Geographically weighted spatial modelling of sediment quality in Lake Okeechobee, Florida

Figures & data

Figure 1. Model selection processes for spatial prediction (OLS: ordinary least square, OK: ordinary kriging; RK: regression-kriging and GWR: geographically weighted regression).

Figure 2. Bathymetry, zones and sample sites of Lake Okeechobee.

Table 1. Summary table of nutrients (mg/g), mud thickness (cm) and elevation (ft).

		TC	CA	FE	TN	TP	Thickness	Elevation
1988	Min.	0.6	41	24	166	38.6	0	−1.27
	1st Qu.	17.75	7297	643	1541	220.7	0	0.31
	Median	107.8	54,377	1700	8621	664	0	2.6
	Mean	118.93	53,799	2695	9094	670.5	12.47	4.32
	3rd Qu.	151.8	85,154	4787	11,319	1076	18.88	8.14
	Max.	481.9	176,020	10,524	36,107	1708.1	66	15.44
	Skewness	1.46	0.48	0.61	1.38	0.16	1.26	0.66
	Kurtosis	1.89	−0.86	−0.56	1.68	−1.42	0.29	−0.91
1998	Min.	1.4	220	112	0	2.2	0	−1.27
	1st Qu.	25.93	10,396	1449	400	165.7	0	0.31
	Median	143.6	51,325	3506	8000	474.7	0	2.78
	Mean	145.06	60,705	7060	9363	650.2	11.17	4.39
	3rd Qu.	182.45	89,439	14,352	12,500	1149.8	13.75	8.15
	Max.	487.1	328,000	21,123	47,800	1793.3	74	15.44
	Skewness	1.06	1.47	0.60	1.47	0.30	1.49	0.61
	Kurtosis	0.35	2.46	−1.35	1.84	−1.48	0.99	−0.95
2006	Min.	1.15	114	39	70	16.64	0	−1.12
	1st Qu.	25.69	6813	716	610	141.39	0	0
	Median	140.77	64,349	2013	8170	397.42	1	0.99
	Mean	139.09	64,217	3429	8926	566.22	8.27	3.16
	3rd Qu.	175.81	94,162	6947	12,500	999.46	14.75	5.94
	Max.	490.55	347,790	8827	41,030	1285.31	51	14.58
	Skewness	1.10	1.68	0.38	1.15	0.13	1.28	1.06
	Kurtosis	0.69	3.83	−1.53	1.07	−1.71	0.65	−0.20

Figure 3. GWR weighting schemes and bandwidths. (a) Fixed weighting scheme. (b) Adaptive weighting schemes.

Figure 4. TP histograms (mg/kg) for 1988, 1998 and 2006.

Table 2. Correlation coefficients and their significances of sediment nutrients (mg/kg), mud thickness (cm) and elevation (ft).

Year		Thickness	Elevation	TP	TN	CA	FE	TC
1988	Thickness	1
	Elevation	−0.5276	1
		<.0001
	TP	0.6046	−0.5472	1
		<.0001	<.0001
	TN	0.1255	0.1959	0.3703	1
		0.1222	0.0152	<.0001
	CA	0.4056	−0.6705	0.6460	0.1286	1
		<.0001	<.0001	<.0001	0.113
	FE	0.6540	−0.6864	0.7936	0.1460	0.6031	1
		<.0001	<.0001	<.0001	0.0718	<.0001
	TC	0.1583	0.1573	0.3382	0.9512	0.1187	0.1596	1
		0.0506	0.0522	<.0001	<.0001	0.144	0.0488
1998	Thickness	1
	Elevation	−0.5982	1
		<.0001
	TP	0.5715	−0.5474	1
		<.0001	<.0001
	TN	0.0301	0.2789	0.3612	1
		0.7131	0.0005	<.0001
	CA	0.2387	−0.5161	0.2611	−0.1659	1
		0.0031	<.0001	0.0012	0.0411
	FE	0.6932	−0.7038	0.8492	0.1469	0.2876	1
		<.0001	<.0001	<.0001	0.0709	0.0003
	TC	0.0675	0.1880	0.3533	0.9506	0.0286	0.1741	1
		0.4085	0.0204	<.0001	<.0001	0.7268	0.0319
2006	Thickness	1
	Elevation	−0.4678	1
		<.0001
	TP	0.7159	−0.4552	1
		<.0001	<.0001
	TN	0.1414	0.1452	0.37545	1
		0.0793	0.0714	<.0001
	CA	0.2918	−0.4579	0.3774	−0.0662	1
		0.0002	<.0001	<.0001	0.4134
	FE	0.7272	−0.4862	0.9374	0.3025	0.3603	1
		<.0001	<.0001	<.0001	0.0001	<.0001
	TC	0.1098	0.0925	0.3332	0.9616	0.0514	0.2556	1
		0.174	0.2522	<.0001	<.0001	0.5257	0.0013

Note: Upper values are the coefficients and bottom ones are the p values based on Pearson correlations.

Table 3. Statistically significant calibrated OLS models for Iron (Fe) and mud thickness and lakebed elevation (Th & Elev).

	1988		1998		2006
Predictors	Fe	Th & Elev	Fe	Th & Elev	Fe	Th & Elev
AIC	1580.78	1657.35	1563.97	1686.89	1461.83	1617.15
R^2	0.72	0.46	0.81	0.46	0.89	0.58
Adj R^2	0.72	0.45	0.81	0.45	0.89	0.57
F-Stat	287.33	47.38	489.51	47.69	907.33	76.11
K(BP)	2.01	3.00	1.56	1.51	0.03	3.45
K(BP)-Prob	0.16	0.22	0.21	0.47	0.86	0.18
JB	22.71	10.30	447.17	29.77	40.41	8.42
Sigma	246.07	342.80	228.58	390.23	146.04	287.40
Neighbours	15,795	15,795	13,665	13,665	14,729	14,729
Stationary	Yes	Yes	Yes	Yes	Yes	Yes
Residuals	Clustered	Clustered	Random	Random	Random	Clustered

Table 4. Analyses of the GWR calibration model (TP vs. Th & Elev).

Year	GWR Models	Adaptive AICc	Adaptive CV	Fixed AICc	Fixed CV
2006	Neighbours	49	54	30,916	28,774
	Residual squares	4,738,304	4,895,445	4,211,677	4,010,590
	Effective number	17.73	16.03	25.51	28.09
	Sigma	221.85	223.54	218.17	216.068
	AICc	1569.80	1570.11	1571.12	1571.41
	R^2	0.78	0.77	0.81	0.82
	R^2 Adjusted	0.74	0.74	0.75	0.76
1998	Neighbours	66	66	44,943	42,884
	Residual squares	12,781,568	12,781,568	12,902,301	12,735,949
	Effective number	11.74	11.74	13.02	13.88
	Sigma	353.55	353.55	357.46	356.66
	AICc	1671.51	1671.51	1673.89	1673.93
	R^2	0.59	0.59	0.59	0.59
	R^2 adjusted	0.55	0.55	0.54	0.54
1988	Neighbours	32	27	30,777.37	21,021
	Residual squares	5,694,144	5,233,681	6,224,684	4,734,359
	Effective number	26.45	31.02	24.47	41.02
	Sigma	255.03	251.14	263.68	254.70
	AICc	1610.11	1611.91	1613.47	1625.79
	R^2	0.76	0.78	0.74	0.80
	R^2 adjusted	0.70	0.71	0.68	0.70

Note: In bold the most accurate models.

Figure 5. Coefficient maps of the GWR model (TP vs. Th & Elev) calibration for 1988, 1998 and 2006.

Table 5. Analyses of the GWR calibration model (TP vs. Fe).

	GWR models	Adaptive CV	Adaptive AIC	Fixed CV	Fixed AIC
2006	Neighbours	32	38	25,048	28,061
	Residual Squares	1,474,546	1,559,402	1,370,525	1,479,068
	Sigma	125.79	127.15	125.87	127.53
	AICc	1442.36	1442.05	1445.88	1445.18
	R^2	0.93	0.93	0.94	0.93
	R^2Adjusted	0.92	0.92	0.92	0.92
1998	Neighbours	114	46	2,583,313	38,985
	Residual Squares	5,721,282	4,772,090	5,851,677	4,754,339
	Sigma	228.39	219.36	228.58	217.70
	AICc	1566.66	1563.92	1566.19	1560.32
	R^2	0.82	0.85	0.81	0.85
	R^2 Adjusted	0.81	0.83	0.81	0.83
1988	Neighbours	13	38	21,434	24,337
	Residual Squares	2,256,157	4,669,867	3,403,058	3,809,536
	Sigma	189.93	220.30	205.77	210.14
	AICc	1582.82	1567.64	1564.55	1563.34
	R^2	0.91	0.81	0.86	0.84
	R^2 Adjusted	0.83	0.77	0.80	0.79

Note: In bold the most accurate models.

Figure 6. Coefficient maps of the GWR model (TP vs. Fe) calibration for 1988, 1998 and 2006.

Figure 7. Scatter plots of the GWR models (TP vs. Th & Elev) validation set for 1988, 1998 and 2006.

Figure 8. Scatter plots of the GWR models (TP vs. Fe) validation set for 1988, 1998 and 2006.

Table 6. Comparison of TP model errors.

	Models	OK	OLS(Fe)	GWR(Fe)	OLS (Th, Elev)	GWR (Th, Elev)	RK
2006	ME	−27.38	31.19	−30.19	40.21	20.82	65.15
	RMSE	331.00	169.96	204.61	325.23	307.60	325.10
	NRMSE	26.09	13.40	16.13	25.64	24.25	25.63
1998	ME	−89.46	136.93	132.81	106.64	100.58	126.48
	RMSE	415.10	374.75	359.83	442.98	389.38	419.14
	NRMSE	23.18	20.92	20.09	24.73	21.74	23.40
1988	ME	−41.74	110.94	109.59	64.15	24.39	51.64
	RMSE	402.10	368.36	375.88	371.97	234.34	371.99
	NRMSE	0.24	0.22	0.23	0.22	0.14	0.22

Note: OK: Ordinary Kriging; OLS: Regression, Th: Thickness, Elev: elevation, RK: Regression-kriging; NRMSE: RMSE/(Max-Min); (In bold the most accurate models).

Figure 9. TP concentration (a, c and e) (mg/kg) and weights (b, d and f) (kg) estimated using the GWR model (TP vs. Fe) for 1988, 1998 and 2006.

Figure 10. TP concentration (a, c and e) (mg/kg) and weights (b, d and f) (kg) using the GWR model (TP vs. Th & Elev) for 1988, 1998 and 2006.

Table 7. TP mass (kg) and changes over time.

	OK model			GWR (Fe) model			GWR (Th + Elev) model
Year	Mass	Change	Change%	Mass	Change	Change%	Mass	Change	Change%
1988	4.25E + 07			4.20E + 07			4.43E + 07
1998	5.89E + 07	1.64E + 07	39%	6.04E + 07	1.84E + 07	44%	6.11E + 07	1.68E + 07	38%
2006	4.14E + 07	−1.75E + 07	−30%	4.10E + 07	−1.94E + 07	−32%	4.01E + 07	−2.10E + 07	−34%