MASKANA.Vol. 9, Ed. 2, 67-74, 20=
18
https://doi.org/1=
0.18537/mskn.09.02.08
Š Author(s) 2018. This work is
distributed under the Creative Commons Attribution 4.0 License.
Research
Article
Unidimensional, non-stationary
modeling of a high mountain river in southern Ecuador
Ana Ochoa-Sánchez1,2,3
1 Dirección de Investigación de la
Universidad de Cuenca, Universidad de Cuenca, Cuenca, Ecuador.
2 Departamento de Recursos Hídrico=
s y
Ciencias Ambientales, Universidad de Cuenca, Cuenca, Ecuador.
3 Facultad de Ingeniería, Universi=
dad
de Cuenca, Cuenca, Ecuador.
4 =
Departamento de Ciencias de la Comp=
utación,
Universidad de Cuenca, Cuenca, Ecuador.
Autora de correspondencia
Fecha de recepción: 19 de septie=
mbre
de 2018 - Fecha de aceptación: 26 de noviembre de 2018
RESUMEN
Las inundaciones son una causa
severa de muertes y pérdidas económicas. Para prevenir, mitigar y reducir l=
os
riesgos por inundaciones y sus consecuencias, los modelos hidráulicos permi=
ten
el análisis y mapeo de dichas inundaciones. Los resultados de un modelo
apropiado, que trabaje en base a condiciones locales, son herramientas vali=
osas
para los gobiernos locales, conduciendo a un manejo sustentable de las llan=
uras
de inundación. Alrededor del mundo, muy pocos ríos de alta montańa han sido
modelados; y, debido a su orografía, la escasez de datos presenta una
dificultad adicional en su investigación. Tomando en cuenta que todos los
modelos unidimensionales asumen que el fondo del río tiene una pendiente
pequeńa, este estudio evalúa dos modelos unidimensionales ampliamente usado=
s:
Mike11 y HEC-RAS, para modelar un río de alta montańa. La mejor configuraci=
ón
del modelo, bajo condiciones topográficamente complejas, y su potencial uso
fueron valorados mediante su calibración y validación. Al contrario de los
resultados obtenidos para el modelo Mike11, tanto en calibración como en
validación, hemos encontrado que el modelo HEC-RAS no es capaz de encontrar=
una
solución estable durante el modelamiento hidrodinámico del río. Este estudio
sienta un precedente en cuanto a modelación unidimensional en ríos de alta
montańa con escasez de datos.
Palabras clave: modelación de ríos 1D, HEC-RAS,
Mike11, ríos de alta montańa, Ecuador.
ABSTRACT
Floods
represent a severe cause of deaths and economic loss. In order to prevent,
mitigate, and reduce flood risks and their consequences, hydraulic models a=
llow
analysing and mapping floods. The results of an appropriate model that works
under local conditions are a valuable tool for local governments leading to
sustainable management of floodplains. Around the world, high-mountain rive=
rs
have been poorly modelled; their orography and data scarcity present an ext=
ra
research difficulty. Considering that all one-dimensional models assume that
the river bed slope is small, this study evaluated two widely applied
one-dimensional models: Mike11 and HEC-RAS, for modelling a high mountain
river. Their best configuration under complex topographical conditions and
their potential use was assessed by calibration and validation of the model=
s.
We found that the HEC-RAS model was not able to define a stable solution of=
the
hydrodynamic modelling of the river, while Mike11 yielded stable results.
Furthermore, the validation of the Mike11 model showed good performance. Th=
is
study sets a precedent in the 1D modelling of high-mountain rivers with data
scarcity.
Keywords=
: 1D riv=
er
modelling, HEC-RAS, Mike11, high-mountain river, Ecuador.
1.&n=
bsp;
INTRODUCTION
Floods
represent about 40% of the natural disasters in the world (Ohl & Tapsell, 2000) and they killed=
most
people by 2016 (Guha-Sapir, Hoyois, & =
Below,
2011). In addition, extraordinary river floods considerably increased
the past years involving economic loss (Cu=
nha
& Krajewski, 2011; Dottori et al., 2018; Gilles, Young, & Schroeder,
2012). Hydraulic models allow analysing and mapping floods that help=
to
prevent, mitigate, and reduce flood risks and their consequences. Different
methodologies are useful for flow modelling and the analysis of river flood
events, from linear interpolation of water level records (0D) (Apel,
Aronica, Kreibich, & Thieken, 2009) to complete hydrodynamic one-dimensional (1D), two-dimensional
(2D), coupled 1D and 2D models (Finaud-Guy=
ot,
Delenne, Guinot, & Llovel, 2011), or even three-dimensional (3D)
models (Pender
& Néelz, 2007). Model selection depends on the information
required, flow characteristics, and type and scale of the specific applicat=
ion.
So far, 1D models are most widely used since they require less information
(cross sections and roughness coefficients) to be robust and to provide good
quality results when the flow is aligned with the main channel axis of the
river (Pender
& Néelz, 2007; Vojinovic & Seyoum, 2011). Although 2D mo=
dels
are more popular lately due to the increase of the computational capacity a=
nd
information availability, they have difficulties when hydraulic structures =
need
to be included, and their computational demand and requirement of informati=
on
is still high.
The one-dimensional hydrodynamic models, HEC-RAS and Mike11, are the most widely used for flood events analysis and flood mapping (Alaghmand, Abdullah, Abustan, & Eslamian, 2012; Andrei, Robert, &= amp; Erika, 2017). The Federal Emergency Management Agency of the US (FEM= A) accepts both for this kind of application = (FEMA, 2018). These models compute one-dimensional solutions of the Saint-V= enart equation. HEC-RAS model is freeware while Mike11 has a commercial license.<= o:p>
All
one-dimensional models assume that the river slope is small, which is not t=
he
case for high mountain rivers. Therefore, this study identifies the possibi=
lity
of using one-dimensional models for flood modelling of a high mountain rive=
r,
their best configuration under these topographical conditions, and their
potential use. The results of an appropriate model that works under such
conditions are a valuable tool for governments leading to sustainable
management of floodplains. This study compares the performance of HEC-RAS a=
nd
Mike11 models and calibrates and evaluates both these models at a high moun=
tain
river.
2.&n=
bsp;
MATERIALS AND METHODS
=
2.1. =
Study area and data availability
The river
branch of the Quinoas River is located at El
Cajas National Park in the Andean region of Ecuador, geographically def=
ined
by 2.7° - 2.8°S and 79.0° - 79.3°W (Fig. 1). The microcatchment area of the
river branch studied is approximately 86.5 km2 and its altitudin=
al
range is between 3,000 and 4,400 m a.s.l. (Fig. 1). The complete Quinuas
microcatchment (94 km2) belongs to the subcatchment of the Río
Tomebamba (380 km2) and the Paute catchment (6148 km2=
).
The river branch length is 11.4 km and its slope changes abruptly along the
river length with a maximum of 18%, a minimum of 1.5%, and a media of 6%. <=
/span>The main channel bottom consists=
of
gravels, cobbles, and a few boulders, while there are short-grass pasture
floodplains.
Three
hydrological stations are situated in strategical locations along the river
branch (Fig. 1). Data from Virgen d=
el
Cajas (VC) station located upstream and Puente
Matadero (PM) station at the downstream of the river constituted the mo=
del
boundary conditions. Data from Chir=
imachay
(CH) station was used to calibrate and validate the hydraulic model. The wa=
ter
level time series with a 5-minute temporal resolution were checked for
homogeneity and outliers. The salt dilution gauging technique applied in th=
e field
allowed building rating curves for the three stations. Four events from aro=
und
a month were selected from one year of data (Table 1). The hydrographs for =
the
boundary conditions during calibration and validation are shown in Figure 2.
The microcat=
chment
was divided in seven contribution areas (Fig. 1) that allowed the model to
distribute the discharge difference between PM and VC stations along the ri=
ver.
|
|
|
Fig=
ure
1. Location of the study area and hydrological stations. Subdivision=
of
the microcatchment into areas of contribution to the river branch.=
|
|
Table |
|||||
|
Event duration |
Maximum discharge
registered [mł/s] |
||||
|
Initial date |
Final date |
VC |
CH |
PM |
|
|
Hydrograph 1 |
07/05/2014 00:00 |
17/05/2014 23:00 |
1.3 |
7.3 |
11.2 |
|
Hydrograph 2 |
05/10/2014 00:00 |
31/10/2014 11:00 |
1.7 |
7.5 |
35.0 |
|
Hydrograph 3 |
13/07/2014 00:00 |
23/07/2014 09:00 |
0.3 |
3.4 |
4.0 |
|
Hydrograph 4 |
18/05/2014 00:00 |
18/06/2014 00:00 |
0.9 |
5.2 |
8.9 |
|
|
|
|
(a) |
(b) |
|
Figure 2.<=
span
lang=3DEN-GB style=3D'font-size:9.0pt;font-family:"Times New Roman",serif;
mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-GB;mso-far=
east-language:
EN-GB'> Events for calibration and evaluation of the model at (a) Virgen =
del
Cajas (VC) station and (b) Puente Matadero (PM) station. |
Hydraulic
models
In this
study, the models HEC-RAS (Version 4.1) and Mike11 (Version 2007) were
configured to perform the one-dimensional unsteady flow in the Quinuas high
mountain river reach. The models configuration, calibration, and evaluation
analysis aimed to represent the river hydraulics under the condition of ste=
ep
slopes. Since models normally assume that the slope is small and supercriti=
cal
flow was expected, the modifications introduced in both these models for the
modelling of a mixed flow regime (MFR: subcritical and supercritical flow) =
are
specified in the following.
Mike11 m=
odel
The
hydrodynamic module (HD) in Mike11 uses an implicit differential scheme
developed by Abbott & Ionescu (1967)
for non-permanent flow calculation in rivers and estuaries. This module can
describe subcritical and supercritical flow through a numerical scheme that
follows the local flow conditions in time and space. The computational sche=
me
is suitable for vertical homogeneous flow from steep rivers to tidal influe=
nced
estuaries (DHI, 2017). Stability
conditions depend particularly on the relationship between the time step and
grid spacing. Mike11 allows selecting between three flow descriptions: dyna=
mic
wave, kinematic wave, and diffusive wave. The first one can be chosen betwe=
en
high order fully dynamic wave and dynamic wave only. It describes flow
considering all the terms of the SaintVenant equation (local acceleration,
convective acceleration, pressure force, gravity force, and friction force).
The kinematic wave assumes a balance between the friction and gravity terms
and, consequently, does not account backwater effects. The diffusive wave
ignores inertial terms (DHI, 2017).
Mike11 dynamic wave approach assumes that the water is incompressible and
homogeneous, the bottom-slope is small, the wavelengths are large compared =
to
the water depth, and the flow is subcritical (DHI,
2007). For supercritical flow, a reduced momentum equation is applied
which neglects the convective acceleration term of the Saint Venant equatio=
n.
For the transition of sub-critical to supercritical flow, a gradual reducti=
on
of the momentum term is introduced for smooth description. Also, the
differential equation is upstream gradually centred as the influence of the
upstream condition increases. Details on the suppression of convective
acceleration are in section 1.35.1 of the Mike 11 Reference Manual <=
span
style=3D'font-size:9.0pt;font-family:"Times New Roman",serif;mso-fareast-fo=
nt-family:
"Times New Roman";mso-ansi-language:EN-US'>(DHI, 2007).
HEC-RAS =
model
The
non-stationary flow component of the HEC-RAS model is able of calculating
one-dimensional flow of natural and artificial channels. The model solves
continuity and momentum equations with a solution scheme, primarily develop=
ed
for subcritical flow, that was adapted from the UNET model by Barkau (1996), and it is known as the
four-point scheme, box scheme, or Preissman scheme. Drastic changes in the
cross sections properties, wave characteristics, and complex hydraulic
structures affect the stability of the scheme (Brunner, 2010). Since the release of Version 3.1,
the model can perform MFR (subcritical, supercritical, hydraulic jumps, and
drawdowns). The so-called Local Partial Inertia (LPI) solution technique
approach is used to carry out the MFR analysis (Fread, 1996). As stated by
Brunner (2010), when this option is turned on, the program monitors the Fro=
ude
number at all cross-sections each time step. As the Froude number gets clos=
e to
1.0, the program automatically reduces the magnitude of the inertial terms =
in
the momentum equation since this increases the models stability. Otherwise,
for Froude numbers equal to or greater than 1.0, the inertial terms are
completely zeroed out and the model is essentially reduced to a diffusion w=
ave
routing procedure (Brunner, 2010).
Models
configuration
During f=
ield
survey, cross sections were measured every 25 m and nearer at the presence =
of
meanders. Geometry was processed in CivilCadŽ and imported afterwards in
HEC-RAS and Mike11. Open boundary conditions corresponded to a hydrograph a=
t VC
(upstream) and water level time series at PM (downstream). Also, hydrograph=
s as
point source inflows were configured in the cases of the microcatchments nu=
mber
2, 3, 4, and 6 (Fig. 1); and as distributed source inflows at the microcatc=
hments
number 5 and 7 (Fig. 1). Initial conditions corresponded to the first disch=
arge
in each hydrograph at VC. Simulations time intervals were 0.5 seconds to
guarantee model stability. Models output temporal resolution was one hour.=
=
2.2. =
Model calibration
Three ev=
ents
were used for model calibration: Hydrographs 1, 2, and 3 (Fig. 2 and Table =
1).
Fifty simulations were run for every hydrograph. The friction coefficient w=
as
one of the most important parameters when calibrating the one-dimensional
models, given the absence along the
river reach of hydraulic structures (i.e., weirs). Mannings coefficient (n) represents friction and can be
approximated by three methods: field surveys, estimations in the literature,
and value adjustments (Vidal, Moisan, Faur=
e,
& Dartus, 2007). Moreover, n
should be calibrated based on observed and simulated water levels. In this
study, we considered field survey results, however, those values where far =
from
the more realistic values available in literature.
|
Table |
||
|
Reach stations [m] |
n |
|
|
Main
channel |
11,400-0 |
0.025-0.050 |
|
Floodplains |
0-2,948.31 and 7,847.88=
-9,693.67 |
0.040-0.080 |
|
2962.06-7828.08 and 9,742.18<=
/span>-11,400 |
0.110-0.600 |
During
calibration, cross section files were created by changing Manning values
randomly (uniform distribution) from a theoretical range according to the
channel and floodplains material of the river (Table 2). At Chirimachay sta=
tion
(CH in Fig. 1), water levels from the simulations were compared to the
observations through the mean error (ME), the mean square error (MSE), the =
bias
percentage (pbias), the Nash-Sutcliffe model efficiency coefficient (NSE), =
the
Kling-Gupta efficiency (KGE), and the volumetric efficiency (VE). The first
coefficient was used to measure the average systematic difference between t=
he
modelled and observed water levels. The MSE was used since it is built up on
two terms: the first corresponds to ME and the second measures the variance=
of
the random error after bias correction. The NSE is dimensionless and a scal=
ed
version of the MSE. NSE does not depend highly on the water level magnitude=
, an
advantage over ME or MSE. The last two coefficients were developed by Gupta, Kling, Yilmaz, & Martinez (2009) and
Criss & Winston (2008), respect=
ively,
to cope with some problems of the NSE like its overemphasis on large flows
relative to other measurements. KGE ranges from -Inf to 1 and VE ranges fro=
m 0
to 1; the closer to one, the more accurate the model is for both coefficien=
ts.
All the metrics were calculated with the hydroGOF R package. Details on the
formulation of each index can be consulted at Zambrano-Bigiarini,
(2017). The simulation with the lowest ME, MSE, and pbias and the
highest NSE, KGE, and VE was defined as the best result possible during
calibration and thus their Mannings coefficients were chosen to evaluate t=
he
model afterwards. Since model results change in function of the change in i=
nput
parameters, it is useful to understand models dependence on the information
from which the model is built. This analysis increases the confidence level=
of
the model and its predictions by comprehending the behaviour of the model, =
its
parameters, and applicability. The Mannings coefficients used during
calibration lead to fifty simulations per event that were represented as a
range of hydrographs that were plot against observations in CH to show the
change in the models results when bed and floodplain resistance were chang=
ed.
=
2.3. =
Model performance evaluation
Hydrogra=
ph 4
(Fig. 2) was compared with model simulation results at CH, using the same
statistic coefficients explained before. At this stage, evaluation need to =
be
completed by a graphical method (Willems, =
2011).
WETSPRO tool (Willems, 2009) was us=
ed to
analyse events characteristics in a time series, such as high flows, cumula=
tive
values representation, and prediction capacity of the model.
3.&n=
bsp;
RESULTS AND DISCUSSION
3.1.=
Mike11 vs. HEC-RAS modelling
Mike11 a=
nd
HEC-RAS modelling of the 11.4 km of the Quinuas river was conducted for his=
torical
events. Figure 3 shows the models results at the most downstream station (P=
M)
in comparison with the water level time series observations (11/10/2013 00:00 - 14/11/2013 00:00). Mike11 yielded a hydrograph
coherent with the water level variations observed in the field (Fig. 3a) wh=
ile
HEC-RAS instability issues were notorious (Fig. 3b). Usually, increasing the
number of cross sections in steep slopes and decreasing the time step, corr=
ects
instability but it was not the case for this HEC-RAS simulation where almost
all flow values were negative and high flow variations were present (Fig. 3=
b).
The current simulation was run with and without MFR, and mixed flow options
(exponent for Froude number reduction factor m and Froude number threshold for eliminating acceleration term=
s)
were modified. However, instability showed in Figure 3b remained. Figure 4
shows the Froude numbers obtained with the HEC-RAS simulation. Results clea=
rly
reveal that along all the 11.4 km of the river, Froude numbers were complet=
ely
out of range. In steep slopes, Froude numbers are expected to be higher tha=
n 1
but Figure 4 shows values up to 1,100 even when outliers were not plot. When
HEC-RAS finds Froude numbers higher than 1, the inertial terms of the
Saint-Venant equation are completely zeroed out and the model is reduced to a diffusion
wave routing procedure (Brunner, 2010). This did not allow the model to find
stable results.
|
|
|
|
(a) |
(b) |
|
Figure 3.<=
span
lang=3DEN-GB style=3D'font-size:9.0pt;font-family:"Times New Roman",serif;
mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-GB;mso-far=
east-language:
EN-GB'> Modelled and observed hydrographs at the downstream PM station of=
the
river. |
|
|
|
Figure 4. =
Froude numbers boxplots at cross sections ranges. Boxplots
interquartile ranges correspond to 1.5 and outliers are not shown. |
|
Table 3. |
|||||||
|
Calibration events |
1 |
ME [m] |
MSE [m2] |
pbias [%] |
NSE |
KGE |
VE |
|
Most
efficient sim. |
-0.01 |
0.00 |
-0.6 |
0.82 |
0.91 |
0.98 |
|
|
Least
efficient sim. |
0.29 |
0.09 |
24.8 |
-18.62 |
-0.05 |
0.75 |
|
|
2 |
|
|
|
|
|
|
|
|
Most
efficient sim. |
0.04 |
0.03 |
3.6 |
-1.64 |
-0.35 |
0.90 |
|
|
Least
efficient sim. |
0.32 |
0.23 |
30.5 |
-22.99 |
-2.48 |
0.68 |
|
|
3 |
|
|
|
|
|
|
|
|
Most
efficient sim. |
-0.01 |
0.00 |
-0.9 |
0.72 |
0.56 |
0.98 |
|
|
Least
efficient sim. |
-0.35 |
0.12 |
-34.5 |
-77.97 |
0.39 |
0.65 |
|
|
Validation
event |
4 |
|
|
|
|
|
|
|
Evaluation
sim. |
0.0004 |
0.0003 |
0.00 |
0.81 |
0.73 |
0.99 |
Mike11
results at Chirimachay station were stable, including the rating curve and
discharge time series (not shown). MIKE11 gives the user the opportunity to choose
between three flow descriptions: dynamic wave, kinematic wave, and diffusive
wave (DHI, 2007). For the dynamic wave approach, it gives two choices: dyna=
mic
wave and high order dynamic wave. The first attempt to model the Quinuas ri=
ver
was done using the kinematic wave approach since this flow description is
recommended for steep slopes (DHI, 2007). The assumption of a balance betwe=
en
friction and gravity means that the kinematic wave approach cannot simulate
backwater effects; and thus, this description is appropriate for relatively
steep rivers without backwater effects (DHI, 2007). However, the model
configured with the kinematic wave method was unstable. The remaining flow
descriptions were used as well; however, stable conditions were only reached
with the high order dynamic wave approach using a time step of 0.5 seconds.=
Bennett, Walton, Dickerson, & Howard (2004) states that the computational
method for determining channel roughness is one such difference between HEC=
-RAS
and Mike11 and they provide a conversion between the two coefficients in or=
der
to find similar results with the models. However, in this study, the roughn=
ess
coefficient was not the cause of the dissimilarity since HEC-RAS was run wi=
th
multiple coefficients and the instability remained. Stability was only achieved when=
the
high order dynamic wave option in Mike 11 was run. During supercritical flo=
w,
Mike11 used the Saint-Venant equation without the convective term while HEC=
-RAS
eliminated the local and the convective acceleration terms. Additionally,
Mike11 modifies the scheme during supercritical conditions. These differenc=
es resulted
in a stable Mike11 simulation. Therefore, Mike 11 software was chosen for the ri=
ver
branch unsteady flow calibration and validation stages.
=
3.2. =
Mike11 model calibration
Fifty
simulations with different Mannings coefficients were run in Mike11 for ea=
ch
of the three hydrographs used for calibration. Water levels were compared, =
and
one simulation has the minimum ME, MSE, and pbias and the maximum KGE, VE a=
nd
NSE; while other simulation has the maximum ME, MSE, and pbias and the mini=
mum
KGE, VE and NSE (Table 3). Figure 5 shows changes in the models results du=
e to
the changes in the Mannings coefficient. The n values from the most efficient model were chosen during this
stage as having better statistical results (Table 4).
|
|
|
|
|
(a) |
(b) |
(c) |
|
Figure 5.<=
span
lang=3DEN-GB style=3D'font-size:9.0pt;font-family:"Times New Roman",serif;
mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-GB;mso-far=
east-language:
EN-GB'> Modelled and observed water levels at CH station during calibrati=
on
stage: (a) Observed Water level 1 corresponds to Hydrograph 1 in Figure 2;
(b) Observed Water level 2 corresponds to Hydrograph 2 in Figure 2; (c)
Observed Water level 3 corresponds to Hydrograph 3 in Figure 2 |
The ME, =
MSE
and pbias of the best simulation showed a low biased model, especially for =
low
and medium flows (water level 1 and water level 3, Table 3). Also, for those
water level magnitudes, the NSE, KGE and VE indexes were more than 0.6 and =
even
0.99, showing a good agreement between model and observations. However, the
second event coefficients showed a model that overestimated water levels in=
30%
and had a poor performance, with negative values of NSE and KGE (Table 3 and
Fig. 5b). These results are understandable given that the high peaks in the
second event gauged at PM (Fig. 2) were very difficult to measure due to the
high turbulence involved.
|
Table 4. Mannings coefficients (n) values chosen during calibration of the Mike 11 model. |
||
|
Reach stations (m) |
n |
|
|
Main
channel |
11,400-0 |
0.032 |
|
Floodplains |
0-2,948.31 and 7,847.88-9,693.67 |
0.040 |
|
2,962.06-7,828.08 and 9,742.18=
-11,400 |
0.593 |
=
3.3. =
Mike11 model performance evaluation
Statisti=
cal
results of the model performance evaluation are shown in Table 4. The errors
showed good performance of the model in all the calculated coefficients. The
unbiased model has an NSE of 0.81 (Table 3). The KGE value during validatio=
n,
showed that the model estimates agreed in 73% with the observed values when=
the
three aspects of validation: correlation, bias, and variability were decomp=
osed
(Gupta et al., 2009). A value of VE=
equal
to the one, in Table 3, means that 99% of water was delivered in a proper t=
ime (Criss & Winston, 2008). Low and high=
flows
were treated equally when evaluating the model with VE. Until now, evaluati=
on
corresponded to an average of high and low flows altogether. Therefore, a
complementary graphical analysis for validation follows.
Mike11 f=
lows
were plotted against observations (see Fig. 6) showing underestimation of t=
he
low and high flows but a notorious correlation. Baseflow was estimated with the
WETSPRO tool and shown in Figure 6.
|
|
|
Fig=
ure
6. Modelled, observed and baseflow time series at CH station during
evaluation stage. |
This
approach allowed finding peaks over a threshold (also called events) that a=
re
useful when peaks occur in a different time step on the observed and modell=
ed
time series. Afterwards, transformation of the events was needed to reach
independency of the residuals on the flow values (homoscedastic residuals).
Figure 7 shows the transformed simulated against observed events together w=
ith
the mean deviation, bisector, and standard deviation.
|
|
|
|
|
Figure 7.<=
span
lang=3DEN-GB style=3D'font-size:9.0pt;font-family:"Times New Roman",serif;
mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-GB;mso-far=
east-language:
EN-GB'> Observed and modelled peak flows at CH station during evaluation
stage. |
Figure 8.<=
span
lang=3DEN-GB style=3D'font-size:9.0pt;font-family:"Times New Roman",serif;
mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-GB;mso-far=
east-language:
EN-GB'> Observed and modelled cumulative values at CH station during
evaluation stage. |
Figure 9.<=
span
lang=3DEN-GB style=3D'font-size:9.0pt;font-family:"Times New Roman",serif;
mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-GB;mso-far=
east-language:
EN-GB'> Observed and modelled events vs return period at CH station during
evaluation stage. |
Displace=
ment
of the bisector from the mean and scattering of the points usually shows wh=
en a
model is biased. In this case, such displacement does not exist since we ha=
ve
an unbiased model. In addition, the river is displayed as a reservoir in Fi=
gure
8, where Mike 11 underestimated cumulative values. In conclusion, Figure 9
depicts the predictable capacity of the model by plotting the events against
their return period. Most of the selected events were well estimated by the
model, and only a peak of around 9 m3/s was underestimated. The
latter is not a final-conclusion due to data scarcity, but it is under
consideration since monitoring is ongoing.
4.&n=
bsp;
CONCLUSIONS
We model=
led
a river branch of the high mountain Quinuas river with the Mike11 and the
HEC-RAS models. Model implementation of both models showed similar complexi=
ty,
so does their operation. However, in this study, the Mike11 model provided
stable results, while the HEC-RAS models instability remained after several
configurations were attempted. Reasons for this discrepancy were found in t=
he
treatment that the models give to supercritical flows. When the Froude numb=
er
is equal or exceeds 1, Mike 11 calculates the Saint-Venant equation excluding the convective
acceleration term, while HEC-RAS eliminates the local and the convective
acceleration terms. Additionally, Mike11 modifies the scheme during
supercritical conditions for a smooth transition from subcritical to
supercritical flow. Therefore, only Mike11 could be used for calibration and
evaluation of the Quinuas river branch.
During
calibration of the Mike11 model, a range of Mannings coefficient (n) values was determined represent=
ing
theoretically bed resistance in the channel and floodplains. We simulated f=
ifty
randomly chosen values for each event of the three selected hydrographs.
Results revealed that the model was sensitive to the bed resistance of the
channel and floodplains. Calibration allowed choosing the optimum values of=
n.
During m=
odel
performance evaluation, we determined that the model was able to estimate w=
ater
levels with almost no bias (ME =3D 0.0004 m, MSE =3D 0.0003 m2) =
and an
NSE of 0.81. Evaluation concludes that the unbiased model has a high predic=
tive
capability, especially at low and medium flows. This model could be useful =
in
the future to implement flood warning systems in the Andean region, a region
characterized for having steep slope rivers.
ACKNOWLEDGMENTS
This
research was funded by the DIUC (Research Directorate of the University of
Cuenca) via the project Desempeńo y fiabilidad de modelos hidráulicos
unidimensionales para la modelación de inundaciones en ríos de montańa.
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