SOLWEIG 1.0 – Modelling spatial variations of 3D radiant fluxes and ...

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702 Int J Biometeorol (2008) 52:697–713 estimated. This was especially evident in the mornings and evenings throughout the annual cycle and was particularly pronounced during the winter season. The underestimation was shown to be as much as 50% during the very first and very last hour of daylight. Thus a relationship was established between CI during clear days and the altitude of the sun. Clear days were objectively selected by fitting a dome-shaped polynomial of the second degree with a determination coefficient (R 2 ) greater than 0.98. The entire dataset (1986–2005) obtained from the SMHI station was used. A total of 96 days was derived from the dataset. The logarithmic relationship in Fig. 4 was then used as a correction factor for the clear-sky solar irradiance: CIcorr ¼ CI þ ð1ð0:15 ln h þ 0:35ÞÞ ð15Þ Model domain and data Göteborg (57°42′N, 11°58′E) is situated on the west coast of Sweden in an aligned joint valley landscape. The city is the second largest city in the country, with nearly 500,000 inhabitants. The model domain covers an area measuring 1400×1400 m in the central part of the city as shown in Fig. 1. This central area has a classical European design, consisting of three to five-storey buildings, narrow street canyons and canals. The mean building height is 16.5 m, with a standard deviation of 6.0 m. Two low hills are found within the model’s domain. The DEM consists of both ground topography within the study area that ranges from 0 to 35 m a.s.l. and building structures that range from 1 to 100 m a.s.l. The DEM is derived from local governmental digital data according to a method presented by Lindberg Fig. 4 Clearness index versus sun elevation on 96 clear days between 1986 and 2005 in Göteborg, Sweden (2005) and the spatial resolution is 1 m. Trees and bushes are not included in the current DEM (Fig. 1). The input data used in the SOLWEIG model were collected hourly and consisted of direct, diffuse and global shortwave radiation obtained from a nearby weather station (1 km west of the study area). The station is run by the SMHI. The air temperature and relative humidity were taken from the same weather station. The available data were collected between 1986 and 2005. The same dataset was used as parameterisation data for cloudiness calculations. The T s data used to parameterise daytime variations of surface temperatures during clear daytime weather conditions were acquired at Site 1 on 13 occasions using a handheld IR instrument (AMiR 7811–20). The surface material at Site 1 is very homogenous consisting of large cobblestones. For model validation, data from integral radiation measurements within the model domain was used. In total, measurements taken over seven days from sunrise to sunset were compared with the results obtained from the model. Three net radiometers (Kipp & Zonen, CNR 1) were mounted on a steel stand in order to measure the threedimensional radiation fields. Shortwave and longwave radiation fluxes from the four cardinal points, as well as those from the upper and lower hemisphere were measured. The instruments had an offset of approximately 20° from the north and were instead positioned perpendicular to the surrounding building walls (Thorsson et al 2006, 2007). Two locations were used, one large open square (Site 1) with a y of 0.95 and a smaller courtyard (Site 2), y =0.65, as shown in Fig. 5. Both sites have cobblestone surfaces and almost no vegetation present. Results In this section, 4 days of measurements covering different weather conditions, locations and the time of year are compared with the results from model results in detail. One clear autumn day, one clear summer day and one semicloudy day at Site 1 are presented, together with one clear autumn day at Site 2. Corrections for clear-sky calculations at high sun zenith angles are also presented. Finally, the overall model performance and spatial variations of modelled Tmrt are shown. Radiation fluxes on clear days Clear summer day at a large square (SITE 1) Figure 6a–c show modelled and measured radiation fluxes and T mrt at Site 1 on 26 July 2006 between sunrise and sunset. This was a clear summer day with large variations
Int J Biometeorol (2008) 52:697–713 703 Fig. 5 The two locations where integral radiation measurements were conducted are marked. A Square (Site 1) and B courtyard (Site 2) of both short and longwave radiation fluxes at different times of the day. In general, the modelled values of both shortwave and longwave fluxes were at the same levels as measured values, except for a few special occasions (Fig. 6a,b). Kwest is underestimated at 1900 hours LST by 250 Wm −2 and all longwave fluxes are underestimated during the morning and evening hours by up to 50 Wm −2 . Ldown during the morning hours (0500–0700 hours LST) is underestimated due to fog. The underestimation of shortwave radiation at 1900 hours LST is due to the hourly time resolution and is further discussed in “Discussion: The temporal resolution”. On average, the difference between modelled and measured values of Tmrt on a clear summer day at Site 1 is 2.3 K. The Tmrt values are underestimated during the first 2 h after sunrise (approximately 5 K) as well as during the last 2 h before sunset (approximately 7 K) (Fig. 6c). Clear autumn day at a large square (Site 1) Figure 7a–c shows modelled and measured radiation fluxes and Tmrt at Site 1 on 11 October 2005 between sunrise and sunset. This was also a clear day, but during the autumn season, with higher sun zenith angles and a shorter daytime period. In general, the model simulates all six shortwave radiation fluxes well (Fig. 7a). Modelled values of K south show a slight underestimation by up to 30 Wm −2 , especially during midday. The largest overestimation of any of the shortwave fluxes is found for the K west component (142 Wm −2 ) at 1600 hours LST (Fig. 7a), due to the time resolution. The differences in the six longwave fluxes are relatively small (Fig. 7b). The modelled longwave fluxes from the four cardinal points give underestimated values during morning and evening hours by up to 10 Wm −2 , and the upward component is overestimated during lunch hours by 10 Wm −2 . The model performance of Tmrt on a clear autumn day at Site 1 shows that the difference between modelled and measured values is 1.7 K (Fig. 7c), on average. The largest differences between modelled and measured values (3.5 K) are found during the first 2 h of the day. Clear autumn day at a small courtyard (Site 2) Figure 8a–c shows modelled and measured radiation fluxes and Tmrt at Site 2 on 7 October 2005 between sunrise and sunset. The measurement point (instrumentation) was in shade all day, except for 2 h in the afternoon (1500 and 1600 hours LST). When the measurement point was shaded, the shortwave radiation fluxes were in agreement with modelled values. However, during the 2 h with direct shortwave radiation evident, the model overestimates all the components which are exposed to direct shortwave radiation (Kwest, Ksouth and K↓) by as much as 200 Wm −2 (Fig. 8a). The longwave fluxes are more complex in an environment with higher y. Since the SOLWEIG-model utilises non-directional calculations of the longwave fluxes from the four cardinal points, it is not able to capture the high measured values of L north (Fig. 8b). The modelled values of Lup are overestimated by 10–15 Wm −2 when the validation pixel is in shadow and by 25 Wm −2 when the validation point is exposed to direct sunlight. T mrt at Site 2 is overestimated by an average of 6.5 K throughout the day. During the two sun-exposed hours at 1500 and 1600 hours LST, T mrt is overestimated by as much as 17 K (Fig. 8c). Radiation fluxes on a semi-cloudy day Figure 9a–c shows modelled and measured radiation fluxes and Tmrt at Site 1 on 1 August 2006 between sunrise and sunset. This was the measurement day with the highest variability due to cloudiness of all the days included in the validation data. It was characterised by occasional cloudiness up to 1600 hours LST, when a fully cloud-covered sky became evident. A light drizzle of rain occurred between 1700 and 1800 hours LST, which explains the missing data at 1700 hours LST in Fig. 9c. The SOLWEIG model appears to estimate both shortwave and longwave radiation fluxes reasonably well, except for a few hours (0700, 0800, 1200–1400 hours LST) at which the shortwave fluxes were incorrectly calculated (Fig. 9a) due to variations of cloudiness between Site 1 and the weather station located 1 km west of Site 1. However, the overall model
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