A parametric method for estimation of leaf area index using landsat ETM+ data

Figures & data

Figure 1. (a) Distribution of reflectance values in SNIR-R. (b) The migration of a single vegetated pixel in SNIR-R during a growing season (Jensen 2009). For full colour versions of the figures in this paper, please see the online version.

Table 1. The information about five sites of BigFoot campaign (study area).

Site name	Latitude	Longitude	Location	Vegetation type
AGRO	40.00662	−88.29103	Champaign, lllinois	Corn, soybean, fallow
HARV	42.53825	−72.17138	Peter sham, Massachusetts	Eastern hardwood, eastern hemlock, red pine, old field meadow
KONZ	39.08228	−96.56025	Manhattan, Central Kansas	Tall grass Prairie, Short grass Prairie, Shrub community
SEVI	34.3602	−106.7003	Belen, NM, USA	Black gramma, blue gramma
TUND	71.2808	−156.6122	Barrow, AK, USA	Arctic tundra

Table 2. Information on LAI field measurements.

Site name	Method of measurements	Date of field measurements	Number of LAI measurements	Mean of LAI values
AGRO	Destructive harvest	27 July 1999	34	6.5
		11 September 1999	36	6
		4 July 2000	49	3.3
HARV	Li-Cor LAI-2000	18 June 2000	8	5.2
		27 July 2001, 28 July 2001	30	5.3
		24 August 2002	28	5.7
KONZ	Li-Cor LAI-2000, Destructive harvest	7 June 2000, 8 June 2000	47	2
		25 August 2000, 26 August 2000	50	2
		16 August 2001	58	2.5
SEVI	Destructive harvest	26 July 2002	47	0.3
		22 August 2002	20	0.5
		9 September 2002	49	0.4
		15 November 2002	41	0.4
TUND	Destructive harvest	7 July 2002	42	0.2
			Total = 539

Figure 2. BigFoot field sampling design (+ signs represent points where LAIs are measured).

Table 3. The information about ETM+ images used in this study.

Site name	Date of in situ data collection	Image acquisition date	Difference between image acquisition date and date of in situ data collection (day)
SEVI	26 July 2002	25 July 2002	1
	22 August 2002	19 August 2002	3
	9 September 2002	4 September 2002	5
	15 November 2002	14 November 2002	1
TUND	7 July 2002	18 July 2002	11
KONZ	7 June 2000, 8 June 2000	7 June 2000	0
	25 August 2000,26 August 2000	26 August 2000	0
	16 August 2001	13 August 2001	3
HARV	18 June 2000	23 June 2000	5
	27 July 2001, 28 July 2001	28 July 2001	0
	24 August 2002	23 August 2002	1
AGRO	27 July 1999	29 July 1999	2
	11 September 1999	6 September 1999	5
	4 July 2000	29 June 2000	5
		Total = 14

Figure 3. Nine parameters used for estimation of LAI in this study (four angles and five distances).

Table 4. The correlation (R² values) between in situ measured LAI with each of the nine parameters, using linear, polynomial (second order), exponential, logarithmic, and power equations.

Parameter\R^2	linear	Polynomial (second order)	Exponential	Logarithmic	Power
SR	0.83	0.85	0.57	0.80	0.72
PVI	0.82	0.85	0.73	0.52	0.60
	0.83	0.83	0.67	0.62	0.37
	0.07	0.13	0.09	0.08	0.11
	0.73	0.74	0.51	0.67	0.52
	0.51	0.53	0.29	0.53	0.27
α	0.83	0.84	0.70	0.55	0.61
ß	0.55	0.76	0.64	0.37	0.49
Ɣ	0.42	0.53	0.48	0.38	0.47

Table 5. Information of five soil lines suggested by different workers.

Reference	Soil type	SL equation	Mean SL
Huete, Post, and Jackson (1984)	Gravel, sand, silt, loam	NIR = 1.166*Red + 0.042
Galvão and Vitorello (1998)	Silt, clay, sand	NIR = 1.368*Red – 0.0117
Baret, Jacquemoud, and Hanocq (1993)	Silica sand, peat, clay, pebble	NIR = 1.176*Red + 0.037	NIR = 1.1628*Red + 0.017
Yoshioka et al. (2010)	Silt, clay, sand	NIR = 1.027*Red – 0.0049
Mobasheri and Bidkhan (2013)	Inorganic clay	NIR = 1.0849*Red + 0.0225

Table 6. Reflectance information for various dry soils.

Reference	Soil type	Reflectance in Red band	Reflectance in NIR band
Weidong et al. (2002)	Clay(45%),silt fine(17.6%),silt gross(6.2%),sand fine(6.4%),sand gross(5.1%)organic carbon(7.9%),organic matter(15.8%),Fe(3.9%),…	0.0838	0.1295
	Clay(10.8%),silt fine(40.5%),silt gross(34.3%),sand fine(5.7%),sand gross(2.4%)organic carbon(0.7%),organic matter(1.5%),Fe(1%),…	0.4020	0.4823
	Clay(12.9%),silt fine(34.6%),silt gross(25.2%),sand fine(9.5%),sand gross(7.7%)organic carbon(2.9%),organic matter(5.9%),Fe(0.8%),…	0.1829	0.3048
	Clay(24.8%),silt fine(16.2%),silt gross(12.6%),sand fine(13.8%),sand gross(25%)organic carbon(1.6%),organic matter(3.2%),Fe(4.4%),…	0.1829	0.2248
	Clay(43.4%),silt fine(17.8%),silt gross(9.8%),sand fine(10.4%),sand gross(5.5%)organic carbon(3.8%),organic matter(7.5%),Fe(4.1%),…	0.1352	0.1848
	Clay(42.2%),silt fine(24.2%),silt gross(16%),sand fine(6.4%),sand gross(1.4%)organic carbon(0.8%),organic matter(1.6%),Fe(3.6%),…	0.2248	0.2819
	Clay(44.7%),silt fine(15.1%),silt gross(10.1%),sand fine(6%),sand gross(8.3%)organic carbon(1.3%),organic matter(2.7%),Fe(3.7%),…	0.1600	0.2133
	Clay(4.5%),silt fine(4.9%),silt gross(16.8%),sand fine(41%),sand gross(28.9%)organic carbon(0.5%),organic matter(0.9%),Fe(0.6%),…	0.2876	0.3733
Lobell and Asner (2002)	Argic Aridisol	0.1358	0.2056
	Xeric Andisol	0.1055	0.1744
	Ustic Mollisol	0.1082	0.1958
	Aridic Entisol	0.1506	0.2795
Whiting, Li, and Ustin (2004)	Basin, low sodicity	0.2900	0.3357
Bryant et al. (2003)	Light colored, sandy loam Entisol	0.2663	0.3290
	Red-colored clay and iron-rich Aridsol	0.1777	0.2280
	Dark-colored silt/loam Mollisol with approximately5% organic matter	0.2663	0.3290
Nocita et al. (2013)	Loam-loess on red sandstone and Luxembourgish sandstone	0.2098	0.2721
Mobasheri and Bidkhan (2013)	Inorganic clay	0.2480	0.2895

Note: The highlighted models are better than others.

Figure 4. Plots of nine mentioned parameters against in situ measured LAI.

Figure 5. Different dry soil positions in SNIR-R and selection of Point B.

Figure 6. The method of choosing Point C.

Table 7. The information about six best fits among 511 different combinations of regression equations for estimation of LAI.

Number	Index name	Regression equation	RMSE	RRMSE (%)	R
1	5P-LAI1	Ɣ	0.751	29.87	0.943
2	5P-LAI2	Ɣ	0.752	29.91	0.943
3	5P-LAI3	Ɣ	0.753	29.95	0.943
4	7P-LAI1	Ɣ	0.753	29.95	0.941
5	8P-LAI1	Ɣ	0.753	29.96	0.941
6	5P-LAI4		0.754	29.99	0.943

Note: The highlighted models are better than others.

Figure 7. Measured versus 5P-LAI3 model predicted values of LAI. Diagonal is 1:1.

Figure 8. Variation of the absolute error and relative error for different values of LAI test data.

Figure 9. Three regression equations in three different regions of the triangle in the SNIR-R. Diagonal is 1:1.

Table 8. Confusion matrix for LAI estimation in three classes of values.

		Predicted
		[0–1]	[1–4]	[4–12]	Total	Producer accuracy (%)
True	[0–1]	49	4		53	92.5
	[1–4]		46		46	100
	[4–12]			36	36	100
	Total	49	50	36	135
	User accuracy (%)	100	92	100

Note: The highlighted models are better than others.

Figure 10. The estimated LAI values by TSM against in situ measured data. Diagonal is 1:1.

Table 9. Comparison between the models proposed in this study with other models in which the BigFoot data are used.

Reference	Model	R	RMSE
Cohen et al. (2006)	Using the information such as Tasseled Cap index, brightness, greenness, wetness and RMA (Reduced Major Axis) regression for nine site of BigFoot	0.94	0.73
Cohen et al. (2003)	Using the information such as Tasseled Cap index, brightness, greenness, wetness and RMA regression for four site of BigFoot	0.90	0.77
Berterretche et al. (2005)	RMA regression for one site of BigFoot	0.84	1.23
	Anisotropic KED (Kriging with an external drift) regression	0.79	1.44
General model (5P-LAI3)	Ɣ	0.94	0.75
Models proposed by triangle segmentation (TSM)	If PVI = [0–0.11] then: Ɣ Else if PVI = [0.11–0.28] then: Else if PVI > 0.28 then:	0.96	0.66

Note: The highlighted models are better than others.

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