water

Article
Flood Frequency Estimation in Data-Sparse Wainganga Basin,
India, Using Continuous Simulation
Gianni Vesuviano * , Adam Griffin and Elizabeth Stewart

UK Centre for Ecology & Hydrology, Wallingford OX10 8BB, UK

* Correspondence: giaves@ceh.ac.uk

Abstract: Monsoon-related extreme flood events are experienced regularly across India, bringing
costly damage, disruption and death to local communities. This study provides a route towards
estimating the likely magnitude of extreme floods (e.g., the 1-in-100-year flood) at locations without
gauged data, helping engineers to design resilient structures. Gridded rainfall and evapotranspiration
estimates were used with a continuous simulation hydrological model to estimate annual maximum
flow rates at nine locations corresponding with river flow gauging stations in the Wainganga river
basin, a data-sparse region of India. Hosking–Wallis distribution tests were performed to identify
the most appropriate distribution to model the annual maxima series, selecting the Generalized
Pareto and Pearson Type III distributions. The L-moments and flood frequency curves of the modeled
annual maxima were compared to gauged values. The Probability Distributed Model (PDM), properly
calibrated to capture the dynamics of peak flows, was shown to be effective in approximating the
Generalized Pareto distribution for annual maxima, and may be useful in modeling peak flows
in areas with sparse data. Confidence in the model structure, parameterization, input data and
catchment representation build confidence in the modeled flood estimates; this is particularly relevant
if the method is applied in a location where no gauged flows exist for verification.

Citation: Vesuviano, G.; Griffin, A.; Keywords: continuous simulation; flood frequency estimation; L-moments; probability distributed
Stewart, E. Flood Frequency model; PDM; generalized Pareto distribution
Estimation in Data-Sparse
Wainganga Basin, India, Using
Continuous Simulation. Water 2022,
14, 2887. https://doi.org/10.3390/ 1. Introduction
w14182887
The summer monsoons experienced in peninsular India lead to regular, significant
Academic Editor: Paolo Mignosa flooding over wide areas. With the rapid expansion of cities such as Mumbai putting
further pressures on the river and drainage network, more extreme flooding has occurred
Received: 10 August 2022
in recent years, affecting millions of people. This century, Mumbai has seen extreme floods
Accepted: 9 September 2022
in 2005 and 2017 [1], and Ahmedabad in Gujarat experienced floods in July 2015 with
Published: 15 September 2022
over 70,000 m3 /s extra flow released from Dharoi dam on the Sabarmati (a tributary of the
Publisher’s Note: MDPI stays neutral Krishna), affecting up to 4 million people [2].
with regard to jurisdictional claims in Most of the research in the region regarding extreme events and monsoon behavior is
published maps and institutional affil- focused on flash flood prediction with short lead times (e.g., [3,4]). However, in terms of
iations. civil engineering projects and settlement planning, long return period (e.g., 100-year) flood
frequency estimation is invaluable to ensure the suitability of flood defenses, irrigation and
hydropower generation projects. In order to perform this estimation and allow it to be used
more widely, the availability of the data must be considered.
Copyright: © 2022 by the authors.
The Central Water Commission (CWC) in India has developed many flood frequency
Licensee MDPI, Basel, Switzerland.
This article is an open access article
estimation methods, with separate calibration in many different sub-zones of India (e.g., [5–7]).
distributed under the terms and
Through this work, catchment descriptor equations making use of area, catchment slope,
conditions of the Creative Commons
river length and event rainfall depth were developed for the 25-, 50- and 100-year return
Attribution (CC BY) license (https:// period floods using multiple linear regression.
creativecommons.org/licenses/by/ Various non-dimensional methods have also been investigated to estimate long return
4.0/). period flood magnitudes [8], primarily using moments of the annual maxima data and a

Water 2022, 14, 2887. https://doi.org/10.3390/w14182887 https://www.mdpi.com/journal/water

Water 2022, 14, 2887 2 of 22

“shape” parameter (area divided by squared channel length) fitted using linear regression.
Rainfall for storm events determined through a depth-duration-frequency relationship
is often used to model flood frequency relationships across India [9,10]. Typically, these
studies have focused on estimating the mean of the annual maximum (AMAX) series,
QBAR. More recently, machine learning has been applied to develop Bayesian decision-
tree models to use catchment descriptors to estimate the median of the AMAX series,
QMED [11]. In a different approach, a continuous gridded hydrological model was used to
estimate QMED in the UK, which was verified at 550 river gauging stations [12].
The objective of this study is to test continuous simulation rainfall-runoff modeling
as a method to estimate AMAX flows, from which flood frequency curves (FFC) can be
generated in order to provide estimates of the magnitudes of long return period floods
to stakeholders, so that their effects can be planned for, in reservoir design, for example.
Unlike statistical analysis of gauged flows, continuous simulation rainfall-runoff modeling
has the potential to be applied at ungauged sites. The main focus is on reproducing AMAX
flows, rather than the whole flow regime, accurately, as AMAX are most commonly used to
develop FFC. Furthermore, accurate reproduction of the whole flow regime may not be
possible at this time as the daily flow data are not naturalized and are subject to significant
artificial influence in the form of dams and other water management schemes [13]. In this
study, we focus on the Wainganga basin, a ~50,000 km2 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.
This paper proceeds as follows. In Section 2, the study region is described, the available
data are highlighted and the hydrological modeling procedures are outlined with their
relative advantages and drawbacks. Section 3 first explains the statistical investigation used
to choose an appropriate probability distribution to describe annual maximum flows in the
region, then illustrates the flood frequency estimation results. Conclusions are presented in
Section 4.

2. Materials and Methods

2.1. Study Region
The Wainganga River is a tributary of the Godavari River, originating near Gopalganj
in the state of Madhya Pradesh. It flows for a length of approximately 600 km before joining
the Wardha River just south of Chamorshi in the state of Maharashtra (Figure 1a).
The Wainganga basin (Figure 1b) is sparsely populated. Nagpur (population 2.4
million), near the Satrapur river gauging station and partly outside the Wainganga basin,
is the only major city. Chhindwara and Gondia are the only other cities in the basin with
a population above 100,000 as of 2011. Chandrapur (population 320,000) lies just outside
the basin on its diagonal south-west side, at a similar latitude to the Rajoli river gauging
station (Figure 1b). Heavy forests dominate the Wainganga valley, including the major
tiger reserves Tadoba Andhari (Maharashtra) and Pench (Madhya Pradesh), which are
themselves connected with other reserves inside and outside the basin via 16,000 km2 of
undisturbed landscape [14] covering approximately one-third of the basin.
The Wainganga River is increasingly being dammed, replacing the forest cover with
water [13,15]. The vast majority of dams are for irrigation, but an increasing number
are being proposed for hydropower, such as the multi-dam Wainganga Hydroelectric
Project [16]. The basin has been identified by India’s Marine Engineering and Research
Institute (MERI) as “of interest” with regards to flooding.
This study considers the Wainganga basin to Ashti gauging station, a few kilometers
upstream of the junction with Wardha. The Wainganga catchment to Ashti gauging station
has an area of approximately 51,500 km2 . 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 km2 in area.
 Water 2022, 14, 2887 3 of 22
2022, 14, x FOR PEER REVIEW 3 of 23

Figure 1. (a) Map of the Wainganga, Godavari and Krishna basins within central/south mainland
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 sta-
tions and cities.India; (b) Close-up of the Wainganga catchment and sub-catchments with named river gauging
stations and cities.
The Wainganga basin
2.2. River (FigureData
Discharge 1b) is sparsely populated. Nagpur (population 2.4 mil-
lion), near the Satrapur river gauging station and partly outside the Wainganga basin, is
The CWC and Indian Meteorological Department (IMD) have over 900 flow gauging
the only major city. Chhindwara and Gondia are the only other cities in the basin with a
stations that measure river stage, discharge, water quality and sediment content, although
population above 100,000 as of 2011. Chandrapur (population 320,000) lies just outside the
most stations only measure a sub-set of these. Most of the discharge is estimated by
basin on its diagonal south-west side, at a similar latitude to the Rajoli river gauging sta-
CWC using an area-velocity method with autographic water level recorders, except in
tion (Figure 1b). Heavy forests dominate the Wainganga valley, including the major tiger
very high flow when slope-area methods are used to estimate discharge. In some periods,
reserves Tadoba Andhari (Maharashtra) and Pench (Madhya Pradesh), which are them-
missing observations are filled with estimates that match the general day-on-day trend
selves connected with other reserves inside and outside the basin via 16,000 km2 of undis-
of the discharge. Daily gauge data were available from the India-WRIS web portal [17]
turbed landscape [14] covering approximately one-third of the basin.
Water 2022, 14, 2887 4 of 22

for periods of between 2 and 40 years per station, from which annual maxima can be
determined. Locations of the nine gauging stations in the Wainganga basin (Figure 1b)
were obtained, and HydroSHEDS terrain elevation data (outlined in Section 2.3) was used
with GIS software to determine the upstream catchment boundary.
Within the Godavari and Krishna basins, 122 river discharge stations (including the 9
in the Wainganga basin) were identified as suitable to determine appropriate distributions
to develop flood-frequency relationships from the AMAX series. Stations were considered
suitable if they had less than 10% missing data during the monsoon season over their
period of record. It is noted that some stations only operated around the monsoon season,
not continuously over the whole year.

2.3. Elevation and Flow Direction Data

The HydroSHEDS [18] and HydroBASINS [19] datasets consist of “hydrologically
corrected” elevation data on a 3 arcsecond resolution (approximately 90 m at the equator),
along with flow direction and accumulation data on a 15 arcsecond resolution. These
products rely mostly on Shuttle Radar Topography Missions outputs and topographic
maps. Hydrological conditioning includes several procedures that force the correct river
network topology into the DEM [20] (pp. 10–13). This dataset was used to determine
the shape and size of the watersheds that drain into the gauging stations, and from this,
which cells in the gridded meteorological datasets (Section 2.4) related, fully or partly,
to each Wainganga sub-catchment. The DEM was also used to further characterize the
sub-catchments in terms of area, average slope and average elevation.
Water bodies were obtained from HydroLAKES [21], which includes all water bod-
ies of area 105 m2 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], gen-
erated 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 × 108 m3 and a
reservoir area of 222 km2 [15].

2.4. Meteorological Data

The production of a simulated flow record for each sub-catchment required rainfall
and evapotranspiration records as input data to the hydrological model. Rainfall data were
derived from a gridded IMD dataset [25], providing daily rainfall totals for all of India
over the period 1901–2015 at 0.25◦ spatial resolution. The Climate Hazards Group InfraRed
Precipitation with Station data (CHIRPS) dataset, version 2.0 [26], was considered as an
alternative to the IMD dataset due to its higher spatial resolution (0.05◦ ) and augmentation
of rain gauge data with satellite data. It was initially assumed that both of these advantages
would allow CHIRPS to detect higher-intensity rainfall features. However, a comparison of
1-day annual maxima from both datasets over their common period of 1981–2015 shows
that IMD normally records the larger 1-day maximum, even though CHIRPS records the
larger annual total. For this reason, IMD was preferred over CHIRPS. Average annual
rainfall (1981–2017) in all study sub-catchments is very similar (minimum = 1264 mm,
maximum = 1391 mm).
Evaporation data were derived from the GLEAM dataset, version 3.3a [27,28], at daily
temporal and 0.25◦ spatial resolution for the period 1980–2018. Potential evaporation for
bare soil, short canopy and tall canopy were estimated using observations of surface net
radiation and near-surface air temperature with the Priestley–Taylor equation. This was
converted to actual evaporation through observations of microwave vegetation optical
depth and estimated root-zone soil moisture, via water balance. GLEAM data are modeled
estimates, not observed.
Water 2022, 14, 2887 5 of 22

2.5. Land Cover Data

Land use and land cover data were obtained from the Harmonized World Soil
Database, version 1.21 [29]. This divides the world into grid cells of (1/12)◦ resolution
and assigns one of seven categories to each grid cell: rain-fed cultivated land, irrigated
cultivated land, forest land, grass/scrub/woodland, built-up land, barren/very sparsely
vegetated land and water body. Table 1 provides broad, statistical information on the nine
gauging stations and their upstream catchments. DPLBAR (mean drainage path length)
and DPSBAR (mean drainage path slope) are equivalent to the FEH catchment descriptors
of the same name [30], derived from HydroSHEDS river network data. CULT, URB and
FOR express the fraction of each sub-catchment belonging to the HWSD Land Use and
Land Cover categories of the same names, indicating “total cultivated land”, “built-up
land” and “forest land”, respectively.

Table 1. Sub-catchments of the Wainganga considered in this study.

DPLBAR DPSBAR CULT URB FOR

Name Start Year End Year Area (km2 )
(km) (m/km) (-) (-) (-)
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
Note(s): DPLBAR = mean drainage path length, DPSBAR = mean drainage path slope, CULT = total cultivated
land fraction, URB = built-up land fraction, FOR = forested land fraction.

2.6. Statistical Flood Frequency Estimation

To compare observed and modeled flood frequency, AMAX series are extracted from
the observed flow and modeled flow, and flood frequency curves (FFC) are plotted for both,
using the same distribution. Therefore, an appropriate distribution for the AMAX must
be selected.
To determine an appropriate distribution, a Hosking–Wallis test was performed using
the L-moment ratios and the ZDIST statistic [31,32] on the whole dataset using the lmomRFA
package from R [33,34].
For each catchment, the ZDIST statistic was calculated as:

ZDIST = [(τ4 − τ4 DIST ) − B4 ]/σ4 (1)

where τ4 is the sample L-kurtosis, τ4 DIST is the expected L-kurtosis under the chosen
distribution, derived as a function of the sample L-skew, B4 is a bias correction term, the
sample mean of a set of simulated copies of (τ4 − τ4 DIST ), and σ4 is the sample standard
deviation of the copies. Any distribution with a value of |ZDIST | < 1.64 was deemed to be
potentially acceptable for that station. The distribution with the smallest value of |ZDIST |
was also recorded, this being referred to as the “chosen” distribution for that station.

2.7. Hydrological Model

In this study, catchment runoff was modeled using the PDM (Probability Distributed
Model) [35]. This is a lumped, conceptual rainfall-runoff model with three storage elements
representing soil (Pareto distribution), surface storage (linear reservoir) and groundwater
storage (cubic reservoir), respectively. The soil store is fed by rainfall and depleted by evap-
otranspiration, recharge and saturation-excess runoff. Recharge is fed into the groundwater
store, saturation-excess runoff is fed into the surface store. Outflows from the groundwater
and surface stores combined give the catchment outflow.
Water 2022, 14, 2887 6 of 22

Initially, each of the nine sub-catchments of the Wainganga basin was modeled in
a lumped configuration. This means that each catchment included all upstream sub-
catchments. For example, lumped modeling of the catchment to Ashti included the entire
upstream area, enclosing the other eight gauging stations. However, the upstream stations
were effectively ignored, as their data were not used in calibration or validation (initially).
After lumped modeling, semi-lumped configurations of non-overlapping sub-catchments
with flow at each upstream gauge translated to the next downstream gauge using kinematic
wave (KW) routing were produced for Ashti, Pauni and Satrapur. KW routing has one
parameter, the wave speed, c. When a river channel is divided into segments, the wave
speed controls how much water moves from one segment to the next during one time
step. Semi-lumped in this context means that each sub-catchment PDM and channel was
modeled using the same parameters.
Lumped, semi-lumped and semi-distributed modeling each have their own advan-
tages and disadvantages. Lumped modeling of one catchment benefits from being able
to use the entire period for which precipitation, evapotranspiration and verification data
are available at one station, while semi-lumped and semi-distributed modeling can only
use the period for which these data are available simultaneously at all stations. However,
lumped modeling cannot account for spatial differences in precipitation across a catchment:
an intense rainfall event near the gauging station could reasonably be expected to generate
a more rapid rise and fall in gauged flow than one in the headwaters. Lumped modeling
can only account for very different soil and land-use types conceptually, through the use
of parallel stores, each of which the model stipulates must necessarily receive the same
rainfall depth per timestep. Semi-lumped modeling can account for spatial rainfall varia-
tions, but not different catchment properties, as the same PDM parameters are used for all
sub-catchments. Semi-distributed models can account for spatial variations in rainfall, soils
and land use, but require different parameter values for each sub-catchment, making them
very difficult to parameterize. Linking parameter values to measurable sub-catchment
properties can simplify calibration greatly, as each model parameter at each sub-catchment
becomes expressible as an equation with a single set of optimized coefficients applicable to
every sub-catchment. However, measurable properties cannot explain all of the variance in
parameter values, so parameter values calculated in this way are never optimal, even if
they may be acceptable.

2.8. Model Calibration and Validation

In all cases, PDM parameter values were optimized to maximize the modified KGE
(Kling-Gupta Efficiency) [36] of the simulated river flow relative to that observed, in units
of mm/day. Modified KGE is a performance metric that compares two time-series in terms
of three components:

KGE’ = 1 − [(r − 1)2 + (β − 1)2 + (γ − 1)2 ] /2

1
(2)

β = µs /µo (3)
γ = (σs /µs )/(σo / µo ) (4)
where KGE’ is the modified KGE statistic, r is the Pearson correlation coefficient, β is the
bias ratio and γ is the variability ratio (all dimensionless). Subscripts s and o indicate
simulated and observed values, respectively. Note that KGE’ values range from −∞ to 1
and values closer to one show better performance. Throughout this study, the first three
years of simulated river flow were discarded and KGE’ was maximized on the remaining
paired simulated and observed data points. Throughout this study, optimal parameter sets
were found using a shuffled complex evolution algorithm [37,38].
Typically, a continuous simulation model is desired to be equally accurate across the
whole range of modeled flows, and both the objective function and range of data used
for calibration reflect this. Within Sections 3.2 and 3.5, the full time-series at each station
(excluding the first three years) was used to calibrate the PDM through maximization of
Water 2022, 14, 2887 7 of 22

KGE’ at each station separately. Section 3.5 imposed the constraint that only a single value
for each parameter can be fitted to all stations; this value was found through optimization
of the mean KGE’ across all stations. In Section 3.6, semi-lumped models were produced
for the three non-headwater catchments, and the PDM and kinematic wave speed were
optimized to maximize KGE’ between the full observed and simulated time-series at the
outlet (excluding the first three years).
If certain flows are considered more important than others, these can be weighted
more highly in the objective function, and less important flows can be ignored. As the
purpose of these models is to improve estimation of annual maximum flows, an objective
function maximizing KGE’ on only the annual maximum flow series was tested for its
ability to recreate the observed flood frequency curve for each station (Section 3.3). This was
tested against conventional (e.g., Section 3.2) calibration in a split-sample test in Section 3.4.
The CWC’s flood frequency estimation procedure for the Lower Godavari sub-zone [5],
which includes the Wainganga basin, is broadly applicable to catchments up to 1000 km2 .
Since the smallest sub-catchment in this study measures 1755 km2 , and most are over
5000 km2 , 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.
Figure 2 depicts the study methodology, including catchment delineation, data prepa-
Water 2022, 14, x FOR PEER REVIEWration, river flow model frameworks, optimization functions, preparation of gauged 8verifi- of 23
cation data and development of flood frequency estimates.

Figure 2.
Figure 2. Study
Study methodological
methodological diagram.
diagram.

3. Results and Discussion

3.1. Distribution Choice
Figure 3 shows the chosen distribution at each of the gauging stations in the dataset,
and Table 2 shows total stations at which each distribution was acceptable and chosen.
 Water 2022, 14, 2887 8 of 22

3. Results and Discussion

3.1. Distribution Choice
Figure 3 shows the chosen distribution at each of the gauging stations in the dataset,
and Table 2 shows total stations at which each distribution was acceptable and chosen.
Although the Generalized Pareto (GPA) is most often the best distribution, the Pearson
Type III (PE3) is the most frequently acceptable. No obvious spatial correlation to the
choice of distribution is visible; these patterns do not match the major river channels or
major topographical features. Within the Wainganga basin, the GPA distribution was
acceptable at all nine stations and the PE3 distribution was acceptable at seven. However,
only two chose PE3 as the best distribution, and another two chose GPA. Generalized
Logistic (GLO) and Generalized Extreme Value (GEV) were also chosen by four and one
Wainganga stations, respectively.

Table 2. Number of stations at which each distribution is acceptable (|ZDIST | < 1.64) and chosen
(|ZDIST | = min(|ZDIST |)) to describe the annual maximum (AMAX) series.

Distribution GLO GEV GNO PE3 GPA

22, 14, x FOR PEER REVIEW Accepted 67 91 95 1019 of 23 92
Chosen 17 17 12 29 47

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

Theoretically, under certain assumptions, all block maxima series, such as the series
of annual maximum river flows, follow the Generalized Extreme Value Distribution
(GEV). However, this and other studies into the optimal choice of distribution in regions
of India have recommended the use of other distributions. The acceptability of the GPA
Water 2022, 14, 2887 9 of 22

Theoretically, under certain assumptions, all block maxima series, such as the series of
annual maximum river flows, follow the Generalized Extreme Value Distribution (GEV).
However, this and other studies into the optimal choice of distribution in regions of India
have recommended the use of other distributions. The acceptability of the GPA distribution
for AMAX flows is variously supported [39,40] and contradicted [41–43] by previous
studies on much smaller datasets of 4 to 18 Indian stations.
In Kerala, south-west India, the Chi-square test, ranking of statistical indicators and
the L-moment ratio diagram highlighted the Generalized Pareto (GPA) and Generalized
Logistic (GLO) distributions for at-site analyses [39]. In the Tel basin in the Mahandi river
system in east India, Guru and Jha [40] considered four stations and, via Kolmogorov–
Smirnov tests, found the GPA to fit best to annual maxima data and the Generalized
Log-Normal (GLN) to fit best to peak-over-threshold data. However, Swetapadma and
Ojha [41], also studying the Mahanadi river system, selected the GEV distribution as the
best-fitting to AMAX data at 18 stations. The Lower Godavari sub-zone was investigated
using artificial neural network methods [42], and the Pearson Type III (PE3) highlighted
through Hosking–Wallis tests as an appropriate distribution. In the Middle Ganga Plains
in India, Kumar et al. [43] used Hosking–Wallis tests to first identify eight (of eleven) sites
Water 2022, 14, x FOR PEER REVIEW 10 of 23
as one homogeneous region, then selected the GEV distribution for that region.
In Figure 4, two examples are shown to discuss features of the Generalized Pareto and
Pearson Type III distributions and how well they fit in different areas of the study region.
region.
The GumbelThereduced
Gumbel variate
reducedisvariate
used toisbetter
used to better distinguish
distinguish the empirical
the empirical return at
return periods pe-
riods
the lowerat the
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Figure
Figure 4. 4. Growth
Growth curves
curves associated
associated to Wadakbal
to (left) (left) Wadakbal
gauginggauging station
station on onRiver,
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QMED m3/s, =
QMED
= 581
581 m 3/s, and (right) Pathagudem gauging station on the Indravathi River, QMED 3= 10,045 m3/s.
and (right) Pathagudem gauging station on the Indravathi River, QMED = 10,045 m /s. Gray ×
Gray × indicate
symbols symbolsranked
indicategauged
rankedAMAX
gaugedflowsAMAX flows
at each at each station.
station.

Firstly,
Firstly, Wadakbal
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fall of 1053 mm, and consists primarily (73%) of cultivated,
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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 estima-
tion up to the 1-in-25-year flood, but does not capture the behavior of tails as well. There-
fore, this paper uses the GPA distribution, since it was accepted by all the Wainganga
Water 2022, 14, 2887 10 of 22

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

Table 3 presents modified Kling-Gupta efficiency (KGE’), its decomposed components
and the Nash–Sutcliffe Efficiency (NSE) for each station. The theoretical best value for each
of KGE’, r, γ, β and NSE is 1.

Table 3. Performance metrics (lumped sub-catchment modeling).

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

The results here show that the PDM is in general appropriate for lumped sub-catchment
modeling of the Wainganga basin, with a mean KGE’ of 0.612 across all nine stations. This
extends existing confidence in continuous simulation modeling, which has generally fo-
cused on much smaller catchments [44–46]. The overall KGE’ values observed for these
catchments depend most strongly on the Pearson product-moment correlation between
observed and modeled flows as there is almost no volumetric bias for any catchment, and
the reported values for the coefficient of variation component of the KGE’ show that the
PDM only slightly underestimates flow variability in most cases. NSE values are generally
much lower than KGE’ values, although NSE at Ashti is favorable in comparison to a recent
study using the SWAT model [47]. Low or negative NSE values may indicate that observed
flows are relatively stable, not that modeled flows are particularly poor [48]. However, the
standard deviations of observed flows at the three stations with the lowest NSE values are
all over 4 mm/day, compared with 2.5 mm/day at Pauni. At Kumhari and Ramakona, the
means and standard deviations of the modeled flows were also similar to those observed,
although at Wairagarh, they were underestimated. Wairagarh is also the catchment with
the highest mean and standard deviation of observed flows (2.6 and 7.1 mm/day).
Despite the performance in KGE’ ranging from reasonable (0.333) to good (0.880), the
calibration metric does not focus strongly on annual maximum flows. This is summarized
in Figure 5, which shows very strong correlations between modeled and observed QMED,
l1 and l2 (first two L-moments), but it has an obvious mild bias, particularly with less
variability (l2 ) 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.
Water 2022,14,
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Figure5.5.Modeled
Figure Modeledvsvsobserved
observedQMED,
QMED,l1l1(sample
(sampleL-mean),
L-mean),l2l2(sample
(sampleL-CV)
L-CV)and
andt3t3(sample
(sampleL-SKEW)
L-SKEW)
fornine
for nineWainganga
Waingangastation
stationAMAX
AMAXrecords.
records.

Thisisislikely
This likely due
due to a number
number of offactors.
factors.Firstly,
Firstly,if ifthethegauged
gauged flows
flowsareare
poor or un-
poor or
certain representations
uncertain representations of reality, thenthen
of reality, the model
the modelmay mayneed need to implement extreme
to implement param-
extreme
eterizations to produce
parameterizations modeled
to produce flows flows
modeled that closely match match
that closely the poor theorpoor
uncertain gauged
or uncertain
flows. Secondly,
gauged poor-quality
flows. Secondly, input datasets
poor-quality may mean
input datasets may that
meanthe model
that thehas to apply
model ex-
has to
treme transformations to the input rainfall and/or evapotranspiration
apply extreme transformations to the input rainfall and/or evapotranspiration to produce to produce a mod-
aeled runoffrunoff
modeled similarsimilar
to the gauged runoff. Thirdly,
to the gauged lumped modeling
runoff. Thirdly, aggregates
lumped modeling all rainfall
aggregates
and
all evapotranspiration
rainfall spatially, meaning
and evapotranspiration spatially, that an intense
meaning that an cloudburst near the catchment
intense cloudburst near the
catchment outlet isin
outlet is modeled modeled
the same inway
the same
as oneway as one over
occurring occurring over the headwaters,
the headwaters, even though even
the
though the travel
travel time to thetime to thestation,
gauging gaugingand station, and the of
the amount amount of attenuation
attenuation occurring occurring
on the wayon
the wayisthere,
there, very is very different
different in bothincases.
both cases.
However, However, hydrological
hydrological models models can attenuate
can attenuate input
input rainfall by a greater or lesser amount through parameterization,
rainfall by a greater or lesser amount through parameterization, and both lumped and and both lumped
and semi-distributed
semi-distributed modeled
modeled runoff
runoff cancan be equally
be equally accurate
accurate [49,50].
[49,50]. Fourthly,
Fourthly, if certain
if certain hy-
hydrological processesare
drological processes areabsent
absentfrom
from thethe conceptual model structure, structure, then
thenthe
theprocesses
processes
that
thatare
arepresent
presentwillwilltry
trytotocompensate,
compensate,but butthey
theymay maytaketakeextreme
extremeparameterizations
parameterizationstoto
dodoso.
so.One
Onephysically
physicallyplausible
plausiblebut butunmodeled
unmodeledprocess processin inthe
theWainganga
Waingangabasin basinmay maybe be
reservoir storage, which could manifest in the model parameterization
reservoir storage, which could manifest in the model parameterization as an increased soil as an increased
soil storage
storage capacity.
capacity. Indeed,
Indeed, cmax,cmax
the, maximum
the maximum soil storage
soil storage capacity,
capacity, takestakes
a valuea value of
of 5900
5900
mm in Rajoli and 2500 mm in Satrapur, while the lowest value it takes is 800 mminin
mm in Rajoli and 2500 mm in Satrapur, while the lowest value it takes is 800 mm
Wairagarh.
Wairagarh.FormalFormalquantification
quantificationofofreservoir
reservoireffects
effectsisiscomplicated,
complicated,asasthe theinteraction
interactionofof
each
eachreservoir
reservoirand andcatchment
catchmentisisuniqueuniqueininIndiaIndia[51].
[51].Finally,
Finally,equifinality
equifinality(multiple
(multipleways ways
totoachieve same answer) may mean that the same KGE’
achieve the same answer) may mean that the same KGE’ can be achievedby
the can be achieved bymore
morethan
than
one parameter set. Equifinality and unrepresented processes are linked, as there are two
Water 2022, 14, 2887 12 of 22
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one parameter set. Equifinality and unrepresented processes are linked, as there are two
flow paths
flowpaths out
pathsout ofofthe
outof PDM,
PDM,aaanominally
thePDM, nominally “fast”
nominally“fast”
“fast”andand
andaaanominally
nominally “slow”
nominally“slow” response.
“slow”response.
response.The The fast
Thefast
fast
flow the
response
response made
made upup the
the vast
vast majority
majority ofofflow
flow ininall
all nine
nine catchment
catchment models—neither
models—neither Kum-
Kum-
response made up the vast majority of flow in all nine catchment models—neither Kumhari
hari
harinor
norRajegaon
Rajegaon produced
produced any
anymodeled
modeled slow
slowflow, and
flow,theand the
themodel
model producing
producing the
themost
most
nor Rajegaon produced any modeled slow flow, and model producing the most was
was
was Salebardi,
Salebardi, atat14.3%
14.3% ofofthe
the total
total flow.
flow. However,
However, the
the seven
seven models
models that
that did
did produce
produce
Salebardi, at 14.3% of the total flow. However, the seven models that did produce slow
slow flow
slowall
flow all
allproduced
produced ititsimilarly:
similarly: drier
drieryears
years had no slow flow,
flow,while ininwetter years,
flow produced it similarly: drier years had nohadslownoflow,
slowwhile while
in wetter wetter years,
years, slow
slow
slow flow
flow increased
increased asasthe
the wet
wet season
season progressed,
progressed, and
and as
as aafraction
fraction
flow increased as the wet season progressed, and as a fraction of individually high peak of
ofindividually
individually high
high
peak
peak flows.
flows. AsAs a aresult,
result, nominally
nominally slow
slow flow
flow contributed
contributed aaconsiderable
considerable
flows. As a result, nominally slow flow contributed a considerable portion to the largest portion
portion to
to the
the
largest
largest AMAX
AMAX flows
flows in
inSatrapur,
Satrapur, Pauni
Pauni and
and Rajoli.
Rajoli. As
As there
there were
were
AMAX flows in Satrapur, Pauni and Rajoli. As there were no modeled dry-season flows for no
nomodeled
modeled dry-season
dry-season
flows
flows
any for
forany
anycatchment,
catchment, catchment,
no flow path nonoflow
flowpath
modeledpath amodeled
modeledaabaseflow-type
baseflow-type baseflow-type flow,
flow, but bothflow, but
flow both
bothflow
butpaths flowpaths
could paths
and
could
could
did and did contribute
and didtocontribute
contribute peak flows to peak flows
to(Figure
peak flows (Figure
6). (Figure 6). 6).

Figure 6.6.Modeled
Figure6.
Figure Modeled total
Modeledtotal flow
totalflow and
flowand slow
andslow flow
slowflow for
flowfor Pauni,
forPauni, May–December
Pauni,May–December 1994.
May–December1994.
1994.

Reduced
Reduced variability
Reducedvariability ininthe
variabilityin the modeled
themodeled flows
modeledflows can
flowscan also
canalso be
alsobe seen
beseen ininthe
seenin the FFC
theFFC produced
FFCproduced by
producedby
by
fitting
fittingaaaGeneralized
fitting GeneralizedPareto
Generalized Paretodistribution
Pareto distributionto
distribution totothe
theobserved
the observedand
observed andmodeled
and modeledAMAX.
modeled AMAX.Examples
AMAX. Examples
Examples
are
arereproduced
are reproducedfor
reproduced forAshti
for Ashti(KGE’
Ashti (KGE’===0.880)
(KGE’ 0.880)and
0.880) andRamakona
and Ramakona(KGE’
Ramakona (KGE’===0.333)
(KGE’ 0.333)in
0.333) ininFigure
Figure7.
Figure 7.7.

Figure
Figure 7.7.Observed
Figure7. Observed and
Observedand modeled
andmodeled flood
modeledflood frequency
floodfrequency curves
frequencycurves for
curvesfor Ashti
forAshti and
Ashtiand Ramakona.
Ramakona.
and Ramakona.

The
Themodeled
The modeledAMAX
modeled AMAXand
AMAX andGeneralized
and GeneralizedPareto
Generalized ParetoFFC
Pareto FFCat
FFC atatAshti
Ashtiis
Ashti isisclearly
clearlyshow
clearly showreasonably
show reasonably
reasonably
low
low errors
errors for
for floods
floods with
with 25–100-year
25–100-year return
return periods.
periods. This
This ability
ability to
to generate
generate
low errors for floods with 25–100-year return periods. This ability to generate a viable aa viable
viable FFC
FFC
FFC
from continuous simulation is similar to that reported in a much smaller (8.41 km 22) urban
from continuous simulation is similar to that reported in a much smaller
from continuous simulation is similar to that reported in a much smaller (8.41 km ) urban (8.41 km )
2 urban
Australian
Australiancatchment
Australian catchment[45].
catchment [45].However,
[45]. However,AMAXs
However, AMAXsat
AMAXs atatAshti
Ashtiare
Ashti areconsistently
are consistentlyunderestimated
consistently underestimatedat
underestimated atat
shorter
shorterreturn
returnperiods.
periods.This
Thisconsistent
consistentunderperformance
underperformanceininmodelingmodelingAMAX AMAXmagnitude
magnitude
Water 2022, 14, 2887 13 of 22

shorter return periods. This consistent underperformance in modeling AMAX magnitude

is perhaps unsurprising, as the KGE’ performance metric focuses on the whole flow hydro-
graph, 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 km2 [46].

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

In this test, KGE’ was maximized only between pairs of observed and modeled AMAX,
in order to attempt to match better the values of interest for flood frequency estimation. A
recent study [52] assessed nine different objective functions to better reproduce extremes;
however, none of these applied higher weights to more relevant observations. Addition-
ally, previous work [53] has considered bias correction to improve FFC derived through
continuous simulation, and also used the fit between the observed and simulated FFC to
calibrate the bias correction. However, maximization of KGE’ directly and exclusively on
AMAX pairs could reduce or eliminate the need for FFC corrections.
Performance according to the KGE’ metric, its components and NSE, all computed on
the full flow time-series (excluding years pre-1983), is shown in Table 4. Model configu-
rations that are not optimized on the full time-series will not necessarily perform well on
the full time-series. However, performance was particularly poor at Rajoli, with severely
underestimated variability and overestimated total flow. Satrapur is the opposite: total
flow was underestimated and variability was overestimated. For Wairagarh, bias and
variability ratios were both close to the optimum, but correlation between values was not
very high. Performance at Ashti and Pauni was arguably still good (in both cases, KGE’ ≈
0.65, although γ and β were not very close to 1).

Table 4. Performance metrics (lumped sub-catchment modeling, optimizing performance on

AMAX only).

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

For comparison, the flood frequency curves generated for Ashti and Ramakona during
this test are presented in Figure 8. Notably, the modeled and observed FFC for Ashti are
near-identical, with the only major difference being for the second-largest AMAX. Despite
the reduction in KGE’ from 0.330 to 0.160, the modeled AMAX at Ramakona are improved
for events rarer than QMED. However, they are still largely unsuitable.
Water 2022,14,
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23

Figure8.8.Observed
Figure Observedand
andmodeled
modeledflood
floodfrequency
frequencycurves
curvesfor
forAshti
Ashtiand
andRamakona
Ramakona(PDM
(PDMoptimized
optimized
for AMAX only).
for AMAX only).

3.4.
3.4.Lumped
LumpedSub-Catchment
Sub-CatchmentModeling
Modelingwith
withaaCalibration/Validation
Calibration/ValidationPeriod
Period
Considering
Consideringthat that the
the PDM
PDM is intended for
is intended for continuous
continuoussimulation
simulationof ofaacatchment,
catchment,ititis
issuspected
suspectedthat
thataaPDMPDMoptimized
optimized forfor something
something other
other than
than continuous
continuous simulation
simulation maymay
behave unpredictably when presented with new data. On the other
behave unpredictably when presented with new data. On the other hand, a PDM that hand, a PDM that
models
modelscontinuous
continuoussimulation
simulation reasonably
reasonablywellwell
should behave
should predictably
behave when when
predictably presented
pre-
with new data. If that predictability means that AMAX are underestimated,
sented with new data. If that predictability means that AMAX are underestimated, then they might
then
be underestimated
they consistently,consistently,
might be underestimated potentially allowing theallowing
potentially development of post-processing
the development of post-
rules to correct them. This cannot be guaranteed with a model that
processing rules to correct them. This cannot be guaranteed with a model that ignores the catchment
ignores the
processes
catchmentonprocesses
every day on of the year
every day ofexcept one,except
the year but it one,
can bebutinvestigated by dividing
it can be investigated by
gauged flow records into calibration and validation periods, using
dividing gauged flow records into calibration and validation periods, using the the AMAX objective
AMAX
function
objectivetofunction
calibrate tothe modelthe
calibrate and the calibrated
model parameters
and the calibrated to estimate
parameters AMAX during
to estimate AMAX
the validation period.
during the validation period.
The gauged flow record for Ashti was divided into two parts, consisting of the final
The gauged flow record for Ashti was divided into two parts, consisting of the final
10 complete years and the 26 years preceding them. The model parameters were fitted
10 complete years and the 26 years preceding them. The model parameters were fitted to
to minimize the error in estimated AMAX for years 1983–2006, ignoring three years for
minimize the error in estimated AMAX for years 1983–2006, ignoring three years for spin-
spin-up, then the calibrated model was applied to the whole record to estimate the final
up, then the calibrated model was applied to the whole record to estimate the final 10
10 AMAX. The observed and AMAX-calibrated (AC) modeled AMAX series for Ashti are
AMAX. The observed and AMAX-calibrated (AC) modeled AMAX series for Ashti are
plotted in Figure 9, alongside the full-flow-regime-calibrated modeled AMAX series (RC).
plotted in Figure 9, alongside the full-flow-regime-calibrated modeled AMAX series (RC).
RC uses the parameters determined in Section 3.3.
RC uses the parameters determined in Section 3.3.
Qualitatively, the AC modeled AMAX are more closely matched during the calibration
period than the validation period. However, it is a common for the performance of any
model to decrease between calibration and validation periods. In fact, for AC, correlation
between modeled and observed AMAX was 0.921 for the calibration period and 0.553 for
the validation period, whereas the respective figures were 0.831 and 0.526 for RC. This
indicates that the lower predictive performance of the AC model for the last 10 years is
mainly due to other factors not related to its ability to predict AMAX when it is applied
outside its calibration period.

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).
 10 complete years and the 26 years preceding them. The model parameters
minimize the error in estimated AMAX for years 1983–2006, ignoring three y
up, then the calibrated model was applied to the whole record to estimat
AMAX. The observed and AMAX-calibrated (AC) modeled AMAX series
Water 2022, 14, 2887 plotted in Figure 9, alongside the full-flow-regime-calibrated modeled
15 of 22 AMA

RC uses the parameters determined in Section 3.3.

Figure 9. Observed (red line) and modeled AMAX series for Ashti when PDM is optimized to match
Figure 9. Observed (red line) and modeled AMAX series for Ashti when PDM is opti
AMAX from 1983–2006 inclusive (blue line) and optimized to match the whole flow regime from
AMAX from 1983–2006 inclusive (blue line) and optimized to match the whole flo
1983–2006 inclusive (yellow line).
1983–2006 inclusive (yellow line).
These results suggest that it might be possible to use a PDM calibrated only to AMAX
data to estimate AMAX outside of the calibration period, although this model will not be
suitable for other purposes: the KGE’ of the AC model on the full flow series was just 0.458
for the calibration period and 0.388 for the validation period.

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

In this test, optimization was performed on each lumped sub-catchment with the
constraint that all nine sub-catchments must use the same parameter values. This gives
guidance on how well a semi-lumped model (non-overlapping catchments with identical
PDM parameterization), linked via kinematic wave routing (with identical wave speeds),
might perform, without the extra work involved in setting up a KW routing scheme and
network topology, and (if successful) greatly simplifies parameterization of the PDM for
ungauged sub-basins of the Wainganga. The optimization was set to maximize mean KGE’
per catchment, with each catchment weighted equally. All monitored runoff time-series
were trimmed to the longest possible common period: 18 July 1992 to 28 December 2014.
While this trimming was not strictly necessary here, it is necessary for semi-lumped and
semi-distributed modeling cases where flow is optimized at all gauging stations (note that
the purpose of this model run is to evaluate the validity of continuing towards semi-lumped
modeling). The flow was modeled over the full 1980–2015 period, hence allowing just over
12.5 years for spin-up. Because of this long spin-up, KGE’ was maximized over the full
common period of gauged record.
Table 5 presents the performance metrics achieved for each catchment separately when
modeling runoff with the optimized single parameter set over the period 1980–2015. In
each case, the performance reported in Table 5 compares simulated and observed flows
over the available flow data in the years 1983 to 2015 (as in Tables 3 and 4).
Water 2022, 14, 2887 16 of 22

Table 5. Performance metrics (lumped sub-catchment modeling, single parameter set).

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

Use of a single parameter set gave poorer model performance, with a mean KGE’ of
0.415 across all nine stations. Among individual catchments, Ashti and Pauni were the
best modeled, as for all other variants of lumped modeling. As all sub-catchments were
weighted equally, it is implied that the calibration data in these two are more accurate—as
the largest catchments, they are the least mountainous proportionally. It may also be
implied that the PDM more accurately represents the dominant flow processes for these
two catchments. In contrast to the initial case, where parameter values were optimized
individually for each catchment, values of the KGE’ components γ (variation) and β (bias)
can vary wildly. The two catchments that performed most weakly with the single parameter
set, Rajoli and Satrapur, were also those where the modeled flow total was far above the
observed flow total (β is the highest). Rajoli was also the catchment with the lowest value of
γ. These contributed to its low KGE’ value of just 0.001, despite the relatively high Pearson
product-moment correlation coefficient of 0.612.

3.6. Semi-Lumped Modeling

Here, three separate semi-lumped models were considered: the Wainganga to Ashti,
divided into nine non-overlapping sub-catchments, the Wainganga to Pauni, divided into
five non-overlapping sub-catchments, and the Wainganga to Satrapur, divided into two
non-overlapping sub-catchments (above and below the Ramakona gauging station). The
other six sub-catchments are headwaters, so semi-lumped modeling was not possible
(Figure 1b). In semi-lumped modeling, each sub-catchment was modeled using a PDM and
routing was performed using a kinematic wave. The same PDM parameter set and wave
speed was fitted to each sub-catchment and river reach within one model; however, values
of each parameter differed between the three models.
Table 6 presents the performance metrics achieved when modeling each catchment in
a semi-lumped configuration. In each case, only the period 18 July 1992 to 28 December
2014 is considered. Because the model run starts in 1980, there were 12.5 years spin-up.
Given that only the flow at one gauge was used for each optimization in this configuration,
KGE”, the value of KGE’ evaluated over the period 1983–2015 (1984–2015 for Satrapur),
is also presented. This has the effect of evaluating the model on data from outside the
calibration period.

Table 6. Performance metrics (semi-lumped modeling, single parameter set).

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

Relative to lumped modeling, KGE’ was slightly worse for Ashti, and slightly better
for Pauni and Satrapur, although it should be noted that the available data periods differ
for lumped and semi-lumped modeling. This supports, to some extent, two previous
Water 2022, 14, 2887 17 of 22

studies comparing the lumped GR5J [54] and semi-distributed GRSD [55]—essentially a
number of GR5J units connected by linear-lag propagation models—which found that semi-
distributed modeling offered no advantage over lumped modeling, either in terms of KGE’
statistic or parameter identification [49,50]. It also partly supports another study, using a
simplified PDM [56], which found that semi-lumped modeling resulted in a small decrease
to Nash–Sutcliffe Efficiency (NSE) relative to lumped modeling when no model parameters
were fixed initially. KGE” shows that the parameters derived through calibration to a
shorter record (1992–2014) are also applicable to a longer one (1983–2015). For all three
catchments, both γ and β were near 1, indicating near-zero bias in the mean and variability
of the modeled flow.
The fitting of one PDM parameter set and wave speed to all sub-catchments within one
model is sub-optimal. However, including this significant constraint to the optimization
only translated into a small decrease in performance, suggesting that it may be worthwhile
to attempt semi-distributed modeling. This would require fitting 89, 49 or 19 parameters,
for Ashti, Pauni or Satrapur, respectively, versus 10 in all cases for semi-lumped modeling.
Regionalization relationships to estimate parameter values could greatly reduce the number
Water 2022, 14, x FOR PEER REVIEW 18 of 23
of parameters that require fitting, potentially to zero in the case where all parameters
are estimated by regionalization (e.g., [57]). Sufficient regionalization would also allow
the catchment to be sub-divided at places other than gauging stations. However, [56]
However,
found [56] found
poor model poor model
performance at theperformance at the internal
internal sub-divisions sub-divisions
of semi-lumped of semi-
catchments
lumped catchments
parameterized through parameterized
regionalization through regionalization
relationships, even whenrelationships,
performance even when
at the per-
outlet
formance at the outlet was high. Furthermore, in this study, only nine
was high. Furthermore, in this study, only nine sub-catchments are gauged, giving very sub-catchments are
gauged, giving very limited data to develop regionalization relationships,
limited data to develop regionalization relationships, while flows that are not at gauging while flows
that arecannot
stations not at gauging
be verified.stations cannot be verified.
Figure 10 shows the
Figure 10 shows the flood floodfrequency
frequencycurves
curvesfor forAshti
Ashtiand
andSatrapur
Satrapurderived
derivedthrough
through
semi-lumpedmodeling.
semi-lumped modeling.Pauni Pauniisisnot
notshown
shownbutbutisismidway
midwaybetween
betweenAshti
Ashtiand
andSatrapur.
Satrapur.
Despiteits
Despite itsvery
verystrong
strongKGE’KGE’value,
value,the
themodeled
modeledand andobserved
observedFFC FFCatatAshti
Ashtidiffer.
differ.Con-
Con-
versely,the
versely, themodeled
modeledand andobserved
observedFFC FFCatatSatrapur
Satrapurare aresimilar,
similar,despite
despitethe
thelower
lowerKGE’.
KGE’.
Figure11
Figure 11shows
showsthat thatthe
thestrong
strongperformance
performanceofofthetheFFCFFCatatSatrapur
Satrapurpartly
partlyarose
arosefrom
fromthethe
fact that the fit of the FFC was not forced by trying to match observed and
fact that the fit of the FFC was not forced by trying to match observed and modeled AMAX modeled AMAX
ininaagiven
givenyear,
year,unlike
unlikethe theKGE’,
KGE’,which
whichlooks
looksatatthe
theordered
orderedtime-series.
time-series.

Figure10.
Figure 10.Observed
Observedandand modeled
modeled floodflood frequency
frequency curves
curves for Ashtifor
andAshti and(semi-lumped
Satrapur Satrapur (semi-lumped
modeling).
modeling).
Water 2022, 14, 2887 18 of 22
Water 2022, 14, x FOR PEER REVIEW 19 of 23

Figure11.
Figure 11.Observed
Observedandand modeled
modeled AMAX
AMAX seriesseries for Pauni
for Ashti, Ashti,and
Pauni and Satrapur
Satrapur for semi-lumped
for semi-lumped modeling.
modeling.
4. Conclusions
4. Conclusions
In this study, we attempted to produce a method for flood frequency estimation in
the Wainganga
In this study,basin
wetoattempted
act as an alternative
to produce to statistical
a method foranalysis that has the
flood frequency potentialin
estimation
to beWainganga
the applied at basin
ungauged
to actsites,
as anand in catchments
alternative largeranalysis
to statistical than those
that for
haswhich existingto
the potential
guidance
be applied at ungauged sites, and in catchments larger than those for which existingusing
[5] is recommended. We did this through continuous simulation modeling, guid-
rainfall
ance [5]and evapotranspiration
is recommended. We records
did thisasthrough
inputs to catchmentsimulation
continuous models. Catchments
modeling, were
using
modeled in aevapotranspiration
rainfall and variety of lumped and semi-lumped
records as inputs to configurations, using Catchments
catchment models. gauged flows to
were
Water 2022, 14, 2887 19 of 22

calibrate and test the models. The models used were the PDM for lumped catchments
and sub-catchments, and the kinematic wave for channel routing of flow from upstream
lumped catchments to the basin outlet during semi-lumped modeling. The Generalized
Pareto distribution was chosen through a Hosking–Wallis approach as the most appropriate
distribution for the region, using a wider set of catchments from the surrounding area.
Performance was variable, but was best for the two most downstream catchments, at
the Ashti and Pauni gauging stations. This held true for all variants of modeling, suggesting
that the exact setup of the catchment model was not one of the most important factors in
achieving a close match between modeled and observed runoff. Semi-lumped modeling
was found to offer similar performance to lumped modeling, despite the sub-optimality
of assigning the same parameter values to all sub-catchments. Semi-distributed modeling
with regionalization of parameter values is potentially valuable for future work but could
not be tested here due to the limited number of gauges available (nine).
The objective of this study was to improve estimation of annual maximum river
flows so that they could be used to estimate extreme flood magnitudes from which flood
frequency curves could be developed for the purpose of estimating long return period flood
magnitudes. Model calibration in most of this study focused on maximizing KGE’ over the
whole range of flows, of which the AMAX value is just one of every 365 or 366 points. While
calibration using KGE’ attempts to match the variability of modeled flows to that observed,
any under-representation of flow variability is likely to affect the most extreme flows first.
An alternative calibration procedure maximizing KGE’ exclusively on annual maxima was
tested, as the AMAX are usually the only flows of interest in extreme-event flood frequency
analysis. This calibration procedure was not found to improve or impair the model’s
predictive performance relative to conventional calibration at the Ashti gauging station in
a split-sample test where the final 10 years of flow were not used in calibration. Calibration
to AMAX could therefore be used at sites where only an AMAX record is reliable, or the
AMAX record is of higher quality than the full river flow time-series, such as stations that
only record during the monsoon season. However, any model calibrated in this way should
be used only for estimating AMAX flows.
In the study area, large amounts of unquantified artificial influence on flows limited
the performance that could be achieved. The scale of artificial influence, particularly from
dams, was not constant over the modeling period. This could not be accounted for in the
hydrological model as the parameters were static for each model run. While it is possible
for the model parameters to change over time (by expressing each parameter value as
an equation that includes time since start), there is uncertainty around the exact form of
the relationship between any parameter value and time, and whether an apparent trend
in time is more accurately represented as a trend in a different covariate that contains a
time-varying component (such as a rainfall or wetness index).
Performance is also limited by the accuracy of the data used throughout the study.
In particular, there is no clear documentation on how the flow observations, which were
used to calibrate the model, were made. It also appears that elevation was not considered
during production of the gridded rainfall data that were used to drive the model, implying
a bias towards rainfall underestimation at higher altitudes. This may be the reason for
poorer performance in matching annual maximum flows in upland headwaters. Improved
performance might be achieved by bias correcting the gridded data against high-altitude
point gauged data, or by adjusting gridded values to account for elevation.

Author Contributions: Conceptualization, G.V., A.G. and E.S.; methodology, G.V. and A.G.; software,
G.V. and A.G.; validation, G.V. and A.G.; formal analysis, G.V. and A.G.; investigation, G.V. and A.G.;
resources, E.S.; data curation, G.V., A.G. and E.S.; writing—original draft preparation, G.V., A.G.
and E.S.; writing—review and editing, G.V., A.G. and E.S.; visualization, G.V. and A.G.; supervision,
E.S.; project administration, E.S.; funding acquisition, E.S. All authors have read and agreed to the
published version of the manuscript.
Water 2022, 14, 2887 20 of 22

Funding: This research was supported by the UKCEH SUNRISE programme, a National Capability
project funded by the Natural Environment Research Council (NERC). The APC was funded by
UKCEH’s UK Research and Innovation (UKRI) Open Access Block Grant (OABG).
Data Availability Statement: Rainfall and river flow data were supplied by the Indian Meteorological
Department and the Indian Central Water Commission. They are available online at https://www.
imdpune.gov.in/Clim_Pred_LRF_New/Grided_Data_Download.html (accessed on 9 August 2022)
and https://indiawris.gov.in (accessed on 9 August 2022), respectively.
Acknowledgments: The authors would like to thank Arpita Mondal and Chingka Kalai for their ad-
vice, and John Wallbank and two anonymous reviewers for reviewing earlier drafts of this manuscript.
Conflicts of Interest: The authors declare no conflict of interest.

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