# Rainfall-Runoff Modelling Using Hydrological Connectivity Index and Artificial Neural Network Approach

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Database

## 3. Methodology

#### 3.1. Artificial Neural Networks (ANNs)

#### 3.1.1. Determination of Input Structure

#### 3.1.2. Data Pre-Processing

#### 3.2. Hydrological Connectivity

^{2}), respectively. The downslope component (${\mathrm{D}}_{\mathrm{dn}}$) takes into account the flow path length that a particle travels to arrive at the designated target or sink. Therefore, ${\mathrm{D}}_{\mathrm{dn}}$ can be expressed as:

#### 3.3. Normalized Difference Vegetation Index

#### 3.4. Evaluation of Results

^{2}), RMSE, and Nash–Sutcliffe model performance coefficient (NS) [60]:

^{2}values represent better correlation between simulated and observed values. The RMSE ranges from 0 to +∞, with 0 indicating a perfect fit of the model to observed values. The range of NS values is from −∞ to 1, with a perfect match of simulated and observed values indicated by 1, a value of 0 indicates that simulated data are no better than taking the mean of the observed data, and values <0 indicate very weak model performance. Generally, $\mathrm{NS}\text{}\text{}0.6$ is considered as acceptable model performance [50].

## 4. Results and Discussion

#### 4.1. Statistical Analysis of Data

#### 4.2. Development and Application of ANN Model

#### 4.2.1. Results of the Best Input Delay Values

#### 4.2.2. ANN Models

^{2}. Results of all models are presented in two main sections: in the first section, we present the results of ANN models that used only hydro-climatic data as inputs (Table 4) and in the second section, results of the combination of hydro-climatic inputs with IC, NDVI, and both NDVI and IC are presented for Haughton River and Calliope River (Table 5 and Table 6).

#### Different Patterns of Hydro-Climate Data

^{2}, the best input pattern in first group was ${\mathrm{P}}_{\mathrm{t}}\text{}\mathrm{and}\text{}{\overline{\mathrm{P}}}_{\mathrm{t}-1,\text{}\mathrm{t}-2}$ for Haughton River and ${\mathrm{P}}_{\mathrm{t}}{\text{}\mathrm{and}\text{}\mathrm{P}}_{\mathrm{t}-1}$ for Calliope River. In the second group, ${\mathrm{P}}_{\mathrm{t}}{,\text{}\overline{\mathrm{P}}}_{\mathrm{t}-1,\text{}\mathrm{t}-2}{\text{}\mathrm{and}\text{}\mathrm{R}}_{\mathrm{t}-1}$ was the best model for Haughton River and ${\mathrm{P}}_{\mathrm{t}}{,\text{}\mathrm{P}}_{\mathrm{t}-1}{\mathrm{and}\text{}\mathrm{R}}_{\mathrm{t}-1}$ for Calliope River (Table 4). Overall, results showed that for both catchments, including rainfall of the previous months increased model accuracy compared to just using rainfall of the same month. This shows the importance of antecedent soil moisture in the runoff generation process [68]. Additionally, including runoff and rainfall together as input data slightly improved model performance for both catchments (Table 4), indicating that only using rainfall is insufficient to precisely estimate runoff, while combining this with antecedent runoff improves predictions [59].

#### Combination of Hydro-Climate, Hydro-Geomorphic and Biophysical Data

^{2}) for models using only hydro-climatic inputs (Table 4) and models using combinations of hydro-climatic data (P and R), hydro-geomorphic (IC) and biophysical data (NDVI) (Table 5 and Table 6) were computed and presented separately for Haughton River and Calliope River (Figure 5a–c). Evaluation of results (compared to models using only hydro-climatic inputs) showed that for Haughton River catchment, IC as the model input, improved NS by 9.77%, R

^{2}by 11.76%, and decreased RMSE by 24.43%; NDVI as the model input, improved NS by 6.24%, R

^{2}by 8.08%, and decreased RMSE by 13.22%; and NDVI together with IC as model inputs, improved NS by 6.92%, R

^{2}by 6.86%, and decreased RMSE by 14.98%. For Calliope River catchment, IC improved NS by 11.25%, R

^{2}by 10.29%, and decreased RMSE by 37.89%; NDVI improved NS by 5.52%, R

^{2}by 6.72%, and decreased RMSE by 11.89%; and NDVI along with IC, improved NS by 7.05%, R

^{2}by 6.93%, and decreased RMSE by 22.48%. Comparison amongst different input patterns showed that IC inputs can better improve the performance of models compared to NDVI inputs in both catchments and the best input patterns during the validation phase based on RMSE, NS and R

^{2}were ${\mathrm{P}}_{\mathrm{t}}{\text{}\mathrm{and}\text{}\mathrm{IC}}_{\mathrm{t}}$ for Haughton River and ${\mathrm{P}}_{\mathrm{t}}{,\text{}\mathrm{R}}_{\mathrm{t}-1}{\text{}\mathrm{and}\text{}\mathrm{IC}}_{\mathrm{t}}$ for Calliope River. On the other hand, NDVI together with IC as model inputs improved the prediction results, but ANN performance is lower compared to using only IC data. These results may be explained by the fact that, since NDVI data was used to compute IC, thus NDVI together with IC input nodes increase the network complexity, without offering information that is essential for the modelling. Overall, our comparisons amongst ANN models showed that combining hydro-climatic data with IC and NDVI produced better results (higher NS and R

^{2}values and smaller RMSE) than models using only hydro-climatic data. These results demonstrate that runoff characteristics are affected by hydro-geomorphic features [47], biophysical data [69] and in general, incorporating catchment geomorphological characteristics within ANN model elevate the performance of R-R modelling [27,42,43].

^{2}= 0.99, validation: R

^{2}= 0.96), than those for Haughton River (calibration: R

^{2}= 0.96, validation: R

^{2}= 0.82).

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Monthly NDVI time series plot compared with monthly rainfall and runoff data for the Haughton River catchment (

**a**) and the Calliope River catchment (

**b**) (2000 to 2018).

**Figure 4.**Frequency distribution histogram and box plot of runoff time series data for catchments of Calliope River (

**a**) and (

**c**) and Haughton River (

**b**) and (

**d**). The dashed-line in the frequency histogram shows the distribution curve.

**Figure 5.**Comparison of average of performance indices (root mean squared error (RMSE), Nash–Sutcliffe model performance coefficient (NS), and coefficient of determination (R

^{2})) for the ANN model with different input patterns in the validation period for Haughton River and Calliope River catchments (

**a**–

**c**).

**Figure 6.**Scatter plot of the best input pattern (bold type in Table 5) of ANN models during the calibration (

**a**) and validation (

**b**) phases in the Haughton River catchment.

**Figure 7.**Scatter plot of the best input pattern (bold type in Table 6) of ANN models during the calibration (

**a**) and validation (

**b**) phases in the Calliope River catchment.

**Figure 8.**Time-series curves of observed runoff versus simulated runoff of the best model using only hydro-climatic inputs (bold type in Table 4) and simulated runoff of the best model using hydro-climatic inputs along with new inputs (bold type in Table 5 and Table 6) during the validation phase for the Haughton River catchment (

**a**) and the Calliope River catchment (

**b**).

Station Name | River | Latitude (N) | Longitude (E) | Datum of Gage (m) | Drainage Area (km^{2}) |
---|---|---|---|---|---|

119003A | Haughton River at Powerline | 19°37′59.3″ | 147°06′37.0″ | 8.875 | 1773 |

132001A | Calliope River at Castlehope | 23°59′05.9″ | 151°05′51.2″ | 2.439 | 1288 |

**Table 2.**Statistical parameters of monthly rainfall, runoff, Normalized Difference Vegetation Index (NDVI) and Index of Connectivity (IC) for the total, calibration and validation datasets for studied catchments.

^{1}

Variable | Statistical Parameter | The Haughton River Catchment | The Calliope River Catchment | ||||
---|---|---|---|---|---|---|---|

Calibration (70%) | Validation (30%) | Total Data | Calibration (70%) | Validation (30%) | Total Data | ||

Number of data $\left(n\right)$ | 153 | 66 | 219 | 153 | 66 | 219 | |

Period (m/y) | March 2000–November 2012 | December 2012–May 2018 | March 2000–May 2018 | March 2000–November 2012 | December 2012–May 2018 | March 2000–May 2018 | |

P (mm) | ${\mathrm{x}}_{\mathrm{min}}$ | 0.01 | 0.27 | 0.01 | 0.00 | 0.00 | 0.00 |

${\mathrm{x}}_{\mathrm{max}}$ | 778.15 | 285.35 | 778.15 | 550.04 | 784.29 | 784.29 | |

$\overline{\mathrm{x}}$ | 80.81 | 56.35 | 73.44 | 65.31 | 81.19 | 70.09 | |

${\mathsf{\sigma}}_{\mathrm{x}}$ | 128.71 | 71.64 | 114.92 | 86.22 | 126.24 | 99.94 | |

${\mathrm{G}}_{1}$ | 2.54 | 1.64 | 2.71 | 3.21 | 3.41 | 3.52 | |

${\mathsf{\beta}}_{2}$ | 7.53 | 2.17 | 9.27 | 13.60 | 15.05 | 16.93 | |

$\mathrm{Cv}$ | 1.59 | 1.27 | 1.56 | 1.32 | 1.55 | 1.43 | |

R (mm) | ${\mathrm{x}}_{\mathrm{min}}$ | 0.17 | 0.56 | 0.17 | 0.00 | 0.05 | 0.00 |

${\mathrm{x}}_{\mathrm{max}}$ | 457.22 | 72.33 | 457.22 | 274.59 | 483.84 | 483.84 | |

$\overline{\mathrm{x}}$ | 26.13 | 9.19 | 21.03 | 10.16 | 21.04 | 13.44 | |

${\mathsf{\sigma}}_{\mathrm{x}}$ | 65.48 | 15.67 | 55.89 | 36.44 | 67.07 | 47.88 | |

${\mathrm{G}}_{1}$ | 4.00 | 2.87 | 4.73 | 5.69 | 5.54 | 6.38 | |

${\mathsf{\beta}}_{2}$ | 18.35 | 7.70 | 26.48 | 35.32 | 35.78 | 50.22 | |

$\mathrm{Cv}$ | 2.51 | 1.70 | 2.66 | 3.59 | 3.19 | 3.56 | |

NDVI | ${\mathrm{x}}_{\mathrm{min}}$ | 0.29 | 0.34 | 0.29 | 0.31 | 0.37 | 0.31 |

${\mathrm{x}}_{\mathrm{max}}$ | 0.68 | 0.68 | 0.68 | 0.72 | 0.69 | 0.72 | |

$\overline{\mathrm{x}}$ | 0.48 | 0.49 | 0.48 | 0.49 | 0.52 | 0.50 | |

${\mathsf{\sigma}}_{\mathrm{x}}$ | 0.10 | 0.09 | 0.10 | 0.10 | 0.09 | 0.10 | |

${\mathrm{G}}_{1}$ | 0.18 | 0.13 | 0.16 | 0.47 | 0.09 | 0.34 | |

${\mathsf{\beta}}_{2}$ | −1.00 | −1.09 | −1.01 | −0.57 | −1.05 | −0.74 | |

IC | ${\mathrm{x}}_{\mathrm{min}}$ | 1.04 | 1.11 | 1.04 | 0.50 | 0.50 | 0.50 |

${\mathrm{x}}_{\mathrm{max}}$ | 1.84 | 1.76 | 1.84 | 1.17 | 1.12 | 1.17 | |

$\overline{\mathrm{x}}$ | 1.33 | 1.38 | 1.34 | 0.88 | 0.88 | 0.88 | |

${\mathsf{\sigma}}_{\mathrm{x}}$ | 0.19 | 0.17 | 0.19 | 0.17 | 0.16 | 0.17 | |

${\mathrm{G}}_{1}$ | −0.84 | −0.37 | −0.69 | −0.40 | −0.35 | −0.39 | |

${\mathsf{\beta}}_{2}$ | −0.12 | −0.84 | −0.38 | −0.84 | −0.81 | −0.83 |

^{1}Note: P is Rainfall, R is runoff (or runoff depth), NDVI is Normalized Difference Vegetation Index, IC is Index of runoff Connectivity, $\left(\mathrm{n}\right)$ is number of data, ${\mathrm{x}}_{\mathrm{min}}$ is the minimum value of the data, ${\mathrm{x}}_{\mathrm{max}}$ is the maximum value of the data, $\overline{\mathrm{x}}$ is the mean of the data, ${\mathsf{\sigma}}_{\mathrm{x}}$ is the standard deviation, ${\mathrm{G}}_{1}$ is the skewness, ${\mathsf{\beta}}_{2}$ is the kurtosis and $\mathrm{Cv}$ is coefficient of variation.

**Table 3.**Cross correlation between monthly runoff and rainfall data with 5% significance limits and Partial autocorrelation for monthly runoff data with 5% significance limits for Haughton River and Calliope River catchments.

Catchment | Lag | Cross-Correlation | Partial-Autocorrelation |
---|---|---|---|

Haughton River | 0 | 0.88 | |

1 | 0.46 | 0.29 | |

2 | 0.11 | −0.07 | |

3 | 0.00 | −0.02 | |

Calliope River | 0 | 0.89 | |

1 | 0.17 | 0.16 | |

2 | 0.08 | 0.02 | |

3 | 0.00 | −0.03 |

**Table 4.**Results of monthly time series modelling by Artificial Neural Network (ANN) with hydro-climatic inputs during calibration and validation.

Catchment | Inputs | Structure | Calibration | Validation | ||||
---|---|---|---|---|---|---|---|---|

RMSE (mm) | NS | R^{2} | RMSE (mm) | NS | R^{2} | |||

Haughton River | ${\mathrm{P}}_{t}$ | 1-9-1 | 25.0 | 0.94 | 0.94 | 10.8 | 0.71 | 0.64 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\text{}\mathrm{P}}_{\mathrm{t}-1}$ | 2-9-1 | 22.2 | 0.95 | 0.95 | 10.4 | 0.73 | 0.74 | |

${\mathrm{P}}_{\mathrm{t}}\text{},{\overline{\text{}\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}$ | 2-10-1 | 21.9 | 0.96 | 0.96 | 9.4 | 0.79 | 0.69 | |

${\mathrm{P}}_{\mathrm{t}}{\text{},\text{}\mathrm{R}}_{\mathrm{t}-1}$ | 2-6-1 | 16.5 | 0.94 | 0.93 | 9.3 | 0.79 | 0.73 | |

${\mathrm{P}}_{\mathrm{t}}{\text{},\text{}\mathrm{P}}_{\mathrm{t}-1}{\text{},\text{}\mathrm{R}}_{\mathrm{t}-1}$ | 3-9-1 | 17.6 | 0.90 | 0.89 | 9.4 | 0.78 | 0.68 | |

${\mathbf{P}}_{\mathbf{t}}\mathbf{,}{\overline{\text{}\mathbf{P}}}_{\mathbf{t}-\mathbf{1}\mathbf{,}\mathbf{t}\mathbf{-}\mathbf{2}}{\mathbf{,}\text{}\mathbf{R}}_{\mathbf{t}\mathbf{-}\mathbf{1}}$ | 3-6-1 | 15.1 | 0.97 | 0.96 | 9.1 | 0.80 | 0.76 | |

Calliope River | ${\mathrm{P}}_{\mathrm{t}}$ | 1-5-1 | 9.8 | 0.96 | 0.96 | 28.7 | 0.81 | 0.81 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\text{}\mathrm{P}}_{\mathrm{t}-1}$ | 2-6-1 | 9.5 | 0.95 | 0.96 | 28.5 | 0.83 | 0.82 | |

${\mathrm{P}}_{\mathrm{t}}\text{},{\overline{\text{}\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}$ | 2-6-1 | 10.5 | 0.95 | 0.94 | 29.8 | 0.73 | 0.74 | |

${\mathrm{P}}_{\mathrm{t}}{\text{},\text{}\mathrm{P}}_{\mathrm{t}-1}$ | 2-10-1 | 9.6 | 0.95 | 0.96 | 28.0 | 0.81 | 0.81 | |

${\mathbf{P}}_{\mathbf{t}}{\text{}\mathbf{,}\text{}\mathbf{P}}_{\mathbf{t}\mathbf{-}\mathbf{1}}{\mathbf{,}\text{}\mathbf{R}}_{\mathbf{t}\mathbf{-}\mathbf{1}}$ | 3-6-1 | 8.1 | 0.97 | 0.97 | 25.7 | 0.85 | 0.85 | |

${P}_{t},{\overline{\text{}P}}_{t-1,t-2}{,\text{}R}_{t-1}$ | 3-6-1 | 9.8 | 0.93 | 0.96 | 29.3 | 0.80 | 0.80 |

**Table 5.**Results of monthly time series modelling by ANN with different inputs during calibration and validation in the Haughton River catchment.

Inputs | Structure | Calibration | Validation | ||||
---|---|---|---|---|---|---|---|

RMSE (mm) | NS | R^{2} | RMSE (mm) | NS | R^{2} | ||

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{NDVI}}_{\mathrm{t}}$ | 2-6-1 | 13.6 | 0.98 | 0.96 | 9.1 | 0.80 | 0.76 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{P}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}$ | 3-10-1 | 8.3 | 0.99 | 0.99 | 7.7 | 0.85 | 0.79 |

${\mathrm{P}}_{\mathrm{t}}{,\overline{\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\mathrm{NDVI}}_{\mathrm{t}}$ | 3-6-1 | 15.1 | 0.97 | 0.95 | 7.8 | 0.85 | 0.79 |

${\mathbf{P}}_{\mathbf{t}}{\text{}\mathbf{,}\mathbf{IC}}_{\mathbf{t}}$ | 2-10-1 | 12.5 | 0.98 | 0.96 | 7.2 | 0.87 | 0.82 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{P}}_{\mathrm{t}-1}{,\mathrm{IC}}_{\mathrm{t}}$ | 3-11-1 | 12.1 | 0.98 | 0.97 | 7.4 | 0.87 | 0.81 |

${\mathrm{P}}_{\mathrm{t}}{,\overline{\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\mathrm{IC}}_{\mathrm{t}}$ | 3-5-1 | 14.8 | 0.97 | 0.95 | 7.4 | 0.87 | 0.81 |

${\mathrm{P}}_{\mathrm{t}}{,\mathrm{NDVI}}_{\mathrm{t}}{,\mathrm{IC}}_{\mathrm{t}}$ | 3-9-1 | 14.7 | 0.97 | 0.96 | 8.2 | 0.84 | 0.76 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{P}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}{,\mathrm{IC}}_{\mathrm{t}}$ | 4-10-1 | 14.2 | 0.97 | 0.97 | 8.4 | 0.83 | 0.75 |

${\mathrm{P}}_{\mathrm{t}}{,\overline{\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\mathrm{NDVI}}_{\mathrm{t}}{,\mathrm{IC}}_{\mathrm{t}}$ | 4-10-1 | 19.2 | 0.95 | 0.93 | 10.1 | 0.75 | 0.71 |

${\mathrm{P}}_{\mathrm{t}}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}$ | 3-6-1 | 14.8 | 0.97 | 0.96 | 8.4 | 0.83 | 0.79 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{P}}_{\mathrm{t}-1}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}$ | 4-11-1 | 19.8 | 0.95 | 0.93 | 9.7 | 0.77 | 0.74 |

${\mathrm{P}}_{\mathrm{t}}{,\overline{\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}$ | 4-11-1 | 14.4 | 0.97 | 0.95 | 8.9 | 0.81 | 0.73 |

${\mathrm{P}}_{\mathrm{t}}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{IC}}_{\mathrm{t}}$ | 3-6-1 | 16.3 | 0.97 | 0.95 | 8.2 | 0.84 | 0.76 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{P}}_{\mathrm{t}-1}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{IC}}_{\mathrm{t}}\text{}$ | 4-6-1 | 15.7 | 0.97 | 0.97 | 8.5 | 0.82 | 0.79 |

${\mathrm{P}}_{\mathrm{t}}{,\overline{\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{IC}}_{\mathrm{t}}$ | 4-6-1 | 13.7 | 0.98 | 0.96 | 8.3 | 0.83 | 0.81 |

${\mathrm{P}}_{\mathrm{t}}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}{,\mathrm{IC}}_{\mathrm{t}}$ | 4-6-1 | 19.7 | 0.95 | 0.93 | 7.5 | 0.86 | 0.80 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{P}}_{\mathrm{t}-1}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}{,\mathrm{IC}}_{\mathrm{t}}$ | 5-5-1 | 17.4 | 0.96 | 0.95 | 8.2 | 0.83 | 0.76 |

${\mathrm{P}}_{\mathrm{t}}{,\overline{\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}{\text{},\mathrm{IC}}_{\mathrm{t}}$ | 5-6-1 | 14.4 | 0.97 | 0.95 | 8.3 | 0.83 | 0.77 |

**Table 6.**Results of monthly time series modelling by ANN with different inputs during calibration and validation in the Calliope River catchment.

Inputs | Structure | Calibration | Validation | ||||
---|---|---|---|---|---|---|---|

RMSE (mm) | NS | R^{2} | RMSE (mm) | NS | R^{2} | ||

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{NDVI}}_{\mathrm{t}}$ | 2-10-1 | 9.3 | 0.96 | 0.92 | 19.0 | 0.92 | 0.93 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{P}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}$ | 3-7-1 | 8.8 | 0.96 | 0.96 | 25.6 | 0.85 | 0.88 |

${\mathrm{P}}_{\mathrm{t}}{,\overline{\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\mathrm{NDVI}}_{\mathrm{t}}$ | 3-6-1 | 7.8 | 0.969 | 0.95 | 29.0 | 0.81 | 0.89 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{IC}}_{\mathrm{t}}$ | 2-10-1 | 8.6 | 0.96 | 0.95 | 18.8 | 0.92 | 0.92 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{P}}_{\mathrm{t}-1}{,\mathrm{IC}}_{\mathrm{t}}$ | 3-9-1 | 6.2 | 0.98 | 0.97 | 20.9 | 0.90 | 0.92 |

${\mathrm{P}}_{\mathrm{t}}{,\overline{\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\mathrm{IC}}_{\mathrm{t}}$ | 3-10-1 | 5.8 | 0.98 | 0.94 | 23.6 | 0.87 | 0.88 |

${\mathrm{P}}_{\mathrm{t}}{,\mathrm{NDVI}}_{\mathrm{t}}{,\mathrm{IC}}_{\mathrm{t}}$ | 3-11-1 | 8.2 | 0.97 | 0.97 | 18.5 | 0.94 | 0.96 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{P}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}{,\mathrm{IC}}_{\mathrm{t}}$ | 4-11-1 | 6.4 | 0.98 | 0.97 | 22.7 | 0.88 | 0.88 |

${\mathrm{P}}_{\mathrm{t}}{,\overline{\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\mathrm{NDVI}}_{\mathrm{t}}{,\mathrm{IC}}_{\mathrm{t}}$ | 4-7-1 | 13.5 | 0.91 | 0.94 | 19.0 | 0.92 | 0.92 |

${\mathrm{P}}_{\mathrm{t}}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}$ | 3-7-1 | 6.5 | 0.98 | 0.98 | 26.5 | 0.84 | 0.86 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{P}}_{\mathrm{t}-1}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}$ | 4-11-1 | 6.4 | 0.98 | 0.95 | 27.6 | 0.83 | 0.83 |

${\mathrm{P}}_{\mathrm{t}}{,\overline{\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}$ | 4-6-1 | 6.8 | 0.98 | 0.98 | 24.1 | 0.87 | 0.88 |

${\mathbf{P}}_{\mathbf{t}}{\mathbf{,}\mathbf{R}}_{\mathbf{t}\mathbf{-}\mathbf{1}}{\mathbf{,}\mathbf{IC}}_{\mathbf{t}}$ | 3-11-1 | 6.1 | 0.98 | 0.99 | 18.0 | 0.95 | 0.96 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{P}}_{\mathrm{t}-1}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{IC}}_{\mathrm{t}}\text{}$ | 4-10-1 | 6.4 | 0.98 | 0.97 | 18.4 | 0.92 | 0.93 |

${\mathrm{P}}_{\mathrm{t}}{,\overline{\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{IC}}_{\mathrm{t}}$ | 4-7-1 | 9.5 | 0.95 | 0.96 | 23.6 | 0.87 | 0.87 |

${\mathrm{P}}_{\mathrm{t}}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}{,\mathrm{IC}}_{\mathrm{t}}$ | 4-10-1 | 6.6 | 0.98 | 0.98 | 22.3 | 0.89 | 0.91 |

${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{P}}_{\mathrm{t}-1}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}{,\mathrm{IC}}_{\mathrm{t}}$ | 5-6-1 | 10.5 | 0.94 | 0.95 | 27.9 | 0.82 | 0.86 |

${\mathrm{P}}_{\mathrm{t}}{,\overline{\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\mathrm{R}}_{\mathrm{t}-1}{,\mathrm{NDVI}}_{\mathrm{t}}{\text{},\mathrm{IC}}_{\mathrm{t}}$ | 5-10-1 | 8.6 | 0.96 | 0.97 | 28.4 | 0.75 | 0.74 |

**Table 7.**Assessment of models based on relative error in peak runoff for the best model using only hydro-climatic inputs and the best model using hydro-climatic inputs along with new inputs for Haughton River and Calliope River catchments.

Input Pattern | Haughton River | Calliope River | ||
---|---|---|---|---|

The Best Model | %RE_{p} | The Best Model | %RE_{p} | |

Hydro-climatic | ${\mathrm{P}}_{\mathrm{t}},{\overline{\text{}\mathrm{P}}}_{\mathrm{t}-1,\mathrm{t}-2}{,\text{}\mathrm{R}}_{\mathrm{t}-1}$ | −36.1 | ${\mathrm{P}}_{\mathrm{t}}{,\text{}\mathrm{P}}_{\mathrm{t}-1}{,\text{}\mathrm{R}}_{\mathrm{t}-1}$ | −17.9 |

Hydro-climatic + IC | ${\mathrm{P}}_{\mathrm{t}}{\text{},\mathrm{IC}}_{\mathrm{t}}$ | −12.8 | ${\mathrm{P}}_{\mathrm{t}}{,\text{}\mathrm{R}}_{\mathrm{t}-1}{,\text{}\mathrm{IC}}_{\mathrm{t}}$ | −3.9 |

Hydro-climatic + NDVI | ${\mathrm{P}}_{\mathrm{t}}{\text{},\text{}\mathrm{P}}_{\mathrm{t}-1}{,\text{}\mathrm{NDVI}}_{\mathrm{t}}$ | −14.0 | ${\mathrm{P}}_{\mathrm{t}}{,\text{}\mathrm{NDVI}}_{\mathrm{t}}$ | −16.4 |

Hydro-climatic + NDVI+IC | ${\mathrm{P}}_{\mathrm{t}}{,\text{}\mathrm{R}}_{\mathrm{t}-1}{,\text{}\mathrm{NDVI}}_{\mathrm{t}}{,\text{}\mathrm{IC}}_{\mathrm{t}}$ | –15.6 | ${\mathrm{P}}_{\mathrm{t}}{,\text{}\mathrm{NDVI}}_{\mathrm{t}}{,\text{}\mathrm{IC}}_{\mathrm{t}}$ | −22.3 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Asadi, H.; Shahedi, K.; Jarihani, B.; Sidle, R.C.
Rainfall-Runoff Modelling Using Hydrological Connectivity Index and Artificial Neural Network Approach. *Water* **2019**, *11*, 212.
https://doi.org/10.3390/w11020212

**AMA Style**

Asadi H, Shahedi K, Jarihani B, Sidle RC.
Rainfall-Runoff Modelling Using Hydrological Connectivity Index and Artificial Neural Network Approach. *Water*. 2019; 11(2):212.
https://doi.org/10.3390/w11020212

**Chicago/Turabian Style**

Asadi, Haniyeh, Kaka Shahedi, Ben Jarihani, and Roy C. Sidle.
2019. "Rainfall-Runoff Modelling Using Hydrological Connectivity Index and Artificial Neural Network Approach" *Water* 11, no. 2: 212.
https://doi.org/10.3390/w11020212