*A GIS-Based Approach for Determining Potential Runoff Coefficient and Runoff Depth… DOI: http://dx.doi.org/10.5772/intechopen.87163*

Anselin Local Moran's Index was performed to test for clustering and local patterns of spatial association [37]. The Global Moran's I indicated that the standard residuals produced from the GWR were significantly dispersed indicating the absence of spatial autocorrelation (Moran's I = −0.025, *p* = 0.111). The algorithm calculated an index for every feature, and 96% of the local *p*-values were not significant (*p* > 0.05). The validation for choosing the GWR also can be justified by the smaller AICc produced (AICc = 1522.83) compared to the OLS (1573). The R<sup>2</sup> for the GWR increased (R2 = 0.35) with a lower adjusted R2 of 0.26. As previously stated, the GWR accounts for nonstationary data that contain local trends for the relationship between the variables. Local trends within the dataset relationships were inevitable due to the complexity of different LC/LU within urban communities. The locally weighted regression coefficients can be seen on the coefficient raster produced by the GWR analysis (**Figure 8**). The coefficients show that LDI influences runoff in locations with more impervious surfaces and higher runoff depths, and forested land cover that consists of low LDI values and low runoff. The coefficients increase from blue to yellow to red, indicating higher relationships between the two variables.

**Table 3** shows statistical values generated from the model according to the optimal sampling distance for nearest neighbors (bandwidth). The sampling kernel type for the GWR was fixed, and therefore provides the bandwidth in meters. The Residual Squares is the sum of squared residuals that represent the distance between the observed and estimated values. Therefore, the data are more related when this value is smaller. With a strong influence from bandwidth, the Effective Number is a measure of the complexity of the model that is used to calculate other variables within the GWR model, and it is useful when compared to other models. The sigma is the estimated standard deviation for the residual sum of squares, which shows


## **Table 2.**

*Lagoon Environments around the World - A Scientific Perspective*

much the independent variables explain the variation in the dependent variable. In

Precipitation 0.009 0.005 1.967 0.050 0.005 0.060 1.001 LDI 0.692 0.071 9.780 <0.0001 0.085 <0.0001 1.001

*Indian River Lagoon chlorophyll* a *concentrations for 2011 (September–December 2011). The concentrations are estimated using medium resolution imaging spectrometer normalized difference chlorophyll index (image source: [29]).*

Intercept 1.032 0.531 1.943 0.053 0.571 0.071

**t-statistic Probability Robust** 

for this tests shows a small R2

= 0.15). The OLS regression also tests for the model significance with the Joint

 = 0.15). The Jarque-Bera statistic tests for model bias that can arise form nonstationary data, misspecification of independent variables, and skewed residuals [30]. In this case, the Jarque-Bera statistic shows no significant model bias (*p* = 0.064). A Global Moran's Index was performed on the residuals of the output file to test for the assumption of no spatial autocorrelation or clustering in the data. The Global Moran's Index showed statistically significant clustering rejecting the null hypothesis that the data are randomly distributed spatially within a global assumption (Moran's I = 0.07, *p* < 0.0001). Therefore, the OLS results should not be used to adequately interpret

Due to the detection of nonstationary and/or heteroscedasticity in the datasets, a GWR was used to adequately assess the relationship. The Global Moran's Index and

The Koenker's BP statistic tests for nonstationary and heteroscedasticity. The null hypothesis is that the dependent and independent variables have a consistent relationship in geographic space, thus being stationary [33]. The Koenker's BP statistic shows significant existence of nonstationary trends between runoff depth and LDI (*p* = 0.004). Therefore, the model significance was interpreted based on the Joint Wald statistic (*p* < 0.0001) which also indicates that the relationship was statistically significant. However, the overall measure of how well the explanatory variables explained the variation in the runoff depth from the OLS analysis was relatively small

accounts for the model complexity. The

**SE**

between the variables

**Robust probability** **VIF**

values (**Table 2**).

the Adjusted R2

**error**

F-statistic and Joint Wald statistic to support the significance of R<sup>2</sup>

relationship between the explanatory variables and runoff depth.

**4.8 Geographically weighted regression**

**130**

relation to the multiple R<sup>2</sup>

the Adjusted R2

*A table of the ordinary least squares model variables.*

**Variable Coefficient Standard** 

multiple R2

**Figure 6.**

(R<sup>2</sup>

**Table 1.**

(R2

*Statistical diagnostic results from the ordinary least squares regression.*


#### **Table 3.**

*Results from the geographic weighted regression analysis.*

that the standard deviation of the observed values for runoff depth were relatively close to the predicted values calculated for the regression model (σ = 0.90).
