ShadingZip: Within-Building Selective Computation of Shading Profiles for Urban Building Energy Models

Abstract

Urban building energy models require time-resolved solar access at the envelope sensor level, making exhaustive ray tracing expensive. ShadingZip reduces ray-tracing evaluations by 67.4% at a 2.6% WMAPE by selectively computing shading for representative sensors within each building. Representatives are identified using sensor metadata (MF), exploratory shading observations (SF), or both (MF+SF); unobserved periods are reconstructed from assigned representatives. ShadingZip is evaluated on 2,691 buildings from ten morphological contexts of over 65,000 buildings under five latitudes. Accuracy is measured using error at building- and surface-aggregation levels. SF and MF+SF outperform MF once the cost of exploratory ray tracing is accepted, although MF+SF provides no consistent advantage over SF. A balanced configuration—SF with 3 exploratory periods and representative ratio 0.20—used 32.6% of exhaustive ray-tracing, with WMAPE below 5% in 49 of the 50 case–latitude combinations. ShadingZip provides a scalable and controllable tradeoff between shading accuracy and workload while preserving full building and surface shading result coverage.

Keywords: Urban Building Energy Modeling, Solar shading, Clustering, Selective computation

Introduction

Urban building energy models (UBEMs) extend building physics simulation to urban scales, supporting retrofit prioritization and planning of distributed renewable energy resources (Hong et al. 2020). In UBEMs, solar exposure is an important boundary condition: radiation gains enter heat balance models and drive Building-Integrated Photovoltaic (BIPV) yields. This exposure depends on obstruction of buildings, terrain, and vegetation, which is costly to resolve as each envelope sensor requires repeated visibility tests. Fast pixel-counting, ray-tracing, and voxel approaches reduce shading computation cost (Hoover and Dogan 2017; Luo et al. 2020; Su and Dogan 2026). These approaches reduce the cost of an individual visibility evaluation, but urban-scale workloads still multiply that evaluation across many sensor-period combinations. Dimensionality reduction has been adopted to identify representative daylight distributions (Kent et al. 2020), yet this post-hoc approach does not reduce the initial simulation workload, motivating an a priori method that selects representative sensor-period combinations before the remaining shading calculations are performed. We therefore introduce ShadingZip to reduce shading calculation effort by selectively computing sensors. Sensors are grouped using metadata or exploratory shading results for limited periods. Full-year computations are only performed for the representative sensors whose profiles are used to reconstruct other sensors within each building. Features, the number of exploratory periods, and the representative ratio are varied to explore the tradeoff between avoidable ray-tracing cost and reconstruction accuracy.

Methodology

ShadingZip (Figure 1) operates on sensor sunlit fraction profiles. Given envelope sensors $\mathcal S_b$ of building $b$, for each sensor $i\in\mathcal S_b$, modeled period $t\in\mathcal T$, and hour $h$, the shading calculation produces sunlit fraction $y_{i,t,h}\in[0,1]$. Each profile contains 19 periods with 24 hourly values. Diffuse irradiance and sky view factors are neither calculated nor reconstructed. We compute complete profiles as ground truth to evaluate ShadingZip, which selectively computes a subset of sensor-periods, driven by clustering over feature family $F$ (Table 1), with $m$ exploratory periods $\mathcal E$, at representative ratio $r$ to derive representative sensors from $\mathcal S_b$; $F$ may include Metadata Features (MF), Shading Features (SF), and their combination (MF+SF). MF requires no ray-tracing. SF and MF+SF use $m\in\{1,2,3\}$, emulating summer solstice, both solstices, and equinox-and-solstices exploration periods. The process is detailed in Algorithm 1 and returns the representatives $\mathcal R_b$, assignments $a$, and observations $Y_{\mathcal E}$.

$F$	Metadata features (MF)	Shading features (SF)	$r$
SF	$\varnothing$	$\mathcal E\in\{\{9\},\{0,9\},\{0,4,9\}\}$ $m\in\{1,2,3\}$	$\begin{gathered}r\in\{0.01,0.02,0.05,\\0.1,0.2,0.35,0.5\}\end{gathered}$
MF	Normal, tilt, roof/façade class, height above base, local surface $(u,v)$	$\mathcal E=\varnothing;\;m=0$
MF+SF		$\mathcal E\in\{\{9\},\{0,9\},\{0,4,9\}\}$ $m\in\{1,2,3\}$

Algorithm 1. Select representatives

1. Method $\operatorname{SELECT-REPRESENTATIVES}(\mathcal S_b,\mathcal E,r,F)$
2. $K_b\gets\min(|\mathcal S_b|,\max(1,\operatorname{round}(r|\mathcal S_b|)))$
3. $Y_{\mathcal E}\gets\operatorname{Raytrace}(\mathcal S_b,\mathcal E);\quad\{\mathbf f_i\}\gets\operatorname{Features}(\mathcal S_b,Y_{\mathcal E},F)$ // Exploratory shading and features
4. $\mathcal C\gets\operatorname{KMeans}(\{\mathbf f_i\},K_b);\quad\mathcal R_b\gets\varnothing$ // Initialize representatives
5. for each $\text{centroid }\mathbf c\in\mathcal C$
6. $i\gets\text{sensor nearest to }\mathbf c$ // Get the real sensor closest to the centroid
7. while $i\in\mathcal R_b$ // Check if the sensor is already selected
8. $i\gets\text{next-nearest sensor}$ // If selected, use the next-nearest
9. $\mathcal R_b\gets\mathcal R_b\cup\{i\}$ // Update representative sensor set
10. for each $i\in\mathcal S_b$
11. $a(i)\gets\underset{j\in\mathcal R_b}{\arg\min}\,\|\mathbf f_i-\mathbf f_j\|_2$ // Assign representative sensor
12. return $\mathcal R_b,\,a,\,Y_{\mathcal E}$

After representative selection, Algorithm 2 calculates the remaining shading periods only for sensors in $\mathcal R_b$. For an exploratory period, each sensor retains its own calculated profile. For non-exploratory periods, sensors copy the calculated profile of the assigned representative, yielding reconstructed profiles $\hat Y_b$. Buildings are streamed sequentially, posing no limit on scalability: once a building is processed, raw results are discarded and memory reclaimed.

Algorithm 2. Compute and reconstruct profiles per building

1. for each $\text{building }b\in\mathcal B$ // Streamed building access
2. $\mathcal R_b,a,Y_{\mathcal E}\gets\operatorname{SELECT-REPRESENTATIVES}(\mathcal S_b,\mathcal E,r,F)$ // Run Algorithm 1
3. if $\mathcal T\setminus\mathcal E\ne\varnothing$ // Check for remaining periods
4. $Y_{\mathcal R}\gets\operatorname{Raytrace}(\mathcal R_b,\mathcal T\setminus\mathcal E)$ // Trace only representative sensors
5. for each $i\in\mathcal S_b,\;t\in\mathcal T$ // For each sensor and period
6. if $t\in\mathcal E,\quad\hat y_{i,t}\gets Y_{\mathcal E}[i,t]$ // Retain the sensor’s calculated result
7. else $\hat y_{i,t}\gets Y_{\mathcal R}[a(i),t]$ // Use the representative’s result
8. $\operatorname{Save}(b,\mathcal R_b,a,\hat Y_b);\quad\operatorname{Discard}(\hat Y_b);\quad\operatorname{AutoGC}()$ // Save results and free memory

We then explore the tradeoff between ray-tracing cost and reconstruction accuracy. Ray-tracing cost is measured relative to exhaustive calculation over all sensor periods. For exploratory periods, ray-tracing is performed for each sensor, whereas for non-exploratory periods, it is calculated for the representatives. Reconstruction accuracy is evaluated using a Weighted Mean Absolute Percentage Error (WMAPE):

Here, $y_{i,t,h}$ and $\hat y_{i,t,h}$ are ground-truth and reconstructed sunlit fractions for sensor $i$, period $t$, and hour $h$. $A_i$ is sensor $i$ area; $\pi_t$ is period $t$ length; $\alpha_{t,h}$ is the solar altitude; $\mathbf n_i$ is the sensor normal; $\mathbf s_{t,h}$ is the direction vector to the sun, and $(\cdot)_+=\max(0,\cdot)$. Unlit sensors were excluded as their percentage error is undefined. Profiles are aggregated for error calculation at surface- and building-levels, emulating how shading data enters BIPV and energy models. For baseline evaluations, sensors were randomly sampled within each building. All evaluations comprised 10 urban cases (Table 4) simulated at 0°, 15°, 30°, 45°, and 60° latitudes. All buildings were retained as obstruction context during shading calculation. A deterministic 10% sample, capped at 300 buildings per case, was selected for reconstruction and error evaluation. All computations were executed on a 24-core Intel Core Ultra 9 275HX processor and 32 GB RAM, with K-means restricted to 4 threads.

Location	Coordinates	Morphological characters	CB	SB	SS
Financial District	40.71, −74.01	Urban, high-rise, street canyon	2,245	225	227,614
Midtown	40.75, −73.99	Urban, high-rise, grid	4,578	300	265,876
Red Hook	40.68, −74.00	Urban, industrial waterfront	6,719	300	102,846
Park Slope	40.67, −73.98	Urban, attached rowhouse	11,157	300	68,126
Riverdale	40.89, −73.91	Suburban, hilly, wooded	2,036	204	81,952
Co-op City	40.86, −73.83	Urban, towers, superblocks	3,698	300	61,399
Bayside	40.76, −73.77	Suburban, semi-detached	12,993	300	41,201
Jackson Heights	40.76, −73.88	Urban, perimeter blocks	17,761	300	60,092
Long Island City	40.75, −73.94	Urban, high-rise, industrial	3,149	300	226,362
Greenridge	40.55, −74.16	Suburban, residential	1,613	162	21,620
Total			65,949	2,691	1,157,088

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Results

The parameter sweep revealed a consistent tradeoff between ray-tracing cost and reconstruction error (Figure 2), with diminishing returns as the representative ratio increased. With the specified hardware, representative selection, reconstruction, and scoring for the selected SF configuration averaged 0.28 ms per sensor. Once at least 2 exploratory periods were accepted, SF and MF+SF generally outperformed the baseline. SF with $m=3$ and $r=0.20$ provided a preferred balance, requiring 32.6% of exhaustive sensor-period ray-tracing evaluations and producing a mean building-aggregated lit-sensor WMAPE of 2.6%. Across the 50 case–latitude combinations, WMAPE ranged from 0.7% to 5.5%, with 49 combinations below 5% (Figure 4). Figure 3 shows that facade-surface error is broadly distributed across orientations at 0° latitude but becomes more concentrated on north-facing facades at higher latitudes. Although the local facade error exceeds the building-aggregated error, the selected configuration retains low-error surfaces across all orientations.

Latitude All five latitudes0°15°30°45°60°

Methods

MFSFMF+SFRandom baseline

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Figure data. Ratios are fractions; multiply by 100 for percentages.

Latitude (°)	Method	Exploratory periods	Representative ratio	Actual relative cost	WMAPE	95% CI lower	95% CI upper
0	MF	0	0.01	0.011759737012504018	0.19000267155811212
0	MF	0	0.02	0.020877703435246517	0.16053409234068125
0	MF	0	0.05	0.04997992859681482	0.12399464623144978
0	MF	0	0.1	0.09998428637446223	0.1019115965400825
0	MF	0	0.2	0.20008062823660575	0.0786249307272162
0	MF	0	0.35	0.34992124076956094	0.057757286850497046
0	MF	0	0.5	0.49996827455965037	0.04440152935993331
0	MF+SF	1	0.01	0.06377238243289854	0.14537416507823697
0	MF+SF	1	0.02	0.07241045588602302	0.11923036738082178
0	MF+SF	1	0.05	0.09998098498645615	0.08552969037465372
0	MF+SF	1	0.1	0.14735353446001684	0.06657937439489858
0	MF+SF	1	0.2	0.24218164780310017	0.04818633882477854
0	MF+SF	1	0.35	0.3841359123080051	0.03215847346434375
0	MF+SF	1	0.5	0.5262857337933531	0.021264274856792227
0	SF	1	0.01	0.06377238243289854	0.1670077887218061
0	SF	1	0.02	0.07241045588602302	0.14365549414360326
0	SF	1	0.05	0.09998098498645615	0.12015492527981551
0	SF	1	0.1	0.14735353446001684	0.1053538261474588
0	SF	1	0.2	0.24218164780310017	0.08630597088453558
0	SF	1	0.35	0.3841359123080051	0.0625588257605913
0	SF	1	0.5	0.5262857337933531	0.04175767298646259
0	MF+SF	2	0.01	0.11578502785329306	0.12514005224941965
0	MF+SF	2	0.02	0.1239432083367995	0.0991730836371343
0	MF+SF	2	0.05	0.14998204137609747	0.06420641018867483
0	MF+SF	2	0.1	0.19472278254557146	0.046243737064841986
0	MF+SF	2	0.2	0.28428266736959457	0.030299509073926065
0	MF+SF	2	0.35	0.4183505838464493	0.017811284985822257
0	MF+SF	2	0.5	0.5526031930270556	0.010491587148486008
0	SF	2	0.01	0.11578502785329306	0.11174408635664906
0	SF	2	0.02	0.1239432083367995	0.08684520567035271
0	SF	2	0.05	0.14998204137609747	0.05976953596332112
0	SF	2	0.1	0.19472278254557146	0.04527685388214871
0	SF	2	0.2	0.28428266736959457	0.031202751535248995
0	SF	2	0.35	0.4183505838464493	0.019941798427623957
0	SF	2	0.5	0.5526031930270556	0.012870490845079578
0	MF+SF	3	0.01	0.16779767327368758	0.11491968559898977
0	MF+SF	3	0.02	0.17547596078757602	0.09035960228871431
0	MF+SF	3	0.05	0.1999830977657388	0.057512067578968734
0	MF+SF	3	0.1	0.24209203063112605	0.04054436057195028
0	MF+SF	3	0.2	0.32638368693608905	0.025685091743305206
0	MF+SF	3	0.35	0.4525652553848934	0.014505423179429412
0	MF+SF	3	0.5	0.5789206522607582	0.00818316717829349
0	SF	3	0.01	0.16779767327368758	0.09939126176593828
0	SF	3	0.02	0.17547596078757602	0.07575097242850706
0	SF	3	0.05	0.1999830977657388	0.0503065354409737
0	SF	3	0.1	0.24209203063112605	0.036609392304805186
0	SF	3	0.2	0.32638368693608905	0.023757969446056806
0	SF	3	0.35	0.4525652553848934	0.013876012102656326
0	SF	3	0.5	0.5789206522607582	0.008087669265610716
15	MF	0	0.01	0.011759737012504018	0.19795843475796268
15	MF	0	0.02	0.020877703435246517	0.16662037015824363
15	MF	0	0.05	0.04997992859681482	0.12866047813352585
15	MF	0	0.1	0.09998428637446223	0.10541995612571226
15	MF	0	0.2	0.20008062823660575	0.08144903921603538
15	MF	0	0.35	0.34992124076956094	0.06008241915120342
15	MF	0	0.5	0.49996827455965037	0.0463704420339315
15	MF+SF	1	0.01	0.06377238243289854	0.15595561487363216
15	MF+SF	1	0.02	0.07241045588602302	0.12727804259786824
15	MF+SF	1	0.05	0.09998098498645615	0.09115412570324247
15	MF+SF	1	0.1	0.14735353446001684	0.0710744427723559
15	MF+SF	1	0.2	0.24218164780310017	0.05145422430710722
15	MF+SF	1	0.35	0.3841359123080051	0.03382984400130263
15	MF+SF	1	0.5	0.5262857337933531	0.02219844144803409
15	SF	1	0.01	0.06377238243289854	0.1758477869182822
15	SF	1	0.02	0.07241045588602302	0.1532450608397766
15	SF	1	0.05	0.09998098498645615	0.12609808789834007
15	SF	1	0.1	0.14735353446001684	0.11084754313143803
15	SF	1	0.2	0.24218164780310017	0.0882505227120879
15	SF	1	0.35	0.3841359123080051	0.06506581123082797
15	SF	1	0.5	0.5262857337933531	0.04900777120296224
15	MF+SF	2	0.01	0.11578502785329306	0.13075894482452105
15	MF+SF	2	0.02	0.1239432083367995	0.10334905315352183
15	MF+SF	2	0.05	0.14998204137609747	0.06744417123916298
15	MF+SF	2	0.1	0.19472278254557146	0.04861240633625555
15	MF+SF	2	0.2	0.28428266736959457	0.0319426661264843
15	MF+SF	2	0.35	0.4183505838464493	0.018981770658999406
15	MF+SF	2	0.5	0.5526031930270556	0.011186307174848685
15	SF	2	0.01	0.11578502785329306	0.11659002252640877
15	SF	2	0.02	0.1239432083367995	0.09036705814134945
15	SF	2	0.05	0.14998204137609747	0.06325369395938309
15	SF	2	0.1	0.19472278254557146	0.047753277908346284
15	SF	2	0.2	0.28428266736959457	0.03330561382537929
15	SF	2	0.35	0.4183505838464493	0.021318808552389462
15	SF	2	0.5	0.5526031930270556	0.013915943125634956
15	MF+SF	3	0.01	0.16779767327368758	0.11874050968740947
15	MF+SF	3	0.02	0.17547596078757602	0.0924691971084676
15	MF+SF	3	0.05	0.1999830977657388	0.058889961779379496
15	MF+SF	3	0.1	0.24209203063112605	0.041520546730552166
15	MF+SF	3	0.2	0.32638368693608905	0.0262481110530541
15	MF+SF	3	0.35	0.4525652553848934	0.014777867926132804
15	MF+SF	3	0.5	0.5789206522607582	0.00827907126085483
15	SF	3	0.01	0.16779767327368758	0.10078616663318357
15	SF	3	0.02	0.17547596078757602	0.07661590061243764
15	SF	3	0.05	0.1999830977657388	0.051339414977406614
15	SF	3	0.1	0.24209203063112605	0.03718983260680116
15	SF	3	0.2	0.32638368693608905	0.023884380371847088
15	SF	3	0.35	0.4525652553848934	0.013749340050911277
15	SF	3	0.5	0.5789206522607582	0.007833423865597931
30	MF	0	0.01	0.011759737012504018	0.2197482287558817
30	MF	0	0.02	0.020877703435246517	0.18404631448764905
30	MF	0	0.05	0.04997992859681482	0.14186037601153062
30	MF	0	0.1	0.09998428637446223	0.1160238124273324
30	MF	0	0.2	0.20008062823660575	0.08954258676824516
30	MF	0	0.35	0.34992124076956094	0.0662296804990184
30	MF	0	0.5	0.49996827455965037	0.05131872433697623
30	MF+SF	1	0.01	0.06377238243289854	0.1664075170837012
30	MF+SF	1	0.02	0.07241045588602302	0.1328117074238848
30	MF+SF	1	0.05	0.09998098498645615	0.09273120526901488
30	MF+SF	1	0.1	0.14735353446001684	0.07014267582009617
30	MF+SF	1	0.2	0.24218164780310017	0.04855233335827502
30	MF+SF	1	0.35	0.3841359123080051	0.03032484354227371
30	MF+SF	1	0.5	0.5262857337933531	0.018531839114032108
30	SF	1	0.01	0.06377238243289854	0.17128636312493797
30	SF	1	0.02	0.07241045588602302	0.1434413980279442
30	SF	1	0.05	0.09998098498645615	0.11279876522289388
30	SF	1	0.1	0.14735353446001684	0.09447258161198753
30	SF	1	0.2	0.24218164780310017	0.0732783878847246
30	SF	1	0.35	0.3841359123080051	0.054549238401578534
30	SF	1	0.5	0.5262857337933531	0.0440095847612601
30	MF+SF	2	0.01	0.11578502785329306	0.1452615581898131
30	MF+SF	2	0.02	0.1239432083367995	0.11300668692938923
30	MF+SF	2	0.05	0.14998204137609747	0.07468522156955983
30	MF+SF	2	0.1	0.19472278254557146	0.05369905909346794
30	MF+SF	2	0.2	0.28428266736959457	0.03492723738104578
30	MF+SF	2	0.35	0.4183505838464493	0.02058161771928193
30	MF+SF	2	0.5	0.5526031930270556	0.011968350401503285
30	SF	2	0.01	0.11578502785329306	0.12760955678180658
30	SF	2	0.02	0.1239432083367995	0.09805381088621073
30	SF	2	0.05	0.14998204137609747	0.06934533124610087
30	SF	2	0.1	0.19472278254557146	0.052024223536865505
30	SF	2	0.2	0.28428266736959457	0.035523429495304036
30	SF	2	0.35	0.4183505838464493	0.022340707430949867
30	SF	2	0.5	0.5526031930270556	0.014093583404225925
30	MF+SF	3	0.01	0.16779767327368758	0.1297388414695315
30	MF+SF	3	0.02	0.17547596078757602	0.09965200488328324
30	MF+SF	3	0.05	0.1999830977657388	0.06440913761798578
30	MF+SF	3	0.1	0.24209203063112605	0.04512812852114871
30	MF+SF	3	0.2	0.32638368693608905	0.028294197743436205
30	MF+SF	3	0.35	0.4525652553848934	0.015800211423920154
30	MF+SF	3	0.5	0.5789206522607582	0.008741101025565353
30	SF	3	0.01	0.16779767327368758	0.10851429585740358
30	SF	3	0.02	0.17547596078757602	0.0819134403759659
30	SF	3	0.05	0.1999830977657388	0.05548366933954559
30	SF	3	0.1	0.24209203063112605	0.03989650811829686
30	SF	3	0.2	0.32638368693608905	0.025391954752671014
30	SF	3	0.35	0.4525652553848934	0.01438392942713499
30	SF	3	0.5	0.5789206522607582	0.008086900756597864
45	MF	0	0.01	0.011759737012504018	0.25135751198517015
45	MF	0	0.02	0.020877703435246517	0.2100080357576985
45	MF	0	0.05	0.04997992859681482	0.16185580107138778
45	MF	0	0.1	0.09998428637446223	0.13227275360753024
45	MF	0	0.2	0.20008062823660575	0.10222122885621576
45	MF	0	0.35	0.34992124076956094	0.07560139430993071
45	MF	0	0.5	0.49996827455965037	0.058809636245209955
45	MF+SF	1	0.01	0.06377238243289854	0.18016236322393667
45	MF+SF	1	0.02	0.07241045588602302	0.14009757680452498
45	MF+SF	1	0.05	0.09998098498645615	0.09636827343254303
45	MF+SF	1	0.1	0.14735353446001684	0.07145764128700241
45	MF+SF	1	0.2	0.24218164780310017	0.04838409715038748
45	MF+SF	1	0.35	0.3841359123080051	0.029228082115330036
45	MF+SF	1	0.5	0.5262857337933531	0.017451385155103274
45	SF	1	0.01	0.06377238243289854	0.17399896300469425
45	SF	1	0.02	0.07241045588602302	0.13961191215264165
45	SF	1	0.05	0.09998098498645615	0.10656209238972011
45	SF	1	0.1	0.14735353446001684	0.08552584094271887
45	SF	1	0.2	0.24218164780310017	0.06351494471849632
45	SF	1	0.35	0.3841359123080051	0.0441141155597617
45	SF	1	0.5	0.5262857337933531	0.033145708908129776
45	MF+SF	2	0.01	0.11578502785329306	0.16923517251577885
45	MF+SF	2	0.02	0.1239432083367995	0.13103779420827388
45	MF+SF	2	0.05	0.14998204137609747	0.08732743045163385
45	MF+SF	2	0.1	0.19472278254557146	0.06272703716492646
45	MF+SF	2	0.2	0.28428266736959457	0.040966743263310006
45	MF+SF	2	0.35	0.4183505838464493	0.024075538853055224
45	MF+SF	2	0.5	0.5526031930270556	0.01394884553340682
45	SF	2	0.01	0.11578502785329306	0.14696494429933005
45	SF	2	0.02	0.1239432083367995	0.11372267187197911
45	SF	2	0.05	0.14998204137609747	0.08063296481936076
45	SF	2	0.1	0.19472278254557146	0.06060033127856613
45	SF	2	0.2	0.28428266736959457	0.04122722234935686
45	SF	2	0.35	0.4183505838464493	0.025465367849313015
45	SF	2	0.5	0.5526031930270556	0.01564210407862445
45	MF+SF	3	0.01	0.16779767327368758	0.14977263830732068
45	MF+SF	3	0.02	0.17547596078757602	0.11421522663550064
45	MF+SF	3	0.05	0.1999830977657388	0.07483386328226391
45	MF+SF	3	0.1	0.24209203063112605	0.05233752307785658
45	MF+SF	3	0.2	0.32638368693608905	0.032869104597049455
45	MF+SF	3	0.35	0.4525652553848934	0.018365739746952926
45	MF+SF	3	0.5	0.5789206522607582	0.010121171944313317
45	SF	3	0.01	0.16779767327368758	0.12456361689546719
45	SF	3	0.02	0.17547596078757602	0.09349037734988555
45	SF	3	0.05	0.1999830977657388	0.06424492830582217
45	SF	3	0.1	0.24209203063112605	0.0464197888267013
45	SF	3	0.2	0.32638368693608905	0.02941882627598915
45	SF	3	0.35	0.4525652553848934	0.016561845003797936
45	SF	3	0.5	0.5789206522607582	0.009103723994057004
60	MF	0	0.01	0.011759737012504018	0.28788335451879576
60	MF	0	0.02	0.020877703435246517	0.23952651891589527
60	MF	0	0.05	0.04997992859681482	0.1845521876860758
60	MF	0	0.1	0.09998428637446223	0.15039232676143882
60	MF	0	0.2	0.20008062823660575	0.11617128593812388
60	MF	0	0.35	0.34992124076956094	0.08604546510630556
60	MF	0	0.5	0.49996827455965037	0.06725314334785722
60	MF+SF	1	0.01	0.06377238243289854	0.19152257202365397
60	MF+SF	1	0.02	0.07241045588602302	0.14698223915741024
60	MF+SF	1	0.05	0.09998098498645615	0.09976120180274205
60	MF+SF	1	0.1	0.14735353446001684	0.07252354698212898
60	MF+SF	1	0.2	0.24218164780310017	0.04742584860724481
60	MF+SF	1	0.35	0.3841359123080051	0.028186573806718292
60	MF+SF	1	0.5	0.5262857337933531	0.01660423739622236
60	SF	1	0.01	0.06377238243289854	0.17748733353238194
60	SF	1	0.02	0.07241045588602302	0.13702321750451005
60	SF	1	0.05	0.09998098498645615	0.10219793152596435
60	SF	1	0.1	0.14735353446001684	0.07935549471102975
60	SF	1	0.2	0.24218164780310017	0.05675652223190787
60	SF	1	0.35	0.3841359123080051	0.03834801529043244
60	SF	1	0.5	0.5262857337933531	0.025568481029679378
60	MF+SF	2	0.01	0.11578502785329306	0.19386390676472104
60	MF+SF	2	0.02	0.1239432083367995	0.14915730832565022
60	MF+SF	2	0.05	0.14998204137609747	0.09970518108344686
60	MF+SF	2	0.1	0.19472278254557146	0.07159722321191393
60	MF+SF	2	0.2	0.28428266736959457	0.04689412630492865
60	MF+SF	2	0.35	0.4183505838464493	0.02771749956901198
60	MF+SF	2	0.5	0.5526031930270556	0.01641138377673562
60	SF	2	0.01	0.11578502785329306	0.16910397173327743
60	SF	2	0.02	0.1239432083367995	0.13101151671424063
60	SF	2	0.05	0.14998204137609747	0.09417471767720331
60	SF	2	0.1	0.19472278254557146	0.07109481003449224
60	SF	2	0.2	0.28428266736959457	0.04877034967712113
60	SF	2	0.35	0.4183505838464493	0.031190489273385778
60	SF	2	0.5	0.5526031930270556	0.020040371670338456
60	MF+SF	3	0.01	0.16779767327368758	0.17216316314640417
60	MF+SF	3	0.02	0.17547596078757602	0.1312596903291768
60	MF+SF	3	0.05	0.1999830977657388	0.0862324638559692
60	MF+SF	3	0.1	0.24209203063112605	0.06063739582716408
60	MF+SF	3	0.2	0.32638368693608905	0.038217151306534504
60	MF+SF	3	0.35	0.4525652553848934	0.021468714815408598
60	MF+SF	3	0.5	0.5789206522607582	0.011984256404598386
60	SF	3	0.01	0.16779767327368758	0.14324745019966467
60	SF	3	0.02	0.17547596078757602	0.10758404610300364
60	SF	3	0.05	0.1999830977657388	0.07485894945500506
60	SF	3	0.1	0.24209203063112605	0.05418835044879209
60	SF	3	0.2	0.32638368693608905	0.03463462432874773
60	SF	3	0.35	0.4525652553848934	0.019689876554119138
60	SF	3	0.5	0.5789206522607582	0.011055629823830904
0	Random baseline			0.011213494565668298	0.29981191936284685	0.29429263980791753	0.30533119891777616
0	Random baseline			0.021120260516054094	0.22561779964829573	0.2228766999430237	0.22835889935356776
0	Random baseline			0.05111625044940402	0.15054991625695738	0.14855000360735976	0.152549828906555
0	Random baseline			0.10105281534334468	0.10715994409995516	0.1060309892127636	0.10828889898714672
0	Random baseline			0.16836575956193478	0.08195479010266783	0.08090873194246137	0.0830008482628743
0	Random baseline			0.1763556445145054	0.07957339417129608	0.07860280577681131	0.08054398256578085
0	Random baseline			0.20110916369368625	0.07382556111981876	0.07303137413710716	0.07461974810253037
0	Random baseline			0.2432079496114384	0.0655427587720911	0.06493562700579927	0.06614989053838294
0	Random baseline			0.3275317002682596	0.05352149822485333	0.053053261316304036	0.053989735133402626
0	Random baseline			0.45373990569429457	0.04126976036918615	0.04074286391461569	0.041796656823756606
0	Random baseline			0.5800794753726597	0.03208080795834491	0.0316812388974423	0.032480377019247525
15	Random baseline			0.011213494565668298	0.30039499311359164	0.2975108842825283	0.30327910194465496
15	Random baseline			0.021120260516054094	0.22996082979522672	0.2276819481719838	0.23223971141846964
15	Random baseline			0.05111625044940402	0.15512937591897183	0.1528857385151736	0.15737301332277007
15	Random baseline			0.10105281534334468	0.11165569071164655	0.10966403755812677	0.11364734386516633
15	Random baseline			0.16836575956193478	0.08471914480028664	0.0838444704844326	0.08559381911614068
15	Random baseline			0.1763556445145054	0.08253421634967388	0.08170315275746949	0.08336527994187827
15	Random baseline			0.20110916369368625	0.07602310814264371	0.07532604764612251	0.0767201686391649
15	Random baseline			0.2432079496114384	0.06757250915024654	0.06692151440038373	0.06822350390010935
15	Random baseline			0.3275317002682596	0.05503356816125111	0.05457405279220195	0.05549308353030027
15	Random baseline			0.45373990569429457	0.04189158987956858	0.04149075266499074	0.04229242709414641
15	Random baseline			0.5800794753726597	0.03252644396338704	0.032120634408593904	0.032932253518180174
30	Random baseline			0.011213494565668298	0.3239974567696056	0.3213799683229319	0.3266149452162793
30	Random baseline			0.021120260516054094	0.24610321221891177	0.24422301668911225	0.24798340774871128
30	Random baseline			0.05111625044940402	0.16653244138533538	0.16448149156822509	0.16858339120244567
30	Random baseline			0.10105281534334468	0.1196504549437572	0.11853541693760346	0.12076549294991094
30	Random baseline			0.16836575956193478	0.09045378457712618	0.0897262872908627	0.09118128186338965
30	Random baseline			0.1763556445145054	0.08816898452892069	0.08748872543330623	0.08884924362453515
30	Random baseline			0.20110916369368625	0.08132629853365238	0.08082109224472875	0.081831504822576
30	Random baseline			0.2432079496114384	0.07225253909814225	0.07165433734424086	0.07285074085204364
30	Random baseline			0.3275317002682596	0.05882825391577707	0.058251153156769826	0.05940535467478431
30	Random baseline			0.45373990569429457	0.04496810990326158	0.044482661175864815	0.04545355863065835
30	Random baseline			0.5800794753726597	0.03460321550103727	0.034264268589163926	0.03494216241291061
45	Random baseline			0.011213494565668298	0.36133535173507497	0.35345379199268145	0.3692169114774685
45	Random baseline			0.021120260516054094	0.2745940345983247	0.27024622290835115	0.27894184628829827
45	Random baseline			0.05111625044940402	0.18467449200339903	0.1820641624221899	0.18728482158460816
45	Random baseline			0.10105281534334468	0.13258034811777727	0.13082815112380844	0.1343325451117461
45	Random baseline			0.16836575956193478	0.09998099055949371	0.09873091102644439	0.10123107009254302
45	Random baseline			0.1763556445145054	0.09752690935374364	0.09637583391601967	0.09867798479146761
45	Random baseline			0.20110916369368625	0.09011580201540419	0.08915110520600583	0.09108049882480254
45	Random baseline			0.2432079496114384	0.07999226942614898	0.07924402190100308	0.08074051695129489
45	Random baseline			0.3275317002682596	0.06480800716493607	0.0641682826713145	0.06544773165855763
45	Random baseline			0.45373990569429457	0.04979327730056051	0.049293544864065626	0.050293009737055396
45	Random baseline			0.5800794753726597	0.038633518782406534	0.038313283056614654	0.038953754508198414
60	Random baseline			0.011213494565668298	0.4027701679620464	0.39234111797426197	0.41319921794983083
60	Random baseline			0.021120260516054094	0.3097044341283648	0.3026212053939094	0.3167876628628202
60	Random baseline			0.05111625044940402	0.20802688776354125	0.2046566642064104	0.2113971113206721
60	Random baseline			0.10105281534334468	0.14848043699358213	0.146521143236627	0.15043973075053726
60	Random baseline			0.16836575956193478	0.11148597368939711	0.11031740677363265	0.11265454060516157
60	Random baseline			0.1763556445145054	0.10861771487659694	0.10742783469841165	0.10980759505478223
60	Random baseline			0.20110916369368625	0.1000104936932222	0.09903143498480203	0.10098955240164235
60	Random baseline			0.2432079496114384	0.08864971457953477	0.08802217528638905	0.0892772538726805
60	Random baseline			0.3275317002682596	0.0720358594893277	0.07147573458784436	0.07259598439081104
60	Random baseline			0.45373990569429457	0.05533573006586345	0.05477384506301785	0.05589761506870906
60	Random baseline			0.5800794753726597	0.043456767739626916	0.04294541855498571	0.04396811692426812

Reading this comparison: ShadingZip sums sensor-wise absolute errors before aggregation. The random baseline estimates building-total profiles, allowing cancellation within a building. Baseline intervals in the tooltips describe the mean of 25 repeats. Dotted lines show exploratory cost floors m/19. Neither cost nor WMAPE is wall-clock runtime.

Latitude All five latitudes0°15°30°45°60°Highlight error band All bands0–5%5–10%10–15%15–20%≥20%not litReset to paper view

Hover, tap, or focus a mark to inspect its values. Use arrow keys to move between marks.

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Data table and source downloads

Original figure data (CSV)

Figure data. Ratios are fractions; multiply by 100 for percentages.

Latitude (°)	Direction (°)	Error band	Surface count	Bin total	Proportion
0	0	0–5%	130	290	0.4482758620689655
0	0	5–10%	29	290	0.1
0	0	10–15%	20	290	0.06896551724137931
0	0	15–20%	13	290	0.04482758620689655
0	0	≥20%	52	290	0.1793103448275862
0	0	not lit	46	290	0.15862068965517243
0	15	0–5%	334	637	0.5243328100470958
0	15	5–10%	61	637	0.09576138147566719
0	15	10–15%	39	637	0.061224489795918366
0	15	15–20%	28	637	0.04395604395604396
0	15	≥20%	96	637	0.15070643642072212
0	15	not lit	79	637	0.12401883830455258
0	30	0–5%	731	1703	0.42924251321197887
0	30	5–10%	293	1703	0.17204932472108045
0	30	10–15%	139	1703	0.08162066940692896
0	30	15–20%	75	1703	0.04403992953611274
0	30	≥20%	174	1703	0.10217263652378156
0	30	not lit	291	1703	0.17087492660011744
0	45	0–5%	89	187	0.47593582887700536
0	45	5–10%	29	187	0.15508021390374332
0	45	10–15%	17	187	0.09090909090909091
0	45	15–20%	4	187	0.0213903743315508
0	45	≥20%	26	187	0.13903743315508021
0	45	not lit	22	187	0.11764705882352941
0	60	0–5%	214	412	0.5194174757281553
0	60	5–10%	42	412	0.10194174757281553
0	60	10–15%	22	412	0.05339805825242718
0	60	15–20%	19	412	0.04611650485436893
0	60	≥20%	57	412	0.1383495145631068
0	60	not lit	58	412	0.1407766990291262
0	75	0–5%	423	826	0.5121065375302664
0	75	5–10%	96	826	0.1162227602905569
0	75	10–15%	54	826	0.06537530266343826
0	75	15–20%	31	826	0.03753026634382567
0	75	≥20%	139	826	0.1682808716707022
0	75	not lit	83	826	0.10048426150121065
0	90	0–5%	96	286	0.3356643356643357
0	90	5–10%	46	286	0.16083916083916083
0	90	10–15%	28	286	0.0979020979020979
0	90	15–20%	17	286	0.05944055944055944
0	90	≥20%	64	286	0.22377622377622378
0	90	not lit	35	286	0.12237762237762238
0	105	0–5%	234	611	0.3829787234042553
0	105	5–10%	81	611	0.132569558101473
0	105	10–15%	44	611	0.07201309328968904
0	105	15–20%	22	611	0.03600654664484452
0	105	≥20%	105	611	0.1718494271685761
0	105	not lit	125	611	0.20458265139116202
0	120	0–5%	619	1778	0.3481439820022497
0	120	5–10%	233	1778	0.13104611923509563
0	120	10–15%	133	1778	0.07480314960629922
0	120	15–20%	67	1778	0.03768278965129359
0	120	≥20%	225	1778	0.1265466816647919
0	120	not lit	501	1778	0.28177727784026996
0	135	0–5%	81	188	0.4308510638297872
0	135	5–10%	27	188	0.14361702127659576
0	135	10–15%	12	188	0.06382978723404255
0	135	15–20%	5	188	0.026595744680851064
0	135	≥20%	26	188	0.13829787234042554
0	135	not lit	37	188	0.19680851063829788
0	150	0–5%	179	456	0.3925438596491228
0	150	5–10%	60	456	0.13157894736842105
0	150	10–15%	37	456	0.08114035087719298
0	150	15–20%	16	456	0.03508771929824561
0	150	≥20%	72	456	0.15789473684210525
0	150	not lit	92	456	0.20175438596491227
0	165	0–5%	373	907	0.41124586549062847
0	165	5–10%	119	907	0.13120176405733186
0	165	10–15%	42	907	0.04630650496141125
0	165	15–20%	26	907	0.02866593164277839
0	165	≥20%	146	907	0.1609702315325248
0	165	not lit	201	907	0.22160970231532526
0	180	0–5%	78	276	0.2826086956521739
0	180	5–10%	23	276	0.08333333333333333
0	180	10–15%	28	276	0.10144927536231885
0	180	15–20%	11	276	0.03985507246376811
0	180	≥20%	84	276	0.30434782608695654
0	180	not lit	52	276	0.18840579710144928
0	195	0–5%	299	610	0.4901639344262295
0	195	5–10%	71	610	0.11639344262295082
0	195	10–15%	27	610	0.04426229508196721
0	195	15–20%	15	610	0.02459016393442623
0	195	≥20%	94	610	0.1540983606557377
0	195	not lit	104	610	0.17049180327868851
0	210	0–5%	696	1679	0.41453245979749853
0	210	5–10%	310	1679	0.18463371054198927
0	210	10–15%	141	1679	0.08397855866587255
0	210	15–20%	64	1679	0.038117927337701016
0	210	≥20%	182	1679	0.10839785586658725
0	210	not lit	286	1679	0.1703394877903514
0	225	0–5%	77	197	0.39086294416243655
0	225	5–10%	31	197	0.15736040609137056
0	225	10–15%	16	197	0.08121827411167512
0	225	15–20%	19	197	0.09644670050761421
0	225	≥20%	36	197	0.18274111675126903
0	225	not lit	18	197	0.09137055837563451
0	240	0–5%	182	407	0.44717444717444715
0	240	5–10%	53	407	0.13022113022113022
0	240	10–15%	26	407	0.06388206388206388
0	240	15–20%	27	407	0.06633906633906633
0	240	≥20%	76	407	0.18673218673218672
0	240	not lit	43	407	0.10565110565110565
0	255	0–5%	373	815	0.45766871165644174
0	255	5–10%	123	815	0.150920245398773
0	255	10–15%	56	815	0.0687116564417178
0	255	15–20%	26	815	0.03190184049079755
0	255	≥20%	150	815	0.18404907975460122
0	255	not lit	87	815	0.1067484662576687
0	270	0–5%	78	265	0.2943396226415094
0	270	5–10%	49	265	0.18490566037735848
0	270	10–15%	19	265	0.07169811320754717
0	270	15–20%	17	265	0.06415094339622641
0	270	≥20%	69	265	0.26037735849056604
0	270	not lit	33	265	0.12452830188679245
0	285	0–5%	263	609	0.4318555008210181
0	285	5–10%	97	609	0.1592775041050903
0	285	10–15%	36	609	0.059113300492610835
0	285	15–20%	23	609	0.03776683087027915
0	285	≥20%	92	609	0.1510673234811166
0	285	not lit	98	609	0.16091954022988506
0	300	0–5%	650	1781	0.36496350364963503
0	300	5–10%	240	1781	0.13475575519371139
0	300	10–15%	134	1781	0.07523862998315553
0	300	15–20%	67	1781	0.037619314991577765
0	300	≥20%	205	1781	0.11510387422796182
0	300	not lit	485	1781	0.27231892195395846
0	315	0–5%	62	190	0.3263157894736842
0	315	5–10%	43	190	0.22631578947368422
0	315	10–15%	18	190	0.09473684210526316
0	315	15–20%	19	190	0.1
0	315	≥20%	23	190	0.12105263157894737
0	315	not lit	25	190	0.13157894736842105
0	330	0–5%	173	442	0.3914027149321267
0	330	5–10%	54	442	0.12217194570135746
0	330	10–15%	30	442	0.06787330316742081
0	330	15–20%	16	442	0.03619909502262444
0	330	≥20%	77	442	0.17420814479638008
0	330	not lit	92	442	0.2081447963800905
0	345	0–5%	389	924	0.420995670995671
0	345	5–10%	121	924	0.13095238095238096
0	345	10–15%	46	924	0.049783549783549784
0	345	15–20%	28	924	0.030303030303030304
0	345	≥20%	138	924	0.14935064935064934
0	345	not lit	202	924	0.21861471861471862
15	0	0–5%	114	290	0.3931034482758621
15	0	5–10%	39	290	0.13448275862068965
15	0	10–15%	16	290	0.05517241379310345
15	0	15–20%	20	290	0.06896551724137931
15	0	≥20%	54	290	0.18620689655172415
15	0	not lit	47	290	0.16206896551724137
15	15	0–5%	285	637	0.4474097331240188
15	15	5–10%	99	637	0.1554160125588697
15	15	10–15%	50	637	0.07849293563579278
15	15	15–20%	28	637	0.04395604395604396
15	15	≥20%	91	637	0.14285714285714285
15	15	not lit	84	637	0.13186813186813187
15	30	0–5%	595	1703	0.34938344098649443
15	30	5–10%	320	1703	0.18790369935408102
15	30	10–15%	189	1703	0.11098062243100411
15	30	15–20%	93	1703	0.0546095126247798
15	30	≥20%	215	1703	0.1262477980035232
15	30	not lit	291	1703	0.17087492660011744
15	45	0–5%	69	187	0.3689839572192513
15	45	5–10%	28	187	0.1497326203208556
15	45	10–15%	26	187	0.13903743315508021
15	45	15–20%	7	187	0.0374331550802139
15	45	≥20%	35	187	0.18716577540106952
15	45	not lit	22	187	0.11764705882352941
15	60	0–5%	197	412	0.47815533980582525
15	60	5–10%	48	412	0.11650485436893204
15	60	10–15%	24	412	0.05825242718446602
15	60	15–20%	15	412	0.03640776699029126
15	60	≥20%	76	412	0.18446601941747573
15	60	not lit	52	412	0.1262135922330097
15	75	0–5%	394	826	0.47699757869249393
15	75	5–10%	94	826	0.11380145278450363
15	75	10–15%	56	826	0.06779661016949153
15	75	15–20%	40	826	0.048426150121065374
15	75	≥20%	158	826	0.19128329297820823
15	75	not lit	84	826	0.1016949152542373
15	90	0–5%	95	286	0.3321678321678322
15	90	5–10%	43	286	0.15034965034965034
15	90	10–15%	36	286	0.1258741258741259
15	90	15–20%	10	286	0.03496503496503497
15	90	≥20%	65	286	0.22727272727272727
15	90	not lit	37	286	0.12937062937062938
15	105	0–5%	237	611	0.3878887070376432
15	105	5–10%	86	611	0.1407528641571195
15	105	10–15%	40	611	0.06546644844517185
15	105	15–20%	32	611	0.05237315875613748
15	105	≥20%	92	611	0.15057283142389524
15	105	not lit	124	611	0.20294599018003273
15	120	0–5%	618	1778	0.34758155230596177
15	120	5–10%	247	1778	0.1389201349831271
15	120	10–15%	127	1778	0.07142857142857142
15	120	15–20%	76	1778	0.04274465691788527
15	120	≥20%	210	1778	0.11811023622047244
15	120	not lit	500	1778	0.281214848143982
15	135	0–5%	86	188	0.4574468085106383
15	135	5–10%	25	188	0.13297872340425532
15	135	10–15%	11	188	0.05851063829787234
15	135	15–20%	5	188	0.026595744680851064
15	135	≥20%	24	188	0.1276595744680851
15	135	not lit	37	188	0.19680851063829788
15	150	0–5%	190	456	0.4166666666666667
15	150	5–10%	58	456	0.12719298245614036
15	150	10–15%	31	456	0.06798245614035088
15	150	15–20%	17	456	0.03728070175438596
15	150	≥20%	69	456	0.1513157894736842
15	150	not lit	91	456	0.19956140350877194
15	165	0–5%	391	907	0.4310915104740904
15	165	5–10%	107	907	0.11797133406835722
15	165	10–15%	41	907	0.04520396912899669
15	165	15–20%	32	907	0.03528114663726571
15	165	≥20%	136	907	0.14994487320837926
15	165	not lit	200	907	0.2205071664829107
15	180	0–5%	83	276	0.3007246376811594
15	180	5–10%	39	276	0.14130434782608695
15	180	10–15%	19	276	0.06884057971014493
15	180	15–20%	16	276	0.057971014492753624
15	180	≥20%	69	276	0.25
15	180	not lit	50	276	0.18115942028985507
15	195	0–5%	306	610	0.5016393442622951
15	195	5–10%	71	610	0.11639344262295082
15	195	10–15%	39	610	0.06393442622950819
15	195	15–20%	18	610	0.029508196721311476
15	195	≥20%	75	610	0.12295081967213115
15	195	not lit	101	610	0.16557377049180327
15	210	0–5%	774	1679	0.46098868374032165
15	210	5–10%	312	1679	0.18582489577129244
15	210	10–15%	99	1679	0.05896366885050625
15	210	15–20%	65	1679	0.03871351995235259
15	210	≥20%	156	1679	0.09291244788564622
15	210	not lit	273	1679	0.16259678379988088
15	225	0–5%	88	197	0.4467005076142132
15	225	5–10%	32	197	0.16243654822335024
15	225	10–15%	18	197	0.09137055837563451
15	225	15–20%	12	197	0.06091370558375635
15	225	≥20%	29	197	0.14720812182741116
15	225	not lit	18	197	0.09137055837563451
15	240	0–5%	192	407	0.47174447174447176
15	240	5–10%	45	407	0.11056511056511056
15	240	10–15%	32	407	0.07862407862407862
15	240	15–20%	21	407	0.051597051597051594
15	240	≥20%	73	407	0.17936117936117937
15	240	not lit	44	407	0.10810810810810811
15	255	0–5%	399	815	0.48957055214723927
15	255	5–10%	122	815	0.14969325153374233
15	255	10–15%	41	815	0.05030674846625767
15	255	15–20%	36	815	0.044171779141104296
15	255	≥20%	132	815	0.1619631901840491
15	255	not lit	85	815	0.10429447852760736
15	270	0–5%	82	265	0.30943396226415093
15	270	5–10%	36	265	0.13584905660377358
15	270	10–15%	28	265	0.10566037735849057
15	270	15–20%	18	265	0.06792452830188679
15	270	≥20%	68	265	0.25660377358490566
15	270	not lit	33	265	0.12452830188679245
15	285	0–5%	268	609	0.4400656814449918
15	285	5–10%	82	609	0.13464696223316913
15	285	10–15%	40	609	0.06568144499178982
15	285	15–20%	24	609	0.03940886699507389
15	285	≥20%	98	609	0.16091954022988506
15	285	not lit	97	609	0.1592775041050903
15	300	0–5%	588	1781	0.33015160022459294
15	300	5–10%	282	1781	0.15833801235261089
15	300	10–15%	150	1781	0.08422234699606962
15	300	15–20%	90	1781	0.05053340819764177
15	300	≥20%	208	1781	0.11678832116788321
15	300	not lit	463	1781	0.25996631106120155
15	315	0–5%	55	190	0.2894736842105263
15	315	5–10%	38	190	0.2
15	315	10–15%	21	190	0.11052631578947368
15	315	15–20%	14	190	0.07368421052631578
15	315	≥20%	38	190	0.2
15	315	not lit	24	190	0.12631578947368421
15	330	0–5%	130	442	0.29411764705882354
15	330	5–10%	65	442	0.14705882352941177
15	330	10–15%	39	442	0.08823529411764706
15	330	15–20%	24	442	0.05429864253393665
15	330	≥20%	89	442	0.20135746606334842
15	330	not lit	95	442	0.2149321266968326
15	345	0–5%	330	924	0.35714285714285715
15	345	5–10%	146	924	0.15800865800865802
15	345	10–15%	62	924	0.0670995670995671
15	345	15–20%	48	924	0.05194805194805195
15	345	≥20%	133	924	0.14393939393939395
15	345	not lit	205	924	0.22186147186147187
30	0	0–5%	61	290	0.2103448275862069
30	0	5–10%	29	290	0.1
30	0	10–15%	24	290	0.08275862068965517
30	0	15–20%	16	290	0.05517241379310345
30	0	≥20%	101	290	0.3482758620689655
30	0	not lit	59	290	0.20344827586206896
30	15	0–5%	185	637	0.2904238618524333
30	15	5–10%	87	637	0.13657770800627944
30	15	10–15%	63	637	0.0989010989010989
30	15	15–20%	42	637	0.06593406593406594
30	15	≥20%	169	637	0.2653061224489796
30	15	not lit	91	637	0.14285714285714285
30	30	0–5%	464	1703	0.2724603640634175
30	30	5–10%	315	1703	0.1849677040516735
30	30	10–15%	179	1703	0.10510863182618908
30	30	15–20%	92	1703	0.0540223135642983
30	30	≥20%	319	1703	0.18731650029359953
30	30	not lit	334	1703	0.19612448620082207
30	45	0–5%	58	187	0.31016042780748665
30	45	5–10%	29	187	0.15508021390374332
30	45	10–15%	21	187	0.11229946524064172
30	45	15–20%	12	187	0.06417112299465241
30	45	≥20%	39	187	0.20855614973262032
30	45	not lit	28	187	0.1497326203208556
30	60	0–5%	184	412	0.44660194174757284
30	60	5–10%	47	412	0.11407766990291263
30	60	10–15%	21	412	0.050970873786407765
30	60	15–20%	19	412	0.04611650485436893
30	60	≥20%	85	412	0.20631067961165048
30	60	not lit	56	412	0.13592233009708737
30	75	0–5%	355	826	0.4297820823244552
30	75	5–10%	105	826	0.1271186440677966
30	75	10–15%	59	826	0.07142857142857142
30	75	15–20%	34	826	0.04116222760290557
30	75	≥20%	189	826	0.2288135593220339
30	75	not lit	84	826	0.1016949152542373
30	90	0–5%	87	286	0.3041958041958042
30	90	5–10%	48	286	0.16783216783216784
30	90	10–15%	31	286	0.10839160839160839
30	90	15–20%	13	286	0.045454545454545456
30	90	≥20%	71	286	0.24825174825174826
30	90	not lit	36	286	0.1258741258741259
30	105	0–5%	236	611	0.3862520458265139
30	105	5–10%	74	611	0.12111292962356793
30	105	10–15%	52	611	0.0851063829787234
30	105	15–20%	26	611	0.0425531914893617
30	105	≥20%	101	611	0.16530278232405893
30	105	not lit	122	611	0.19967266775777415
30	120	0–5%	627	1778	0.3526434195725534
30	120	5–10%	240	1778	0.13498312710911137
30	120	10–15%	127	1778	0.07142857142857142
30	120	15–20%	73	1778	0.04105736782902137
30	120	≥20%	211	1778	0.1186726659167604
30	120	not lit	500	1778	0.281214848143982
30	135	0–5%	81	188	0.4308510638297872
30	135	5–10%	33	188	0.17553191489361702
30	135	10–15%	7	188	0.03723404255319149
30	135	15–20%	6	188	0.031914893617021274
30	135	≥20%	24	188	0.1276595744680851
30	135	not lit	37	188	0.19680851063829788
30	150	0–5%	194	456	0.42543859649122806
30	150	5–10%	52	456	0.11403508771929824
30	150	10–15%	30	456	0.06578947368421052
30	150	15–20%	25	456	0.05482456140350877
30	150	≥20%	58	456	0.12719298245614036
30	150	not lit	97	456	0.21271929824561403
30	165	0–5%	396	907	0.43660418963616315
30	165	5–10%	107	907	0.11797133406835722
30	165	10–15%	53	907	0.05843439911797133
30	165	15–20%	38	907	0.04189636163175303
30	165	≥20%	113	907	0.12458654906284454
30	165	not lit	200	907	0.2205071664829107
30	180	0–5%	94	276	0.34057971014492755
30	180	5–10%	39	276	0.14130434782608695
30	180	10–15%	21	276	0.07608695652173914
30	180	15–20%	14	276	0.050724637681159424
30	180	≥20%	58	276	0.21014492753623187
30	180	not lit	50	276	0.18115942028985507
30	195	0–5%	321	610	0.5262295081967213
30	195	5–10%	65	610	0.10655737704918032
30	195	10–15%	31	610	0.05081967213114754
30	195	15–20%	17	610	0.027868852459016394
30	195	≥20%	75	610	0.12295081967213115
30	195	not lit	101	610	0.16557377049180327
30	210	0–5%	718	1679	0.42763549731983325
30	210	5–10%	319	1679	0.18999404407385348
30	210	10–15%	131	1679	0.07802263251935676
30	210	15–20%	51	1679	0.030375223347230494
30	210	≥20%	180	1679	0.1072066706372841
30	210	not lit	280	1679	0.16676593210244192
30	225	0–5%	91	197	0.4619289340101523
30	225	5–10%	31	197	0.15736040609137056
30	225	10–15%	14	197	0.07106598984771574
30	225	15–20%	12	197	0.06091370558375635
30	225	≥20%	31	197	0.15736040609137056
30	225	not lit	18	197	0.09137055837563451
30	240	0–5%	172	407	0.4226044226044226
30	240	5–10%	55	407	0.13513513513513514
30	240	10–15%	26	407	0.06388206388206388
30	240	15–20%	24	407	0.05896805896805897
30	240	≥20%	86	407	0.2113022113022113
30	240	not lit	44	407	0.10810810810810811
30	255	0–5%	388	815	0.47607361963190187
30	255	5–10%	109	815	0.13374233128834356
30	255	10–15%	63	815	0.07730061349693251
30	255	15–20%	30	815	0.03680981595092025
30	255	≥20%	136	815	0.1668711656441718
30	255	not lit	89	815	0.10920245398773006
30	270	0–5%	82	265	0.30943396226415093
30	270	5–10%	35	265	0.1320754716981132
30	270	10–15%	17	265	0.06415094339622641
30	270	15–20%	14	265	0.052830188679245285
30	270	≥20%	86	265	0.32452830188679244
30	270	not lit	31	265	0.1169811320754717
30	285	0–5%	244	609	0.4006568144499179
30	285	5–10%	91	609	0.14942528735632185
30	285	10–15%	34	609	0.05582922824302135
30	285	15–20%	19	609	0.031198686371100164
30	285	≥20%	117	609	0.1921182266009852
30	285	not lit	104	609	0.17077175697865354
30	300	0–5%	521	1781	0.29253228523301517
30	300	5–10%	244	1781	0.13700168444693991
30	300	10–15%	145	1781	0.08141493542953397
30	300	15–20%	85	1781	0.04772599663110612
30	300	≥20%	301	1781	0.16900617630544637
30	300	not lit	485	1781	0.27231892195395846
30	315	0–5%	41	190	0.21578947368421053
30	315	5–10%	32	190	0.16842105263157894
30	315	10–15%	25	190	0.13157894736842105
30	315	15–20%	15	190	0.07894736842105263
30	315	≥20%	51	190	0.26842105263157895
30	315	not lit	26	190	0.1368421052631579
30	330	0–5%	94	442	0.21266968325791855
30	330	5–10%	57	442	0.12895927601809956
30	330	10–15%	33	442	0.0746606334841629
30	330	15–20%	27	442	0.06108597285067873
30	330	≥20%	131	442	0.29638009049773756
30	330	not lit	100	442	0.22624434389140272
30	345	0–5%	200	924	0.21645021645021645
30	345	5–10%	103	924	0.11147186147186147
30	345	10–15%	89	924	0.09632034632034632
30	345	15–20%	50	924	0.05411255411255411
30	345	≥20%	256	924	0.27705627705627706
30	345	not lit	226	924	0.24458874458874458
45	0	0–5%	39	290	0.13448275862068965
45	0	5–10%	36	290	0.12413793103448276
45	0	10–15%	20	290	0.06896551724137931
45	0	15–20%	12	290	0.041379310344827586
45	0	≥20%	103	290	0.35517241379310344
45	0	not lit	80	290	0.27586206896551724
45	15	0–5%	122	637	0.19152276295133439
45	15	5–10%	83	637	0.130298273155416
45	15	10–15%	43	637	0.06750392464678179
45	15	15–20%	38	637	0.059654631083202514
45	15	≥20%	225	637	0.3532182103610675
45	15	not lit	126	637	0.1978021978021978
45	30	0–5%	370	1703	0.2172636523781562
45	30	5–10%	258	1703	0.15149735760422783
45	30	10–15%	194	1703	0.11391661773341162
45	30	15–20%	112	1703	0.06576629477392835
45	30	≥20%	403	1703	0.2366412213740458
45	30	not lit	366	1703	0.21491485613623018
45	45	0–5%	43	187	0.22994652406417113
45	45	5–10%	38	187	0.20320855614973263
45	45	10–15%	12	187	0.06417112299465241
45	45	15–20%	24	187	0.12834224598930483
45	45	≥20%	40	187	0.21390374331550802
45	45	not lit	30	187	0.16042780748663102
45	60	0–5%	153	412	0.3713592233009709
45	60	5–10%	57	412	0.1383495145631068
45	60	10–15%	24	412	0.05825242718446602
45	60	15–20%	23	412	0.055825242718446605
45	60	≥20%	92	412	0.22330097087378642
45	60	not lit	63	412	0.1529126213592233
45	75	0–5%	312	826	0.37772397094430993
45	75	5–10%	118	826	0.14285714285714285
45	75	10–15%	73	826	0.08837772397094432
45	75	15–20%	43	826	0.05205811138014528
45	75	≥20%	189	826	0.2288135593220339
45	75	not lit	91	826	0.11016949152542373
45	90	0–5%	74	286	0.25874125874125875
45	90	5–10%	46	286	0.16083916083916083
45	90	10–15%	35	286	0.12237762237762238
45	90	15–20%	17	286	0.05944055944055944
45	90	≥20%	78	286	0.2727272727272727
45	90	not lit	36	286	0.1258741258741259
45	105	0–5%	202	611	0.33060556464811786
45	105	5–10%	86	611	0.1407528641571195
45	105	10–15%	55	611	0.09001636661211129
45	105	15–20%	31	611	0.05073649754500818
45	105	≥20%	112	611	0.18330605564648117
45	105	not lit	125	611	0.20458265139116202
45	120	0–5%	598	1778	0.3363329583802025
45	120	5–10%	222	1778	0.12485939257592801
45	120	10–15%	134	1778	0.07536557930258718
45	120	15–20%	88	1778	0.049493813273340834
45	120	≥20%	252	1778	0.14173228346456693
45	120	not lit	484	1778	0.2722159730033746
45	135	0–5%	70	188	0.3723404255319149
45	135	5–10%	33	188	0.17553191489361702
45	135	10–15%	12	188	0.06382978723404255
45	135	15–20%	6	188	0.031914893617021274
45	135	≥20%	28	188	0.14893617021276595
45	135	not lit	39	188	0.2074468085106383
45	150	0–5%	169	456	0.3706140350877193
45	150	5–10%	61	456	0.1337719298245614
45	150	10–15%	41	456	0.08991228070175439
45	150	15–20%	23	456	0.05043859649122807
45	150	≥20%	66	456	0.14473684210526316
45	150	not lit	96	456	0.21052631578947367
45	165	0–5%	359	907	0.3958103638368247
45	165	5–10%	107	907	0.11797133406835722
45	165	10–15%	65	907	0.07166482910694598
45	165	15–20%	29	907	0.03197353914002205
45	165	≥20%	137	907	0.15104740904079383
45	165	not lit	210	907	0.23153252480705622
45	180	0–5%	84	276	0.30434782608695654
45	180	5–10%	36	276	0.13043478260869565
45	180	10–15%	23	276	0.08333333333333333
45	180	15–20%	14	276	0.050724637681159424
45	180	≥20%	66	276	0.2391304347826087
45	180	not lit	53	276	0.19202898550724637
45	195	0–5%	283	610	0.4639344262295082
45	195	5–10%	89	610	0.14590163934426228
45	195	10–15%	39	610	0.06393442622950819
45	195	15–20%	21	610	0.03442622950819672
45	195	≥20%	76	610	0.12459016393442623
45	195	not lit	102	610	0.16721311475409836
45	210	0–5%	651	1679	0.38773079213817746
45	210	5–10%	321	1679	0.19118522930315665
45	210	10–15%	149	1679	0.08874329958308518
45	210	15–20%	71	1679	0.04228707564026206
45	210	≥20%	188	1679	0.11197141155449672
45	210	not lit	299	1679	0.1780821917808219
45	225	0–5%	82	197	0.41624365482233505
45	225	5–10%	27	197	0.13705583756345177
45	225	10–15%	24	197	0.1218274111675127
45	225	15–20%	13	197	0.06598984771573604
45	225	≥20%	32	197	0.16243654822335024
45	225	not lit	19	197	0.09644670050761421
45	240	0–5%	159	407	0.3906633906633907
45	240	5–10%	57	407	0.14004914004914004
45	240	10–15%	29	407	0.07125307125307126
45	240	15–20%	19	407	0.04668304668304668
45	240	≥20%	95	407	0.2334152334152334
45	240	not lit	48	407	0.11793611793611794
45	255	0–5%	346	815	0.4245398773006135
45	255	5–10%	115	815	0.1411042944785276
45	255	10–15%	68	815	0.0834355828220859
45	255	15–20%	36	815	0.044171779141104296
45	255	≥20%	157	815	0.19263803680981595
45	255	not lit	93	815	0.11411042944785275
45	270	0–5%	68	265	0.25660377358490566
45	270	5–10%	32	265	0.12075471698113208
45	270	10–15%	31	265	0.1169811320754717
45	270	15–20%	18	265	0.06792452830188679
45	270	≥20%	81	265	0.30566037735849055
45	270	not lit	35	265	0.1320754716981132
45	285	0–5%	195	609	0.32019704433497537
45	285	5–10%	93	609	0.15270935960591134
45	285	10–15%	57	609	0.09359605911330049
45	285	15–20%	26	609	0.042692939244663386
45	285	≥20%	132	609	0.21674876847290642
45	285	not lit	106	609	0.17405582922824303
45	300	0–5%	430	1781	0.24143739472206627
45	300	5–10%	239	1781	0.13419427288040428
45	300	10–15%	154	1781	0.08646827624929815
45	300	15–20%	100	1781	0.05614823133071308
45	300	≥20%	299	1781	0.1678832116788321
45	300	not lit	559	1781	0.31386861313868614
45	315	0–5%	38	190	0.2
45	315	5–10%	24	190	0.12631578947368421
45	315	10–15%	18	190	0.09473684210526316
45	315	15–20%	15	190	0.07894736842105263
45	315	≥20%	64	190	0.3368421052631579
45	315	not lit	31	190	0.1631578947368421
45	330	0–5%	61	442	0.13800904977375567
45	330	5–10%	39	442	0.08823529411764706
45	330	10–15%	33	442	0.0746606334841629
45	330	15–20%	30	442	0.06787330316742081
45	330	≥20%	161	442	0.36425339366515835
45	330	not lit	118	442	0.2669683257918552
45	345	0–5%	148	924	0.16017316017316016
45	345	5–10%	68	924	0.0735930735930736
45	345	10–15%	62	924	0.0670995670995671
45	345	15–20%	50	924	0.05411255411255411
45	345	≥20%	320	924	0.3463203463203463
45	345	not lit	276	924	0.2987012987012987
60	0	0–5%	27	290	0.09310344827586207
60	0	5–10%	27	290	0.09310344827586207
60	0	10–15%	20	290	0.06896551724137931
60	0	15–20%	19	290	0.06551724137931035
60	0	≥20%	112	290	0.38620689655172413
60	0	not lit	85	290	0.29310344827586204
60	15	0–5%	90	637	0.141287284144427
60	15	5–10%	63	637	0.0989010989010989
60	15	10–15%	55	637	0.08634222919937205
60	15	15–20%	43	637	0.06750392464678179
60	15	≥20%	245	637	0.38461538461538464
60	15	not lit	141	637	0.22135007849293564
60	30	0–5%	251	1703	0.1473869641808573
60	30	5–10%	239	1703	0.14034057545507928
60	30	10–15%	220	1703	0.12918379330593072
60	30	15–20%	117	1703	0.06870229007633588
60	30	≥20%	448	1703	0.2630651790957134
60	30	not lit	428	1703	0.25132119788608337
60	45	0–5%	31	187	0.1657754010695187
60	45	5–10%	31	187	0.1657754010695187
60	45	10–15%	18	187	0.0962566844919786
60	45	15–20%	13	187	0.06951871657754011
60	45	≥20%	57	187	0.3048128342245989
60	45	not lit	37	187	0.19786096256684493
60	60	0–5%	134	412	0.32524271844660196
60	60	5–10%	52	412	0.1262135922330097
60	60	10–15%	30	412	0.07281553398058252
60	60	15–20%	16	412	0.038834951456310676
60	60	≥20%	114	412	0.2766990291262136
60	60	not lit	66	412	0.16019417475728157
60	75	0–5%	247	826	0.2990314769975787
60	75	5–10%	114	826	0.13801452784503632
60	75	10–15%	83	826	0.10048426150121065
60	75	15–20%	33	826	0.039951573849878935
60	75	≥20%	243	826	0.29418886198547217
60	75	not lit	106	826	0.12832929782082325
60	90	0–5%	59	286	0.2062937062937063
60	90	5–10%	40	286	0.13986013986013987
60	90	10–15%	31	286	0.10839160839160839
60	90	15–20%	18	286	0.06293706293706294
60	90	≥20%	101	286	0.3531468531468531
60	90	not lit	37	286	0.12937062937062938
60	105	0–5%	183	611	0.2995090016366612
60	105	5–10%	84	611	0.13747954173486088
60	105	10–15%	58	611	0.09492635024549918
60	105	15–20%	33	611	0.054009819967266774
60	105	≥20%	119	611	0.19476268412438624
60	105	not lit	134	611	0.2193126022913257
60	120	0–5%	510	1778	0.28683914510686165
60	120	5–10%	240	1778	0.13498312710911137
60	120	10–15%	142	1778	0.0798650168728909
60	120	15–20%	80	1778	0.04499437570303712
60	120	≥20%	273	1778	0.15354330708661418
60	120	not lit	533	1778	0.2997750281214848
60	135	0–5%	67	188	0.35638297872340424
60	135	5–10%	35	188	0.18617021276595744
60	135	10–15%	8	188	0.0425531914893617
60	135	15–20%	8	188	0.0425531914893617
60	135	≥20%	31	188	0.16489361702127658
60	135	not lit	39	188	0.2074468085106383
60	150	0–5%	155	456	0.3399122807017544
60	150	5–10%	61	456	0.1337719298245614
60	150	10–15%	33	456	0.07236842105263158
60	150	15–20%	10	456	0.021929824561403508
60	150	≥20%	91	456	0.19956140350877194
60	150	not lit	106	456	0.2324561403508772
60	165	0–5%	300	907	0.33076074972436603
60	165	5–10%	128	907	0.14112458654906285
60	165	10–15%	62	907	0.06835722160970231
60	165	15–20%	32	907	0.03528114663726571
60	165	≥20%	170	907	0.1874310915104741
60	165	not lit	215	907	0.237045203969129
60	180	0–5%	70	276	0.2536231884057971
60	180	5–10%	36	276	0.13043478260869565
60	180	10–15%	28	276	0.10144927536231885
60	180	15–20%	14	276	0.050724637681159424
60	180	≥20%	73	276	0.2644927536231884
60	180	not lit	55	276	0.19927536231884058
60	195	0–5%	260	610	0.4262295081967213
60	195	5–10%	94	610	0.1540983606557377
60	195	10–15%	41	610	0.06721311475409836
60	195	15–20%	27	610	0.04426229508196721
60	195	≥20%	84	610	0.1377049180327869
60	195	not lit	104	610	0.17049180327868851
60	210	0–5%	584	1679	0.34782608695652173
60	210	5–10%	298	1679	0.17748659916617035
60	210	10–15%	161	1679	0.0958904109589041
60	210	15–20%	81	1679	0.048243001786777845
60	210	≥20%	255	1679	0.15187611673615248
60	210	not lit	300	1679	0.1786777843954735
60	225	0–5%	70	197	0.3553299492385787
60	225	5–10%	34	197	0.17258883248730963
60	225	10–15%	12	197	0.06091370558375635
60	225	15–20%	21	197	0.1065989847715736
60	225	≥20%	37	197	0.18781725888324874
60	225	not lit	23	197	0.116751269035533
60	240	0–5%	149	407	0.36609336609336607
60	240	5–10%	50	407	0.12285012285012285
60	240	10–15%	32	407	0.07862407862407862
60	240	15–20%	19	407	0.04668304668304668
60	240	≥20%	106	407	0.26044226044226043
60	240	not lit	51	407	0.12530712530712532
60	255	0–5%	301	815	0.3693251533742331
60	255	5–10%	106	815	0.13006134969325153
60	255	10–15%	74	815	0.09079754601226994
60	255	15–20%	49	815	0.06012269938650307
60	255	≥20%	193	815	0.23680981595092024
60	255	not lit	92	815	0.11288343558282209
60	270	0–5%	56	265	0.21132075471698114
60	270	5–10%	33	265	0.12452830188679245
60	270	10–15%	19	265	0.07169811320754717
60	270	15–20%	21	265	0.07924528301886792
60	270	≥20%	98	265	0.36981132075471695
60	270	not lit	38	265	0.14339622641509434
60	285	0–5%	184	609	0.3021346469622332
60	285	5–10%	90	609	0.1477832512315271
60	285	10–15%	52	609	0.08538587848932677
60	285	15–20%	36	609	0.059113300492610835
60	285	≥20%	135	609	0.22167487684729065
60	285	not lit	112	609	0.1839080459770115
60	300	0–5%	375	1781	0.21055586749017405
60	300	5–10%	207	1781	0.11622683885457608
60	300	10–15%	163	1781	0.09152161706906232
60	300	15–20%	99	1781	0.05558674901740595
60	300	≥20%	348	1781	0.19539584503088153
60	300	not lit	589	1781	0.33071308253790005
60	315	0–5%	28	190	0.14736842105263157
60	315	5–10%	20	190	0.10526315789473684
60	315	10–15%	17	190	0.08947368421052632
60	315	15–20%	17	190	0.08947368421052632
60	315	≥20%	70	190	0.3684210526315789
60	315	not lit	38	190	0.2
60	330	0–5%	46	442	0.10407239819004525
60	330	5–10%	28	442	0.06334841628959276
60	330	10–15%	25	442	0.05656108597285068
60	330	15–20%	24	442	0.05429864253393665
60	330	≥20%	193	442	0.43665158371040724
60	330	not lit	126	442	0.2850678733031674
60	345	0–5%	114	924	0.12337662337662338
60	345	5–10%	60	924	0.06493506493506493
60	345	10–15%	58	924	0.06277056277056277
60	345	15–20%	55	924	0.05952380952380952
60	345	≥20%	345	924	0.37337662337662336
60	345	not lit	292	924	0.31601731601731603

Each facade surface receives one vote. Each occupied direction bin sums to 100%, including “not lit.” Highlighting dims other bands without renormalizing the data. North is 0°, increasing clockwise.

Latitude All five latitudes0°15°30°45°60°Highlight case All casesRed HookLong Island CityCo-op CityJackson HeightsPark SlopeBaysideRiverdaleFinancial DistrictGreenridgeMidtownReset to paper view

Hover, tap, or focus a mark to inspect its values. Use arrow keys to move between marks.

Expand figureDownload SVGDownload PNGDownload visible data (CSV)

Data table and source downloads

Original figure data (CSV)

Figure data. Ratios are fractions; multiply by 100 for percentages.

Latitude / mean	Case / mean	WMAPE
0	Red Hook	0.006804321678177354
0	Long Island City	0.009776988186670712
0	Co-op City	0.012263967243620218
0	Jackson Heights	0.012930630029008303
0	Park Slope	0.01398223839320629
0	Bayside	0.02294489079771096
0	Riverdale	0.028759864542643426
0	Financial District	0.035324621363404536
0	Greenridge	0.03191808721077165
0	Midtown	0.03954258792101192
0	Latitude mean	0.02142481973662254
15	Red Hook	0.007242849389634833
15	Long Island City	0.010284754098403246
15	Co-op City	0.012290805120998564
15	Jackson Heights	0.013307134206061583
15	Park Slope	0.014843120012817918
15	Bayside	0.023894259718158093
15	Riverdale	0.0281780103394807
15	Financial District	0.03551025985038106
15	Greenridge	0.03334870638042589
15	Midtown	0.03865554522250768
15	Latitude mean	0.021755544433886952
30	Red Hook	0.008659214036236226
30	Long Island City	0.011481659350416572
30	Co-op City	0.013812794799290092
30	Jackson Heights	0.014103653120068763
30	Park Slope	0.01706621790607637
30	Bayside	0.02669877503185295
30	Riverdale	0.02893032654617155
30	Financial District	0.03703656807153549
30	Greenridge	0.03624995394365587
30	Midtown	0.03993066976388016
30	Latitude mean	0.023396983256918406
45	Red Hook	0.011447570520782066
45	Long Island City	0.014759378123851299
45	Co-op City	0.017303600371545953
45	Jackson Heights	0.01766590747885551
45	Park Slope	0.02166380189905993
45	Bayside	0.033476645368978486
45	Riverdale	0.031664375605265645
45	Financial District	0.0414835745898595
45	Greenridge	0.044522381203547214
45	Midtown	0.04403307553466833
45	Latitude mean	0.02780203106964139
60	Red Hook	0.01589054959898882
60	Long Island City	0.019363584047082976
60	Co-op City	0.022554242130182083
60	Jackson Heights	0.024064775175987936
60	Park Slope	0.028218548223553814
60	Bayside	0.042570335581516905
60	Riverdale	0.03574017567779699
60	Financial District	0.04575653140250819
60	Greenridge	0.05518599071903305
60	Midtown	0.049318461514495045
60	Latitude mean	0.033866319407114584
Case mean	Red Hook	0.01000890104476386
Case mean	Long Island City	0.013133272761284962
Case mean	Co-op City	0.01564508193312738
Case mean	Jackson Heights	0.016414420001996416
Case mean	Park Slope	0.019154785286942862
Case mean	Bayside	0.029916981299643475
Case mean	Riverdale	0.030654550542271664
Case mean	Financial District	0.03902231105553775
Case mean	Greenridge	0.04024502389148673
Case mean	Midtown	0.04229606799131262
Case mean	Latitude mean	0.025649139580836776

Case and latitude margins are unweighted arithmetic means of the cell ratios. They differ from the signal-pooled values in Figure 2. The blue outline marks the largest core cell; highlighting preserves the full matrix and its color scale.

Discussion

Exploratory shading observations capture obstruction-dependent temporal structure that geometry alone cannot reliably encode. Consequently, SF and MF+SF outperform MF once one exploratory period is affordable, suggesting MF may introduce variation unrelated to shading-profiles. SF with $m=3$ and $r=0.20$ provides the clearest balance between accuracy and ray-tracing workload. The matched-cost random downsampling baseline confirms that the improvement is not explained by reduced evaluated sensor count alone. Exploratory shading directs computation toward sensors whose temporal profiles better represent the remaining sensors, yielding approximately 2.2× lower WMAPE. Moreover, random downsampling estimates aggregate building profiles, whereas ShadingZip reconstructs outputs for every sensor and retains building and surface identities, and is particularly useful for location-based queries adopted in window or BIPV models. Orientation-dependent errors qualify the strong building-level performance. North-facing facades exhibit higher surface errors at higher latitudes as their smaller signal produces a sensitive WMAPE denominator, yielding limited contribution to building-level error. The nearly uniform orientation pattern at 0° suggests little directional bias in the evaluated sample. Meanwhile, ShadingZip addresses a different aspect of computational cost from pixel-counting, ray-tracing, or voxel acceleration methods. Those methods reduce the cost of each evaluation, whereas ShadingZip reduces the number of evaluations requested. They are therefore complementary and may provide compound savings when combined.

Conclusion and implications

ShadingZip reduces shading computation by tracing complete profiles only for representative sensors selected within each building. Across ten morphologies and five latitudes, SF with $m=3$ and $r=0.20$ achieved a mean building-aggregated lit-sensor WMAPE of 2.6% saving 67.4% ray-tracing effort. Future work should determine whether the same selective representation can jointly reconstruct sky-patch visibility or sky-view factors. Meanwhile, ShadingZip still depends on exploratory ray-tracing; future ray-tracing-free methods could learn conditional distributions of shading profiles from geometry and context directly.

References

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Citation

Chengxuan Li, Zihan Jimmy Wang, Timur Dogan. 2026. ShadingZip: Within-Building Selective Computation of Shading Profiles for Urban Building Energy Models. ASIM 2026. Author manuscript.

Copy BibTeX

@inproceedings{shading-zip2026,
  title={ShadingZip: Within-Building Selective Computation of Shading Profiles for Urban Building Energy Models},
  author={Chengxuan Li and Zihan Jimmy Wang and Timur Dogan},
  booktitle={ASIM 2026},
  year={2026},
  note={Accepted manuscript}
}