HESSHydrology and Earth System SciencesHESSHydrol. Earth Syst. Sci.1607-7938Copernicus PublicationsGöttingen, Germany10.5194/hess-21-4245-2017The critical role of uncertainty in projections of hydrological extremesMeresaHadush K.RomanowiczRenata J.romanowicz@igf.edu.plInstitute of Geophysics Polish Academy of Sciences, Warsaw, PolandRenata J. Romanowicz (romanowicz@igf.edu.pl)29August2017218424542582December201620December20165July201715July2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://hess.copernicus.org/articles/21/4245/2017/hess-21-4245-2017.htmlThe full text article is available as a PDF file from https://hess.copernicus.org/articles/21/4245/2017/hess-21-4245-2017.pdf
This paper aims to quantify the uncertainty in projections of
future hydrological extremes in the Biala Tarnowska River at Koszyce gauging
station, south Poland. The approach followed is based on several climate
projections obtained from the EURO-CORDEX initiative, raw and bias-corrected
realizations of catchment precipitation, and flow simulations derived using
multiple hydrological model parameter sets. The projections cover the 21st
century. Three sources of uncertainty are considered: one related to climate
projection ensemble spread, the second related to the uncertainty in
hydrological model parameters and the third related to the error in fitting
theoretical distribution models to annual extreme flow series. The
uncertainty of projected extreme indices related to hydrological model
parameters was conditioned on flow observations from the reference period
using the generalized likelihood uncertainty estimation (GLUE) approach, with
separate criteria for high- and low-flow extremes. Extreme (low and high) flow
quantiles were estimated using the generalized extreme value (GEV)
distribution at different return periods and were based on two different
lengths of the flow time series. A sensitivity analysis based on the analysis
of variance (ANOVA) shows that the uncertainty introduced by the hydrological
model parameters can be larger than the climate model variability and the
distribution fit uncertainty for the low-flow extremes whilst for the
high-flow extremes higher uncertainty is observed from climate models than
from hydrological parameter and distribution fit uncertainties. This implies
that ignoring one of the three uncertainty sources may cause great risk to
future hydrological extreme adaptations and water resource planning and
management.
Introduction
Hydrological models are useful in water resource planning and management,
flood and drought prediction, assessments of catchment-scale impacts of
climate change, and the understanding of system dynamics. In particular,
coupling of hydrological models and climate models is important in
understanding the influence of climate changes on low and high flows
(Lawrence and Hisdal, 2011; Meresa et al., 2016). Research on the impact of
climate changes on future hydrological extremes is usually performed by an
application of hydrological models to the projected meteorological inputs
under assumed future climate scenarios (Wilby and Harris, 2006; Honti et al.,
2014). The standard procedure consists of a chain of consecutive actions,
starting from the choice of a general circulation model (GCM) driven by an
assumed greenhouse gas emission scenario, through downscaling of climatic
forcing to a catchment scale, e.g. using the regional climate model (RCM),
hydrological modelling and estimation of hydrological extreme indices using
statistical tools. Each of the serially linked processes involves
uncertainties that propagate through the computational pathway. Among many
possible sources of uncertainty, the main sources are the uncertainties
related to future climate scenarios, climate models, downscaling techniques
and hydrological modelling. We cannot directly assess the impact of the first
three sources of uncertainties on predictions of hydrological extremes in the
future due to a lack of observations of future climate realizations. This is
one of the reasons why the term projections is used instead of predictions
(Honti et al., 2014). Therefore these first three sources of uncertainty have
an “epistemic” nature and cannot be decreased (Beven, 2016). On the other
hand, the introduction of conditioning based on available past observations
of climatic and hydrological variables allows a decrease of the
“predictive” hydrological model uncertainty to be achieved. The calibrated
hydrological models are forced with climate projections derived from climate
models. However, hydrological models that produce acceptable results for an
observed baseline period may respond differently when forced with the climate
change scenario (Gosling and Arnell, 2011; Thompson et al., 2013; Lespinas et
al., 2014). For several decades interest in hydrological structural and
parameter uncertainty has been increasing and has become an important part of
modelling (Ouyang et al., 2014; Sellami et al., 2014; Osuch et al., 2015). It
has been widely verified and acknowledged that different model structures and
parameterizations can lead to similar responses and, thus, there are no
unique structure and parameter sets for acceptable or behavioural
hydrological model responses for reproducing the observation data (Beven,
2006; Poulin et al., 2011). In addition to the parameter and structural
uncertainty (Poulin et al., 2011), the hydrological model is also exposed to
uncertainty which arises from various sources not directly mentioned above,
including interdependency among the climate models (Wilby and Harris, 2006;
Ghosh and Katkar, 2012; Tian et al., 2016) or downscaling of GCM projections
(Sunyer et al., 2015; Vormoor et al., 2015).
The issues of uncertainty in hydrological modelling and hydrological
projections due to climate change are not new; there is much research
published on this subject in global and regional studies (Todd et al., 2011;
Addor et al., 2014; Abbaspour et al., 2015). However, few of the case studies
at a catchment level were trying to assess the influence of uncertain future
and hydrological parameter uncertainty (Poulin et al., 2011; Bennett et al.,
2012; Steinschneider et al., 2012, 2015; Vormoor et al., 2015). In a number of
studies the hydrological model structural and parametric errors are dealt
with using a multi-model approach and introducing weights for hydrological
model parameter sets following assumed goodness of fit criteria, e.g. in the
form of a likelihood function (Wilby and Harris, 2006; Steinschneider et al.,
2012; Addor et al., 2014). Addor et al. (2014) concentrated on the influence
of different hydrological model structure, involving three hydrological
models, emission scenarios, climate models, post-processing and catchments.
Their results indicate that influence of model structure varies with the
catchment. However, the authors did not take into account hydrological model
parameter uncertainty, which is included in the present paper. Following the
results presented by Demirel et al. (2013a) the choice of the GCM/RCM has
larger influence than the choice of the emission scenario on the projections
of low-flow indices. Similar findings for the high-flow indices were
presented by Osuch et al. (2016). There is general agreement that we cannot
avoid uncertainty in climate models (Knutti and Sedlacek, 2012). The question
arises as to how large the uncertainty is and if it is acceptable to the
end user in adaptations to climate change and flood and drought risk
assessments.
In this study, we assess the critical role of uncertainty in the projection
of future hydrological extremes in the Biala Tarnowska mountainous catchment
in Poland in the 21st century. We consider three sources of uncertainty.
These are epistemic climate projection uncertainty, hydrological model
parameter uncertainty and uncertainty of extreme index estimates (the error
in fitting theoretical distribution models to annual extreme flow series). We
restricted the sources of epistemic uncertainty to that which have the
largest impact – i.e. climate model spread, omitting the uncertainty related
to bias correction and emission scenario. The error related to the
distribution fit was included as an essential part of the extreme index
evaluation, which requires extrapolation of annual maximum or minimum flow
distributions to higher-order quantiles (e.g. 1-in-100 year, or 1-in-200
year). Osuch et al. (2016) presented the influence of emission scenario,
climate model, bias correction method and catchment on flow indices in a case
study that included the same catchment, Biala Tarnowska. In this respect, our
paper is an extension of that paper, focusing on the influence of
hydrological model parameter uncertainty on annual maximum and minimum flow
projections.
The location of the study catchment.
We apply a non-formal approach to estimate the uncertainty related to
hydrological model parameters – namely, the generalized likelihood uncertainty
estimation (GLUE) method of Beven and Binley (1992, 2014). The other sources
of uncertainty are dealt with by means of a direct assessment of variability
in extreme index estimates. Seven climate projections applied are derived
from the high-resolution regional climate change ensemble within the World
Climate Research Program Coordinated Regional Downscaling
Experiment (EURO-CORDEX) initiative (Jacob et al., 2014). Two separate
goodness-of-fit criteria are chosen to constrain the hydrological parameter
uncertainty of high- and low-flow estimates.
In this way, different parameter sets are chosen for the description of high-
and low-flow catchment regimes. This approach does not eliminate the problem
of parameter non-stationarity but helps to choose the model behaviour
adequate to the flow regime. The uncertainty related to the distribution fit
is analysed in two stages, using, separately, the 30-year-long and 130-year-long time series of future flow projections to derive the quantiles of
maximum and minimum annual flows. The popular method of a comparison of
changes in flow quantiles between the reference period and future periods is
based on relatively short (e.g. 30-year) periods. It is well known that an
extrapolation of a distribution function based on a 30-year-long time series
towards 1-in-100-year quantiles involves very large errors (Strupczewski et
al., 2011). Even the estimates of 1-in-30-year quantiles based on the 30-year-long data are biased with large errors. We compare these errors with those
involved on 1-in-30-year quantile estimates obtained using the 130-year-long
time series. The question we pose is whether the estimates of future trends
of extreme indices and their relative changes can be useful at all in view of
the uncertainties involved.
The paper is organized into five sections. Sections 2 and 3
describe, respectively, the case study and the methodology applied. Section 4
presents the results and discussions of the uncertainty
analysis and derived changes in future low- and high-flow extremes; Sect. 5
presents the conclusions.
Study area and hydro-climatic dataStudy area and observed data characteristics
The Biala Tarnowska catchment, located in the mountainous part of Poland, was
chosen as a case study. This catchment is one of the representative Polish
catchments chosen following an extensive analysis of available
hydro-meteorological and geomorphological data (Romanowicz et al., 2016a).
The catchment area is about 967 km2, with forests covering much of the
upper elevations and the river is characterized by nearly natural conditions.
The location of the catchment is given in Fig. 1. Precipitation varies in
intensity and duration over the catchment area. Observations from five
gauging stations were used to derive areal precipitation in the catchment by
means of Thiessen polygons. No elevation correction was applied in this
study. However, it was applied to the same catchment by Benninga et al. (2016)
and showed that the increase in precipitation due to the elevation is about
3 %. The annual maximum precipitation, annual minimum streamflow and
annual mean streamflow of the catchment were 68.3 mm day-1, 0.4 and
5.43 m3 s-1 respectively over the observation period 1971–2000.
Biala Tarnowska has a mixed (rainfall and snow-melt originated) flood regime.
In this study, daily hydro-meteorological observations and estimated
potential evapotranspiration were used as an input to the hydrological model
HBV (Bergstrom, 1995).
Observed hydrological and climate daily time series of
precipitation, temperature and flow for 39 years from November 1970 to
October 2010 were obtained from the Institute of Meteorology and Water
Management (IMGW) in Poland. Daily potential evapotranspiration was
calculated using the temperature-based Hamon approach (Hamon, 1961). The
daily flow data from the Koszyce Wielkie hydrological station for a period of
39 years (1971–2010) were used in the calibration (1971–2000) and
validation (2001–2010) stages.
List of RCMs/GCMs used in this study.
GCMRCMExpansion nameInstituteEC-EARTHRCA4Regional-scale modelSwedish Meteorological and Hydrological InstituteEC-EARTHHIRHAM5Atmospheric modelDanish Meteorological InstituteEC-EARTHCCLM-4-8-17Community land modelNCAR UCAREC-EARTHRACMO22ERegional atmospheric climate modelDanish Meteorological InstituteMPI-ESM-LRCCLM4-8-17Community land modelMax Planck Institute for MeteorologyMPI-ESM-LRRCA4Regional-scale modelMax Planck Institute for MeteorologyCNRM-CM5CCLM4-8-17Community land modelCERFACS, FranceFuture climate data
Daily temperature and precipitation projections were obtained from the
EURO-CORDEX initiative project (http://www.eurocordex.net/) which
provides regional climate projections at a spatial resolution of
12.5 km (EUR-11) for median (RCP4.5) emission
scenario and covering the time period 1971–2100 (Kotlarski et al., 2014).
This ensemble contains four different RCMs driven by three different GCMs.
The names and model affiliations are given in Table 1. The RCP4.5 was applied
because it is a stabilization scenario and thus assumes the imposition of
emissions mitigation policies. The RCP4.5 is derived from its own
“reference”, or “no-climate-policy”, scenario. This reference scenario is
unique to RCP4.5 and differs from RCP8.5, RCP6.0 and RCP2.6 (Jacob et al.,
2014). The influence of the emission scenario on flood indices was studied by
Osuch et al. (2016) whilst the low flows were analysed by Demirel et
al. (2013a) and Osuch et al. (2017). Those studies indicated that the choice
of emission scenario has a relatively small influence on the results as
compared to climate model spread.
MethodologyResearch approach
The approach applied here to the derivation of future projections of flow
extremes follows the forward modelling chain (Wilby and Harris, 2006) and
consists of the following steps:
Choice of climate projections simulated
using the ensemble of GCMs/RCMs under the assumed carbon emission scenario
(here RCP4.5) and dynamically downscaled to the catchment scale.
Bias
correction of projected meteorological time series of temperature and
precipitation.
Hydrological simulations of flow using raw and
bias-corrected meteorological projections for a set of hydrological model
parameters.
Derivation of extreme flow indices using empirical and
distribution-based frequency analysis tools and two different lengths of time
series (30 and 130 years) of the analysed flow extremes. The assessment of
projection uncertainty is performed by running multiple simulations and
evaluating the impact of each of the chain modules on the total uncertainty
of the results (Wilby and Harris, 2006; Steinschneider et al., 2012).
Climate projections: bias correction
The downscaling of the GCM output using either statistical or dynamic (RCM)
approaches does not take into account any feedback mechanisms existing within
land-surface processes and therefore the meteorological projections can be
biased (Falloon et al., 2014). Several studies have identified the need to
check and correct bias, in the GCM/RCM output, before its use in impact
studies (Gudmundsson et al., 2012; Gutjahr and Heinemann, 2013; Teutschbein
and Seibert, 2013; Teng et al., 2015). Most of those studies were focused on
mean output values. Osuch et al. (2016) compared five different
distribution-based quantile mapping (QM) techniques applied in the derivation
of extreme flow indices (flow quantiles and mean annual maximum flow). Their
results showed the single gamma distribution mapping to be the one which
produced the observed characteristics most accurately of all the techniques
and regions studied. However, the QM technique applied to simulated
precipitation series in the reference period (1971–2000) may result in an
alteration of the modelled maximum runoff (Ehret et al., 2012; Teng et al.,
2015). On the other hand, the low extreme values require bias-corrected
precipitation input due to the persistent and unrealistic drizzle present in
raw precipitation data. The drizzle effect (i.e. too many days with very low
precipitation intensity and too few dry days) is related to the performance
of climate models. It presents itself in the form of frequent rainfall of a
very small intensity. The physics behind precipitation generation is very
complex and involves processes operating on a wide range of scales. The
frequent “drizzle” is produced mainly by convective parameterization. It
appears in many climate models and invokes errors in the intensity and
frequency of precipitation (Maraun, 2013). A correction can be performed
using the number of wet days in a month (Osuch et al., 2016). Because of this
bias in precipitation, using direct climate model outputs as inputs to
hydrological modelling for low-flow analysis often leads to unrealistic
results and therefore bias correction is required in the case of low-flow
projections. Temperature projections are corrected using the empirical QM
approach.
Hydrological modelling
The HBV hydrological model version applied is based on Lindstrom et
al. (1997) and is written in MATLAB. It is a lumped conceptual
multi-reservoir-type model for daily runoff simulation from daily inputs
(Lindstrom et al., 1997). The original MATLAB code from the Twente
University, NL, was further developed and adjusted for the purpose of climate
impact studies in the Institute of Geophysics PAS. The model uses
precipitation, air temperature and potential evaporation data as inputs. The
HBV model has four main routines: (i) snow, (ii) soil moisture, (iii) fast
response, and (iv) slow response. These routines are governed mainly by
14 HBV parameters, of which six (TT, TTI, CFMAX, DTTM, CFR,
WHC), three (FC, LP, BETA), three (KF, ALPHA, CFLUX) and two
(KS, PERC) parameters represent each routine respectively. Not
all HBV model parameters have significant impact on the simulated flows. The
HBV model was applied in different hydro-climatic conditions by many
researchers (e.g. Demirel et al., 2013b; Seibert and Vis, 2016). Romanowicz
et al. (2013) discussed the most sensitive parameters of the HBV model for
both high-flow and low-flow characteristics. Other studies of the HBV model
parameter sensitivity were presented by Osuch (2015) and Osuch et al. (2015).
The set of six most sensitive parameters for the extreme high- and low-flow
conditions was chosen following those studies. These are FC, BETA, LP,
KS, CFMAX and PERC. A full description of the HBV hydrological model
which we used can be found in Osuch et al. (2015). Osuch et al. (2015) also
compared three sensitivity analysis techniques to describe the HBV model
parameter interactions. The studies mentioned show that the sensitivity of
HBV model parameters vary depending on the catchment characteristics and time
period of model evaluation. The parameters chosen were the most sensitive in
the wide range of input variability. The other HBV model parameters show
small influence on model output independent of the event type. The
application of different evaluation criteria for low- and high-flow
conditioning allows for treating the parameters according to their influence
on the flows, i.e. it takes into account model output sensitivity (Saltelli
et al., 2006). We used the output of Osuch et al. (2015) to eliminate less
sensitive HBV model parameters in order to minimize computational cost.
Hydrological models are usually calibrated using the available observations
under the assumption of stationarity of their parameters. Depending on the
purpose of the modelling, different criteria may be used (Romanowicz et al.,
2013). Usually, the research is aimed at finding the compromise of a model
performance between high- and low-flow simulations. The Nash–Sutcliffe
criterion (NSE) (Nash and Sutcliffe, 1970) belongs to those most widely used.
When based on the whole calibration observation series, it provides parameter
sets that favour medium-to-high flows (Gupta et al., 2009). Deckers et
al. (2010) applied different time periods of observations related to high and
low flows. The authors used multi-objective criteria that combined different
aspects of model performance. However, we do not always need to look for a
compromise in model performance when choosing the parameter sets of a model.
Where hydrological extremes are concerned, the average model performance is
not of interest. Rather, we want to obtain robust model performance for very
low or very high flow values. Therefore, in this study we use in parallel two
objective functions to encapsulate the high- and low-flow characteristics. The
NSE criterion JNSE is used here to calibrate the high-flow-oriented HBV
model. The low-flow HBV model is calibrated using the NSE for the logarithm
of flow (JlogNSE). The criteria are defined as follows:
JNSE=1-∑t=1T(Qt,sim-Qt,obs)2∑t=1T(Qt,obs-Qt,obs‾)2JlogNSE=1-∑t=1T(logQt,sim-logQt,obs)2∑t=1T(logQt,obs-logQt,obs‾)2,
where Qt,sim denotes simulated flow in time t (here
days), t=1,…,T, Qt,obs denotes observed flow in time
t, Qt,obs‾ denotes mean observed flow and
logQt,obs‾ denotes mean of logarithm of flows.
Depending on the formulation of the problem, either deterministic or
stochastic methods can be used to derive a set of the best model parameters
(Romanowicz and Macdonald, 2005). In this study we use a stochastic
formulation and we apply the GLUE approach of Beven and Binley (1992) to calibrate the HBV model and
provide an estimation of the model parameter uncertainty.
Hydrological model parameter uncertainty
The GLUE approach is one of the non-formal statistical methods that involve
direct Monte Carlo (MC) simulations. The entire parameter space is explored by
running the model simulations for a large number of parameter combinations
and evaluating the model response using some chosen goodness-of-fit criterion
(Beven, 2007). The idea of an optimal system representation is rejected and
the equifinality concept is accepted for the behavioural parameter sets.
Following that approach, the parameter space is sampled over the whole
feasible range and the errors between simulated model results and
observations are used to derive the parameter set weighting. The number of
samples depends on the number of model parameters but also on the model
computing times and it may vary from hundreds to hundreds of thousands (Beven
and Binley, 2014). Many research papers recommend over 10 000 MC
simulations (Jin et al., 2010; Romanowicz et al., 2013; Houska et al., 2014).
In this study we apply the version of GLUE that uses the behavioural
parameter sets, defined by a threshold value of the selected criterion
(Beven, 2006). The behavioural thresholds for both criteria are selected
following the model performance in the calibration period. The choice of high
threshold values results in narrow confidence limits of the predictions and
(usually) a small behavioural parameter set. However, when the chosen
threshold is too high, the 0.95 confidence limits do not include 95 % of
the observations. On the other hand, too low a threshold value will result in
too wide confidence limits. Therefore it is important to choose the right
threshold value. In this work the threshold values are chosen by the “trial
and error approach”. The choice of two different criteria, one for high and
one for low-flow extremes, yields two different behavioural parameter sets
describing model performance in two different (low- and high-flow)
hydro-meteorological conditions.
Uncertainty related to fitting the generalized extreme value
distribution (GEV) to extreme flow projections
The choice of the generalized extreme value distribution (GEV; Coles, 2001)
followed the validation of suitability of this distribution to describe the
projected annual maximum and minimum flows using probability plots for the
Biala Tarnowska. The GEV distribution model was applied to all the climate
models and the a posteriori hydrological model parameter sets. The
MATLAB-based GEV-fitting algorithm provides estimates of the median and the
0.95 confidence bands for the parameters of GEV distribution. These
parameters were subsequently used to obtain lower and upper confidence bands
of quantiles of extreme index distribution through the inverse GEV model
(Coles, 2001, Eq. 3.4). In order to simplify the procedure, instead of
sampling from the GEV parameters within the parameter space common to all
hydrologic and climate model simulations, we sampled from each set of
parameters assuming a normal distribution with the variance specified by the
GEV parameter lower and upper 0.95 confidence values, and in addition,
assuming the independence of the GEV model parameters. The obtained 0.95 GEV
distribution confidence values were used to estimate the spread of results
related to the distribution fit. Bearing in mind that the aim of this study
was to assess the ranges of uncertainty of extreme indices rather than their
exact values, and the large number of simulations, it was not possible to
choose among different distribution functions the best distribution for each
projected time series.
Sensitivity analysis using ANOVA: variance decomposition
Many global sensitivity methods have been proposed and used, such as the Fourier
amplitude sensitivity test (FAST), regional sensitivity analysis (RSA),
analysis of variance (ANOVA), parameter estimation software (PEST), and Morris
and Sobol methods (Saltelli et al., 2006). Among these methods, ANOVA has
proved to be one of the most robust and effective tools to analyse both
continuous and discrete factors (Montgomery, 1997), and is widely applied in
hydrology (Bosshard et al., 2013; Zhan et al., 2013; Lagerwalla et al., 2014;
Addor et al., 2014; Giuntoli et al., 2015; Osuch, 2015). We used the ANOVA
approach due to its numerical facility (MATLAB) and ability to evaluate the
main and interactive effects between the factors considered. To identify the
relative contribution of each source of uncertainty, corresponding to the
parameter sets (P), climate models (C) and parameter
distribution sets (D), from the spread of flow quantile change in
the near and far future, we use the following ANOVA model:
Tijk=μ+Pi+Cj+Dk+(P+C)ij+(P+D)ik+(C+D)jk+εijk,
where Tijk is total sum square error for the specific hydrological
extreme indicator (e.g. relative change in the empirical high-flow quantile
at 30-year return period QT30) for the ith parameter set range, jth
climate model and kth distribution parameter range and μ is the
overall mean, and εijk denotes the white Gaussian error.
Design of numerical experiments
We present here an assessment of the uncertainty in projected hydrological
extremes for two different lengths of data periods. Firstly, the annual
maximum and minimum (7-day average) flow quantiles are derived for
30-year periods, the so-called near future (2021–2050), and far future
(2071–2100) and are compared with the reference period (1971–2000). Secondly,
a frequency analysis of annual maximum and minimum flows is performed based
on the whole 130 years of seven GCM/RCM projections for the period
1971–2100. Since the Biala Tarnowska flow projections do not show any
non-stationarity in extreme flow events (Meresa et al., 2017), it is possible
to compare the uncertainty of estimates of extreme indices obtained from the
30-year-long and 130-year-long time series. It can be expected that the
uncertainty of extreme flow quantiles will be larger for short time series,
but we do not know how much larger it can be and therefore that comparison is
not obvious. The comparison can help in answering our research question on
how reliable is the approach commonly used in climate impact studies
consisting of a comparison of 30-year-based estimates of extreme flow indices
between reference and future periods.
HBV parameter ranges: upper band (UB), lower band (LB); fixed
parameters have lower and upper bands equal.
ParameterDescriptionLBUBUnitFCMaximum soil storage0.1250mmBETAShape coefficient0.017–LPSM threshold for reduction of evaporation0.11–KSRecession coefficient for runoff from base flow0.00050.3dPERCPercolation rate occurring when water is available0.01100mm d-1CFMAXSnowmelt rate020mm-1∘C d-1DTTMTT correction to give a threshold temperature0.14840.1484mm-1∘C d-1CFRRefreezing factor0.27790.2779–WHCWater holding capacity of snow0.0010.001mm mm-1ALFAMeasure for non-linearity of flow in quick runoff0.22550.2255–KFRecession coefficient for runoff from quick runoff0.28260.2826dCFLUXRate of capillary rise1.00031.003mm d-1TTITemperature threshold interval length2.52.5∘CTTTemperature threshold for snowfall1.01451.0145∘C
As explained in Sect. 3.3, a stochastic formulation is applied to the
estimation of the HBV model parameters. That means that 20 000 simulations of
the HBV model were run for the 30-year-long calibration period (1971–2000)
with parameters sampled randomly within the assumed parameter ranges
(Table 2). That number was dictated by the practical requirement of dealing
with not too large data files. The parameter ranges were chosen following the
results of deterministic optimization performed earlier and reported by
Romanowicz et al. (2016) and they include the derived optimal values. The
range of parameter variability was chosen following the HBV model sensitivity
studies reported by Osuch (2015) and Benninga (2015). It should be noted that
the WHC parameter related to refreezing is very small, indicating
that no refreezing process is accounted for. Following the sensitivity
studies, that parameter has no influence on the model calibration, which can
be explained by the lack of relevant observations. Default parameter values
could be used in that case, but that would mean that we impose information
that we do not possess.
As discussed earlier, we focus on three sources of uncertainty: the first
related to the HBV model input, in the form of ensemble projections of
temperature and precipitation, the second related to hydrological model
parameter uncertainty and the third related to the extreme index distribution
fitting uncertainty. The latter was evaluated using 10 000 MC normal
samples of the GEV model parameter space performed for each of behavioural
parameter sets (Sect. 4.2). As a result we obtained 20 000 daily flow
simulations 130 years long for raw and bias-corrected climate model
projections for an ensemble of seven GCMs/RCMs listed in Table 1. This gives
a total of 280 000 flow time series used to derive extreme flow quantiles.
We apply the QM-corrected precipitation projections for the estimation of
low-flow extremes and raw precipitation projections for high-flow extremes.
The choice of raw precipitation data for high-flow indices allowed for the
elimination of errors related to bias correction in the estimates (Romanowicz
et al., 2016b). On the other hand, the bias correction of precipitation
projections is necessary for the low-flow indices due to the drizzle effect
of climate models.
Results and discussionVariability of projected precipitation and temperature series
In the following section, we present an analysis of the variability of
maximum precipitation and temperature series on an annual basis to see the
correlation between the projected climate and hydrological extremes. The idea
behind presenting the precipitation changes was to show their possible
relation with the changes in flow extreme indices. For a catchment of that
size, annual maximum and mean sums of precipitation are well correlated with
the flow patterns when the rainfall-driven flood regime prevails. The
temperature changes, on the other hand, present the changes in the
evaporation losses, and possibly indicate changes in the flood regime. In
Fig. 2, precipitation and temperature time series for the Biala Tarnowska
catchment obtained from the seven GCMs/RCMs under the RCP4.5 scenario
are shown. The periods cover the whole length of historical and projected
years (1971–2100). The upper panel of Fig. 2 presents annual sum
precipitation based on corrected precipitation projections, the annual
maximum precipitation based on raw projections is shown in the middle panel,
and temperature mean projections for bias-corrected data are presented in the
lower panel. Low-flow patterns are affected by long-term precipitation which
is reflected in annual precipitation sums, while the high-flow events have a
short timescale and correspond to precipitation maxima. The results show a
visible increase of the annual mean temperature and mean values of annual
sums of precipitation and annual maxima do not show visible changes with
time.
Climate model projections for the Biala Tarnowska catchment in the
1971–2100 period based on the seven climate models from the GCM/RCM
combinations, (a) projected bias-corrected annual sum
precipitation, (b) projected raw annual maximum daily
precipitation, and (c) projected bias-corrected annual maximum daily
temperature; each coloured dot represents an individual climate model and the
black line plot represents the median of the seven GCM/RCM combinations.
Calibration and validation of hydrological model: GLUE analysis
The calibration was performed using the observed precipitation and
temperature from the Biala Tarnowska catchment and flow records from the
Koszyce gauging station for the period 1971–2000 for the calibration and
2001–2010 for the validation stage. We applied the JNSE
criterion (Eq. 1) for the high flow and the JlogNSE criterion
(Eq. 2) for the low flow to all the simulated flow series. The thresholds for
the criteria, called likelihood thresholds, were evaluated (Beven and Binley,
2014) by the “trial and error approach”. As a result, two multiple sets
(each including thousands of parameter sets) representing “high” and
“low” flow modes of the HBV model performance have been derived. The
threshold value of a goodness-of-fit criterion determining the GLUE-based
behavioural model parameter set for high-flow indices was selected at 0.55 of
the JNSE. The threshold value was selected to assure that
95 % of observations lay within the 0.95 confidence bands. The sample
size of this behavioural set is 8616. The maximum Nash–Sutcliffe efficiency
(JNSE) values over the calibration and validation periods are
0.79 and 0.75, respectively. The low-flow model parameter set was selected
using the NSE of log-transformed flow values (JlogNSE) with the
threshold set at 0.3 and the sample size obtained is 1625. The maximum
JlogNSE value in calibration and validation period is 0.6212 and
0.6995 respectively. The maximum JNSE value in calibration and
validation is 0.7827 and 0.8128 respectively.
The CDF of flow for the calibration period for the HBV model;
(a) presents model predictions conditioned on the JNSE,
while (b) presents the predictions conditioned on the
JlogNSE criterion; the CDFs of observations (red line) are shown
against the CDFs of the HBV predictions (blue line) and the associated
95 % confidence bounds (dashed line).
The HBV model extreme projections for the best HBV model parameter
sets for the Biala Tarnowska at Koszyce in 1971–2100 based on seven climate
models from the GCM/RCM ensemble; (a): projected annual maximum
daily flow for the HBV parameter set corresponding to the best
JNSE value; (b) projected annual minimum daily flow for
the HBV parameter set corresponding to the best JlogNSE value; the
red dashed line shows an ensemble mean for the 1971–2100 period.
Figure 3 shows the cumulative density functions (CDFs) of observed daily
hydrographs for the calibration and validation periods, as well as the CDFs of
flow estimates generated from the posterior distribution of the HBV model
parameters. The upper panel presents the CDF of model predictions conditioned
on the JNSE, while the lower panel presents the CDF of
predictions conditioned on the JlogNSE criterion. Also shown are
the 0.95 confidence bands in the form of dashed lines. These confidence bands
are much narrower for the JlogNSE weights than for the
JNSE conditioning. This indicates the strong influence of low-flow predictions on the HBV model performance. Moreover, the shape of the
CDFs suggests that the logarithmic transformation of flows gives a superior
match of simulations to the observations in comparison with the
JNSE criterion. In Fig. 4, the “best” annual extreme time
series of projected flow, corresponding to the deterministic “optimal”
parameter sets for the River Biala Tarnowska at Koszyce, are shown. The upper
panel of Fig. 4 presents annual maximum flows, and the annual minimum flows
are presented in the lower panel. These results were obtained from the HBV
model simulations fed by the precipitation and temperature projections
obtained from the seven GCMs/RCMs under the RCP4.5 scenario for the
parameter sets from the MC parameter samples giving the highest weights
derived from the JNSE for the high flows, and JlogNSE
for the low flows, respectively. The raw precipitation projections were
applied to study the high-flow index whilst bias-corrected precipitation data
were used for the low-flow index studies. Obtained flow projections, shown in
Fig. 4, follow the precipitation projections shown in Fig. 2, with annual
maximum flow values even 4 times larger than historical events occurring
after 2016 for some GCM/RCM projections. These time series cover the
whole length of the reference and projected years simulated (1971–2100) in
an attempt to identify temporal variability in the high- and low-flow indices.
Changes in extreme flow quantiles (30-year periods) due to the climate model spread
The empirical quantiles of the future annual maximum and minimum flow
projections for the 30-year periods, including the reference period
1971–2000, the near-future period 2021–2050 and the far-future period
2071–2100, are shown in Fig. 5. These results present the empirical frequency
curves obtained for the best performing hydrological model parameter set for
seven climate models listed in Table 1, neglecting the hydrological model
parameter uncertainty. These empirical quantiles are strongly controlled by
the extreme events, which may have the form of outliers (Fig. 5a). A
comparison of the median return periods obtained for the near and far future
with the median in the reference period illustrates the predicted changes in
quantiles. Small decreases in annual minimum flow and increases in annual
maximum flow for both near- and far-future periods can be observed. In the
case of maximum annual flow (Fig. 5a), the reference quantile curves (dashed
red lines) are always lower than those from the climate model ensemble
medians (dashed green lines), implying increases in both frequency and
magnitude of annual maximum flows. Following a similar reasoning it can be
deduced that the magnitudes of annual minimum flows show small decrease in
the future (Fig. 5b).
Empirical flow quantiles of annual maximum flow (a) and
annual minimum flow (b) and future climates (near and far future)
for the best sets of the HBV model parameters and seven GCM/RCM
realizations; the green dashed line denotes the mean value from all the GCM/RCM realizations in each period (near- and far-future period), the red dashed
line denotes the averaged results obtained for the reference period; each
black line represents an individual climate model.
The results for high-flow extremes are consistent with those published by
Osuch et al. (2016), which is not surprising when we note that the same
GCM/RCM projections were used for the study catchment. The decrease of annual
minimum flows in the future is also consistent with the results published by
Meresa et al. (2016). From Fig. 5a, upper panel, we note that the uncertainty
of the empirical high-flow quantile at 30-year return period (QT30)
related to the climate model spread exceeds 100 %
(600 m3 s-1) in the near future. In contrast, the spread of
QT30 of annual maximum flows in the far future decreases to
500 m3 s-1 (Fig. 5a, lower panel). Similarly, also the low-flow
QT30 shows smaller spread for the far-future period (Fig. 5b). The fact
that the spread is more evenly distributed for minimum flows compared to
maximum flows is related to the influence of the climate model spread on the
simulations. It shows that climate change extremes have larger influence on
flood frequency than on low-flow frequency. The smaller spread of the
far-future projected changes was also observed in the other climate impact
studies on the same catchment (Osuch et al., 2016) for both the RCP4.5 and
RCP8.5 emission scenarios using the HBV model. Research is ongoing to
explain that phenomenon.
It is important to note that 30-year-based quantiles are highly uncertain and
show unrealistic changes which are not visible in long annual extreme series.
Moreover, these changes in 30-year-based quantiles are caused by
inter-decadal variability and they depend on the starting year of those
30-year periods. This might explain large differences in the estimates of
future quantile changes obtained in a number of studies (Kundzewicz et al.,
2017).
Total uncertainty ranges of annual extreme flow quantiles based on
the GEV distribution for projections over 30-year periods for the Biala
Tarnowska at Koszyce; (a), (c) and (e) present the
annual maximum flow; (b), (d) and (f) show annual
minimum flow; (a, b) the reference period (1971–2000);
(c, d) near-future (2021–2050); and (e, f) far-future
(2071–2100) periods.
Evaluation of combined uncertainty in extreme flow quantiles for 30- and 130-year periods
The empirical frequency curves do not allow the extrapolation of a return
period beyond the available number of simulation years to be performed and
instead theoretical distributions fitted to the data are applied. In
addition, quantiles are nonlinearly dependent on flow extremes and
averaging of the best hydrological projections is not equivalent to averaging
over the whole set of realizations resulting from the behavioural parameter
sets. The results of fitting the GEV distribution to annual maximum and
minimum flow for 30-year periods, including the reference period
(1971–2000), the near-future period (2021–2050) and the far-future period
(2071–2100), are presented in Fig. 6. The blue and light pink areas in Fig. 6
present the uncertainty arising from the combined effect of the hydrological
model parameter uncertainty, ensemble spread and uncertainty related to the
GEV fitting, respectively, for the maximum annual flow (Fig. 6a, c, e) and the
minimum annual flow (Fig. 6b, d, f). The quantiles of annual maximum flow show
significant spread among the fitted GEV distributions, which is more
pronounced for higher recurrence intervals whilst the quantiles of minimum
annual flow are spread evenly. Comparison of empirical and theoretical
distribution-based flood frequency curves indicates that “outliers” (single
very high flow events) have smaller influence on the distribution-based than
on empirical flood frequency analyses (Figs. 5a, 6a, c, e).
Total uncertainty ranges of flow quantiles for the River Biala
Tarnowska at Koszyce based on the GEV distribution for projections over
130-year period (1971–2100): (a) annual maximum flow and
(b) annual minimum flow; the blue shaded area denotes the
climate model uncertainty, the green shaded area denotes the hydrological
model uncertainty, the pink shaded area denotes the distribution fit
uncertainty, red dotted lines denote the median of climate ensembles, black
dotted lines denote the median of hydrological model parameter sets and blue
dotted lines denote the median of the distribution fit.
Change in width of 0.95 confidence intervals for QT30 for
annual maximum and minimum flow estimated using time periods of a different
length (30-year and 130-year long).
The uncertainties originating in the climate models and the hydrological
model parameters were calculated based on a range of the differences between
the 0.975 upper confidence bands and 0.025 lower confidence bands as a
measure of the uncertainty in the ensemble projections that were made using
multiple GCMs/RCMs, hydrological model behavioural parameter sets and
distribution parameter sets (FFA). When comparing the total uncertainties, it
becomes clear that uncertainties from climate projections, hydrological model
parameter and distribution parameter sets cannot be independently assessed to
generate reliable predictive bounds for the estimates of hydrological
extremes and their characteristics.
Total variance in estimates for the percentage change in QT30
in 2021–2050 relative to the 1971–2000 reference period. Each colour
represents the relative contribution of uncertainty in percent; C denotes
climate model; D – distribution fit; P – hydrological model parameters;
ERROR denotes the Gaussian error (Eq. 3); and a “star” denotes the
correlation between the factors (C, D and P). Panel (a) presents high-flow results whilst panel (b) presents low-flow results.
Figure 7 presents integrated uncertainty of frequency curves of annual
maximum flow (panel a) and annual minimum flow (panel b), based on the
130 years (1971–2100) of MC simulations of the HBV model. Each shading
represents the contribution of a different uncertainty source (the colours
are additive). The green colour denotes the hydrological model uncertainty,
the blue corresponds to climate model spread and the pink colour describes
the GEV distribution fit error. The red dotted lines denote the median of
climate ensembles, black dotted lines denote the median of hydrological model
parameter sets and the blue dotted lines denote the median related to the GEV
distribution parameter fit. This kind of analysis does not illustrate the
interactions between different sources of uncertainty. Generally, the
uncertainty from climate models is larger than the other two for the high-flow quantiles. On the other hand, for the low-flow quantiles, hydrological
model parameter uncertainty contributes more than the other two sources to
the uncertainty of the minimum flow frequency.
The uncertainties of the quantiles of annual maximum flow due to total
uncertainty accounted for (climate models, parameter sets, distribution
fitting parameter sets) for the 30-year (Fig. 6) and 130-year (Fig. 7) periods
show significant differences. Table 3 gives a summary of confidence interval
ranges obtained for the QT30 based on different time periods. In
general, the QT30 estimated using the 30-year period is characterized by
a much larger confidence intervals compared to the QT30 estimated using
the 130-year period. The differences in the width of confidence
intervals vary from about 200 m3 s-1 for the reference period to
1500 m3 s-1 for the near-future period (2021–2050) compared to the
130-year period QT30 estimates. Due to the extrapolation errors, that
difference will increase substantially for the QT100 index, thus
questioning the usefulness of those estimates. The relative differences
obtained for the annual minimum flow QT30 estimates are smaller,
suggesting that low-flow quantiles are less susceptible to the errors related
to the length of the evaluation period.
The comparison of flood frequency curves obtained from 30- and 130-year series
of annual extremes is not possible. However, what we compare is the
uncertainty range of flow quantiles derived from 30-year-long and 130-year-long
annual extreme series. Such comparison is not related to non-stationary
condition of the extremes but rather to the number of events included in the
frequency derivation.
The results of the study show that the uncertainties in extreme maximum and
extreme minimum indices behave differently. In extreme high flow, larger
uncertainty is observed from the climate model (ensemble) spread than from
the other sources. In contrast, for low flows the uncertainty related to
hydrological model parameters has a larger impact than the other uncertainty
sources studied. The important role of hydrological model uncertainty in low-flow predictions has already been noticed in forecasting (Beninga et al.,
2017). That effect can be explained by the ratio of the prediction noise (in
this case described by the hydrological model uncertainty) to the input
signal which is much higher for low flows. Demirel et al. (2013b) explored
the influence of uncertainty in input, hydrological model parameters and
initial conditions on a 10-day ensemble flow forecasts. The results showed
that parameter uncertainty had the largest effect on the mean value low-flow
forecasts, which is consistent with the present paper findings. This implies
that ignoring one of the three uncertainty sources may cause great risk to
future hydrological extreme adaptations and water resource planning and
management. Steinschneider et al. (2012) used the formal statistical approach
to quantify uncertainty quantiles of monthly flow projections including
climate, hydrological model parameter and distribution fit uncertainties. In
this study we applied the non-formal statistical approach for projections of
daily annual extreme low- and high-flow indices.
Variance decomposition of quantile <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mi>T</mml:mi><mml:mn mathvariant="normal">30</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> values
Figure 8 shows the results of an application of the ANOVA variance
decomposition technique to the percentage change of QT30 quantiles
derived for the near-future period 2012–2050 relative to the reference
period 1971–2000 for high flows (panel a) and low flows (panel b).
The analysis was performed on the flow simulation sets including all three
sources of uncertainty and conditioned by the JNSE weights for
high-flow quantiles and JlogNSE weights for low-flow quantiles.
The symbols correspond to those used in Eq. (3). Correlation between
parameters is marked with a star.
The sensitivity analysis presented in Fig. 8 confirms our earlier results on
the major influence of the climate model spread on the total QT30
variability for high flows and supreme influence of hydrological model
parameters on the variability of low-flow QT30. There is also a
difference in the influence of distribution fit uncertainty, which is much
larger for low-flow QT30 variability than for high flow. The sensitivity
analysis also confirms the inter-dependence of different sources of
uncertainty, visible mainly for high-flow extremes.
Conclusions
The results of the research on the assessment of the uncertainty of extreme
hydrological indices can be summarized in the following points:
In order to eliminate influence of bias correction on flow maxima,
the analysis of changes in the quantiles of maximum annual flow projections
was based on the raw projections of precipitation. However, the analysis of
low-flow projections was based on the bias-corrected data to avoid the
drizzle effect which affects the low-flow characteristics.
Conditioning of the hydrological model was performed using different criteria
for low and high flows in order to ensure the best model fit for the
extremes. This does not solve the problem of the non-stationarity of model
parameters but permits a focus on parameter sets adequate for low- and high-flow regimes.
Analysis of the influence of the length of time series records on the
uncertainty bands of the low- and high-flow quantile estimates and their
changes suggests that the range of quantiles of return periods QT30 is
up to 4 times smaller when the long-term flow projections are used. The
low-flow QT30 quantiles are less influenced by the length of the record.
Taking into account the three uncertainty sources considered, the uncertainty
of the estimate of 1-in-100-year return maximum flow based on the 1971–2100
time series exceeds 200 % of its median value with the largest influence
of the climate model uncertainty, whilst the uncertainty of the 1-in-100-year
return minimum flow is of the same order (i.e. exceeds 200 %), but is
mainly influenced by the hydrological model parameter uncertainty.
A sensitivity analysis using ANOVA performed on the relative total
uncertainty for QT30 quantiles shows the largest influence of climate
model and interactions between climate model and distribution fit uncertainty
for high flows, whilst uncertainty of hydrological model parameters and
distribution fit have the largest influence on the uncertainty of low-flow
quantiles.
The analyses were performed for a catchment with stationary future
extreme flow projections; in the case of nonstationary extreme flows,
nonstationary frequency analysis would have to be applied with even larger
uncertainty of extreme estimates than those presented here.
The study has pointed to the need to explore different approaches to
projections of climate change.
The temperature and precipitation projections for the period 1970–2100 were obtained from the EUROCORDEX website (http://www.euro-cordex.net/), which provides regional climate projections for Europe at 50 km (EUR-44) and 12.5 km (EUR-11) resolution. Daily observations of precipitation and temperature for the Biala Tarnowska catchment and flow at Koszyce Wielkie gauging station were obtained from the Institute of Meteorology and Water Management (IMGW-PIB), Poland (http://www.imgw.pl)
Acknowledgements
This work was supported by the project CHIHE (Climate Change Impact on
Hydrological Extremes), carried out in the Institute of Geophysics Polish
Academy of Sciences, funded by Norway Grants
(contract no. Pol-Nor/196243/80/2013) and partly supported within statutory
activities no. 3841/E-41/S/2016 of the Ministry of Science and Higher
Education of Poland. The hydro-climate data were provided by the Institute of
Meteorology and Water Management (IMGW), Poland. Edited by: Jan
Seibert Reviewed by: two anonymous referees
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