**3.3 Runoff depth**

*Lagoon Environments around the World - A Scientific Perspective*

constant along with LC/LU.

**3. Data analysis**

**3.1 LC/LU accuracy assessment**

Cohen's kappa (K) coefficient [22].

which is shown in Eq. (1) [23].

= *C*<sup>0</sup> + (1 − *C*0) \_\_\_\_ *<sup>S</sup>*

**2.4 Precipitation for runoff depth**

are provided in the Geographic Coordinate System and World Geodetic System of 1984 datum (GCS\_WGS\_84). The data for soil classification were acquired for six Florida coastal counties: Volusia, Brevard, Indian River, St. Lucie, Martin, and Palm Beach. Tabular information for the soil texture was extracted from the Web Soil Survey Microsoft Access Database file and imported into the ArcMap 10.5 software. The data contained a variety of different soil names for classification: muck, Myakka fine sand, and Turnbull muck, that are all used for determining the slope

The runoff depth represents the amount of rainfall that is converted into runoff

Before assessing the PRCs for the study area, the LC/LU image was tested for its accuracy. The accuracy assessment test consisted of collecting 600 referenced points using a stratified random method that randomly assigns points in each class. A 2016 Digital Globe basemap in ArcMap 10.5 of a higher spatial resolution (0.62 m) was utilized to visually interpret the land cover for each reference point. The output table consisted of a confusion matrix that displays the error of omission, the error of commission per class, and overall accuracy ranging from 0 to 1. Another test for accuracy of the LC/LU classification image included calculating the

Potential runoff coefficient (PRC) values were derived to represent ratio of the rainfall that would convert to surface runoff per pixel. The PRC for the IRL area was determined by combining the soil texture, LC/LU, and the slope data. The PRC is calculated from a linear relationship between the runoff coefficients and slope,

*<sup>s</sup>* <sup>+</sup> *so* (1)

[16]. Therefore, rainfall data for the Halifax River and IRL watershed were collected to calculate the runoff depth using the runoff coefficients. The data were acquired from the National Oceanic and Atmospheric Administration (NOAA) National Weather Service (NWS) River Forecast Center (RFC) website. The data were downloaded in the ArcGIS shapefile format as point data with a projection of the Hydrologic Rainfall Analysis Projection (HRAP) grid coordinate system that has a North Pole Stereographic projection, and a grid resolution of 4762.5 m (https://water.weather.gov/precip/download.php). The rainfall data are acquired in a multi-sensor process that uses radar and rain gauge to estimate the precipitation. After extracting the point data, the shapefiles were converted into raster data. Due to estimation of multi-sensor collected data, the data are first stored in a binary file format called XMRG. This file is then read into the HRAP grid coordinate system through the NWSRFS Operational Forecast System using the NEXRAD Mean Areal Precipitation Preprocessor (MAPX) to associate grid points from XMRG data to

represent the hourly average precipitation for each area [21].

**124**

**3.2 PRC**

The total precipitation values were collected for eleven years (2006–2016), and imported into ArcMap 10.5 to be interpolated. The precipitation values (in.) for each of the years were interpolated using the Kriging method with a spherical semivariogram model. The method assumes that the values are more related when in close proximity, and the spatial autocorrelation decreases with distance. After the precipitation was interpolated for each year, the data were multiplied (cell-bycell) by the PRC raster of the corresponding year using the raster calculator tool provided in ArcMap 10.5 toolboxes. The output of the images provided the runoff depth (centimeters) for each year, and the average runoff depth for the eleven-year period (2006–2016) was calculated per pixel (10 m). The outputs of this image can delineate potential sources of runoff for inland waterbodies that may be connected to the lagoon through a network of drainage systems.

Concentrations of chlorophyll *a* in the IRL during the 2011 super algal bloom were compared to runoff depth of surrounding areas. Kamerosky et al. [29] estimated and mapped the Chi *a* concentrations using the Medium Resolution Imaging Spectrometer (MERIS) platform aboard the European Space Agency (ESA) Environmental Satellite (ENVISAT) and calculated Normalized Difference Chlorophyll Index (NDCI) [29, 30].

#### **3.4 Linear regression between LDI and runoff depth**

In order to meet proper data conditions for linear regression analysis in ArcMap 10.5, the raster images were sampled into vector data as a point feature class. Land development intensity (LDI) data was collected from the Florida Department of Environmental Protection (FDEP) Geospatial Open Data Site (http://geodata.dep.state.fl.us/). The LDI serves as a human disturbance gradient that incorporates land use and energy used per unit area [31]. It is used in watershed modeling to delineate human-dominated areas, and to scale the human induced impacts on physiological, biological, and chemical processes. A total of 600 points were randomly placed within the Halifax River and IRL watershed via "Create Random Points" tool. Points that were placed over large waterbodies were deleted, leaving 528 sample points left for the analysis. Values from the LDI and runoff depth were extracted to the points.

To adequately assess the relationship between urbanized areas of intense impervious coverage and surface runoff, an ordinary least squares (OLS) regression analysis and geographically weighted regression (GWR) was performed in ArcGIS 10.5. These regression analyses use bandwidth methods to find the

optimal sampling distances between data points, adding a geospatial component to regression analysis. The OLS regression is designed as a "Global Model" with an assumption that the explanatory and dependent variables have global trends over a particular study area. In simplified context, it is assumed that the data are continuous throughout the area therefore being "stationary" data.

For the OLS analysis, the Jarque-Bera statistic tests for model bias that can arise from nonstationary data, misspecification of independent variables, and skewed residuals [32]. Due to the positively skewed data for LDI and runoff depth values, a logarithmic transformation was applied to data to ensure a normal distribution of the datasets while making the variance independent of the mean. The Koenker's Studentized Breusch-Pagan (Koenker BP) statistic tests for nonstationary with a null hypothesis that the dependent and independent variables have a consistent relationship in geographic space, thus being stationary [33]. A rejected null hypothesis of this test indicates that there are local trends between the variables within the study area.

Presence of significant spatial autocorrelation using the Global Moran's Index (Moran's I) is based on the assumption of stationary data. In this case there will be clustering of standard residuals from heteroscedasticity, thus indicating a local model such as GWR is more appropriate. Therefore, the standard residuals produced from both regression analyses were tested for significant clustering using the Moran's I test. On the other hand, a GWR is a "nonstationary" model that accounts for the local trends in relationships between the variables. In OLS analysis, LDI data from the FDEP and 11-year mean precipitation were used as the independent variable, and the 11-year mean runoff depth as dependent variable. The GWR only included the LDI as independent, and runoff depth as dependent variable due to collinear relationships with rainfall within clustered locations within the study area.
