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

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710 Int J Biometeorol (2008) 52:697–713 Fig. 12 Spatial variations of T mrt (°C) in the city centre of Göteborg, Sweden at 1500 hours LST on 11 October 2005. The spatial resolution is 1 m. The letters a through f are points of interest referred to in the text Shortwave radiation fluxes The shortwave fluxes are relatively easy to estimate, since actual values of shortwave radiation are used as input in SOLWEIG. However, some features of the shortwave fluxes should be discussed. Firstly, the reflection term in Eq. 3 is a simplification and some differences between modelled and measured shortwave fluxes could therefore arise. This is most obvious for the southerly component of shortwave radiation (asseeninFigs.7a and10). Since the instruments were situated at a measuring height of 1.1 m – the centre of gravity for a standing person – and therefore reflection from ground surfaces was present, the shortwave fluxes for all the sidefacing instruments were influenced. In particular, modelled values of K south turned out to be lower than measured values. Secondly, all three components of shortwave radiation (diffuse, direct and global) are required as input in the model. It could sometimes be difficult to obtain such data from a nearby weather station. However, there are many existing methods for the calculation of shortwave radiation fluxes which could be used instead of actual measured values (e.g. Olseth and Skartveit 1993; Roderick 1999; Gueymard 2000). Longwave radiation fluxes The process of estimating longwave fluxes is much more complicated than is the case for shortwave fluxes. None of the longwave fluxes is measured directly and used as input data in the model. Instead they are estimated based on other meteorological parameters and empirical constants. The model developed by Jonsson et al. (2006) estimates the downward fluxes of longwave radiation reasonably well, after the modelled values have been reduced by 25 Wm −2 . The reason for the general overestimation of L↓ when using the empirical relationship set up by Prata (1996) is unknown. However, this aspect is shown by both Jonsson et al. (2006) and Duarte et al. (2006). L↑ is calculated based on the value of Ta and the relationship is derived from the linear relationship between the solar elevation and the maximum difference between the ground surface and air temperatures on clear days (Fig. 2). The daily temperature wave follows a sinusoidal path, where the amplitude is taken from Fig. 2 and the period is twice the length of time between sunrise and 1400 hours LST, which is the peak of the surface temperature wave. There are a few uncertain variables in the calculation of Ts. The initial value of Ts at sunrise is unknown and set at −3.4 K lower than Ta. This is based on the difference between T s and T a at a sun elevation of zero degrees (Eq. 12). This initial value appears to be underestimated, especially during clear weather conditions with intensive radiative cooling during the night (e.g. Figs. 6b and 7b). The relationship in Fig. 2 is established from data measured at Site 1. In reality, however, this figure should vary depending on the material, slope and aspect of
Int J Biometeorol (2008) 52:697–713 711 the surface of interest. The same relationship is also giving a small underestimation of L ↑ during a clear day in July at Site 1 (Fig. 6b) and a small overestimation of L↑ during a clear day in October at Site 1 (Fig. 7b). More parameterised data should be included in Fig. 2 in order to obtain a better estimation of L↑. Further, in the current version Ts is set equal to Ta in shaded areas. This will underestimate Ts. However, the effect will be reduced since shaded areas are often in dense urban environments where nocturnal cooling is reduced due to low values of y . According to Ali-Toudert (2005), a standing body absorbs more than 70% of the energy in the form of longwave irradiance in the daytime, which demonstrates the importance of accurate longwave radiation simulations/ measurements for the estimations of Tmrt. This is especially important in complex urban settings where emitted longwave radiation from the surrounding walls represents a large part of the human energy balance. When no direct shortwave radiation is evident, the longwave fluxes become even more important for a correct estimation of Tmrt. The general overestimation of Tmrt at SITE 2 could be explained by an overestimation of the longwave radiation fluxes from south, east, west and up at the more dense urban location (Fig. 8b). The main reason why SOLWEIG 1.0 overestimates longwave radiation at SITE 2 is because of the properties depicted in Eq. 13e. Although the distance from a specific pixel and the average distance to the building walls diminishes, L →GROUND remains the same. In reality, as a building wall is approached, the ground surface area decreases in the direction of the approached wall. At present, this is the main setback in SOLWEIG 1.0 and should be improved in subsequent versions of the model (see “Conclusions and future prospects”). Another reason why large discrepancies are found at Site 2 could be that the modelled value of y is too high. High trees rise above the roofs of buildings to the west and block parts of the visible sky. If vegetation were included as an additional set of information then y would probably be lower at Site 2. The absence of vegetation is therefore another drawback of the current model, which will affect T mrt when present. Apart from the trees mentioned above, almost no vegetation is found at the two validation sites used in this study. In addition, the air mass between the pixel of interest and the building’s walls are not considered, which could influence the longwave fluxes from the four cardinal points. Nevertheless, this effect is considered to be minimal. The temporal resolution In general, the performance of the model at SITE 1 (SVF= 0.95) is very good, with some exceptions (Figs. 6, 7 and 9). The largest discrepancies of T mrt are found at late afternoons and early evenings and are mainly due to large differences between the modelled and measured values of shortwave radiation fluxes. This is mainly because of the temporal resolution of the meteorological input data. Since just one image of shadow patterns represents a 60-min period in SOLWEIG 1.0, a pixel is either in the shade or exposed to the sun for a full hour, which might not be the case in reality. The shadow pattern is generated in the middle of each hour. In reality, a location could be in the shade during the first 40 min of an hour and then exposed to sunlight during the remaining 20 min. The SOLWEIG model calculates this location as if it were in the shade for the entire hour, even if that is not the case. This may result in underestimations or overestimations of the shortwave radiation fluxes and consequently of T mrt if a location is moving either out of, or into, the shade (e.g. Fig. 6a at 1900 hours LST and Fig. 8a at 1500 and 1600 hours LST). For very complex urban structures, this issue could result in large discrepancies throughout the daily cycle if a location of interest is constantly moving in and out of the shade. There is a quite simple solution to this problem, which is not included in the current version of the SOLWEIG model. Generating several images of shadow patterns for each hour (e.g. each 15 min) would include information about the amount of time a pixel is in the shade during a specific hour; this information could then be used to arrive at better estimations of the radiation fluxes for each specific hour. This, however, will complicate the modelling and increase the computation time for each model run, since more images of shadow patterns must be generated. Model sensitivity A number of parameterisation parameters in the SOLWEIG 1.0 model are only established from published material and it is necessary to understand the model’s sensitivity if these parameters are altered. Examples of these input parameters are the surface albedo, emissivity of walls and ground, accuracy and precision of the DEM used and the calculation of the position of the sun. The albedo was originally set to 0.15 and ground and wall emissivity to 0.95 and 0.90, respectively, according to Oke (1987). A small sensitivity test was carried out on Site 1 on 11 October 2005, during which some of these parameters were altered. When the albedo was increased from 0.15 to 0.20, Tmrt increased by 0.2°C and the total shortwave radiation flux increased by 20.4 Wm −2 during midday. When ground emissivity was increased from 0.95 to 0.98, Tmrt increased by 0.9°C and the total shortwave radiation flux increased by 51.4 Wm −2 . Consequently, these parameters have a limited effect on the estimation of Tmrt in the SOLWEIG 1.0 model. The overall performance of the fluxes shown in Fig. 10 is relatively good. The higher RMSE values found in the lateral shortwave fluxes due to the effect of the temporal
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