This article was downloaded by: [University of Newcastle, Australia] On: 28 December 2014, At: 07:59 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK International Journal of River Basin Management Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/trbm20 Effect of climate change on navigation channel dredging of the Parana River a b c c Massimo Guerrero , Mariano Re , LeanDro David Kazimierski , Ángel Nicolás Menéndez & d Rita Ugarelli a Hydraulic Laboratory, University of Bologna, Bologna, Italy b Hydraulics Laboratory, National Institute for Water, Ezeiza, Buenos Aires, Argentina c Hydraulics Laboratory, National Institute for Water, Ezeiza, Buenos Aires, Argentina d SINTEF, Oslo, Norway Accepted author version posted online: 04 Jul 2013.Published online: 02 Sep 2013. To cite this article: Massimo Guerrero, Mariano Re, LeanDro David Kazimierski, Ángel Nicolás Menéndez & Rita Ugarelli (2013) Effect of climate change on navigation channel dredging of the Parana River, International Journal of River Basin Management, 11:4, 439-448, DOI: 10.1080/15715124.2013.819005 To link to this article: http://dx.doi.org/10.1080/15715124.2013.819005 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. 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River Basin Management Vol. 11, No. 4 (December 2013), pp. 439–448 # 2013 International Association for Hydro-Environment Engineering and Research Research paper Effect of climate change on navigation channel dredging of the Parana River MASSIMO GUERRERO, Hydraulic Laboratory, University of Bologna, Bologna, Italy Downloaded by [University of Newcastle, Australia] at 07:59 28 December 2014 MARIANO RE, Hydraulics Laboratory, National Institute for Water, Ezeiza, Buenos Aires, Argentina. Email: [email protected]ﬁ.uba.ar (Author for correspondence) LEANDRO DAVID KAZIMIERSKI, Hydraulics Laboratory, National Institute for Water, Ezeiza, Buenos Aires, Argentina ÁNGEL NICOLÁS MENÉNDEZ, Hydraulics Laboratory, National Institute for Water, Ezeiza, Buenos Aires, Argentina RITA UGARELLI, SINTEF, Oslo, Norway ABSTRACT This paper presents an analysis of the effect of climate change on modifying the dredging cost to maintain the navigation channel at the actual capacity of the Parana waterway (Argentina). The Parana2Paraguay Rivers system is one of the most important inner navigation waterways in the world, where approximately 100 million tons of cargo are transported per year. Maintenance of the navigation channel requires continuous dredging by Hidrovı́a SA (limited liability company), which is responsible for ensuring the minimum water depth for navigation. A failure event occurred during January 2012 when a bulk cargo carrier ran aground, interrupting ﬂuvial trading for 10 days. Numerical models were applied to simulate hydro-sedimentation processes at the Lower Parana River to estimate dredging costs for a given ﬂow discharge. The resulting function relates the sedimentation rate (i.e. the dredging effort required to keep the present depth for vessel draft) to forcing hydrology conditions. This function and the statistical evaluation of climate scenarios were used to calculate the probability of failure for navigation and the associated cost of channel maintenance. The most appropriate dredging effort was estimated by detecting the minimum total cost (i.e. dredging plus failure) to varying the yearly average discharge and by analysing the sensitivity of the total cost to different degrees of economic impact. Keywords: Parana River; climate change impact; navigation channel maintenance 1 Iguazu, approximately 1500 and 2000 km northwest and northeast from Buenos Aires, respectively, at the border of Argentina with Paraguay and Brazil (Figure 1(a) and 1(b)). Fluvial trading in the downstream part of this system, from Buenos Aires to Santa Fe, has increased continuously over the last 10 years, passing from approximately 4100 to 5100 vessels of mostly bulk cargo, tanks and containers (Gómez et al. 2012). The Parana River is navigable for most of its route in Argentina, but low water-depth sections (‘pasos’ in Spanish) drastically reduce the admitted vessel draft. Sediment deposition in the navigation channel therefore requires regular and systematic dredging to maintain the channel capacity. For the main portion of the Parana waterway in Argentina, i.e. the Oceanic and Fluvial2 Maritime channels from Rio de la Plata at the ocean inlet to Santa Introduction Freight transportation in the world is performed primarily by means of seas and large rivers because navigation is the most inexpensive medium per unit weight. The Parana2 Paraguay navigation route is a relevant resource for the Mercosur and, in particular, for Argentina. In Argentina, 84% of import2export goods are transported by navigation versus a world average of 90%, and 50% of that trade is transported by Parana navigation (Gardel 2008). This route is approximately 2500 km long, including long sections of the Parana and Paraguay Rivers and three navigation channels of different capacities: Oceanic for 10 m draft vessels, Fluvial2Maritime for 7 m draft vessels and Barcacera for 3 m draft vessels. The Parana2Paraguay waterway links the ocean to Asunción and Received 18 February 2013. Accepted 20 June 2013. ISSN 1571-5124 print/ISSN 1814-2060 online http://dx.doi.org/10.1080/15715124.2013.819005 http://www.tandfonline.com 439 Downloaded by [University of Newcastle, Australia] at 07:59 28 December 2014 440 Massimo Guerrero et al. Figure 1 (a) La Plata Basin; (b) the Parana-Paraguay water way; and (c) the study section at Rosario with Paso Borghi. Fe (Figure 1(b)), the sediment volume displaced for the year is approximately 25 × 106 m3 (Garcı́a 2008). Determining future efforts that must be expended in dredging will provide important knowledge for the National Ports and Waterways Authority and for the concession company Hidrovı́a SA (limited liability company). Hidrovı́a SA has been in charge of the maintenance of the aid system for navigation and for dredging from Santa Fe to the ocean since 1995. The cost effectiveness of freight transportation by means of the Parana waterway depends mainly on the expected water depth and consequent admitted vessel draft. Climate change may affect navigation in rivers (Hawkes et al. 2010). Changes in rainfall over a watershed alter the occurrence of extreme hydrological conditions and indirectly modify navigability. Climate may also force changes in river morphology by modiﬁed erosion and sedimentation that, in turn, affect vessel manoeuvres and the operational efﬁciency of navigation structures. Sung et al. (2006), De Wit et al. (2007) and Millerd (2011) focused on water-level modiﬁcation due to variations in hydrology that would eventually impact navigation. Bed-level change effects on navigation channels were considered to a lesser extent by Verhaar et al. (2010). This paper presents a method to predict the cost to maintain current admittance for vessel draft and the corresponding probability that the predicted dredging effort will be exceeded given the probability distribution of the yearly average discharge. In this context, navigation channel failure is deﬁned as the impossibility of maintaining actual admittance for oceanic vessels (10 m draft) by means of dredging. The method was applied to the Lower Parana River near Rosario (Argentina). The low water-depth section, i.e. the Paso Borghi, of that area may present considerable limitations to ﬂuvial trading by means of oceanic vessels because the largest ports for agriculture and steel industry production are located near Rosario. This part of the Lower Parana is representative of the Fluvial2Maritime waterway from Santa Fe to the Parana River bifurcation (Parana de las Palmas and Parana Guazu) at the beginning of the lower delta, which is a navigation channel 350 km in length. The navigation channel morphodynamic dependence on yearly average discharge at the Lower Parana River was simulated in a quasi-steady-state approach by our own developed numerical models (HIDROBID II and AGRADA), as introduced in Section 2 of this document. These models were developed and already well tested on the Parana navigation channel (Menéndez 1990, 1994, Re et al. 2012). The simulation of the depth-averaged ﬂow ﬁeld (i.e. 2D-H simulations), performed by HIDROBID II, provided boundary conditions for the following 2D-V-morphodynamics runs. The AGRADA modelled the bidimensional morphodynamics of the dredged trench within the vertical plane aligned to the streamﬂow, i.e. a 2D-V scheme, for a given yearly average discharge, with the bottom level being preliminarily dredged to current admittance, i.e. 10 m draft vessel. Section 3 reports on the assessed functions that relate the simulated sedimentation rate to the yearly average discharge. The sedimentation rate is assumed to correspond to the dredging effort to maintain the navigation channel. The statistical distributions of the twentieth century and of future discharge are also presented in Section 3. Given these functions and under the framework of ‘Risk Assessment’ (ISO 2009, Ugarelli and Røstum 2012), the most appropriate management approach, in terms of sustainable dredging efforts, is discussed in Section 4 with respect to the Effect of climate change on navigation channel dredging hydrology of the past century and to predicted future scenarios, assuming the current unit cost of dredging and reliable costs of failure per day. Downloaded by [University of Newcastle, Australia] at 07:59 28 December 2014 2 The morphodynamic modelling Two of our own developed numerical models were applied with the objective of simulating the average rate of sedimentation at the navigation channel, which was assumed to correspond to the dredging rate. To this end, the channel morphodynamics was simulated with a quasi-steady-state approach, given the yearly average discharge as the hydrological steady-state condition. The method is based on the reasonable assumption that, for short-term modiﬁcations, the navigation channel is not affected by changes in river morphology. Inter-decade morphodynamics was observed (Castro et al. 2007) and modelled (Nones et al. 2012, 2013, Guerrero et al. 2013) at the Lower Parana. Three-month bathymetry of the navigation channel is regularly used to deﬁne the dredging plan for the following period. This difference in time scales also corresponds to different space scales, with the navigation channel width being approximately 100 m, whereas the river cross-section is several kilometres wide. The overall river morphology was considered a ﬁxed boundary, and a 25 km section, including the Paso Borghi and an additional upstream stretch (Figure 1(c)), was hydraulically simulated to provide boundary conditions for subsequent modelling of the navigation channel morphodynamics. These boundary conditions include water levels, ﬂow velocities and planimetric misalignments between the navigation channel axis and the streamﬂow. The selected method also implies geometrical oversimpliﬁcations of the simulated domain. For large river sections, such as the 25 km Rosario reach, the depth-averaged scheme (i.e. 2D-H model) reliably represented the overall hydraulics, while the development of the dredged trench was simulated within the vertical plain (i.e. 2D-V model) aligned with the main streamﬂow (Figure 2). 441 The applied method consists of two steps: (1) a simulation of boundary conditions on the regional scale (i.e. the 25 km section) was obtained by means of the 2D-H HIDROBID II model (Menéndez 1990) and (2) a 2D-V model AGRADA (Menéndez 1994, Re et al. 2012) was applied to simulate manmade trench development at a given yearly average discharge, with the bottom level being preliminarily dredged to current admittance, i.e. 10 m draft vessel. 2.1 Method implementation and validation Navigation channel maintenance across the Paso Borghi (Figure 1(c)) requires signiﬁcant dredging activity. This stretch was therefore selected as a relevant case study to characterize navigation channel dredging between Santa Fe and the Parana River bifurcation, at the beginning of the lower delta, as well as the consequent cost of maintenance. Given the actual depth of dredging, the Paso Borghi extends over a 431.3 – 438.5 km stretch of the Parana navigation route, with the longitudinal coordinates upstream rising, as reported in Figure 1(b). The National Ports and Waterways Authority provided access to the database of dredged volumes distributed along the navigation channel during the year April 2008 – April 2009. This data set shows that the operations were concentrated in two subsections: the upper Paso Borghi (from 436.8 to 438.5 km) and the lower Paso Borghi (from 431.3 to 433.9 km). Validation of the method used for the upper Paso Borghi is reported in this paper. To verify the numerical modelling, representative dredging rates were assessed from dredged volumes and then compared to simulated sedimentation rates. The dredging rate per year was determined for 100 m segments of the dredged channel. The upper Paso Borghi was ﬁnally grouped into three subsections that follow the operational dredging rate along the channel, as reported in Figure 3. The time between dredging operations was calculated for each segment, yielding a typical period of approximately 60 days between dredging episodes. The ﬁrst step of the method gave the depth-averaged ﬂow ﬁeld at the regional scale (i.e. the 25 km Rosario reach of Figure 1(c)), which includes the Paso Borghi. The 2D-H (i.e. Figure 2 The navigation channel stream ﬂow misalignment within the river stretch (a and b) and the 2D-V AGRADA model scheme (b and c). Downloaded by [University of Newcastle, Australia] at 07:59 28 December 2014 442 Massimo Guerrero et al. Figure 3 Schematic interpretation of dredging rates for the upper Paso Borghi; the record of dredged volumes (dredging record) along the navigation channel is compared to the operated simpliﬁcation (model scheme) into simulated subsections (1– 3) corresponding to three stream tubes. vertically averaged) model was applied and calibrated, relying on the bathymetric survey carried out in 2009 over the Rosario reach (Guerrero and Lamberti 2013). The simulation domain covers the active channel of the river from 455 km of the navigation route to the Rosario2Victoria Bridge (430 km). The measured ﬂow discharge (of approximately 13,600 m3/s on June 29 – July 3, 2009) and water level were imposed at upstream and downstream boundaries, respectively, and a calibration was performed on the basis of the measured ﬂow-velocity proﬁles (by means of Doppler proﬁlers) concurrent to the bathymetry survey (Guerrero et al. 2011, Guerrero and Lamberti 2013). The second step was to apply the 2D-V hydromorphodynamic model simulating sedimentation into the dredged trench. This model calculates the sedimentation rate for the three subsections of the Paso Borghi, accounting for suspended and bed load and consequent morphological evolution. The hydrodynamic parameters and variables (i.e. speciﬁc ﬂow discharge, water depth, angle between the channel axis and the streamﬂow) were available from the ﬁrst step. The validation period (12 April 2008– 12 April 2009) for sedimentation rate assessment was characterized by 14,700 m3/ s as average discharge. Stream tubes conveying 250 m3/s each were deﬁned on the basis of the 2D-H simulations. One stream tube for each subsection of Figure 3 was selected, providing the hydraulic parameters for the 2D-V simulations. The available data from periodic bathymetric surveys of the dredged channel during the validation period were applied to represent the navigation channel shape in the 2D-V scheme, which was ﬁnally modelled with a trapezoidal cross-section with a 116 m wide bottom and 1-over-5 sloped sides, also in agreement with the dredging project (Figure 2(b) and 2(c)). Regarding the sedimentological parameters, different references were considered for implementation of the 2D-V morphodynamic model. The mean grain size and the porosity of the river bed sediment were assumed to be equal to 260 mm and 0.4, respectively, on the basis of the available data along the navigation route (Menéndez 2002). The settling velocity was 0.037 m/s according to the van Rijn formulation (1987). Modelled proﬁles of suspended sediment concentration near the dredged trench were consistent with the available proﬁles measured in the Rosario area of the Lower Parana (Royal Boskalis and Ballast Ham Dredging 2012). The resulting mean concentrations are in agreement with the evidence from the suspended sediment survey using backscatter proﬁling (Guerrero et al. 2011). The suspended over bed-load ratio was equal to approximately 7, consistent with ﬁeld data reported in Szupiany et al. (2010). The morphodynamic model simulates sediment entrapment by the dredged trench from the streamﬂow. This process gives rise to trench migration and diffusion, ultimately resulting in a ﬂat river bed. The upstream bank advances because of sediment settling, the downstream bank retreats because of erosion and the gravitational force diffuses sediment particles sliding over the banks. Simulations that were performed spanned the time between dredging operations, yielding the sedimentation rate per unit length for each subsection to be compared to the dredging rates, as recast in Figure 3. The sedimentation rate was assessed by the difference between initial (i.e. just dredged) and ﬁnal proﬁles of the simulated trench over the simulated time period (i.e. one year). Table 1 reports the resultant rates of sedimentation for the three subsections of the Paso Borghi and the corresponding dredging rates. Given the applied oversimpliﬁcations and our aim to support dredging management in light of climate change, the agreement between these data appears to be sufﬁciently accurate. The applied method reliably simulated the order of magnitude of the dredging rates that were applied to reliably predict the future efforts required for dredging. Table 1 Simulated rates of sedimentation and corresponding dredging rates within the validation period (12 April 2008–12 April 2009) at the upper Paso Borghi. No. Subsections (km) 1 436.75–437.55 2 437.55–438.05 3 438.05–438.55 Average for the upper P. Borghi Speciﬁc discharge (m3/m/s) Dredged volume (m3/m/day) Simulated rate of sedimentation (m3/m/day) 12.4 11.1 11.9 – 0.14 0.30 0.41 0.28 0.26 0.64 0.41 0.44 Effect of climate change on navigation channel dredging 3 Downloaded by [University of Newcastle, Australia] at 07:59 28 December 2014 3.1 Prediction of the need for dredging Climate scenarios Under the CLARIS-LPB research project (A Europe-South America Network for Climate Change Assessment and Impact Studies in La Plata Basin), the La Plata Basin surface hydrology was represented using the variable inﬁltration capacity (VIC) macro-scale semi-distributed model (Liang et al. 1994, 1996, Nijssen et al. 1997). The VIC model simulates river runoff from precipitation on a monthly scale. The details of the model and its validation can be found in Su and Lettenmaier (2009), Saurral (2010) and Montroull et al. (2012). The same project also provided the resulting monthly discharges from the hydrological VIC model when forced with past climate and four regional climate models (RCMs): PROMES (UCLM, Spain), covering a continuous run from 1991 to 4CA (SMHI, Sweden), for 1981 – 2100; RegCM3 (USP, Brazil), with information for the periods 1981 – 2048 and 2071 – 2090; and LMDZ (IPSL, France), with information for the periods 1991 – 2048 and 2071 – 2100. The RCMs were forced with different global climate models. The reliability of the scenarios that were produced was determined on the basis of the ability of the selected RCMs to reproduce the present climate features. More information on this dataset can be obtained in Saurral et al. (2013). The cumulative distributions of yearly averaged values of monthly discharges from the VIC are reported in Figure 4 for the four RCM data sets and for the past century. The same ﬁgure also reports the histogram for the period 1995 – 2012, which corresponds to the period of dredging activity by Hidrovı́a SA, and the histogram of the entire future data set, which represents a reliable means for predicting future scenarios. Since 1995, the most likely values of yearly average discharge have been larger than 15,000 m3/s. The mean discharge of the period 1995 – 2012 was approximately 17,000 m3/s, but most Figure 4 Cumulative distributions of yearly average discharge corresponding to the past century, the 1995–2012 period, future scenarios from four RCMs (PROMES, RCA, LMDZ and RegDM3) and the mean prediction (scenarios mean). 443 of the values were near to the median value of 15,800 m3/s, with only a few exceptions exceeding 18,000 m3/s. The dredged volume from the ocean to Santa Fe was approximately 25 × 106 m3/year as an average over the same period (Garcı́a 2008), with 40% (10 × 106 m3/year) from Santa Fe to the Parana River bifurcation, at the beginning of the lower delta, and the rest (approximately 60%) from Parana de las Palmas and Rio de la Plata dredging. The values of 13,600 and 14,700 m3/s (corresponding to June 29– July 3, 2009 and the period April 2008 – April 2009, respectively) to calibrate the 2D-H and 2D-V models, respectively, are consistent with the yearly average values resulting from VIC equal to about 15,500 m3/s for 2008 and 2009. In fact, the water level2discharge relation in Santa Fe gave discharge reductions of 12% and 5% for the ﬁve days in 2009 and the year from April 2008, respectively, with respect to the yearly averages. These calibration values were derived from Acoustic Doppler Current Proﬁler (ADCP) measurements in Rosario (Guerrero and Lamberti 2013) and the 1D hydraulic models validated on the Parana River (Jaime and Ménendez 1997, Nones et al. 2012, 2013). By considering the entire twentieth century, the yearly average discharge presents a larger variability, yielding 35% of the observed values lower than 15,000 m3/s. These values were grouped mostly in the mid-century (Guerrero et al. 2013). As seen in Figure 4, a clear increase can be argued for the probability of exceeding 15,000 m3/s passing from 50% of the twentieth century to 90%, on average, over the four RCMs considered. This occurrence, on average, will likely reduce the costs of navigation channel maintenance because of the corresponding increase in average water depths and admittance for vessel draft. 3.2 Sedimentation rate functions The validated method was applied to predict the need for future dredging. To this end, and given the climate change in most reliable scenarios, a sedimentation rate function of the yearly average discharge was extrapolated within the interval 11,000– 20,000 m3/s, which also corresponds to the most probable interval for discharge over the last century (Figure 4). River morphology modiﬁcation may affect the navigation channel on a larger time scale (Guerrero et al. 2013) than the scale of the dredging operation timetable. The river morphology was therefore assumed to be a ﬁxed boundary; the long-term effects of climate change on the navigation channel are beyond the scope of this work. The dredging rate to keep the present admittance for vessel draft, i.e. 10 m draft, was simulated at different discharges, representing cases where the managing authority will observe hydrological modiﬁcations (i.e. the change in the yearly average water level) and adjust the dredging reference level accordingly to maintain the admittance. Table 2 reports the simulated yearly average discharge and corresponding sedimentation rate for the lower (431.3 – 433.9 444 Massimo Guerrero et al. Table 2 Simulated average rates of sedimentation along the Paso Borghi. Flow discharge (m3/s) Downloaded by [University of Newcastle, Australia] at 07:59 28 December 2014 11,115 11,970 12,825 13,680 14,535 15,390 16,245 17,100 17,955 18,810 Lower Borghi (m3/m/day) Upper Borghi (m3/m/day) Weighted average (m3/m/day) 0.76 0.93 1.05 1.27 1.26 1.25 1.26 1.24 1.17 0.99 0.44 0.52 0.57 0.63 0.60 0.56 0.57 0.54 0.52 0.51 0.61 0.74 0.82 0.97 0.95 0.92 0.93 0.91 0.86 0.76 km) and upper (436.8 –438.5 km) Paso Borghi and as a weighted average for the entire Paso. The simulated discharges were chosen on the basis of assessed dredging rates with the objective of accurately representing the discharge-dredging rate function. The highest sedimentation rates were observed within the interval of 13,500 –17,000 m3/s. Two opposing effects inﬂuence the actual rate, giving rise to the discharge interval that most affects the navigation channel: (1) the trappingefﬁciency of the dredged trench increases at low discharge because the low water depth requires a deeper trench and (2) sediment mobility is proportional to ﬂow discharge. Low mobility of sediment prevails at low discharge, whereas low trapping efﬁciency is dominant at high water depth and discharge. In both cases, the dredging rate will be limited to the resulting low rate of sedimentation. Figure 5 Interpolation functions of simulated sedimentation rate and probability distributions of the yearly average discharge. 4 Results and discussion The simulated average rates of sedimentation along the Paso Borghi (Table 2) were ﬁtted using the parabolic equation or a smoothing spline (Figure 5). The expected sedimentation rate and the consequent cost of dredging were estimated for a variable yearly average discharge, q. The direct consequence of interrupting navigation because of water depth that is too low, i.e. the direct cost of failure, was roughly estimated on the basis of a relevant event that occurred in January 2012, when the Aristeas-P bulk cargo of more than 30,000 tons ran aground 25 km upstream of Rosario and interrupted ﬂuvial navigation for 10 days (Gómez et al. 2012). Summing the dredging and failure costs for varying discharges yielded the most appropriate management approach in terms of minimum total cost and the corresponding yearly allowance for dredging. The parabolic and spline interpolations, r(q), in Figure 5 were assumed to represent the average dredging rate to ensure 10 m draft along the 350 km navigation channel from Santa Fe to the Parana River bifurcation at the beginning of the lower delta. Given the reference period 1995 –2012, the yearly average discharge was 17,000 m3/s, corresponding to approximately 0.91 m3/m/day, regardless of the applied interpolation, and to a record high of 10 × 106 m3/year for the dredged volume from Santa Fe to the Parana River bifurcation. These values were used to scale the rate functions into the total volume to be dredged per year. The river morphology and sedimentation features downstream of the Parana bifurcation deviate signiﬁcantly from the studied reach. Additional pasos should therefore be modelled to further extend the method applicability by means of a weighted function of the sedimentation rate along the entire waterway. The volume to be dredged was calculated to be within the interval 7.0– 10.5 × 106 m3/year, regardless of the assumed interpolation, but the maximum value corresponded to 14,200 m3/s and 15,400 m3/s for the spline and parabolic interpolations, respectively. This change is reﬂected in Figure 5, where the applied interpolation functions are reported. The volume to be dredged was multiplied by the actual cost per dredged unit volume, equal to 4.48 US$/m3, resulting in a total dredging cost, CD(q), which varied in the range of 29– 47 × 106 US$/year, regardless of the assumed interpolation. Figure 5 also shows the normal distributions (within the range 11,000 – 20,000 m3/s) of the probability of yearly average Downloaded by [University of Newcastle, Australia] at 07:59 28 December 2014 Effect of climate change on navigation channel dredging discharges, p(q), for the twentieth century and for the four RCMs representing the future. The maximum sedimentation rate (and volume to be dredged) almost corresponds to the mean discharge of the twentieth century. Future discharges will likely increase drastically, yielding a lower probability for the maximum volume to be dredged. The discharge that has the greatest effect on the river channel morphology, i.e. the effective discharge, corresponds to 15,000 m3/s on average over the twentieth century (Guerrero et al. 2013). Based on this evidence, an interrelationship between the river and the navigation channel morphologies can be hypothesized. At present, almost the same discharge values appear to affect both morphodynamics processes the most, notwithstanding an order of magnitude between the river and the navigation channel space scales. This occurrence may reﬂect a substantial equilibrium between hydrology conditions and river channel morphology that mobilizes most of the bed sediment for discharge values close to the yearly average. Climate change will drive different hydrology conditions, with the yearly average discharge varying from 16,800 to 20,900 m3/s. The river morphology modiﬁcations will require many decades to achieve a new equilibrium, and the navigation channel morphodynamics will respond quickly. The river morphology was considered to be a ﬁxed boundary, and the sedimentation rate functions did not depend on the varying hydrology. As a result of long-term modiﬁcations, the sedimentation rate functions in Figure 5 may migrate slowly towards the future discharge distribution. Over the long term, the maximum rate may be realigned to the modiﬁed mean of the yearly average discharge. The cost of failure per year, CF(q), was assumed to scale with the probability of the expected sedimentation rate being lower than the actual sedimentation rate. Past and future probabilities of sedimentation rates that are lower than the actual sedimentation rate depend on the assessed normal distributions, p(q), 445 of the yearly average discharge and on the applied interpolation functions, r(q), to simulated sedimentation rate values. Once the expected yearly average discharge, q∗ , was ﬁxed, the corresponding CF was estimated by multiplying the daily cost of failure, c, for the total days characterized with a sedimentation rate greater than the expected rate r(q∗ ). CF|q=q∗ = 365 · c · r.r(q∗ ) p(q) · dq. (1) The total cost, CT(q), was ﬁnally estimated by summing the total dredging cost and the cost of failure per year. CT(q) = CD + CF. (2) Figure 6(a) and 6(b) reports the resulting total cost over the corresponding yearly average discharge and dredging volume, respectively, for the two applied interpolation functions, the past and future normal distributions and the assumed cost of failure per day. The cost of failure per day was roughly estimated from the Aristeas-P accident. On 18 January 2012 the Aristeas-P oceanic cargo vessel ran aground at 390.4 km near Rosario while sailing to the UK from San Lorenzo (445 km). This occurrence completely interrupted the waterway for 10 days, affecting 54 vessels that were forced to stand by ﬂuvial docks, delaying navigation plans and the delivery of goods. The Aristeas-P blockade was particularly noticeable and rare because most such events result in autonomous vessel manoeuvres that allow for continued sailing and do not give rise to economic consequences. Gómez et al. (2012) investigated the direct costs of the obstruction of navigation in the case of the 2012 major Figure 6 Total cost function of yearly average discharge (a) and of dredging volume (b) for spline (S.) and parabolic (P.) ﬁttings. Downloaded by [University of Newcastle, Australia] at 07:59 28 December 2014 446 Massimo Guerrero et al. event that were incurred due to the increased docking and chartering times of oceanic Panamax vessels at the Parana waterway. The docking fee in the Rosario port is equal to 0.14 US$/ton/day, whereas the average chartering fee for Panamax vessels has ﬂuctuated, varying from 30,000 to 10,000 US$/day over the last two years, depending on speciﬁc agreements. Assuming consequences for failure similar to the Aristeas-P, the economic direct loss per day was roughly estimated by multiplying the total load capacity of 54 blocked vessels by the Rosario docking fee, resulting in approximately 230,000 US$/ day, given that the average Panamax vessel load capacity is equal to 30,000 tons. The increase in chartering time was accounted for by 10,000 US$/day per individual vessel. The direct economic loss was approximately 770,000 US$/day. Given the variability of the chartering fee for Panamax vessels and the uncertainty of failure consequences, a sensitivity analysis was conducted on the resulting total cost by applying a unit cost of failure varying from 0.25 × 106 to 2 × 106 US$/day. Figure 6(a) and 6(b) reports the sensitivity analysis results in terms of total cost functions for expected yearly average discharge and the corresponding volume to be dredged, respectively. Regardless of the resulting total cost function, the most appropriate management approach is for the expected discharge corresponding to the maximum expected sedimentation rate and volume to be dredged, i.e. r(q∗ ) ¼ max(r) in Eq. 1. In this case, the total cost is minimum and equal to the maximum cost of dredging (47 × 106 US$/year), with the integral in Eq. 1 being equal to zero, corresponding to zero probability of failure. The corresponding discharge varies slightly relative to the assumed function of sedimentation rate, ﬁnally resulting in symmetric and deviated functions of the total cost in Figure 6(a) for parabolic and spline interpolations, respectively. The failure cost per day and the probability distribution of the yearly average discharge strongly affected the resulting cost function, with the cost of dredging being of a lower order of magnitude compared to the cost of failure per year. Future climate changes, on average, will halve the total cost, given the same failure cost per day (Figure 6(b)). The minimum total cost is well deﬁned for increasing values of the unit cost of failure, while it is smoothed in the case of lower consequences of failure per day, especially when the spline interpolation is applied (Figure 6(a)), reﬂecting a better balance between dredging and failure costs. Passing from past to future hydrology scenario introduces more sensitivity of the total cost to the operational investment for dredging of the navigation channel. For future hydrology and given the same daily cost of failure, the plotted functions in Figure 6(b) approach the minimum more slowly. With different sensitivities, a reduced investment in navigation channel maintenance may produce relevant economic losses rising to an order of magnitude higher than the predicted maximum cost per year for dredging. The analysis that was performed demonstrates that the failure cost is dominant in ﬁxing the total cost, and the most appropriate strategy for navigation channel maintenance corresponds to the maximum predicted effort for dredging (i.e. expected maximum rate of sedimentation). This ﬁnding suggests that, from the perspective of economic investment, the Parana waterway capacity may be increased. The maintenance of the actual admittance (10 m draft) gave rise to a relatively low dredging cost when compared to the resultant economical shortcomings due to no admittance (i.e. failure costs). An increased waterway capacity may also give rise to more serious consequences for failure events because of the interruption of improved service. The proposed method could therefore also be applied to investigate the actual inﬂuence of the waterway capacity enlargement by comparing the additional cost of dredging to the increasing consequences of failure. 5 Conclusions This paper presented an analysis that was performed to investigate the effect of climate change on the dredging cost required to maintain the navigation channel at actual capacity in the Parana waterway. The proposed method applied two of our own developed numerical models to simulate the navigation channel morphodynamics and the consequent need of dredging per year, given the expected yearly average discharge. The HIDROBID II model assessed the depth-averaged velocity ﬁeld for a case study of the 25 km Rosario reach of the Lower Parana. The results from this model provided the boundary conditions for the AGRADA model, which simulated the dredged trench morphodynamics within the streamﬂow vertical section crossing the low-depth area of the Paso Borghi. To maintain the present admittance for vessel draft from Santa Fe to the Parana River bifurcation at the beginning of the lower delta, the variable cost was found to be in the range of 29 – 47 × 106 US$/year for the yearly average discharge, with the maximum roughly corresponding to the river effective discharge, which was found to be equal to 15,000 m3/s. Past-century and future distributions of the yearly average discharge were assessed under the CLARIS-LPB research project using the semi-distributed hydrological model, VIC, which was forced with past climate and four RCMs. These distributions provided the failure probability of the waterway for a varying yearly average discharge to assess the failure cost per year. The most appropriate investment for dredging was estimated by detecting the minimum total cost (i.e. dredging plus failure) for a varying discharge. Given the variability of the chartering fee for Panamax vessels and the uncertainty of failure consequences, a sensitivity analysis was also conducted on the resulting total cost by applying a unit cost of failure that varied from 0.25 × 106 to 2 × 106 US$/day. The unit cost was approximately 0.8 × 106 US$/day, based on the documented economic losses, for the oceanic cargo accident that occurred in 2012. Downloaded by [University of Newcastle, Australia] at 07:59 28 December 2014 Effect of climate change on navigation channel dredging The unit cost of failure and the probability distribution of the yearly average discharge strongly affect the resulting cost function, with the cost of dredging being of a lower order of magnitude compared to the cost of failure per year. Future climate change, on average, will halve the total cost, given the same failure cost per day. With different sensitivities, a reduced investment in maintenance of the navigation channel may produce relevant economic losses that rise to an order of magnitude higher than the predicted maximum cost per year of dredging. The analysis that was performed demonstrates that the failure cost is dominant in ﬁxing the total cost, and the most appropriate strategy for navigation channel maintenance resulted in the maximum predicted effort for dredging. The proposed method can also be applied to investigate the actual convenience of the enlargement of the waterway capacity by comparing the additional cost of dredging to the increasing consequences of failure. Acknowledgements This research has received funding from the European Community’s Seventh Framework Programme (FP7/2007 – 2013) under Grant Agreement No. 212492 (CLARIS LPB. A Europe-South America Network for Climate Change Assessment and Impact Studies in La Plata Basin). References Castro, S.L., et al., 2007. 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