Advertisement

Water Resources Management

, Volume 32, Issue 15, pp 4879–4893 | Cite as

Using Climate-Flood Links and CMIP5 Projections to Assess Flood Design Levels Under Climate Change Scenarios: A Case Study in Southern Brazil

  • Artur Tiago Silva
  • Maria Manuela Portela
Article
  • 95 Downloads

Abstract

The Intergovernmental Panel on Climate Change (IPCC) assessed with medium confidence that there has been an anthropogenic influence in the intensification of heavy rainfall at the global scale. Nevertheless, when taking into account gauge-based evidence, no clear climate-driven global change in the magnitude or frequency of floods has been identified in recent decades. This paper follows up on a previous nonstationary flood frequency analysis in the Itajaí River, which is located in the Southeastern South America region, where evidence of significant and complex relationships between El Niño-Southern Oscillation (ENSO) and hydrometeorological extremes has been found. The identified climate-flood link is further explored using sea surface temperature (SST) output from CMIP5 models under different representative concentration pathway (RCP) scenarios. Results are inconclusive as to whether it is possible to make a statement on scenario-forced climate change impacts on the flood regime of the Itajaí river basin. The overall outcome of the analysis is that, given that sample sizes are adequate, stationary models seem to be sufficiently robust for engineering design as they describe the variability of the hydrological processes over a large period, even if annual flood probabilities exhibit a strong year-to-year dependence on ENSO.

Keywords

Nonstationarity Flood frequency analysis Climate change Design life level CMIP5 

1 Introduction

The Intergovernmental Panel on Climate Change (IPCC), through its Special Report on Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation (SREX, Field et al. 2012) assessed that it is likely that there have been more statistically significant increases in extreme rainfall in more regions than there have been decreases. Furthermore there is a medium confidence that there has been an anthropogenic influence in the intensification of heavy rainfall at the global scale. Nevertheless, when taking into account gauge-based evidence, no climate-driven global change in the magnitude or frequency of floods has been identified in recent decades. Regarding this issue, the SREX report states: ‘overall, there is low confidence in projections of changes in fluvial floods. Confidence is low due to limited evidence and because the causes of regional changes are complex’.

In light of the conclusions of the IPCC SREX report, Kundzewicz et al. (2013) opt to take a cautionary stance and, rather than waiting for answers on the greenhouse-gas-forcing flood change issue, encourage ‘the continuation of empirical and model-based science and a “no regrets” strategy for limiting flood losses’.

In the technical literature, the projection of flood hazard under climate change scenarios usually takes the following model chain approach: “emission scenario → general circulation model (GCM) → downscaling → catchment model → flood frequency analysis” (e.g., Dankers Feyen 2009). These model chains have a complex and difficult implementation and their results are associated with high uncertainty (Merz et al. 2014). There are several sources of uncertainty in the model chain approach, one of the main ones being well-known shortcomings of all GCMs in simulating regional and local rainfall, due to the inadequate representation of small scale processes which are influenced by local orography and land surfaces which are not resolved at GCM scales (Hall et al. 2014). This can be improved with higher-resolution Regional Climate Models (e.g., Kendon et al. 2018), thereby potentially bypassing the downscaling step in the model chain.

Delgado et al. (2014) argue that, if a strong climate-flood link is identified, it can be used to directly project future flood changes using GCM output, and propose the shortened climate change model chain “emission scenario → general circulation model (GCM) → nonstationary flood frequency analysis”, thereby bypassing downscaling, rainfall, and catchment modeling. This approach was taken by, e.g., Condon et al. (2015). Merz et al. (2014) see great potential in this approach and single it out as one of the emerging perspectives for flood risk assessment and management, as its simplicity enables the rapid derivation of large ensembles of flood hazard projections as soon as new GCM output is made available.

In this article, the shortened model chain approach proposed by Delgado et al. (2014) is applied to exploit the link between the flood regime in the Itajaí-açu river, in Southern Brazil, and ENSO using sea surface temperature (SST) outputs from 34 atmosphere-ocean GCMs from the Coupled Model Intercomparison Project Phase 5 (CMIP5, Taylor et al. 2012), which is used in the Fifth IPCC Assessment Report (AR5), for the hypothetical design life 2016-2065 (50 years). For CMIP5, instead of emission scenarios, the IPCC adopted Representative Concentration Pathway (RCP) scenarios (Moss et al. 2010). This does not alter the above mentioned model chains except for changing their first element.

Notwithstanding the advantages of the selected model chain for projecting flood hazard under climate change, it should be noted that GCM limitations go well beyond rainfall simulation errors. In fact, even the recent generation CMIP5 GCMs still need further development in order to realistically simulate the most basic ENSO characteristics and other fundamental atmospheric processes (Guilyardi et al. 2012; Bellenger et al. 2013). Given these limitations, we are not yet at the stage where GCM output is the answer to bridge the major impediment to full applicability of nonstationary flood frequency models to engineering design, as discussed in Silva et al. (2016, 2017b): the nonexistence of climate covariate data long into the future. For that reason, the objective of this article is not an exploration of future dynamics of the flood regime in the study region. Rather, in agreement with suggestions of Serinaldi and Kilsby (2015) regarding the use of GCM experiments output in nonstationary flood frequency analysis, the objective here is to carry out a sensitivity analysis of a nonstationary flood frequency model under the understanding that GCM experiments output can provide a somewhat reasonable hypothetical evolution of a climate index under a certain scenario.

2 Data and Methods

2.1 Nonstationarity of Floods in the Itajaí-açu River

The Itajaí-açu River drains to the South Atlantic ocean (Fig. 1) and its basin’s topography features steep mountains at the South, West and Northwest of the valley and plains at the Northeast (Muñoz and de Morisson Valeriano 2013). The basin has a history of devastating floods due to frequent extreme rainfall events, and the river’s lower reaches are prone to flooding (Martins and Clarke 1993). A particularly devastating flood occurred on July 1983, during a strong El-Niño event (Martins and Clarke 1993; Silva et al. 2016), causing extensive damage to the city of Blumenau (US$ 1.1 × 109) (Tachini 2010) and 49 deaths across the basin (Xavier et al. 2014).
Fig. 1

Itajaí River basin. Location of the utilized gauging station and existing flood control reservoirs (adapted from Silva et al. 2017b)

Silva et al. (2017b) applied a nonstationary flood frequency analysis, using Poisson-Generalized Pareto (GP) models under a peaks-over-threshold approach and a Bayesian inferential paradigm, to study the influence of ENSO on the flood regime in the Itajaí-açu River. Poisson-GP models assume that the annual exceedance counts follow a Poisson distribution while the flood exceedance magnitudes follow a GP distribution. The CDF of the Poisson-GP model is given by
$$ F(x)= \exp\left\lbrace-\lambda\left[1-\kappa\left( \frac{x-u_{0}}{\sigma}\right)\right]^{\frac{1}{\kappa}}\right\rbrace , \kappa \ne 0 , x>u_{0} $$
(1)
where λ, σ and κ are, respectively the Poisson, scale and shape parameters, and u0 is the selected threshold (in this case, m3/s, Silva et al. 2016).

The streamflow data used in this study were collected by the Brazilian National Water Agency, ANA (http://hidroweb.ana.gov.br). The climate covariate used in this analysis, N34, is the Niño 3.4 December-through-February (DJF) mean SST anomaly. The Niño 3.4 region is a rectangular area in the Equatorial Pacific defined from 5S-5N and 170W-120W. Historical data of this climate index was obtained from the HadISST1 database by Rayner (2003, http://www.esrl.noaa.gov/psd/gcos_wgsp/Timeseries/Data/nino34.long.data).

Exploratory data analyses detailed in Silva et al. (2016, 2017b), suggested that the Poisson and GP scale parameters follow a quadratic and cubic polynomial relationship with the N34 covariate, respectively. Accordingly those authors posited the candidate models presented in Table 1.
Table 1

Dependence functions of the Poisson and GP scale parameters of the over-threshold occurrence counts and peak magnitudes models

Model

Dependence structure

Stationary Poisson

\(\lambda \left (\mathbf {c}\right )=\lambda _{0}\)

Nonstationary Poisson

\(\lambda \left (\mathbf {c}\right )=\lambda _{0} + \lambda _{1} \mathrm {N34} + \lambda _{2} \mathrm {N34}^{2} \)

Stationary GP

\(\sigma \left (\mathbf {c}\right )=\sigma _{0}\)

Nonstationary GP

\(\sigma \left (\mathbf {c}\right )=\sigma _{0} + \sigma _{1} \mathrm {N34} + \sigma _{2} \mathrm {N34}^{2} + \sigma _{3} \mathrm {N34}^{3}\)

Using Bayesian model selection tools, such as Bayes factors and Deviance Information Criterion (DIC), Silva et al. (2017b) found strong evidence against the stationarity assumption in favor of the nonstationary candidates in Table 1. DIC is a Bayesian alternative to AIC in the sense that models with a lower DIC score are favored. Bayes factors, Bi,j, can be seen as a Bayesian alternative to likelihood ratio tests as they assess the plausibility of two different models \(\mathcal {M}_{i}\) and \(\mathcal {M}_{j}\). According to Davison (2003, p. 583) a value of 2log Bi,j > 10 indicates that there is very strong evidence against \(\mathcal {M}_{j}\) in favour of \(\mathcal {M}_{i}\). Table 2 shows the results pertaining to Bayes factors and DIC, and Fig. 2 shows the observed annual maxima and the quantile functions of both the stationary (Poisson + GP) and Nonstationary (NS Poisson + NS GP) models.
Table 2

POT models: statistics of the parameters’ posterior distribution; Bayes factors; DIC

Model

Parameter

Posterior distribution

\(2\log B_{i0}\)

DIC

  

Mode

MCMC mean (st. dev.)

  

Poisson

\(\lambda _{0}\)

3.513

3.524 (0.213)

0.000

344.021

NS Poisson

\(\lambda _{0}\)

2.933

2.948 (0.249)

14.036

331.630

 

\(\lambda _{1}\)

0.253

0.256 (0.254)

  
 

\(\lambda _{2}\)

0.693

0.721 (0.217)

  

GP

\(\sigma _{0}\)

445.751

448.861 (38.346)

0.000

4056.595

 

\(\kappa \)

-0.086

-0.093 (0.058)

  

NS GP

\(\sigma _{0}\)

455.166

460.180 (46.404)

43.331

4052.697

 

\(\sigma _{1}\)

-134.568

-138.348 (63.410)

  
 

\(\sigma _{2}\)

-12.615

-2.942 (27.337)

  
 

\(\sigma _{3}\)

59.041

59.882 (24.335)

  
 

\(\kappa \)

-0.035

-0.040 (0.059)

  

* Mean and standard deviation of the distribution on the log scale

Fig. 2

Annual maximum series (AMS) sample. Stationary model (left): posterior predictive (continuous line) and parameter mode distributions and 95% credibility intervals. Nonstationary model (right): posterior predictive (continuous lines), parameter mode (dashed lines) and 95% credibility intervals (dotted lines) for 2 nonexceedance probabilities as functions of N34. The darkness of the shadings is proportional to the pointwise posterior density of the corresponding quantiles (adapted from Silva et al. 2017b)

The calculations of Bayes factors and DIC in Table 2 required the use of a Markov chain Monte Carlo (MCMC) algorithm to generate a large sample (Nsim = 10000) from the posterior parameter distribution. A more detailed treatment of the application of Bayesian technique to this case study is provided in Silva et al. (2017b). Paulino et al. (2003) and Robert (2007) provide a general overview of Bayesian statistics.

2.2 Analysis Setup

2.2.1 Prediction

The Bayesian posterior predictive distribution of future events, W, is integrated over all possible posterior realizations of the parameter vector, 𝜃 , thereby allowing the integration of the natural variability and sampling uncertainty in a single flood hazard estimation (Merz and Thieken 2005). The predictive density is defined by
$$ g(w|\mathbf{x})={\int}_{\Theta} g(w|\boldsymbol{\theta})\pi(\boldsymbol{\theta}|\mathbf{x}) d\boldsymbol{\theta} $$
(2)
where g(w|𝜃) is the probability density function of future events, x is the sample and π(𝜃|x) is the posterior parameter density.
Silva et al. (2017b) combined this concept with that of the flood hazard measure proposed by Rootzėn and Katz (2013) termed ‘design life level’ (DLL), which is defined as the flood level or flow with a probability p of being exceeded over a design life period T1 : T2. The approximation of the posterior predictive distribution of the DLL, using Nsim MCMC output simulations is
$$ \hat{F}_{T_{1}:T_{2}}(w|\mathbf{x})=\frac{1}{N_{sim}} \sum\limits_{i = 1}^{N_{sim}} \prod\limits_{t=T_{1}}^{T_{2}} F_{t}(w|\boldsymbol{\theta}_{i}) $$
(3)
where Ft(⋅) is the CDF of annual maximum floods at year t. The application of this flood hazard measure under nonstationarity is dependent on the availability of covariate data during the design life period. In this work, CMIP5 output is used to obtain several possible realizations of the climate covariate in the design life period of 2016:2065.

2.2.2 CMIP5 Data

Projections of monthly SST averaged over the Niño 3.4 region under climate change scenarios were obtained from output data from CMIP5 experiments with models forced by RCP scenarios. CMIP5 experiment data were obtained from the KNMI Climate Explorer database (Trouet and van Oldenborgh 2013, https://climexp.knmi.nl/). Four RCP scenarios were considered: RCP2.6, RCP4.5, RCP6 and RCP8.5. RCPs are labeled according to a rough estimate of the radiative forcing in the year 2100, relative to preindustrial conditions. The high emission RCP8.5 indicates an increase in radiative forcing throughout the 21st century before reaching 8.5 W m− 2 by the end of the century; there are two intermedyiate scenarios, RCP4.5 and RCP6; and a low scenario in which radiative forcing peaks at the middle of the 21st century and decay to 2.6 W m− 2 by 2100. Hence, RCPs can be interpreted as incrementally low to high greenhouse gas concentration pathway scenarios in the order RCP2.6→RCP4.5→RCP6→RCP8.5. van Vuuren et al. (2011) provide a detailed overview of the development and main characteristics of the RCP scenarios.

Table 3 lists the institutions and names of the CMIP5 experiments considered in this study, along with the number of realizations or runs by each experiment for each RCP scenario. Some experiments have more than one realization per scenario, in which case the distinction between realizations is due to initializing RCP forcing from historical GCM runs with different, but equally realistic, starting conditions (i.e., initializing from different times of a control run) or they might be produced by different “perturbed physics” versions of the same model (Taylor et al. 2011).
Table 3

CMIP5 experiments considered for analysis and corresponding number of realizations per RCP scenario

Institute

Experiment

Number of realizations per scenario

  

RCP2.6

RCP4.5

RCP6

RCP8.5

CSIRO-BOM

ACCESS1-0 *

0

1

0

1

ACCESS1-3 *

0

1

0

1

 

BCC

BCC-CSM1-1

1

1

0

1

 

BCC-CSM1-1-M

1

1

1

0

CCCMA

CanESM2

5

4

0

5

RSMAS

CCSM4

6

6

6

6

NSF-DOE-NCAR

CESM1-BGC

0

1

0

1

 

CESM1-CAM5

3

3

3

2

CCMC

CMCC-CM *

0

1

0

1

 

CMCC-CMS *

0

1

0

1

CNRM-CERFACS

CNRM-CM5 *

1

1

0

5

CSIRO-QCCCE

CSIRO-Mk3-6-0

10

10

10

10

EC-EARTH

EC-EARTH

1

6

0

6

FIO

FIO-ESM

3

3

3

3

NOAA GFDL

GFDL-CM3

1

3

1

1

 

GFDL-ESM2G *

1

1

1

1

 

GFDL-ESM2M

1

1

1

1

NASA GISS

GISS-E2-H

3

15

3

3

 

GISS-E2-H-CC *

0

1

0

0

 

GISS-E2-R

3

17

3

3

 

GISS-E2-R-CC

0

1

0

0

MOHC

HadGEM2-AO *

1

0

1

0

 

HadGEM2-CC *

0

1

0

1

 

HadGEM2-ES *

4

4

3

3

INM

INMCM4

0

1

0

1

IPSL

IPSL-CM5A-LR

4

4

1

4

 

IPSL-CM5A-MR *

1

1

0

1

 

IPSL-CM5B-LR *

0

1

0

1

MIROC

MIROC5 *

3

3

3

3

MPI-M

MPI-ESM-LR *

3

3

0

3

 

MPI-ESM-MR

1

3

0

1

MRI

MRI-CGCM3

0

1

1

1

NCC

NorESM1-M

0

1

1

1

 

NorESM1-ME *

0

1

1

1

* Null hypothesis of the Brown-Forsythe test was not rejected (Section 2.2.4)

2.2.3 Defining N34 (DJF) Under Climate Change Scenarios

The N34 covariate was calculated from centered monthly Niño 3.4 SST of the HadISST1 database by subtracting each month’s long-term mean SST, monthwise, and annually averaging the december-through-February SST anomaly. A preliminary analysis of the CMIP5 data under RCP forcing revealed that the same approach was not feasible for calculating projections of the N34 covariate. This is due to an evident warming of Equatorial Pacific SSTs in the 21st century in all RCP scenarios. Figure 3 illustrates this warming trend in December SST, relative to HadISST1 data, for a particular run (labeled ‘r2i1p1’) of the HadGEM2-ES experiment. The warming is particularly evident after RCP forcing kicks in, in 2006. Results for other months are very similar. If the ocean is increasingly warmer than the long-term average, then the N34 covariate would appear to be a permanent El Niño state (i.e., a warm anomaly).
Fig. 3

December SST in the Niño 3.4 region according to the HadISST1 dataset and one CMIP5 experiment run

To deal with the upward trend in mean SST under RCP forcing, the data were detrended using the methodology described by Lindsey R (2013), which is employed by the United States National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center: each 5-year period uses a 30-year average centered on the first year in the period. For example, the 2006-2010 period is compared to the 1991-2021 average, and so on.

2.2.4 GCM Selection

After calculating the N34 covariate from CMIP5 data using the procedure described in Section 2.2.3, a preliminary analysis of the resulting N34 time series revealed that some of the models did not adequately simulate the variance of the covariate: while some GCMs produced N34 time series with a very low variance, resulting in mostly ENSO-neutral years, others produced N34 realizations with a very high variance, characterized by an exaggerated proportion of strong El Niño/La Niña events, relative to the observed N34 regime from the HadISST1 dataset, particularly during the flood model estimation period (hydrologic years, starting on 1 October, from 1934/35 to 2013/14). This is illustrated in Fig. 4, where the observed N34 series can be compared to CMIP5 model runs with very low (Fig. 4b) and very high (Fig. 4c) variance.
Fig. 4

N34 time series obtained from the HadSST1 dataset (a) and from two CMIP5 experiments (b and c)

In light of the aforementioned limitations in preserving N34 variance from some GCMs, not all of the experiments listed in Table 3 were used in the analysis. A statistical test was employed to identify the experiments whose N34 variance was significantly different from the HadISST1 data, which were not considered. The utilized statistical test was the modified robust Brown-Forsythe Levene-type test based on absolute deviations from the median, which is implemented in the function levene.test() of the lawstat package (Hui et al. 2008) in R (R Core Team 2013). Given k random samples with variances \({\sigma _{i}^{2}}\), i = 1,2,...,k, the null hypothesis of the Brown-Forsythe test considers that all variances are equal, \(H_{0}:{\sigma _{1}^{2}}={\sigma _{2}^{2}}=...={\sigma _{k}^{2}} \) vs. the alternative hypothesis \(H_{1}:{\sigma _{i}^{2}}{\ne \sigma _{j}^{2}}\) for at least one ij (Brown and Forsythe 1974).

The samples used for the Brown-Forsythe test correspond to the subsets of the HadISST1 and CMIP5 model realizations spanning from 1970/71 to 2005/06, when the RCP forcing of the GCMs starts. In a similar approach to that of Delgado et al. (2014), the N34 time series were pooled so that for each pool there was a set of time series that were derived from the same experiment. Rejection of the null hypothesis implied that the pool being tested was excluded from the analysis. This way, entire experiments were excluded instead of individual realizations, thereby preserving the variability of different runs within the same experiment. The significance level used was 5%. The experiments for which the null hypothesis was not rejected are marked with an asterisk in Table 3. Table 4 shows the number of remaining GCM runs per scenario after dismissing the excluded experiments.
Table 4

Number of collected CMIP5 experiment runs and remaining number of runs after selection criteria were applied

 

RCP2.6

RCP4.5

RCP6

RCP8.5

Total

All

57

103

43

73

276

After Brown-Forsythe test

14

21

9

23

67

After dismissing runs with N34 values exceeding the limits defined in Fig. 5 during the design life

8

13

4

14

39

Upon further analysis of the N34 time series produced by the GCMs which were not rejected by the test of equal variances, it was found that many of them had N34 values well outside the range of the observed series in the period used for estimating the nonstationary model. Some model runs produced occurrences of N34 values larger than 3 and/or lower than -3, while the range of values used in estimation is [− 1.835,2.392]. While the plausibility of the occurrence of such anomalies is not disputed, the fact remains that, as with any regression model, using nonstationary models to predict flood probabilities outside the range of the observed covariate values bears careful consideration since it requires extrapolation beyond the observed data. This is even more relevant for models such as nonstationary, where a cubic polynomial link on the scale parameter of the generalized Pareto (GP) distribution implies a steep decrease and increase of flood quantiles near the lower and upper boundaries of the covariate, respectively, as illustrate in Fig. 5 for F = 0.75. However, this is not to say that a slightly larger value than the observed maximum (e.g. N34 = 2.4) cannot be reasonably taken into account. To deal with that situation, an admitted range of N34 values was defined by adding 10% of the observed range on either side (Fig. 5). N34 series produced by GCM runs with values outside of that range were dismissed from further analysis. Table 4 shows the remaining number of runs after this selection criterion was employed.
Fig. 5

Admitted range of GCM realizations of the N34 covariate during the design life, which is equal to observed range increased by 10% on either side. Annual maximum floods at Apiúna plotted against N34

3 Results

The predictive distributions of the design life level (DLL) were computed using GCM output data from the experiments selected in Section 2.2.4 and the nonstationary model posterior parameter MCMC samples obtained using the methodology described in Silva et al. (2017b). A design life of 50 years was considered, starting on the hydrologic year 2016/17.

Figure 6 shows individual CMIP5 predictive DLL estimates organized by RCP scenario as well as the DLL of the stationary model for a design life of 50 years. For each scenario, the DLL curves show a range of results that both increase and decrease flood hazard estimates relative to the stationary model. However there is no consistent upward or downward shift according to increasing greenhouse gas pathway forcings, via the RCP scenarios, i.e., apart from a single estimate that is a clear outlier (in RCP8.5), there is no clear difference between the range of results of scenarios RCP2.6 through RCP8.5. Figure 7 shows the DDL estimates based on 4 runs of a particular model, HadGEM2-ES, under the RCP4.5 forcing scenario. These results show how the same climate model, under the same forcing, but spawned from 4 members of a historical ensemble with different initial states, can result in discernably different climate-informed flood design values.
Fig. 6

DLL for the life period 2016/17-2065/66 (50 years) for the stationary and nonstationary models with the climate covariate calculated from CMIP5 model output under the representative concentration pathway (RCP) scenarios

Fig. 7

DLL for the life period 2016/17-2065/66 (50 years) for the stationary and nonstationary models with the climate covariate calculated from the output of 4 runs of the HadGEM2-ES model under the representative concentration pathway scenario RCP4.5

Figure 8 shows the CMIP5 ensemble mean DLL estimates for each RCP scenario, which are obtained by averaging the predictive DLL probabilities for each flood quantile, together with the DLL of the stationary model. It is apparent that, although the results of Fig. 6 show both positive and negative changes in flood hazard estimate relative to the stationary model, the ensemble mean results under either scenario are not much different from the stationary model results.
Fig. 8

Scenario-wise ensemble mean DLL for the life period 2016/17-2065/66 (50 years) for the stationary and nonstationary models with the climate covariate calculated from CMIP5 model output under the representative concentration pathway (RCP) scenarios

The above results diverge from global flood risk projections under climate change undertaken by Hirabayashi et al. (2013), using output from 11 CMIP5 model and a global river routing model. For the RCP8.5 scenario, those authors project an increase in flood hazard characterized by a multimodel median return period of 5-25 years in the 21st century, of the discharge of the 100-year flood in the 20th century, in the Southeastern South American region.

4 Conclusions

Given the practical results relevant to the case study at hand, we conclude that, to date, it remains impossible to make a statement on scenario-forced climate change impacts on the Itajaí river basin with any reliable statistical significance, since, for the 2016/17-2065/66 design life, the predictive DLL estimates of the nonstationary model do not differ greatly between different scenarios. Furthermore, the ensemble mean results are not clearly different from the results of the stationary model for a design life of 50 years. This suggests that, unless future climatic fluctuations are significantly different from those observed in recent decades and from the CMIP5 model outputs used in the analysis, the stationary model is sufficiently robust for engineering design as it describes the variability of the process over a large period, even if annual flood probabilities exhibit a strong year-to-year dependence on ENSO. Nothwithstanding the local trait of this case study, these conclusions may be extended to similar analyses carried out in other regions of the Globe where the flood regime displays a sensitivity to ENSO. Using data global peak discharge data from 1958–2000, Ward et al. (2014) found that the flood regimes of river basins covering over one third of the world’s land surface, were sensitive to ENSO phase.

It is important to acknowledge the many drawbacks faced during the analysis presented in this article, from the reports in the technical literature of the ineptitude of CMIP5-generation GCMs in reproducing basic characteristics of the ENSO phenomenon, cited in Section 1, to the exclusion of the vast majority of GCM realizations of the N34 covariate by considering two reasonable and prudent selection criteria. This justifies the interpretation of results with some degree of skepticism. Nevertheless, the CMIP5 models used here are the current state-of-the-art GCMs adopted by the IPCC and their results, despite the inherent uncertainties, are used by policy makers to develop adaptation options to climate change. Therefore, even under the assumption that the N34 series obtained from CMIP5 outputs do represent possible future realizations of the climate covariate, it is reasonable to conclude that the results presented here do not provide evidence supporting a clear advantage of nonstationary flood models, over stationary ones, for engineering design purposes.

To conclude, we stress that the analysis presented in this article is inherently dependent upon the ability of current generation GCMs to simulate ENSO. In that regard, it is worthwhile to mention an assertion made by Bellenger et al. (2013) on CMIP5 and ENSO: many CMIP5 models are simulating more processes than they did in CMIP3 (the preceding generation of GCMs), which, by adding degrees of freedom to the models, make simulating Earth’s climate more challenging. Those authors comment that, since ENSO properties in CMIP5 are not degraded with respect to CMIP3, there is added confidence for future improvements on the climate modeling enterprise. Therefore, it would be worthy to repeat this analysis when the next-generation GCMs are made available.

Notes

Acknowledgments

A previous shorter version of the paper (Silva et al. 2017a) has been presented in the 10th World Congress of EWRA “Panta Rhei” Athens, Greece, 5–9 July 2017. The authors thank the guest editor and two anonymous reviewers for their valuable comments and suggestions.

Compliance with Ethical Standards

Conflict of interests statement

None.

References

  1. Bellenger H, Guilyardi E, Leloup J, Lengaigne M, Vialard J (2013) ENSO representation in climate models: from CMIP3 to CMIP5. Clim Dyn 42(7-8):1999–2018.  https://doi.org/10.1007/s00382-013-1783-z CrossRefGoogle Scholar
  2. Brown MB, Forsythe AB (1974) Robust tests for the equality of variances. J Am Stat Assoc 69(346):364–367.  https://doi.org/10.1080/01621459.1974.10482955 CrossRefGoogle Scholar
  3. Condon LE, Gangopadhyay S, Pruitt T (2015) Climate change and non-stationary flood risk for the upper truckee river basin. Hydrology and Earth System Sciences 19(1):159–175.  https://doi.org/10.5194/hess-19-159-2015, https://www.hydrol-earth-syst-sci.net/19/159/2015/ CrossRefGoogle Scholar
  4. Dankers R, Feyen L (2009) Flood hazard in Europe in an ensemble of regional climate scenarios. J Geophys Res 114(D16).  https://doi.org/10.1029/2008jd011523
  5. Davison AC (2003) Statistical models. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  6. Delgado JM, Merz B, Apel H (2014) Projecting flood hazard under climate change: an alternative approach to model chains. Nat Hazards Earth Syst Sci 14(6):1579–1589.  https://doi.org/10.5194/nhess-14-1579-2014 CrossRefGoogle Scholar
  7. Field C, Barros V, Stocker T (2012) Managing the risks of extreme events and disasters to advance climate change adaptation. Special report of the intergovernmental panel on climate change (ipcc). Technical report, Intergovernmental Panel on Climate Change. Cambridge University Press, GenevaGoogle Scholar
  8. Guilyardi E, Bellenger H, Collins M, Ferrett S, Cai W, Wittenberg A (2012) A first look at enso in cmip5. Clivar Exchanges 17(1):29–32Google Scholar
  9. Hall J, Arheimer B, Borga M, Brázdil R, Claps P, Kiss A, Kjeldsen TR, Kriauciuniene J, Kundzewicz ZW, Lang M, Llasat MC, Macdonald N, McIntyre N, Mediero L, Merz B, Merz R, Molnar P, Montanari A, Neuhold C, Parajka J, Perdigão RAP, Plavcová L, Rogger M, Salinas JL, Sauquet E, Schär C, Szolgay J, Viglione A, Blöschl G (2014) Understanding flood regime changes in Europe: a state-of-the-art assessment. Hydrol Earth Syst Sci 18(7):2735–2772.  https://doi.org/10.5194/hess-18-2735-2014, https://www.hydrol-earth-syst-sci.net/18/2735/2014/ CrossRefGoogle Scholar
  10. Hirabayashi Y, Mahendran R, Koirala S, Konoshima L, Yamazaki D, Watanabe S, Kim H, Kanae S (2013) Global flood risk under climate change. Nat Clim Chang 3(9):816CrossRefGoogle Scholar
  11. Hui W, Gel YR, Gastwirth JL et al (2008) lawstat: an R package for law, public policy and biostatistics. J Stat Softw 28:1–26CrossRefGoogle Scholar
  12. Kendon EJ, Blenkinsop S, Fowler HJ (2018) When will we detect changes in short-duration precipitation extremes? J Clim 31(7):2945–2964CrossRefGoogle Scholar
  13. Kundzewicz ZW, Kanae S, Seneviratne SI, Handmer J, Nicholls N, Peduzzi P, Mechler R, Bouwer LM, Arnell N, Mach K, Muir-Wood R, Brakenridge GR, Kron W, Benito G, Honda Y, Takahashi K, Sherstyukov B (2013) Flood risk and climate change: global and regional perspectives. Hydrol Sci J 59(1):1–28.  https://doi.org/10.1080/02626667.2013.857411 CrossRefGoogle Scholar
  14. Lindsey R (2013) In Watching for El Niño and La Niña, NOAA Adapts to Global Warming. https://www.climate.gov/news-features/understanding-climate/watching-el-ni Accessed 14 Jan 2016
  15. Martins ESP, Clarke RT (1993) Likelihood-based confidence intervals for estimating floods with given return periods. J Hydrol 147 (1-4):61–81.  https://doi.org/10.1016/0022-1694(93)90075-k CrossRefGoogle Scholar
  16. Merz B, Thieken AH (2005) Separating natural and epistemic uncertainty in flood frequency analysis. J Hydrol 309(1-4):114–132.  https://doi.org/10.1016/j.jhydrol.2004.11.015 CrossRefGoogle Scholar
  17. Merz B, Aerts J, Arnbjerg-Nielsen K, Baldi M, Becker A, Bichet A, Blöschl G, Bouwer LM, Brauer A, Cioffi F, Delgado JM, Gocht M, Guzzetti F, Harrigan S, Hirschboeck K, Kilsby C, Kron W, Kwon HH, Lall U, Merz R, Nissen K, Salvatti P, Swierczynski T, Ulbrich U, Viglione A, Ward PJ, Weiler M, Wilhelm B, Nied M (2014) Floods and climate: emerging perspectives for flood risk assessment and management. Nat Hazards Earth Syst Sci 14(7):1921–1942.  https://doi.org/10.5194/nhess-14-1921-2014 CrossRefGoogle Scholar
  18. Moss RH, Edmonds JA, Hibbard KA, Manning MR, Rose SK, van Vuuren DP, Carter TR, Emori S, Kainuma M, Kram T, Meehl GA, Mitchell JFB, Nakicenovic N, Riahi K, Smith SJ, Stouffer RJ, Thomson AM, Weyant JP, Wilbanks TJ (2010) The next generation of scenarios for climate change research and assessment. Nature 463(7282):747–756.  https://doi.org/10.1038/nature08823 CrossRefGoogle Scholar
  19. Muñoz VA, de Morisson Valeriano M (2013) Mapping of flood-plain by processing of elevation data from remote sensing. In: Mathematics of planet earth. Springer, pp 481–484.  https://doi.org/10.1007/978-3-642-32408-6_106
  20. Paulino CDM, Turkman MAA, Murteira B (2003) Estatística Bayesiana. Fundação Calouste GulbenkianGoogle Scholar
  21. R Core Team (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/
  22. Rayner NA (2003) Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century. J Geophys Res 108(D14).  https://doi.org/10.1029/2002jd002670
  23. Robert C (2007) The Bayesian choice: from decision-theoretic foundations to computational implementation, 2nd edn. Springer Texts in Statistics, SpringerGoogle Scholar
  24. Rootzėn H, Katz RW (2013) Design life level: quantifying risk in a changing climate. Water Resour Res 49(9):5964–5972.  https://doi.org/10.1002/wrcr.20425 CrossRefGoogle Scholar
  25. Serinaldi F, Kilsby CG (2015) Stationarity is undead: uncertainty dominates the distribution of extremes. Adv Water Resour 77:17–36.  https://doi.org/10.1016/j.advwatres.2014.12.013 CrossRefGoogle Scholar
  26. Silva AT, Naghettini M, Portela MM (2016) On some aspects of peaks-over-threshold modeling of floods under nonstationarity using climate covariates. Stoch Env Res Risk A 30(1):207–224.  https://doi.org/10.1007/s00477-015-1072-y CrossRefGoogle Scholar
  27. Silva AT, Portela MM, Naghettini M (2017a) On the use of climate-flood links and CMIP5 projections to predict flood hazard under climate change scenarios. In: 10th world congress on water resources and the environment, EWRA 2017Google Scholar
  28. Silva AT, Portela MM, Naghettini M, Fernandes W (2017b) A bayesian peaks-over-threshold analysis of floods in the itajaí-açu river under stationarity and nonstationarity, vol 31.  https://doi.org/10.1007/s00477-015-1184-4
  29. Tachini M (2010) Avaliação de danos associados às inundações no município de blumenau. PhD thesis, Universidade Federal de Santa CatarinaGoogle Scholar
  30. Taylor KE, Balaji V, Hankin S, Juckes M, Lawrence B, Pascoe S (2011) CMIP5 data reference syntax (drs) and controlled vocabulariesGoogle Scholar
  31. Taylor KE, Stouffer RJ, Meehl GA (2012) An overview of CMIP5 and the experiment design. Bull Amer Meteor Soc 93(4):485–498.  https://doi.org/10.1175/bams-d-11-00094.1 CrossRefGoogle Scholar
  32. Trouet V, van Oldenborgh GJ (2013) KNMI climate explorer: a web-based research tool for high-resolution paleoclimatology. Tree-Ring Res 69(1):3–13.  https://doi.org/10.3959/1536-1098-69.1.3 CrossRefGoogle Scholar
  33. van Vuuren DP, Edmonds J, Kainuma M, Riahi K, Thomson A, Hibbard K, Hurtt GC, Kram T, Krey V, Lamarque JF, Masui T, Meinshausen M, Nakicenovic N, Smith SJ, Rose SK (2011) The representative concentration pathways: an overview. Clim Chang 109(1-2):5–31.  https://doi.org/10.1007/s10584-011-0148-z CrossRefGoogle Scholar
  34. Ward PJ, Eisner S, Flörke M, Dettinger MD, Kummu M (2014) Annual flood sensitivities to El Niño–Southern Oscillation at the global scale. Hydrol Earth Syst Sci 18(1):47–66.  https://doi.org/10.5194/hess-18-47-2014 CrossRefGoogle Scholar
  35. Xavier DR, Barcellos C, de Freitas CM (2014) Eventos climáticos extremos e consequências sobre a saúde: o desastre de 2008 em santa catarina segundo diferentes fontes de informação. Ambient soc 17(4):273–294.  https://doi.org/10.1590/1809-4422asoc1119v1742014 CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.CEris, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal

Personalised recommendations