# An Assessment of the Influence of Uncertainty in Temporally Evolving Streamflow Forecasts on Riverine Inundation Modeling

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodologies

#### 2.1. River Forcing

#### 2.2. Flood Inundation Model

^{2}); S

_{0-x}and S

_{0−y}are the bottom elevation slopes (unitless) in the x and y directions, respectively; n is the Manning’s roughness coefficient (0.035); Δx and Δy are the dimensions (m) of a grid cell; and Δt is the variable time step (s). The friction slope was calculated by Manning’s equation [24].

_{in}is the total streamflow (m

^{3}/s), and q

_{in−x}and q

_{in−y}are the proportions of the total streamflow (m

^{3}/s) in the x and y directions, respectively. The NWM’s forecast streamflow was loaded only at the head reaches of the channel network by being introduced into both the continuity equation and momentum equations as the upstream boundary conditions. For all the remaining downstream reaches in the network, the NWM’s forecast lateral inflow was loaded into the continuity equation only to conserve mass; the lateral inflow represents the rainfall-caused overland runoff and usually comes with a relatively much smaller velocity than the river flow, and thus the flow acceleration or deceleration due to the discharge of the lateral inflow was neglected in this study. The hydrologic forcing generated by the NWM was only “one-way” coupled to the inundation hydraulic model; in other words, the former was applied as the boundary condition to drive the latter, whereas the reverse direction was not simulated by this frame. The proportions of boundary inflow in the x and y directions were approximated by the tangent directions of the NHDPlusV2 streamlines, which the NWM adopts for building the stream network.

#### 2.3. Statistical Metrics

_{95%}) were used to compare the observed and modeled water levels:

^{th}location, η

_{max,i}is the observed water surface elevation at location i, z* is the corresponding standard score, $\sigma $ is the standard deviation, ${\widehat{Q}}_{i}$ is the forecast quantity, $\overline{Q}$ is the observed mean value, and N is the total number of pairs of comparisons. The ME can be positive or negative; the closer to zero the value is, the more accurate the model results are. The ME

_{95%}represents the variation of the model results. For extent mapping, the modeling performance was assessed by two binary measures: fit (F) [18,25] and Peirce’s skill score (PSS) [26]:

#### 2.4. Case Study

#### 2.5. Automated Coupling Workflow

## 3. Results and Discussion

#### 3.1. Verification of Streamflow Forcing

#### 3.2. Inundation Validation

_{95%}. Across all days of river forcing applied, the maximum water surface elevations were underestimated by less than 1 m on average. The forcing of 8 October 2016 achieved the best overall accuracy with an ME of −0.06 m. This corresponds with the previous observation that 8 October 2016 was one of a few river forcing datasets whose hydrographs had larger peaks than the observed ones (Figure 3).

#### 3.3. Error Propagation

#### 3.4. Accuracy Measure of River Forcing

#### 3.5. Tradeoff in Domain Size

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Study sites with the 10 km long rectangular bound centered on the 10 clusters of riverine high water marks.

**Figure 2.**General workflow and an example network of the river reaches to be loaded by lateral inflow and streamflow boundary conditions.

**Figure 3.**Comparisons between the hydrographs observed from the United States Geological Survey (USGS) stream gauges and the hydrographs developed by the National Water Model streamflow forecasts.

**Figure 4.**Nash–Sutcliff efficiency coefficients for comparing the National Water Model (NWM) forecast streamflow with the United States Geological Survey (USGS) observed streamflow.

**Figure 5.**The mean error and the 95% confidence levels of the errors of the simulated peak water surface elevations.

**Figure 7.**The percent bias of the total volume of the National Water Model (NWM) streamflow forecasts was compared to the NSE (

**a**) and PBIAS (

**b**) of the simulated peak water elevations. The red line refers to the linear fit. Abbreviations: PBIAS-V-NWM, percent bias of the total volume of NWM forecast streamflow; NSE-RIFT, Nash–Sutcliffe efficiency of the peak water elevations simulated by Rapid Inundation Flood Tool; PBIAS-RIFT, percent bias of the peak water elevations simulated by Rapid Inundation Flood Tool; R

^{2}, coefficient of determination.

**Figure 8.**The percent bias of the National Water Model (NWM) streamflow forecasts was compared to the F (

**a**) and PSS (

**b**) of the simulated maximum flood extents. The red line refers to the linear fit. Abbreviations: PBIAS-V-NWM, percent bias of the total volume of NWM forecast streamflow; F-RIFT, the measure of fit of the maximum flood extents simulated by Rapid Inundation Flood Tool; PSS-RIFT, Peirce’s skill score of the maximum flood extents simulated by Rapid Inundation Flood Tool; R

^{2}, coefficient of determination.

**Figure 9.**The changes in the statistics of the simulated peak water surface elevations (

**a**) and maximum extents (

**b**) as well as the changes in the computational costs (

**c**) along with the increase in the size of the forcing domain. The forecast streamflow of 8 October 2016 was used for all simulations. Abbreviations: F, the measure of fit; PSS, Peirce’s skill score.

**Figure 10.**The changes in simulated inundated areas along with the increase in the size of the forcing domain where forcing was loaded, compared to the flood extents published by the U.S. Federal Emergency Management Agency (FEMA).

**Table 1.**Locations of the selected United States Geological Survey (USGS) stream gauges and their intersected National Water Model (NWM) reaches.

Gauge ID | Name | Latitude | Longitude | NWM Reach ID |
---|---|---|---|---|

02134500 | Lumber River at Boardman, NC | 34°26’33" | −78°57’37" | 9131716 |

02135000 | Little Pee Dee R. at Galivants Ferry, SC | 34°03’25" | −79°14’50" | 9114416 |

02089000 | Neuse River near Goldsboro, NC | 35°20’15" | −77°59’51" | 11239411 |

02088500 | Little River near Princeton, NC | 35°30’41" | −78°09’37" | 8786063 |

02134170 | Lumber River at Lumberton, NC | 34°37’13" | −79°00’40" | 9129886 |

02103000 | Little River at Manchester, NC | 35°11’36" | −78°59’08" | 8846189 |

Forecast | 1 Oct | 2 Oct | 3 Oct | 4 Oct | 5 Oct | 6 Oct | 7 Oct | 8 Oct | 9 Oct | 10 Oct | 11 Oct | 12 Oct | 13 Oct | 14 Oct | 15 Oct |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

PBIAS | −0.60 | −0.62 | −0.85 | −0.60 | −0.89 | −0.17 | −0.15 | −0.15 | −0.21 | −0.45 | −0.54 | −0.58 | −0.54 | −0.52 | −0.51 |

NSE | 0.07 | 0.14 | −0.37 | 0.23 | −0.52 | 0.31 | 0.28 | 0.25 | −0.64 | 0.31 | 0.38 | 0.35 | 0.46 | 0.50 | 0.53 |

Forecast | 1 Oct | 2 Oct | 3 Oct | 4 Oct | 5 Oct | 6 Oct | 7 Oct | 8 Oct | 9 Oct | 10 Oct | 10 Oct | 10 Oct | 10 Oct | 10 Oct | 10 Oct |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

PBIAS | −0.03 | −0.03 | −0.03 | −0.03 | −0.03 | −0.02 | −0.01 | 0.00 | −0.01 | −0.02 | −0.03 | −0.03 | −0.03 | −0.03 | −0.03 |

NSE | 0.98 | 0.98 | 0.98 | 0.98 | 0.98 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.98 | 0.98 | 0.98 | 0.98 | 0.98 |

Forecast | 1 Oct | 2 Oct | 3 Oct | 4 Oct | 5 Oct | 6 Oct | 7 Oct | 8 Oct | 9 Oct | 10 Oct | 11 Oct | 12 Oct | 13 Oct | 14 Oct | 15 Oct |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

F | 0.57 | 0.60 | 0.51 | 0.63 | 0.50 | 0.67 | 0.70 | 0.73 | 0.69 | 0.68 | 0.66 | 0.63 | 0.61 | 0.59 | 0.58 |

PSS | 0.56 | 0.59 | 0.49 | 0.62 | 0.48 | 0.66 | 0.70 | 0.74 | 0.70 | 0.68 | 0.65 | 0.63 | 0.60 | 0.58 | 0.56 |

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**MDPI and ACS Style**

Feng, Y.; Judi, D.R.; Rakowski, C.L. An Assessment of the Influence of Uncertainty in Temporally Evolving Streamflow Forecasts on Riverine Inundation Modeling. *Water* **2020**, *12*, 911.
https://doi.org/10.3390/w12030911

**AMA Style**

Feng Y, Judi DR, Rakowski CL. An Assessment of the Influence of Uncertainty in Temporally Evolving Streamflow Forecasts on Riverine Inundation Modeling. *Water*. 2020; 12(3):911.
https://doi.org/10.3390/w12030911

**Chicago/Turabian Style**

Feng, Youcan, David R. Judi, and Cynthia L. Rakowski. 2020. "An Assessment of the Influence of Uncertainty in Temporally Evolving Streamflow Forecasts on Riverine Inundation Modeling" *Water* 12, no. 3: 911.
https://doi.org/10.3390/w12030911