'^' means 'to the power of'
pi - 3.14159; e = 2.718228;
Surface area of a sphere - 4piR^2
Units
1 micron (micrometre)
= 10^-6 metres; millimicron = 10^-9 metres = 1 nanometre
1 gram = 10^-3 kg;
= 10^-6 megagrams (tonnes); 10^-9 gigagrams; = 10^-12 teragrams (Tgrams);
= (femto);= (atto).
1 gram = 10^3 milligrams;
= 10^6 micrograms; = 10^9 nanograms; = 10^12 picograms
1 kg = 10^3 grams;
= 10^-3 tons; = 10^-9 Tgrams
1 kg = 10^6 milligrams
= 10^9 micrograms = 10^12 nanograms = 10^15 picograms
1 litre = 10^3 millilitres
(ccs) = 10x10x10 decametres = 10^-12 km^3 (1 km^3 = 10^12 litres)
1 short ton =.907184
tonnes; 1 long ton = 1.0160469 tonnes
1 ppm = 1 kg / 10^6
kg or 1 gram / 10^6 grams, etc.; = 1 mgram/kg.
Atomic mass, major
elements: Si - 28.09; Ti - 47.88; Al - 26.98; Fe - 55.85; Mg - 24.31; Ca
- 40.08; Na - 22.99; K - 39.1; P - 30.97;
oxygen - 16; Cl -
35.45; carbon - 12.01; S - 32.07
Concentration - micromoles/litre
= 10^-6 moles/litre = 10^-9
moles/millilitre
(Mass concentration
= Atomic mass x micromoles/litre x 10^-9 kg/kg;
e.g. Ca, 558000 x
35.45 x 10^-9 = 0.0198 kg/kg)
Concentration - millimoles/litre
= 10^-3 moles/litre = 10^-6
moles per millilitre
(Mass concentration,
e.g. Mg, = 54 x 24 x 10^-6 = .00129 kg/kg)
Equatorial radius
6,378.137 km
Polar radius
6,356.752 km
Equivolume sphere
radius
6,371 km (4 pi R^2)
Surface area of the
earth
5.1 x 10^8 km^2
Circumference
40,030 km (2 pi R)
Mass, M
5.97369 x 10^24 kg
Mean Density
5.5148 x 10^3 kg / m^3
Density of continental
crust
2.7500 x 10^3 kg / m^3
Gravity at equator
9.7803267 m / s^2
Gravity at poles
9.832186 m / s^2
Mean land elevation
825 m
Mean ocean dept
3,770 m
Depth of ridge crests
below sea level
2,500 m
Area of oceans excluding
continental margins
3.1 x 10^8 km^2
Land area of continental
crust
1.48 x 10^8 km^2
Continental crust
plus continental margins
2 x 10^8 km^2
Average thickness
of continental crust
38 km
Average thickness
of oceanic crust
6 km
Volume of continental
crust
7.6 x 10^9 km^3
Volume of continental
sediments on ocean floors
1.6 x 10^8 km^3
Age of the Earth
4.5 Ma
Total length of active
ocean ridges
56,000 km
Average rate of prod,
oceanic crust (Mes. - Cen.)
25 km^3 /yr
Present day production
of oceanic crust
17 km^3 /yr
Ave product / km of
ridge length (Mes. - Cen.)
450 km^3 /km /Ma
Total length of destructive
margins
37,000 km
Average velocity of
subduction
80 km /Ma
Ave subduction rate
/ km of margin (Mes. - Cen.)
675 km^3 /km /Ma
Volume of rain water
entering the oceans from rivers
4 x 10^16 kg (= 4 x 10^4 km^3)
Calculated surface
of oceans at 71% of 5.1 x 10^8:
3.62 x 10^8 km^2
Calculated volume
of the oceans if depth is
3.73 1.354 x 10^9 km^3
Calculated surface
of the continents at 29%:
1.479 x 10^8 km^2
********************************************************************
Sources: Pinet, P.R. 1992. Oceanography. West Publishing Co.,
p. 152, Water
Reservoirs (in units of 10^6 km^3)
Volume %
Oceans 1370 97.25
Ice masses 29 2.05
Groundwater 9.5 0.68
Lakes 0.125 0.01
Atmosphere 0.013 0.001
Rivers 0.0017 0.0001
Biosphere 0.0006 0.00004
p. 154, Water
Fluxes, (in km^3/yr)
Precip on land 110300
Evap from land 72900
Water entering rivers
37400 (c. 4 x 10^4 km^3/yr) (4 x 10^16 kg)
Precip on oceans 385700
Evap from oceans 423100
Total precip 496000
Total evap 496000
***************************************************************************
(S x 4 x 0.71 x 1 x
.035 / 2 km^3 = S x 0.05 x 1012)
If all the salt in
the oceans were spread over only the continents, its thickness would be:
(2.224 x 10^7) km^3
/ (1.4824 x 10^8) km^2 = 151 m.
Calculated another
way using approximations, where S is the surface area of the Earth, the
salt thickness would be:
(Surface area of the
Earth x oceanic prop x depth of oceans x salt conc. x SG of sea water x
SG salt) / (Surface area of the Earth x continent proportion) = (S x 0.71
x 4 x 1 x 0.035 / 2) / (S x 0.29) km = 0.05 / 0.3 = c. 0.165 km = 165 metres.
The calculated thickness
is similar to the estimate of 500 feet (170 m) of Swensen
(If the salt in the
sea could be removed and spread evenly over the Earth's land surface it
would form a layer more than 500 feet thick, salty.ref)
If the salt were spread
over the whole of the Earth, its thickness would be :
(2.224 x 10^7 / 5.10101
x 10^8 x 1000) metres = 44 metres
The thickness in the
oceans only would be 2.224 x 10^7 km^3 / 3.63 x 10^8 x 1000 metres = 61
metres
****************************************************************************************
Sources: Data extracted from Open University Publications:
The Ocean Basins, p. 26
Lithsphere is 250 km
thick under the continents.
Lithosphere is 100
km thick under the oceans.
The Ocean Basins, p.27
Maximum height -
8.5 km
Average height -
0.8 km
Averge depth of sea
- 3.7 km
Maximum depth -
11.04
21% of earth's surface
lies between sea level and 1 km
23.2% lies between
4 - 5 km depth
The Ocean Basins, p. 28
Pacific
Atlantic
Indian
World Mediter.
Oceanic area 10^6,
180
107
74
361
2.5
Land area drained
10^6
19
69
13
101
Ocean/drainage area
9.5
1.6
5.7
3.6
Average depth, km
3.94
3.31
3.84
3.73 1.5
Ave volume
1.346x10^9 km^3
= 1.345x10^21 litres
Ave mass (Vol x 1.0265)
1.382x10^21 kg
Area as % of total:
Mid-ocean ridges,
%
35.9
31.2
30.2
32.7
Trenches, %
2.9
.7
.3
1.7
Shelf and slope, %
13.1
19.4
9.1
15.3
Rise, %
2.7
8.5
5.7
5.3
Abyssal deeps, %
42.9
38.1
49.3
41.9
Volcanic edifices,
% 2.5 2.1 5.4 3.1
Meditteranean
Surface area -
2.5 10^ km^2
Average depth
1.5 km
Volume
3.75 x 10^6 km^3
Amount of salt
3.75 x 10^6 x 10^12 x .035 = 1.3 x 10^17 kg
Area of the floor
of the Meditteranean -
2 x 10^6 km^2
Equivalent thicknes
of salt -
32.8 m
Thickness of salt
in the Miocene Messinian deposits -
1 km
Loss of water from
the Mediterranean by evaporation -
4.7 x 10^3 km^3
Precipitation in the
Med. -
1.2 x 10^3 km^3
Rivers contribute
to the Med -
0.25x10^3 km^3
Net loss through precipitation
-
3.25 x 10^3 km^3, made up by addition of Atlantic water.
Time to dry up if
no replacement =
1.15 x 10^3 years
The Ocean Basins, p. 100 - Hydrothermal/normal sea water compositions:
Hydrothermal vent solution at c. 350C at 21N on the East Pacific Rise, ppm by weight;
pH of the vent solution is 4.0 whereas normal seawater is about 8.
If 1.7 x 10^14 kg of seawater circulates through th oceanic crust each year and if it picks up 460 ppm (460 ppm = 4.60 x 10^-4 kg / kg) then 7.8 x 10^10 kg of Ca is added to the seas, compared with 5 x 10^11 kg introduced from rivers.
vent,
seawater,
ppm
ppm
Cl
17300 = 0.0173 kg/kg
19500 = 0.0195 kg/kg
Na
9931 = 0.0099 kg/kg
10500 = 0.0105 kg/kg
Mg
-
1290 = 0.00129 kg/kg
SO42-
-
905
H2S
210
-
Ca
860
400
K
975
380
Sr
8
8
Si
600
3
Ba
5-13
2x10^-2
Zn
7
5x10^-3
Mn
33
1x10^-4
Fe
101
2x10^-4
Ocean Chemistry, p. 6
Sediments
Atlantic
Pacific
Indian
World
Calcareous ooze
65.1
36.2
54.3
47.1
Pteropod ooze
2.4
0.1
-
0.6
Diatom ooze
6.7
10.1
19.9
11.6
Radiolarian ooze
-
4.6
.5
2.6
Pelagic clay
25.8
49.0
25.3
38.1
% size of ocean
23
53.4
23.6
100
Ocean Chemistry, p.15
Ratio of illite to
quartz = 4, except South Pacific = 7
Illite:
N Atlantic 60;
S. Atlantic 50;
North Pacific 40;
Indian 35;
S. Pacific 28
Ocean Chemistry, p.18
Concentration
Total Amount
in the oceans
in the oceans
ppm
tonnes (1 tonne = 10^3 kg)
Cl
1.95x10^4
2.57x10^16 kg
Cl-
(Cl
0.0195 kg/kg
2.57x10^19 kg (1.95x10^-2 x 1.32 x10^21))
Na
1.077x10^4
1.42x10^16 kg
Na+
Mg
0.129 "
0.71 "
Mg2+
Ca
0.0412 "
0.0545 "
Ca2+
K
0.038 "
0.0502 "
K+
S
0.0905 "
0.12 "
SO42- (= 2.7 ppm )
Br
67
8.86x10^13
Br-
(Br
67x10^-6 kg/kg
8.86x10^16 kg)
C
28
3.7 HCO3-,
CO32-, CO2
N
11.5
1.5
N2, NO3-, NH4+
Sr
8
1 .06
O
6
7.93x10^12
B
4.4
5.82
Si
2
2.64
P
6x10^-2
7.93x10^10
HPO42-, PO43-, H2PO4-
(P
6x10^-8 kg/kg
7.93x10^13)
Ti
1x10^-3
1.32x10^9
Ti(OH)4
Al
4x10^-4
5.29x10^8
Al(OH)4-
(Al
4x10^-10 kg/kg
5.29x10^11 kg)
Mn
1x10^-4 1.32x10^11 kg
(1x10^-10 x 1.32 x10^21)
Mn2+, MnCl+
Cu
1
1.32
Fe
5.5x10^-5
7.26x10^7
Zr
3
3.97
Nb
1
1.32
Be
5.6 x10^-6
7.4 x10^6
Au
4 "
5.29
AuCl2-
La
3 "
3.97
La(OH)3
Nd
3 "
3.97
Pb
2 "
2.64
Ce
1 "
1.32
Y
1.3 "
1.73
Yb
8x10^-7
1.06
Sm
5x10^-8
6.61x10^4
Eu
1
1.32
Seawater, p. 30
Ave % of 10 most abundant elements in the Earths crust, wt %, compared with seawater, kg/kg or kg/litre):
Element Crust in seawater % in solution
Si
28.2
Al
8.2
Fe
5.6
Ca
4.2
0.000412 kg/kg
1.7
Na
2.4
0.01076
74.7
K
2.1
0.000387
3.1
Mg
2.3
0.001294
Ti
0.6
Mn
0.1
P
0.1
*****************************************************************************************
Sources: Pinet, P.R. 1992. Oceanography. West Publishing Co., p. 134
Dissolved
substance in river water
ppm
kg/kg
%
Bicarbonate
58.8
5.88 x10^-5 kg/kg
48.7
Ca2+
15
1.50 x10^-5 kg/kg
12.4
SiO2
13.1
1.31 x10^-5 kg/kg
10.8
SO42-
1.2
1.20 x10^-6 kg/kg
9.3
Cl
7.8
7.80 x10^-6 kg/kg
6.5
Na+
6.3
6.30 x10^-6 kg/kg
5.2
Mg2+
4.1
4.10 x10^-6 kg/kg
3.4
K+
2.3
2.30 x10^-6 kg/kg
1.9
NO3-
1.0
1.00 x10^-6 kg/kg
0.8
(Fe,Al)2O3
0.9
9.00 x10^-7 kg/kg
0.8
Remainder
0.3
3.00 x10^-7 kg/kg
0.3
Total per year delivered
to oceans = c. 4 billion tonnes (10^-4 kg/kg x 4 x 10^16 kg)
Photic zone rarely
extend below 200m of the ocean
3/4 of organic matter
in sinking particles that leave the photic zone are decomposed and recycled
in the upper 500-1000 m of
the water column.
At the compensation depth the oxygen produced by phytoplankton during
photosynthesis equals the amount
they consume in respiration
over a 24 hour period.
****************************************************************************************************************
Sources: The following tables are from Berner, E.K. and Berner, R.A., 1987,The Global Water Cycle, Prentice Hall, New Jersey.
TABLE 8.3 Replacement Time with Respect to River Addition, Tau(r), for Some Major and Minor Dissolved Species in Seawater.
Concentration - micromoles/litre
= 10^-6 moles/litre = 10^-9 moles/millilitre
(Mass concentration
= Atomic mass x micromoles/litre x 10^-9 kg/kg;
e.g. 558000 x 35.45
x 10^-9 = 0.0198 kg/kg)
Component
River
Seawater
Tau(r) (1000 yr)
Water
Cl-
230
558,000 (= 0.0198 kg/kg)
87,000
Na-
315
479,000
55,000
Mg--
150
54,300
13,000
S04--
120
28,900
8,700
Ca++
367
10,500
1,000
K+
36
10,400
10,000
HCO3-
870
2,000
83
H4SIO4
170
100
21
NO-3
10
20
72
Orthoph-
0.7
1
50
osphate
Sources: Based on Tables 8.1 and 8.2 and data of Meybeck 1979, 1982 for world average river water.
Tau(r) = ([SW]/[RW])Tau(w),
where Tau(w) = replacement (residence) time of H2O = 36,000 yr;
W = river water; SW
= seawater, and concentration in micromoles per litre = VtM.
TABLE 8.4 Major Processes of Organic Matter Decomposition in Marine Sediments.
Reactions succeed one
another in the order written as each oxidant is completely consumed
Oxygenation (oxic)
CH2O + O2
= CO2 + H2O
Nitrate reduction
(mainly anoxic)
5CH2O +
4NO3- = 2N2
+ CO2 + 4HCO3-
+ 3H2O
Manganese oxide reduction
(mainly anoxic)
CH2O +
2MnO2 + 3CO2+ H2O = 2Mn++ + 4HCO3-
Ferric oxide (hydroxide)
reduction (anoxic)
H2O + 4Fe(OH)3
+ 7CO2 = 4Fe++ + 8HCO3- + 3H2O
Sulfate reduction
(anoxic)
2CH2O +
SO4- - = H2S + 2HCO3-
Methane formation
(anoxic)
2CH2O =
CH4 + CO2
Note: Organic matter
schematically represented as CH2O.
TABLE 8.7 Concentration Changes of Some Major Seawater Constituents Upon Reacting with Basalt at High Temperatures
Concentration (a mM
= a millimoles/litre = a x 10^-3 moles/litre = a x 10^-6 moles per millilitre,
and e.g. concentration in
kg/kg of Mg = 54 x
24 x 10^-6 = .00129 kg/kg)
Constituent Seawater Galapagos Delta (mM)
Mg++
54
0
- 54
Ca++
10
35
25
K+
10
19
9
SO4--
29
0
- 29
H4SiO4
0.1
~20
~20
Delta Ca++ -
Delta S04--
-
-
54
Note: mM = ~millimoles
per liter. Sources: data are for the
Galapagos spreading center at 350C and are taken from the extrapolation
of
Edmond et al. (1979).
Delta = concentration
difference between 350' C ~Galapagos water and ~seawater.
Delta Ca++ - Delta
S04-- = total Ca++ released to solution.
TABLE 8.9 Change in Concentration in Interstitial Water for Various Ions versus
Depth in a Sediment from the Brazil Basin, South Atlantic Ocean (Station CH 1 1 ~5-DD)
Sediment
Concen
Change - Pore Water Overlying Seawater (mM)
Depth
-tration
(cm)
pH
DNa+
DMg++ DCa++
DK+ DHCO3-
DS04--
0
7.4
0.00
0.00
0.00
0.00
0.00
0.00
5
7.5
0.07
-0.04
0.17
-0.05
0.19
0.05
15
7.3
0.09
-0.35
0.45
-0.11
0.25
0.04
30
7.5
0.46
-0.42
0.50
-0.08
0.34
0.06
60
7.5
0.45
-0.58
0.76
-0.11
0.68
0.06
100
7.2
0.56
-0.78
0.97
-0.16
0.82
-0.01
195
7.4
0.95
-1.09
1.18
-0.26
1.12
-0.13
Sources: Adapted
from F. L. Sayles. "The Composition and Diagenesis of Interstitial Solutions.
1. Fluxes Across the
Seawater-Sediment
Interface in the Atlantic Ocean,". Geochimica et Cosmochimica Acta, 43.
p. 532. Copyright 1979
by
Pergamon Press, reprinted by permission of the publisher. Note: Negative
Delta values refer to uptake by the sediment
(loss
from pore water). mM = millimoles per litre; = 10^-3 moles per litre.
TABLE 8.12 Rates of Addition via Rivers of Major Elements to the Ocean (as Dissolved Species) and Rates of Net Loss from the Ocean by Transfer of Sea Salt to the Continents via the Atmosphere
Rate of Addition
Rate of Net Sea Salt Loss
Species
from Rivers, (Tg/yr)
to Atmosphere (Tg/yr)
Cl-
308
40
Na+
269
21
S04- - -S
143
4
Mg++
137
3
K+
52
1
Ca++
550
0.5
HCO3-
1980
--
H4SiO4-Si
180
--
Sources: River-water
data from Meybeck 1979; cyclic salt data from Chapter 5 of Berner and Berner
1987. Note: Tg = 1012 g.
Based
on river water input of 37,400 km3/yr; includes pollution.
TABLE 8.13 The Oceanic Chloride Budget (Rates in Tg/yr)
Present-Day Budget
Inputs
Outputs
Rivers (natural)
215
Net sea-air transfer
40
Rivers (pollution)
93
Pore-water burial
17
Total 308 Total 57
Long-Term
(Balanced) Budget
Inputs
Outputs
Rivers
215
NaCl evaporative
deposition
166
Net sea-air transfer
40
Pore-water burial
9
Total
215
Note: Tg = 1011 g.
Replacement time for Cl- is 87 million years.
TABLE 8.14 The Oceanic Sodium Budget (Rates in Tg/yr)
Present-Day Budget
Inputs
Outputs
Rivers (natural)
193
Cation exchange
42
Rivers (pollution)
76
Net sea-air transfer
21
Pore-water burial
11
Total
269
Total
74
Long-Term
Budget
Inputs
Outputs
Rivers
193
NaCl deposition 108
Net sea-air transfer
21
Cation exchange
21
Pore-water burial
6
Basalt-seawater
Reaction
37
Total
193
(Balanced)
Budget for Past 100 Million Years
Inputs
Outputs
Rivers
137
Volcanic-seawater
reaction
119
In biogenic CaCO3
15
Net sea-air transfer
3
Total
137
Note: Tg = 1012
g. Replacement time for Mg++ is 13 million years.
TABLE 8.17 The Oceanic Potassium Budget (Rates in Tg/yr)
Long-Term (Balanced) Budget
Inputs Outputs
Rivers
52
Fixation on clay
near river mouths
4
Volcanic-seawater
Sea-air transfer
1
reaction (high-
temperature
30
Total
82
Low-temperature volcanic-
seawater reaction or
slow fixation in deep
sea or reverse weathering
77
Total
82
Note: Tg = 1012
g.
Replacement time for K+ is 10 million years.
TABLE 8.18 The Oceanic Calcium Budget (Rates in Tg/yr)
Present-Day
Budget
Inputs
Outputs
Rivers
550
CaCO3 deposition:
Volcanic-seawater
Shallow water
520
reaction
191
Deep sea
440
Cation exchange
37
Total 778
Total
960
Budget
for Past 25 Million Years
Inputs
Outputs
Rivers
550
CaCO3 deposition:
Volcanic-seawater
Shallow water
240
reaction
191
Deep sea
440
Cation exchange
19
Evaporitic CaSO4
deposition
49
Total
760
Total
729
Note: Tg = 1012
g.
Replacement time (rivers only) for Ca is 1 million years.
TABLE 8.19 The Oceanic Bicarbonate Budget (Rates in Tg/yr)
Present-Day
Budget
Inputs
Outputs
Rivers
1980
CaCO3 deposition:
Biogenic pyrite
Shallow water
1580
formation
145
Deep sea
1340
Total 2125 Total 2920
Budget
for Past 25 Million Years
Inputs
Outputs
Rivers
1980
CaCO3 deposition:
Biogenic pyrite
Shallow water
730
formation
145
Deep sea
1340
Total
2125
Total
2070
Note: Tg =1012
g. Replacement time for HCO3- (river input only) is 83,000 years.
TABLE 8.20 The Oceanic Silica Budget (Rates in Tg/yr).
Present-Day
Budget
Inputs
Outputs
Rivers
180
Biogenic silica deposition
Basalt-seawater
Antarctic Ocean
117
reaction
30
Bering Sea
13
Total
210
North Pacific Ocean
7
Sea of Okhotsk
7
Gulf of California
5
Walvis Bay
3
Estuaries
38
Other areas
<13
Total
190~-203
Source: Outputs
from DeMaster 1981.
Notes: Tg = 1012g.
To convert to Tg of SiO2, multiply by 2.14. The replacement time for riverborne
H4SIO4 is 21,000 years. The removal value for estuaries may be a maximum.
TABLE 8.21 The Oceanic Phosphorus Budget (Rates in Tg/yr)
Present-Day
Budget
Inputs
Outputs
Rivers:
Organic P burial
2.0
Natural dissolved
P
CaCO, deposition
0.7
(organic plus ~ortho-P)
1.0
Dissolved P from
Adsorption on volcano-
pollution
1.0
genic Fe oxides
0.11
Particulate reactive
P
Phosphorite formation
<0.11
(mostly pollution)
2.0
Rain (plus dry
Fish debris deposition
<0.02
fallout)
0.2
Total
4.2
Total
2.8-2.9
Long-Term
(Balanced) Budget
Inputs
Outputs
Rivers:
Dissolved ortho-P
0.4
Organic P burial
0.5
Dissolved organic
P
0.6
CaCO3 deposition
0.5
Adsorption on volcano-
Particulate reactive
P
0.1
genic Fe oxides
0.1
Rain (plus dry fallout)
0.1
Phosphorite formation
0.1
Total
1.2
Total
1.2
Source:River
input data from Meybeck 1982; data from Froelich et al. 1982.
Note: Tg = 1012
g. The replacement time for phosphorus via river addition (of dissolved
orthophosphate only) is 50,000 years.
TABLE 8.22 The Oceanic Nitrogen Budget (Rates in Tg/yr)
Present-Day
Budget
Inputs
Outputs
Rivers:
Organic N burial in
sediments
14
Natural dissolved
De-nitrification
40 - 120
inorganic N (88% as
Total
54 - 134
NO3- -N)
4.5
Natural dissolved
organic N
10
Pollutive dissolved
N
7
Particulate organic
N
21
Rain and dry deposition
20
Fixation of N2
10-90
Total
73-153
Note: Tg = 1012g.
The replacement time for NO3- added by rivers is 72,000 years.