Mathematical modelling of salt water intrusion in a Northern Portuguese estuary

Transcription

1 Matematical modelling of salt water intrusion in a Nortern Portuguese estuary JOSÉ L. S. PINHO 1 & JOSÉ M. P. IEIRA 1 Department of Civil Engineering, niversity of Mino, , Braga, Portugal jpino@civil.umino.pt Department of Civil Engineering, niversity of Mino, , Braga, Portugal jvieira@civil.umino.pt Abstract Salinity intrusion is a key issue for estuarine water quality management. Aquatic ecosystem sustainability is igly dependent on salinity concentration dynamics and must be studied for eac particular environment. Salinity intrusion into te estuary of te river Lima, in te nort-western region of te Iberian Peninsula, was studied based on a two-dimensional ydrodynamic and mass transport model. Tide eigts and river discarges are te major causes affecting salinity intrusion, and ave been analyzed by means of estuarine circulation simulation for different scenarios. Te upstream propagation of te salinity front under unfavorable conditions reaces a river section located at about 1 km upstream te river mout. Te developed model constitutes a powerful tool for evaluation of te salinity intrusion pattern in te river Lima estuary, and an auxiliary instrument for decision making in river basin water management. Key words Salt intrusion, ydrodynamics, matematical modelling INTRODCTION Te study of estuaries is of ig difficulty since tese water systems usually involve complex geometries, ydrodynamics, and transport patterns. In fact, te interface between fres and salt waters forced by river discarges, tides and wind presents specific caracteristics tat affect te mixing properties of te estuarine water masses. Tere is a large variability in estuaries depending on te differences in te tides, river discarges and te way tese factors interact wit topograpy (Dyer, 1997). Te salinity distribution witin te estuary is commonly used for classification purposes (Pritcard, 1955; Cameron and Pritcard, 1963, cited in Dyer, 1997). However, te estuaries salinity structure can be modified by alterations of river discarges regime caused by dam construction and batymetric canges due to eiter sediment fluxes variation or sand 1

2 removals. Tese modifications can significantly impact establised water uses like agricultural, domestic and industrial supply. Te extent of salinity intrusion depends on te balance between fres water discarges and saltwater flow from te sea. Tis penomenon can be reasonably predicted recurring to matematical models supported by monitored data. Tese tools can be used to quantify ow muc fres water is required to counterbalance salinity intrusion at te upstream water intakes. In te river Lima estuary, located in te nortern region of Portugal, ydroinformatic tools are being used in assessing te salinity intrusion in tis water body. Te tools include two main components: a ydrological model of te river basin, and a ydrodynamic/transport model (WES-HL, 1996; WES-HL, 000) of te lower section of te river. Tis paper presents preliminary results of matematical modelling of te second modelling component. Salinity spatial distribution is caracterized for a set of scenarios establised according te key actions affecting te extents of salinity intrusion. Moreover, tese results will be used to define a monitoring program to collect data for models calibration and validation. METHODOLOGY Matematical formulations Saltwater intrusion analysis must be based on a fully dynamic model description. In te absence of stratification, te RMA/ RMA4 software (WES-HL, 1996, WES-HL, 000) packages are an excellent tool to predict salinity intrusion. If vertical stratification prevails a two-dimensional vertical modelling approac or a tree-dimensional (Pino, 001) approac must be applied. Different criteria, suc as te flow ratio or te estuary number (Dyer, 1997) for anticipation of stratification conditions can be used. Tese criteria are generally based on te ratio of bot river and tidal flows. For te river Lima estuary salinity intrusion studies, te

3 3 application of te above mentioned criteria leads to a classification of eiter stratified, partially mixed and well mixed conditions, depending on te considered river flow regime. However, stratified conditions are always confined to te lower estuary and well mixed conditions occur wen te most severe salinity intrusions take place associated wit extreme low flow events. Considering tese preliminary results, well mixed conditions for te estuary were assumed, since te most unfavourable salinity intrusion scenarios correspond to low river discarges. Hydrodynamic model Te two-dimensional in te orizontal plane (DH) ydrodynamic model was implemented using te RMA software tat is based on te finite element metod (WES-HL, 1996). Tis model can be applied for situations were te water flow does not exibit a significant vertical variation, as was mentioned before. It solves te dept-integrated equations of fluid mass and momentum conservation in two orizontal directions. Te forms of te solved equations are: ( ) [ ] ( ) [ ] 0 = y x t (1) ( ) = ε cos y x C g kw X g x g f y x t v a ϕ () ( ) = ε y x C g sen kw y g y g f y x t v a ϕ (3)

4 were x and y are te orizontal Cartesian coordinates, t is te time, and are te vertical average of te orizontal velocity components, a is te air density, W v is te wind velocity, ϕ is te wind direction, C is te Cezy coefficient and ε is te turbulent viscosity coefficient, is te water density, is water dept, is te water surface elevation, k is an empirical wind sear coefficient and f te Coriolis parameter. Transport model Te mass transport model, RMA4 (WES-HL, 000) is applied to simulate dept-average advection-diffusion processes in aquatic environments. Te model can be used for te evaluation of any conservative substance tat is eiter dissolved in te water or tat may be assumed to be neutrally buoyant witin te water column. Te model is also used for investigating te pysical processes of migration and mixing of a soluble substance in reservoirs, rivers, bays, estuaries and coastal zones. Te generalized computer program solves te dept-integrated equations of te transport and mixing process. Te form of te dept averaged transport equation is: C t x y x C C x y C (4) x y y ( C) ( C) ( E ) ( E ) k C = 0 were, C is te local concentration of salt, E x and E y are te local dispersion coefficients in te x and y direction, respectively, and k C is te local mass transfer rate from source/sink processes. Tis equation is solved numerically using a modified version of te RMA4 software (Pino, 001). CASE STDY Study area Te international river Lima basin (Fig. 1), located in te nortern region of te Iberian Peninsula, is mainly used for water supply, agricultural irrigation and ydropower generation. Wit a total drainage area of km, (47.1% of te area in Portugal and 5.9% of te 4

5 area in Spain), te river Lima basin as a mean elevation of 437 m wit several peaks above 1300 m, and an average population density of 11 inabitants/km (minimum of 10 at Melgaço and maximum of 363 at iana do Castelo). Te annual mean rainfall at te Portuguese part of te basin is 164 mm. In average, 73% of te precipitation occurs during te umid season (six monts) and 7% during te dry season. Main tributaries are rivers Lagoa de Antela, Cadones, Castro Laboreiro, ez, Labruja and Estorãos at te rigt side and rivers Faramontaos, Salas, ade and Trovela at te left side. Two ydropower plants (Lindoso and Touvedo) are in operation since 199 wit an installed power of MW. A storage volume of 74 m3 is possible wit tese two dams. Tis water use constitutes a determinant factor tat must be considered in any water management policy adopted for te salinity intrusion control. Ponte de Lima Laneses bridge iana do Castelo Spain Portugal Fig. 1 Location of te study area. Te modelled area occupies te lower part of te river basin, were te main residential and industrial areas are located. For modelling purposes, te river reac considered in tis study 5

6 begins downstream Ponte de Lima weir and ends at te river mout, in a distance of approximately km. Model implementation Te river Lima estuary ydrodynamic and salt transport model was implemented using a finite element mes wit 6087 triangular quadratic elements (Fig. b)). Tis mes was generated considering a minimum interior angle of 5º and a maximum element area constraint of m. Model bottom topograpy was defined using batymetric data collected during 003 in te navigation cannel of te iana do Castelo arbour and recurring to te river profile depicted in Fig. a). Two open boundaries were considered: an open ocean boundary at te estuary mout (iana do Castelo), and an open river boundary at te upstream section of te river (Ponte de Lima). At tis location, te river discarges were imposed in te ydrodynamic model and a null concentration of salinity in te mass transport model. At te open ocean boundary surface tide elevations were imposed, estimated according to te Topex-Poseidon satellite observation data troug te SR95 program (JPL, 1996). Te average salinity concentration adopted at te ocean boundary was 35 psu. 6

7 Elevation (m) Longitudinal profile Distance to Ponte de Lima weir (m) Q(t) Elevation (m) (t) Q(t) River discarge (t) Tidal elevation a) Elements: 607 Nodes: 1501 b) Fig. Hydrodynamic and transport model: a) Batymetry and river longitudinal profile; b) DH finite element mes. Model Calibration and validation As mentioned before, results obtained in tis work will be used to define a compreensive monitoring programme to collect data for model calibration and validation. Selection of monitoring stations locations for water surface elevations, current velocities and salinity concentrations as well as te coice of te most convenient field work period will be made 7

8 according preliminary results obtained wit te ydrodynamic and mass transport model. Meanwile, at tis work pase, model parameters were establised using values determined in similar studies, available data for te iana do Castelo tidal gauge station and oter qualitative data observed in te field. Tus, values of 40 m 1/3 s -1 for te Manning-Strickler equation coefficient and 0 m s -1 for te turbulent viscosity coefficient were adopted. Fig. 3 depicts model computed (lines) and predicted (dots) tidal elevations at te iana do Castelo tidal gauge station Tidal elevation (m) January January 005 January January January January January 005 Fig. 3 Hydrodynamic model. Computed (lines) and predicted (dots) tidal elevations at te iana do Castelo tidal gauge station. Te diffusion coefficient was automatically defined by te model after eac time step, based upon a provided Peclet number, wic is based upon te element size and calculated velocity witin eac element. Tis number is te nondimensional parameter developed by rationing te advective terms to te diffusive terms in te governing equations. 8

9 RESLTS AND DISCSSION Simulated Scenarios Simulated scenarios were defined considering te two key actions on salinity intrusion: river discarge and tide eigt. Adopted tide eigts are representative of te neap-spring tidal range. For river discarges four different values were adopted: te minimum one (9 m 3 s -1 ) corresponds to te guarantied mean discarge during dry season (April to September) wit a probability of 95%; te 54 m 3 s -1 value is approximately te guarantied annual mean discarge wit a probability of 50%; te value of 31.5 m 3 s -1 corresponds to an intermediate situation; and 300 m 3 s -1, corresponding to a typical value for ydropower generation periods (ydropower plants ave an installed capacity of about 50 m 3 s -1 ). Worked out scenarios are summarised in Table 1, were adopted river discarges values at Ponte de Lima weir and tide eigt at te ocean boundary are presented. Table 1 Simulated scenarios. River discarge Tide eigt (m) (m 3 s -1 ) Spring tide Average tide -.55 Neap tide S1 S S S4 S5 S S7 S8 S S10 S11 S1 Tese scenarios represent te most relevant situations for evaluation of te salinity intrusion. Comparison of scenarios S1, S4, S7 and S10, allows te evaluation of te river discarge effect during unfavourable tidal regimes. For eac flow discarge is also possible to analyse te effect of different tide eigts in te salinity intrusion considering scenarios belonging to lines of Table 1. Te impact of Alto Lindoso and Touvedo dams discarge flows can be evaluated during spring tides (S10) and neap tides (S1). Te total simulation time for all considered scenarios was set in 96 ours in order to evaluate te effect of te considered conditions in te salinity intrusion extent. 9

10 Hydrodynamics Te ydrodynamic simulations were carried out in two steps: in te first step te transient solution between a ydrostatic situation and te dynamic solution was acieved; and in te second step two tidal periods were computed using, as initial conditions, results corresponding to te final time step of te solution previously computed. Altoug te model calibration process as not been yet completed it is possible to present some qualitative results (Fig. 4). Te maximum current velocities occur near te railway bridge of iana do Castelo (yellow and red zone in Fig. 4) for spring tide and for te lowest river discarge considered in te simulated scenarios during flood tide and for te maximum river discarge during ebb tide. Dept average velocity at tis location varies from 84 cms-1 (S1) to 6 cms-1 (S10) during flood tide and from 9 cms-1 (S1) to 106 cms-1 (S10) during ebb tide. Flood Ebb Scenario S1 Scenario S10 Fig. 4 Hydrodynamic model: current velocities for te arbour zone during ebb and flood for scenarios S1 and S10. 10

11 Salinity intrusion Te salinity gradient for average river discarges is limited to te estuary region located between te ocean boundary and te igway bridge (located near te rigt extremity of te bigger island Fig. 5). However, it must be stressed tat under tese scenarios te applied model formulation (valid for well mixed conditions) only gives a coarse approximation since stratified conditions are expected to take place. Depicted results in Fig. 5 correspond to salinity concentrations for bot spring and neap tides. Scenario S7 96 ours Scenario S9-96 ours Fig. 5 Salinity concentration for scenarios S7 and S9 after 96 ours of simulation time. Definition of te maximum extent of salinity intrusion depends on te establised concentration limit. For tis work a concentration of 1 psu was adopted. Moreover, te intrusion extent will be variable according to tide stage. For te most unfavourable scenario (S1) te extent variation during te last simulated tidal period is about 5600 m (Fig. 6). Ebb tide 8.5 ours Flood tide ours Fig. 6 Mass transport model: intrusion extent during ebb and flood under conditions of scenario S1 11

12 Te upstream propagation of te salinity front can be observed in Fig. 7, during a spring tide considering a low river discarge. Te salinity intrusion, as defined before, reaces a river section located m upstream te river mout (300 m downstream Laneses bridge). Considering te obtained simulations results it is possible to estimate a front propagation average velocity of 130 m-1. Simulation time 6.5 ours Simulation time 6.5 ours Simulation time 6.5 ours Simulation time 6.5 ours Fig. 7 Mass transport model: intrusion extent for successive tide flood events (S1). Te influence of te two key actions in te salinity intrusion can be observed in Fig.8 and Fig.9. Te occurrence of spring or neap tidal conditions implies a difference in te salinity intrusion of 5700 m, considering te concentration limit (1 psu) previously mentioned. River discarge flows iger tan 54 m3s-1 (S7) during spring tides leads to salinity concentrations lower tan 5 psu in te estuary zone downstream te railway bridge. However, tis location must be confirmed by field works or recurring to a transport model capable of simulate stratified conditions. 1

13 Scenario S1 88,5 ours Scenario S3 88,5 ours Fig. 8 Mass transport model: intrusion extent for different tidal conditions. Scenario S1 96 ours C (psu) Scenario S10 96 ours Fig. 9 Mass transport model: salinity concentration gradient for te adopted extreme river discarges. CONCLSIONS Te salinity intrusion extents for te river Lima estuary were estimated recurring to a DH ydrodynamic and mass transport model. ariations of te salinity front propagation wit tide eigt and river discarges were evaluated. From te results obtained it can be concluded tat te salinity intrusion reaces a river section located about 1 km upstream te river mout, for te most unfavourable conditions (spring tides and low flow river discarges). For more frequent river flows, te salinity gradients occur mainly downstream te igway bridge (5 km from river mout). However, for tese conditions a more accurate evaluation must be acieved using a tree-dimensional model. 13

14 Acieved results will be used as an important auxiliary source of information in order to select gauge stations for measurements of tidal water elevations, current velocity, and salinity concentrations. Once adequately calibrated, te developed model will constitute a powerful tool in assessing te impacts of batymetric alterations in te salinity intrusion. Also, it can be used to establis discarge operational scemes of te upstream ydropower plants safeguarding downstream water intakes. Acknowledgement Te autors would like to tank to te Administration of te port of iana do Castelo for te autorization to use its batymetric data in tis work. REFERENCES Dyer, K.R. (1997). Estuaries : a pysical introduction, Second Edition. J. Wiley and Sons Ltd., Cicester. 195pp. Pritcard, D.W. (1955). Estuarine circulation patterns. Proc. Am. Soc. Civ. Eng., 81, No Cameron, W.M. and Pritcard, D.W. (1963). Estuaries. In: Te sea. ol. (II). M.N. Hill (ed) Interscience, New York. p WES-HL (1996) sers Guide To RMA ersion 4.3, S Army Corps of Engineers - Waterways Experiment Station Hydraulics Laboratory, icksburg, SA. WES-HL (000) sers Guide To RMA4 WES ersion 4.5, S Army Corps of Engineers - Waterways Experiment Station Hydraulics Laboratory, icksburg, SA. Pino JLS.(001) Matematical modelling application to ydrodynamics and water quality studies of coastal zones. PD Tesis. niversity of Mino, Braga, Portugal (in Portuguese). JPL. A collection of global ocean tide models. Jet Propulsion Laboratory, Pysical Oceanograpy Distributed Active Arcive Center, Pasadena, CA; (1996) RL: ttp://podaac.jpl.nas.gov/ 14