Canopy width prediction models for the Gurbantunggut Desert

doi:10.7522/j.issn.1000-694X.2022.00001

Journal of Desert Research ›› 2022, Vol. 42 ›› Issue (4): 139-150.DOI: 10.7522/j.issn.1000-694X.2022.00001

Canopy width prediction models for the Gurbantunggut Desert

Mingna Wang¹(), Dinghai Zhang²(), Zhishan Zhang³, Lining Lu²

^1.School of Finance and Economics /, Gansu Agricultural University，Lanzhou 730070，China
^2.College of Science, Gansu Agricultural University，Lanzhou 730070，China
^3.Shapotou Desert Research and Experimental Station，Northwest Institute of Eco-Environment and Resources，Chinese Academy of Sciences，Lanzhou 730000，China

Received:2021-09-26 Revised:2022-01-13 Online:2022-07-20 Published:2022-08-29
Contact: Dinghai Zhang

Abstract

Abstract:

The Gurbantunggut Desert， the main distribution area of fixed and semi-fixed dunes， is the second largest desert in China with a relatively large variety of sand-fixing shrubs. The canopy width is an essential parameter for the visualization of sand-fixing shrubs， which is also a necessary variable for the growth of desert vegetation. The purpose of this study was to assess the main sand-fixing shrubs on three types of sand dunes （fixed， semi-fixed， mobile dunes） in the sand zone. The experiment uses 12 base models， Backpropagation Neural Network （BP）， Support Vector Machine （SVM） machine learning algorithms to develop a canopy width prediction model based on the height and crown length rate of sand-fixing shrubs. To compare the two machine learning algorithm fits，canopy prediction models suitable for the experiment was selected. The results were as follows：（1） The different optimal canopy width prediction models had a difference in dune types and shrub species， and the fixed and semi-fixed dune models outperform the mobile dune models. The three dune types were optimally fitted to the M2 （Quadratic Model） model. （2） The optimal models fitted for Haloxylon persicum on semi-fixed and mobile dunes were M2 and M7（Gompertz） model， respectively. The best-fitting model for Calligonum mongolicum was M2 model. In contrast， the better-fitting models for Serpentine and Artemisia ordosica were M2 and M7 model on semi-fixed and mobile dunes， respectively. Generally， the models of M2 and M7 had a better predictors of different types of shrub crown width values. （3） The Radial Basis Function （RBF） kernel-based support vector regression machine was better than the BP neural network model in crown width prediction.

Key words: plant height, crown width, crown length rate, base model, BP neural network, support vector machine

CLC Number:

Q948.1

Mingna Wang, Dinghai Zhang, Zhishan Zhang, Lining Lu. Canopy width prediction models for the Gurbantunggut Desert[J]. Journal of Desert Research, 2022, 42(4): 139-150.

Figures/Tables 14

Table 1 Basic information for sand-fixing shrubs on different types of sand dunes

沙丘类型	固沙灌木	数量 /株	冠幅 /m	株高 /m	冠长率
固定沙丘	全部	2 344	0.56±0.48	0.74±0.58	0.85±0.87
	白梭梭	1 142	0.64±0.46	0.91±0.58	0.81±1.08
	梭梭	1 202	0.48±0.48	0.58±0.53	0.89±0.62
半固定沙丘	全部	1 651	0.48±0.43	0.42±0.44	1.18±0.55
	白梭梭	169	0.92±0.72	1.20±0.90	0.81±0.43
	沙拐枣	268	0.78±0.34	0.45±0.16	1.79±0.73
	蛇麻黄	122	0.30±0.10	0.25±0.06	1.21±0.35
	油蒿	1 092	0.36±0.31	0.30±0.22	1.08±0.45
流动沙丘	全部	1 187	0.66±0.54	0.45±0.38	1.67±1.18
	白梭梭	323	0.40±0.40	0.65±0.60	0.67±0.48
	沙拐枣	474	0.82±0.48	0.40±0.19	2.18±1.31
	蛇麻黄	63	1.75±0.76	0.47±0.18	3.81±1.53
	油蒿	327	0.46±0.28	0.32±0.18	1.52±0.73

Table 2 Basic model of canopy width prediction

模型	名称	表达式	模型	名称	表达式
M1	Linear	$y = a + b x 1 + c x 2$	M7	Gompertz	$y = a e x p [- b e x p (- c x 1 - d x 2)]$
M2	Quadratic	$y = a + b x 1 + c x 12 + d x 2 + e x 22$	M8	Growth	$y = e x p (a + b x 1 + c x 2)$
M3	Power	$y = a x 1 b + c x 2 d$	M9	Gauss	$y = a e x p (- [(x 1 - b - x 2 - c) / d] 2)$
M4	Exponential	$y = a e x p (b x 1 + c x 2)$	M10	Mitscherlinch	$y = a [1 - e x p (- b x 1 - c x 2)]$
M5	Logarithmic	$y = a + b l g (x 1) + c l g (x 2)$	M11	Hossfeld	$y = 1 / (a + b x 1 + c x 2)$
M6	Logistic	$y = a / [1 + b e x p (- c x 1 - d x 2)]$	M12	HossfeldⅠ	$y = [(x 1 + x 2) / (a + b x 1 + c x 2)] 2$

Table 2 Basic model of canopy width prediction

模型	名称	表达式	模型	名称	表达式
M1	Linear	$y = a + b x 1 + c x 2$	M7	Gompertz	$y = a e x p [- b e x p (- c x 1 - d x 2)]$
M2	Quadratic	$y = a + b x 1 + c x 12 + d x 2 + e x 22$	M8	Growth	$y = e x p (a + b x 1 + c x 2)$
M3	Power	$y = a x 1 b + c x 2 d$	M9	Gauss	$y = a e x p (- [(x 1 - b - x 2 - c) / d] 2)$
M4	Exponential	$y = a e x p (b x 1 + c x 2)$	M10	Mitscherlinch	$y = a [1 - e x p (- b x 1 - c x 2)]$
M5	Logarithmic	$y = a + b l g (x 1) + c l g (x 2)$	M11	Hossfeld	$y = 1 / (a + b x 1 + c x 2)$
M6	Logistic	$y = a / [1 + b e x p (- c x 1 - d x 2)]$	M12	HossfeldⅠ	$y = [(x 1 + x 2) / (a + b x 1 + c x 2)] 2$

Table 3 Fitting results of crown width prediction model for three main sand-fixing shrubs on sand dunes

沙丘类型	模型	参数					评价指标				模型检验 P
沙丘类型	模型	a	b	c	d	e	R²	RMSE	MAE	MAPE/%	模型检验 P
固定沙丘	M1	-0.090	0.736	11.580			0.793	0.216	0.001	23.91	<0.001
	M2	-0.223	0.717	28.580	0.017	-90.970	0.838	0.192	0.001	24.90	<0.001
	M3	0.527	1.344	0.211	0.680		0.812	0.206	0.132	37.48	<0.001
	M6	2.228	23.370	1.767	68.660		0.817	0.203	0.124	34.21	<0.001
	M7	2.563	4.213	0.928	33.120		0.816	0.204	0.117	25.54	<0.001
	M10	445.100	0.002	0.016			0.782	0.222	0.140	36.42	<0.001
半固定沙丘	M1	-0.278	0.818	35.430			0.886	0.144	0.092	44.82	<0.001
	M2	-0.458	1.119	53.070	-0.131	-619.700	0.916	0.124	0.090	62.19	<0.001
	M6	1.686	47.560	3.656	109.800		0.892	0.141	0.082	42.73	<0.001
	M7	1.924	5.998	1.786	58.250		0.905	0.132	0.073	25.51	<0.001
	M12	0.484	0.571	-9.855			0.896	0.138	0.127	86.48	<0.001
流动沙丘	M1	-0.280	0.836	33.710			0.714	0.288	0.179	38.26	<0.001
	M2	-0.663	1.689	49.570	-0.410	-295.500	0.811	0.234	0.152	75.29	<0.001
	M3	0.679	0.935	43.210	1.162		0.669	0.310	0.225	76.95	<0.001
	M6	1.849	39.620	2.880	101.600		0.748	0.270	0.166	37.89	<0.001
	M7	2.051	6.202	1.583	58.010		0.748	0.271	0.162	29.08	<0.001

Table 4 Prediction model of crown width of sand-fixing shrub Haloxylon ammodendron

模型	参数					评价指标				模型检验P
模型	a	b	c	d	e	R²	RMSE	MAE	MAPE/%	模型检验P
M1	-0.0184	19.640	0.836			0.855	0.183	0.096	24.92	<0.001
M2	-0.0293	35.590	0.827	-2 653.000	0.054	0.877	0.168	0.092	34.26	<0.001
M3	8.4840	0.911	1.190	1.274		0.844	0.190	0.113	38.14	<0.001
M7	0.2730	4.301	297.300	9.932		0.856	0.183	0.099	27.53	<0.001
M10	99.1200	0.011	0.008			0.824	0.202	0.013	47.90	<0.001

Table 5 Prediction model of crown width of sand-fixing shrub Haloxylon persicum

沙丘类型	模型	参数					评价指标				模型检验 P
沙丘类型	模型	a	b	c	d	e	R²	RMSE	MAE	MAPE/%	模型检验 P
固定沙丘	M2	0.021	30.040	0.640	-934.900	0.324	0.820	0.193	0.115	18.95	<0.001
	M3	1.346	0.561	1.217	1.461		0.797	0.205	0.135	28.39	<0.001
	M5	0.636	0.057	0.060			0.790	0.208	0.135	47.94	<0.001
	M6	0.211	22.000	797.600	16.720		0.790	0.209	0.122	23.09	<0.001
	M7	0.273	4.301	297.300	9.932		0.855	0.183	0.121	20.10	<0.001
	M9	0.211	0.187	0.166	0.085		0.794	0.220	0.102	19.75	<0.001
半固定沙丘	M1	0.649	80.090	0.766			0.915	0.209	0.161	21.27	<0.001
	M2	0.110	0.147	1.018	-0.028	0.803	0.935	0.183	0.015	33.68	<0.001
	M6	0.289	47.830	1 592.000	13.490		0.923	0.199	0.016	20.81	<0.001
	M7	0.430	5.643	675.600	5.699		0.924	0.197	0.016	18.05	<0.001
	M12	0.360	-140.600	1.278			0.931	0.188	0.025	46.15	<0.001
流动沙丘	M1	0.019	32.750	0.585			0.878	0.139	0.008	48.74	<0.001
	M2	0.032	55.830	0.684	-0.892	0.450	0.891	0.131	0.009	83.36	<0.001
	M6	0.153	31.430	1 203.000	21.550		0.880	0.138	0.009	47.45	<0.001
	M7	0.182	4.839	602.300	10.740		0.884	0.135	0.008	29.54	<0.001
	M12	0.257	-71.620	1.821			0.870	0.143	0.014	65.18	<0.001

Table 6 Prediction model of crown width of sand-fixing shrub Calligonum mongolicum

沙丘类型	模型	参数					评价指标				模型检验 P
沙丘类型	模型	a	b	c	d	e	R²	RMSE	MAE	MAPE/%	模型检验 P
半固定沙丘	M1	-0.060	33.550	1.740			0.914	0.101	0.009	13.51	<0.001
	M2	-0.093	61.640	2.185	-6 652.000	-5.849	0.937	0.086	0.007	15.63	<0.001
	M4	0.012	446.500	21.760			0.904	0.107	0.014	24.51	<0.001
	M5	0.661	0.060	0.062			0.906	0.106	0.009	18.64	<0.001
	M7	0.344	5.638	319.400	16.400		0.928	0.092	0.009	13.04	<0.001
	M8	-4.406	446.500	21.770			0.904	0.107	0.014	24.51	<0.001
	M12	0.158	-27.890	1.363			0.905	0.107	0.016	24.75	<0.001
流动沙丘	M1	-0.060	28.220	2.029			0.832	0.198	0.013	18.48	<0.001
	M2	-0.102	50.730	2.700	-3 261.000	-7.165	0.893	0.158	0.010	23.20	<0.001
	M5	0.723	0.065	0.070			0.824	0.202	0.014	37.35	<0.001
	M6	0.232	44.960	665.400	41.890		0.851	0.186	0.011	16.01	<0.001
	M7	0.281	6.239	334.000	21.940		0.847	0.189	0.011	15.54	<0.001

Table 7 Prediction model of crown width of sand-fixing shrub Ephedra distachya

沙丘类型	模型	参数					评价指标				模型检验 P
沙丘类型	模型	a	b	c	d	e	R²	RMSE	MAE	MAPE/%	模型检验 P
半固定沙丘	M1	-0.031	23.560	1.276			0.852	0.022	0.0014	5.15	<0.001
	M2	-0.041	42.350	1.224	-6 987.000	0.591	0.971	0.017	0.0012	4.48	<0.001
	M3	123.500	1.316	69.690	2.380		0.907	0.030	0.0020	7.03	<0.001
	M4	0.005	691.700	37.460			0.951	0.022	0.0016	5.90	<0.001
	M5	0.348	0.030	0.022			0.956	0.021	0.0015	5.46	<0.001
	M6	0.113	42.940	1041.000	57.230		0.961	0.020	0.0014	4.71	<0.001
	M7	0.253	5.450	357.000	19.570		0.962	0.019	0.0013	4.59	<0.001
	M8	-5.329	691.700	37.460			0.951	0.022	0.0016	5.89	<0.001
	M12	0.151	-42.480	2.166			0.903	0.031	0.0013	4.58	<0.001
流动沙丘	M1	-0.126	37.390	3.396			0.938	0.190	0.0172	17.95	<0.001
	M2	-0.127	33.130	3.745	542.900	-3.189	0.936	0.193	0.0164	25.06	<0.001
	M3	1 132.000	1.726	13.430	1.638		0.903	0.239	0.0216	33.48	<0.001
	M4	0.024	252.500	20.040			0.949	0.173	0.0204	20.64	<0.001
	M6	0.468	49.280	422.600	36.010		0.965	0.143.	0.0161	11.10	<0.001
	M7	0.880	5.689	158.100	13.390		0.965	0.143	0.0160	11.00	<0.001
	M8	-3.731	252.500	20.040			0.949	0.173	0.0204	20.65	<0.001
	M12	0.121	-11.050	0.951			0.952	0.167	0.0212	14.99	<0.001

Table 8 Prediction model of crown width of sand-fixing shrub Artemisia ordosica

沙丘类型	模型	参数					评价指标				模型检验 P
沙丘类型	模型	a	b	c	d	e	R²	RMSE	MAE	MAPE/%	模型检验 P
半固定沙丘	M1	-0.027	26.930	1.105			0.931	0.082	0.0059	48.75	<0.001
	M2	-0.031	38.140	0.848	-3 818.000	3.386	0.936	0.079	0.0058	52.44	<0.001
	M4	0.006	657.400	26.190			0.923	0.087	0.0072	73.71	<0.001
	M6	-198.100	-3.110	658.900	26.170		0.922	0.087	0.0039	27.75	<0.001
	M7	0.251	6.083	456.200	17.500		0.962	0.061	0.0037	21.08	<0.001
	M8	-5.054	657.200	26.180			0.923	0.087	0.0072	73.68	<0.001
	M12	0.174	-36.430	1.552			0.933	0.081	0.0077	75.89	<0.001
流动沙丘	M1	-0.025	18.080	1.328			0.873	0.101	0.0072	20.69	<0.001
	M2	-0.046	42.410	1.471	-5 710.000	-2.100	0.916	0.082	0.0065	29.66	<0.001
	M6	0.136	33.280	711.700	50.990		0.872	0.101	0.0070	17.78	<0.001
	M7	0.196	5.013	315.500	22.630		0.878	0.099	0.0068	16.66	<0.001
	M12	0.122	-18.180	1.901			0.862	0.105	0.0152	57.28	<0.001

Table 9 The results of machine learning of crown width prediction for main sand-fixing shrubs on three types of sand dunes

机器学习算法类型	沙丘类型	R²	RMSE	MAE	MAPE/%
BP神经网络	固定沙丘	0.9040	0.0408	0.1255	29.17
	半固定沙丘	0.9190	0.1474	0.1149	52.78
	流动沙丘	0.9100	0.0530	0.1355	29.57
SVM支持向量机	固定沙丘	0.9997	0.0052	0.6694	1.69
	半固定沙丘	0.9997	0.0074	0.9428	2.87
	流动沙丘	0.9997	0.0081	1.0892	2.64

Fig.1 The results of the reduced major axis of machine learning for main sand-fixing shrubs on three types of sand dunes

Table 10 BP neural network model results of different sand-fixing shrubs

固沙灌木	沙丘类型	R²	RMSE	MAE	MAPE/%
白梭梭	固定沙丘	0.9045	0.0720	0.1558	30.44
	半固定沙丘	0.9525	0.2316	0.1682	26.10
	流动沙丘	0.9770	0.0349	0.0871	51.10
梭梭	固定沙丘	0.9018	0.1327	0.1289	34.56
沙拐枣	半固定沙丘	0.9995	0.5153	1.1836	2.92
沙拐枣	流动沙丘	0.9943	0.9350	3.6987	6.56
蛇麻黄	半固定沙丘	0.9992	0.2251	0.3356	1.21
蛇麻黄	流动沙丘	0.9379	0.3153	0.3177	22.78
油蒿	半固定沙丘	0.9977	0.3750	0.9080	2.75
油蒿	流动沙丘	0.9537	0.2177	0.0905	22.41

Fig.2 The results of the reduced major axis of BP neural network model for different sand-fixing shrubs

Table 11 SVM model for prediction of crown width of different sand-fixing shrubs

固沙灌木	沙丘类型	R²	RMSE	MAE	MAPE/%
白梭梭	固定沙丘	0.9998	0.0054	0.0085	1.23
	半固定沙丘	0.9990	0.0167	1.4147	3.52
	流动沙丘	0.9999	0.0081	0.8021	4.22
梭梭	固定沙丘	0.9998	0.0052	0.0086	2.76
沙拐枣	半固定沙丘	0.9998	0.0068	0.5695	1.03
沙拐枣	流动沙丘	0.9998	0.0071	0.7826	1.57
蛇麻黄	半固定沙丘	0.9998	0.0061	0.1177	0.42
蛇麻黄	流动沙丘	0.9997	0.0073	0.8457	0.42
油蒿	半固定沙丘	0.9862	0.0595	0.9805	2.92
油蒿	流动沙丘	0.9960	0.0317	0.5290	1.46

Fig.3 The results of the reduced major axis of SVM model for different sand-fixing shrubs.

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Canopy width prediction models for the Gurbantunggut Desert

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