Assessing the Influence of the River Discharge on the Minho Estuary Tidal Regime

Journal of Coastal Research SI 56 1405-1409 ICS2009 (Proceedings) Portugal ISSN 0749-0258 Assessing the Influence of the River Discharge on the Minho Estuary Tidal Regime J. L. Reis, A. S. Martinho, A. A. Pires-Silva and A. J. Silva Instituto Hidrográfico, Rua das Trinas, Instituto Superior Técnico, TULisbon, 49, 1249-093, Lisboa, Portugal Av. Rovisco Pais, 1049-001 Lisboa, joana.reis@hidrografico.pt Portugal aps@civil.ist.utl.pt santos.martinho@hidrografico.pt jorge.silva@hidrografico.pt ABSTRACT REIS, J. L., MARTINHO, A.S., PIRES-SILVA, A.A. and SILVA A.J., 2009. Assessing the influence of the river discharge on the Minho estuary tidal regime. Journal of Coastal Research, SI 56 (Proceedings of the 10th International Coastal Symposium), 1405 1409. Lisbon, Portugal, ISSN 0749-0258. Tides are an important factor in estuary circulation patterns, contributing for the complexity of these environments. In estuaries, the hydrodynamic components of tides gain importance compared with the constituents of pure astronomical origin that mostly characterize ocean tides. The main purpose of this work was to characterize the tide in the river Minho estuary and compare it with the tide in the nearby coast. Water height measurements were obtained from three pressure gauges deployed along the river in Caminha, Vila Nova de Cerveira and Segadães. Minho water levels were compared with those from Viana do Castelo in the Atlantic coast. Besides other results, it was observed that the tide is asymmetric, flood dominant and strongly influenced by bathymetric constrains and river flow. The harmonic analysis method was applied to the data and the resulting harmonic constants were analysed. The amplitude of the major lunar semi-diurnal constituent decreases upstream but its first harmonic increases along with compound constituents. Due to the strong influence of river discharge, harmonic predictions did not agree with the tide observations in periods of extreme river flow. In consequence, a prediction equation was derived based on harmonic and wavelet analysis of the hydrometric level in a station upstream of Segadães and maregraphic observations in the three points of observation. The results improved significantly. ADITIONAL INDEX WORDS: Harmonic analysis, Tidal predictions, Wavelets INTRODUCTION Estuaries are complex coastal environments due to physical factors such as river flow, tides and tidal currents, composition of the sediments, waves and wind. Namely, tides and tidal currents are a great source of energy, contributing to the turbulence and mixing of these coastal environments (MAO et al, 2004). Tidal phenomenon is caused by the gravitational interactions of the Moon, Sun and Earth and the centrifugal forces associated with their movements (DOODSON and WARBURG, 1973). The resultant tide generating force produces the periodic movement of rise and fall of the sea s surface, usually known as tide. When the tide is propagating upstream in an estuary, it is deformed from its original form, approximately sinusoidal, due to the non-linear growth of compound constituents and harmonics of the main astronomical tidal constituents. The development of these constituents is the result of friction, non-linear advection and channel s cross section constraints, as the tidal wave oscillates within the estuary (GODIN, 1999). These non-linear contributions should not be neglected and are important to predict the water height in a certain place. Additionally to the tide, there are others effects that change the water level and that are only predictable in a medium/short term. The most significant of these effects are atmospheric pressure, winds and river discharge. For example, an intense river flow scenario may generate extreme high water levels and trigger coastal and estuarine/river floods, especially in high tide periods. This work aims to characterize the Minho estuary tidal regime and assess the way bathymetry and river discharge may influence tidal propagation to the estuary s interior. It was based on the data collected from observational campaigns conducted by the Portuguese Hydrographic Institute under the project ECOIS, Estuarine Contributions to Inner Shelf Dynamics. Minho River is an international river in the north of Portugal that crosses Portuguese and Spanish territory. It is born in Serra de Meira, in Spain, and flows into the Atlantic Ocean, in Portugal, in front of Caminha and La Guardiã. The limits of its estuary extend approximately between Valença and the river mouth (INSTITUTO DA ÁGUA, 2001). The estuary s mean depth is about 4 m relative to the Portuguese chart datum or Hydrographic Zero (ZH) and has a maximum depth of 23 m near Vila Nova de Cerveira. Between the mouth and V. N. de Cerveira, the estuary presents several sand banks that in low tide become islands of small dimensions. In general terms, this estuary is characterized by several bathymetric constraints like strangling or rapid variations of the bathymetry. 1405

River Discharge and Tidal Regime the HC that minimize the sum of square errors, i.e. the differences between observed water heights and those produced by the sum of the possible constituents. This method can be applied for any length of the observed time series and extracts tidal constituents reducing leakage, since the exact frequency of the tidal constituents is known. Harmonic analysis was applied to the tidal signals in Minho estuary using the algorithm developed by SIMON (1974). Figure 1. Map of the North of Continental Portugal with the locations of the instruments. TIDAL AND HYDROMETRIC DATA SETS In order to study Minho estuary tidal regime, water heights of three tidal stations along the river were analyzed: in the upstream direction, Caminha, V. N. de Cerveira and Segadães. The tidal stations were equipped with pressure gauges. The period of observations spanned for two years, from August 24 th 2005 to June 5 th 2007. To compare the tide in the estuary with the ocean tide, records from Viana do Castelo, were analyzed. This coastal station is 35 km south of Caminha. Figure 1 shows the north of Continental Portugal where the tide gauge stations were located. Raw data consisted of water heights sampled every six minutes. With this sampling period, data might include high frequency phenomena, like wind waves, so it was filtered using a 9 th order Butterworth filter with a cut-off period of 2 hours. The data was also corrected from the inverse barometer effect, i.e. the sea level adjustment to barometric pressure variations (PUGH, 1987). Also, and as required by the harmonic analysis algorithm, the water heights time series were resampled hourly. Hydrometric data was collected at Foz do Mouro station (Ref. 01G/03H in http://snirh.pt) that is indicative of the river discharge in the estuary. This station is 37 km upstream of Segadães, close to the Mouro river confluence and downstream of Frieira dam, in Spain. This dam controls directly the flow registered in Foz do Mouro. METHODS Harmonic Analysis The main purpose of tidal data analysis is to determine the amplitude and phase of as much tidal constituents as possible, within a certain period of measurements. The frequency of each tidal constituent is obtained through the equilibrium tide theory and is constant in any place of the earth s surface. However, the phase and amplitude of each constituent change from place to place and can t be determined by the tidal generating forces equilibrium theory. Harmonic analysis, through mean square regression, is the appropriate method to estimate the amplitudes and phases, known as harmonic constants (HC), (SPEER and AUBREY, 1985). The mean square regression method consists in the determination of Wavelet Analysis Conventional Fourier analysis involves the determination of the Fourier amplitudes in frequency intervals equally spaced and determined through multiples of the fundamental frequency. Although the Fourier transform provides information about the frequency content in the signal, it gives no indication of the localization of these frequencies in time. The Wavelet transform is localized in both time and frequency and has the ability to analyze the variability of a signal in these domains. Therefore, it s an appropriate technique to analyze phenomena that have a transient character (MAK, 1995; LAU and WENG, 1995). Wavelet transform uses base functions, known as wavelets, which can be applied to the complete time series with flexible resolution in time and scale (frequency). As a result, the wavelet coefficients are obtained at different scales and in different sections of the signals, which constitute the outcome of the regression of the original signal with the wavelets. This property of the wavelet transform allows not only the detection in time of signals of short time length and frequency, but also analyzes the variability of low frequency in the time or frequency domains. Orthogonal discrete wavelets are commonly used in the decomposition and reconstruction of time series (FOUFOULA- GEORGIOU and KUMAR, 1994; LAU and WENG, 1995). The Daubechies discrete wavelet of order 30, was applied to the observed water heights in the Minho estuary and to the hydrometric level in Foz do Mouro. This wavelet is obtained through equations 1 and 2 that represent, respectively, the scale function and the wavelet. 2 2 1 2 2 2 where 1 2 1 for 0,1,,2 1 and the scale coefficients h(n) are obtained through higher order polynomial solutions (FOUFOULA-GEORGIOU and KUMAR, 1994). In the discrete wavelet analysis, time series can be decomposed into approximations (A) and details (D). The approximations correspond to the high scale or low frequency content, while the details correspond to the low scale or high frequency content. Table 1 gives, for each component, the corresponding period in hours. Table 1: Period, in hours, of each of the components that result from the wavelet decomposition of the signal (in an hourly basis) with the Daubechies wavelet of 30 th order. Component Period (in hours) D 1 2 4 D 2 4 8 D 3 8 16 D 4 16 32 A 4 > 32 1406

Reis et al. Figure 2. Tidal and hydrometric time series from 23 rd November to 15 th December 2006 RESULTS AND ANALYSIS OF TIDAL CHARACTERISTICS Observed Water Heights and Hydrometric Levels Almost two years of data, from 24 th August 2005 to 5 th June 2007, were analyzed. The tide in Minho estuary is of a semidiurnal type with a low diurnal inequality. Viana do Castelo station, in the Atlantic coast, presents the highest tidal amplitude and a more regular tidal curve. Inside Minho estuary there s a marked decrease of tidal amplitude. The tidal amplitude at V.N. de Cerveira and Segadães are smaller than at Caminha but very similar to each other. In the former it is difficult to distinguish spring from neap tides in low water periods. This pattern can also be seen at Caminha but in a less obvious way. At the estuary s tidal stations there s a progressive increase of mean level in the upstream direction, due mainly to the non complete development of the low tide. This fact may be related with the silting up in Caminha region. Since the water flows only through a small channel and is kept in a small bay the flow is slower below mean tide level and the tide has no time to develop to the low water level. Viana do Castelo tidal curve is apparently sinusoidal but in Minho estuary there s some asymmetry in tidal curves. The time between low and high tide is smaller than the time between high and low tide, indicating flood dominance. Naturally, this asymmetry is most evident in the stations upstream of Caminha. Figure 2 presents a detail of the series of data from 23 rd November to 15 th December 2006 a period in which the river discharge is intense. Mean sea level increased between 23 rd November and 15 th December due to the high river flow registered during that period. This effect is more evident in V. N. de Cerveira and Segadães. In Segadães, from 7 to 12 th December, the intense river flow superimposed the astronomical tidal signal. The maximum hydrometric level has reached 13 m and was registered in 8 th December 2006 corresponding to a daily mean river flow of 2500 m 3 /s. V. N. de Cerveira and Segadães water heights follow quite closely the hydrometric curve registered in Foz do Mouro during the period mentioned. Thus, in the stations upstream of Minho estuary tidal observations are clearly influenced by the river flow, especially during periods of strong river discharge. Harmonic Constants In order to study and predict the tide inside river Minho estuary, harmonic analysis was applied to the hourly data registered. 368 days of data were used, beginning in 24 th August 2005 that allowed the separation of 60 tidal constituents. In all tidal stations M 2 has the highest amplitude although it decreases upstream. On the other hand, M 2 s first harmonic, M 4, increases upstream. Higher harmonics, M 6 and M 8, do not exhibit such amplification pattern upstream. Like M 4, S 2 first harmonic, S 4, also increases upstream. Compound constituents like MS f, SO 1, MK 3, MN 4 or MS 4, have their amplitude being increased upstream although the amplitude difference is higher from Caminha to V. N. de Cerveira than from V. N. de Cerveira to Segadães. This is due to the bathymetric constraints that are more significant between Caminha and V. N. de Cerveira. According to FRIEDRICHS and AUBREY (1988), the ratio between the amplitudes of M 4 and M 2 is a measure of the non-linear distortion of the tidal wave. This value increases from Caminha, where it is equal to 0.046, to the stations upstream and reaching 0.216 in Segadães. Thus, the tidal distortion level is amplified when the tidal wave propagates upstream. This is an indicator of the increase of non-linearity resulting from the combined effect of the transfer of spectral energy from M 2 to M 4 and the energy dissipation due to friction. Through the HC it is possible to generate tidal predictions. Due to the influence of river discharge on the tidal observations, the predictions presented an increasing error in the upstream direction. So, an alternative prediction algorithm was necessary to keep up with the variations of river flow. Wavelet Components The Daubechies wavelet of order 30 was applied to the observations in Minho estuary and, for comparison, to the data from Viana do Castelo. The signal was decomposed to the 4 th level and the period associated with which one of the components is presented in Table 1. From that table it can be seen that the semi-diurnal constituents are included in the D3 component and the diurnal in D4. Figure 3 presents the results for Segadães tidal station (the whole period of observations). The D3 component presents the highest amplitude among the other components: approximately 2 m in Viana do Castelo and 1 m in Segadães. The D2 component, which includes the forthdiurnal constituents, has considerable amplitudes inside the Minho estuary reaching 40 cm in Segadães contrasting with the less than 5 cm observed in Viana do Castelo. The oscillations with periods higher than 32 hours, like sea level variations, are represented by A4 component. During periods of higher river discharge, A4 component presents extreme values but the amplitudes of the other components decrease significantly. In particular, considering the 1407

River Discharge and Tidal Regime Table 2: Adjustment coefficients for Minho estuary tidal stations Station Adjustement coeficients p 1 p 2 p 3 p 4 a 1 b 1 c 1 Caminha 0,0631 2,1960 0,0814 2,0560 1,016 0,7099 17,072 V. N. de Cerveira 0,1394 2,3010 0,2477 1,5610 1.069 0.05795 8.846 Segadães 0,2330 2,2500 0,4121 1,0700 1.142-0.03254 6.296 Figure 3. Daubechies wavelet of 30 th order applied to the Segadães observed water heights (in meters). period between 10000 and 12000 hours of observation (Figure 3), the amplitudes of the details (D) tend to zero, including the D3 component that contains the semi-diurnal constituents. (This window of observations corresponds to the period depicted in Figure 2). PREDICTION ALGORITHM FOR THE TIDE IN MINHO ESTUARY Since tidal predictions by harmonic analysis fail to match the observed water heights during periods of extreme river flow, an alternative prediction expression was derived for the observation stations in the Minho estuary. Generically, the proposed expression has the form present in equation 3 3 where h is the predicted water height, f is a low frequency term that gives the mean water height as a function of a component of the hydrometric level observed in Foz do Mouro and is a high frequency term composed of a function of the harmonic prediction in the tidal station,, modified by a tidal attenuation coefficient,. In the determination of the low frequency term, polynomials of 1 st degree were adjusted to the relation between the A4 component of the observed water heights at the tidal stations and the same component of the hydrometric level observed at Foz do Mouro. Based on the graphical representation obtained, two straight lines were adjusted for two distinct hydrometric levels: low to medium (until 7 m) and high (higher than 7 m). The final expression of the f term is given by equation 4.,, 7 7 4 where p 1, p 3, and p 2 and p 4 are the corresponding regression coefficients, and is the A4 component of the hydrometric level observed in Foz do Mouro. In what concerns the high frequency term the key issue is the estimation of the attenuation coefficient,. The application of the Daubechies wavelet to the observed water heights showed that the D3 component of the signal, that contains the main astronomical constituents, decreased its amplitude whenever the hydrometric level at Foz do Mouro increased. The scatter plot between the ratio of the D3 component of the water heights observations in Minho estuary and the same component of the harmonic tidal predictions and the A4 component of the hydrometric level in Foz do Mouro showed that it was possible to adjust a Gaussian function to that relationship. The expression of the attenuation coefficient is then given by equation 5 5 where a 1, b 1 and c 1 are the parameters of the Gaussian curve. So, the final expression of the proposed algorithm is given by equation 6 6 where is given by equation 4 and the adjustment coefficients for each of the tidal stations are given in Table 2. The prediction expression derived (equation 6) is only dependent of the tidal prediction through harmonic analysis for the tidal station and the A4 component of the hydrometric level expected in Foz do Mouro. This equation was applied to the three stations in study in the Minho estuary and the results along with harmonic predictions were compared with observations. Figure 4 presents such comparison for Segadães tidal station. In addition, a quantitative assessment of the fitting was carried out and the root mean error and the maximum error were estimated. Figure 5 presents the results obtained for the root mean square error (RMSE). The prediction algorithm proposed in this work (equation 6), gives root mean square errors significantly smaller than those obtained from harmonic analysis prediction, in every station. In Figure 5 it is also noticeable that the difference between the root mean square errors obtained from the two methods increases upstream. As a tidal station becomes influenced by river discharge, the prediction expression proposed will get better results, because it takes into consideration the expected hydrometric level at Foz do Mouro. The maximum error obtained with the proposed algorithm is also smaller than the one obtained with tidal harmonic prediction. For example, at the Segadães tidal station 4.5 m of maximum error were obtained through prediction by harmonic analysis contrasting with the 1.0 m obtained through equation 6. Again, and concerning this latter statistics the difference between the two methods also increases upstream. 1408

Reis et al. Figure 4. Comparison between both prediction methods for Segadães tidal station. RMSE (m) 0,6 0,5 0,4 0,3 0,2 0,1 0,0 Caminha V. N. de Cerveira Segadães Prediction given by equation 6 Harmonic Prediction Figure 5. Root mean square error obtained between harmonic prediction and the expression of prediction proposed for the tidal stations in Minho estuary (equation 6). CONCLUSIONS The deployment of three tidal gauges in Minho estuary allowed verifying that the tide is semi-diurnal with low diurnal inequality. In the station of V. N. de Cerveira and Segadães it was clear that the tidal ebb does not develop completely making it difficult to distinguish spring from neap tides in low water periods. There s also some asymmetry in the tidal curves in the Minho estuary that reveal flood dominance. In periods of high river flow tidal observations are highly influenced by river discharge. Due to this fact, predictions using harmonic analysis are unable to reproduce the main features of the tidal curve. In consequence, a prediction expression was developed that combines harmonic prediction and wavelets analysis of the hydrometric level expected in Foz do Mouro. This development proved successful in reducing forecast/hindcast errors. FRIEDRICHS, C. T. and AUBREY, D. G., 1988. Non-linear Tidal Distortion in Shallow Well mixed Estuaries: a Synthesis. Estuarine, Coastal and Shelf Science, 27, 521-545. GODIN, G., 1999. The Propagation of Tides up Rivers with Special Considerations on the Upper Saint Lawrence River. Estuarine, Coastal and Shelf Science 48, 307-324. FOUFOULA-GEORGIOU, E. and KUMAR, P., 1994. Wavelets in Geophysics, Academic Press. 373p. Instituto da Água, 2001. Plano de Bacia Hidrográfica do Rio Minho Relatório Final. Ministério do Ambiente e do Ordenamento do Território. LAU, K.-M. and WENG, H., 1995. Climate Signal Detection Using Wavelet Transform: How to Make a Time Series Sing. Bulletin of the American Meteorological Society, Vol. 76, No. 12. MAK, M., 1995. Orthogonal Wavelet Analysis: Interannual Variability in the Sea Surface Temperature. Bulletin of the American Meteorological Society, Vol. 76, No. 11. MAO, Q.; SHI, P.; YIN, K.; GAN, J. and QI, Y., 2004. Tides and tidal currents in the Pearl River Estuary. Continental Shelf Research 24, 1797-1808. PUGH, D. T., 1987. Tides, Surges and Mean Sea Level. Chichester: Wiley, 472 p. SIMON, B., 1974. Calcul des Constantes Harmoniques de la Marée. Brest: EPSHOM. SPEER, P. E. and AUBREY, D. G., 1985. A Study of Non-linear Tidal Propagation in shallow Inlet/Estuarine Systems Part II: Theory. Estuarine, Coastal and Shelf Science, 21, 207-224. http://snirh.pt/ (consulted in September 2007) ACKNOWLEDGEMENTS The authors would like to thank Câmara Municipal de Vila Nova de Cerveira and Câmara Municipal de Valença for the authorization to deploy tidal gauges in V. N. de Cerveira and Segadães, respectively. This study is a contribution to the ECOIS project (POCTI/CTA/48461/2002), supported by Fundação para a Ciência e Tecnologia. LITERATURE CITED DOODSON, A.T. and WARBURG, H.D., 1973. Admiralty - Manual of Tides. Reprinted Edition, London, U.K.: Hydrographic Department, Admiralty, 270p. 1409