INTERANNUAL FLUCTUATIONS OF MARINE HYDROLOGICAL CYCLE CASE OF THE SEA OF NOSY-BE

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1 INTERANNUAL FLUCTUATIONS OF MARINE HYDROLOGICAL CYCLE CASE OF THE SEA OF NOSY-BE RASOLOZAKA Nirilanto Miaritiana (, a), RABEHARISOA Jean Marc (a), RAKOTOVAO Niry Arinavalona (a), RATIARISON Adolphe Andriamanga (a) ABSTRACT (a) Atmospheric, Climate and Oceans Dynamics Laboratory (DyACO), Physics and Applications, University of Antananarivo Madagascar This work aims to study the interannual fluctuations and predictability of the marine hydrological cycle in the sea area of Nosy-Be stretching from.5 S to 3 S and 46 E latitude to E longitude. Sea surface temperature, sea surface salinity and water balance were analyzed by various statistical tools. The 5 years temporal memory of the water balance, his years delay compared to the salinity, was respectively deduced by autocorrelation and cross-correlation. The results found by the cross-correlation method is confirmed by the analysis of moving averages. We have taken the linear regression model to forecast the exchange atmosphere-sea. The salinity was used as a predictor variable hydrological and after years as a predictand. I. INTRODUCTION The island of Nosy-Be, located in the northwest of Madagascar, adopts a disrupted climate that affects very closely a change in salinity and temperature of the sea surface in the course of a year data []. Indeed, the maritime area that we considered off Nosy Be is between.5 S and 3 S latitude and 45.5 E and 48 E longitude 5. variables (precipitation, evaporation, temperature and salinity). - Study the evolution of the exchange-sea atmosphere: it will assess its predictability (and their mechanisms) associated with different time scales. We could spend to build a forecasting model that will be acceptable or even good, in a wide time range for the difference between evaporation-precipitation (water balance). To do this, after listing the materials and methods that we have used, we present the results followed by syntheses mentioned account held in our study. Figure. Area of study This work aims to: - Estimate the recent interannual fluctuations in sea water cycle off Nosy Be, based on different hydrological About the marine hydrological cycle: The general hydrologic cycle is the set of processes of transformation and transfer of water across the globe [2]. The marine hydrological cycle is the exchange taking place between the sea-air interface and all the fluctuations of entering and leaving water in that given sea. Hypothesis: in our case the supply of freshwater, groundwater seepage, and the storage variations are negligible. So our study of the marine hydrological cycle will be limited by the study of the water balance (variation of the difference Evaporation and Precipitation), and the study of mass movements due to ocean currents (through the Author, Student, nirilanto.rasolozaka@gmail.com

2 temperature and salinity). All the mechanism is illustrated by the following figure: - A B C D E F - A2 B2 C2 D2 E2 F2 A3 B3 C3 D3 E3 F3-2 A4 B4 C4 D4 E4 F4 A5 B5 C5 D5 E5 F5 latitude -3 A6 B6 C6 D6 E6 F longitude Figure 2. Mechanism of the marine hydrological cycle II. METHODOLOGIES: II.. Materials: We have downloaded daily reanalysis data from the ECMWF (European Climatic Medium-Range Weather Forecast) website taken between January, 979 to December 3, 25 for evaporation, precipitation and the SST (Sea surface temperature). And from the NOAA (National Oceanographic and Atmospheric Administration) site, we downloaded our Sea Surface Salinity data (SSS) in monthly averages, taken between January 98 and December 25. A new variable that we called hydrological balance variable was created to illustrate the exchange between atmosphere and ocean, it is the difference between evaporation and precipitation. Statistical tools: we used many kind of statistical tools such as the main component analysis, autocorrelation and cross correlation, the trend test and Mann Kendall, and linear regression. Note that all the work was done using Matlab, Excel and Xlstat. II. 2. Methods: II.2.. Principle component analysis With data from two different sites, we have two different subdivisions of data shown in the two following figures: Figure 3.a. Study area divided into 36 grid point for the water balance and the SST latitude Figure 3.b. Study area divided into 2 grid point for the SSS II.2.2. Autocorrelation and intercorrelation [3] With annually averaged, centered and reduced data types we apply the following formula: i=n k C k = n [(x i x )(y i+k y )] i= With C k the correlation coefficient and n the number of measurements. Whatever the order of the autocorrelation coefficient k is: - C k A A2 A3 A4 A longitude x and y: studied time series For autocorrelation, a single time series is studied, so x = y. And for the cross-correlation, x is the causal variable, that is to say x causes y. With a confidence interval taken for reduced number of data given by the formula: B B2 B3 B4 B5 C C2 C3 C4 C5 D D2 D3 D4 D5

3 σ z = n 3 t The Hurst exponent H: this exponent allows us to test the robustness of our results. It classifies the time series according to the nature of their memory or their structure of dependency. If : axe F dec mar avr Plan (F, F2), 95,7% mai nov oct jun jul sep aou.5 < H< : long term memory < H<.5 : anti-persistant phenomenon H =.5: no memory II.2.3 Trend analysis, Mann-kendall test: In mathematics, trend is the evolution of a time series over the time [4]. Mann-Kendall test is a nonparametrical test used to detect the presence of a trend in a time series [5]. Consider an observation sequence x, x 2,, x n for which we are doing two hypothesis: H : The observation X i are ordered randomly, no trend H : The alternative hypothesis where there is an increasing or decreasing trend. The trend is statistically significant when the p-value test is less than 5%. II.2.4. Linear regression: The goal using this tool is to establish a linear relationship between a dependent variable y and independent variable x to then be able to forecast y when x is measured using the linear equation y = b x + b ± ε. [6] axe F Figure 4.a. Representation of the variables in the F-F2 plan, study of the water balance axe F Figure 4.b. Representation of the variables in the F-F2 plan, study of the SST.8.6 Plan (F, F2), 69.97% jan fev fev mar jul aou jun sep mai oct nov avr jan dec axe F Plan (F, F2), 95,7% fev jan III. RESULTS III.. Principle component analysis The three circles represent the correlations of the average values of each month in our database for the water axe F mar avr mai dec nov oct sep aou jun jul balance, SST and SSS axe F Figure 4.c. Representation of the variables in the F-F2 plan, study of the SSS

4 The correlation of months for the 3 hydrological variables coincide with two seasons in Madagascar The majority of the precipitation comes from the evaporation of the sea evolution of SSS and SST is connected with the water balance and offset by the marine traffic III.2. Evolution of time series analysis The autocorrelation of the water balance is shown by the figure 4. There is 5 years of a memory effect of the water balance with.3534 correlation. Therefore, the Hurst exponent of the signal is equal to.67 so we can say that the water balance has a long term memory. Figure 6.a: Intercorrelation of the water balance and the SST Figure 6.b Intercorrelation of the water balance and the SSS III.3. Time series analysis: III.3.. Trend analysis and Mann-Kendall test: Figure 5. Autocorrelation of the water balance The two following figures (fig. 5.a and fig. 5.b) represent respectively the correlation between water balance and SST, and the water balance and the SSS. SST and SSS are here taken as causal variables. A peak is observed at the th X-axis (fig 5.a), which means that the water balance is years in advance compared to the SST. For the second figure (fig. 5.b), There is a remarkable peak in the th negative x-axis, which means that the water balance is years late compared to the SSS. According to this following table, only SST has a trend, but the two other hydrological variables have only fluctuations. Table : Results of Mann-Kendall test for different hydrological variables Variables p-value H Trend type Water balance,244 Non significant SST,23 Significant SSS,6728 Non significant III.3.2. Average analysis: In the figure below (fig. 6), red curves are the moving averages taken for 5 years. According to the moving average line SST, and the trend analysis, we can clearly say that SST has an increasing trend. For the water balance, the maximum peak of its moving average was in the year 2, the maximum peak of the SST in the year 2, and that of the SSS in 99. After analyzing these

5 Bilan hydrologique Annuelle en [mm] developments, we can confirm the results of the correlation seen previously and induce that: the water balance is years in advance compared to the SST, and years late compared to the SSS. So we can forecast the water balance from SSS Bilan hydrologique Annuelle Moyenne Global Moyenne Mobile TEMPS en [année] Figure 7. Annual average, global average, and moving average of water balance (a), SST (b), SSS (c) III.4. Example of forecast model for the exchange atmosphere-ocean: LINEAR REGRESSION We can see in the fig. 7 below the example of linear model to predict the year j + with the equation giving the water balance, the figure giving the data and the regression line. Figure2.a Water balance = SSS SST Annuelle en [ C] SSS Annuelle en [g/kg ou PSU] SST annuelle Moyenne Global Moyenne Mobile TEMPS en [année] SSS annuelle 35.2 Moyenne Global Moyenne Mobile Figure2.b Figure2.c TEMPS en [année] But before considering the linear equation of regression, we have to verify some parameters that are shown in the following tables. Table 2: Evaluation of the value of the information brought by variables Sum of Mean Pr > Source ddl squares square F-test F Model 8,27 8,27,43,2 Residues 24 7,393,725 Total 25 25,664 Table 3: Adjustment coefficient R (correlation coefficient),57 R² (coefficient of determination),33 R²aj. ( adjusted coefficient of determination),3 SCR 7,2 The principle of the regression is that we have a good model if the f-test of Fisher is much more than, and then the correlation coefficient is considerable and high. In our case, the F-test is equal to.43, which is much larger than, and the correlation coefficient is.57., which is considerable but not much high. So we can say that we have an admissible model. IV. CONCLUSION Figure 8: Data and regression line For one year, the marine hydrological cycle, played by the water balance is offset by the marine traffic. First, the evolution of the water balance has a memory effect of 5 years, which is a long-term memory. This results a similar behavior of the water balance for 5 years. On the other hand, the study of the correlation and analysis of averages tells us with a confidence level of 95% that the water balance is years in advance compared to the SST, and

6 years late compared to the SSS. An example of a linear model was declared as "acceptable" for the prediction of water balance from the SSS taken with a forecast horizon of years. In future studies, we could consider to build a nonlinear model, such as artificial neural network to perfect our forecast. REFERENCES [] B. Piton et al., 98: «Atlas Hydrologique du Canal de Mozambique», Travaux et documents de l O.R.S.T.O.M [2] S. I. Seneviratne, 8 janvier 26: «Le cycle hydrologique: Observations et modélisation», Institut de Recherche sur l Atmosphère et le Climat, ETH Zurich, Suisse, École doctorale STUE, [3] N. Croiset, B. Lopez (BRGM): HYPE, Outil d analyse statistique des séries temporelles d évolution de la qualité des eaux souterraines, Manuel d utilisation, Rapport final [4] B. LOPEZ et al., Février 2: «Evaluation des tendances d'évolution des concentrations en polluants dans les eaux souterraines. Revue des méthodes statistiques existantes et recommandations pour la mise en œuvre de la DCE.» Rapport final [5] A. Poulin, Professeure, ÉTS, MGC-92, 9/4/3: «MODÉLISATION HYDROLOGIQUE COURS 4 : DONNÉES HYDRO-MÉTÉOROLOGIQUES (2/2)», Ecole de technologie Supérieur, [6] S. Le Digabel: «Régression linéaire simplemth232d», Ecole Polytechnique de Montréal H26(v2)M