Observation data from DYFAMED site, in northwestern Mediterranean Sea between 1995 and 2011, are used to study mathematical forecasts of sea water surface pH evolution over the next century. In a preliminary study, daily and monthly data have been used to compute total inorganic carbon (
Since the beginning of the 19th century, the industrial era has produced an increasing amount of CO_{2}. The evolution of CO_{2} concentration in the atmosphere during the last decades has been extremely important and several studies show and underline its effects on climate change (see [
The increasing trend of global atmospheric CO_{2} concentrations roughly follows that of the global anthropogenic injection into the atmosphere. Nowadays, we know that the world ocean (covering 71% of the Earth’s surface) acts as the biggest buffer for the atmospheric CO_{2} concentration by absorbing an important part of it.
Studies show that the ocean absorbs about 2
Predictions for the end of the century suggest a mean decrease of about 0.3 pH units to 0.5 pH units (see [
The absorbed CO_{2} affects the ocean through several factors. Partial pressure of CO_{2} in the atmosphere rises with anthropogenic evolution, while in water partial pressure is affected by surface absorption and biogeochemical processes. Those modifications of properties directly affect sea surface CO_{2} absorption. The variations in total inorganic carbon (
The Mediterranean Sea which represents
Around the Mediterranean Sea, human population and activity have substantially increased since 1950. Consequently partial anthropogenic CO_{2} pressure reaches higher levels [
The aim of this paper is to estimate the longterm trend of sea surface water pH in the Mediterranean Sea using the measurements performed at DYFAMED for the temperature, salinity, total alkalinity, pressure, and total dissolved carbon from 1995 to 2011. Due to the missing data (measurements from years 1995 to 1997 and other unavailable monthly data) required for computing pH values, the monthly time series has been obtained by considering the mean values of the pH between 1995 and 2011. The used cubic spline polynomial interpolation will provide a time series which moves in a smooth way during the period for known data. This also will serve us to make forecast of the mean pH evolution. In this paper, two standard extrapolations scenarios are presented as the limits on the level of pH values evolution: a linear evolution of the pH annual mean values, and an exponential one.
The first one is quite simple and is used as a reference for the observations and comparisons. The exponential evolution is considered for a more realistic behavior of the observed evolution in ocean’s water. Evolution of mean pH values is studied with these two extreme scenarios where a random term based on observed monthly variations was also added in order to take into account the stochastic nature of pH fluctuations. The observed decrease of mean pH values for both scenarios remains bounded and the obtained behaviour in the form of cyclic oscillations agrees with the existing temporal variabilities of seawater pH.
Moreover, all these evolutions lead to the conclusion that the forecast could not exceed 50 years. The observed differences during simulations are too high to fit to something realistic. The importance of the predicted pH decrease also depends on the considered scenario and its own decrease speed. The impact of this decrease on environment and biology will also depend on which scenario is considered as well as on how they will adapt to the pH changes. Most studies present the effect of the acidification but without conclusion on the gravity of the acceleration of this modification of sea water pH (see [
The approach used in this paper assumes that the mean pH values estimated from the measured data move in a smooth and continuous way to make a reasonable estimate about its future evolution. It is known that the used cubic spline method of interpolation as well as other methods of seasonal adjustment and trend estimation is relatively weak at the end of series where volatility of the spline function may be observed. Indeed, at the end of the series only the past information is available, not the future. This was easily overcome in this study by extending the original monthly series using a vector made of 13 points including the last pH value of the previous year and the twelve newly calculated by the considered linear and exponential forecasting methods.
Estimations of the annual pH values for the referenced time series are based on measurements made on the DYFAMED (DYnamique des Flux Atmosphériques en MEDiterranée) site (
Measurements of salinity (
The missing data (
Temperature and salinity data were fitted with hydrological data from DYFAMED measurements. The TABLE CURVE 3Dv4.0 software was used to test thousands of equation to determine an appropriate function to fit to the
Between 1995 and 1997,
The time series of surface water pH at 10 meterdepth were computed using the CO2SYS software [
We used a polynomial interpolation method, the cubic spline, which is a powerful tool for data analysis. This method is used first to fill in the gaps of missing data points within a monthly time series of mean pH values and allows to draw smooth curves through a number of points. Using this process, series of unique cubic polynomials are fitted between each of the data points. These polynomials will have the same slope and curvature at the points where they join. At the end point of the data set on which we fit the function with spline curves there are no joining polynomials. This will provoke uncertainties which will be overcome using a forecasting method to extend the original series.
For each year the cubic spline polynomial interpolation method is used with an extended input time series consisting of a vector made of 13 points instead of the 12 original monthly data. This will include the last pH value of the previous year. The new twelve points will be calculated using two extrapolation procedures which are described below. Starting from the initial monthly time series, the interpolation will be applied on values that evolve year over year without discontinuities.
For each extrapolation, we will present results for a simple, deterministic forecast, as well as results for a forecast including a random term. Seasonal mean from 1995 to 2011 pH data [
Data and interpolated pH on the 12 months of the reference year. The error bars represent the range between minimum and maximum observed pH from 1995 to 2011.
The seasonal mean pH values of the first year are used to initialize the forecasts. The evolution year over year is then computed by the next two steps: evolution of the monthly values by extrapolation and interpolation of the pH.
For the curve displayed in Figure
In this paper, we consider two extrapolation methods for a forecast over a century. Those extrapolations will be used to provide insight into the limits of pH variability at the sea surface based on DYFAMED site data.
The first one is based on the relative short term observation (over 11 years) of a linear decrease of 0.003 unit of pH per year [
The second one is taken from forecasts applied on IPCC results [
For both extrapolations/forecasts, we will add a random term based on observed monthly standard variations [
Figure
Initial pH data, interpolated pH,
Month  Mean measured pH data  Modified pH 


Observed pH from 1995 to 2011  

Minimum  Maximum  
January  8.1027  8.1124  +0.0097  0.0581  8.0756  8.1337 
February  8.1062  8.1107  +0.0045  0.1202  8.0686  8.1888 
March  8.1081  8.1081  0.00  0.1506  8.0599  8.2106 
April  8.1052  8.1052  0.00  0.0760  8.1094  8.1854 
May  8.0954  8.0954  0.00  0.1406  8.0455  8.1861 
June  8.0775  8.0775  0.00  0.1772  8.0033  8.1805 
July  8.0516  8.0516  0.00  0.2423  7.9624  8.2047 
August  8.0610  8.0610  0.00  0.1250  7.9981  8.1231 
September  8.0989  8.0959  −0.003  0.0928  8.0197  8.1125 
October  8.1035  8.1085  +0.005  0.0767  8.0859  8.1627 
November  8.1079  8.1119  +0.004  0.0000  8.1166  8.1166 
December  8.1134  8.1134  0.00  0.1185  8.0796  8.1982 
Forecast of pH sea surface water with a constant decrease of
Two (out of 30) representative evolution forecasts with random evolution around the linear variation.
We can observe that after a century the mean pH will decrease from
The acidification evolution is more complex than a simple linear evolution over a century. Anthropogenic CO_{2} in the atmosphere will evolve depending on human action in the world and so partial pressure on the sea surface water too. The absorbed CO_{2}, the temperature, the salinity (with sea level, e.g.), and biological activity will modify these evolutions. Ocean could absorb a big amount of CO_{2}, but it is assumed that there is a limit in the quantities that could be absorbed as shown in previous studies on north Atlantic ocean [
In order to obtain a more realistic forecast we applied a random variation to the constant decrease. Results from two (out of 30) representative averages of the 500 runs of random variation around the mean are presented in Figure
The time period of 100 years chosen for the forecasts is relatively long. Noncoherent values could rise over the years. After 50 years of simulation, amplitude variations of most forecasts simulations become higher than 0.3 pH units. These results indicate that such forecast is highly variable after 50 years and thus probably unreliable after this period. The two simulation forecast results (Figure
Running average values for linear decrease with random factor and differences with the simple linear evolution.
First year  50th year  100th year  

Running average Figure 


( 



( 
Running average Figure 


( 

0.00 

(0.00) 
On the performed simulations, maximum observed variations are from
Based on IPCC observations and predictions we can assume that atmospheric CO_{2} will dramatically increase before the end of the century. An exponential growth of anthropogenic CO_{2} is observed at the beginning of the industrial era. The modifications of the ocean acidity by absorption of the anthropogenic gases may follow a kind of exponential growing as presented in [
Based on [
The decrease of 0.3 units on the 100 years corresponding to the 21st century is still represented in this scenario. We have a soft decrease at the beginning of the forecast and a slow acceleration over the years. The evolution may be different with such modifications of sea water pH. However, with both constant decrease and the following exponential evolution we have a loss of 0.3 units on a 100year period.
Here, the first, 50th, and 100th years running average values are
Exponential profile for an evolution forecast over the next 100year period.
Two (out of 30) representative simulation results with random variation around exponential pH extrapolations.
In order to have a better comparison between linear and exponential evolution, we add a random factor based on monthly standard variation values.
As presented for the linear evolution, forecasts longer than 50 years show large differences and variations on a year period to be considered consistent. For example, the variations on a year period could reach more than
The running average values for two (out of 30) representative simulation results (Figure
Running average values for exponential decrease with random factor and differences with the simple exponential evolution.
1st year  50th year  100th year  

Running average for Figure 


( 



( 
Running average for Figure 


( 



( 
The annual mean variations present more differences with this evolution than with the linear decrease. The main parameters of these variations are the average variation values used as coefficients for the random evolution. Some results have shown high increase in the amplitude variation (more than 300% of the initial yearly pH variation around the 40th year) or strong modifications over the time period.
We consider that those results are not representative of realistic forecasts to be used in comparisons. The biggest variation amplitude observed among eligible results is presented in (Figure
The evolution of carbon chemistry and acidification in the Mediterranean Sea seems to be higher than those observed in other oceans. Previous studies ([
We notice that the limit of the reliable values for these forecasts is around 50 years. The amplification of pH variations considered as erratic became too high around year 50. Therefore we have considered forecasts reliable up to 50 years, not beyond. The performed simulations have shown that extrapolation methods should be chosen carefully in order to avoid the creation of aberrant values on a long enough time period.
The accuracy of the data and the modifications done for this study are under the observed variation of pH over the 11 years used as reference. The extrapolations and the values used for the initial year of each test are the main point of this study.
The number of 500 runs for each average results presented in this paper is an arbitrary decision. Yet a higher number of runs for the calculation of an average result would be useless. This value is voluntarily high in order to obtain usable results and additional runs would not provide further information at this level of detail.
Some results could seem usable over the full 100year period (see Figure
The linear approach provides a base for the comparisons. The two main points that are underlined in the results are the observed decrease variations and the annual mean amplitudes. Running average values provide meaningful information about the variations which lead to useful curves drawing the amplitude modifications. With a random variation, the resulting deviation of the average profile is quite large only after 50 years. Consequently, we have opted for running average values from 1 to 50 years of extrapolations.
Simple linear approach forecasts a pH of
Linear and exponential extrapolations give, respectively, running average values of
At first glance this simple study indicates that the exponential evolution is a more realistic mathematical method to fit to the natural evolution. The running average pH values obtained up to 50 years are slightly higher (
In summary according to the exponential extrapolation over 50 years (which represent around year 2060), pH in surface water at DYFAMED would be
In any case, pH in surface water of the Mediterranean Sea is decreasing at a rate of
The authors declare that there is no conflict of interests regarding the publication of this paper.
The research leading to these results has received funding from the European Community’s Seventh Framework Programme under Grant agreement 265103 (Project MedSeA). Authors acknowledge the Dyfamed/Moose observation system, Dr. Koffi Marcellin Yao, and Dr. Olivier Marcou for useful information and work.