## Introduction

Energy fluxes that occur across the boundary of the earth's surface provide the fundamental driving force for many atmospheric, hydrological, and biological processes. In complex terrain, the variability of topography and radiative properties of the surface combine to generate complicated spatial and temporal patterns of surface radiation budgets. Improving the understanding of the controls of spatial variability of radiation components is a necessary goal for improved modeling of downstream applications, such as mesoscale meteorology (Chen et al. 2001), watershed hydrology (Famiglietti and Wood 1994), and biophysical processes (Franklin 1995). Many of the relationships between radiation and other environmental processes, such as turbulent fluxes, are nonlinear, making subgrid- or subpixel-scale variability a necessary quantity for spatial aggregation.

Surface radiation modeling in complex terrain has been the focus of numerous studies in recent decades, although these studies have tended to focus on individual components, including incident shortwave radiation (Whiteman and Allwine 1986; Dubayah et al. 1990; Whiteman 1990; Dubayah and van Katwijk 1992; Dubayah 1994; Dubayah and Rich 1995; Kumar et al. 1997), net shortwave radiation (Dubayah 1992; Dubayah and Loechel 1997), longwave radiation (Marks and Dozier 1979), and net all-wave radiation (Nunez 1980). The use of remote sensing to estimate surface energy fluxes has yielded valuable spatial information (Lhomme and Monteny 1993; Sun and Mahrt 1994; Humes et al. 1997; Laymon et al. 1998; McKeown and Leighton 1999) and has been combined with digital elevation data to improve determination of both radiation and heat fluxes in complex terrain (Duguay 1995; Schneider et al. 1996; Dubayah and Loechel 1997). These studies have been limited mostly to one or two radiative components. Yet, as a fundamental energetic input for many environmental processes, there is a need to understand the spatial distribution of net all-wave radiation and the way in which each component has an impact on its spatial variability.

The current study examines the spatial distribution of each component of the surface radiation budget by using traditional mathematical approaches (Kondratyev 1977) combined with topographic modeling and surface cover classification from satellite imagery to calculate radiant fluxes across a complex landscape. The primary goal is to examine the relative importance of a variety of surface attributes on the spatial variability of net radiation and to assess the role of landscape complexity by comparing regions of strongly varying spatial autocorrelation, both of topography and surface cover. Analyses are based on simulations of radiative fluxes on midsummer days in clear-sky, anticyclonic conditions in the Tekapo watershed, situated in the Southern Alps of New Zealand (44°S, 170°E). This study was conducted as part of a wider project that examined surface energy exchanges and boundary layer development in complex terrain, the Lake Tekapo Experiment (LTEX; Sturman et al. 2003).

*Q*

*K*

*L*

*K*

*K*

*L*

*L*

*Q**,

*K**, and

*L** are net all-wave, shortwave, and longwave radiation, respectively. Here,

*K*↓ is incident shortwave radiation, made up of direct-beam (

*K*

_{S}) and diffuse-beam (

*K*

_{D}) components. The parameter

*K*↑ is reflected shortwave radiation,

*L*↓ is incident longwave radiation, and

*L*↑ is outgoing longwave radiation. The sign convention used here assigns positive values to downward fluxes and negative values to upward fluxes. Arrows represent the direction normal to the local surface.

The traditional view of the surface radiation budget as described by Eq. (1) is significantly more complicated in the case of complex terrain (Fig. 1). Direct-beam shortwave radiation varies spatially because of the application of the cosine law to slope properties and because of shading effects. Diffuse-beam shortwave radiation also varies over space because of its partial anisotropy (Kondratyev 1977), and because of the role of sky view factor *υ* on the isotropic portion. An additional contribution to *K*↓ is the proportion of reflected shortwave radiation received from surrounding terrain (*K*_{R}). The source of incoming longwave radiation is also divided between surrounding terrain (*L*_{T}) and the overlying atmosphere (*L*_{A}), depending on *υ.* Not included in this schematic is spatial variability of the radiative properties of the surface, which is typically significant in complex terrain because of interaction between climatic, geomorphic, hydrological, and ecological systems, although this role is included in this study. Also not included in this schematic is the role of clouds, which increase the ratio of diffuse- to direct-beam shortwave radiation, thereby reducing spatial variability of radiation within the shadow of the cloud. On the other hand, clouds that favor locations for development, such as over ridges, can have a large effect on spatial variability of radiation within a region of complex terrain. However, the focus in this study is on the role of surface attributes in generating spatial variability of radiation, so clear-sky days were selected for simulation. Given the large spatial range of flux densities expected for each component of the surface radiation budget, it is not surprising that observations of net radiation in mountainous terrain have yielded patterns that have contrasted strongly and sometimes contradicted each other (e.g., Greenland and Clothier 1975; Rott 1979; Whiteman et al. 1989; Konzelmann et al. 1997; Wenzel et al. 1997; Kalthoff et al. 1999; Iziomon et al. 2001). For example, Rott (1979) and Konzelmann et al. (1997) both reported increases in *Q** at higher elevations, whereas Wenzel et al. (1997) found a slight decrease. Differences in these observations are typically assigned to various local factors, such as slope aspect, cloudiness, fog persistence, and local temperature lapses.

## Model overview and site description

The surface radiation model presented in this paper is based on the “SRAD” topographically driven surface radiation scheme, which determines solar irradiance, reflectance, and fluxes of longwave radiation over a surface (Moore et al. 1993; Wilson et al. 1996; Gallant 1997; Wilson and Gallant 2000). Spatial modeling of surface cover and topography is used explicitly to model control of spatial distribution of radiation fluxes, so it is particularly suited to complex topographical sites. Data used to initialize the model are few and are mostly standard meteorological observations, which enhances usability of the model in remote locations. Model simulations were conducted for 1 and 12 February 1999. These days were selected for clear skies, so that topographic and surface-cover controls could be examined in isolation from cloud effects. These days were also intensive observation days during LTEX, so the maximum amount of data was available for evaluating model performance. The locations of observation stations are shown in Fig. 2d, and site and instrument details are provided in Table 1.

### Topographic modeling and surface-attribute setting

A digital elevation model (DEM) was generated for the Tekapo watershed with 100-m gridpoint spacing from 20-m-interval contour data and hydrological information for lake levels. From the DEM, slope angle and aspect were calculated with a central finite-difference scheme (Wilson and Gallant 2000). The sky view factor was estimated at each DEM grid point using the one-dimensional horizon algorithm of Dozier et al. (1981) at 22.5° intervals around the horizon. This algorithm was also used to calculate shading effects from surrounding terrain at 12-min time intervals during the solar path above the horizon. Estimation of both *υ* and shading parameters produces errors near domain boundaries because no terrain is acknowledged outside of these limits. Simulations were therefore conducted using a DEM with an area that was 44% larger than the Tekapo watershed area portrayed in Fig. 2.

Surface-cover distribution was assigned using supervised classification of Indian Remote Sensing Satellite (*IRS-1C*) imagery at a resolution of 20 m. Imagery was captured in February of 1997 when snow cover was at its minimum spatial extent, which corresponds with the time of radiation simulations made in this study. Figure 2 presents maps of elevation, slope angles, slope aspect, and surface cover. There are three broad divisions to the surface characteristics of the study area, and the boundaries for these are indicated in Fig. 2b. The northwest section is composed of high relief and elevation, with surface cover dominated by snow, ice, and rock. The southeast boundary of the watershed is composed of moderate slope angles and elevations ranging between 1000 and 2000 m. The surface cover of this area is dominated by short and tall tussock species (Festuca novae-zealandiae and Chionochloa rigida, respectively) and by the lake surface. To the south is the relatively low-lying and gently sloping basin area with degraded tussock surface cover, which consists of low-density marginalized short tussock species with large areas of bare, frost-heaved soil. The distribution of surface area for each of these attributes is provided in Fig. 3.

The spatial resolution selected for this application reflects the need to identify subgrid-scale landscape elements. For example, the watershed area is approximately the area represented by a single grid point in a regional atmospheric model, 0.1 of a grid point in a forecasting model, and 0.01 of a grid point in a general circulation model. Previous work has shown that the spatial autocorrelation of *K*↓ modeled over topographic grids is short: usually less than 300 m and almost always less than 1000 m for a wide variety of landscapes (Dubayah et al. 1990; Dubayah 1992, 1994; Dubayah and van Katwijk 1992). Dubayah et al. (1990) examined the role of DEM resolution on incoming solar radiation and found a large increase in spatial autocorrelation with a decrease in model resolution, linked closely with an increase in spatial autocorrelation of topographic properties, and an overall decrease in slope angles. The importance of resolution is clearly linked to the application of results. McKenny et al. (1999) compared modeled results from SRAD using 20-m-resolution and 100-m-resolution DEMs. The outputs displayed similar means, but the range of estimates was greater for the 20-m DEM. They concluded that 100-m resolution was sufficient for many applications in their 900 km^{2} study area.

### Model calculations and parameterization

*K*↓ in clear skies followed several steps. Extraterrestrial irradiance on a horizontal surface just outside the earth's atmosphere (

*K*

_{oh}) was initially calculated using

*K*

_{oh}

*I*

*r*

^{2}

*Z ,*

*I*is the solar constant (∼1356 W m

^{−2}),

*r*is the ratio of the earth–sun distance to its mean, and

*Z*is the zenith angle (Gates 1980; Fleming 1987). The zenith angle is the angle of the solar beam relative to the surface normal and can be estimated from

*Z*

*δ*

*δ*

*h,*

*δ*is the declination of the sun (ranging to 23.5° either side of the equator), and

*h*is the hour angle of the sun from solar noon (Wilson and Gallant 2000).

*K*

_{Sh},

*K*

_{D}) was calculated using

*τ*is the transmission coefficient or fraction of radiation incident at the top of the atmosphere that reaches the ground along the vertical path, and

*m*is the air mass, given by

*m*= sec

*Z*= 1/cos

*Z*(Gates 1980; Linacre 1992). However,

*m*is only accurately calculated this way when

*Z*is less than about 60°, because the curvature of the earth unrealistically inflates pathlengths at angles greater than this value (Kondratyev 1977). For optical pathlengths of greater than 60°, values are taken from List (1968). Because

*τ*increases with elevation because of reduced pathlength and atmospheric aerosol density,

*τ*lapse rate was defined and a reference

*τ*was extrapolated across the domain as a function of elevation. The lapse rate used in this study was 0.0008 m

^{−1}(after Wilson and Gallant 2000) and the reference transmissivity value was calculated from extinction and airmass values recorded at the Mount John University Observatory (located 50 m from A7 in Fig. 2d).

*K*

_{D}was then divided into circumsolar (

*K*

_{Dc}) and isotropic (

*K*

_{Di}) portions using a circumsolar coefficient

*γ*of 0.25 (after Linacre 1992), and

*K*

_{Di}was reduced by a factor of 1 −

*υ.*The values

*K*

_{Dc}and

*K*

_{S}were then calculated for sloping surfaces using

*K*

_{S}

*K*

_{Sh}

*i,*

*i*is the angle between the solar beam and normal to the sloping surface, which can be derived from

*i*

*s*

*z*

*s*

*z*

*A*

*A*

_{s}

*s*is the slope angle,

*A*is the solar azimuth angle, and

*A*

_{s}is the azimuth angle of the slope. The grid points with and without shading (both self-shading and shading from surrounding terrain) at each time interval were then determined, and

*K*

_{S}and

*K*

_{Dc}were removed from shaded grid points. The contribution of reflected shortwave radiation (

*K*

_{R}) arriving at each grid point from surrounding terrain was also determined using

*K*

_{R}

*K*

_{S}

*K*

_{D}

*υ*

*α,*

*α*is albedo. Total shortwave radiation (

*K*

_{ts}, or

*K*↓) for clear skies was calculated from

*K*

_{ts}

*K*

_{Dc}

*γ*

*K*

_{Di}

*γ*

*K*

_{S}

*K*

_{R}

Surface albedo *α* was determined by hourly observations over each of the major surface classes during clear-sky days in February of 1999, using two pyranometer pairs, one at a fixed location (A8) and one roving station (A3, A4), and handheld measurements over a variety of surfaces (Table 2). These values were then assigned to individual grid points across the model domain using the surface classification scheme (Fig. 2d). However, hourly observations of *α* showed diurnal variability, strongly related to solar incident angle. This suggests that not only does *α* vary spatially as a function of changes in surface type, but the spatial variability changes over time. Furthermore, the diurnal pattern of *α* varied significantly between surface types. Last, because *α* is related to solar incident angle, it will vary across the topographic domain as well as through the solar cycle. In this study, mean diurnal albedo was used for each of the surfaces except water. Because all water grid points can be assumed to be horizontal, hourly average *α* was input at hourly time steps. A proxy for the maximum potential error associated with using diurnal mean *α* for each surface type is estimated in Table 2 by multiplying the standard deviation of hourly observations of *α* for each surface class by the spatial average *K*↓. This would be most significant for the water surface, followed by tall and short tussock, with a maximum error of approximately 10% of *K*↓.

*S*:

*K*

_{th}is the total

*K*↓ for the equivalent horizontal grid point. The formulation to determine changes in temperature over space includes the effect of a leaf area index (LAI) on surface irradiance (Wilson and Gallant 2000):

*T*

_{b}is the temperature at the reference station, Δ

*T*is the rate of near-surface air temperature change with elevation along the slope (°C m

^{−1}× 10

^{3}),

*z*is the elevation of the grid point (m MSL),

*z*

_{b}is the elevation (m MSL) of the temperature reference station,

*C*is a constant, and LAI

_{max}is the hypothetical maximum leaf area (=10). LAI values for each surface-cover class were derived from vegetation density surveys and were input as a georeferenced surface grid using the surface-cover classification scheme. Longwave radiation fluxes were subsequently determined from the surface and air temperature by

*L*

_{0}

*σT*

^{4}

_{0}

_{0}

*L*

*T*

_{0}is surface temperature (K) and ε

_{0}is surface emissivity, and by

*L*

_{a}

*σT*

^{4}

_{a}

*υ*

*υ*

*L*

*T*

_{a}is the air temperature (K) and ε

_{a}is apparent atmospheric emissivity calculated from

*T*

_{a}and vapor pressure

*e*

_{a}using Brutsaert's (1975) formulation:

Accuracy of longwave components is clearly dependent on the spatial representativeness of input data. Of greatest concern in this case is the rate of change of surface radiative temperature with elevation because only two stations were available for parameterization. In particular, the variability of surface cover is not included as a variable, and the errors associated with this omission can be seen in the validation data (following section). Infrared channels on satellite platforms can be used to predict spatial variability of surface temperature (Schneider et al. 1996), but return times for high-resolution satellite sensors and cloud cover currently limit applicability of this approach. The three pairs of stations used to derive the mean Δ*T* were sited to represent spatially the variability in topography within the watershed. Sensitivity analysis for spatial variability of air temperature is reported in section 3c.

### Model evaluation

Model performance was evaluated for simulations of 1 and 12 February 1999 by comparing model output with data collected at two sites for which complete radiation budgets were determined and with a third site that measured only *K*↓. Details of validation sites can be found in Table 1 and Fig. 2d. These stations were sited over varying surface types, including sloping terrain (A4), significant local shading (A2, A3), and a range of surface cover (Table 1). Furthermore, *K*_{D} was measured at A8 on both days, and *K*_{S} was estimated from *K*↓ − *K*_{D}. Hourly average radiation flux densities at these sites are plotted against model output for all components in Fig. 4, and statistics for each component can be found in Table 3.

The small overestimation of *K*↓ by the model is likely to have resulted from an underestimation of optical transmissivity *τ,* because *K*_{S} is also overestimated and *K*_{D} is underestimated. From Eqs. (4) and (5), it can be seen that as *τ* decreases, the ratio of *K*_{S}:*K*_{D} also decreases. Longwave radiation fluxes were simulated less accurately. The value of *L*↓ is generally overestimated during the day because of the underestimation of atmospheric column temperature by air temperature measured at 3 m; the opposite is true at night. More accurate modeling of *L*↓ should include integrated temperatures through the atmospheric column (using balloon or aircraft-borne instruments) or derived parameters for adjusting near-surface air temperatures (Brutsaert 1975). The apparent randomness of scatter across the 1:1 line in *L*↑ validation is somewhat misleading because, when broken down into individual days, it was apparent that most underestimation occurred over the rock surface, which had higher radiative temperatures than the reference surface of degraded tussock, whereas the snow tussock surface had lower overall radiative temperatures, illustrating the need to account for thermal properties of each individual surface. Both the asymmetric pattern of *K*↓ at the sloping site (A4) and the times of shading at A2 and A3 were captured well by the model.

## Results

### Diurnal average radiation fluxes

Components of the surface radiation budget modeled for the Tekapo watershed on 12 February 1999 are presented in Fig. 5. Simulated *K*↓ (Fig. 5a) contains a large range of values (450 W m^{−2}), although the standard deviation is only 10% of this. Highest flux densities can be found on high-altitude, north-facing slopes of moderate angle; smallest fluxes occur on steeper south-facing slopes. The distribution of flux densities shows that approximately 50% of grid points fall within a narrow range (∼20 W m^{−2} departure from the mean) because of the equally large distribution of nearly flat grid points over the study area (Fig. 3b).

The spatial distribution of mean diurnal *K*↑ simulated for the watershed shows a similar pattern (Fig. 5b). Despite a large range in values, the spatial standard deviation is only 33 W m^{−2} because the distribution of grid points is heavily skewed toward the lower values. The secondary histogram peak is associated with the high *α* of snow and ice, which is particularly emphasized on north-facing surfaces. The very low *α* of the lakes (0.07) and the relatively low *α* of both the rock and degraded tussock surfaces (0.13 and 0.14, respectively) are also evident in this map. The influence of surface *α* on spatial variability of *K*↑ is more clearly delineated over the gentler topography of the basin area, where the range in *K*↓ is smallest; in the mountainous terrain, variability is associated with both topographic variability of *K*↓ and heterogeneity of surface cover. For example, one-half of the total range of *K*↑ occurs within the area covered by snow and ice, because of the large differences of *K*↓ found between moderate north- and steep south-facing slopes. The importance of incorporating the spatial distribution of surface cover into surface radiation models in complex terrain is clear when comparing Fig. 4b with Fig. 2d.

The results of longwave radiation calculations for 12 February 1999 are presented in Fig. 4c. The value of *L** generally decreases with increasing elevation because the mean diurnal rate of change of surface temperature with elevation is lower than that of the near-surface atmosphere. This effect is enhanced by the generally larger *υ* found at higher elevations, because lower *L*↓ occurs when *υ* is larger. The strong control of elevation is clear when comparing the histograms of *L** (Fig. 4c) with elevation (Fig. 3a). However, because elevation is strongly skewed toward lower values, the spatial standard deviation of *L** is only 14.3 W m^{−2}.

The spatial distribution of diurnal mean *Q** is presented in Fig. 4d. The total spatial range in mean diurnal *Q** is 278 W m^{−2}, the mean is 149 W m^{−2}, and the standard deviation is 49 W m^{−2}. The range in values occurs between high-altitude, north-facing rock surfaces with very high *Q** and south-facing ice surfaces at which a *Q** loss occurs. Because these surfaces cover a small proportion of the watershed, the distribution of *Q** is weighted toward the relatively homogeneous terrain to the south at which values of 165 W m^{−2} ± 10% are found. In general, the north-facing slopes and water surfaces yield the highest *Q** values; south-facing slopes and snow surfaces yield the lowest values. The large, gently sloped basin area also receives above-average *Q**; the east- and west-facing slopes, particularly steeper slopes, receive moderate to low magnitudes of *Q**.

### Hourly variability in radiation components

A time series of spatial average *K*↓, *L**, and *Q** on 12 February 1999 is presented in Fig. 6. The greatest variability in *K*↓ occurs in midmorning and midafternoon. This pattern was also evident in simulations of the Konza Prairie with randomly distributed aspects (Dubayah et al. 1990) and was found to be a function of optical depth. In a hypothetically clear atmosphere (*τ* = 0), maximum variance would occur at zenith. However, as *τ* decreases, the solar zenith angle at which maximum variance occurs increases (Dubayah et al. 1990). For the average *τ* over the current study area (0.77), maximum variance calculated using the Dubayah et al. (1990) formulation occurred at approximately 0845 and 1515 local apparent time.

The influence of greater surface heating than air heating during the day increased *L*↑ relative to *L*↓, thereby decreasing *L**. The spatial variability of *L** is also greatest during these hours, because Δ*T* is largest. The much lower *L** in the afternoon than in the morning occurs because surface temperature is highest in the afternoon, whereas air temperature decreases as a result of cold-air advection from regional circulations in the afternoon (Kossmann et al. 2002). Overall, the magnitude of spatial variability is relatively small when compared with *K*↓. The large difference in the significance of the roles that *L** and *K** play in *Q** is evident in the diurnal *Q** statistics. Mean magnitudes and variability are both lowest at night when *L** controls *Q**. During the day, when *K** dominates the radiation budget, the spatial average and standard deviation are both an order of magnitude greater.

### Sensitivity analysis

In this section, the roles of individual surface properties in spatial variability of surface radiative fluxes are assessed in isolation to determine the relative importance of each variable.

#### Elevation

Estimated prior to the calculation of slope effects, the range in elevation in the Tekapo watershed generates a spatial range in mean *K*↓ of 85 W m^{−2} but a standard deviation of only 18.2 W m^{−2}, because elevation distribution in terms of watershed area is strongly skewed toward lower values (Fig. 3a). For *L**, when elevation alone controls spatial distribution (i.e., when *υ* = 1, LAI = 0, and *S* = 1), the spatial standard deviation is 11.1 W m^{−2}, explaining most of the overall spatial variability of *L**.

#### Slope properties

Sensitivity analysis of *K*_{S} to slope properties was conducted by calculating *K*_{S} at a reference location for the full range of slope attributes found throughout the watershed, thereby isolating slope effects from elevation, location, and shading controls. Figure 7 illustrates the combined controls of surface aspect and slope angle on *K*↓ when integrated over the daylight period of 12 February. For this time period, daily surface irradiance is at a maximum for north-facing slopes with a slope angle of 26°. This maximum decreases rapidly towards the south and higher slope angles (with an overall range of 410 W m^{−2}). To ascertain the influence of the actual spatial distribution of slope aspect and angle on *K*↓, the shortwave radiation ratio *S* as defined in Eq. (10) was calculated for each grid point, allowing the combined influence of slope properties to be assessed independent of elevation controls. The daylight spatial standard deviation of *S* was 0.11, which equates to a standard deviation of *K*↓ as a function of slope properties of 33 W m^{−2}, dominating the overall variability of *K*↓.

To isolate these two variables, the influence of slope angle was tested by putting in the full range of slope angles while rotating the aspect to follow the sun. Aspect was tested by fixing the slope angle to the median angle found in the watershed (33°) for the full range of aspect. For slope angle, the daylight-mean range is 195 W m^{−2}, or 33% of the daylight-mean irradiance value; slope aspect produced a range of 274 W m^{−2} (91% of the mean). Of the two parameters, then, slope aspect has a greater control on *K*_{S} at the surface than does slope angle, although both generate considerable variability in the overall radiation budget. This result agrees with findings reported by Dubayah et al. (1990) for a Kansas site with much smaller relief, indicating that these relationships are scalable.

#### Shading effects

Figure 8 illustrates the extent of shading from surrounding terrain at five times of the day (12 February). In the early morning and late afternoon, a large proportion of the surface area is influenced by shading. In the middle of the day, midmorning, and midafternoon, the coverage of shading is significantly reduced because of the lower zenith angle of the sun and the approximately north–south orientation of the main valley systems. The shaded area is also smaller in the late afternoon than in the early morning, because of the smaller spatial extent of high terrain on the western side of the watershed. At all hours, shading is most extensive in the steeper and higher terrain to the north.

*K*↓ associated with shading [

*K*

_{(shad)}] can be estimated by

*A*

_{(shad)}is the area of the watershed in shadow,

*A*

_{(tot)}is the total watershed area, and the overbar for

*K*

_{ts}indicates the spatial mean. Applying Eq. (15) to three-hourly shadow maps illustrates a relatively small diurnal-mean reduction in

*K*↓ by shading, because the increase in shaded area corresponds with a decrease in

*K*↓ because of the increase in optical pathlength (Table 4). The spatially and temporally averaged diurnal reduction in

*K*↓ as a function of shading is subsequently only 43.7 W m

^{−2}, or 9.4% of mean

*K*↓. Again, increased topographic complexity apparently results in an overall decrease in

*K*↓ and an increase in the range of

*K*↓ as a function of shading.

#### Air temperature

Spatial variability of *L*↓ caused by spatial variability of temperature throughout the watershed was assessed by comparing *L*↓ calculated for both observed and modeled air temperatures (where modeled temperatures were based on the reference air temperature and average Δ*T*) for each station. For these calculations, it was assumed that ε_{a} = 0.6 and *υ* = 1. The diurnal and spatial average of *L*↓ difference between the two input temperatures was 9.4 W m^{−2}. The value of Δ*T* during the middle of the day has greater variability than at night, because of the large spatial variability in local-to-regional-scale circulations and the associated cold-air-advection regimes occurring on clear summer days (Kossmann et al. 2002). The calculation of temperature in the model assumes that Δ*T* observed in the watershed up to 1500 m can be extrapolated to the top of the model domain (2900 m). This assumption may be valid during the day when the well-mixed boundary layer extends above ridge height. The inversions observed in the valley atmosphere at night, however, may be considerably shallower and may be confined within the valley atmosphere below ridge level. In the model, the temperature inversion is extended to the upper limits of the model domain, thereby presumably overestimating temperature at ridge tops. Thus, *L** is probably lower over the ridge tops and mountain peaks in reality than is predicted by the model. Overestimation of air temperature by 5°C when the correct temperature was 0°C and ε_{a} = 0.6 would generate an error in *L** of +14.5 W m^{−2} (8%). However, because this effect occurs at the highest elevations, this error is restricted to a relatively small number of grid points (Fig. 3).

#### LAI and *S*

For the range of LAI and *S* values found within the Tekapo watershed, air temperature was estimated to vary by up to 3°C as a function of Eq. (11). At 20°C, with a clear-sky atmospheric emissivity of 0.6, the difference in *L*↓ associated with this range of temperature is only 10.6 W m^{−2}, or 4%. Therefore, error in the approximation of LAI used in this application is unlikely to yield significant error in *L**, and both *S* and LAI have a low overall impact on the spatial variability of longwave radiation within the watershed. This finding, however, is influenced by the low density of vegetation in the study area as compared with other (particularly forested) watersheds, where LAI is likely to play a more significant role (McKenny et al. 1999).

### Role of landscape complexity

Scale is a central issue in defining spatial variability of fluxes, and this has been examined in the past by changing input DEM resolution (Dubayah et al. 1990; McKenny et al. 1999). However, although this serves to alter spatial autocorrelation of topography, it does not examine other important spatial attributes, such as surface cover. In this study, three watershed subareas (WS) with greatly different mean and variability of all surface attributes were compared to assess the effect of “landscape complexity,” which includes both topographic and surface cover complexity, on the surface radiation budget. The boundaries for each WS were selected qualitatively based on elevation, slope, and surface-cover maps as described in section 2a and illustrated in Fig. 2b. The descriptive spatial statistics for topographical properties (elevation, slope angle, and slope aspect), radiation ratios, and radiation flux densities for each WS are provided in Table 5. From WS1 to WS3, a large drop occurs in elevation and slope angles, as well as in the variability in both properties. These statistics describe three distinct classes of topography from extremely complex to simple. Spatial average *S* increases while spatial standard deviation decreases markedly between WS1 and WS3. Spatial average albedo is similar in each WS although variability is double in WS1 when compared with WS2 and WS3, indicating the potential importance of surface cover on radiative properties. In the breakdown of radiation components, mean *K*↓ is reduced in the more complex terrain, and spatial variability is greatly increased. It is important to note that the decrease in spatial average *K*↓ is not a function of complexity itself but is due to *S* being less than 1, which means slope aspects are not uniformly distributed and on aggregate are slightly south-facing. Mean *L** also decreases in more complex topography (although negligibly), suggesting that elevation controls outweigh the control of *υ,* at least for this terrain configuration. Variability is also greater in more complex terrain, although the inter-WS differences for *L** are negligible when compared with *K**. Because shortwave radiation has been found to dominate the radiation budget and mean albedo is similar in each WS, the difference in spatial average *Q** between the WS most strongly resembles that of *K*↓, which is accounted for by *S.* Of more interest is the large increase in spatial variability of *Q** in the more complex terrain.

A comparison of spatial average and spatial standard deviation *Q** among the three WS at hourly intervals is plotted in Fig. 9. The reduction in *Q** at WS1 occurs throughout the day except during nocturnal hours at which time higher values result from the reduced sky view factor. However, this effect is negligible when compared with the reduction of *Q** during the daytime. The generally west-facing property of many slopes in WS2 increases the mean *Q** as compared with WS1 in the afternoon, which is also lower than both WS1 and WS3 in the morning. The differences in spatial variability of *Q** among each WS are substantial (Fig. 9b), with peak standard deviations differing by 200 W m^{−2}. The timing of peaks in variance are the same for all WS, illustrating the control of solar zenith angle and *τ* on the timing of peak variance, irrespective of topographic properties.

## Discussion

A considerable range of magnitudes in all radiation components can be found across a complex landscape such as the Tekapo watershed. This fact has important implications for many climatological, hydrological, and biological processes and patterns. For example, spatial variability in radiation components in the Tekapo watershed was found to have strong controls on spatial variability of sensible heat flux (Oliphant et al. 2000) and evapotranspiration (Oliphant 2000). Furthermore, the differences in sensible heat flux were found to have a significant impact on spatial variability in boundary layer characteristics and airflow (Kossmann et al. 2001). It is therefore necessary to account for radiation components with sufficient accuracy and resolution to reveal this variability. In particular, slope properties, elevation, shading effects, surface albedo, and sky view factor are the most important parameters, respectively, to model accurately and at a spatial resolution that reflects the scale of variability for these parameters across the landscape.

Despite the large spatial range in radiation flux density, spatial averaging over three subareas with strongly contrasting levels of surface complexity resulted in similar values. This result is not surprising because it can be expected that, were slope properties completely randomly distributed, the spatial averages of *K*↓ would be the same, despite the variability in slope angles among WS. This is not necessarily the case with *L*↓, because atmospheric processes distribute energy in nonradiative ways, potentially altering regional air temperatures. Outgoing radiative fluxes may also produce different regional averages, because not all absorbed incoming radiant energy is radiated outward; some is transferred through turbulent and conductive processes. Therefore, differences in regional average *α* should yield differences in regional average *Q**.

However, the understanding that radiation components may scale more or less linearly is not transferable to environmental variables that depend in some way on radiation, such as snowmelt, evapotranspiration, sensible heating, or photosynthesis, which cannot be scaled in the same way because of nonlinearity in their relations. Therefore, understanding of the magnitude of subgrid variability of surface radiation fluxes and how they are governed by surface attributes is essential for a variety of applications. However, to transfer findings of different landscape complexity to other study sites, an objective classification scheme is required that incorporates both topographic factors (such as *S*) and surface-cover variability.

## Conclusions

The magnitude and causes for spatial variability in surface radiative fluxes was examined in a complex alpine watershed in the Southern Alps of New Zealand. The radiative flux components were simulated using a topographical surface radiation model, the results of which compared well with observations made at a range of sites. Sensitivity studies were conducted to isolate the role of spatial variability of surface characteristics in generating variance in the radiation budget. In order of most to least important, these characteristics were found to be slope aspect, slope angle, elevation, albedo, shading, sky view factor, and leaf area index.

The role of landscape complexity in the spatial distribution of fluxes was investigated by considering three subareas of the watershed that contain strongly contrasting scales of autocorrelation of topography and surface cover. The increase in landscape complexity yielded a small decrease in *Q** but a large increase in spatial variability that was governed most significantly by *K*↓. Other radiative components yielded similar spatial averages between topographically different areas although spatial variability in all fluxes was significantly increased with greater complexity. Therefore, although regional averages scaled more or less linearly, subregional-scale spatial variability differed dramatically.

## Acknowledgments

This research was made possible through funding by Marsden Fund Grant UOC602, awarded by the Royal Society of New Zealand. Original source code for SRAD was obtained from the Centre for Resource and Environmental Studies, Australian National University. Satellite imagery was provided by Canterbury Regional Council, New Zealand. The authors also thank John Thyne for invaluable computing and GIS support, the participants of LTEX for field support, and the farmers of the Tekapo watershed for permission to use their land. The comments of three anonymous reviewers were also very helpful.

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Maps of the Tekapo watershed showing (a) elevation, (b) slope angles, (c) slope aspect, and (d) surface cover. Meteorological and radiation stations (A1–A8) are indicated

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Maps of the Tekapo watershed showing (a) elevation, (b) slope angles, (c) slope aspect, and (d) surface cover. Meteorological and radiation stations (A1–A8) are indicated

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Maps of the Tekapo watershed showing (a) elevation, (b) slope angles, (c) slope aspect, and (d) surface cover. Meteorological and radiation stations (A1–A8) are indicated

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Histograms of surface area for different landscape attributes: (a) elevation, (b) slope angles, (c) slope aspect, and (d) surface cover

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Histograms of surface area for different landscape attributes: (a) elevation, (b) slope angles, (c) slope aspect, and (d) surface cover

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Histograms of surface area for different landscape attributes: (a) elevation, (b) slope angles, (c) slope aspect, and (d) surface cover

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Scatterplots of modeled vs observed hourly radiation fluxes for 12 Feb 1999: (a) *K*↓, (b) *K*↑, (c) *K*_{S}, (d) *K*_{D}, (e) *L**, and (f) *Q**

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Scatterplots of modeled vs observed hourly radiation fluxes for 12 Feb 1999: (a) *K*↓, (b) *K*↑, (c) *K*_{S}, (d) *K*_{D}, (e) *L**, and (f) *Q**

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Scatterplots of modeled vs observed hourly radiation fluxes for 12 Feb 1999: (a) *K*↓, (b) *K*↑, (c) *K*_{S}, (d) *K*_{D}, (e) *L**, and (f) *Q**

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Maps of modeled radiation components across the Tekapo watershed for 12 Feb 1999: (a) *K*↓, (b) *K*↑, (c) *L**, and (d) *Q**

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Maps of modeled radiation components across the Tekapo watershed for 12 Feb 1999: (a) *K*↓, (b) *K*↑, (c) *L**, and (d) *Q**

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Maps of modeled radiation components across the Tekapo watershed for 12 Feb 1999: (a) *K*↓, (b) *K*↑, (c) *L**, and (d) *Q**

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Diurnal plots of spatial mean and standard deviation of (a) *K*↓, (b) *L**, and (c) *Q** modeled for the Tekapo watershed, 12 Feb 1999

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Diurnal plots of spatial mean and standard deviation of (a) *K*↓, (b) *L**, and (c) *Q** modeled for the Tekapo watershed, 12 Feb 1999

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Diurnal plots of spatial mean and standard deviation of (a) *K*↓, (b) *L**, and (c) *Q** modeled for the Tekapo watershed, 12 Feb 1999

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Modeled diurnal-mean direct-beam *K*↓ for a single grid point in the Tekapo watershed for 12 Feb 1999, showing sensitivity to both slope angle and aspect

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Modeled diurnal-mean direct-beam *K*↓ for a single grid point in the Tekapo watershed for 12 Feb 1999, showing sensitivity to both slope angle and aspect

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Modeled diurnal-mean direct-beam *K*↓ for a single grid point in the Tekapo watershed for 12 Feb 1999, showing sensitivity to both slope angle and aspect

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Series of maps showing modeled terrain shadows in the Tekapo watershed for 0600, 0900, 1200, 1500, and 1800 local apparent time 12 Feb 1999

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Series of maps showing modeled terrain shadows in the Tekapo watershed for 0600, 0900, 1200, 1500, and 1800 local apparent time 12 Feb 1999

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Series of maps showing modeled terrain shadows in the Tekapo watershed for 0600, 0900, 1200, 1500, and 1800 local apparent time 12 Feb 1999

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Diurnal plots comparing modeled hourly (a) spatial average and (b) spatial standard deviation of *Q** for three watershed subareas on 12 Feb 1999

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Diurnal plots comparing modeled hourly (a) spatial average and (b) spatial standard deviation of *Q** for three watershed subareas on 12 Feb 1999

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Diurnal plots comparing modeled hourly (a) spatial average and (b) spatial standard deviation of *Q** for three watershed subareas on 12 Feb 1999

Citation: Journal of Applied Meteorology 42, 1; 10.1175/1520-0450(2003)042<0113:SVOSRF>2.0.CO;2

Details of observational stations and data used either for initializing or validating simulations

Daylight mean albedo _{α} for five surfaces, and potential error of *K*↑ associated with variabiltiy of solar incident angle, found by multiplying σ_{α} by spatial average *K*↓

Descriptive statistics of the relationship between observed and modeled radiation fluxes from the combined datasets of A1, A4, and A8 on 1 Feb 1999 and A1, A3, and A8 on 12 Feb 1999

The reduction of *K*↓ associated with shading in the Tekapo watershed for 12 Feb 1999. Times are local apparent time

Descriptive spatial statistics [listed as mean (std dev)] for topographical properties and daily average radiative fluxes in three Tekapo watershed subareas