Journal of Geographical Sciences >
Spatial nonstationary characteristics between grass yield and its influencing factors in the Ningxia temperate grasslands based on a mixed geographically weighted regression model
Song Xiaolong (1991‒), PhD Candidate, specialized in remote sensing monitoring of grassland resources and research on foragelivestock balance. Email: songxl@stu.nxu.edu.cn 
Received date: 20211117
Accepted date: 20220309
Online published: 20220825
Supported by
Ningxia Key R&D Project(2018BEB04007)
Ningxia Colleges and Universities FirstClass Discipline Construction (Grass Science Discipline) Project(NXYLXK2017A01)
Spatial models are effective in obtaining local details on grassland biomass, and their accuracy has important practical significance for the stable management of grasses and livestock. To this end, the present study utilized measured quadrat data of grass yield across different regions in the main growing season of temperate grasslands in Ningxia of China (August 2020), combined with hydrometeorology, elevation, net primary productivity (NPP), and other auxiliary data over the same period. Accordingly, nonstationary characteristics of the spatial scale, and the effects of influencing factors on grass yield were analyzed using a mixed geographically weighted regression (MGWR) model. The results showed that the model was suitable for correlation analysis. The spatial scale of ratio residentarea index (PRI) was the largest, followed by the digital elevation model, NPP, distance from gully, distance from river, average July rainfall, and daily temperature range; whereas the spatial scales of night light, distance from roads, and relative humidity (RH) were the most limited. All influencing factors maintained positive and negative effects on grass yield, save for the strictly negative effect of RH. The regression results revealed a multiscale differential spatial response regularity of different influencing factors on grass yield. Regression parameters revealed that the results of Ordinary least squares (OLS) (Adjusted R^{2 }= 0.642) and geographically weighted regression (GWR) (Adjusted R^{2 }= 0.797) models were worse than those of MGWR (Adjusted R^{2 }= 0.889) models. Based on the results of the RMSE and radius index, the simulation effect also was MGWR > GWR > OLS models. Ultimately, the MGWR model held the strongest prediction performance (R^{2} = 0.8306). Spatially, the grass yield was high in the south and west, and low in the north and east of the study area. The results of this study provide a new technical support for rapid and accurate estimation of grassland yield to dynamically adjust grazing decision in the semiarid loess hilly region.
SONG Xiaolong , MI Nan , MI Wenbao , LI Longtang . Spatial nonstationary characteristics between grass yield and its influencing factors in the Ningxia temperate grasslands based on a mixed geographically weighted regression model[J]. Journal of Geographical Sciences, 2022 , 32(6) : 1076 1102 . DOI: 10.1007/s1144202219865
Figure 1 Location and sample distribution of the study area (Yuanzhou District, Guyuan, Ningxia, China) 
Figure 2 Pearson correlation analysis of influencing factors on grass yield 
Table 1 Influencing factors and descriptions included in the analysis of grass yield 
Variable  Abbreviation  Unit  Variable description 

Intercept  Intercept  g  Intercept term of the model 
Average rainfall in July  AJR  mm  Average July rainfall 
Relative humidity  RH  %  Percentage of water vapor pressure in the air vs. saturated water vapor pressure at the same temperature 
NPP  NPP  gC·m^{‒2}·a^{‒1}  Net primary production capacity of vegetation, refers to the total amount of organic matter accumulated by photosynthesis in unit area and unit time of green plants, minus the remaining part after autotrophic respiration 
Ratio residentarea index  PRI    Proportion of impervious surface in the surface area per unit area: $P R I=\frac{B L U E}{N I R}$, where blue and NIR are the pixel reflectance values of blue and near infrared wavelengths, respectively 
Elevation  DEM  m  Altitude of sample point 
Daily temperature range  DTR  ℃  Difference between maximum and minimum daily temperatures 
Distance from gully  DS  m  Distance from sample point to valley 
Distance from road  DP  m  Distance from sample point to road 
Distance from river  DR  m  Distance from sample point to river 
Night light  NL    Night light distribution in the study area 
Figure 3 Spatial distribution of influencing factors across Yuanzhou District (NPP: Net primary production; PRI: Ratio residentarea index; DEM: Elevation; AJR: Average rainfall in July; NL: Night light; DP: Distance from road; DS: Distance from gully; DR: Distance from river; DTR: Daily temperature range; RH: Relative humidity) 
Table 2 Multicollinearity diagnosis results among influencing factors 
Variable  Tolerance  VIF 

AJR  0.244  4.092 
RH  0.248  4.029 
NPP  0.459  2.180 
PRI  0.755  1.325 
DEM  0.445  2.249 
DTR  0.248  4.025 
DS  0.792  1.262 
DP  0.804  1.243 
DR  0.754  1.327 
NL  0.877  1.140 
Table 3 Comparison of statistical parameters of different linear regression models: ordinary least squares (OLS), geographically weighted regression (GWR), and mixed GWR (MGWR) 
Parameter  OLS  GWR  MGWR 

Residual sum of squares  959.816  236.960  23.701 
2 loglikelihood  3697.432  3138.206  2558.904 
Classic AIC  3731.432  3270.442  2159.397 
AICc  3731.660  3273.816  2951.878 
BIC/MDL  3831.737  3660.555  2331.959 
CV  5863.375  4370.185   
R^{2}  0.643  0.801  0.891 
Adjusted R^{2}  0.642  0.797  0.889 
Figure 4 Fitting results of different linear regression models 
Table 4 Estimates of OLS model parameters 
Variable  Coefficient  Ttest  Significance (p) 

Intercept  366.649  8.482  0.000 
AJR  20.505  3.867  0.000 
RH  14.883  2.593  0.010 
NPP  7.321  2.305  0.021 
PRI  6.363  2.580  0.010 
DEM  74.194  27.200  0.000 
DTR  40.112  7.649  0.000 
DS  17.548  5.498  0.000 
DP  3.870  1.490  0.004 
DR  9.427  4.379  0.000 
NL  7.397  1.181  0.004 
Table 5 Estimates of GWR model parameters 
Variable  Min  Max  Lwr Quartile  Median  Upr Quartile 

Intercept  664.366  165.834  373.563  451.646  
AJR  49.684  92.181  12.087  6.980  35.114 
RH  39.418  144.282  11.053  8.416  27.694 
NPP  6.232  32.852  10.403  15.679  23.962 
PRI  7.563  2.873  3.637  2.698  1.007 
DEM  13.540  99.800  3.165  33.316  59.446 
DTR  95.718  54.511  24.421  3.836  12.769 
DS  32.859  0.367  20.809  10.443  4.266 
DP  38.467  41.975  7.914  0.182  8.727 
DR  56.344  59.046  18.597  2.029  18.442 
NL  53.406  56.678  10.603  1.480  10.847 
Table 6 Estimates of MGWR model parameters 
Variable  Mean  STD  Min  Median  Max 

Intercept  0.827  1.170  1.119  0.817  2.834 
DEM  0.040  0.165  0.340  0.001  0.188 
NL  0.456  2.361  4.255  0.002  8.176 
PRI  0.003  0.003  0.001  0.003  0.012 
NPP  0.077  0.112  0.213  0.042  0.585 
DS  0.011  0.054  0.245  0.013  0.237 
DP  0.073  0.156  0.415  0.054  0.301 
DR  0.180  0.300  0.757  0.232  0.859 
DTR  1.227  1.316  4.145  0.715  0.561 
RH  3.013  1.329  4.979  2.750  1.274 
AJR  1.687  1.313  0.267  1.498  3.938 
Figure 5 Spatial patterns of regression coefficients for influencing factors of grass yield based on the mixed geographically weighted regression (MGWR) model (a. AJR: Average rainfall in July; b. PRI: Ratio residentarea index; c. DEM: Elevation; d. RH: Relative humidity; e. NL: Night light; f. DP: Distance from road; g. DS: Distance from gully; h. DR: Distance from river; i. DTR: Daily temperature range; j. NPP: Net primary production) 
Table 7 Bandwidth comparison between classical GWR and MGWR models 
Variable  MGWR  GWR 

Intercept  43  1218 
DEM  150  1218 
NL  43  1218 
PRI  1348  1218 
NPP  113  1218 
DS  49  1218 
DP  43  1218 
DR  50  1218 
DTR  46  1218 
RH  43  1218 
AJR  46  1218 
Figure 6 Prediction results of grass yield for temperate grasslands according to each linear regression model 
Figure 7 Scatterplots of the observed vs. predicted grass yields 
Table 8 Statistical parameters for the different linear regression models analyzed 
Model  ME  MAE  RMSE  Radius 

OLS Model  7.0112  75.7841  104.9458  184.0735 
GWR Model  4.6232  70.5916  97.6234  156.5453 
MGWR Model  3.9770  65.2953  92.6180  39.0543 
[1] 

[2] 

[3] 

[4] 

[5] 

[6] 

[7] 

[8] 

[9] 

[10] 

[11] 

[12] 

[13] 

[14] 

[15] 

[16] 

[17] 

[18] 

[19] 

[20] 

[21] 

[22] 

[23] 

[24] 

[25] 

[26] 

[27] 

[28] 

[29] 

[30] 

[31] 

[32] 

[33] 

[34] 

[35] 

[36] 

[37] 

[38] 

[39] 

[40] 

[41] 

[42] 

[43] 

[44] 

[45] 

[46] 

[47] 

[48] 

[49] 

[50] 

[51] 

[52] 

[53] 

[54] 

[55] 

[56] 

[57] 

[58] 

[59] 

[60] 

[61] 

[62] 

[63] 

[64] 

[65] 

[66] 

[67] 

[68] 

[69] 

[70] 

[71] 

[72] 

[73] 

[74] 

/
〈  〉 