# Hydrological Early Warning System Based on a Deep Learning Runoff Model Coupled with a Meteorological Forecast

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data-Driven Techniques

#### 2.1.1. Artificial Neural Networks

#### 2.1.2. Deep Learning Based on LSTM Neural Networks

**h**

_{i}denote the output vectors and

**c**

_{i}denote the cell states, all of them evaluated at the i-th time step.

#### 2.2. Hydrological Description of the Study Area

#### 2.3. Coupled Model of a Meteorological Forecast with a Short-Range Runoff Forecast

#### 2.3.1. Input Data

- Watershed geomorphology: The geomorphological characteristics were calculated from NASA Shuttle Radar Topography Mission (SRTM) version 3.0 global 1 arc second. For this aim, the watershed associated to each one of the flow stations was defined, and the information was summarized in one single table that list as a function of the elevation, the following information: Watershed area (km
^{2}); length of the mainstream (km); maximum, minimum and average elevation of the watershed; and the average slope. This table is read at each time to create time series of the geomorphological information as a function of the 0 °C isotherm elevation that splits the watershed into solid and liquid precipitation areas. Besides the watershed area, the time-series of the length of the mainstream, and the average slope and maximum elevation of the watershed were used as inputs of the data-driven weather-runoff models, as they are associated with the computation of the concentration time of the watershed [40]. The average elevation of the watershed was used to vertically interpolate the precipitation time-series from the GFS-NCEP meteorological model. - Meteorological forecast: The weather forecast was obtained from a statistical scaling of gridded data of the GFS provided by NCEP, from which we obtained precipitation and air relative humidity at the average elevation of the watershed below the 0 °C isotherm, and air temperature at 2 m above the terrain in 3500 m a.s.l, and this reference terrain elevation was the same for all of the nine catchments. This last variable was chosen based on preliminary trial and error tests that showed that it gave better results in the representation of diurnal flow pulses during snow melt. We tested for other constant reference elevations (2000 and 4000 m a.s.l), and the results were not sensitive to this value. Furthermore, without good results, we also tested as reference temperature, the temperature at the average elevation of the catchment below the 0 °C isotherm that varies in time. We used the forecast datasets with a horizontal resolution of 0.5 × 0.5 degree, available from 2004 to present, and with a horizontal resolution of 0.25 × 0.25 degree, available from 2007 to present. Vertical scaling of the GFS information was made by linearly interpolating the meteorological variables as a function of the terrain elevation, using the GFS grid points located in a 0.5 degree of radius, regardless of the horizontal resolution of the GFS model, following the vertical scaling methodology described in [41]. Furthermore, each forecast starts with the weather forecast and is updated every 6 h, at 0:00, 6:00, 12:00 and 18:00 h UTC-time.
- Initial condition: The present flow conditions of all nine flow stations were obtained from real-time hour measurements of the General Direction of Water of the Chilean government; so that, the observed flow was used as an initial condition (t = 0).

#### 2.3.2. Data-Driven Weather-Runoff Forecast Models

#### 2.4. Evaluation Metrics for Model Skills

^{3}/s) and quantifies the standard error in the prediction.

#### 2.5. Structure of the Data-Driven Weather-Runoff Forecasts Models

## 3. Results

#### 3.1. Performance of ANN versus DL Weather-Runoff Forecast Models

^{3}/s and 4.3 m

^{3}/s for ${Q}_{\mathrm{max}}$ and ${\mathrm{Q}}_{\mathrm{avg}}$, respectively (see Table 5). With respect to performance in predicting the entire time-series of the flow for the following 3 days, Figure 11 shows the comparison between the observed and predicted flow for different cases identified with open circles in Figure 10. These examples were chosen based on the cumulative frequency of the average observed flow, using percentiles of 99.9%, 99.6%, 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91% and 90%, for panels (a) to (l), respectively. Finally, Figure 11 compares predicted and observed flow time-series for the maximum flow event. Similar figures for the rest of the flow stations are found in the Supporting Information.

#### 3.2. Performance of the Early Warning System

^{3}/s, Figure 12a), and in May of 2012 (with a maximum flow of 546.1 m

^{3}/s, Figure 12b). For each event, the DL weather-runoff forecast model was run several times, starting at different days before the time at which the maximum flow was observed. As an example, Figure 12 shows three of these runs: One that starts 6 days before the peak flow and ends before the flow start to rise (black line that starts with the circle and ends with the black x); the second (blue simulation) that starts 4 days the peak flow, at the beginning of the storm, and ends before the peak flow was observed; and the third simulation starting on 2 days before the peak flow, in the middle of the storm, and ending after the peak flow has passed. Similarly, Table 6 shows the errors of time to peak ET

_{p}(Equation (13)), and peak discharge, EQ

_{p}(Equation (12)), calculated for each one of the different simulations.

_{p}and ET

_{p}(Table 6), the relative error in predicting the maximum flow tends to be smaller for larger maximum flows, and it takes positive values; so that, in this case, the model predicts maximum flows slightly smaller than the measurements. With respect to the error in the time to maximum flow, it is equal to 0 most of the time.

## 4. Discussion

^{3}/s.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

- -
- Online flow measurements: http://dgasatel.mop.cl/
- -
- GFS-NCEP meteorological analysis and forecast: https://www.ncdc.noaa.gov/data-access/model-data/model-datasets/global-forcast-system-gfs
- -
- NASA Shuttle Radar Topography Mission (SRTM) version 3.0: https://search.earthdata.nasa.gov/.

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Study site: (

**a**) Altitudinal profile along the 33.4° S parallel. (

**b**) Map of study area with station location, watershed definition, and glacier location (white areas). Orange watersheds correspond to flow stations in Mapocho River, and blue watershed corresponds to flow stations in Maipo River.

**Figure 5.**(

**a**) Architecture for the Artificial Neural Networks (ANN) model, (

**b**) architecture for the Deep Learning (DL) model.

**Figure 6.**Root mean square error (RMSE) of a Maipo en el Manzano validation subset as a function of: (

**a**) Transfer function for the ANN model, (

**b**) the number of hidden layers, (

**c**) the number of hidden units.

**Figure 7.**RMSE of a Maipo en el Manzano validation subset as a function of transfer function for the DL model.

**Figure 8.**RMSE of a Maipo en el Manzano validation subset as a function of the number of LSTM and FFNN hidden layers for the DL model, (

**a**) results for one LSTM layer, (

**b**) results for two layers of LSTM, (

**c**) results for three layers of LSTM, (

**d**) results for four layers of LSTM.

**Figure 9.**RMSE of a Maipo en el Manzano validation subset as a function of the number of hidden units in the LSTM layers for the DL model.

**Figure 10.**(

**a**) Comparison between observed and predicted ${Q}_{\mathrm{max}}$ for flow station 1 and the DL model. (

**b**) Same as (

**a**) for the average flow ${Q}_{\mathrm{avg}}$. (

**c**,

**d**) same as (

**a**,

**b**) for the ANN model. Red open circles define examples plotted in Figure 11.

**Figure 11.**Comparison between predicted and observed flow for different cases identified with red open circles in Figure 11, associated to percentiles of 99.9%, 99.6%, 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91% and 90%, for panels (

**a**–

**l**), respectively. (

**m**) Plots predicted and observed time-series for the event with maximum flow.

**Figure 12.**Time series of observed flow (grey line) for the events of (

**a**) April 2016 and (

**b**) May 2012 in Maipo en el Manzano station. Time series in black, blue and red are different predicted flows that star in the circle and ended with the x mark.

River | ID | Flow Station Name | Area (km^{2}) | Z_{min} (m a.s.l) | Z_{max} (m a.s.l) | Z_{avg} (m a.s.l) | Slope (%) | Stream Length (km) | Glacier Area (km^{2}) | % Glacier in Watershed | First Data |
---|---|---|---|---|---|---|---|---|---|---|---|

Maipo River | 1 | Maipo en El Manzano | 4839 | 882 | 6550 | 3180 | 63.8 | 118.7 | 370.7 | 7.7 | March 2004 |

2 | Río Volcan en Queltehues | 523 | 1353 | 5967 | 3364 | 64.6 | 41.3 | 63.8 | 12.2 | March 2014 | |

3 | Río Olivares antes Junta Río Colorado | 783 | 1525 | 6500 | 3364 | 68.7 | 48.7 | 94.1 | 12.0 | March 2013 | |

4 | Río Colorado antes Junta Río Olivares | 543 | 2369 | 6047 | 3689 | 67.6 | 29.5 | 81.2 | 15.0 | August 2008 | |

Mapocho River | 5 | Mapocho Los Almendros | 637 | 968 | 5417 | 2778 | 56.8 | 39.5 | 20.1 | 3.2 | April 2016 |

6 | Estero Arrayán Montosa | 217 | 1227 | 3829 | 2509 | 53.1 | 24.8 | 0.3 | 0.1 | March 2004 | |

7 | Río Molina antes Junta San Francisco | 300 | 1335 | 5417 | 2647 | 50.9 | 25.5 | 5.3 | 1.8 | January 2012 | |

8 | Estero Yerba Loca antes Junta San Francisco’ | 109 | 1630 | 5350 | 3416 | 68.2 | 18.1 | 8.9 | 8.1 | January 2012 | |

9 | Río San Francisco antes Junta Estero Yerba Loca | 136 | 1586 | 4853 | 3126 | 60.6 | 23.0 | 6.0 | 4.4 | January 2012 |

**Table 2.**Summary of hydrological features of the train, test and validation subsets for each of the studied watershed.

River | ID | Subset | Number of Data Block | Flow (m^{3}/s) | ||||
---|---|---|---|---|---|---|---|---|

Max | Average | Min | Percentile (90%) | Percentile (99%) | ||||

Maipo River | 1 | Train | 74,780 | 1078.6 | 121.1 | 32.8 | 209.6 | 517.8 |

Validation | 21,366 | 1078.6 | 119.8 | 33.6 | 207.5 | 459.3 | ||

Test | 10,683 | 1078.6 | 124.6 | 33.6 | 222.1 | 525.0 | ||

2 | Train | 72,282 | 61.6 | 9.1 | 0.1 | 22.8 | 48.1 | |

Validation | 20,652 | 61.6 | 9.6 | 0.1 | 24.5 | 50.2 | ||

Test | 10,326 | 61.6 | 9.2 | 0.1 | 23.1 | 49.9 | ||

3 | Train | 68,258 | 124.1 | 9.7 | 0.4 | 25.9 | 75.2 | |

Validation | 19,502 | 88.5 | 9.7 | 0.4 | 27.2 | 74.3 | ||

Test | 9751 | 124.1 | 10.2 | 0.4 | 26.7 | 75.2 | ||

4 | Train | 76,946 | 165.0 | 7.6 | 0.4 | 27.1 | 56.2 | |

Validation | 21,985 | 165.0 | 7.9 | 0.4 | 27.5 | 58.6 | ||

Test | 10,992 | 165.0 | 8.1 | 0.4 | 28.6 | 58.6 | ||

Mapocho River | 5 | Train | 66,317 | 26.8 | 1.5 | 0.1 | 2.7 | 9.3 |

Validation | 18,948 | 26.8 | 1.4 | 0.1 | 2.6 | 7.6 | ||

Test | 9474 | 26.8 | 1.5 | 0.1 | 2.6 | 8.1 | ||

6 | Train | 39,768 | 20.4 | 1.5 | 0.1 | 2.6 | 12.9 | |

Validation | 11,362 | 20.4 | 1.6 | 0.4 | 3.0 | 11.3 | ||

Test | 5681 | 20.4 | 1.5 | 0.3 | 2.7 | 12.8 | ||

7 | Train | 48,610 | 256.6 | 4.3 | 0.4 | 7.8 | 27.3 | |

Validation | 13,889 | 256.6 | 4.2 | 0.4 | 7.8 | 29.3 | ||

Test | 6944 | 256.6 | 4.2 | 0.4 | 7.4 | 28.9 | ||

8 | Train | 78,629 | 8.5 | 1.2 | 0.1 | 2.8 | 5.9 | |

Validation | 22,465 | 8.5 | 1.2 | 0.1 | 2.8 | 5.5 | ||

Test | 11,233 | 8.5 | 1.2 | 0.1 | 2.7 | 5.5 | ||

9 | Train | 41,520 | 3.3 | 0.3 | 0.1 | 0.5 | 2.5 | |

Validation | 11,863 | 3.1 | 0.3 | 0.1 | 0.5 | 2.1 | ||

Test | 5931 | 3.3 | 0.3 | 0.1 | 0.5 | 2.6 |

Parameters and Functions | Value |
---|---|

Transfer function | Linear/Relu |

Number of hidden layers | 1–5 |

Number of hidden neurons | 25–400 |

**Table 4.**Parameters and functions associated with DL forecast model. FFNN stands for feedforward neural network. LSTM for long short-term memory.

Parameters and Functions | Value |
---|---|

Transfer function (FFNN) | Linear/Relu |

Number of LSTM layers | 1–4 |

Number of hidden FFNN layers | 0–3 |

Number of neurons in the LSTM layers | 50–400 |

Number of neurons in the FFNN layers | 50–400 |

**Table 5.**Summary of errors for data-driven weather-runoff forecast models. The testing subset was used for computing these indexes.

River | ID | Variable | DL Model | ANN Model | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

$\mathrm{RMSE}/{\mathit{Q}}_{\mathrm{avg}}$ | $\mathrm{NSE}$ | $\mathrm{RMSE}\text{}({\mathbf{m}}^{3}/\mathbf{s})$ | ${\mathit{C}}_{\mathit{x}\mathit{y}}$ | $\mathrm{RMSE}/{\mathit{Q}}_{\mathrm{avg}}$ | $\mathrm{NSE}$ | $\mathrm{RMSE}\text{}({\mathbf{m}}^{3}/\mathbf{s})$ | ${\mathit{C}}_{\mathit{x}\mathit{y}}$ | % Glacier in Watershed | |||

Maipo | 1 | ${Q}_{\mathrm{max}}$ | 0.049 | 0.996 | 5.829 | 0.998 | 0.155 | 0.955 | 18.344 | 0.982 | 7.7 |

${Q}_{\mathrm{avg}}$ | 0.028 | 0.998 | 2.705 | 0.999 | 0.074 | 0.988 | 7.199 | 0.995 | |||

2 | ${Q}_{\mathrm{max}}$ | 0.146 | 0.983 | 1.285 | 0.992 | 0.255 | 0.949 | 2.248 | 0.977 | 12.2 | |

${Q}_{\mathrm{avg}}$ | 0.206 | 0.973 | 0.485 | 0.987 | 0.582 | 0.784 | 1.370 | 0.885 | |||

3 | ${Q}_{\mathrm{max}}$ | 0.143 | 0.990 | 1.326 | 0.995 | 0.583 | 0.840 | 5.412 | 0.939 | 12.0 | |

${Q}_{\mathrm{avg}}$ | 0.109 | 0.993 | 0.629 | 0.997 | 0.180 | 0.980 | 1.037 | 0.994 | |||

4 | ${Q}_{\mathrm{max}}$ | 0.214 | 0.986 | 1.519 | 0.993 | 0.823 | 0.799 | 5.836 | 0.919 | 15.0 | |

${Q}_{\mathrm{avg}}$ | 0.103 | 0.993 | 0.484 | 0.996 | 0.229 | 0.964 | 1.076 | 0.983 | |||

Mapocho | 5 | ${Q}_{\mathrm{max}}$ | 0.082 | 0.995 | 0.115 | 0.998 | 0.261 | 0.952 | 0.366 | 0.977 | 3.2 |

${Q}_{\mathrm{avg}}$ | 0.072 | 0.992 | 0.082 | 0.996 | 0.127 | 0.974 | 0.144 | 0.988 | |||

6 | ${Q}_{\mathrm{max}}$ | 0.097 | 0.994 | 0.142 | 0.997 | 0.319 | 0.932 | 0.464 | 0.968 | 0.1 | |

${Q}_{\mathrm{avg}}$ | 0.055 | 0.995 | 0.062 | 0.998 | 0.105 | 0.983 | 0.118 | 0.992 | |||

7 | ${Q}_{\mathrm{max}}$ | 0.355 | 0.984 | 1.385 | 0.992 | 1.279 | 0.797 | 4.991 | 0.895 | 1.8 | |

${Q}_{\mathrm{avg}}$ | 0.055 | 0.998 | 0.012 | 0.999 | 0.144 | 0.986 | 0.032 | 0.993 | |||

8 | ${Q}_{\mathrm{max}}$ | 0.075 | 0.994 | 0.086 | 0.997 | 0.199 | 0.958 | 0.229 | 0.981 | 8.1 | |

${Q}_{\mathrm{avg}}$ | 0.048 | 0.997 | 0.043 | 0.999 | 0.119 | 0.983 | 0.107 | 0.993 | |||

9 | ${Q}_{\mathrm{max}}$ | 0.093 | 0.996 | 0.026 | 0.998 | 0.277 | 0.964 | 0.077 | 0.982 | 4.4 | |

${Q}_{\mathrm{avg}}$ | 0.147 | 0.994 | 0.348 | 0.997 | 0.529 | 0.921 | 1.250 | 0.960 |

**Table 6.**Errors of time to peak, ET

_{p}, and peak discharge, EQ

_{p}, calculated for different starting time of simulations with the DL weather-runoff model for two flood events. The time 0 days 0 h corresponds to the time at which the maximum flow was observed.

April 2016 | May 2012 | ||||||
---|---|---|---|---|---|---|---|

Starting Time of Simulation | Q_{max} | EQ_{p} | ET_{p} | Starting Time of Simulation | Q_{max} | EQ_{p} | ET_{p} |

(m^{3}/s) | (%) | (h) | (m^{3}/s) | (%) | (h) | ||

−3 days 15 h | 527.1 | 0.1 | 0 | −3 days 2 h | 386.2 | 3.1 | 0 |

−3 days 3 h | 705.1 | −0.5 | 0 | −2 days 14 h | 546.1 | 0.6 | 0 |

−2 days 15 h | 1078.6 | 0.5 | 0 | −2 days 2 h | 546.1 | 0.5 | 0 |

−2 days 3 h | 1078.6 | 0.6 | 0 | −1 day 14 h | 546.1 | 0.5 | 0 |

−1 day 15 h | 1078.6 | 0.6 | 0 | −1 day 2 h | 546.1 | 1.7 | 0 |

−1 day 3 h | 1078.6 | −0.1 | 0 | 0 day 14 h | 546.1 | −0.3 | 0 |

0 day 15 h | 1078.6 | 0.4 | 0 | 0 day 2 h | 546.1 | 13.2 | 0 |

0 day 3 h | 1078.6 | 3.2 | 0 | 0 day 1 h | 144.4 | 5.4 | 0 |

0 day 9 h | 429.1 | −1.0 | 0 | 0 day 1 h | 88.3 | 2.0 | 0 |

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**MDPI and ACS Style**

de la Fuente, A.; Meruane, V.; Meruane, C.
Hydrological Early Warning System Based on a Deep Learning Runoff Model Coupled with a Meteorological Forecast. *Water* **2019**, *11*, 1808.
https://doi.org/10.3390/w11091808

**AMA Style**

de la Fuente A, Meruane V, Meruane C.
Hydrological Early Warning System Based on a Deep Learning Runoff Model Coupled with a Meteorological Forecast. *Water*. 2019; 11(9):1808.
https://doi.org/10.3390/w11091808

**Chicago/Turabian Style**

de la Fuente, Alberto, Viviana Meruane, and Carolina Meruane.
2019. "Hydrological Early Warning System Based on a Deep Learning Runoff Model Coupled with a Meteorological Forecast" *Water* 11, no. 9: 1808.
https://doi.org/10.3390/w11091808