were available here to develop and eval- uate a model that includes both effects. The efficacy of a simple scheme to calculate L↑ with a ‘‘corrected’’ near-surface air temperature in place of a true surface temperature was also demonstrated. It was found unnecessary to make nighttime corrections to ac- count for T0 2 Ta differences at the most urbanized site. Cloud impacts on daytime L↓ were incorporated using a method that relies on the notion that cloud effects on solar transmittance can form the basis of a surrogate parameter in the longwave region. The results of the NARP for urban sites are better than those achieved by regression models and are com- parable to the TEB ISBA model that uses the same number of meteorological inputs and an urban canyon representation but requires specification of more surface and subsurface properties. Both daytime and nighttime L↓ continue to be the largest sources of error in esti- mating Q* when using only near-surface inputs. In par- ticular, the effects of clouds on longwave radiation ex- change are handled poorly. At present, no estimates of nocturnal cloud are included and there is no explicit recognition of cloud height (type). Acknowledgments. Data collection was funded by grants to SG from NSF 0095284 and NATO (Łódź), USDA Forest Service (Chicago), and Southern Cali- fornia Edison (LA). This analysis was supported by NSF 0095284. The help of Drs. Krzysztof Fortuniak, Kazim- ierz Klysik (University of Łódź), and Valéry Masson (Météo-France) are gratefully acknowledged. REFERENCES Arnfield, A. J., 1982: An approach to the estimation of the surface radiative properties and radiation budgets of cities. Phys. Geogr., 3, 97–122. ASHRAE, 1981: ASHRAE Handbook 1981 Fundamentals. ASHRAE, 797 pp. Badescu, V., 1997: Verification of some very simple clear and cloudy sky models to evaluate global solar irradiance. Sol. Energy, 61, 251–264. Barr, S., and D. L. 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