EVALUATING ANNUAL DAYLIGHTING PERFORMANCE THROUGH STATISTICAL ANALYSIS AND GRAPHS: THE DAYLIGHTING SCORECARD

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1 EVALUATING ANNUAL DAYLIGHTING PERFORMANCE THROUGH STATISTICAL ANALYSIS AND GRAPHS: THE DAYLIGHTING SCORECARD Benjamin Futrell, LEED AP Center for Integrated Building Design Research School of Architecture/College of Arts & Architecture University of North Carolina Charlotte 9201 University City Boulevard Charlotte, NC Dale Brentrup, AIA Center for Integrated Building Design Research School of Architecture/College of Arts & Architecture University of North Carolina Charlotte 9201 University City Boulevard Charlotte, NC ABSTRACT Architects, engineers, and lighting designers can now perform dynamic climate-based daylighting simulations, made possible by the development of related algorithms and software. These simulations output annual hourly, or sub-hourly, illuminance data for an array of calculation points. New metrics, based on this wealth of data, are being developed to describe location/climate dependent daylighting performance. These metrics are quickly replacing traditional static ones, e.g., the Daylight Factor (DF). One challenge they face is to capture the annual, or time-period based, performance of a daylit space. Existing dynamic climate-based metrics, such as Useful Daylight Illuminance (UDI) [1] and Daylight Autonomy (DA) [2], are very useful; however, these metrics neither communicate the magnitude of under/over illumination nor the distribution and spatial/temporal variance of annual illuminance levels of a daylit space, critical information for characterizing annual daylighting performance. This paper explores the use of a new method of evaluating annual daylighting performance that includes the use of a proposed Daylighting Scorecard (DS). Statistical analysis and graphing techniques are utilized to quickly communicate significant daylighting performance attributes of an analyzed space. The DS, along with other statically derived information, is used to efficiently and effectively compare the daylighting performance of many simulated design variants. In addition, the DS is shown to be useful when characterizing the performance of actual daylit spaces in which hourly illuminance data was logged. 1. INTRODUCTION Methods of daylighting performance evaluation continue to be advanced and developed in order to find solutions to daylighting design problems that are better than those that would have been found using traditional methods. Over the past century, the Daylight Factor (DF) - the percentage of exterior illuminance at a point inside a building typically measured under overcast sky conditions - has been the main measurement by which to evaluate daylighting performance. The DF has several reasons for its popularity: 1) it is simple and easy to understand; 2) it is easily measured/calculated, either by hand (using tools such as B.R.S. Daylight Factor Protractor and the Graphic Daylighting Design Method), by constructing scale models and taking physical measurements, or by computational modeling and simulation; 3) it facilitates straightforward comparisons between the performance of alternative designs. However, the DF - because it is based on a static generic sky model - does not capture critical information about location-specific daylighting performance, such as the spatial and temporal variation in daylight levels caused by local sky cover patterns and solar angles. Advances in the detail and accuracy of climate records, climate-based sky and sun models, daylighting simulation algorithms, and personal computing power have made possible dynamic (time-step) climate-based daylighting simulations. Based on the wealth of data generated by these simulations, more sophisticated performance evaluation methods than the DF have been/are being developed. Dynamic daylighting simulations (DDS) typically output hourly daylight illuminance values at calculation points uniformly arrayed across a daylit room at workplane height (typically 30 inches), in contrast to the DF which calculates a

2 single value per calculation point. This information is important because it captures, within time-step simulations, spatial variation in daylight levels between calculation points and, between time-step simulations, temporal variations of each calculation point. Two popular daylighting performance evaluation metrics, based on hourly daylight illuminance measurements, are Daylight Autonomy (DA) and Useful Daylight Illuminance (UDI). Both metrics are based on the percentage of occupied time that a calculation point s illuminance is within a desired range. For DA, this range is simply greater than a set minimum value, typically 30 or 50 fc. UDI places both a lower and upper constraint on the desired range, typically greater than or equal to 10 fc and less than or equal to 2000 fc. Like the DF, DA and UDI describe the daylighting performance of a calculation point with a single number, although the percentage of time outside of the desired range can also be calculated for DA and UDI. DA and UDI are significant improvements over the DF since they account for the local sky and sun conditions, room-specific lighting criteria, and time of occupancy of a daylighting design problem. With a single percentage, DA and UDI effectively and succinctly communicate the frequency at which appropriate illuminance levels are satisfied within a room on an annual basis. Likewise, the frequency of under and, with UDI, over illumination can also be expressed. However, DA and UDI do not express the general magnitude of over or under-illumination that occurs within a space on an annual basis. In addition, DA and UDI do not directly account for spatial and temporal variations of daylight illuminance levels. Along with the maintenance of appropriate daylight illuminance across time and space, spatial and temporal uniformities of daylight illuminance are also characteristics of a well daylight space. Measurements based on spatial and temporal variations are valuable for evaluating the daylighting performance of a particular space. Hourly illuminance values of calculation points of a space can be analyzed to determine the magnitude of these variations. This information becomes even more valuable when used to comparatively evaluate the daylighting performance of a population of many candidate design solutions whose creation is made possible by parametric modeling software. 2. NEW APPROACHES FOR DAYLIGHTING PERFORMANCE EVALUATION A method of evaluating annual daylighting performance that incorporates the assessment of temporal and spatial daylight illuminance variations has been developed and is described below. The method uses datasets of annual hourly illuminance values measured at workplane height during the occupied hours of the analyzed space. The calculation points are assumed to be uniformly distributed across the space at a fine enough resolution to accurately sample and represent the overall workplane daylight illuminance characteristics of the space. To measure spatial daylight variation, hourly sub-datasets are created that contain the daylight illuminance values of each calculation point for that hour. The standard deviation of each hourly sub-dataset is calculated and recorded. Each standard deviation value gives an indication of the spatial variation of daylight illuminance values for the hour it represents. The mean of all hourly standard deviation values is used as a measure of annual spatial daylight illuminance variation for a particular design solution. This measurement is referred to as Spatial Daylight Variation (SDV). To measure temporal daylight variation, a sub-dataset is created for each calculation point that contains all the hourly daylight illuminance measurements for that calculation point. The standard deviation of each calculation point sub-dataset is calculated and used as a measure of the temporal variation of daylight illuminance for that calculation point. The mean of all these standard deviation values is used as a measure of annual temporal daylight illuminance variation for a particular design solution. This measurement is referred to as Temporal Daylight Variation (TDV). To help identify design solutions with good annual daylight uniformity, (those with low SDV and TDV values), SDV and TDV values of particular designs are plotted on a graph (Fig. 2). These plots are also useful for understanding the range of SDV and TDV values associated with a large population candidate design solutions. SDV and TDV values are helpful for understanding the annual daylight illuminance uniformity of a design, but they do not indicate how frequently calculation point values are within an appropriate daylight illuminance range. To accomplish this, UDI, within a target illuminance range, is used. More specifically, UDI values are calculated at each calculation point and then averaged to get an overall Mean UDI value (MUDI). To help understand how particular design solutions perform relative to others (in terms of

3 appropriate daylight illuminance frequency and uniformity), each solution s MUDI is plotted against the mean of its SDV and TDV values (referred to as Overall Daylight Variation (ODV)). Fig. 3 shows the MUDI and ODV values of many candidate design solutions plotted on a graph. To help understand not only the frequency that daylight illuminance values occur in under, appropriately, and over illuminated ranges but also the magnitude of under and over illumination in a particular space, a specialized graph referred to as the Daylighting Scorecard (DS) was developed. Fig. 4, 5, and 6 are DSs for three different spaces. The DS is based on a frequency distribution plot of all annual hourly daylight illuminance measurements for a particular space. Under, appropriately, and over illuminated ranges are indicated by bold dashed lines on the graph. For example, Fig. 4 has bold lines at the 30 and 200 fc, indicating that these are the boundaries of the daylight illuminance ranges. Ideal daylight performance is conceptualized as all daylight illuminance values clustered within the desired illuminance range. The area of the frequency distribution bars (based on bins of 10 fc) in each illuminance range is representative of the frequency of daylight illuminance measurements within those ranges. A percentage value is placed below each daylight illuminance range that shows the percentage of daylight illuminance values within that range. Other information, not central to the focus of this paper, is shown on the DS, including a cumulative frequency curve, and the mean and standard deviation of the graph s daylight illuminance values. Traditionally, daylighting performance metrics have been graphically embedded into building design drawings (plans and sections) and 3D digital models. While this is very useful for visualizing how daylighting performance varies spatially, it does not facilitate the efficient comparison of many candidate design alternatives. The approach presented here intentionally avoids visually embedding daylighting performance data into building representations. By doing so, one can focus on the defined performance criteria. The standardized graphs used in this method allow for the daylighting performance of spaces of various size and shape to be compared directly. 3. CASE STUDY A case study based on the method described above is presented here. This case study has emerged from daylighting design questions raised during design assistance projects undertaken in the Daylighting + Energy Performance Laboratory (D+EPL), part of the Center for Integrated Building Design Research in the School of Architecture at UNC-Charlotte. The D+EPL partners with architectural firms and industrial manufacturers interested in conducting a detailed daylighting analysis of a design project or product. Typically, during these projects, design recommendations (such as the head-height of windows, type of glass, depth of exterior shading and interior lightshelves, etc.) are made by a process that begins with sizing elements based on experience and rules of thumb. The design is then refined through iterative modeling and simulation of daylighting performance. Iterative changes to a design are made, in part, by intuition. In retrospect, D+EPL researchers have wondered if better performing designs exist than those pursued. Simulations of design iterations are costly in terms of time, and often the rate of daylighting analysis cannot keep pace with the demands of the fast building design schedule. There is little time during the early phases of a building design project to invest in iterative daylighting simulation. After the initial Schematic Design and Design Development phases, little change to the building design can be made. A way of quickly identifying high-performing designs and understanding the magnitude of difference between their performance values and other candidate designs is needed. A simple south-facing room was chosen for analysis. Window head height, ceiling slope, exterior shade depth, interior lightshelf depth, and ceiling reflectance were chosen as design factors to investigate. To generate a population of 960 candidate design solutions to analyze, each design factor was varied from a low level to a high level. Each design solution is represented, or coded, by a unique combination of numbers that indicate the level each design factor is set to for that particular design solution. Table 1 shows the investigated design factors, their ranges, and their number of intermediate levels investigated. TABLE 1: DESIGN FACTORS Factor Range Levels Window Head Height (0-3) Ceiling Slope -5 to +5 3 (0-2) Exterior Shade Depth (0-3) Interior Lightshelf Depth (0-3) Ceiling Reflectance 60% - 90% 5 (0-4)

4 Fig. 1 shows renderings of selected design solutions labeled by their respective identity codes. Fig. 2 graphs the SDV and TDV values of each candidate design solution of the analyzed population. Each dot represents a single design. Fig. 2 shows that a wide range of SDV and TDV exist in the analyzed population. Distinct patterns are also apparent in Fig. 2: clusters of design solutions caused by similar influential designs factor settings and the diverging of these clusters (repeated four times) caused by changes in influential design factor settings. The letter a in Fig. 2 identifies a design solution with desirable (low) SDV and TDV values. Design solution a is also identified on Fig. 1. Fig. 3 graphs the MUDI and ODV values of each candidate design solution of the analyzed population, and shows that a wide range of MUDI and ODV values exist in the population. Distinct patterns, similar to those in Fig. 2, are also apparent in Fig. 3. Design solution a is identified in Fig. 3 and shown to have a poor MUDI value. Two design solutions ( b and c ) with desirable MUDI and ODV values are identified in Fig. 3. Design solutions b and c are also identified in Fig. 1 and Fig. 2. c b a b c Fig. 3: MUDI and ODV (Mean of Spatial and Temporal Variance Means) of the analyzed design solution population. a Fig. 1: Renderings of samples from the analyzed design solution population. c a b Fig. 2 indicates that both design solutions b and c have relatively good SDV and TDV values. Fig. 4 through 6 are DS for design solutions a, b, and c. In Fig. 4, it can be seen that, although design solution a has a relatively good daylight variance, its UDI is very low (30.1%), caused by a great frequency of values below the defined appropriate range. Figure 5 confirms the high MUDI value of design solution b by showing a high frequency (73.1%) of values in the appropriate illuminance range. Figure 6 shows that design solution c has the highest frequency of values in the appropriate illuminance range, 79%; however, this comes at the cost of poorer daylight uniformity, as indicated by Fig. 2. The analyst can use this information to better understand the performance tradeoffs between design solutions b and c. He or she may choose to conduct a higher resolution analysis of design solutions within the region of the design space that contains solutions b and c, or may at once determine that one design solution is better than the other. Fig. 2: SDV (Spatial Variance Mean) and TDV (Temporal Variance Mean) of the analyzed design solution population.

5 4. DISCUSSION AND CONCLUSION Daylighting performance information produced and represented by the described method can help one balance the value of appropriate illumination levels with spatial and temporal uniformity for many candidate design solutions. In addition, the metrics described can be used as optimization and constraint functions in optimization algorithms. Criteria for temporal and spatial variance can be established to distinguish feasible and infeasible design solutions based on daylight uniformity performance. Fig. 4: DS of design solution a. The DS can also be used to evaluate the daylighting performance of actual spaces whose daylight illuminance levels have been logged for a sufficiently long period of time. 5. REFERENCES [1] Nabil, A. and Mardaljevic, J. Useful daylight illuminance: a new paradigm for assessing daylight in buildings, Lighting Research & Technology, 37 (1) (2005) [2] C.F. Reinhart, Lightswitch-2002: a model for manual and automated control of electric lighting and blinds, Solar Energy 77 (1) (2004) Fig. 5: DS of design solution b. Fig. 6: DS of design solution c.