# A Comparison of In-Sample and Out-of-Sample Model Selection Approaches for Artificial Neural Network (ANN) Daily Streamflow Simulation

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Acquisition

^{2}, of which 81.66% is classified as developed urban area according to the 2011 National Land Cover Database (NLCD2011) land use land cover (LULC) classification [30]. The main waterway in the HSARB is the San Antonio River, which originates in the metropolitan area of San Antonio, flows southeast across downtown San Antonio and merges with the Medina River in the city’s southern suburbs. Thus, the most downstream point of the drainage basin is located at the southern tip of the HSARB. The streamflow close to the watershed outlet is measured by a USGS surface streamflow gauge (USGS 08178565). The Lower Medina River Basin (LMRB), centered at 98.698° west longitude, 29.319° north latitude, is located west of the San Antonio urban area and shares a short watershed boundary with HSARB. LMRB has a drainage area of 929.29 km

^{2}and is much less developed in comparison to the HSARB. The dominant land cover types at LMRB are shrub, pasture, and cultivated crop, covering 25.97%, 15.72%, and 14.38% of the entire LMRB, respectively. The major waterway in LMRB is the Medina River, which flows southeast and merges into the San Antonio River at the outlet of LMRB. The streamflow measurement station closest to the watershed outlet is USGS gauge 08181500, which covers most of the drainage area of the LMRB, located about 7 km from the watershed outlet. The proximity in geographic locations of the two study watersheds helps to reduce uncertainties that may arise in model comparison, as the neighboring watersheds have similar climatology, geology, and hydrology.

#### 2.2. ANN Model Description

#### 2.3. Model Selection Approaches

#### 2.3.1. Blocked Cross-Validation

#### 2.3.2. AIC and BIC

#### 2.4. Model Performance Measures

#### 2.5. ANN Models Setup

_{t}), precipitation of the previous n days (P

_{t−n}), daily mean air temperature (T

_{t}), streamflow measurement from the upstream gauge stations (Q

_{u}, USGS 08178000, USGS 08180700), and total precipitation for the preceding n days (P

_{n}). Precipitation and temperature were selected as inputs mainly because they are the most relevant meteorological variables for hydrological impact studies [55]. In addition, the total precipitation of previous time steps is included to represent the antecedent moisture condition in scenarios 4 and 5. The downstream discharge (Q, USGS 08178565, USGS 08181500) close to the watershed outlets are the training targets. The input combinations proposed here avoid using the streamflow of preceding time steps at the estimated site, which allows for application of the modeling approach in regions where streamflow observations are incomplete.

## 3. Results and Discussion

#### 3.1. Optimum Hidden Layer Size Selection

#### 3.2. Statistical Summary of Model Performance

#### 3.3. Best Model Structure

## 4. Summary and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Study Area, the headwaters San Antonio River Basin (HSARB), and the Lower Medina River Basin (LMRB) with NLCD LULC classification and USGS Stream Gages displayed.

**Figure 3.**Model statistical performance of prediction scenarios 1 through 5 for the HSARB watershed (

**a**−

**e**). The best performance measures of each scenario (i.e., the smallest AIC and BIC, the largest NSE) are highlighted in red.

**Figure 4.**Model statistical performance of prediction scenarios 1 through 5 for the LMRB watershed (

**a−e**). The best performance measures of each scenario (i.e., the smallest AIC and BIC, the largest NSE) are highlighted in red.

**Figure 5.**Daily precipitation, observed, and simulated streamflow of testing phase for (

**a**) HSARB, S3-6; (

**b**) HSARB, S5-7; (

**c**) LMRB S3-2; (

**d**) LMRB S3-9.

**Figure 6.**Scatter plots of testing phase daily streamflow of (

**a**) HSARB, S3-6; (

**b**) HSARB, S5-7; (

**c**) LMRB S3-2; (

**d**) LMRB S3-9.

Performance Rating | NSE | PBIAS (%) | RSR |
---|---|---|---|

Very good | $\mathrm{NSE}\ge 0.7$ | $\left|\mathrm{PBIAS}\right|\le 25$ | $\mathrm{RSR}\le 0.5$ |

Good | $0.5\le \mathrm{NSE}<0.7$ | $25<\left|\mathrm{PBIAS}\right|\le 50$ | $0.5<\mathrm{RSR}\le 0.75$ |

Satisfactory | $0.3\le \mathrm{NSE}<0.5$ | $50<\left|\mathrm{PBIAS}\right|\le 70$ | |

Unsatisfactory | $\mathrm{NSE}<0.3$ | $\left|\mathrm{PBIAS}\right|>70$ | $\mathrm{RSR}>0.75$ |

Prediction Scenario | Input Combination | Output |
---|---|---|

1 | P_{t}, P_{t−1}, P_{t−2}, P_{t−3}, P_{t−4}, Q_{u} | Q |

2 | P_{t}, P_{t−1}, P_{t−2}, P_{t−3}, P_{t−4}, T_{t} | Q |

3 | P_{t}, P_{t−1}, P_{t−2}, P_{t−3}, P_{t−4}, T_{t}, Q_{u} | Q |

4 | P_{t}, P_{t−1}, P_{t−2}, P_{t−3}, P_{t−4}, P_{n} | Q |

5 | P_{t}, P_{t−1}, P_{t−2}, P_{t−3}, P_{t−4}, P_{n}, Q_{u} | Q |

Scenario | Hidden Nodes | Training | Testing | ||||||
---|---|---|---|---|---|---|---|---|---|

AIC | BIC | NSE | PBIAS | RSR | NSE | PBIAS | RSR | ||

1 | 5 | 10.299 | 10.397 | 0.841 | 10.8 | 0.399 | 0.558 | −47.8 | 0.664 |

2 | 3 | 11.393 | 11.453 | 0.519 | 9.9 | 0.694 | 0.474 | −36.7 | 0.725 |

3 | 6 | 10.258 | 10.389 | 0.849 | 8.6 | 0.388 | 0.574 | −48.5 | 0.652 |

4 | 5 | 11.406 | 11.504 | 0.519 | 11.1 | 0.694 | 0.512 | −31.8 | 0.698 |

5 | 4 | 10.337 | 10.425 | 0.834 | 9.4 | 0.407 | 0.577 | −45.7 | 0.650 |

Scenario | Hidden Nodes | Training | Validation | Testing | ||||||
---|---|---|---|---|---|---|---|---|---|---|

NSE | PBIAS | RSR | NSE | PBIAS | RSR | NSE | PBIAS | RSR | ||

1 | 4 | 0.774 | 11.3 | 0.474 | 0.707 | 29.6 | 0.538 | 0.566 | −48.8 | 0.659 |

2 | 10 | 0.537 | 8.8 | 0.680 | −0.229 | 65.7 | 1.105 | 0.465 | −36.8 | 0.731 |

3 | 7 | 0.764 | 11.5 | 0.486 | 0.690 | 33.7 | 0.555 | 0.567 | −47.6 | 0.658 |

4 | 10 | 0.525 | 10.6 | 0.689 | −0.106 | 62.3 | 1.049 | 0.478 | −30.5 | 0.723 |

5 | 7 | 0.790 | 11.4 | 0.457 | 0.717 | 31.3 | 0.529 | 0.581 | −40.0 | 0.647 |

Scenario | Hidden Nodes | Training | Testing | ||||||
---|---|---|---|---|---|---|---|---|---|

AIC | BIC | NSE | PBIAS | RSR | NSE | PBIAS | RSR | ||

1 | 2 | 12.707 | 12.746 | 0.920 | 16.2 | 0.282 | 0.269 | 18.8 | 0.854 |

2 | 4 | 13.559 | 13.634 | 0.816 | −10.8 | 0.429 | 0.451 | −58.6 | 0.741 |

3 | 2 | 12.666 | 12.710 | 0.924 | 15.2 | 0.276 | 0.310 | 20.4 | 0.830 |

4 | 7 | 13.488 | 13.618 | 0.831 | −15.2 | 0.411 | 0.603 | −47.9 | 0.630 |

5 | 5 | 12.779 | 12.884 | 0.916 | 10.4 | 0.289 | 0.400 | 4.6 | 0.775 |

Scenario | Hidden Nodes | Training | Validation | Testing | ||||||
---|---|---|---|---|---|---|---|---|---|---|

NSE | PBIAS | RSR | NSE | PBIAS | RSR | NSE | PBIAS | RSR | ||

1 | 8 | 0.920 | 14.0 | 0.283 | 0.282 | −35.0 | 0.845 | 0.574 | 3.5 | 0.653 |

2 | 8 | 0.817 | −11.9 | 0.427 | 0.115 | −53.0 | 0.939 | 0.444 | −61.5 | 0.745 |

3 | 9 | 0.916 | 16.6 | 0.290 | 0.290 | −32.8 | 0.841 | 0.658 | −7.3 | 0.585 |

4 | 9 | 0.817 | −11.7 | 0.427 | 0.066 | −54.6 | 0.964 | 0.582 | −48.7 | 0.647 |

5 | 10 | 0.916 | 13.8 | 0.289 | 0.283 | −35.2 | 0.845 | 0.320 | 11.6 | 0.824 |

Study Watershed | Selection Criteria | Best Model | Study Watershed | Selection Criteria | Best Model |
---|---|---|---|---|---|

HSARB | AIC | S3-6 | LMRB | AIC | S3-2 |

BIC | S3-6 | BIC | S3-2 | ||

BlockedCV | S5-7 | BlockedCV | S3-9 | ||

Predictive Performance | S5-5 | Predictive Performance | S3-9 |

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**MDPI and ACS Style**

Mei, X.; Smith, P.K. A Comparison of In-Sample and Out-of-Sample Model Selection Approaches for Artificial Neural Network (ANN) Daily Streamflow Simulation. *Water* **2021**, *13*, 2525.
https://doi.org/10.3390/w13182525

**AMA Style**

Mei X, Smith PK. A Comparison of In-Sample and Out-of-Sample Model Selection Approaches for Artificial Neural Network (ANN) Daily Streamflow Simulation. *Water*. 2021; 13(18):2525.
https://doi.org/10.3390/w13182525

**Chicago/Turabian Style**

Mei, Xiaohan, and Patricia K. Smith. 2021. "A Comparison of In-Sample and Out-of-Sample Model Selection Approaches for Artificial Neural Network (ANN) Daily Streamflow Simulation" *Water* 13, no. 18: 2525.
https://doi.org/10.3390/w13182525