Oceanography TeamMentor: Jinchun Yuan

Kadarice Joyce Candy Graves Thaddeus Fairley

Estimating the Distribution of CO2 Parameters in Surface Water of the Indian Ocean from Temperature and Salinity

Abstract

The distribution of CO2 parameters in the ocean is important for understanding the fate of anthropogenic carbon emission and its effects on global climate change. Among the four essential parameters, pH, alkalinity (TA), pCO2, and total inorganic carbon (Tco2), any two of them are sufficient to fully define the aquatic CO2 system. Traditionally, each CO2 parameters was determined using either field sampling or in situ sensors which are inefficient. As a result, temporal and spatial variations of CO2 system are poorly understood. Recently, linear correlations between CO2 parameters and temperature, salinity, and concentrations of dissolved organic carbon (DOC) and particulate organic carbon (POC) of various surface waters have been developed (Lohronze and Cai 2006, Berryman et al. 2007, Small and Reid 2007, Yuan 2009). Since sea surface temperature (SST) can be determined from satellite sensors, concentrations of DOC and POC can be estimated from satellite data, and the satellite sensor for sea surface salinity will be launched soon, these correlations will enable estimation of global distribution of CO2 parameters from satellite data. We have tested these linear equations by predicting CO2 parameters from sea surface temperature and salinity along cruise transects in the Indian Ocean. We have compared our prediction with field measurements of CO2 parameters and evaluated the potential of these linear equations for estimating CO2 parameters. The final research paper presents our final results, which show which formula could possibly be future ways of estimating the distribution of CO2.

What Is R2?R2 is a statistical measure of how well a regression line correlates with real data points. Values for R2 range from 0 to 1, where 0 indicates no correlation and 1 indicates perfect correlation. R2 is the percentage explained by an equation. (http://www.mathbits.com/)

What is the slope?The slope is the number that is found right before the variable “x”. The purpose of the slope is to show the amount of variation is in the formula. The objective is to get to as close to the number 1 as possible. The scale for the slope ranges from 0 to 1 with one being a perfect slope.

(http://www.aiaccess.net/)

What is pCO2?pCO2 is a partial pressure of carbon dioxide. It is a gas at STP and exists in Earth’s atmosphere. The world’s oceans readily exchange carbon dioxide (CO2) with the atmosphere. The CO2 dissolves in water to an extent determined by its partial pressure and the chemical reactions of the dissolved carbon dioxide with other solutes. (http://www.ozcoasts.org.)

Methods Field measurements from cruise transects of the Indian Ocean were obtained

from the CDIAC website during June 29 2002- July 25 2002. Cruise plots created from the Indian cruise were IO3, 1O8, IO9, I10.

  Because of the extent amount of raw data collected during the cruise, it was best

to divide measurements into three sectors. The first set consisted of data collected from I03. The second data set included measurements from 108 and the first half of I09 (IO9a). Last, measurements from the second half of I09 and I10 were combined. This division yielded three sets of results.

  The data was sorted using analysis software, Microsoft Excel. Data that

contained a pressure greater than 15 dbar was excluded; measurements with salinity of -.999 were also excluded from calculations. These data measurements were removed to provide better accuracy. A linear relationship between field measurements and estimated formulas were applied to data. The comparison resulted in a linear regression plot allowing us visualize and compare calculated pCO2 versus estimated pCO2.

Formula Chart for IO3Formulas

Name Formula R2 Slope Y-Intercept

YuanTA= -0.6945 (T)+54.6610 (S)+409.2734

TCO2= -6.7064 (T)+ 50.1983 (S)+383.7813

0.924

0.838

1.272

1.009

-640.2

-37.43

MilleroTA=-114+68.8(S) 0.932 1.016 -40.07

Summer Team 2007 pCO2=-7.1275 (T)+12.2405 (S)+-0.2267 (65)+123.9069 0.246 -0.332 466.5

Academic Year Team 2007pCO2= 12.47(T)+-14.32(S)+33.19(0.23)+575.26

pCO2=14.53(T)+55.3(S)+0.12(65)+45.13(0.23)-2024.95

0.318

0.518

0.632

1.243

190.5

-101.1T = TemperatureS = Salinity

Graphs for the “IO3 Data”

2280 2290 2300 2310 2320 2330 2340 235022202240226022802300232023402360

f(x) = 1.27211761192444 x − 640.237517436565R² = 0.924895032106086

ALKALI UMOL/KG (YUAN)ALKALI UMOL/KGLinear (ALKALI UMOL/KG)Linear (ALKALI UMOL/KG)

Cal

cula

ted

TA

Measured TA

194019501960197019801990200020101880190019201940196019802000

f(x) = 1.00910233395324 x − 37.4351166521196R² = 0.838646672260129

TCARBN UMOL/KG (YUAN) TCARBN

UMOL/KGLinear (T-CARBN UMOL/KG)Linear (T-CARBN UMOL/KG)

Measured TCO2

Cal

cula

ted

TCO

2

2260 2280 2300 2320 2340 23602200

2250

2300

2350f(x) = 1.01634312390224 x − 40.0757337365194R² = 0.932736675765786

ALKALI UMOL/KG (MILLERO)

ALKALI UMOL/KGLinear (ALKALI UMOL/KG)

Measured TA

Calc

ulat

ed T

A

Continued Data

310 320 330 340 350 360 370320330340350360370380

f(x) = − 0.33267190974754 x + 466.545437291124R² = 0.246714549208487

Calculated PCO2 (Summer Team 2007)

Calculated PCO2 (SummerTeam07

Linear (Calculated PCO2 (Sum-merTeam07)

Linear (Calculated PCO2 (Sum-merTeam07)

Linear (Calculated PCO2 (Sum-merTeam07)

Cal

cula

ted

pCO

2

Measured pCO2

310 320 330 340 350 360 370350360370380390400410420430440

f(x) = 0.631970516632781 x + 190.541194077354R² = 0.318842952040788

Calculated pCO2(AYTeam07Form1)

Calculated pCO2(AYTeam07Form1)

Linear (Calcu-lated pCO2(AYTeam07Form1))

Measured pCO2

Cal

cula

ted

TCO

2

310 320 330 340 350 360 370270290310330350370

f(x) = 1.24305718424325 x − 101.135325837622R² = 0.518238446161145

Calculated pCO2(AYTeam07Form2)Calculated

pCO2(AYTeam07Form2)Linear (Calculated pCO2(AYTeam07Form2))

Measured pCO2

Cal

cula

ted

pCO

2

ResultsAfter truncating all of data that was defined and the calculations were done, the data showed that Yuan’s and Millero’s formulas were the most accurate ones. Yuan’s formula for alkalinity was very close to the data that was given. The R-Square for this correlation is 0.924. This was an exceptional number because the closer to one the r-square the better the correlation. Yuan’s second formula tested alkalinity. The r-square for this formula was 0.838. This simply means that this formula was not as good as the first but not too bad.. It has about twenty percent error in it. Millero used a simple linear regression to test the total alkalinity also. The r-square for his correlation was 0.932. This means that his formula has very little error. These formulas show that if the temperature and salinity are given then one can calculate the alkalinity. This is more empirical than theoretical. Theoretically if one has the DIC, alkalinity, or pH, he or she can calculate the pCO2. This theory is tested in the academic year 2007 Undergraduate Research Experience (URE) team and also the summer 2007 Undergraduate Research Experience team. The URE 2007 summer team used a multiple linear regression to estimate the pCO2. The r-square for this team’s data was 0.246. This shows that this formula works very poorly with this data. The academic year team’s formula also tested pCO2. The first formula’s r-square was 0.318 and the second formula’s r-square was 0.518.

Data Provided by:Thaddeus Fairley

Formula Chart for IO8 and IO9a Data Formulas

Equation From: R2: Formula: Slope: Y-intercept

Academic Year 2007 .235 PCO2=(12.47*T)+(14.32*S)+(33.19*0.23)+575.26 2.023 .235

Academic Year 2008 .495 PCO2=(14.53*T)+(55.30*S)+(0.12*65)+(45.13*.23)+(-2024.95) -0.461 398.2

Millero .901 TA= 114+68.80(S) .727 636

Yuan(TA) .935 TA=(-0.6946*T)+(54.6610*S)+409.2734021 .919 -182.7

Yuan(TCO2) .948 TCO2=(-6.7064*T)+(50.1983*S)+383.7813 1.062 -106.4

Summer Team 2007 .661 PCO2=(7.1275*T)+(12.2405*S)+(0.2267*65)+123.9063 2.448 -472.8

T=Temperature S=Salinity

Graphs from IO8 and IO9a Data

2000 2100 2200 2300 24002000

2100

2200

2300

2400f(x) = 0.919893778191426 x + 182.770067379728R² = 0.935875631829675

ALKALI UMOL/KG (YUAN)

ALKALI UMOL/KG Linear (ALKALI UMOL/KG)

Linear (ALKALI UMOL/KG)

Linear (ALKALI UMOL/KG)

Cal

cula

ted

TA

Measured TA

1700 1800 1900 2000 2100 22001800

1900

2000

2100

2200

f(x) = 1.06264498849745 x − 106.426386039749R² = 0.948449992292548

TCARBN UMOL/KG (YUAN) TCARBN

UMOL/KGLinear (TCARBN UMOL/KG)Linear (TCARBN UMOL/KG)C

alcu

late

d TC

O2

Measured TCO2

2000 2100 2200 2300 24002000

2100

2200

2300

2400f(x) = 0.727190101839512 x + 636.037530574633R² = 0.901424719264899

ALKALI UMOL/KG (Millero)

ALKALI UMOL/KGLinear (ALKALI UMOL/KG)Linear (ALKALI UMOL/KG)

Cal

cula

ted

TA

Measured TA

Continued Data

0 100 200 300 400 500 6000.0

200.0400.0600.0800.0

1000.01200.01400.01600.0

f(x) = 2.44818331115823 x − 472.799329252904R² = 0.661028336837974

Cal pCO2(Summer Team 2007)

pCO2 in (matm)Linear (pCO2 in (matm))Linear (pCO2 in (matm))C

alcu

late

d pC

O2

Measured pCO20 20 40 60 80 100 120 140 160 180

0.0200.0400.0600.0800.0

1000.01200.01400.01600.0

f(x) = 2.02299688146801 x + 230.26244107244R² = 0.235614365129314

Cal PCO2 Academic Year 2007(Equ.1)

pCO2 in (matm)Linear (pCO2 in (matm))Linear (pCO2 in (matm))

Measured pCO2

Cal

cula

ted

pCO

2

0.0 500.0 1000.0 1500.0 2000.0

-200

-100

0

100

200

300

400

f(x) = − 0.461417043489377 x + 398.256850102722R² = 0.495017585306519

Cal PCO2(Academic Yr. Equ.2)

Cal PCO2(Academic Yr. Equ.2

Linear (Cal PCO2(Academic Yr. Equ.2)

Linear (Cal PCO2(Academic Yr. Equ.2)

Linear (Cal PCO2(Academic Yr. Equ.2)

Cal

cula

ted

pCO

2

Measured pCO2

ResultsThe results from the data I worked with showed that only two of the equations of the equations had close results in some way. The most accurate I would have to say was the equation given to us by Yuan. His equation showed us a better R2 which is exactly what we were looking for. Even though the other equations did accept the numbers and variables in good fashion, the equations still wasn’t as close to what we were looking for. The R2 for the Millero and Yuan’s equation was as closer to one than any other of the R2 in any of the other equations. Dr.Yuan’s equation also gave us great feedback with the results from his equation. The R2 for Milero’s equation turned out to be .901, the slope was .727, and the y-intercept was 636. His results were similar in some ways to the results from Yuan. Yuan’s equation for Alkalinity came out with the following results: R2 was .935, the slope was .919, and the y-intercept was -182.7. The results for his equation for Carbon Dioxide came out to be: R2 of .948, slope of 1.062, and y-intercept of -106.4. The equations from the Academic Years 2007 and 2008 weren’t as effective as Milero’s and Yuan’s equations. The R2 for the Academic Year 2007 was .235, the slope was 2.023, and the y-intercept was .235. There was also a second formula that the Academic Team 2007 formulated, the R2 was .495, the slope was -0.461, and the y-intercept was 398.2. For the Summer Team 2007, their equation was also as ineffective as the Academics Team’s equations. The R2 for them turned out to be .661, the slope was 2.448, and the y-intercept was -472.8.

Data Provided by:Kadarice Joyce

Formula Chart for IO9b and IO10 DataFormula

Name Formula R Square

Slope Y-intercept

Yuan’s Alkalinty Equation

y =(-0.694554629)*(temperture)+(54.66100164)*(salinty)+(409.2734021)

0.913 0.895 248.3

y=(-6.706358308)*(temperture)+(50.19832435)*(salinty)+(383.7812623)

0.952 0.818 350.8

Academic Year 2007 (1)

y =+(12.47*temperture)+(-14.32*salinty)+(33.19*0.23)+575.26

0.371 1.076 34.01

Academic Year 2007 (2)

y=(14.53*temperture)+(55.3*salinity)+(0.12*65)+(45.13*0.23)+(-2024.95)

0.546 0.561 98.76

Summer Team 2007 y =(-7.127532)*(temperture)+(12.2405364)*(salinty)+(-0.2267359)*(65)+(123.906899)

0.349 0.038 577.5

Millero y= ( -114)+(68.8)*(salinity) 0.915 1.074 -175.5T- TemperatureS- Salinity

Graphs from the IO9b and IO10 Data

2180 2200 2220 2240 2260 2280 2300 2320 2340 23602100

2150

2200

2250

2300

2350

2400

f(x) = 0.895663835651216 x + 248.394041614459R² = 0.913290699635361

Series1Linear (Series1)Linear (Series1)

Cal

cula

ted

TA

Measured TA

ALKALI UMOL/KG (YUAN)

1800 1850 1900 1950 2000 20501750

1800

1850

1900

1950

2000

2050

f(x) = 0.818530097757062 x + 350.874442460743R² = 0.952516844954719

TCARBN UMOL/KG (YUAN)

Series1Linear (Series1)

Measured TCO2

Cal

cula

ted

pCO

2

250.0 270.0 290.0 310.0 330.0 350.0 370.0 390.0 410.0300

320

340

360

380

400

f(x) = 0.0387790253256086 x + 328.265701360001R² = 0.000206483426438364

Cal pCO2(Summer Team 2007)

Series1Linear (Series1)

Measured pCO2

Cal

cula

ted

pCO

2

Continued Data

300 320 340 360 380 400 420300320340360380400420440460480500

f(x) = 1.07624043030614 x + 34.0109347894293R² = 0.371832093813367

Cal PCO2 Academic Year 2007(Equ.1)

07 Academic yearEquation 1Linear (07 Academic yearEquation 1)

Cal

cula

ted

pC

O2

Measured TA

300.0 320.0 340.0 360.0 380.0 400.0 420.0230

250

270

290

310

330f(x) = 0.561335268322573 x + 98.7607886484457R² = 0.546184910654285

Cal PCO2(Academic Yr. Equ.2)

07 Academic year Equation 2Linear (07 Academic year Equation 2)

Measured pCO2

Cal

cula

ted

pCO

2

2150 2200 2250 2300 23502050

2100

2150

2200

2250

2300

2350

2400

f(x) = 1.07420098417091 x − 172.495186007924R² = 0.91556168981912

ALKALI UMOL/KG (Millero)

Series1Linear (Series1)

Mearsured TA

Cal

cula

ted

TA

Results The results from the first equation by the Academic year 2007 displayed

an R2 value of 0.371, a slope of 1.076 and a y-intercept value of 34.01, Figure 14, this chart measured pCO2. The second equation obtained from the Academic year 2007 also measured pCO2. Final calculations from this equation were; R2 amounted to 0.546, slope; 0.561, and the y-intercept came to be 98.76 (Figure 15).

Millero’s equation configured an R2 value of 0.915, a slope of 1.074, and -175.5 was the final y-intercept value (Figure 16).

The first Yuan equation measured alkalinity. The R2 calculated from this plot was 0.913, with a slope of 0.895 and a y-intercept value of 248.3 (Figure 16). Yuan’s second linear equation measured TCO2. The value of R2 of this graph is 0.952; with a slope value of 0.818 and y intercept value of 350.8 (Figure 17).

Data Provided by:Candy Graves

ConclusionThere is a need to develop innovative

methods that accurately assess regional carbon dioxide levels based on satellite remote sensing data. Although the academic and summer formulas fail to accurately estimate pCO2 in the Indian Ocean, the potential of the Yuan equation ability to predict pCO2 levels in the Indian Ocean appears to be high. Future studies can be done to see if equations apply to other oceans.

References1) Ashley D. Berryman, Diaminatou Goudiaby, Phillip Moore (2008). “A

Multiple Linear Regression of pCO2 against Sea- Surface Temperature, Salinity, and Chlorophyll a at Station ALOHA and its Potential for Estimate pCO2 from Satellite Data.” Elizabeth City, NC.

2) Wei-Jun Cai Steven E. Lohrenz and (2005). “Satellite ocean color assessment of air-sea fluxes of CO2 in a river-dominated coastal margin”. Geophysical Research Letters, Vol. 33.

3) Thierry Delcroix, Alain Dessier, Michael J. McPhaden, Yves Gouriou (2004). “Time and space scales for sea surface salinity in the tropical oceans.” Elsevier. Toulou, France.

4) Frank J. Millero, Kitack Lee, Mary Roche (1997). “Distribution of alkalinity in the surface waters of the major oceans” Marine Chemistry. Miami, Fl.

5) MyAsia Reid andLee Smalls Jr. (2008). “A Multiple Linear Regression of pCO2 against Sea Surface Temperature, Salinity, and Chlorophyll a at Station BATS and its Potential for Estimate pCO2 from Satellite Data” Elizabeth City, NC.

Questions/Comments?

Acknowledgments

Mentor: Jinchun Yuan Principal Investigator: Dr. Linda Hayden

We thank director, Dr. Linda Hayden for the opportunity to conduct research through the Undergraduate Research Experience. Thanks to our team mentor, Dr. Jinchun Yuan for his direction and guidance. Thanks to mentors Mr. Jeff Wood, Mr. Jamie Powell, and Dr. Benjamin Branch for their support during the summer 2009 URE at Elizabeth City Sate University