Julien Chevallier
email: julien.chevallier@ipag.fr

Khuong Duc

Nguyen
email: duc.nguyen@ipag.fr

Juan Carlos Reboredo
email: juancarlos.reboredo@usc.es

A Conditional Dependence Approach to CO 2 -Energy Price Relationships

Keywords: JEL Classification: C44, L94, Q40 carbon price, energy markets, fuel-switching, vine copula

This paper uses the conditional vine copula approach to model the dependence structure between European-based carbon allowances and major energy prices. It makes two central contributions to the related literature. First, we extend the previous works of Reboredo (2013, 2014) by allowing for complete coverage of energy markets including natural gas, coal, and electricity, beyond the carbon-oil dependencies. Second, we simultaneously investigate the multivariate dependence among all variables in the system so that each of them can interact with the others based on a rich variety of bivariate copula functions. The consideration of the electricity market in this context offers the possibility to gauge its influences through the computation of the fuel-switching mechanism. We mainly find that there is a reliable and positive link between coal and gas prices, and between coal and oil prices, with or without the presence of electricity prices, while a weak and positive link is detected between Brent and gas prices. Carbon prices co-move only weakly with energy prices, and their link to oil and gas prices is negative. Moreover, the switch from coal to gas does not occur when the relative price of fuels taking into account carbon costs is assessed. This happens because the fuel-switching mechanism is still more costly than carbon abatement. Our findings remain intact when alternative electricity prices are used.

Introduction

Establishing the stochastic relationships intertwined in carbon and energy markets remains a challenging task as far as it is related to the climate change targets of carbon emission reductions, carbon efficiency of power generation, transition to renewable energy, and optimal energy investments (e.g., [START_REF] Ding | Carbon-efficient scheduling of flow shops by multi-objective optimization[END_REF][START_REF] Bonneuil | Optimal transition to renewable energy with threshold of irreversible pollution[END_REF]Zhang and Chen, 2017). Previous contributions in the field, notably [START_REF] Aatola | Price determination in the EU ETS market: theory and econometric analysis with market fundamentals[END_REF], have generally discovered a strong link between the fundamentals (i.e., electricity, gas and coal prices) and the price of European Union Allowances (EUA). More importantly, the EUA forward prices tend to fluctuate closely with fundamentals, particularly with the price of electricity and also the gas-coal difference. [START_REF] Hammoudeh | What explain the short-term dynamics of the prices of CO 2 emissions?[END_REF] have taken a closer look at the short-run dynamics by using a Bayesian Structural VAR. Their structural model allows us to identify that a positive shock affecting crude oil prices generates an initial positive impact on the CO 2 allowance prices. Regarding gas and coal, an unexpected increase in the natural gas prices tends to reduce the price of CO 2 emissions, whereas coal prices affect carbon prices only when the electricity price is omitted. Ji, Zhang and Geng (2018) study information linkages and spillover among the carbon-energy system. Their return and volatility connectedness features that crude oil, clean energy, and coal play a pivotal role. Their network confirms that the electricity market is the main net information receiver affected by the carbon market. This dynamic spillover approach has been applied recently as well by [START_REF] Zhang | Global financial crisis and rising connectedness in the international commodity markets[END_REF] in commodity markets against the background of the financial crisis and also by [START_REF] Zhang | Oil shocks and stock markets revisited: measuring connectedness from a global perspective[END_REF] for the oil-stock relationship.

Whenever potential interactions are at stake, several methodological frameworks (such as time series and neural networks) can be used to detect them. In recent contributions, [START_REF] Lutz | Nonlinearity in cap-and-trade systems: the EUA price and its fundamentals[END_REF] made use of the regime-switching GARCH model to investigate the nonlinear relation between the carbon price and its fundamentals including energy prices, macroeconomic risk factors and weather conditions. Their findings indicate that gas, coal, and oil can be deemed to be reliable price drivers of the CO 2 price and that their influence depends on high-versus low-volatility regimes. [START_REF] Koch | Dynamic linkages among carbon, energy and financial markets: a smooth transition approach[END_REF] adopts a smooth transition approach to model the conditional correlations between carbon and energy prices and finds much closer carbon-energy price linkages during 2008-2012 (when compared with [2005][2006][2007]. These conditional correlations are further dependent on market uncertainty conditions. Previous empirical findings have in common a high degree of substitution among the three primary energy sources (i.e., crude oil, natural gas, and coal). Another relevant analytical framework is the dependence-switching CoVaR-copula model, applied by Ji, Liu, Nehler, and Salah Uddin (2018), to (clean) energy returns and uncertainty changes; by Ji, Bouri, Roubaud, and Shahzad (2018) to energy and agricultural commodities; and by [START_REF] Kumar | Dependence structure between the BRICS foreign exchange and stock markets using the dependence-switching copula approach[END_REF] to the BRICS stock and foreign exchange markets. In these empirical applications, tail dependence for different market conditions can be indeed estimated using a dependence-switching copula model.

In this paper, we further extend the investigation of the cross-relationships between the CO 2 price and energy markets by advancing two central contributions. The first contribution deals with the choice of data. We decided to work not only with CO 2 , oil, gas and coal but also with the price of electricity. The rationale behind this idea is that variations in electricity prices have significant implications on the choice of power plants and fuels, which in turn affect carbon emissions and their prices. Meanwhile, the fluctuations in carbon prices can change the merit order of coal and gas plants whereby the efficiency of the plants and the fuel costs are critical decision factors. The exact relationship between energy and carbon prices could thus be biased if the dynamics of electricity prices is ignored. Here, the influence of the electricity variable is captured through the construction of a specific spread, which we termed the 'fuel-switching price'. [START_REF] Delarue | Price determination of ETS allowances through the switching level of coal and gas in the power sector[END_REF] defined it as the CO 2 price at which a gas-fired power plant is as economically and equally profitable as a coal-fired power plant. It exists for every pair of gas and coal plants. The fuel-switching price thus brings meaningful content for energy economists and policymakers. However, its influence has been omitted in most of the previous literature, except in engineering journals (see [START_REF] Delarue | Robust MACCs? The topography of abatement by fuel switching in the European power sector[END_REF].

The second contribution is a methodological one because we capture the dependence structure by resorting to the vine copula approach. This methodological framework offers the advantage of modeling various dependence structures and also their potential to construct a rich set of distributions, in the spirit of [START_REF] Reboredo | Modeling EU allowances and oil market interdependence: implications for portfolio management[END_REF][START_REF] Reboredo | Volatility spillovers between the oil market and the European Union carbon emission market[END_REF]. 1 We go one step further than these previous works by examining the dependence structure between a more extensive array of time series in the carbon and energy spheres from a multivariate setting perspective.

The objective of this paper is to develop a time series model including the fuel-switching price that allows for various interesting applications for economists, as suggested by Zachmann (2013). Indeed, to the extent that multi-commodity options are quite common in electricity markets, the ability of the stochastic model to statistically capture the commodity co-movements would help assess the effectiveness of these options. The results from our vine copula analysis mainly show a complex dependence structure between the price variables under consideration. In particular, we find a strong dependence between the fuel-switching price, coal and gas prices. The dependence is positive and high between coal prices, and the switch variable with symmetric upper and lower tail dependence; whereas it is harmful and high between gas prices and the switch variable. We also find that CO 2 prices weakly co-move with energy prices, especially with the switch variable (as a proxy for electricity prices) that displays low and negative dependence. Overall, high carbon costs do not appear as a sufficient criterion to trigger the switch from coal-to gas-fired plants (potentially owing to the engineering costs accrued by shut down/power up installations in the process).

The rest of this paper is structured as follows. Section 2 provides a brief review of the inter-relationships between energy and carbon markets. Section 3 presents the data. Section 4 describes the methodology. Section 5 contains the empirical results. Finally, Section 6 summarizes the main findings.

Power sector and CO pricing

In the power sector, the marginal generation technology is essential to the determination of electricity prices. 2 There is thus 'merit order' which ranks the different generation units by marginal costs from the cheapest technology to the most expensive. [START_REF] Sijm | CO 2 price dynamics: the implications of EU emissions trading for the price of electricity[END_REF] show that several parameters including fuel prices, plant efficiencies, carbon intensity, and carbon costs are critical for this ranking. Likewise, the merit order of power plants may change with the introduction of carbon costs through climate policy instruments.

In the following, we build on the notations developed by Delarue et al. (2008) who derived the E-Simulate model at the KU Leuven university in Belgium. 3 This is a European simulation model of interconnected power system networks that are developed according to the physical characteristics of the electricity grid. Assuming no carbon costs, the marginal cost of electricity is represented by the ratio between fuel costs and the plants' efficiencies, such as:

M C = F C η (1)
where M C is the marginal cost, F C is the fuel cost, and η is the plant's efficiency. 4When the carbon costs are introduced, the marginal cost for each plant accounts for an emissions factor which typically depends on the fuel and the quantity of fuel burnt:

M C = F C η + EF η EC ( 2
)
where EF is the emissions factor and EC is the emissions costs. The switching point between a given coal plant and a given gas plant can be defined as the emissions cost that equalizes marginal costs; that is, M C gas = M C coal . This represents the allowance cost that leads to a switch between two plants in the merit order. This price interacts with various factors related to fuel prices, energy efficiency, and associated CO 2 emissions:

EC switch = η coal F C gas -η gas F C coal η gas EF coal -η coal EF gas (3)
If the carbon price is higher than this cost, then generating electricity from gas is more profitable than from coal. Besides, the allowance cost of the switching point varies linearly with the coal-to-gas price ratio. Consider the fuel price ratio r = F Cgas F C coal , then write the so-called switching point:

EC switch = (η coal r -η gas )F C coal η gas EF coal -η coal EF gas = ar-b (4)
with a = η coal F C coal ηgasEF coal -η coal EFgas and b = ηgasF C coal ηgasEF coal -η coal EFgas . Eq.( 4) shows that the switching point depends linearly on the fuel price ratio. It also shows that switching can occur even with zero allowance costs. The denominator is positive if ηgas η coal > EFgas EF coal . This relationship is verified in practice: the emissions factor for gas-fired power plants is nearly half of that for coal-fired power plants. Additionally, the efficiency of gas-fired power plants (especially CCGT) is usually higher than that for coal-fired power plants.

If r > ηgas η coal , then EC switch > 0. It means that the carbon cost for switching is positive. On the contrary, it is interesting to notice that fuel-switching could even occur will null carbon costs. Therefore, for a given (>0) coal price, it is theoretically possible to have a gas price that is low enough to influence the power producers' fuel-switching behavior, even with null carbon costs (whenever the coal-to-gas ratio is equal to the ratio of the gas and coal efficiencies, see e.g. [START_REF] Delarue | Short-term CO 2 abatement in the European power sector[END_REF]).

The introduction of CO 2 costs provides incentives for generators to use gas instead of coal at the switching point. Depending on the load and the number of gas units available, the emissions cost profile differs.

In practice, the main abatement opportunities occur by switching from coal to gas. Notice switching from/to oil is limited in Europe. Similarly, switching from/to nuclear is difficult because nuclear energy is not flexible.

To compute the switch price, we plug in the values cost ngas = 0.5 as the production cost of one MWh of electricity based on net CO 2 emissions of gas (e.g. the efficiency of the typical gas plant, expressed in EUR/MWh), cost coal = 0.4 the production cost of one MWh of electricity based on net CO 2 emissions of coal (e.g. the efficiency of the typical coal plant, expressed in EUR/MWh), tCO2 coal = 364.68 the emissions factor (expressed in kgCO 2 eq/MWhp) of a conventional coal-fired plant, and tCO2 ngas = 210.96 as the emissions factor (expressed in kgCO 2 eq/MWhp) of a conventional gas-fired plant (see Delarue andD'haeseleer (2007, 2008), Delarue et al. (2008)).

Technical values for typical coal-or gas-fired power installations are required for the computation of the switch price, which is a theoretical (unobserved) price that needs to be computed for this study. The references provided above are taken from recognized engineering journals regarding the calibration of the E-Simulate model at the K.U. Leuven in Belgium, which was used extensively to model the electricity grid in Europe. Several scholars (see, e.g., [START_REF] Convery | Market and price developments in the European Union emissions trading scheme[END_REF] or even the EU DG Clima have re-used their estimates in several reports.

As long as the carbon price lies below this switching price, coal plants are more profitable than gas plants -even after taking carbon costs into account.

In the next section, we will examine in more detail the effects of EUA prices, on the one hand, energy and power prices, on the other hand.

Data

Data description

Our dataset consists of the ICE ECX EUA Daily Futures -SETT. PRICE (in Euro per ton of CO 2 ), the Crude Oil-Brent Cur. Month FOB U$/BBL, the ICE Natural Gas 1 Mth.Fwd. P/Therm, the Coal ICE API2 CIF ARA Nr Mth $/MT -SETT.PRICE, and the fuel-switching price; computation is detailed in Section 2. Energy prices are pictured in Figure 1.

We obtained 1598 daily prices that spanned the period from 1 January 2010 to 19 May 2016. All price series were converted to US dollars using the bilateral exchange rates given by the European Central Bank and the Federal Reserve Bank of St. Louis. From daily prices, including the fuel-switching price, we computed the price returns at each time t as (p t -p t-1 )/p t-1 , where p t denotes the price at time t 5 .

5 Notice in our paper, we are not using logarithmic returns. It is not possible given that our switch variable can take positive or negative values. Therefore, we use the percentage change of the level of series as given by (pt-pt-1) pt-1

, where p t denotes the price level of the corresponding series at time t.

Descriptive statistics

Table 1 reports the descriptive statistics and the basic stochastic properties for carbon allowance price returns (EUA), oil price returns (Brent), gas price returns (Gas), coal price returns (Coal) and fuel-switching price returns (Switch). The mean returns are close to zero for all series and are relatively low concerning their standard deviations. Standard deviations and differences between maximum and minimum values show that the Switch series is much more volatile than the other series. Coal prices display lower volatility. Negative values for skewness are only observed for the Switch variable; the other variables only display positive skewness. All the returns exhibit excessive kurtosis, confirming the presence of fat tails in the marginal distributions or a relatively high probability of extreme observations. The Jarque-Bera test for normality rejects the normality of the unconditional distribution for all the series. The Ljung-Box statistic for autocorrelation up to 20th order in the returns suggests the presence of serial correlation in the Coal and Switch series and no evidence of serial correlation for the other series. Finally, the results of the Lagrange multiplier for the ARCH (ARCH-LM) statistic for serially correlated squared returns indicate that ARCH effects are likely to be found in all the return series.

[Insert Table 1 here]

Methodology

We study multivariate dependence between carbon allowance prices and major energy prices, considering the dependence structure between (a) CO 2 , Brent, natural gas and coal prices, because this helps track interactions between the CO 2 market and each of the major energy markets in a multivariate and integrated setting. (b) CO 2 , Brent and electricity prices (Switch), because this reveals the influence of the electricity market on carbon allowance prices and the substitutability potential for crude oil with the other two energy sources (Gas & Coal). (c) CO 2 , Brent, natural gas, coal and electricity prices, because these reveal interactions between carbon allowance prices and all energy prices. For multivariate dependence modeling, we employ the vine copulas briefly described below.

Modelling multivariate dependence with vine copulas

A copula function is a uniform multivariate distribution function of a d-dimensional multivariate random vector with support in [0, 1] d . According to the Sklar's (1959) theorem, the copula function C(•) is related to the cumulative distribution function of a random vector, F (x 1 , x 2 , ..., x d ), via:

C(u 1 , u 2 , ..., u d ) = F (x 1 , x 2 , ..., x d ), (5)
where

u i = F i (x i )
is the value of the marginal distribution function of the variable x i for i = 1, ..., d. The converse of Eq. ( 5) is also true: any multivariate distribution function can be written using its marginal distributions and a copula function. Assuming that the marginals and copula C are differentiable, then the density representation of the copula is given by

f (x 1 , x 2 , ..., x d ) = f (x 1 )f (x 2 ) • • • f (x d )c(F 1 (x 1 ), F 2 (x 2 ), ..., F d (x d )), (6)
where f i (x i ) are the marginal densities and c(•) is the copula density given by

c(u 1 , u 2 , ..., u d ) = ∂ d C(u 1 , u 2 , ..., u d ) ∂u 1 ∂u 2 • • • ∂u d . (7)
Thus, the multivariate density is represented by the product of the marginal densities and the multivariate copula density that accounts for the structure of dependence. This feature allows for model flexibility by untying univariate marginals distribution estimates from dependence estimates.

Although several multivariate copulas (such as the Gaussian, Student-t or Archimedean copulas) have been used to model multivariate dependence, they lack modeling flexibility for a large number of variables (e.g., by imposing the same structure of dependence for bivariate pairs). Therefore, vine copulas -which were initially proposed by Joe (1996) -have been developed to describe multivariate dependence.

Vine copulas are multivariate copulas that are generated using a hierarchical structure given by a cascade of bivariate copulas (pair copulas), where each bivariate pair copula captures the conditional dependence between two random variables. Vine copulas are obtained by decomposing the joint probability density in Eq. ( 6) by iterative conditioning. However, a crucial issue in this density decomposition is the choice regarding the order of the variables. The literature includes several vine specifications that are made of different pair-copula constructions composed of d(d -1)/2 bivariate copulas (see, e.g., Bedford andCooke, 2001, 2002;[START_REF] Kurowicka | Uncertainty Analysis with High Dimensional Dependence Modelling[END_REF]Aas et al., 1999). In our research, we focus on three vine models with different hierarchical tree structures that have been widely employed in the empirical literature, namely, C-vine, D-vine, and R-vine copulas. Specific details on those copulas are reported in the Appendix.

Marginal and copula models

The marginal densities and the bivariate copulas are the main building blocks of multivariate dependence modeled using a vine copula. The marginal models and copula specifications used in the empirical analysis are described as follows.

To account for the main characteristics of the distribution of energy price changes (such as leverage, fat tails and asymmetries), we consider that the conditional mean and variance of the returns (r t ) are given by an autoregressive moving average (ARMA) model with p and q lags given by:

r t = φ 0 + p j=1 φ j r t-j + q h=1 ϕ h ε t-h + ε t , (8)
where t = σ t z t such that z t is a zero mean and the unit variance i.i.d. random variable that follows a Student-t density distribution and σ 2 t is the conditional variance, with dynamics described by a threshold generalized autoregressive conditional heteroskedasticity (TGARCH) specification:

σ 2 t = ω + r k=1 β k σ 2 t-k + m h=1 α h ε 2 t-h m h=1 λ h 1 t-h ε 2 t-h , (9)
where ω is a constant, σ 2 t-k is the GARCH component, ε 2 t-h is the ARCH component and 1 t-h is the indication function equal to 1 if ε t-h < 0 and otherwise equal to 0. The parameter λ captures asymmetric effects in such a way that when λ > 0, the future conditional variance will proportionally increase more following a negative shock than following a positive shock of the same magnitude.

To model bivariate dependence, we use ten different copula specifications to capture different characteristics of dependence, such as tail independence and symmetric and asymmetric tail dependence. Table 3 summarizes the main features of all the copula functions specifications used in the empirical analysis.

[Insert Table 3 here] Marginal and copula parameters are obtained following a two-step procedure. First obtained by maximum likelihood are the parameters for the univariate marginal models in Eq. ( 8)-( 9) and also the standardized residuals that will be the pseudo-sample observations for the copula. 6 Next obtained are the parameters of the vine copula using the sequential maximum likelihood estimation procedure, as introduced by Aas et al. (2009) and discussed in Hobaek and Haff (2013). This consists of sequentially estimating pair copula parameters and conditioning them on the parameters of the previous levels of the vine structure. Thus, given the selected tree, for the first tree level we estimate the bivariate copula parameters by maximum likelihood and choose the best pair copulas-from the family reported in Table 3-using the Akaike information criterion, as described in Brechmann and Czado (2011) and [START_REF] Dißmann | Selecting and Estimating Regular Vine Copulae and Application to Financial Returns[END_REF]. Then, for the next tree level, we compute the pseudo-sample observations from the estimated copulas of the previous level using Eq. [START_REF] Bonneuil | Optimal transition to renewable energy with threshold of irreversible pollution[END_REF] and then obtain the copula parameter estimates for this tree. This process is repeated sequentially until tree d -1.

Results

Results for the marginal distribution models

Table 4 reports the estimation results for the marginal models described in Eqs. ( 8)-( 9). The parameters p, q, r and m were selected for different combinations of values ranging from zero to a maximum lag of two, using, for this purpose, the AIC values. Accordingly, an ARMA(0,0)-TGARCH(1,1) specification was selected for all return series except the coal series, where a single lag was considered to account for serial correlation as described in Table 1. The estimation results indicate that the conditional volatility is quite persistent for all the series. Volatility asymmetric effects are observed for all the series, except coal. Furthermore, neither autocorrelation nor ARCH effects remained in the residuals of the marginal models.

[Insert Table 4 here]

We assessed the adequacy of the marginal distribution model by testing the null that the standardized residuals were uniform (0,1). We used the Kolmogorov-Smirnov, Cramervon Mises and Anderson-Darling tests, which compare the specified theoretical distribution function with the empirical distribution function. The last three rows of Table 4 report the p values for those tests, which indicate that the null of the correct specification of the distribution function cannot be rejected at the 5% threshold level. We also checked for the presence of structural breaks in the standardized residuals by using the exponential likelihood ratio F-statistic-as developed by [START_REF] Andrews | Tests for parameter instability and structural change with unknown change point[END_REF], [START_REF] Andrews | Optimal tests when a nuisance parameter is present only under the alternative[END_REF] and [START_REF] Hansen | Approximate asymptotic P values for structural change tests[END_REF]-which endogenously identifies one structural breakpoint. For all series, we were unable to reject the null of no change point in the standardized residuals. Similarly, the multiple breakpoint tests developed by Bai and Perron (1998) was unable to identify any structural change in the standardized residuals. The marginal models are, thus, accurately specified and the copula model can correctly capture the dependence structure among energy prices.

Results for the vine copula models

We now discuss the empirical results for three different market situations with and without the fuel-switching price variable. This analysis offers the possibility to assess the role of the switch variable in the formation of coal prices.

CASE 1: CO 2 , Brent, natural gas and coal prices. Note: For each edge, we have indicated the name of the best pair copula (see Table 3) and its estimated parameter value with the corresponding standard error (in parenthesis) and Kendall's tau (in brackets).

We first estimated the three vine copula models in Eqs. ( 10), ( 12) and ( 13) using the pair copulas in Table 3 for CO 2 , Brent, natural gas and coal prices. Table 5 reports results for different selection criteria; the best copula fit was achieved by the C-vine copula model represented in Figure 2, along with the corresponding information on the pair copulas. Accordingly, the dependence structure between prices for CO 2 and energy is dominated by coal, which exhibits greater dependence with Brent and gas prices (with Kendall's taus of 0.16 and 0.22, respectively) than with CO 2 prices.

[Insert Table 5 here]

The EU ETS was designed to foster innovation in technologies that are less carbonintensive than coal, which is often the cheapest alternative for power production. The introduction of carbon costs is meant to integrate the social value of carbon into the business models of user companies. We can observe, with this first set of results, that coal is the benchmark polluting technology and that it is difficult to trigger a move towards a lowcarbon era.

Moreover, Figure 2 reveals that conditional dependence between Brent and gas prices and Brent and CO 2 prices is weak; this is also the case for conditional dependence between gas and CO 2 prices. The best pair copulas reveal that there is no upper or lower tail dependence. This result is consistent with the fact that spikes in energy prices are independent and so are not transmitted between different energy sources. Overall, our evidence indicates that coal, oil, and gas prices are, on average, integrated, even though they behave as if independent in the case of extreme upwards or downwards movements; in contrast, CO 2 prices co-move weakly with different energy prices.

We now investigate in more depth whether inclusion of the electricity market (switch variable) will reveal any new interplays between CO 2 and the energy markets. Different selection criteria show that there is no difference between the three vine copula structures. Figure 3 depicts a similar structure for the three models. The results for multivariate dependence between CO 2 , Brent and electricity prices for the three vine copula models are presented in Table 6. Note: For each edge, we have indicated the name of the best pair copula (see Table 3) and its estimated parameter value with the corresponding standard error (in parenthesis) and Kendall's tau (in brackets).

[Insert Table 6 here]

Estimation of the multivariate dependence structure indicates that there is weak dependence between CO 2 and Brent, and also between Brent and switch, as Kendall's tau takes low values (0.03 and -0.02, respectively). Likewise, the dependence between CO 2 and switch as given by the Gaussian copula is extremely weak. For all the pairs, we find evidence of no tail dependence, indicating that these prices are always independent of extreme upward or downward energy price movements.

This second set of results indicates that power companies did not immediately introduce carbon cost pricing into their usual dark and spark spreads. At the time of initial allocation of CO 2 allowances, these were free and, given their price evolution until the early phase of the financial crisis launched in 2008, there were insufficient incentives to reduce coal use and increase gas use, even though there were moments when gas was cheaper than coal. To ensure profitability, the power company needs a sufficiently significant and stable price gap between the two fuels for several weeks or months, after accounting for all costs related to the switch between fuels (engineers need several days to close down a facility and open a new one). In Phase III, we would expect the expectations of these companies to change dramatically with the move to auctioning (i.e., with the need to bid for each CO 2 allowance). This increases the burden of CO 2 costs and adds to the fuel-switching formula (clean spark and explicit dark spreads). CASE 3: CO2, Brent, natural gas, coal and electricity prices.

[Insert Table 7 here] In considering CO 2 prices simultaneously with the four energy prices, the results of the selection criteria for multivariate dependence reported in Table 7 indicate that -based on an analysis of their tree hierarchical structures -the R-and D-vine copula structures yield similar results and outperform the C-vine structure. Note: For each edge, we have indicated the name of the best pair copula (see Table 3) and its estimated parameter value with the corresponding standard error (in parenthesis) and Kendall's tau (in brackets). Pair dependence in the first tree indicates the existence of positive and significant dependence between Brent and coal prices, and also between gas and coal prices. There is also strong negative dependence between the gas and switch variables, with Kendall's tau of -0.52, and positive dependence between Brent and CO 2 prices is weak, with Kendall's tau of 0.03.

In the second tree of the multivariate dependence structure, there is a positive dependence between Brent and gas prices and there is also strong positive conditional dependence (Kendall's tau of 0.52) between the coal and switch variables. The latter finding is also consistent with evidence of symmetric upper and lower tail dependence, given that the Student-t copula is the best model in describing the coal-switch dependence structure. In contrast, there is weak dependence between coal and CO 2 prices (Kendall's tau of 0.03) and between the Brent and natural gas prices (Kendall's tau of 0.07). The third tree reveals weak conditional dependence between gas and CO 2 prices, and also weak dependence between Brent prices and the switch variable. Finally, the fourth tree indicates that conditional dependence between CO 2 prices and the switch variable is very weak and negative, as indicated by an associated Kendall's tau of -0.02.

Overall, when all energy prices are included in the multivariate dependence analysis, the primary evidence provided by different vine copula model structures can be summarized as follows. First, there is a strong dependence between electricity prices, as measured by the switch variable, and coal and gas prices. Dependence is, however, positive and high between coal prices and the switch variable, with symmetric upper and lower tail dependence, whereas dependence is negative and high between gas prices and the switch variable. Second, there is a strong positive dependence between coal and gas prices and between coal and Brent prices, which may reflect concomitant increases in energy prices in economic boom periods. Third, CO 2 prices weakly co-move with energy prices, with negative dependence on Brent and gas prices. Finally, CO 2 prices are weakly and negatively associated with the switch variable, suggesting that high carbon costs will not activate the switch from coal-fired to gas-fired plants.

It is worth noting that the finding of a positive link between coal prices and the switch variable in the first case described in the previous paragraph typically suggests that energy producers, to produce electricity, tend to shift between energy sources as an input at the installation level. In practice, the switch from coal to gas occurs when relative prices make gas (cheaper as a baseline fuel) more profitable than coal as an input for electricity production at the installation level, after taking into account carbon costs. Inversely, an increase in gas prices will prevent the switch from gas to coal plants when assessing the relative price of fuels (including carbon costs). In this case, electricity producers would keep operating the installation with the baseline technology.

Finally, the nature of dependence among energy and carbon emissions prices does not differ with and without electricity prices since their relationships are mostly described by the same symmetric copulas (Frank, Gaussian, and Student-t copulas). The exceptions include the relationship between electricity prices on the one hand, and natural gas and coal prices, on the other hand. The robustness of our dependence results was checked by considering potential structural breaks in market dependence or time-varying dependence. Concretely, the dependence analysis was performed by splitting the sample period into two subsamples (January 2010 to July 2013 and August 2013 to May 2016) and considering time-varying parameter pair copulas. The empirical evidence from the structural break analysis fully confirms the dependence results reported for the whole sample period and by the reported static copulas. 7

Robustness

We have checked the robustness of our results by considering daily spot prices form EPEX spot for Germany/Austria instead of our switch variable 8 . Indeed, the main empirical findings show that for cases 2 and 3 (note that case 1 does not focus on power prices) our evidence on dependence remains similar. We typically find that hierarchical dependence in case 2 for EUA, Brent and power prices remained identical and with similar bivariate dependence structures. Similarly, for case 3 among EUA, Brent, coal, gas and power prices the hierarchical dependence changed from a D-vine to a C-vine, even though bivariate dependence results point to similar evidence than the one we reported for the switch variable. Overall, analysis with EPEX spot prices is entirely consistent with the evidence we obtain by using the switch variable.

Discussion

If we look at the big picture -that is, how the obtained results can be used in the current debate on CO 2 emissions -, then we need to reflect on the experience gathered with carbon and GHG trading systems, while focusing on the performance of these mechanisms as they have been implemented in practice.

The United Nations Framework Convention on Climate Change (UNFCCC) clearly states that greenhouse-gas concentrations in the atmosphere coming from anthropogenic interference need to be stabilized as much as possible to prevent climate change to a 2 degrees Celsius scenario at the 2050 to 2100 horizon (see [START_REF] Hoffert | Energy implications of future stabilization of atmospheric CO 2 content[END_REF].

At the European level, several scholars have analyzed the contribution of the EU ETS to the management of CO 2 emissions with reductions, if any, coming from abatement at the cheapest sources of pollution. Based on early 2005-2007 data, Ellerman and Buchner (2007) have documented design flaws giving rise to possible over-allocation in the system. The scheme has also been affected by erratic (low) allowance price movements in the wake of inter-Phases I and II banking restrictions (see, e.g., [START_REF] Alberola | European carbon prices and banking restrictions: evidence from Phase I (2005-2007)[END_REF].

In this paper, based on 2010-2016 European data, we contribute to this debate by empirically establishing that high CO 2 prices alone are insufficient to push the electricity producers to switch from coal-fired plants to gas-fired plants. In practice, this means that the emissions trading scheme is not functioning at its maximum potential to provide incentives for polluters to switch to the lower carbon-intensive fuel (gas). This happens because of the price differential between coal and gas that is not compensated enough by the introduction of carbon costs in the range of 20 to 30 euros per ton of CO 2 -equivalent. Our central policy implication for the GHG emissions debate is that the tutelary value of carbon should be much higher than the current historical means. Perhaps, the CO 2 price should oscillate in the range of a hundred euros per ton to effectively foster the switch away from coal pollution towards gas-fired power installations.

Concerning the industry operations management, we can advance another practical implication of our paper. If the relative price differential between gas and coal (including carbon costs) is sufficient to trigger the fuel-switching mechanism, then practically this task requires manual engineering work. That is to say, a team of engineers and technical assistants needs to manually operate the factory to shut down a coal-fired installation and redirect power production towards a gas-fired installation. The whole process could take over a day and a half to three days before the factory can be considered as shut down. Therefore, we uncover in this paper that in reality, the fuel switching mechanism occurs on fewer occasions than economists initially believed it would in theory (fostering the targeted carbon emissions abatement). In a nutshell, it is because the price differential (including a massive carbon cost, most likely higher than the 35 Euro historical high) must be prolonged for several days (ideally a week or two) before it becomes profitable actually to shut down a factory and open-up another.

Conclusion

Global climate change seriously affects environmental quality, human health, and economic activity, and it requires coordinated policies from countries around the world. Central to the threats of climate change is the increasing tendency of global CO 2 emissions, which constitute the single most important greenhouse gas in the atmosphere with a contribution of 64% out of all long-lived greenhouse gases since 1750. The 2012 greenhouse gas bulletin of the World Meteorological Organization (WMO) documents a 140% increase in carbon emissions, compared to their level before the industrial era. In Europe, the European Commission has undertaken, since the early-1990s, some initiatives to reduce carbon emissions and combat the consequences of climate change, mainly through the European Climate Change Programme (ECCP). These initiatives include, among others, the establishment of the EU ETS for companies to trade out their emission allowances, proposals on the taxation of energy products, and policy measures to promote electricity from renewable energy and voluntary commitments by car makers to reduce CO 2 emissions. This framework requires a comprehensive understanding of the behavior of carbon prices under the effects of not only energy prices but also the prices of electricity produced with different energy sources.

In this study, we have made use of a vine copula approach to investigate the multivariate dependence patterns between carbon prices and energy prices, including electricity prices. The integration of the electricity prices into the analysis is particularly relevant because they influence the choice of power plants and primary fuels, and ultimately carbon emissions and their prices. Moreover, the vine copula-based approach allows to capture a wide range of multidimensional dependence characteristics (i.e., average dependence, upper and lower tail dependence, and asymmetric dependence) of the price variables under consideration for the changing market states through time. The effect of the electricity prices is here accounted for by the use a fuel-switching price, which is defined as the CO 2 price level for which a gas-fired power plant is as profitable as a coal-fired power plant. We conducted our empirical analysis in three different scenarios to shed light on the role of carbon and electricity prices: i) the dependence structure of energy prices without electricity prices (Case 1); ii) the dependence structure of oil prices, carbon prices, and the fuel-switching price (Case 2); and iii) the dependence structure of all the energy prices (Case 3). For each scenario, we estimate three different multivariate dependence structures with the best copula model for each pair of variables: C-vine, D-vine, and R-vine copulas.

Our results mainly show evidence of a strong and positive link between coal and gas prices, and between coal and oil prices, with or without the presence of electricity prices. However, contrary to the centrality of coal prices in the absence of electricity prices (Scenario 1), the dependence structure is much more complicated in the case where electricity prices are included (Scenario 3). Specifically, we find a positive and high dependence between electricity prices and coal, but negative and high between electricity prices and gas prices. This means that a higher electricity price implied by, for example, a higher consumption can cause a decrease in gas prices but an increase in coal prices and thus more carbon emissions. A weak and positive link is also found between Brent and gas prices, which typically reflects the competition between oil and gas in both consumption and production processes. Due to their substitutes, if the price of one energy source increases significantly, then the end consumers and producers will move to another source of energy, causing its price to rise. This finding is particularly apparent during booming economic activities, as reported in [START_REF] Aloui | Dependence and extreme dependence of crude oil and natural gas prices with applications to risk management[END_REF] who use GARCH-based copula approach to investigate the conditional dependence structure between the crude oil and natural gas markets, and also to derive implications for portfolio risk management in extreme economic conditions.

Another important finding is that carbon prices are only weakly associated with energy prices and their link to gas prices is negative. The latter finding is obtained when electricity prices are included in the multivariate dependence analysis and, thus, implies that high CO 2 prices reduce the prices of gas thanks to a decrease in demand. It is worth noting that the main findings for dependence structure remain intact when we replace our switch variable by daily spot prices form EPEX spot electricity prices for Germany/Austria. Finally, our results suggest that high CO 2 prices alone are insufficient to push the elec-

Appendix. Vine copula models

This appendix describes the main features of the three vine copula models we use in our empirical analysis of multivariate dependence: C-vine, D-vine, and R-vine copulas. A C-vine copula has a multivariate density given by:

f (x 1 , x 2 , ..., x d ) = d k=1 f k (x k ) d h=2 c 1,h (F 1 (x 1 ), F h (x h )) d-1 j=2 d-j i=1 c j,j+1|1,...,j-1 (F (x j |x 1 , ...x j-1 ), F (x j+1 |x 1 , ...x j-1 )). (10)
where the conditional distribution functions between variables x i and x j can be obtained (see [START_REF] Joe | Multivariate Models and Dependence Concepts[END_REF] as:

F i|j (x i |x j ) = c i|j [F i (x i ), F j (x j )] = ∂C ij [F i (x i ), F j (x j )] ∂F j (x j ) , (11)
with c i|j denoting the conditional distribution of variable i given the variable j with a joint distribution function C ij . The dependence structure of this decomposition can be represented graphically as a hierarchical tree structure. C-vine trees have a star structure where the first root node of the first tree T 1 considers the dependence of one variable concerning the other variables as represented by the edge connecting the two nodes. This dependence is given by bivariate copulas (reflected in the second term of Eq. ( 10)). The tree is then expanded in such a way that the edges of the previous tree form the nodes of the successive trees and, thus consider hierarchical conditional dependencies (reflected in the third term of Eq. ( 10)).

In each tree, one variable plays a pivotal role as it shapes the root node, chosen as the node that maximizes the sum of pairwise dependencies (as measured by Kendall's tau) regarding this node. A D-vine copula has a multivariate density given by:

f (x 1 , x 2 , ..., x d ) = d k=1 f k (x k ) d-1 h=1 c h,h+1 (F h (x h ), F h+1 (x h+1 )) d-1 j=2 d-j i=1 c i,i+j|i+1,...,i+j-1 (F (x i |x i+1 , ...x i+j-1 ), F (x i+j |x i+1 , ...x i+j-1 )). (12)
The specific ordering of the variables in the D-vine construction is, as can be observed, different from that of the C-vine. The first tree (T 1 ) models dependence between the first and second variables, the second and third variables, and so on, using bivariate copulas.

The edges connecting the nodes represent this dependence relationship. The second tree (T 2 ) models the conditional dependence between the first and the third variables, given the second variable, between the second and fourth variables, given the third variable, and so on. This process continues through different trees to the last tree, where only one bivariate dependency remains. We thus have d(d -1)/2 pair copula models. The ordering of the variables in the first tree is crucial because it fully determines the dependence structure of the remaining trees in the D-vine. From d!/2 possible orderings, the best ordering is selected to capture as much dependence as possible (as measured by Kendall's tau) in the first tree (see [START_REF] Nikoloulopoulos | Vine copulas with asymmetric tail dependence and applications to financial return data[END_REF].

According to [START_REF] Kurowicka | Uncertainty Analysis with High Dimensional Dependence Modelling[END_REF], an R-vine copula consists of linked trees T 1 ,...,T d-1 with nodes N i and edges E i for i = 1, ..., d -1. The first tree has d nodes and E 1 edges, whereas each tree of the remaining trees, i = 2, ..., d -1, T i has nodes

N i = E i-1 .
Besides, two edges in tree T i are joined in tree T i + 1 if they share a common node in tree T i (proximity condition). The edges in an R-vine tree are identified by conditioned nodes denoted by e = j(e), k(e)|D(e), where D(e) is the conditioning set. Accordingly, the multivariate density of the R-vine copula is given by The C-vine is a special case of the R-vine when each tree has a unique node with degree d -i (the root node). As shown in Morales-Napoloes et al. (2010), there are many different R-vines. To select the most appropriate R-vine, the structure of the tree is selected using the maximum spanning tree that solves the following optimization problem for each tree: max edges e={i,j} in spanning tree

f (x 1 , x 2 , ..., x d ) = d k=1 f k (x k ) d-1 i=1 e E i c j(e),k (
|τ ij |, (14)
where τ i,j denotes the pairwise empirical Kendall's tau and a spanning tree is a tree on all nodes. Notes: This table reports the ML estimates and z statistic (in brackets) for the parameters of the marginal distribution models defined in Eqs. ( 8)-( 9). The lags p, q, r and m were selected using the AIC for different combinations of values ranging from 0 to 4. Q( 20

Figure 1 :

 1 Figure 1: Energy Prices

Figure 2 :

 2 Figure 2: C-vine copula tree for Brent (B), gas (G), coal (C) and EUA (E).

CASE 2 :

 2 CO 2 , Brent and electricity prices (switch).

Figure 3 :

 3 Figure 3: D-vine copula tree for Brent (B), switch (S) and EUA (E).

Figure 4 :

 4 Figure 4: D-vine copula tree for Brent (B), gas (G), coal (C), switch (S) and EUA (E).

Figure 4

 4 Figure 4 represents this dependence structure, along with information on the pair copulas.Pair dependence in the first tree indicates the existence of positive and significant dependence between Brent and coal prices, and also between gas and coal prices. There is also strong

  e)|D(e) (F (x j(e) |x D(e) ), F (x k(e) |x D(e) )). (13) where x D(e) denotes the sub-vector of x = (x 1 , ..., x d ) indicated by the indices contained in D(e).

  ) is the Ljung-Box statistic for serial correlation in the model residuals computed with 20 lags. Q(20)2 represents the Ljung-Box statistics for serial correlation in the squared residual model calculated with 20 lags. ARCH is the Engle's LM test for the ARCH effect in the residuals up to 20th order. K-S, C-vM and A-D denote the Kolmogorov-Smirnov, Cramér-von Mises and Anderson-Darling test for adequacy of the distribution model. P -value (in square parenthesis) below 0.05 indicates rejection of the null hypothesis. Asterisk ( * ) indicates the significance at 5%.

Table 2 reports

 2 information on the Pearson linear correlation coefficient, with values indicating that Brent with Gas, Brent with Coal and Coal with Gas display positive dependence, Switch with Gas displays negative dependence and Switch with Coal displays positive dependence. All other pairs show very low or nonlinear dependence.

[Insert Table

2 here]

Table 1 :

 1 Descriptive statistics for price returns.Notes: Daily data for the period 1 January 2010 to 19 May 2016. JB is the statistic for the test of normality. Q(20) is the Ljung-Box statistics for serial correlation in the squared returns computed with 20 lags. ARCH-LM is Engle's LM test for heteroskedasticity, computed using 20 lags. An asterisk ( * ) indicates rejection of the null hypothesis at the 5% level.

		EUA	Brent	Gas	Coal	Switch
	Mean	0.0001 -0.0001 0.0015	0.0002	-0.0023
	Std. Dev.	0.0288 0.0173 0.0212	0.0101	0.2664
	Max.	0.2279 0.1061 0.1695	0.0728	1.7781
	Min.	-0.1186 -0.0633 -0.0942 -0.0837	-1.7269
	Skewness	0.3143 0.3955 1.2901	0.0952	-0.3450
	Kurtosis	7.9177 6.1943 11.5108 18.0435	17.9146
	JB	1636.6 * 721.1 * 5266.2 * 15070.7 * 14842.1 *
	Q(20)	22.02	16.08	25.64	52.73 *	53.93 *
	ARCH-LM	8.32 *	10.27 *	2.30 *	4.82 *	14.10 *

Table 2 :

 2 Pearson correlation matrix.

		EUA Brent Gas Coal Switch
	EUA	1
	Brent	0.04	1
	Gas	0.02	0.11	1
	Coal	0.03	0.15	0.25	1
	Switch -0.02 -0.01 -0.21 0.09	1

Table 3 :

 3 Copula models.

Table 4 :

 4 Parameter estimates for the marginal distribution models.

		EUA	Brent	Gas	Coal	Switch
	Mean equation
	φ 0	0.000	-0.000	-0.000	-0.000	-0.001
		(0.38)	(0.75)	(-1.83) (-1.01)	(0.03)
	φ 1				0.112 *
					(5.21)
	Variance equation
	ω	0.000 *	0.000	0.000 *	0.000 *	0.000 *
		(2.49)	(0.77)	(2.44)	(8.62)	(3.67)
	α 1	0.054 *	0.008	0.038 *	0.021 *	0.071 *
		(3.41)	(1.23)	(3.55)	(6.86)	(2.12)
	β 1	0.913 *	0.967 *	0.933 *	0.949 *	0.761 *
		(67.74) (130.67) (77.96) (69.61) (40.88)
	λ	0.052 *	0.050 *	0.050 * -0.021 *	0.670 *
		(2.51)	(4.80)	(2.31)	(-6.44)	(4.95)
	Tail	5.712 *	7.946 *	4.780 *	2.130 *	2.887 *
		(7.26)	(4.73)	(8.88)	(12.46) (11.65)
	Log-Likelihood	3658.25 4440.58 4189.28 5181.01 1408.41
	Q(20)	21.95	12.18	18.79	23.94	22.08
		[0.34]	[0.91]	[0.53]	[0.24]	[0.33]
	Q(20)2	13.41	15.62	10.20	27.76	7.84
		[0.85]	[0.74]	[0.96]	[0.12]	[0.99]
	ARCH(20)	0.74	0.77	0.49	1.35	0.42
		[0.77]	[0.76]	[0.96]	[0.13]	[0.98]
	K-S	[0.85]	[0.21]	[0.47]	[0.36]	[0.12]
	C-vM	[0.91]	[0.25]	[0.55]	[0.34]	[0.11]
	A-D	[0.93]	[0.38]	[0.23]	[0.25]	[0.11]

Table 5 :

 5 Case 1: Selection criterion for vine copula models.

		C-vine D-Vine R-Vine
	Loglikelihood 92.67	90.52	92.31
	AIC	-173.35 -169.04 -172.62
	BIC	-141.09 -136.79 -140.36

Table 6 :

 6 Case 2: Selection criterion for vine copula models.

		C-vine D-Vine R-Vine
	Loglikelihood	2.91	2.91	2.91
	AIC	0.18	0.18	0.18
	BIC	16.31	16.31	16.31

Table 7 :

 7 Case 3: Selection criterion for vine copula models.

		C-vine	D-Vine	R-Vine
	Loglikelihood 1172.24 1173.05 1173.05
	AIC	-2318.48 -2320.11 -2320.11
	BIC	-2248.58 -2320.11 -2320.11

It is worth noting that we are not leaning towards establishing causal relationships in this paper. The very logic of copula is instead to study dependencies; that is, how are markets linked in average and extreme market conditions, with a specific focus on the moderating role played by the electricity variables.

In the electricity price forecasting literature, electricity prices are either taken as they are or transformed with functions which can handle negative prices (such as probability integral transform), see e.g., Uniejewski, Weron and Ziel (2018).

The notations developed in this section draw substantially on previous works by Chevallier (2011) and Chevallier and Goutte (2017).

In this paper, we do not consider the costs associated with regulatory changes, workforce, and operations and maintenance. This assumption allows us to make the model more inclined to empirical work.

We cannot conduct robustness checks on raw data because raw returns are not i.i.d. Therefore, econometric theory teaches us to infer dependency relationships from residuals instead. This is standard practice in copula estimation (see Jaworski et al., 2010 for a review).

For reasons of brevity, results for the structural break test and for time-varying pair copulas are not reported here, but are available on request.

The detailed results are not reported here for the sake of concision but can be entirely made available upon request to the authors. We wish to thank an anonymous reviewer for this valuable suggestion.

tricity producers to switch from coal-fired plant to gas-fired plant because they are only weakly and negatively associated with the electricity prices proxied by the switch variable.

Dependence features

Copula family positive negative symmetric Lower tail Upper tail


Georges Vachaud
email: georgesvachaud5@gmail.com

Fanny Quertamp

Thi San

Ha Phan

Tien Dung

Tran Ngoc

Thong Nguyen

Xuan Loc Luu

Anh Tuan Nguyen

Nicolas Gratiot

PHAN Thi San Ha

Nguyen Thong

Loc

Tuan

Flood-related risks in Ho Chi Minh City and ways of mitigation

Keywords: adaptation to urban inundation, tropical rain, wave set-up by tides, tsunamis, dam failure, climate change, subsidence, urban planning strategy

1-Introduction

Ho Chi Minh City is a low elevation coastal megacity with a very large and rapidly increasing population. Economic activity is also very high and rising in line with the population increase. Like most megacities in South East Asia or India that were built within a delta's boundaries, HCMC is affected by flood related risks aggravated by the conjunction of heavy rains and high tide levels. This situation is driven by three factors: low elevation of the land above sea level, extensive urban growth yielding to soil subsidence, and an extension of impervious areas resulting in increased runoff.

Over the last 300 years, HCMC has gone through several phases of expansion. Because the city is bordered by the Saigon River and intersected by several creeks, water has always been a fundamental part of its identity. In the late 18th and early 19th centuries, the Nguyen Dynasty expanded the canal network to improve waterway transportation and facilitate commercial activity. Under French rule in the first half of the 20 th century the urban face of Saigon underwent major changes, in particular the canals intersecting the city center were filled to create tree-lined boulevards [START_REF] Nu | Le réseau des canaux et arroyos à Saigon -Cholon jusqu'à la première moitié du xx° siècle : évolution du processus d'utilisation du réseau hydraulique entre flux commerciaux et urbanisation coloniale[END_REF].

Swampy areas were also filled to build residential areas and concomitantly, the network of remaining canals was progressively used as an open-air sewage system (domestic as well as industrial waste water) [START_REF] Givental | The Ho Chi Minh City canals: assessing vulnerability and resilience factors[END_REF]. Water is now the main focus of all worldwide climate-related issues and HCMC finds itself on the top-ten list of cities categorized as being in the greatest danger of coastal flooding [START_REF] Small | A global analysis of human settlement in coastal zones[END_REF]ISPONRE, 2009). This paper proposes a multiple perspective approach to characterize the principal risks of flooding caused directly by heavy tropical rain and runoff and/or high tide wave-setup, and ways to mitigate them. First, field measurements were taken throughout the urban area to quantify flooding by rain and to assess the flood risks in those neighborhoods. This quantification is complemented by numerical simulations to characterize the risks of submersion caused by either tsunami waves or the rupture of a dam as well as data related to the expected increase in future sea levels. Once the main results of these flood related risks are cross-referenced and assessed we discuss possible urban planning for Ho Chi Minh City's future development.

2-Material methods

Study site

HCMC is located in a low-elevation coastal zone in the upper border of the Mekong Delta and 65% of its territory is at an altitude below 1.5 m above sea level (Fig 1). It is characterized by a subtropical monsoon climate with two distinguished seasons. The rainy season extends from May to November with a heavy period from September to October. In total, about 160 rain events occur yearly with an average cumulated rainfall of roughly 2000 mm. Because of the convective pattern of precipitation events, the rain is non-uniformly distributed at the scale of the megacity, with considerable differences from one district to another for a given storm event. This variability at short spatial scale is currently not accounted for in weather forecast reports. In conjunction with heavy precipitation, HCMC is also affected by the combined effects of semi-diurnal tides waves, with amplitude reaching a maximum of 1.5 m, and high water discharge from both upstream rivers; namely the Saigon and Dong Nai rivers.

HCMC has been experiencing severe accelerated urbanization since the start of the last decade with up to 100% of land surface constructed upon in some sectors [START_REF] Nguyen | Size, shape and dispersion: urban form evolution in Saigon river basin and its impacts on hydrologic performance from 1990 to 2010. 49 th ISOCARP Congress[END_REF]. Heavy rain intensity and lack of sewage infrastructure makes the megacity highly vulnerable to flood risk. As shown in the present study, the spatio-temporal dynamics of flooding in HCMC differs significantly when driven by rainfall or river overflow.

Monitoring rain and flood zones

Since 2002, a monitoring network has been developed to survey urban flooding at the street scale (Tran Ngoc, 2002) and includes 11 automatic rain gauges distributed all over the city as well as monitoring cameras installed in 2013. This network is completed by visual observations to characterize the submerged areas, i.e., to measure water depth, duration and spatial extension of any inundations. Since 2009, inundation areas have been systematically classified into two typologies: submerged areas are referred to as "old" for those that are regularly submerged from year to year, or "new" for those appearing in different locations from year to year.

Numerical modeling

To assess another risk of flooding by tsunami or dam failure, numerical simulations were undertaken with Telemac2D code [START_REF] Lang | [END_REF]. This software is based on the Barré de Saint Venant equations and assumes 2D shallow water conditions. Initially developed by Electricité de France (EDF), it was chosen for its ability to solve large-scale problems with reasonable computation time.

The first case study aimed to evaluate the effects of a tsunami that could occur due to an ocean quake (with different levels) in the East Sea: a potential earthquake area because of its geological structure. Hypothetical numerical runs were conducted by placing the epicenter about 240 km from Vietnam's south coast. The purpose was to determine the spatio-temporal characteristics of tsunami waves and help authorities set up early warning procedures. As presented in Fig 2a, the numerical domain extended up to HCMC. The discretization scheme consisted of 1,045,000 triangular elements, varying in size from 500 to 4,000 m for the seaward extension of the domain to a size of 10 m to describe the streets in the urban context. Different cases of earthquake magnitude corresponding to 7.6, 7.8, 8.0, and 8.35 on the Richter scale were simulated. It took one hour of computation to simulate ten hours using an Intel server cluster on parallel mode with 16 cores.

The second case study was undertaken with the same numerical model and grid of discretization, but focused on the domain located upstream of HCMC. It aimed to assess the city's submersion risk in the event of the Dau Tieng dam failure, which is located eighty kilometers upstream of HCMC. This earth dam was constructed between 1981 and 1985 for agricultural irrigation in the provinces surrounding HCMC and has a total capacity of 1.58 billion m 3 of water and maximum water level of 28 m. The study area (Fig 2b) extended from the Dau Tieng Lake to the estuary and represented a surface of 5,000 km 2 . It was discretized with 270,000 triangular elements. The simulation was done for a failure width of 500m, corresponding to a maximum instantaneous flow discharge of 40,000 m 3 /sec in a section located ten kilometers downstream of the dam. demonstrates that heavy rain events exceeding 100 mm are not rare and can be observed every year. However, important inter annual variability can also be observed.

3-Results and discussion

Coupled effects of rainfall and urbanization

Another important result is that some locations are systematically submerged, yet each year new flood sites can be observed (Fig 3b). The total number of submerged locations was the highest in 2008 (126 locations), as a result of a very sharp increase in building density since the beginning of the 1990's. During this period, the impervious surface increased 8 fold in the flood-prone area and the population increased by 2 fold [START_REF] Nguyen | Size, shape and dispersion: urban form evolution in Saigon river basin and its impacts on hydrologic performance from 1990 to 2010. 49 th ISOCARP Congress[END_REF]. This figure also shows that the number of submerged sites changed considerably over the 2008-2015 period. First, it decreased steeply from 2008-2011 to reach a minimum of 30 inundated sites. This can be related to the reduction from 4 to 1 of rainfall events larger than 100mm (Fig3-a) , and also to large scale restructuration of the drainage infrastructure in the downtown area (Tran Ngoc, T.D., 2015). The resurgence of flooding observed in 2013-2014 is likely due to the development of peri-urban zones with poor sewer installation and poor maintenance , and to the increase of rainfall events It also seems that the time needed to reduce flooding (by drainage infrastructure) in the areas transitioning from small houses and gardens in 2008 to full urbanization in 2014 was much longer than anticipated, as illustrated in Fig 3c .    Another consequence of intensive urbanization is that soil subsidence has reached a rate of 0.02 to 0,04 m/yr in some sectors and is illustrated in Fig 4a . This subsidence is greatest in the city center along the Saigon River (districts 7, 12, Binh Thanh, Thu Duc) and in the southwest peri-urban sectors (districts 6, 8 and Binh Chanh). In these sectors, old traditional houses have been demolished to make way for high-rise buildings (some of them more than 50 floors) and commercial centers. Subsidence here is the result of intensive groundwater pumping to secure building basements and is also linked to the construction of a new underground metro system due for completion in 2019. [START_REF] Dinh | Mapping ground subsidence phenomena in HCMC through the radar interferometry technique using ALOS PALSAR data[END_REF] also demonstrated the impact of geology because the most severe rates of subsidence were observed in the Holocene silt loam areas along the Saigon River and in the southwest of the city. It is obvious that this process leads to an accumulation of runoff and limits the evacuation by gravity of the flooded zones.

Overall, it is clear the city has several flood-prone areas with submersion levels varying

Incidental flooding driven by wave propagation

Two numerical simulations were performed to determine the flood risk for several districts along the Saigon River that could result in wave propagation originating from either a tsunami in the East Sea or a reservoir dam failure upstream of HCMC, respectively.

For a quake reaching an intensity of 8.0 on the Richter scale, the average celerity of a tsunami's waves from the earthquake's epicenter to the estuary is about 20.5m/sec. The change in sea level height after 1.5 hours is presented in Fig 5a . The tsunami's peak arrives at the estuary after approximately 3.25 hours and here the highest water level attains seven meters. The wave reaches downtown HCMC after an additional 4.5 hours (Fig 5b) and induces a wave between 1.5 and 3 m above the initial street level according to the different simulations considered. It is worth noting that during propagation along the mangrove fringe, tsunami waves could be greatly dissipated by this type of ecosystem [START_REF] Barbier | Coastal ecosystem-based management with nonlinear ecological functions and values[END_REF]. It was not possible to include this mitigating effect in our simulation but it should be taken into consideration in the future.

The second case study of failure at the Dau Tieng dam is presented in Fig 6 . The flood wave has an amplitude that decreases rapidly from a peak of nearly 18 m at 20 kms downstream of the dam to less than one meter in the city center. As shown in Fig 6, the fluctuations due to tidal forcing (dashed black line) are comparable to those related to the impact of dam failure (solid black line). From this, it seems clear that HCMC is moderately vulnerable in the event of dam failure at Dau Tieng. The existence of a floodplain located upstream of HCMC where discharged water can spread may explain these simulated results. While the spread would protect HCMC's infrastructure and inhabitants, it would undoubtedly cause major damage in the upstream agricultural zones.

The conclusion that can be drawn from these simulations is that the risk of flooding from a tsunami would most likely be much larger than from dam failure.

3.3-Long-term vulnerability

A realistic flood risk assessment and its long-term evolution should also take into underlines that without a drastic reduction (50%) in greenhouse gas emissions, the area of South Vietnam could be seriously affected by the conjunction of two effects:

-from a hydrometeorological perpective, an increase in the occurrence of typhoons and extreme rainfall (by 10 to 20%) is anticipated, with a strong impact on river flow and riverbank erosion.

-from an ocean perspective, an increase of the sea surface temperature to 30°C or more in the South Pacific zone combined with the melting of Antartica ice sheet could produce a sea-level rise of 1 m by the end of this century if greenhouse gaz emissions continue unabated, as recently analyzed by R.M de Conto, D. Pollard (2016) on the basis of innovative numerical simulations coupling ice sheet and climate dynamics The situation will certainly be exacerbated by the impact of human activities on soil subsidence at both the urban and regional scale. In addition to the megacity situation discussed in section 3.1 and presented in Fig 4, agricultural practices in the Mekong Delta are responsible for a very worrying situation, as pointed out by [START_REF] Erban | Groundwater extraction, land subsidence, and sea-level rise in the Mekong Delta, Vietnam 2014[END_REF]. Through a set of observations obtained by satellite radar imagery over the delta from 2006 to 2010, the authors clearly highlighted a rate of soil subsidence varying between 0.02 and 0.04 m/year and an average decrease by 0.30 m per year of groundwater levels. A similar interplay between groundwater levels and soil subsidence was also reported by Dinh et al. (2014) for the HCMC region.

Consequently, the subsidence of soil at the regional scale could be higher than the rise in sea level by the end of this century. The cumulative effects could result in the lowering of the average soil level with respect to the sea level by 0.03 to 0.05 m/year; in other words, a 1.5 to 2.5 m rise in a 50 year period. The submersion of the quasi totality of the coastal fringe is to be feared: the loss of agricultural land (notably rice) due to salinization and the consequent migration of millions of inhabitants would have an enormous impact. A significant part of this migratory flux would probably be in the direction of HCMC, where large areas could also be submerged.

3.4-Urban planning strategy

In light of these results, it seems evident that to achieve sustainable development there needs to be revision of Ho Chi Minh City's urban development policies with a much greater emphasis on and integration of flood management strategies. For the time being, the city's rate of urbanization is advancing at an alarming rate, with former wetlands being filled and transformed into new development areas such as Phu My Hung and Thu Thiem. The megacity's continual expansion raises questions about the capacity of the soil to absorb runoff and its impact on floods [START_REF] Kim | Integrated urban flood risk management approach in context of uncertainties: case study Ho Chi Minh City[END_REF]. Since 2008, authorities in HCMC have been developing a Master Plan of coordinated urban expansion to be in place by 2025. This plan proposes the adoption of a multi-center city model with four major development areas and several additional urban projects. As can often be observed, there is a gap between planning and reality (ADETEF, 2012). Experts and local policy makers are in agreement that alternative measures need to be integrated [START_REF] Lempert | Ensuring robust flood risk management in Ho Chi Minh City[END_REF]. In particular, investment in infrastructure needs to comply with land use policies, construction law and urban planning in order to implement the concept of a sustainable city at different scales. Furthermore, the development of urban areas alongside existing waterways and in low-lying swampy areas is met with institutional, technical and financial challenges.

At the institutional level, the challenge is to implement a coherent urban planning policy by breaking it down into national, regional and urban levels. It is crucial to promote a transversal approach (land use, urban planning and water management), to adopt a multi-scale vision, and to avoid single-sector and single-project approaches [START_REF] Eckert | Pacific News Nr 31. Climate Change and challenges for the urban development of Ho Chi Minh City/Vietnam[END_REF]. At the technical level, development of relevant urban planning tools is required at the planning stage: environmental impact studies should be enforced to ensure sustainable water balance when a wetland site is filled. Setting-up monitoring networks and access to acquired data is a prerequisite to develop robust scenarios coupling measurement, statistics and numerical simulations. A further challenge concerns the need for innovative construction techniques adapted to the geology of particular sites. This would include the construction of underground works such as metro lines and basement parking areas.

These challenges have been debated during workshops with policymakers in order to consider the water-related problems of urbanization in an integrated way. For example, the rivers and channels in HCMC were long considered as being for transport only, but they are now also considered as recreational areas and important for the city's identity as they improve the quality of life for residents. Recent urban development projects in the HCMC metropolitan area have already brought major improvements by greening riverbanks and improving water quality in the creeks and Saigon River.

One of the main challenges for Ho Chi Minh City's future is to allocate more space to green and blue belts in planned layouts. Urban multi-functional basins (Fig 7a) could respond to hydrological and environmental issues by preserving areas for storm water retention and storage of tidal flow volumes (rising tide). They could also integrate urban and landscape planning at different scales (PADDI, World Bank, 2014).

An integrated territorial approach needs to account for the specific context of the estuary and the city. It should connect sites with surrounding neighborhoods by prioritizing the entity of 'the park ' and enhancing the river embankment's value. This would help the city to adopt a more sustainable urbanization policy, particularly in the implementation of city water infrastructure projects, and to mitigate and reduce flooding hazards. In addition, upgrading and use of the water network will also create favorable conditions for the development of waterway transportation and river tourism.

In 2012, the Centre de Prospective et d'Etudes Urbaines de Ho Chi Minh Ville (PADDI) proposed several courses of urban action relating to large civil engineering projects for dike network construction in order to reduce the risk of flooding, for example:

-Reducing flow velocity by facilitating the spread of the rising tide flow upstream.

-Developing storm water storage facilities away from tidal influence in order to reduce the discharge flow in sewage networks after a storm (or a dam failure) and the risks of overflow on roads at high tide.

-Facilitating rain water infiltration by preserving natural environments or installing storm water infiltration ponds.

A good example is the upcoming creation of a new urban area by the name of Thu Thiem, which is presently a swamp in one of the meanders of the Saigon River (Fig 7b). The plan includes a residential area and large urban park that takes into account possible inundation and includes an artificial lake for water retention. Because of its strategic location just in front of the city center, Thu Thiem should have the capacity to mitigate tidal floods and high water events through man-made canals, lakes and mangrove areas and at the same time to accommodate over 130,000 residents.

4-Conclusion 14

The mitigation of water related risks is a priority for many megacities, especially those located in low-elevation tropical coastal areas. Considering the vulnerability of HCMC and its economic importance at the regional scale, a multidisciplinary approach has been adopted to evaluate the interplay between urban development planning and floodrelated risks within the framework of natural hazards and of climate and humaninduced changes.

In recent years, many studies have been conducted to assess the vulnerability of this megacity to rainfall induced flooding. Based on spatial monitoring of rainfall and of the flooded areas, the results showed that the risk is especially intense during building construction phases. Maintenance of the drainage network appears to be a simple and essential measure to ensure optimal functioning of properly sized sewers.

We further analyzed the risk of flooding by tsunami or dam failure. The numerical simulations undertaken show that HCMC is more vulnerable to inundation by tsunami than by dam failure. This asymmetric response of the watershed to wave propagation mainly results from topographic effects. In the event of a dam failure, wave energy would be rapidly dissipated by spreading out over the flood plain upstream of HCMC.

The habitations and infrastructure of this rural region would undoubtedly be severely affected. In the case of a tsunami, wave energy would be amplified during its propagation into the river network. It is worth noting that the dissipation of wave energy during its landward propagation into the mangrove fringe has not been taken into account in the present simulation and could mitigate the effects presented in the simulations.

Recent satellite based observations of the megacity and of the Mekong Delta, have demonstrated that without a drastic reduction in greenhouse gas emissions the combination of both the effects of soil subsidence and the expected impact of climate change on rising sea levels could lead to submersion of a large part of the Lower Mekong Basin, including low elevation areas of HCMC within a period of 30 to 50 years.

The current Master Plan for HCMC will be revised in the next few years. As part of this process, the Department of Urban Planning and Architecture (DUPA) is currently working on methodology to integrate climate change issues into the new urban plan, especially to assign specific land use as a key adaptive instrument. An example of this new plan of action is that HCMC is also developing some sectorial measures to build retention basins in several districts, and to limit urban extension in the wetlands. It is clear that integrating sea defense services provided by mangrove areas should be a prerequisite to any planned seaward urbanization.

The development plans can only be efficient if there is coordination between national and local authorities as well as technical departments. The "Climate change Office", established in 2012, will undoubtedly play a major role in the implementation of measures to increase the resilience of the city.

5-Acknowledgements

This paper was prepared within CARE (Centre Asiatique de Recherches sur l'Eau) a joint research laboratory between HCM University of Technology and Grenoble-INP, and implemented through RESCIF, the Network of Excellence in Engineering Sciences of the French Speaking Community (www.rescif.net/en ).

List of figures

Fig

  Fig 3a represents the number of storm events observed in HCMC from 2007 to 2014 and

  from 0.15 to 0.65 m (Fig 4b -produced by the Earth Observation Service of ESA) resulting from rainfall variability and/or high tide wave set-up and that both are impacted by subsidence. Comparison between figures 4a and 4b clearly demonstrates this conjunction between subsidence and flooding.

  account the effects of human-induced climate change. A series of scientific works coordinated by the Intergovernmental Panel on Climate Change (IPCC) and summarized in its 5th IPCC Report (part 2, Impact, Adaptation and Vulnerability, March 2014)

Fig 1 -

 1 Fig 1 -Elevation Map; the green color corresponds to an altitude lower than 1.5 m

Fig 3 -

 3 Fig 3 -Flooding by rain in HCMC. A) Number and typology of rainfall events, from 2007 to

Fig 4 -

 4 Fig 4 -A-Historical Mapping of subsidence rate produced by radar interferometry from

Fig 2 -

 2 Fig 2 -Description of the numerical grid domain for the simulation of tsunami waves (A)

Fig 3 -

 3 Fig 3 -Flooding by rain in HCMC. A) Number and typology of rainfall events from 2007 to

  Fig 4 -A-Historical Mapping of subsidence rate produced by radar interferometry from

The work has been conducted with the financial support of Région Auvergne-Rhône Alpes, France within CMIRA/COOPERA research funding program. We would like also to thank the Agence Universitaire de la Francophonie, AUF for financing the EPH2 project.

IGE is part of Labex OSUG@2020 (ANR10 LABX56)