Daylight Diagram – A Method to Map and Analyse the Temporal Conditions of Daylight Intensity

This study proposes and examines a new method and diagram for revealing and analysing temporal and transitional daylight conditions based on computational modelling and simulations. For a human to experience and decipher the world, daylight is a predominant resource to engage with the surroundings. With humans spending the prevalent time inside buildings, it is important to understand and design the daylight environments in the early phases of design processes. The aim is to retain and reveal the information of high-resolution simulations and to explore, test and verify the capacities of the method in comparison to Illuminance, Daylight Factor and Daylight Autonomy values. The research design uses digital modelling and representation techniques combined with computational simulation methods for daylight analysis, evaluation and communication. Eight digital test cases show that the proposed Daylight Diagram enables the observation of temporal daylight dynamics. The proposed method and diagram employ existing simulation systems, allowing a fast integration and use in early-phase design processes as a key instrument to design advanced daylight phenomena and conditions focusing on transitional and temporal daylight intensities.


Introduction
Daylight is central to human existence.For a human to experience and decipher the world, daylight is the predominant resource to engage with the surroundings.As humans spend the prevalent time inside buildings, with Western populations reaching 90% occupancy indoors [1,2], it is important to understand and design the built environment with daylight in the early phases of design.With the advancements in computing power and methods, simulations have become a potent investigation and design approach to analyse and predict daylight conditions inside buildings.The rise of paired digital modelling and simulation processes over the last two decades has provided architects, designers and engineers with new instruments to explore and create design propositions [3][4][5][6].While computational methods have increased in diversity, speed and accuracy, national and international standards and industry certification systems appear to maintain an 'on-principle-level' or 'low-resolution' approach to daylighting analysis and design.Building Research Establishment Environmental Assessment Methodology (BREEAM) states that at least 80% of the floor area in occupied spaces has an average daylight factor of 2% [7].Deutsche Gesellshaft für nachhaltiges Bauen (DGNB) states that 50% of the 1320 (2024) 012005 IOP Publishing doi:10.1088/1755-1315/1320/1/012005 2 usable area throughout a building has a Daylight Factor (> 3% very good, >2% medium, >1% slight, < 1% none) [8].Leadership in Energy and Environmental Design (LEED) states that Daylight Illuminance levels should be minimum 270 Lux and maximum 5400 Lux in clear sky conditions on September 21 at 9 a.m and 3 a.m.[9].The Danish and European building code (DS/EN 17037) criteria for daylight provision is that a space is considered to provide adequate daylight illuminance if a target illuminance level is achieved across a fraction of the reference plane within a space for at least half of the daylit hours [10,11].This is a bit convoluted, but the typical target illuminance level is 300 Lux, the reference plane's fraction is 50% of the space, and half of the daylit hours is 50% of the occupancy time of the space.The recommendation and relations are captured in the Daylight Autonomy (DLA) calculation method, which again is promoted by the Illuminating Engineering Society of North America [12] to evaluate the daylight quality of spaces.Due to the relative complexity of the DLA calculation method, computational simulation methods are used for this process.A simpler method, adopted from manual measurements, is the Daylight Factor (DF) method [13] which calculates the indoor light level in relation to the outdoor light level, providing a percentage of the outdoor available light.Due to the simplicity of the factors and model, the Daylight Factor is often found in industry guides [14], where an average DF > 2% is considered daylit.In contrast, an average DF > 5% is strongly daylit.
The challenge with all these evaluation and benchmark numbers is that they do not identify, represent, or communicate the temporal and dynamic conditions of daylight in a space over time.If a space has an average (annual) DF = 3%, it could lack daylight in winter and be prone to glare conditions in summer.The same problem could be caused during a singular day, as the solar vector and sky conditions (clear, haze, cloudy) change significantly across 24 hours.In a similar concern, a DLA > 50% could present suitable conditions in the morning and the afternoon, not during midday.While the state-of-the-art simulations calculate across the year, hourly, the resulting output, scores and representation of the daylight environment are reduced to singular numbers that do not reveal the dynamics of the specific daylight conditions and temporal conditions related to design and context.
The previous solutions for simulating, representing and decoding temporal daylight conditions are based on false colour rendering, applying a gradient colour map, where the distribution of daylight is shown on the reference plane, figure 1.This method works well to show the spatial distribution of daylight, where numbers and colours typically are based on an annual average value.Most simulation methods allow the specification of singular hours (or even sub-hour intervals) or specified periods of the year, such as Summer, Winter, October, week 42 etc.Other recent mapping methods show the percentage of time, or hours, on each simulation node (colour mesh field) to indicate the prevalence of the daylight value [15].While this adds an understanding of time into the map, it does not show or analyse the temporal and dynamic conditions of daylight hourly, daily and annually.
The potential for new methodological solutions is to include multiple time domains in one diagram, thereby creating a representation of the daylight simulation procedure, which retains and reveals detailed daylight intensity for every hour of the year.In acoustics, sound energy is always mapped in relation to octave bands (frequencies), as the spreading of sound waves is dependent on the wavelength [16].An expanded mapping of this relation includes time, with the three axes including sound energy, frequency and time.Together this forms the FFT Waterfall Diagram, that allows advanced analysis of temporal acoustic conditions.In daylight studies, wave frequency is typically not in focus, which allows two time domains to be plotted together with daylight intensity, creating the potential of a three-dimensional diagram, which shows the temporal conditions of daylight across every hour of a whole year.
This study attempts to construct a new Daylight Diagram, which retains and reveals the information of high-resolution simulations, and to explore, test and verify the capacities of the method in comparison to Illuminance, Daylight Factor and Daylight Autonomy values.The Daylight Diagram is intended as a complementary method to daylight analysis, and design focused on temporal daylight intensity conditions.
The paper presents the idea and inspiration for the Daylight Diagram, the computational methods used to construct and evaluate the proposed method, experimental studies based on parametric modelling and simulation processes, and results description based on a comparative analysis between what the Daylight Diagram shows in difference to Daylight Factor and Daylight Autonomy values and associated colour mappings.A discussion of the methods and results is then included providing the basis for a brief conclusion to the study and its contributions.

Methods
The research design uses digital modelling and representation techniques combined with computational simulation methods for daylight analysis, evaluation and communication.Results from the simulation studies are compared to daylight standards and as a comparative analysis between the experiments within this study.

Design Computation and Simulation Studies
Digital design models for testing the proposed Daylight Diagram are created in two case groups of A) generic rectangular space geometries with generic apertures (window geometries) and no ground and context conditions, and B) bespoke space geometries with varied apertures (window geometries) and no ground and context conditions.For each of the two groups, four space-aperture variations are created, figure 2. In group A) the space geometry has dimensions 8x5x3 meters.Apertures are positioned in the space to examine an East/West facing composition, an East facing composition, a North facing composition, a South facing composition.The size of the apertures in each of the four test compositions is defined by gradually modifying the opening area to reach 4% Daylight Factor of each test space, figure 1.The generic rectangular geometries study aims to understand and explore the temporal daylight variance between the test space when the Daylight Factor is constant.In study group B), four bespoke test spaces and apertures, figure 1 and 2, are defined by varied plan geometries while maintaining the 40m2 footage of the rectangular test spaces in study A).Apertures are positioned with similar orientations to study A).Alike to study A) apertures are modified gradually, albeit to reach 2% Daylight Factor, then observe and analyse the temporal daylight conditions exposed in the Daylight Diagram.The decreased DF factor, compared to study A, is chosen experimentally to reach a better comparative analysis between B cases.

Figure 2. Eight digital models in two groups, each with three simulation processes for Illuminance (left), Daylight Autonomy (center) and Daylight Factor (right) in each test case.
The Daylight Diagram is based on the idea of revealing the temporal daylight conditions by mapping hourly light intensity in relation to the time domains of a day (24 hours) and a year (365 days).Time domains are mapped on the x-axis and y-axis, hours and days, respectively, and light intensity on the zaxis.The correlation between time (every hour of the year) and light intensity creates a cloud of points in the diagram.To make light intensities and their temporal and transitional properties eligible, a line is drawn from point to point in the x-axis, creating a wave-form that can be understood and analysed by the investigator/designer, figure 3.As mentioned, this method is inspired by the FFT Waterfall diagrammatic method from acoustics, where sound energy is mapped in relation to time and frequency domains.The resulting curves provide the possibility to analyse the diagram three-dimensionally.Two threshold values can be added to the diagram, providing lower and upper light intensity (Lux) limits.This can be dynamically set and has been fixed to 300 Lx (lower limit) and 2000 Lx (upper limit) in these studies.The Daylight Diagram is based on simulated hourly data for an entire year.The dataset is in this study based on a climate-based point-grid simulation procedure, using the Rhinoceros-Grasshopper-Ladybug software framework, which utilizes the Radiance simulation engine [17] and Energy-Plus weather data [18].The weather data used for the studies are for Copenhagen, Denmark.The computational model schematic structure includes, 1) geometric/material models of test spaces/materials, 2) weather data, 3) simulation model properties (test point-grid, sky conditions etc.) 4) daylight analysis procedure (Illuminance, Daylight Factor, Daylight Autonomy), 5) Colour mapping of analysis procedures inside test space and 6) Daylight Diagram, figure 4.

Results
The test spaces of the A case experiments are all the same, simple in form and apertures.The apertures of each space are modified for the average DF to be 4% (+/-0.1%).While the DF remains the same, the Daylight Diagram reveals large variances across the year and day between the cases.The DF alone would in such cases be both misleading and non-informative.The difference between case A3 and A4 are striking, just as the difference between A1 and A2 have distinctively different daylight conditions across the day.The characteristics of each test space and apertures are clearly revealed in the diagram, showing, e.g.high afternoon/eve intensity of A2 and morning/afternoon intensity of A1.

Figure 5. Four A test case based on a simple, rectangular 40m2 test space with varying apertures, all with DF = 4%, yet with highly varied temporal daylight intensities between the test cases.
Similar results are found for the B test cases, where the apertures of the different test space geometries are modified to DF = 2% (+/-0.1%).Not surprisingly, the temporal daylight intensities revealed in the Daylight Diagram reduced compared to the A test cases, but the variance is similar, despite the increased spatial complexity.While some standards propose that DF => 2% is sufficient in daylight level, the B3 case shows that only a limited period exceeds the 300 Lux threshold, as shown by the yellow mapping.In contrast, while limited to DF = 2% (+/-0.1%) the B4 test case experience significant glare around midday for large parts of the year, as shown by the white mapping.The contrast between the two daylight conditions and the temporal conditions of the light intensities could not have been identified through singular DF or DLA values.

Discussion
Daylight predictions in design processes using simulations are based on numerical models.The evaluation of daylight sufficiency and quality are largely based on these simulations, and they are today focused on delivering numbers that encapsulate the daylight condition of a space, by the use of a number, such as DF and DLA.While these are widely acknowledged and used, they do not reveal the temporal conditions of daylight intensities.However, we know this is how the real world is experienced.It does not allow daylight designers to investigate and propose advanced daylight phenomena and experiences based on temporal dynamics, where space, material, human, and environment can be explored and designed for bespoke and context-specific conditions.The proposed Daylight Diagram is a step towards retaining a higher fidelity of the computational simulations, providing new and expanded understandings of the light environment designed or to be designed.The Daylight Diagram should not be seen as a replacement for other methods, but as complementary, particularly with the spatial colour gradient mappings used in this study.
With the quality and quantity of daylight design directly impacting artificial lighting sources, a better understanding of daylight dynamics through the Daylight Diagram could be suggested to improve the conditions, analysis and design of alternative light sources.Such influence could lead to better management of electrical light sources for better light experiences and a reduction of the energy used for electrical light systems, thereby aiding design decision processes for sustainable architectures based on advanced daylight architectures.
Similarly, when developing the material composition of a project, it could be imagined that the Daylight Diagram would provide insights to support how surfaces increase/decrease reflected light energy in general and the solar vector in specific, providing a direct relationship between the dynamic path of the sun at a given location with the resulting daylight mapping.The knowledge of such analysis would support material choice which both increases light quality and the selection of sustainable materials supporting the daylight design intent.
Also, further advancements of the Daylight Diagram could include spatial information.Such inclusion may, however, blur the clarity of the proposed diagram and counteract the ability to observe and design from the current Daylight Diagram information.More research is required, potentially coupled with how such methods are used in practice and what that means for design decision-making.

Conclusion
The idea, basis and structure for a Daylight Diagram are proposed in this research with the aim of revealing temporal daylight intensities based on computational simulations.The test cases show that the proposed Daylight Diagram reveals temporal daylight dynamics that are difficult or potentially impossible with the current use of singular benchmark values and methods.The proposed method and diagram employ existing simulation routines, allowing a fast integration and use in early-phase design processes as a key instrument to design advanced daylight phenomena and conditions with a focus on transitional and temporal daylight intensities.It is argued that the Daylight Diagram may also inform better design decision processes for artificial lighting design and material development, as part of increasing the sustainable capacity of daylight design in the built environment.

Figure 1 .
Figure 1.Digital models based on generic and bespoke geometries are used as test cases for developing and evaluating the proposed Daylight Diagram and to demonstrate the capacities of the diagram to illustrate temporal conditions.
Values above the 300 Lx threshold are plotted in yellow on the diagram's xy-plane and values above 2000 Lx are plotted in white on the diagram's xy-plane.This technique attempts to create a direct reading of which hours a year the lux level exceeds the threshold of sufficient light and what hours a year may be problematic for glare conditions.

Figure 3 .
Figure 3.The anatomy of the proposed Daylight Diagram.The diagram is represented in a parallel projection but can be viewed and rotated as necessary within the 3D model for detailed qualitative analysis.

Figure 4 .
Figure 4. Schematic structure of the simulation model used for the study.For each experimental study, simulating the test spaces and apertures, Illuminance analysis, Daylight Autonomy analysis, Daylight Factor analysis and Daylight Diagram analysis are conducted.

Figure 6 .
Figure 6.Four B test cases with varied spatial compositions and apertures, but all with an average DF = 2%, show a high variance in temporal daylight conditions, particularly for the B1, B2 and B4 cases.