Limitations of BSDF and DSHGC approaches

3.3.1. Spectral accuracy

The most severe limitation that BSDF-based approaches share is probably the spectral simplification on which the methods are based. The values forming the Klems matrix are based on integrated spectral properties considering different bands, such as the global radiation spectrum or the visible light spectrum. In his work of 1994, Klems (1994b) himself already pointed out that the BSDF approaches focus on the ‘spatial and angular aspects of systems rather than the spectral properties’. He even showed in the paper’s appendix that his approach only works if the spectral selectivity is restricted to one layer at most. All other system layers have to be considered spectrally flat, i.e. having the same reflectance or transmittance value over the entire considered spectral range. Klems notes explicitly:
As the method is applied to progressively more complicated systems, such as colored blinds or shades combined with tinted or selective glazing, or multiple blind or curtain systems of different colors, the treatment could become less accurate and eventually inapplicable. (Klems, 1994b, p.4)
Excluding rare special photonic applications that are able to perform wavelength conversion, generally, the wavelength of the incidence radiation will not change while propagating through the fenestration system, meaning that the initial spectral components will be absorbed, transmitted or reflected but not absorbed and reemitted with a different wavelength. Hence, the Klems approach can be multiplied into a series of independent, parallel calculations limited to appropriate spectral bands. However, this increases the complexity of the method significantly, and it is difficult or almost impossible to define an “all-purpose” segmentation of the global radiation spectrum that would be suitable for most applications. Internally, LBNL Window can use 15 different bands (17 wavelength points) to cover the global radiation spectrum. However, the approach is not fully implemented as the BSDF information of the shading device is not available in this format. The raytracing tool Radiance used to compute the BSDFs of shading uses only integrated values. Therefore, depending on the input data, either only the solar (=entire global radiation) or only the visible spectrum is usually considered in an integrated way. This separation into visible and solar radiation is also frequently found in standard building performance simulation tools. However, for energetic purposes, the use of such integrated values has to be questioned. Considering the entire radiation spectrum from ultraviolet to near-infrared, the assumption of ‘flat’ reflectance is not suitable, as even objects that appear white, grey, black or clear (transparent) in the visible light spectrum will usually be spectrally selective in the non-visible ranges. Hence, using the BSDF information of independent components to determine the properties of the entire system may imply a significant systematic error.

3.3.2. Spatial averaging

Generally, all currently applied methods are based on the Klems approach that captures angularly resolved information on the reflected or transmitted radiation but does not include any information regarding its spatial (i.e. locational) distribution. Therefore, the approach is intrinsically based on the assumption that each layer represented by BSDF information is homogeneous and infinitely extended. Consequently, the impact on any other layer caused by an inhomogeneously structured layer or geometric boundary effects cannot be modelled with this approach. Boundary effects are State-of-the-art analysis RadiCal, D. Rüdisser 23 generally relevant for virtually every glazing, as the glazing is either embedded in a window reveal or interrupted by framing structures. The significance of the boundary effect will, of course, decrease when the undisturbed area is large relative to its boundary.
The effect of the inhomogeneity of a layer is relevant in combination with boundary effects or any further inhomogeneous layer. Klems notes that the effect can be neglected as, typically, there will be no relevant spatial correlation between any two layers. This is true for small-scale structures, like fabric, grids or, to some extent, Venetian blinds. However, this will generally not be the case for devices with large-scale structures in the dimension of the glazing. Typical examples are horizontal louvres or overhangs mounted on top of a window, but also glazings or films with fritted or printed structures. More generally, it can be said that the effect is significant for all systems where the device’s actual positioning relative to the glazing or any layer with structures of the same dimensions is relevant. Very apparent examples are provided by kinetic shading mechanisms where fritted or coated structures can be moved relative to each other to change the system’s solar transmittance, e.g. of modern foil constructions (Flor et al., 2018). While the layerwise BSDF-based modelling would entirely break down for such applications, it can also lead to significant errors for more classical applications comprising large structures. This is the case for many vertically and horizontally oriented systems, as well as for fixed and movable devices, such as louvres, overhangs, hinged shading systems, canopies, fins, brise-soleis etc. In most of these applications, the spatial concentration of light shading or diffusing effects to specific regions is not an unintended or marginal side-effect but the actual intended effect. The geometric properties are usually specifically designed to exploit such behaviour. Therefore, it is essential that any methods used in the design or performance assessment process for such systems can capture such effects accurately.

3.3.3. Polarisation

At present, all commonly used methods for modelling fenestration systems that include shading devices do not consider the change of the polarisation state of the transmitted or reflected light beam. On the one hand, the ISO standard methods (see section 3.4) exclude polarisation by definition, as they are restricted to near-normal incidence. In the case of near-normal incidence, polarisation effects are irrelevant. On the other hand, the BSDF methods, which were specifically developed to model transmittance and reflectance at oblique angles, implicitly assume that the provided coefficients are valid for the intensity (or flux density) of light beams with a neutral polarisation state. This neutral state can only be assumed (to some extent) for the radiation incident on the first layer. After the first scattering process, regardless of whether transmission or reflection, any ray with an oblique incidence angle will show a significant polarisation that will affect the outcome of any further scattering process (see sections 4.2.4 and 4.7).

3.3.4. Angular dependence

As discussed, the angular dependence of the transmittance and reflectance are derived based on simplified models. In fact, the angular dependencies, in turn, depend on the wavelength of the incidence light. While the effect is limited in the visible spectral range for bulk materials, there is still a State-of-the-art analysis RadiCal, D. Rüdisser 24 significant variation if the entire global radiation spectrum ranging from 300 nm to 2500 nm is considered. Furthermore, the effect is particularly pronounced if coatings are present, as spectral filtering is the designed function of these layers. Apart from these intended effects, exploited, e.g. for anti-reflective coatings, solar-protection coatings or low-E coatings, there can also be unintended effects that can, for example, lead to a colouring effect if coated materials are viewed at higher angles. All mentioned angular effects cannot be modelled appropriately based on simplified models. Valid results can only be achieved by solving Fresnel equations in a spectrally resolved way and by using the materials’ accurate spectral properties.

3.3.5. Modelling of direct solar radiation

Another issue that is linked to the usually limited angular resolution of the Klems-matrix is the modelling of direct solar radiation. In the commonly applied 3-phase method, the contribution of direct radiation is included in the angular patch corresponding to the sun’s incidence direction. This is also true for the outgoing Klems patch if the system does not diffuse the direct beam. Hence, on a clear day, the sun’s radiance value is reduced by several orders of magnitude and instead distributed on a Klems patch covering a relatively large solid angle (see Figure 6 and Figure 75). As this averaging does not represent the true angular extent and radiance of direct solar radiation, it will cause significant inaccuracies if further BSDF layers are considered. This is especially true for the inhomogeneous structures discussed in the Spatial averaging section above.

3.3.6. Energetic model

The underlying thermal model of the two-layer method (Bueno et al., 2017) and previous DSHGC approaches are based on necessary simplifications. The thermal model does not consider the layered structure of the glazing itself, which appears essential as modern tripled-glazed units show high thermal resistance values that will cause significant temperature differences among the individual glass panes. On the one hand, the temperature deltas will directly affect the energy balance model applied in the approach. On the other hand, it will have a secondary effect, as the absolute and relative temperature changes will significantly impact the gas layers’ thermal conductivities. Beyond this issue, the choice of the constant thermal conductivity parameters 𝐺𝑖 that determine the additional heat flow from the two layers to the interior seems somewhat arbitrary. The recommended values are likely to have empirical origins, but no further explanations, options or models for adaption to different fenestration systems or climates are provided. Apart from these issues, assuming stationary thermal properties by applying constant thermal transmittance (U-value) to characterise the glazing system seems problematic. Though some fitting formulas to adjust the U-value for different boundary conditions (climates) are presented, these relations will usually strongly depend on the actual layering of the glazing systems and actual thermal boundary conditions. Hence, it is difficult to propose a generalised approach. All methods providing DSHGC values have to anticipate results and boundary conditions of the dynamic thermal simulations to which they will be applied. This constitutes a circular reference that can only be addressed with the assumption of constant standard values.
The integration of BSDFs created with LBNL Window (or otherwise) into EnergyPlus, referred to as 3-phase method, allows layer-wise energetic modelling similar to the method proposed here. However, the approach suffers from the BSDF-related issues discussed above, especially for fenestration systems containing shading layers.