Estimation of daylight availability in Kolkata and approximation of indoor daylight levels for different daylighting methods

Figures & data

Table 1 . Ten years (2005–2014) monthly average GHI, DNI and temperature (T) for Kolkata.

Month	Unit area energy content of GHI (kWh/m^2)	Unit area energy content of DNI (kWh/m^2)	T (°C)
January	138.669	157.515	17.68
February	150.763	162.24	21.8
March	190.778	176.104	27.02
April	200.373	167.353	30.33
May	191.853	134.267	30.98
June	150.526	84.886	29.64
July	142.831	72.639	27.6
August	139.621	73.557	27.49
September	138.162	90.139	27.05
October	142.856	123.482	25.62
November	138.573	148.147	21.99
December	133.692	157.11	17.94

Figure 1. Monthly hourly average GHI in Kolkata.

Figure 2. Monthly hourly average DHI in Kolkata.

Figure 3. Monthly DHI to GHI ratio for Kolkata for the period of 2005–2015 .

Table 2 . Global and diffuse luminous efficacy coefficients of Perez model.

Sky category	Sky clearness ($\epsilon$)		Coefficients of global luminous efficacy (Kg)				Coefficients of diffuse luminous efficacy (Kd)
	Lower limit	Upper limit	ai	bi	ci	di	ai	bi	ci	di
Overcast	1	1.065	96.63	−0.47	11.5	−9.16	97.24	−0.46	12	−8.91
	1.065	1.23	107.54	0.79	1.79	−1.19	107.22	1.15	0.59	−3.95
	1.23	1.5	98.73	0.7	4.4	−6.95	104.97	2.96	−5.53	−8.77
	1.5	1.95	92.72	0.56	8.36	−8.31	102.39	5.59	−13.95	−13.9
	1.95	2.8	86.73	0.98	7.1	−10.94	100.71	5.94	−22.75	−23.74
	2.8	4.5	88.34	1.39	6.06	−7.6	106.42	3.83	−36.15	−28.83
	4.5	6.2	78.63	1.47	4.93	−11.37	141.88	1.9	−53.24	−14.03
Clear	6.2	–	99.65	1.86	−4.46	−3.15	152.23	0.35	−45.27	−7.98

Table 3 . Various IESNA recommended daylight availability constants.

Sky condition	Atmospheric extinction coefficient (c)	Sunrise to sunset illuminance ratio (A) in klx	Solar Altitude Illuminance Coefficient (B) in klx	Solar altitude illuminance exponent (C) in klx
Clear	0.21	0.8	15.5	0.5
Partly cloudy	0.80	0.3	45	1
Cloudy	^a	0.3	21	1

^a For no direct sun, E_dn= 0.

Table 4 . Sky ratio ranges corresponding to different sky conditions.

Sky condition	Sky ratio
Clear	<0.3
Partly cloudy	0.3–0.8
Cloudy	>0.8

Table 5 . Average global luminous efficacy (lm/W) in Kolkata.

Month/hour	7:30	8:30	9:30	10:30	11:30	12:30	13:30	14:30	15:30	16:30	17:30
Jan	76.14	85.65	94.42	99.91	102.93	102.53	102.26	101.10	98.97	107.76	96.90
Feb	79.03	90.56	97.07	100.99	103.31	104.25	104.12	103.07	102.07	103.47	98.24
Mar	85.46	94.63	100.16	103.64	105.61	106.19	105.86	104.70	102.61	101.53	126.75
Apr	87.72	97.39	102.88	105.70	107.32	107.91	107.44	105.89	105.59	105.60	116.90
May	94.56	102.79	108.57	112.21	114.42	114.63	113.71	112.07	109.48	105.41	113.60
Jun	99.62	105.51	110.17	113.24	114.24	115.08	116.15	114.53	112.94	110.50	114.77
Jul	98.05	104.54	108.29	111.84	113.94	116.03	116.08	115.00	112.50	109.88	113.11
Aug	92.63	101.95	108.44	112.66	114.18	115.88	114.54	113.83	111.34	110.84	115.42
Sep	96.13	101.35	107.79	110.96	114.20	114.71	113.84	111.71	109.76	108.24	125.52
Oct	91.31	97.38	104.66	107.72	110.35	110.04	110.04	108.32	105.49	111.91	95.30
Nov	84.11	91.31	98.79	103.03	104.16	104.60	105.20	102.99	99.84	118.91	95.34
Dec	78.66	90.16	95.12	99.86	101.64	102.45	101.82	101.57	99.08	117.94	96.05

Table 6. Average diffuse luminous efficacy (lm/W) in Kolkata.

Month/hour	7:30	8:30	9:30	10:30	11:30	12:30	13:30	14:30	15:30	16:30	17:30
Jan	52.98	94.15	105.60	112.00	114.98	115.28	115.88	116.40	114.39	116.60	97.57
Feb	61.81	92.82	106.40	112.53	115.67	116.95	117.84	118.71	117.52	117.05	98.77
Mar	79.87	102.01	111.85	116.35	118.26	118.45	118.87	119.72	120.23	121.48	126.73
Apr	102.88	113.12	115.63	118.35	119.58	120.45	120.88	120.68	122.36	118.96	117.18
May	124.33	132.76	137.53	139.72	141.06	140.46	139.67	139.68	139.71	138.53	118.58
Jun	132.85	137.10	139.66	141.07	147.08	147.72	142.85	142.65	143.95	145.14	120.35
Jul	129.40	134.78	142.50	145.25	146.27	141.97	142.69	143.09	142.36	142.89	131.34
Aug	124.03	136.44	143.36	147.13	146.89	141.48	147.25	148.93	148.82	144.79	134.33
Sep	110.33	134.90	142.02	134.69	147.51	147.63	147.17	146.20	147.66	152.15	125.50
Oct	96.47	124.20	124.35	128.40	138.15	136.81	138.44	138.69	139.06	127.99	96.00
Nov	76.15	107.57	116.95	121.49	118.94	120.07	124.85	124.01	123.78	119.10	96.00
Dec	60.89	92.56	107.29	112.45	114.45	116.43	116.34	117.06	117.64	118.16	96.70

Table 7. Average global horizontal illuminance (klx) in Kolkata.

Month/hour	7:30	8:30	9:30	10:30	11:30	12:30	13:30	14:30	15:30	16:30	17:30
Jan	10.82	27.29	44.55	60.08	67.19	65.92	60.46	45.35	26.30	6.20	0
Feb	14.41	36.09	56.62	71.47	78.09	74.96	66.35	53.25	33.18	12.20	0.02
Mar	24.40	48.04	69.99	86.23	94.42	91.89	80.34	61.43	40.37	16.72	0.49
Apr	32.66	56.28	80.00	94.33	100.76	98.56	85.50	66.64	44.96	19.50	1.79
May	34.80	59.00	75.21	86.23	88.74	89.73	79.88	64.96	43.55	21.65	3.85
Jun	28.37	46.21	61.55	72.90	80.04	73.76	59.24	48.96	32.59	17.76	4.43
Jul	28.90	47.60	60.72	74.21	77.13	67.77	58.26	46.94	33.72	22.47	6.32
Aug	25.89	47.70	69.30	79.11	81.89	69.52	65.84	52.46	41.21	16.24	3.28
Sep	30.18	49.90	69.60	81.56	82.29	71.02	61.51	45.81	29.62	11.30	0.36
Oct	26.19	46.97	65.89	76.94	76.33	67.03	53.96	40.03	21.77	5.22	0
Nov	20.39	39.07	57.76	70.03	73.54	68.70	56.77	39.01	18.37	1.08	0
Dec	13.15	31.41	46.77	59.92	64.03	60.81	51.84	36.42	17.41	1.27	0

Table 8. Average diffuse horizontal illuminance (klx) in Kolkata.

Month/hour	7:30	8:30	9:30	10:30	11:30	12:30	13:30	14:30	15:30	16:30	17:30
Jan	5.97	17.87	25.43	29.71	32.01	30.82	29.01	24.69	19.35	6.20	0
Feb	8.19	19.74	26.31	30.36	32.15	32.55	30.78	26.8	21.67	11.5	0.02
Mar	14.16	23.43	28.86	32.15	33.96	34.82	33.36	29.54	23.53	14.32	0.49
Apr	22.33	30.1	32.74	35.44	36.62	36.19	34.49	31.51	26.37	16.38	1.79
May	26.08	33.63	37.51	40.08	40.73	41.76	40.44	35.75	28.57	20.35	3.85
Jun	27.42	38.76	44.16	48.07	49.76	48.97	41.96	38.32	28.9	17.76	4.43
Jul	26.49	37.81	41.73	47.21	49.58	47.07	42.88	37.23	31.04	20.79	6.32
Aug	22.77	33.21	38.73	42.17	46.9	45.82	44.63	36.96	29.27	15.86	3.28
Sep	17.75	29.67	35.97	36.31	41.32	41.61	39.61	34.91	24.61	11.30	0.36
Oct	16.81	27.93	31.19	34.36	39.59	41.35	35.46	28.65	19.91	5.22	0
Nov	12.62	24.08	29.91	34.06	33.98	33.35	31.53	25.8	17.46	1.08	0
Dec	7.64	18.2	25.78	30.08	29.92	29.14	27.35	22.77	15.06	1.27	0

Table 9. Average direct horizontal solar illuminance (klx) in Kolkata.

Month/hour	7:30	8:30	9:30	10:30	11:30	12:30	13:30	14:30	15:30	16:30	17:30
Jan	0	2.26	10.99	21.23	28.86	31.79	29.37	22.14	12.01	0	0
Feb	0.01	3.91	14.91	26.95	35.88	39.64	37.47	29.81	18.31	0	0
Mar	0.57	8.90	22.89	36.33	45.73	49.32	46.47	37.67	24.56	10.38	0
Apr	3.40	15.87	31.33	44.84	53.66	56.38	52.51	42.72	28.62	13.25	0
May	6.27	20.08	35.51	48.48	56.67	58.89	54.75	44.92	30.88	15.41	0
Jun	6.60	20.26	35.47	48.37	56.69	59.20	55.58	46.31	32.78	0	0
Jul	5.20	18.39	33.78	47.16	56.06	59.18	56.04	47.12	33.73	18.34	0
Aug	3.66	16.28	31.84	45.54	54.65	57.78	54.35	44.99	31.14	15.59	0
Sep	2.46	13.97	28.86	41.87	50.17	52.30	47.91	37.74	23.65	9.18	0
Oct	1.19	10.28	23.28	34.71	41.63	42.67	37.64	27.50	14.57	0	0
Nov	0.22	5.87	16.42	26.37	32.52	33.42	28.88	19.92	9.07	0	0
Dec	0.01	2.95	11.67	21.08	27.53	29.25	25.84	18.13	8.42	0	0

Table 10. Average horizontal sky (diffuse) illuminance (klx) in Kolkata.

Month/hour	7:30	8:30	9:30	10:30	11:30	12:30	13:30	14:30	15:30	16:30	17:30
Jan	3.72	13.13	21.25	27.53	31.53	32.98	31.79	28.03	21.96	6.69	5.64
Feb	5.38	15.26	23.86	30.58	34.97	36.73	35.72	32.02	25.9	8.45	3.97
Mar	9.7	19.76	28.45	35.18	39.49	41.09	39.82	35.81	29.34	20.85	5.25
Apr	14.66	24.43	32.75	39.06	42.94	44.12	42.44	38.11	31.4	22.78	6.14
May	17.56	26.87	34.76	40.67	44.22	45.16	43.4	39.09	32.52	24.13	6.93
Jun	17.84	26.97	34.74	40.62	44.22	45.29	43.75	39.71	33.45	12.01	7.66
Jul	16.56	25.91	33.93	40.09	43.95	45.28	43.95	40.07	33.91	25.88	7.87
Aug	14.96	24.67	33	39.37	43.36	44.71	43.23	39.13	32.66	24.25	6.92
Sep	13.46	23.26	31.54	37.74	41.45	42.38	40.45	35.83	28.85	19.96	4.72
Oct	11.31	20.79	28.67	34.42	37.66	38.13	35.81	30.87	23.65	7	5.52
Nov	8.14	17.22	24.77	30.27	33.35	33.79	31.55	26.8	19.87	5.39	3.26
Dec	5.02	14.07	21.71	27.43	30.84	31.71	29.98	25.76	19.34	5.37	3.62

Table 11. Total average daylight illuminance (klx) in Kolkata.

Month/hour	7:30	8:30	9:30	10:30	11:30	12:30	13:30	14:30	15:30	16:30	17:30
Jan	3.72	15.39	32.24	48.76	60.39	64.77	61.16	50.17	33.97	6.69	5.64
Feb	5.39	19.17	38.77	57.53	70.86	76.37	73.19	61.83	44.21	8.45	3.97
Mar	10.27	28.66	51.34	71.50	85.23	90.42	86.29	73.48	53.90	31.23	5.25
Apr	18.05	40.30	64.09	83.91	96.60	100.50	94.95	80.83	60.02	36.02	6.14
May	23.83	46.96	70.26	89.15	100.89	104.05	98.15	84.01	63.39	39.54	6.93
Jun	24.44	47.22	70.21	89.00	100.91	104.49	99.33	86.02	66.22	12.01	7.66
Jul	21.77	44.30	67.71	87.25	100.02	104.46	99.99	87.19	67.64	44.22	7.87
Aug	18.61	40.96	64.84	84.91	98.00	102.49	97.58	84.12	63.80	39.84	6.92
Sep	15.92	37.23	60.40	79.61	91.61	94.69	88.36	73.57	52.49	29.14	4.72
Oct	12.50	31.07	51.95	69.13	79.29	80.81	73.45	58.37	38.22	7.00	5.52
Nov	8.36	23.09	41.20	56.64	65.87	67.21	60.43	46.72	28.94	5.39	3.26
Dec	5.03	17.02	33.38	48.51	58.37	60.96	55.82	43.89	27.77	5.37	3.62

Figure 4. Comparison of Measured Solar Illuminance Values with Computed Solar Illuminance Values for April Month.

Figure 5. Estimation of daylight illuminance transmission into a room through an eastward window with motorised shading control with data obtained from Perez model.

Figure 6. Estimation of daylight illuminance transmission into a room through an eastward window with motorised shading control with data obtained from IESNA recommended calculation procedure.

Figure 7. Estimation of average horizontal workplane illuminance from light pipe simulation with data obtained from Perez model.

Figure 8. Estimation of average horizontal workplane illuminance from light pipe simulation with data obtained from IESNA recommended calculation procedure.

Figure 9. Estimation of average horizontal workplane illuminance from skylight simulation with data obtained from Perez model.

Figure 10. Estimation of average horizontal workplane illuminance from skylight simulation with data obtained from IESNA recommended calculation procedure.

Figure 11. Estimation of daylight illuminance transmission into a room through a clerestory from light shelf simulation with data obtained from Perez model.

Figure 12. Estimation of daylight illuminance transmission into a room through a clerestory from light shelf simulation with data obtained from IESNA recommended calculation procedure.

Figure 13. Percentage cumulative frequency curves of global and diffuse horizontal illuminance for applied Perez model.

Figure 14. Percentage cumulative frequency curves of total daylight illuminance and horizontal sky illuminance for applied IESNA recommended calculation procedure.

Figure 15. Percentage cumulative frequency curves of global and diffuse luminous efficacy for applied Perez model.

Figure 16. Plots of GHI vs. global horizontal illuminance and DHI vs. diffuse horizontal illuminance for the applied Perez model.

Figure 17. Plots of GHI vs. total daylight illuminance and DHI vs. horizontal sky illuminance for the applied IESNA recommended calculation procedure.

Table 12. Statistical Errors in the Estimation of Indoor Daylight Illuminance Levels.

Daylighting method/device	Matched-pair variables	RMSE	%RMSE	MAE	%MAE
Window shading control	Estimated daylight illuminance transmission from measurement data – estimated daylight illuminance transmission from application of Perez Model	279.82	2.01	266.51	1.91
	Estimated daylight illuminance transmission from measurement data – estimated daylight illuminance transmission from application of IESNA recommended calculation procedure	379.61	9.91	352.06	9.19
Light Pipe	Estimated average horizontal workplane illuminance from measurement data – estimated average horizontal workplane illuminance from application of Perez Model	6.86	2.84	6.18	2.56
	Estimated average horizontal workplane illuminance from measurement data – estimated average horizontal workplane illuminance from application of IESNA recommended calculation procedure	48.85	20.23	44.14	18.28
Skylight (Overcast Sky Condition)	Estimated average horizontal workplane illuminance from measurement data – estimated average horizontal workplane illuminance from application of Perez model	37.74	2.84	33.98	2.56
	Estimated average horizontal workplane illuminance from measurement data – estimated average horizontal workplane illuminance from application of IESNA recommended calculation procedure	268.68	20.23	242.75	18.28
Skylight (Clear Sky Condition)	Estimated average horizontal workplane illuminance from measurement data – estimated average horizontal workplane illuminance from application of Perez model	38.27	2.78	34.24	2.48
	Estimated average horizontal workplane illuminance from measurement data – estimated average horizontal workplane illuminance from application of IESNA recommended calculation procedure	280.13	20.33	253.36	18.39
Light Shelf	Estimated daylight illuminance transmission from measurement data – estimated daylight illuminance transmission from application of Perez model	218.72	2.07	172.01	1.63
	Estimated daylight illuminance transmission from measurement data – estimated daylight illuminance transmission from application of IESNA recommended calculation procedure	2392.71	22.68	2172.13	20.59