# Flood Frequency Estimation in Data-Sparse Wainganga Basin, India, Using Continuous Simulation

^{*}

## Abstract

**:**

## 1. Introduction

^{3}/s extra flow released from Dharoi dam on the Sabarmati (a tributary of the Krishna), affecting up to 4 million people [2].

^{2}sub-basin of the Krishna basin in central mainland India with just nine permanently gauged sites that is increasingly being dammed for irrigation and hydropower.

## 2. Materials and Methods

#### 2.1. Study Region

^{2}of undisturbed landscape [14] covering approximately one-third of the basin.

^{2}. Nine sub-catchments are considered, each directly upstream of a gauging station and therefore not necessarily near a confluence. The nine sub-catchments range from approximately 1750 to 36,000 km

^{2}in area.

#### 2.2. River Discharge Data

#### 2.3. Elevation and Flow Direction Data

^{5}m

^{2}or greater, linked to be consistent with the main HydroSHEDS DEM. HydroLAKES data in India are derived from two sources: SRTM Water Body Data [22], generated as a by-product of the SRTM, and the Global Reservoir and Dam (GRanD) dataset, v1 [23,24], which notes more than 100 reservoirs in India. This dataset includes natural lakes and does not include some recent major reservoirs, such as that created by Gosekhurd Dam, near Pauni gauging station, with an effective storage capacity of 7.40 × 10

^{8}m

^{3}and a reservoir area of 222 km

^{2}[15].

#### 2.4. Meteorological Data

#### 2.5. Land Cover Data

#### 2.6. Statistical Flood Frequency Estimation

_{DIST}statistic [31,32] on the whole dataset using the lmomRFA package from R [33,34].

_{DIST}statistic was calculated as:

_{DIST}= [(τ

_{4}− τ

_{4}

^{DIST}) − B

_{4}]/σ

_{4}

_{4}is the sample L-kurtosis, τ

_{4}

^{DIST}is the expected L-kurtosis under the chosen distribution, derived as a function of the sample L-skew, B

_{4}is a bias correction term, the sample mean of a set of simulated copies of (τ

_{4}− τ

_{4}

^{DIST}), and σ

_{4}is the sample standard deviation of the copies. Any distribution with a value of |Z

_{DIST}| < 1.64 was deemed to be potentially acceptable for that station. The distribution with the smallest value of |Z

_{DIST}| was also recorded, this being referred to as the “chosen” distribution for that station.

#### 2.7. Hydrological Model

#### 2.8. Model Calibration and Validation

^{2}+ (β − 1)

^{2}+ (γ − 1)

^{2}]

^{½}

_{s}/μ

_{o}

_{s}/μ

_{s})/(σ

_{o}

_{/}μ

_{o})

^{2}. Since the smallest sub-catchment in this study measures 1755 km

^{2}, and most are over 5000 km

^{2}, it is not appropriate to compare the CWC’s method to the one tested in this study. Methodological validation is conducted against gauged data only.

## 3. Results and Discussion

#### 3.1. Distribution Choice

^{2}, upstream of the Krishna near the Western Ghats. This dry catchment receives an average annual rainfall of 1053 mm, and consists primarily (73%) of cultivated, irrigated land. At its most extreme, almost no flow can be seen in the Sina for multi-year periods, and as such, even the annual maximum can nearly reach zero. In this case, Figure 4 shows that both the GPA and PE3 distributions fit similarly, and this is frequently true for the drier catchments, typically found towards the west of the Krishna and Godavari basins.

^{2}on the Indravathi River in the lower reaches of the Godavari, located towards the east coast of peninsular India. Its larger area in part accounts for the higher discharge, as does the higher average annual rainfall of approximately 1800 mm, a direct result of the seasonal monsoons. This region is also 60% forested due to this climate. In this case, the apparent lower bound to the AMAX series seen in Figure 4 (except for two outliers) may be due to this large amount of somewhat predictable rainfall. Here, we see that the Generalized Pareto distribution captures the magnitude of the most extreme events at both tails. On the other hand, the PE3 distribution fits the central behavior very well, which still allows reasonable estimation up to the 1-in-25-year flood, but does not capture the behavior of tails as well. Therefore, this paper uses the GPA distribution, since it was accepted by all the Wainganga stations under the Hosking–Wallis test, and the climate in the Wainganga basin is more similar to Wadakabal than to Pathagudem.

#### 3.2. Lumped Sub-Catchment Modeling

_{1}and l

_{2}(first two L-moments), but it has an obvious mild bias, particularly with less variability (l

_{2}) modeled than observed. It is expected that use of Nash–Sutcliffe Efficiency as an objective function would reduce the modeled flow variability further, as the KGE (and later KGE’) metrics were developed in response to the tendency of NSE to downplay the observed flow variability. Presumably, the slight underestimations in flow variability found for most catchments (those with γ < 1) relate to the most extreme values, i.e., the annual maxima and minima.

_{max}, the maximum soil storage capacity, takes a value of 5900 mm in Rajoli and 2500 mm in Satrapur, while the lowest value it takes is 800 mm in Wairagarh. Formal quantification of reservoir effects is complicated, as the interaction of each reservoir and catchment is unique in India [51]. Finally, equifinality (multiple ways to achieve the same answer) may mean that the same KGE’ can be achieved by more than one parameter set. Equifinality and unrepresented processes are linked, as there are two flow paths out of the PDM, a nominally “fast” and a nominally “slow” response. The fast response made up the vast majority of flow in all nine catchment models—neither Kumhari nor Rajegaon produced any modeled slow flow, and the model producing the most was Salebardi, at 14.3% of the total flow. However, the seven models that did produce slow flow all produced it similarly: drier years had no slow flow, while in wetter years, slow flow increased as the wet season progressed, and as a fraction of individually high peak flows. As a result, nominally slow flow contributed a considerable portion to the largest AMAX flows in Satrapur, Pauni and Rajoli. As there were no modeled dry-season flows for any catchment, no flow path modeled a baseflow-type flow, but both flow paths could and did contribute to peak flows (Figure 6).

^{2}) urban Australian catchment [45]. However, AMAXs at Ashti are consistently underestimated at shorter return periods. This consistent underperformance in modeling AMAX magnitude is perhaps unsurprising, as the KGE’ performance metric focuses on the whole flow hydrograph, of which only one point out of every 365 or 366 is an AMAX; this criticism is equally applicable to Nash–Sutcliffe efficiency and other time-series performance metrics. The consistent underestimation of the entire FFC at Ramakona may be related to the creation of the gridded rainfall data. Ramakona contains some very steep and mountainous areas, and it does not seem that elevation was included as a covariate in the rainfall interpolation process [25]. However, from a purely KGE perspective, the performance of the PDM at Ramakona, and across all nine Wainganga sub-catchments generally, is close to that of EPA-SWMM when applied to simulate continuous runoff from two rural, highly seasonal south Australian catchments of 27 and 122 km

^{2}[46].

#### 3.3. Lumped Sub-Catchment Modeling (Optimizing AMAX Performance Only)

#### 3.4. Lumped Sub-Catchment Modeling with a Calibration/Validation Period

#### 3.5. Lumped Sub-Catchment Modeling (Single Parameter Set)

#### 3.6. Semi-Lumped Modeling

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Map of the Wainganga, Godavari and Krishna basins within central/south mainland India; (

**b**) Close-up of the Wainganga catchment and sub-catchments with named river gauging stations and cities.

**Figure 3.**Hosking–Wallis distribution test results over the Krishna and Godavari basins. Wainganga sub-catchments are outlined in black.

**Figure 4.**Growth curves associated to (

**left**) Wadakbal gauging station on the Sina River, QMED = 581 m

^{3}/s, and (

**right**) Pathagudem gauging station on the Indravathi River, QMED = 10,045 m

^{3}/s. Gray × symbols indicate ranked gauged AMAX flows at each station.

**Figure 5.**Modeled vs observed QMED, l

_{1}(sample L-mean), l

_{2}(sample L-CV) and t

_{3}(sample L-SKEW) for nine Wainganga station AMAX records.

**Figure 8.**Observed and modeled flood frequency curves for Ashti and Ramakona (PDM optimized for AMAX only).

**Figure 9.**Observed (red line) and modeled AMAX series for Ashti when PDM is optimized to match AMAX from 1983–2006 inclusive (blue line) and optimized to match the whole flow regime from 1983–2006 inclusive (yellow line).

**Figure 10.**Observed and modeled flood frequency curves for Ashti and Satrapur (semi-lumped modeling).

Name | Start Year | End Year | Area (km^{2}) | DPLBAR (km) | DPSBAR (m/km) | CULT (-) | URB (-) | FOR (-) |
---|---|---|---|---|---|---|---|---|

Ashti | 1965 | 2016 | 51579 | 339.0 | 33.4 | 0.470 | 0.051 | 0.394 |

Kumhari | 1986 | 2017 | 8417 | 118.0 | 38.9 | 0.461 | 0.040 | 0.380 |

Pauni | 1964 | 2016 | 36023 | 217.0 | 36.9 | 0.499 | 0.057 | 0.349 |

Rajegaon | 1985 | 2017 | 5393 | 69.7 | 48.7 | 0.366 | 0.043 | 0.527 |

Rajoli | 1986 | 2015 | 2675 | 54.5 | 19.2 | 0.489 | 0.033 | 0.405 |

Ramakona | 1986 | 2017 | 2488 | 82.3 | 54.9 | 0.538 | 0.041 | 0.295 |

Salebardi | 1985 | 2014 | 1768 | 44.0 | 30.4 | 0.439 | 0.037 | 0.469 |

Satrapur | 1984 | 2015 | 11161 | 142.0 | 44.5 | 0.519 | 0.059 | 0.305 |

Wairagarh | 1992 | 2015 | 1755 | 42.5 | 41.1 | 0.233 | 0.030 | 0.704 |

**Table 2.**Number of stations at which each distribution is acceptable (|Z

_{DIST}| < 1.64) and chosen (|Z

_{DIST}| = min(|Z

_{DIST}|)) to describe the annual maximum (AMAX) series.

Distribution | GLO | GEV | GNO | PE3 | GPA |
---|---|---|---|---|---|

Accepted | 67 | 91 | 95 | 101 | 92 |

Chosen | 17 | 17 | 12 | 29 | 47 |

Catchment | KGE’ | r | γ | β | NSE |
---|---|---|---|---|---|

Ashti | 0.880 | 0.881 | 0.998 | 1.007 | 0.760 |

Kumhari | 0.512 | 0.513 | 0.965 | 1.001 | 0.057 |

Pauni | 0.858 | 0.858 | 1.007 | 1.008 | 0.712 |

Rajegaon | 0.669 | 0.670 | 0.975 | 1.006 | 0.352 |

Rajoli | 0.548 | 0.558 | 0.905 | 1.010 | 0.183 |

Ramakona | 0.333 | 0.335 | 0.952 | 0.993 | −0.262 |

Salebardi | 0.648 | 0.654 | 0.937 | 1.003 | 0.346 |

Satrapur | 0.573 | 0.575 | 0.964 | 0.981 | 0.194 |

Wairagarh | 0.486 | 0.488 | 0.971 | 1.032 | −0.026 |

Catchment | KGE’ | r | γ | β | NSE |
---|---|---|---|---|---|

Ashti | 0.647 | 0.860 | 0.922 | 1.315 | 0.602 |

Kumhari | 0.356 | 0.399 | 1.030 | 0.769 | 0.001 |

Pauni | 0.667 | 0.744 | 1.132 | 0.833 | 0.510 |

Rajegaon | 0.353 | 0.561 | 0.855 | 1.452 | −0.163 |

Rajoli | −0.516 | 0.561 | 0.612 | 2.398 | −0.659 |

Ramakona | 0.160 | 0.299 | 0.993 | 1.462 | −1.250 |

Salebardi | 0.397 | 0.637 | 0.753 | 1.413 | 0.209 |

Satrapur | 0.350 | 0.517 | 1.373 | 0.775 | −0.033 |

Wairagarh | 0.437 | 0.441 | 0.949 | 0.963 | −0.030 |

Catchment | KGE’ | r | γ | β | NSE |
---|---|---|---|---|---|

Ashti | 0.658 | 0.763 | 1.049 | 0.758 | 0.574 |

Kumhari | 0.324 | 0.493 | 0.903 | 0.563 | 0.230 |

Pauni | 0.738 | 0.790 | 1.060 | 0.854 | 0.608 |

Rajegaon | 0.514 | 0.665 | 0.824 | 0.694 | 0.427 |

Rajoli | 0.001 | 0.612 | 0.703 | 1.871 | −0.179 |

Ramakona | 0.293 | 0.349 | 0.742 | 0.900 | 0.020 |

Salebardi | 0.503 | 0.668 | 0.664 | 0.845 | 0.433 |

Satrapur | 0.291 | 0.505 | 0.803 | 1.468 | −0.211 |

Wairagarh | 0.416 | 0.472 | 0.872 | 0.784 | 0.172 |

Catchment | KGE’ | r | γ | β | NSE | KGE’’ |
---|---|---|---|---|---|---|

Ashti | 0.867 | 0.868 | 0.980 | 1.003 | 0.741 | 0.860 |

Pauni | 0.874 | 0.874 | 0.999 | 1.000 | 0.749 | 0.844 |

Satrapur | 0.575 | 0.579 | 0.955 | 0.970 | 0.214 | 0.518 |

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**MDPI and ACS Style**

Vesuviano, G.; Griffin, A.; Stewart, E.
Flood Frequency Estimation in Data-Sparse Wainganga Basin, India, Using Continuous Simulation. *Water* **2022**, *14*, 2887.
https://doi.org/10.3390/w14182887

**AMA Style**

Vesuviano G, Griffin A, Stewart E.
Flood Frequency Estimation in Data-Sparse Wainganga Basin, India, Using Continuous Simulation. *Water*. 2022; 14(18):2887.
https://doi.org/10.3390/w14182887

**Chicago/Turabian Style**

Vesuviano, Gianni, Adam Griffin, and Elizabeth Stewart.
2022. "Flood Frequency Estimation in Data-Sparse Wainganga Basin, India, Using Continuous Simulation" *Water* 14, no. 18: 2887.
https://doi.org/10.3390/w14182887