Breathing Planet Earth: Analysis of Keeling’s Data on CO₂ and O₂ with Respiratory Quotient (RQ), Part I: Global Respiratory Quotient (RQ_Glob) of Earth

Abstract

In biology, respiratory quotient (RQ) is defined as the ratio of CO₂ moles produced per mole of oxygen consumed. Recently, Annamalai et al. applied the RQ concept to engineering literature to show that CO₂ emission in Giga Tons per Exa J of energy = 0.1 ∗ RQ. Hence, the RQ is a measure of CO₂ released per unit of energy released during combustion. Power plants on earth use a mix of fossil fuels (FF), and the RQ of the mix is estimated as 0.75. Keeling’s data on CO₂ and O₂ concentrations in the atmosphere (abbreviated as atm., 1991–2018) are used to determine the average RQ_Glob of earth as 0.47, indicating that 0.47 “net” moles of CO₂ are added to which means that there is a net loss of 5.6 kg C(s) from earth per mole of O₂ depleted in the absence of sequestration, or the mass loss rate of earth is estimated at 4.3 GT per year. Based on recent literature on the earth’s tilt and the amount of water pumped, it is speculated that there could be an additional tilt of 2.7 cm over the next 17 years. While RQ of FF, or biomass, is a property, RQ_Glob is not. It is shown that the lower the RQ_Glob, the higher the acidity of oceans, the lesser the CO₂ addition to atm, and the lower the earth’s mass loss. Keeling’s saw-tooth pattern of O₂ is predicted from known CO₂ data and RQ_Glob. In Part II, the RQ concept is expanded to define energy-based RQ_Glob,En, and adopt the CO₂ and O₂ balance equations, which are then used in developing the explicit relations for CO₂ distribution amongst atm., land, and ocean, and the RQ-based results are validated with results from more detailed literature models for the period 1991–2018.

1. Introduction

According to Biology Online [1], life is defined as “a distinctive characteristic of a living organism from a dead organism or non-living thing, as specifically distinguished by the capacity to grow, metabolize, respond (to stimuli), adapt, and reproduce”. On the other hand, non-biological systems (NBS) include thermal systems (e.g., heat engines, power plants, etc.) which convert the chemical energy of fossil fuels (FF) into work via rapid oxidation or combustion. The NBS “breathe” in oxygen, oxidizes FF, which includes natural gas, oil, and coal, and “breathe” out CO₂ and H₂O. The metabolism of nutrients (or fuels) in many biological systems (including BS, humans, land and ocean animals, plants, etc.) involves slow oxidation, consuming oxygen, and then breathing out CO₂. In biology, the ratio of moles of CO₂ produced to O₂ moles used in the release of energy is called the respiration quotient (RQ). Like NBS and BS, the earth undergoes a breathing cycle, but with a difference. While NBS, particularly humans, cannot naturally produce oxygen, terrestrial ecosystems include trees and plants on land, and phytoplankton (PP) in oceans “breathe” in CO₂ and “breathe” out O₂ under photosynthesis (PS), where C is stored as the growth mass of biomass. In addition, biomass undergoes a “respiration” process, which is used to oxidize sugars for life-sustaining functions during the growth of biomass [2,3]. In addition to CO₂ from FF, the dead organic matter releases CO₂ ≈ 50 GT/year). The net primary product (NPP) of C i during the photosynthesis is the difference between the gross primary production (GPP, ≈120 GT of C/year and the C used in the respiration process (≈60 GT of C/year) and hence the NPP during photosynthesis is about 60 GT of C/year while decomposition of biomass is about 50 GT/year. Thus, the NEP of the ecosystem is 10 GT/year [4]. It is apparent that biomass serves as a CO₂ sink and an O₂ source in the growth of biomass, (i.e., CO₂ is split into C(s) and O₂). As used here, the term biomass represents both terrestrial and ocean-based plants. For biomass growth, the CO₂ literature uses a photosynthetic quotient (PQ = O₂ mols produced/CO₂ mols used), which is the inverse of RQ used in biology and various other terms (more details in Section 3).

In addition, CO₂ is mainly released from the combustion of FF (e.g., coal, oil, gasoline, diesel, kerosene, and natural gas) in power plants, land uses, and industrial processes; the corresponding decrease in O₂ in the atm is due to the consumption of fossil fuels. The CO₂ emissions reached about 36.3 giga tons (GT) of CO₂ in 2021, and a majority (almost 80%) of the total carbon emissions have been due to coal and liquid fuels, with about 20% from the combustion of gaseous fuels [5].

Apart from biomass, which serves as the CO₂ sink, CO₂ is also stored in the ocean. The difference between CO₂ produced and CO₂ sinks via biomass and ocean storage results in the accumulation of CO₂ in the atmosphere {d[CO₂]/d}_atm, and the difference between O₂ consumed for oxidation of FF and O₂ produced by biomass results in the net depletion of O₂ from the atmosphere {d[O₂]/dt}_atm. Since 1958, Keeling has monitored this change in CO₂ and O₂ concentrations by taking air samples from the atm over several decades and presenting Keeling’s curves, which exhibit a saw tooth pattern for both CO₂ and O₂. These saw tooth patterns and the inverse relation between CO₂ and O₂ (i.e., CO₂ increases when O₂ decreases in the atm and vice versa) reveal certain similarities to the RQ concept in biology. The biology literature assumes that the energy release per unit mole of oxygen, or higher heating value per unit mole, or Peta mole of oxygen {HHV_O₂), is constant at about 448 Exa J per Peta mole of O₂ consumed for oxidation. The RQ concept was recently extended to engineering literature [6,7]. It was shown that the CO₂ released in giga tons per unit Exa J is equal to 0.1 ∗ RQ (more details in Section 3.3.1). This relation was also used to estimate the CO₂ tax per km or mile driven rather than using the weight of the vehicle for taxation as currently done in the EU [6]. The lower the RQ (e.g., natural gas with RQ = 0.5), the lower the CO₂ emitted, and the higher the RQ (e.g., coal, RQ ≈ 1), the higher the CO₂ emitted for the same energy released. In order to minimize the amount of CO₂ added to the atm, it is of interest to select FF, which has the lowest amount of CO₂ released for fixed energy release.

2. Literature Review

The literature review is divided into the following sections: (i) CO₂ source from FF and other global warming gases, (ii) Keeling’s data on CO₂ and O₂ in the atmosphere (atm), (iii) CO₂ and global warming, (iv) CO₂ sources and sinks, O₂ sources and sinks, and models, and (v) the need for current work.

2.1. Fosssil Fuel, Land Use and CO₂

Large quantities of CO₂ released from the combustion of FF (about 87 % of CO₂) play a major role in climate forcing [8]. Further CO₂ is also released due to the land use (LU, 13 %, fire, deforestation, domestic wood consumption, decomposition of dead wood in soil, etc.) by humans. The combined CO₂ from FF and LU will be referred to as CO₂ from FFLU. Global warming gases include CO₂, CH₄, N₂O [9], and chlorofluorocarbons (CFC) with various degrees of global warming potential (GWP). The GWP of biofuels was evaluated by Holtsmark and compared against the impacts of fossil fuels [10]. Biomass and other renewable fuels (e.g., ethanol produced from plant materials), including nutrients consumed by BS, are considered to be carbon neutral, and hence the CO₂ released due to the oxidation of renewable fuels is not considered in the carbon footprint, while the C emitted during the combustion of FF is accounted for in the carbon footprint. Due to anthropogenic activities, each fuel has its own share of global warming, irrespective of whether the fuel is renewable or non-renewable. For the period 1950–1982, Boden et al. [5] estimated the emission of CO₂ using the fuel production data, and C oxidized to CO₂. The impact of residential energy consumption on GHG emissions and policies that can be implemented to reduce energy utilization were reviewed by Nejat et al. [11].

2.2. Keeling’s Data on CO₂ and O₂ and Saw Tooth Pattern

Using monthly data from weather stations close to volcano Mauna Loa, Hawaii (NO AA Global Monitoring Lab, Mauna Loa Observatory (MLO), North flank of Mauna Loa Volcano, Hawaii, elevation: 3397 m above sea level (far from human population) on CO₂ and O₂ (1960–2021), Keeling plotted CO₂ and O₂ vs. year (Figure 1), which is known as Keeling’s curve [12,13]. The curves reveal the asynchronous “choreography between atmospheric CO₂ and O₂” and the saw-tooth pattern on CO₂ and O₂. Instead of “per meg” units of Keeling, ppm (4.8 per MEG = 1 ppm) is used for CO₂ concentrations in the current text. Figure 1 reveals a cyclic saw-tooth pattern of small peaks and valleys (note: captions of figures contain more information so that text could be reduced). Balkanski et al. [14] attribute the CO₂ cycle to terrestrial (land) biotic activity. Particularly during fall and winter (FW, Fall: September, October, and November; Winter: December, January, and February), the release of CO₂ due to the combustion of fossil fuels and the sink of oxygen from the atm. dominate the CO₂ sink and O₂ production for the growth of biomass. Thus, during FW, ΔCO₂ > 0 and ΔO₂ < 0. The reverse happens in spring and summer (SS, Spring: March, April, May; Summer: June, July, August); the sink of CO₂ and production of O₂ via biomass growth and limited outgassing of O₂ from the ocean (due to warm temperatures) dominate the CO₂ source and O₂ sink for energy release from power plants, resulting in ΔCO₂ < 0 and ΔO₂ > 0 in SS [15]. The amplitude of CO₂ oscillation is about 6 ppm. The net effect of FW and SS behaviors is positive production of CO₂ per year, resulting in an increase of atmospheric CO₂ in ppm.

2.3. CO₂ and Global Warming

The CO₂ record shows that the normal level of CO₂ for centuries was about 300 ppm; however, it reached 414.7 ppm in 2021 and 424 ppm in May 2023 [18]. An increase of 2 ppm of CO₂/year (i.e., almost 15.6 GT of CO₂ added to atm) is related to a global warming rate of 0.0125 °C/year [19]. The synchronous dance between CO₂ and Antarctic temperatures is illustrated in Figure 2, while Figure 3 shows the temperature since 1875. The rising global temperature of the earth is shown to reduce the PS process; hence, by 2040, CO₂ sink due to biomass growth will be reduced by almost 50% [20].

The relationship between CO₂, warming temperature rise, saturation pressure of water vapor, and hence the increasing number of hurricanes, wildfires, etc., is well established [25]. There is also increased seaweed (Sargassum, which smells like rotten eggs–due to hydrogen sulfide) growth due to global warming and rainfall. Assuming ocean temperatures are the same as the global average temperature, the author estimated the variation in saturation pressure, which is shown in Figure 3. Assuming the % increase in hurricanes from 2012 to 2022 is proportional to the % increase in saturation pressure (about 12%). The data from the autopiloted Saildrone Explorer SD 1045 boat indicated a 10% increase in hurricanes and an 8% increase in storms [26], but rain increased only by 1.3% per K rise. The increased ocean temperature will also result in the release of O₂ from oceans (a decrease of 0.2–0.5% per year from oceans). The warmer the ocean, the more vapor in a region and the lesser the barometric pressure, resulting in a higher wind velocity and faster growth of hurricanes [27].

Figure 3. Relation between the global temperature (primary axis, solid line) and the saturation pressure of water (secondary axis, dashed line); temperature data taken from Ref. [28] and pasted onto EXCEL sheet. Global Average T in °C = 2.326 × 10⁻⁴ ∗ year² − 0.02539 ∗ year + 11.39, Year: (Specified year-1875) P^sat by the author using ln(P^sat) = A − B/(T + D), P^sat in bar, T in °C, A = 12.22, B = 4120.6, D = 237.9: For 2002, temperature rise per year = 0.044 °C/year, and 0.44 °C/decade. Increasing global temperature causes increasing saturation pressure (P^sat); evaporation rate is proportional to P^sat.

Figure 3. Relation between the global temperature (primary axis, solid line) and the saturation pressure of water (secondary axis, dashed line); temperature data taken from Ref. [28] and pasted onto EXCEL sheet. Global Average T in °C = 2.326 × 10⁻⁴ ∗ year² − 0.02539 ∗ year + 11.39, Year: (Specified year-1875) P^sat by the author using ln(P^sat) = A − B/(T + D), P^sat in bar, T in °C, A = 12.22, B = 4120.6, D = 237.9: For 2002, temperature rise per year = 0.044 °C/year, and 0.44 °C/decade. Increasing global temperature causes increasing saturation pressure (P^sat); evaporation rate is proportional to P^sat.

2.4. CO₂ Sources and Sinks, O₂ Sources and Sinks, and Models

There is extensive literature on CO₂ emissions and CO₂ distribution amongst atm, land, and ocean biomasses and oceans. The CO₂ sinks and O₂ sources are mainly land biomass plants, trees, and ocean PP and CO₂ sinks via ocean storage. Zhu et al. used Integrated Biosphere Simulator or global vegetation model to estimate the effects of climate change and CO₂ fertilization on CO₂ budget at the local subtropical area of China covered with evergreen forest [29].

The global carbon project summarizes several models for the global C budget: (Table 4 in Ref. [30]): (i) Model for CO₂ via land use [31], (ii) Computer model for CO₂ flux from land to atm, CO₂ sink from global vegetation (land-based biomass [32]), which includes growth function models, (iii) Global ocean bio-geochemistry models, and (iv) Ocean CO₂ flux model. Terhaar et al. proposed a new model—An observation-based estimate of ocean carbon sink [33,34]. Gloege et al. modeled ocean uptake by estimating the CO₂ flux across the air-sea interface using iterative global ocean biogeochemical models (GOBMs), which include ocean circulation. For the first guess, they use results from earlier models. Li et al. proposed an emission-driven earth system model for predicting the variations in the global carbon budget (GCB) [35] and presented variations in the GCB (1970–2018). Yakir et al. summarizes the use of carbonyl sulfide (COS) as a tracer gas to measure changes in CO₂ uptake via PS [36]. To improve the circulation of CO₂ sinks in the ocean, artificial deep-water pumping is recommended, and models are presented in ref. [37].

This model details the capture of CO₂ in terms of C-N-P ratios, particularly for micro- and macro-algae-based biomass in conditions ranging from tropical to subpolar oceans. Li’s model of land and oceanic sinks is based on the oxygen budget [38]. Zhu et al. used Integrated Biosphere Simulator or global vegetation model to estimate the effects of climate change and CO₂ fertilization on CO₂ budget at the local subtropical area of China covered with evergreen forest [29]. Control of climate change requires that CO₂ emissions are minimized and CO₂ sinks are maximized, with the ultimate goal of ‘net-zero’ emissions as per the Paris Agreement [39].

Most of these models require extensive computation tools to estimate CO₂ sinks in GT/year for land and ocean sinks, but they are probably more accurate since they account for temperature, soil conditions, ocean circulation, etc. These models were checked by comparing the results for total CO₂ capture by atm, land and ocean with CO₂ release by FFLU. Hence, there is always a carbon imbalance when CO₂ budget analysis is conducted [40]. None of the literature contains explicit relations for CO₂ sinks amongst the atmosphere, land, and ocean in terms of the RQ of FF and BM. Those relations provide (i) the first guess for the iterative models and (ii) the governing parameters that affect CO₂ distributions. Further, the present model uses CO₂ and O₂ balance, and hence there is no C imbalance in the current model. While the NASA website [41] contains curve fits to a saw tooth pattern using a polynomial function (quadratic and cubic) with the addition of a sinusoid with time ‘t’ elapsed in years since 1982, the current work uses the RQ method to explain the saw tooth pattern of O₂ given CO₂ data. Thus, the goal of the current work is to make use of Keeling’s data on CO₂ and O₂, along with known RQ values of FF and land and ocean biomasses to obtain simple, explicit results for CO₂ distribution in GT/year and distribution as a % of total CO₂ released via FFLU. In order to achieve the above goals, Part I provides an overview of the RQ concept, a tabulation of the RQ values of FF and BM, and a presentation of global RQ. Part II presents the CO₂ and O₂ balances and the results for the distribution of CO₂ sinks amongst atm, biomasses (land and ocean), and ocean water.

The specific objectives for Part I, methodology, results, and discussion are briefly summarized below:

(i) Perform a brief overview of RQ in biology and engineering and its relation to terms used in conventional CO₂ and photosynthesis (PS) literature, (ii) Relate RQ to CO₂ in Giga Tons (GT) per unit energy released, (iii) Use the reported data on CO₂ emissions in GT and fossil energy in Exa J to estimate the RQ of the mix of fossil fuels (RQ_FF) used worldwide (gas, liquid, and coal), (iv) Use Keeling’s data on CO₂ and O₂ in the atm and curve fit the data using linear and quadratic fits, and (v) Define and estimate the global respiratory quotient (RQ_Glob) of “breathing” planet earth and its significance for the CO₂ addition to the atm and CO₂ storage in the oceans.

3. Materials and Methods

The methodology consists of the following: (i) the RQ concept for CO₂ sources (FF combustion, Section 3.1) and values of RQ for FF, which are properties of FF (ii) RQ concept for CO₂ sinks (biomasses, Section 3.2), (iii) comparison of RQ with terms used in PS literature, (iv) RQ values for FF and biomasses and the relations between CO₂ in tons per unit energy release, and RQ, (v) RQ of FF for CO₂ sources under complete combustion (FF in power plants and automobile engines) and incomplete combustion (oil and gas flares), (vi) Relations between CO₂ in tons per unit energy input and RQ of biomass for CO₂ sinks, (vii) RQ_FFLU for the CO₂ released from both FF and land use (LU) and RQ of a mix of various types of FF, and (viii) definition of Global RQ {RQ_Glob} for planet earth, a non-property, using Keeling’s data. Section 4 presents the results for (i) the RQ of the fossil fuel mix used worldwide, (ii) curve fit constants for linear and quadratic fits of Keeling’s data on CO₂ and O₂, and (iii) an estimation of RQ_Glob, physical meaning of RQ_Glob and its implications on CO₂ emissions in the atmosphere, atmospheric pressure, mass loss of earth due to mining of FF, and prediction of saw tooth pattern of O₂ from given CO₂ data and RQ_Glob.

3.1. Respiratory Quotient (RQ) fr CO₂ Sources

3.1.1. Respiratory Quotient (RQ)

The biology literature describes the breathing and overall metabolic processes of BS in terms of the respiratory quotient (RQ), defined as:

$$R{Q}_{nut}=\frac{N_{C{O}_2,nut}=}{N_{O_2,nut}}=\frac{N_{C,nut}}{N_{O_2,nut}}$$

(1)

where RQ_nut is the RQ of nutrient s a property, N_CO₂,nut is the number of moles of CO₂ released when nutrient is oxidized, N_C,nut is the number of C atoms in the nutrient, and N_O2,nut is the number of moles of O₂ used in oxidation.

Caution: a few of the references in both biology and CO₂ literature (e.g., [42,43]) use the inverse definition (i.e., O₂ moles used/CO₂ moles released) for the RQ, and the results in those manuscripts must be interpreted accordingly. For humans or any BS-oxidizing nutrients (glucose C₆H₁₂O₆, carbohydrate (CH), fat (F), and proteins (P)) produced by the digestive system from food intake, the RQ can be estimated from the chemical formula of the three nutrients [44]:

C₆H₁₂O₆ + 6 O₂ → 6 CO₂ + 6 H₂O, HHV_O2 = 469 kJ/mole O₂, RQ = 1

(2)

Dividing by 6, one can write the above equation on a unit carbon formula (UCF) basis:

CH₂O + 1 O₂ → 1 CO₂ + 1 H₂O, HHV_O₂ = 469 kJ/mole O₂, RQ = 1

(3)

with UCF represented by CH₂O, the higher heating value of fuel (HHV) = 2813 kJ/mole of C₆H₁₂O₆ or HHV = 402.3.1 kJ/mole of CH₂O, HHV_O2, the energy released per mole of O₂ used = 2813/6 = 469 kJ per mole of O₂. The =RQ of 1 for glucose indicates that 1 mole of CO₂ is released for every mole of O₂ used in the oxidation of CH within the body of BS. For the oxidation of fat (C₁₆H₃₂O₂), RQ = 0.7. Humans use a mix of CH (RQ = 1) and F (RQ = 0.7); hence, typically, 0.7 ≤ RQ ≤ 1 for a mix of nutrients metabolized. On the other hand, the RQ can also be determined from the analysis of nasal exhaust gas (or automobile exhaust gas); hence, one can determine the % of fat oxidized in the mix of CH and F [45]. The same methodology is adopted for the RQ of thermal power plants when a mix of natural gas, oil, and coal is used globally. For internal combustion engines (automobiles, gas turbines, etc.) fired with any HC liquid fuels or HC mixed with ethanol, the exhaust gas can yield RQ values [7]. Note that RQ, as defined in Equation (1), is a property of fuel whe fuel is used in a thermal system.

3.1.2. Significance of Respiratory Quotient (RQ) and RQ Values for Nutrients and Fuels

Why is RQ important for humans and planet earth? The CO₂ released from the metabolism of nutrients in the cells of various organs within a human is collected by the bloodstream, which transfers CO₂ to alveoli in the lungs for eventual nasal exhaust. Typically, the normal CO₂ in veins is at partial pressure p_CO2 (40 mm Hg or 1.2 milli-moles/L). Thus, for seniors with respiratory acidosis (when all CO₂ cannot be breathed out, the blood becomes acidic due to CO₂ storage exceeding 1.3 milli mole/L) with higher levels of p_CO2, a diet with a low RQ (i.e., fat [46]) is recommended [47,48,49,50,51]. Note that during acidosis, the RQ of nasal exhaust (RQ_vent = CO₂ ventilated/O₂ consumed) is a non-property < RQ_nut, which is normally about 0.8. While RQ_nut is a property of a nutrient or mix of nutrients that can be tabulated (e.g.,

Table 1. RQ of Fossil fuels and Biomasses represented by Chemical formula CH_hO_o. Gasoline CO₂ in kg per gal = 13.2; RQ for gasoline with HHV of gasoline 0.132 GJ/gal. Gasoline CO₂ in lb. per gal = 29; RQ for gasoline with HHV of gasoline 0.125 MMBtu/gal.

Fuel	“h” or H/C	“o” or O/C,	RQ	HHV (kJ/kg) 1
Wyoming coal	0.70	0.18	0.92	18,347
Gasoline (C8H18), YC = 0.85, ρ = 0.75 kg/L	2.25	0.00	0.64	47,968
Diesel (C12H23), ρ = 0.84 kg/L	1.92	0.00	0.68	46,350
#6 low S fuel oils	0.12	0	0.73	42,900
Methane CH4	4.00	0.00	0.50	55,426
Organic acid (e.g., malic acid, C4H6O5) M = 134.1	1.5	1.25	1.33	9993
Sargassum 2 (seaweed), CH1.74N0.025O1.42S0.018.	1.74	1.42	1.57	20,120 (DAF)
Human Body wet (60% H2O, 40% dry) {C1.54H3.24N0.228O0.733, Ca0.037P0.032}.3.33 H2O(l), or {1.54 CH2.1N0.15O0.48Ca0.024P0.021}. 3.33 H2O(l) based on Ultimate analysis in Ref [52]	2.1	0.48	0.76	23,500 (Boie, dry, no P oxid)
Generic PP: Cx(H2O)w (NH3)yHzH3PO4 (a) Without Nitrification (b) With Nitrification	{3 + 2w + 3y + z}/x {3 + 2w + 3y + z}/x	(w + 4)/x (w + 4)/x	1 + (1/4)(z/x) 1 + 2(y/x) + (1/4)(z/x)
Ocean Plankton CxH2w+3y+z+3NyO4P, [53]			x/{x + 2y + z/4)
Planktonic marine algae 3: Redfield–Ketchum–Richards Formula: C106 H263 O110 N16 P [53]; x = 106, y = 16, w = 106, C106 H263 O110 N16 P + 138 02 = 106 CO2 + 16 HN03 + H3P04 + 122 H2O RQ = 0.72 to 1.11 Note 1	2.481	1.038	0.77, 0.72 to 1.11 with an average of 0.82 [54]
Keeling land vegetation via PS and respiration [55]			0.95 (land)
Carbo-hydrate, CH (e.g., glucose) C6H12O6 or CH2O or sugars	1.0	1.0	1.0
Fats C16H32O2 [7]	2.0	0.1	0.7
Lipids: C40H74O5	1.85	0.125	0.73 or 0.68–0.8 [56]
PProteins, C4.57H9.03N1.27O2.25S0.046 [45]	1.98	0.49	0.8–0.9, see also [56]

Note 1: The histogram in Ref. [57] suggests RQ from 0.6 to 0.9 as the maximum number of occurrences, while RQ ranges from 0.3 to 3.1 [57]. The same Ref. seems to suggest RQ < 1, since RQ = 1/{1 + 0.25 ∗ (H/C) − 0.5 ∗ (O/C) + 1.25 ∗ (N/C) + 1.25 ∗ (P/C)} [58]. ¹ Divide the units of kJ/kg by 2.205 to obtain BTU/lbm, and kJ/mole by 2.32 to obtain BTU/lbmole. ² Sargassum, data based on ultimate analyses reported in [59]. ³ Ref. [60] reports chemical composition of various kinds of phytoplankton: diatoms, other autotrophs, heterotrophs, detritus, and most of them have very similar atom ratios. On average, CH_1.66N_0.15O_0.56P_0.014Si_0.046, O₂ st = 1.15 moles, RQ = 0.87.

), RQ_vent is not since it depends upon blood capacity and, hence, how much CO₂ is stored by the blood.

A similar problem exists for the “breathing but aging planet”, with human activities resulting in CO₂ release from FF into the atm and increasing storage of CO₂ by oceans. So, for the same energy needs, stoichiometric O₂ consumption is fixed for most FF (natural gas, oil, coal), and hence low RQ fuels generate less CO₂ per unit energy. The FF with high RQ values generates more CO₂, which results in increased storage of CO₂ in the oceans, called the “lifeblood of the earth” [61], making them more acidic (i.e., less pH) [62], and affecting the growth of PP and, hence, the release of O₂ from the oceans. Thus, with increasing CO₂ in the atm, the earth needs FF with lower RQ values [7] (e.g., CH₄ or natural gas with RQ = 0.5), just like doctors recommend a low-RQ diet for seniors.

The RQ values under complete oxidation and HHV for limited fuels, including fossil fuels (FF) and nutrients, are presented in Table 1. The RQ values indicate that the impact of FF (gas, oil, and coal) on emissions of CO₂ is not equal. Coals typically have values close to 1, while natural gas (mostly CH₄) has low RQ values at 0.5 [7].

3.2. Respiratory Quotient (RQ), Redfield Ratio (RR), Exchange Ratio (ExRExR), Photosynthetic Quotient (PQ) for CO₂ Sinks

Photosynthesis (PS) is a process in which CO₂ and H2O react to produce C-rich biomass (typically C-H-O) and O₂ with energy input from the sun. Compared to combustion of FF or biomass (e.g., CH₂O is also a biomass, Equation (3)), where CO₂ is a source and O₂ is a sink with energy release, biomass growth serves as a CO₂ sink and an O₂ source with energy input from sun. For biomass CH₂O(s) growth via PS, one may use the inverse of the oxidation reaction (Equation (2)), given by:

6CO₂ + 6H₂O→, C₆H₁₂O₆,+ 6O₂, RQ_BM = 1

(4)

On a UCF basis, one may divide Equation (4) by (6), and hence

CO₂ + H₂O→ CH₂O(s) + O₂, 469 kJ input per mole of O₂, RQ_BM = 1

(5)

which is the inverse of Equation (3). CH₂O is one type of biomass. Each mole of CO₂ sinks results in the addition of one mole of C to biomass and one mole of release of O₂. Thus, 1 mole of O₂ requires 469 kJ per mole of O₂ production; this number varies within a narrow range and is almost constant for any fuel or biomass. For biomass growth under PS, the global warming literature uses various terms: RR, PQ, ExR, and regeneration quotient (RgQ) [14], which are defined as

$$P{Q}_{BM}=Ex{R}_{BM}=R{R}_{BM}={\left(RgQ\right)}_{BM}=\frac{N_{O_2,BM}}{N_{C{O}_2,BM}}=\frac{N_{O_2,BM}}{N_{C,BM}}=\frac{1}{R{Q}_{BM}}$$

(6)

where RR_BM, the RR of biomass, and ExR is Keeling’s exchange ratio. The RQ_BM is defined as

$$R{Q}_{BM}=\frac{N_{C{O}_2,BM}}{N_{O_2,BM}}=\frac{N_{C,BM}}{N_{O_2,BM}}$$

(7)

where N_CO₂,BM is the net CO₂ moles consumed by any biomass {=CO₂ consumed -CO₂ used in respiration} in the conversion to organic matter, and similarly, N_O2,BM is the net O₂, moles produced = {O₂ produced via PS—O₂ used in respiration}. Note that when RQ_BM = 1, RR _BM = PQ_BM = (ExR)_BM = (RgQ)_BM = 1 [42].

Mann et al. presented the average composition of marine organic matter (MOM; P:N:C:O₂ = 1:16:106:138 [63]) and RQ_MOM [43]. For the given MOM composition, RQ_MOM = 0.768 or RR = 1.3 (a value close to fat in BS). For ocean biomass (Table 1), RR = 150 mol of O₂ produced/106 mol of CO₂ fixed = 1.41 [59], RQ_BM = 0.71.

For estimating the RQ of biomasses and coals, the ultimate analyses are first converted into a chemical formula on a UCF basis (CH_hN_nO₀S_s), where h = H/C, N/C, o = O/C ratio, and s = S/C, etc., and then the RQ is estimated using the empirical chemical formula: {1/(1 + h/5-o/₂ + s)}. For most land-based biomass, RQ_LMB ≈ 1 {(LBM), Appendix A.1}. The PQ and RQ_OWBM values for ocean water biomasses (OWBM) are known to vary from 1.0 to 1.8 {RQ_OWBM from 0.55 to 1} in the Southern Ocean and 1.0 to 1.4 {RQ_OWBM from 0.72 to 1} in non-polar oceanic areas. The average value of RQ_OWBM = 0.8, or PQ = 1.25 [64]. Ref. [57] reports that the various PP groups in oceans have an {RQ_OWBM} _median ≈ 0.88 and an RQ average of 1.11. Marino et al. demonstrated that oxygen concentrations in oceans and hence the carbon sink in a biome depend strongly on the RR (RQ. Based on a review in Ref. [57], the RQ of marine PP respiration assumes a constant value of RQ_OWBM = 0.8. These values will be used in Part II to obtain the carbon budget and distribution amongst the atmosphere, land and ocean biomasses, and ocean storage.

3.3. Relation between Respiratory Quotient (RQ) and CO₂ Released in Tons for CO₂ Sources

For carbon sources, the CO₂ in GT per Exa J of energy output (for CO₂ sources) or input (for CO₂ sinks) is obtained in terms of RQ values.

3.3.1. CO₂ Sources

Consider the combustion of FF, which is a CO₂ source, and the definition of RQ. With constant HHV_O2, each Exa J of energy released by FF requires {1/HHV_O₂} Peta moles of O₂. Thus, CO₂ in Peta moles released per Exa J of energy = RQ ∗ {1/HHVO_₂}. Using the molecular weight of CO₂,

$$C{O}_2,\left(\frac{GT}{ExaJ}\right)=\frac{M_{C{O}_2}}{HH{V}_{O_2}}RQ=0.1 \ast RQ ,\frac{M_{C{O}_2}}{HH{V}_{O_2}}\approx 0.1$$

(8)

where M_CO₂ = 44.01 g/mole = 44.01 GT/Peta mole and HHV_O2 = 448 Exa J/Peta mole of O₂. This value of 448 Exa J/Peta mole of O₂ yields was cross-checked by estimating the energy released as 112 Exa J per electron mole transfer, where the number of electron mole transfer = 4 ∗ stoichiometric moles [65]. This number checks with the value of 111.1 Exa J per Peta electron mole transfer used in biology literature [66]. If the approximation of constant HHV_O2 is not used and if measured heating values (MJ/kg fuel) are used for well-known C-H-O fuels (e.g., hydrocarbons, alcohols, aromatics, coal, and biomasses with known empirical chemical formula), the CO₂ in GT/Exa J and RQ can be directly estimated. The plot of CO₂ in GT/Exa J vs. RQ reveals almost the same slope as 0.1 (Figure 4). See Ref. [7] and the caption of Figure 4 for more details. Selecting English units,

$$C{O}_2,\left(\frac{Tons}{MMBtu}\right)=0.116 \ast RQ$$

(9)

Since C in tons = CO₂ in tons ∗ 12.01/44.01 = 0.27 ∗ CO₂ in tons, then Equations (8) and (9) become:

$$C,\left(\frac{GT}{ExaJ}\right)=0.027 \ast RQ$$

(10)

$$C,\left(\frac{Tons}{MMBtu}\right)=0.032 \ast RQ$$

(11)

It is seen that for coals dominated by C atoms (Table 1), RQ ≈ 1, and hence CO₂ in GT per Exa J = 0.1 (or 0.116 short tons per MMBtu), while for CH₄ (or natural gas), it is only 0.05 Giga Tons per Exa J.

The higher the RQ values of FF fuels, the more CO₂ or C in Giga Tons per Exa J of energy is released. On the other hand, if CO₂ in Giga Tons per Exa J is known for a mix of fossil fuels (natural gas, fuel oil, coal, etc.), then the RQ of the mix can be determined (See Section 3.4.1 for more details).

3.3.2. RQ for Incomplete Combustion

The RQ values listed in Table 1 and the CO₂ tons per GJ relations in Equations (8)–(11) are best suited for fuels undergoing complete oxidation for applications focused on energy conversion to work. However, RQ’s and Equations (8)–(11) may not be suitable for fuels undergoing moderate to severe incomplete combustion. Consider the release of pure CH₄ from cattle feedlots and the incomplete oxidation of flare gas near oil fields and refineries with CO₂ and CH₄ released into the atm. CH₄ is also a global warming gas, but with a CO_2eq of around 10.4 (i.e., 10.4 times more potent than CO₂ in causing global warming on a mole basis and a 28.5 mass basis called GWP). For these cases, the RQ is estimated by using the following relation:

$$R{Q}_{Glob,CO2+CH4}=\frac{{\left\{[C{O}_2]+[C{H}_4] \ast GWP\right\}}_{atm}}{{\left\{[O_2]\right\}}_{atm}},GWP for C{H}_4=10.4$$

(12)

where [CO₂], [O₂], and [CH₄] are concentrations in ppm. If pure CH₄ production in moles/year (=1000 ∗ volume in SCM per year/24.5 or 1.159 ∗ SCF or CH₄ mass in g per year/16.05) is known, then

$$\begin{array}{l}C{O}_2 eq \left(\frac{GT}{year}\right)=\frac{C{O}_{2,eq} \ast 1000 \ast 44.01}{\left\{24.5 \ast {10}^{15}\right\} }\ast {\dot{V}}_{C{H}_4}\\ =C_{SI} \ast C{O}_{2,eq}\ast {\dot{V}}_{CH4},C_{SI}=1.7963 \ast {10}^{-12}\end{array}$$

(13)

where ${\dot{V}}_{C{H}_4}$ is volume flow rate in SCM per year

$$C{O}_{2}eq \left(\frac{GT}{year}\right)=C_{Eng }\ast C{O}_{2}eq\ast {\dot{V}}_{C{H}_4} , C_{Eng}=4.8991 \ast {10}^{-12}$$

(14)

where ${\dot{V}}_{C{H}_4}$ is volume flow rate in SCF per year. Natural gas flaring is the combustion of natural gas (≈CH₄) typically associated with oil extraction. Even though the CH₄ flaring has negative environmental effects, the transport of gas is not cost-effective due to a lack of gas pipelines. The average combustion efficiency is 91%, including lit and unlit (3–5%) periods, malfunction, and incomplete combustion [67]. For the gas flares,

$$C{O}_2\left(\frac{GT}{year}\right)=C_{SI} \ast \eta \ast {\dot{V}}_{C{H}_4} , C_{SI}=\frac{1000 \ast 44.01}{24.5 \ast {10}^{15}}=1.796\ast {10}^{-12}$$

(15)

$$C{O}_2\left(\frac{GT}{year}\right)=C_{Eng} \ast \eta \ast {\dot{V}}_{C{H}_4}, C_{Eng}= 5.0966 \ast {10}^{-14}$$

(16)

where η is the burned or oxidized fraction of CH₄.

$$C{O}_2,eq\left(\frac{GT}{year}\right)=C_{SI} \ast (1-\eta ) \ast C{O}_2,eq \ast {\dot{V}}_{C{H}_4} , C_{SI}=1.7963\ast {10}^{-12}$$

(17)

$$C{O}_2,eq\left(\frac{GT}{year}\right)=C_{Eng} \ast (1-\eta ) \ast C{O}_2,eq \ast {\dot{V}}_{C{H}_4} , C_{Eng}= 5.0966 \ast {10}^{-14}$$

(18)

$$C{O}_2, \left(\frac{GT}{year}\right)=C_{SI}\ast {\dot{V}}_{C{H}_4}\left\{\eta +(1-\eta )\ast C{O}_{2,eq}\right\}$$

(19)

According to the World Bank’s global gas flaring tracker for 2021, about 140 Giga SCM of natural gas was flared, which releases almost 5 Exa J of energy per year when burned completely. Thus, if 100% is burned, then CO₂ emission is 0.25 GT of CO₂ (which checks with the relation given by Equation (8) with RQ = 0.5 and energy release = 5 Exa J/year). If 0% is burned, then with a CO_{2 eq} of 10.4, the CO₂ eq emission for CH₄ is 2.62 GT/year. If 90% is burned and 10% is unburned, then a total of 0.49 GT of CO₂/year (=0.25 ∗ 0.9+ 0.1 ∗ 2.62, Equation (19)), which checks with World Bank data, but 0.47 GT of CO₂ equivalent is released.

3.3.3. RQ for CO₂ Sinks and GT of CO₂ Sink per Unit Energy Input

Land and ocean biomasses serve as CO₂ sinks and O₂ sources. The biomass term is generalized to include terrestrial (land), ocean water, or marine-based biomass and microorganisms. For these CO₂ sinks, Equations (8)–(11) can be equally applied, and in this case, they represent the CO₂ sink per unit energy input reaching the chlorophyll via PS. Replacing RQ by RQ of growing biomass, RQ_BM,

$$\begin{array}{l}C{O}_2\left(\frac{GT}{Exa J}\right)=0.1 \ast R{Q}_{BM}\\ C{O}_2\left(\frac{GT}{MMBtu}\right)=0.116\ast R{Q}_{BM}\end{array}$$

(20)

$$\begin{array}{l}C\left(\frac{GT}{Exa J}\right)=0.027 \ast R{Q}_{BM}\\ C\left(\frac{shortTon}{MMBtu}\right)= 0.032\ast R{Q}_{BM}\end{array}$$

(21)

It is assumed that the RQ_BM during growth is the same as the RQ_BM during the oxidation process; see also Ref. [17], which presumes that the RQ_BM = 1. If $\dot{C}$(s) sink data in GT/year are available for biomass, then CO₂ in GT/year = 3.667 ∗ C(s) in GT/year and CO₂ moles per year = (1/12.01) ∗ $\dot{C}$(s). The O₂ moles produced per year = (1/12.01) ∗ $\dot{C}$(s)/RQ_BM. If biomass happens to be C(s) or CH₂O(s), RQ_BM = 1. The ocean RQ_OWBM has a small spatial variability consistent with previous data [58], and the mean RQ_OWBM is around 0.7. It is seen in Part II that the RQ of combined land and ocean water-based biomasses is dominated by LBM since net O₂ added to atm. is dominated by land-based biomass.

Consider the ocean biomasses, which serves as a CO₂ sink. For PP,

• Generic PP: C_x(H₂O)_w (NH₃)_yH_zH₃PO₄ or C_xH_3+2w+3y+z N_y O_w+4 P

Oxidation Reaction: C_xH_3+2w+3y+z N_y O_w+4 P + {x + (1/4) z} O₂→xCO₂ +y NH₃+ H₃PO₄ + {w + (½) z}H₂O, without nitrification

Nitrification reaction, NH₃ + 2O₂→ HNO₃ + H₂O

Overall reaction

C_xH_3+2w+3y+z N_y O_w+4 P+ {x +2y+ (1/4) z} O₂→xCO₂ + y HNO₃ + H₃PO₄ +{w +y+ (½) z)}H₂O

(i)

The ocean plants growth via photosynthesis: (See Table 1) is given by,

106 CO₂ + 16 NO₃⁻ + H₂PO₄⁻ + 17 H⁺ → C₁₀₆H₂₆₃O₁₁₀N₁₆ P + 138 O₂,

RQ_OWBM = {106/138} = 0.77,

(ii)

Planktonic marine algae: The Redfield–Ketchum–Richards Formula is given as (CH₂O)₁₀₆(NH₃)₁₆ (H₃PO₄), or C₁₀₆ H₂₆₃ O₁₁₀ N₁₆ P [53] and M = 3553.3 g/mol. Thus, x = 106, y = 16, and w = 106. The RQ is estimated at 0.77. For the RQ based on the traditional Redfield–Ketchum–Richards equation and algae production, see Refs. [43,68].

(iii)

Oceanic cyanobacteria and algae: photosynthesis and respiration, RQ = 0.77 [37].

2.

Seaweed or Sargassum: A bright seaweed also absorbs CO₂ and produces O_2, but it reflects more of the sun’s radiation compared to PP. Using the ultimate analyses reported in [7,69], the chemical formula on the UCF basis is given as CH_1.74N_0.025O_1.42S_0.018 (See

Table A1. Respiration quotient (RQ) and C-Sink (g/g biomass) for Biomasses. Y_C, Carbon sink in g per g dry ash-free biomass, Boie Est (HHV, kJ/kg) = {35160 Y_C + 116225 ∗ Y_H − 11090 ∗ Y_O + 6280 Y_N + 10465 Y_S, where Y_C, Y_H, Y_N, Y_O, and Y_S are mass fractions of carbon, hydrogen, nitrogen, oxygen, and Sulphur in a C-H-N-O-S fuel. Table contains measured values of HHV. Min Y_C (g of C/g biomass): 0.346, Max Y_C: 0.544 Min RQ (mols CO₂ used/mols O₂ prod): 0.938, Max RQ: 1.046. Source data: [82,96].

Name	H/C	N/C	O/C	S/C	O/H	HHV, kJ/g	YC	YH	YN	YO	YS	RQBM
Field crops
Alfalfa seed straw	1.373	0.0183	0.654	1.602 × 10−4	0.476	18.45	0.468	0.054	0.01	0.407	0.0002	0.984
Bean straw	1.547	0.0166	0.785	8.718 × 10−5	0.507	17.46	0.430	0.0559	0.0083	0.449	0.0001	1.006
Corn cobs	1.499	0.0086	0.733	8.042 × 10−5	0.489	18.77	0.466	0.0587	0.0047	0.455	0.0001	0.992
Corn stover	1.515	0.0120	0.745	8.582 × 10−5	0.492	17.65	0.437	0.0556	0.0061	0.433	0.0001	0.994
Cotton stalks	1.527	0.0261	0.744	1.898 × 10−4	0.487	15.83	0.395	0.0507	0.012	0.391	0.0002	0.990
Rice straw (fall)	1.318	0.0144	0.657	7.173 × 10−4	0.499	16.28	0.418	0.0463	0.007	0.366	0.0008	0.998
Rice straw (weathered)	1.351	0.0230	0.768	1.732 × 10−3	0.568	14.56	0.346	0.0393	0.0093	0.354	0.0016	1.046
Wheat straw	1.376	0.0121	0.685	9.539 × 10−4	0.497	17.51	0.432	0.05	0.0061	0.394	0.0011	0.997
Orchard prunings
Almond prunings	1.226	0.0110	0.598	7.302 × 10−5	0.488	20.01	0.513	0.0529	0.0066	0.409	0.0001	0.993
Black Walnut	1.390	0.0038	0.652	7.522 × 10−5	0.469	19.83	0.498	0.0582	0.0022	0.433	0.0001	0.979
English Walnut	1.346	0.0064	0.651	7.534 × 10−5	0.484	19.63	0.497	0.0563	0.0037	0.431	0.0001	0.989
Vineyard prunings
Cabernet Sauvignon	1.493	0.0153	0.707	3.216 × 10−4	0.474	19.03	0.466	0.0585	0.0083	0.439	0.0004	0.980
Chenin Blanc	1.459	0.0154	0.655	5.461 × 10−4	0.449	19.13	0.480	0.0589	0.0086	0.419	0.0007	0.964
Pinot Noir	1.468	0.0156	0.685	7.947 × 10−5	0.467	19.05	0.471	0.0582	0.0086	0.430	0.0001	0.976
Thompson seedless	1.449	0.0139	0.687	7.912 × 10−5	0.474	19.35	0.474	0.0577	0.0077	0.433	0.0001	0.981
Tokay	1.449	0.0135	0.670	2.353 × 10−4	0.462	19.31	0.478	0.0582	0.0075	0.426	0.0003	0.973
Energy crops
Camaldulensis	1.425	0.0052	0.674	7.645 × 10−5	0.473	19.42	0.490	0.0587	0.003	0.440	0.0001	0.981
Globulus	1.461	0.0069	0.688	7.775 × 10−5	0.471	19.23	0.482	0.0592	0.0039	0.442	0.0001	0.979
Grandis	1.449	0.0027	0.701	7.751 × 10−5	0.484	19.35	0.483	0.0589	0.0015	0.451	0.0001	0.988
Casuarina	1.426	0.0104	0.670	1.541 × 10−4	0.469	19.44	0.486	0.0583	0.0059	0.434	0.0002	0.979
Cattails	1.452	0.0148	0.742	3.486 × 10−4	0.511	17.81	0.430	0.0525	0.0074	0.425	0.0004	1.007
Popular	1.436	0.0083	0.677	7.732 × 10−5	0.471	19.38	0.485	0.0585	0.0047	0.437	0.0001	0.980
Sudan grass	1.427	0.0233	0.660	6.722 × 10−4	0.462	17.39	0.446	0.0535	0.0121	0.392	0.0008	0.973
Forest residue
Black Locust	1.338	0.0096	0.620	7.384 × 10−5	0.464	19.71	0.507	0.0571	0.0057	0.419	0.0001	0.976
Chaparral	1.288	0.0099	0.643	2.396 × 10−4	0.499	18.61	0.469	0.0508	0.0054	0.402	0.0003	0.999
Madrone	1.476	0.0011	0.703	1.561 × 10−4	0.476	19.41	0.480	0.0596	0.0006	0.450	0.0002	0.983
Manzanita	1.466	0.0030	0.696	1.555 × 10−4	0.475	19.3	0.482	0.0594	0.0017	0.447	0.0002	0.982
Ponderosa Pine	1.446	0.0010	0.676	2.282 × 10−4	0.467	20.02	0.493	0.0599	0.0006	0.444	0.0003	0.977
Ten Oak	1.475	0.0022	0.693	7.835 × 10−5	0.470	18.93	0.478	0.0593	0.0012	0.441	0.0001	0.978
Redwood	1.404	0.0008	0.636	2.219 × 10−4	0.453	20.72	0.506	0.0598	0.0005	0.429	0.0003	0.968
White Fur	1.451	0.0009	0.686	7.645 × 10−5	0.472	19.95	0.490	0.0598	0.0005	0.448	0.0001	0.980
Food and fiber processing wastes
Almond hulls	1.392	0.0180	0.666	8.181 × 10−5	0.478	18.22	0.458	0.0536	0.0096	0.406	0.0001	0.985
Almond shells	1.578	0.0221	0.705	1.666 × 10−4	0.447	19.38	0.450	0.0597	0.0116	0.423	0.0002	0.960
Babassu husks	1.269	0.0044	0.631	2.978 × 10−4	0.497	19.92	0.503	0.0537	0.0026	0.423	0.0004	0.998
Sugarcane bagasse	1.420	0.0073	0.663	8.362 × 10−5	0.467	17.33	0.448	0.0535	0.0038	0.396	0.0001	0.977
Coconut fiber dust	1.194	0.0077	0.592	1.192 × 10−3	0.495	20.05	0.503	0.0505	0.0045	0.396	0.0016	0.996
Cocoa hulls	1.289	0.0530	0.515	9.321 × 10−4	0.399	19.04	0.482	0.0523	0.0298	0.331	0.0012	0.938
Cotton gin trash	1.580	0.0453	0.689	0	0.436	16.42	0.396	0.0526	0.0209	0.363	0	0.952
Macadamia shells	1.091	0.0057	0.548	6.885 × 10−5	0.502	21.01	0.544	0.0499	0.0036	0.397	0.0001	1.001
Olive pits	1.518	0.0063	0.669	1.535 × 10−4	0.441	21.39	0.488	0.0623	0.0036	0.435	0.0002	0.957
Peach pits	1.324	0.0052	0.554	3.534 × 10−4	0.419	20.82	0.530	0.059	0.0032	0.391	0.0005	0.949
Peanut hulls	1.419	0.0305	0.649	9.822 × 10−4	0.457	18.64	0.458	0.0546	0.0163	0.396	0.0012	0.970
Pistachio shells	1.440	0.0098	0.668	7.678 × 10−5	0.464	19.26	0.488	0.0591	0.0056	0.434	0.0001	0.974
Rice hulls	1.248	0.0084	0.657	1.829 × 10−4	0.526	16.14	0.410	0.043	0.004	0.359	0.0002	1.017
Walnut shells	1.359	0.0036	0.651	7.495 × 10−5	0.479	20.18	0.500	0.0571	0.0021	0.434	0.0001	0.986
Wheat dust	1.466	0.0630	0.638	1.720 × 10−3	0.436	16.2	0.414	0.051	0.0304	0.352	0.0019	0.953
Trees
Maple wood (dry)	1.414	0.0042	0.619	0.000	0.438	16.2	0.506	0.0602	0.0025	0.417	0	0.958
Mesquite (as rec)	1.358	0.0122	0.578	2.578 × 10−4	0.426	16.7	0.436	0.0498	0.0062	0.336	0.0003	0.952
Junifer (as rec)	1.370	0.0049	0.563	7.599 × 10−5	0.411	19	0.493	0.0568	0.0028	0.370	0.0001	0.943
Sea Weeds [69]
Sargassum tenerrimum	1.741	0.0248	1.420	1.809 × 10−2	0.816	-	0.321	0.047	0.0093	0.607	0.0155	1.345
Sargassum sp. 1	1.593	0.0532	0.965	0.000	0.606	-	0.403	0.054	0.025	0.518	0	1.092
Sargassum sp. 2	1.777	0.0461	0.674	0.000	0.379	14.7	0.255	0.0381	0.0137	-	0	0.903
Sargassum horneri	1.512	0.0161	0.647	1.355 × 10−2	0.428	15.44	0.489	0.0622	0.0092	0.422	0.0177	0.936
Sargassum fluitans Dirty	1.629	0.0460	0.725	1.442 × 10−2	0.445	13.87	0.270	0.037	0.0145	0.261	0.0104	0.944
Sargassum fluitans Wash	1.523	0.0362	0.706	7.579 × 10−3	0.464	15.27	0.391	0.05	0.0165	0.367	0.0079	0.966
OTHERS	0.000	0.0000	0.000	0.000	0.000	0	0.000	0	0	0.000	0	0.000
Pineapple	1.898	0.0171	0.799	0.000	0.421	15.27	0.401	0.064	0.008	0.427	0	0.930
Grass	1.585	0.0190	0.717	8.325 × 10−4	0.452	15.27	0.450	0.06	0.01	0.430	0.001	0.963

, Appendix A.1). Thus, for seaweed, RQ_BM = 1.57, which is unusually high compared to land-based biomasses. It serves as a good CO₂ sink but decomposes and releases NH₃ and H₂S (odors like rotten eggs) along with CO₂. For different seaweeds, Ref. [69] presents ultimate analyses; the author determined the chemical formula and estimated that the RQ of seaweeds could vary from 0.95 to 1.34 (Appendix A.1). The measured RQ values are from 0.99 to 2.38 (or PQ from 0.42 to 1.01), while the theoretical values are from 0.77 to 1 (PQ from 1.0 to 1.3) [70].

3.4. Respiratory Quotient (RQ) of Fossil Fuels and Biomass

3.4.1. RQ of Fossil Fuels (FF)

The RQ can be readily determined for fuels with known chemical formulas. For many solid fuels, ultimate analyses are available (e.g., coal, biomass) and they can be used to derive UCF [7]. When coal, oil, and gas are used as fossil fuels globally, and if % energy delivered is known, then the RQ of this mixture of fuels (RQ_FF) can be determined. Two methods are suggested for determin0ng RQ_FF of a mix of FF.

Method I: Use reported data on global CO₂ in GT/year and reported annual fossil energy release in Exa J per year [40], then compute GT per Exa J, and use Equation (8) for an estimation of the RQ_FF.

Method II: Use the RQ values of gas, liquid, and solid fuels (FF) listed in Table 1. RQ_gas = 0.5 (CH₄ or natural gas), RQ_oil = 0.73 (# 6 Fuel oil low S), RQ_coal ≈ 1, estimate their energy fractions (EF) from the global data presented and use the formula RQ_FF = RQ_gas ∗ EF _gas + RQ_liq EF_oil + RQ_coal ∗ EF_coal [7]. Note that the global RQ_FF will keep changing depending on the energy fractions of coal, gas, and oil.

3.4.2. Respiratory Quotient for the Combined Fossil and Land Use (LU) CO₂ (RQ_FFLU)

In addition to CO₂ from FF [71,72,73], land use (LU) (e.g., cutting down forests and burning, soil degradation, fire, clearing lands for agriculture, etc.) also releases CO₂. In addition to ref. [21] see also the carbon dioxide information analysis center, for anthropogenic emissions. For the years 2007–2016, LU energy accounted for 13% of anthropogenic CO₂ emissions. The land use in 2016 contributed CO₂ of 5.6 GT, while the contribution from fossil combustion amounts to 35.4 GT of CO₂ [73]. Also see 2020 Special Reports: Land Use, Land-Use Change, and Forestry [74]. The major fraction of CO₂ emitted is from FF > 0.8, and the land use energy fraction for CO₂ ≤ 0.2. The combination of FF and LU is represented by the acronym FFLU, which includes CO₂ contributed by both FF and land use (LU). It is noted that FF is the dominant source of CO₂. Thus, the RQ for combined FF and LU is defined as

$$R{Q}_{FFLU}=\frac{N_{C{O}_2,FFLU}}{N_{O_2,FFLU}}$$

(22)

where N_CO₂,FFLU, CO₂ released by FFLU, and O₂ consumed by FFLU. Thus, the RQ of fossil fuel (RQ_FF) and the RQ from land use (RQ_LU) are combined to yield an effective RQ_FFLU [7]:

RQ_FFLU = RQ_FF ∗ EF_FF + RQ_LU ∗ EF_LU ∗ RQ

(23)

where EF_k is the energy fraction contributed by fuel k, which same as is ratio of oxygen consumed by fuel k to total oxygen consumed for fuel mix. Ref [7] shows that EF_k contributed by fuel k is the same as the ratio of O₂ consumed by fuel k to the total O₂ consumed by all fuel types due to the constancy of HHV_O₂. RQ_FF = 0.73–0.78 and the land use EF_LU ≈ 0.2. For LU, RQ_LU is set at 1 when estimating RQ_FFLU.

3.5. Global Respiratory Quotient (RQ_Glob) for Planet Earth

The breathing systems within the green planet earth include power plants (NBS, CO₂ “exhaled” and air/O₂ “inhaled”), humans (BS, CO₂ “exhaled” and air/O₂ “inhaled”), and biomass on land and in the ocean (BS, CO₂ “inhaled” and O₂ “exhaled”). As summarized in previous sections, the net CO₂ mol added to the atmosphere is the difference between CO₂ released by FFLU and the sum of CO₂ sinks via biomass and ocean storage, and the O₂ mols depleted from the atm is the difference between O₂ mols consumed by FFLU and O₂ mols produced by biomass. Following the RQ definition used for FF, the global respiratory quotient of planet earth {RQ_Glob} is defined as

$$R{Q}_{Glob}=\left(\frac{{\left\{\frac{d\left[C{O}_2\right]}{dt}\right\}}_{atm}}{{\left|\frac{d\left[O_2\right]}{dt}\right|}_{atm}}\right)$$

(24)

where [d{CO₂}/dt]_atm (ppm/year, positive) represents the net CO₂ added to the atm per year {i.e., the slope of CO₂ vs. year} and the net O₂ depleted from the atm per year [d{O₂}/dt]_atm, slope of O₂ vs. year in ppm/year, usually negative}. Both slopes can be readily evaluated from linear and quadratic curve fits for Keeling’s data on CO₂ and O₂ concentration in the atm.

3.6. Data

For presenting the quantitative results on all RQ’s and RQ_Glob, the following data are required:

(i).

Annual fossil and land use energy or annual C or CO₂ emission data for FF and LU. Reported data on CO₂ are in GT/year and fossil energy consumption in Exa J/year. Data are selected from the carbon dioxide and information analysis center (CDIAC) [71,72,73,74,75]. This method is termed Method I.

(ii)

With global energy release data for each fuel type (gas, oil, and coal) and determining the fraction of energy contributed by these three types of FF [76], and the RQ values of gas, oil, and coal (Table 1) and Equation (23), the RQ_FF can be estimated. This method is termed Method II.

(iii)

Respiration Quotient for FF (RQ_FF) and LU (RQ_LU), RQ_LBM, and RQ_OWBM.

(iv)

Curve fit constants for linear and quadratic fits of Keeling’s data on CO₂ and O₂ vs. years.

See column 3 of

Table 2. List of formulas for RQ and other estimations for linear and quadratic curve fits for Keeling’s curves.

Parameter of Interest	Linear Fit	Quadratic Fit
CO2 in atm., ppm	a1 ∗ years + a0, linear fit, years = current year-1991 a1 = 2.082 ppm /year, a0 = 350.5 ppm, R2 = 0.9709 when all data (multiple data within a year) was used {Fit: 381.7 ppm in 2006, Data in 2006 (average): 381.5 ppm} (average)	c2 ∗ years2 + c1 ∗ years + c0, years = current year-1991 c2 = 0.01889, c1 = 1.473, c0 = 354.1, R2 = 0.9804 when all data (multiple data within a year) was used Fit: 380.5 ppm in 2006, data in 2006: 381.5}
O2 in atm., ppm	b1 ∗ years + b0 b1 = −4.438 ppm/year, b0 = 209488, R2 = 0.9839 {Fit O2: 209,421, Data O2 = 209,423 ppm}	d2 ∗ years 2 + d1 ∗ years + d0, d2 = −0.04347265 ppm/year2, d1 = −3.0332 ppm/year., d0 = 209,480 ppm, R2 = 0.9896, {Fit O2: 209,425, with no of years since 1991 = 15, data O2 = 209,423 ppm}
d[CO2]/dt = CO2 change per year, ppm in atm./year	a1, positive, (Constant and independent of year) {2.082 ppm/year}	2 ∗ c2 ∗ year + c1 = {0.0378 ∗ year + 1.473} {Fit 2.041 ppm/year with no. of years since 1991 = 15}
d[CO2]/dt, CO2 added to atm. GT in/year or required amount of CO2 to be sequestered if d[CO2]/dt needs to be zero.	a1 ∗ 7.77, (Constant and independent {16.2 GT of CO2 added per year or 4.41 GT of C/year}	{2 ∗ c2 ∗ year + c1} ∗ 7.77 = {0.0378 ∗ year + 1.473} ∗ 7.77 {15.9 GT/year or 4.33 GT of C/year}
d[O2]/dt = O2 change per year, ppm in atm./year	b1, negative, (Constant and independent of year {−4.438 ppm/year}	2 ∗ d2 ∗ years + d1 = −0.0870 ∗ year − 3.0332 = −4.0438 {−4.305 ppm/year}
d[O2]/dt, Net O2 removed from atm. In GT/year or required amount of O2 to be added if d[|O2|]/dt in atm. Needs to be 0.	|b1| ∗ 5.65, (Constant and independent {25.07 GT of O2 depleted year}	{2 ∗ d2 ∗ year + d1} ∗ 5.65 = |{0.0870 ∗ year − 3.0332}| ∗ 5.65 {24.3 GT/year}
$R{Q}_{Glob}={\left\{\frac{d\left[{CO}_2\right]}{\left|d\left[O_2\right]/dt\right|}\right\}}_{atm}$,	$\frac{a_1}{b_1}$, (Constant and independent of year) {RQG, lob = 0.469}	$\left(\frac{2\ast c_2\ast year+c_1}{\left|2\ast d_2\ast year+{ \mathrm{d}}_1\right|}\right)$, decreases slightly with years, {RQGlob = 0.470}
Earth’s annual mass loss rate due to Net C(s) mined, GT per year	RQGlob ∗ |b1| ∗ 0.177, 1 or a1 ∗ 2.12, 4.43 GT/year}	RQGlob ∗ 0.177 ∗ |2 ∗ d2 ∗ year + d1| Or |2 ∗ d2 ∗ year + d1| ∗ 2.12, {4.334 GT/year}

for a listing of all formulas and a listing of data for quantitative evaluations.

$${\dot{N}}_{O_2,FF}=\left(\frac{{\dot{E}}_{FFLU}}{HH{V}_{O2}}\right)=2.232\ast {10}^{-3}\ast {\dot{E}}_{FFLU}$$

where, ${\dot{N}}_{O_2,FF}$, oxygen consumed in Peta moles per year; ${\dot{E}}_{FFLU}$ annual energy consumption by FFLU (Exa J/year). Other necessary data are presented below Table 2 caption.

For generating numbers for various parameters of interest listed in Table 2, the following data were used:

(a)

${\dot{E}}_{FFLU}$ = 460.21 in 2006 [73]. HHV_O2 = 448 kJ/mole of O₂ = 0.448 ∗ 10⁻³ Giga J/mole or 448 Exa J/Peta mole.

(b)

For the year 2006, the oxygen consumption rate = 1.027 Peta mols/year with energy per year of 460.21 Exa J/year.

(c)

RQ_FF = 0.75, RQ_FFLU = 0.775 with energy fraction from LU, EFLU = 0.11; RQ_LBM, = 1, RQ_OWBM = 0.87, See also Ref. [77], which quotes PQ = 1.1 or RQ_LBM = 0.91 for terrestrial plants.

4. Results and Discussion

4.1. RQ of Fossil Fuels (FF)

As outlined in Section 3.4.1, the RQ was determined by two methods:

Method I. Figure 5 shows the results on fossil energy consumed (secondary Y-axis), Peta J/10, CO₂ in million tons/year (secondary Y-axis), and RQ_FF (primary Y-axis) vs. years (Equation (8)). It is seen that CO₂ produced by world-wide consumption of gas (RQ = 0.5), oil, and coal (RQ = 1) and energy released from all three sources of FF increased by almost 70%, while the RQ_FF estimated increases slightly with the years, indicating more use of coal. The average is about 0.75. The RQ_FF satisfies the inequality 0.5 < RQ_FF < 1.

Method II. Figure 6 shows a comparison of RQ_FF estimated using both Methods I and II. As before, RQ_FF estimated is slightly higher (1991–2009) but almost the same as the RQ from Method I for years beyond 2015.

4.2. RQ of FFLU {Combined FF and LU}

C emission data from FF and LU vs. year were collected along with energy released from FF, but land use energy data were not reported. Then, using C emission data for LU and assuming RQ_LU ≈ 1, the land use energy was estimated by using Equation (8). With known total energy (FF + LU) in Exa J and known CO₂ in GT for both FF and LU, RQ_FFLU vs. year was estimated. Figure 7 shows the results. The RQ_FFLU average is about 0.78, which is slightly more than the RQ_FF due to the higher RQ of the land-use fuel source.

4.3. RQ of Land Biomass (RQ_LBM) and Ocean Water Based Biomass (RQ_OWBM)

Appendix A.1 lists the ultimate analyses of several biomasses. Using the ultimate analysis, an empirical chemical formula was derived. For many biomass fuels listed in Ref. [82], Y_C (mass C sink in kg per kg of biomass) varies from 0.346 (rice straw) to 0.5441 (macadamia shells). See Appendix A.1 for the tabulation of RQ_BM. The RQ_LBM for land-based dry biomass ranges from 0.94 to 1.05 with an average of 1, which corresponds to a plant with UCF as CH₂O or a plant with pure C. It is noted that Huang et al. assumed RQ_LBM = 1, as though LBM has the chemical formula CH₂O [12]. Keeling quotes RQ_LBM = 0.95, which corresponds to the UCF, CH₂O_0.4 [55].

CO₂(g) + H₂O (l) → CH₂O (s) + O₂ (g), RQ_LBM = 1

Figure 7. Comparison of RQ of FF and RQ of RQ combined FF and LU {RQ_FFLU}. Fossil energy data and fossil and land use C (thus CO₂) emission data are from Ref. [73]. Ref. [83] contains world energy data by oil, gas, and coal, 1800–2022. Land use includes CO₂ emitted via deforestation and CO₂ production via food and wood for construction. Land use CO₂ emissions are about 13–20% of total anthropogenic emissions [https://unfccc.int/topics/land-use/workstreams/land-use—land-use-change-and-forestry-lulucf, accessed on 3 November 2023]. Since land use CO₂ in GTt/Exa J = 0.1 ∗ RQ_LU RQ [7] and RQ_LU ≈ 1 for LU this relation provides an estimate of energy released from land use data.

Figure 7. Comparison of RQ of FF and RQ of RQ combined FF and LU {RQ_FFLU}. Fossil energy data and fossil and land use C (thus CO₂) emission data are from Ref. [73]. Ref. [83] contains world energy data by oil, gas, and coal, 1800–2022. Land use includes CO₂ emitted via deforestation and CO₂ production via food and wood for construction. Land use CO₂ emissions are about 13–20% of total anthropogenic emissions [https://unfccc.int/topics/land-use/workstreams/land-use—land-use-change-and-forestry-lulucf, accessed on 3 November 2023]. Since land use CO₂ in GTt/Exa J = 0.1 ∗ RQ_LU RQ [7] and RQ_LU ≈ 1 for LU this relation provides an estimate of energy released from land use data.

4.4. Keeling’s Data on CO₂ and O₂ in ppm and Curve Fits

4.4.1. Keeling’s Data on CO₂ and O₂

The monthly data file presented by NOAA starting in 1990 was converted into Excel-based data. The calendar period since 1990 was first converted into days in order to capture the zigzag pattern by both CO₂ and O₂, and O₂ concentration in “per meg” units was converted into ppm basis, and the plot of CO₂ and O₂ vs. days/10 (Figure 8) reveals the zigzag pattern. Looking at the annual history of [CO₂ ] and [O₂] vs. year, it is clear that the concentration of CO₂ starts increasing while that of O₂ keeps decreasing from 1990 onwards. An explanation of the zigzag pattern is provided in Section 1 of the Introduction.

4.4.2. The Curve Fits to Keeling’s Data and Estimation of d[CO₂]/dt and d[O₂]/dt

Two types of curve fits to Keeling data (from 18 April 1991 to 26 January 2021) on [CO₂] and [O₂] concentrations were obtained.

Linear Fit for CO₂ and O₂

If the fit is given in terms of (x′ = days/10), say CO₂ in ppm = a₁ ‘x’+ a_0′ then the fit in terms of year is given as CO₂ in ppm = a_1′ year ∗ (365/10) + a₀. Let a₁ = a_1′ ∗ (365/10), a_0′ = a_0. Thus, the trend line with a linear fit after conversion from days into years yields:

CO₂ in ppm = a₁ ∗ years+ a₀, a₁ = 2.0789, a₀ = 350.5 (linear fit), R₂ = 0.9709, linear, where years = Year of interest-1991, Year of interest ≥ 1991

In Column 3 of Table 2, the computed numbers for 2006 are given in parentheses in braces { } along with Keeling’s data.

d[CO₂]/dt, ppm per year = a₁ = 2.0789.

O₂ in ppm = b₁ ∗ years+ b₀, b₁ = −4.438 ppm/year, b₀ = 209,488 (linear fit), R₂ = 0.9839

d[O₂]/dt ppm/per year = b1 = −4.438 ppm per year

Column 3 of Table 2 lists the linear curve fit constants along with corresponding derived formulae for several parameters of interest.

HHV_O₂ = 448 kJ/mole = 0.448 ∗ 10⁻³ Giga J/mole or 448 Exa J/Peta mole

4.4.3. Quadratic Fit for CO₂ and O₂ of Table 2

Since the atm contains air of mass of 5.13 × 10²⁴ g or 1.77 × 10⁶ Peta mol, 1 ppm change of any species by 1 ppm atm = 0.177 Peta mols and, as such, requires a large amount of change of species like CO₂ and O₂. More fossil fuel use results in more conversion of “carbon” from the ground to CO₂, more addition to the atmosphere, and more drop in O₂ concentration in the atmosphere, and thus slopes will become steeper in the future. Therefore, a linear fit is not reasonable, and the quadratic fit may reveal such an outcome.

Better accuracy is required, and hence the R² for the fit must be as high as possible. Thus, a quadratic fit was selected.

[CO₂] = CO₂ in ppm = c₂ ∗ years² + c₁ ∗ years + c₀, c₂ = 0.01892, c₁ = 1.473, c₀ = 354.1, R² = 0.9804

$${\left\{\frac{d\left[C{O}_2\right]}{dt}\right\}}_{atm}=2\ast c_2\ast year+{ \mathrm{c}}_1=0.03784 \ast year+1.473$$

where ${\left\{\frac{d\left[C{O}_2\right]}{dt}\right\}}_{atm}$ in ppm/year and

[O₂] = O₂in ppm = d₂ ∗ years² + d₁ ∗ years + d₀, d₂ = −0.04347265, d₁ = −3.0332, d₀ = 209480, R² = 0.9896

$${\left\{\frac{d\left[O_2\right]}{dt}\right\}}_{atm}=2 \ast d_2 \ast year+{ \mathrm{d}}_1=-0.0870 \ast year-3.0332$$

where ${\left\{\frac{d\left[O_2\right]}{dt}\right\}}_{atm}$ in ppm/year. It is clear that R² is higher for a quadratic fit.

Column 3 of Table 2 summarizes coefficients fitted curves for both linear and quadratic fits. It also shows the comparison of results between curve fits and actual data. More is the energy consumption, more is the O₂ consumption and steeper the slopes of CO₂ and O₂ curves.

4.5. Estimation of Global Respiration Quotient (RQ_Glob)

4.5.1. Global RQ Based on CO₂ Added to Atm and O₂ depleted from Atm

The global respiration coefficient is defined as

$$R{Q}_{Glob}=\frac{{(d\left[C{O}_2\right]/dt)}_{atm}}{\left|{(d\left[O_2\right]/dt)}_{atm}\right|}$$

(25)

where slopes are provided from curve fit constants on Keeling’s curves.

Linear fit: The linear fit indicates that CO₂ increases by 2.09 ppm per year while atmospheric oxygen decreases at a rate of 4.438 ppm per year. Using a linear fit for Keeling’s data on CO₂ and O₂ over 30 years (1991–2021) and Equation (24),

$$R{Q}_{Glob}=\frac{a_1}{b_1}=\frac{2.0789}{4.438}=0.468, for linear fit$$

(26)

where “years” represents the (Year of interest—1991).

Quadratic Fit: Selecting a quadratic fit,

$$\frac{d\left[C{O}_2\right]}{dt}=2\ast c_2\ast year+{ \mathrm{c}}_1=0.03784 \ast year+1.473$$

(27)

where $\frac{d\left[C{O}_2\right]}{dt}$ in ppm/year. Using Equation (24),

$$R{Q}_{Glob}=\left(\frac{2\ast c_2\ast years+c_1}{\left|2\ast d_2\ast years+{ \mathrm{d}}_1\right|}\right)=\frac{0.03784 \ast years+1.473}{\left|-0.0435 \ast years-3.0332\right|}, quadratic fit$$

(28)

See Column 3 of Table 2, Column 4 where results are tabulated for a quadratic fit. It is clear that RQ changes with the year. Columns 3 and 4 compare the results for linear and quadratic fits.

Figure 9 shows the variation of RQ_Glob with year based on a quadratic fit; it shows that RQ_Glob decreases from 0.48 to 0.46 while a linear fit yields a constant value of 0.47. The decrease in RQ_Glob is attributed to increasing CO₂ storage in the ocean. The RQ_Glob is not a property, while RQ_FF and RQ_BM are properties. The RQ_Glob is somewhat similar to the RQ_vent in biology. More detailed discussions are presented in the next section.

4.5.2. RQ_Glob < RQ_FFLU and Physical Meaning of RQ_Glob

The d[CO₂]/dt represents the net accumulation of CO₂ in atm. It is the difference between CO₂ added by FFLU and the sum of CO₂ sink by biomass and storage by oceans. Similarly, the magnitude of {d[O₂]/dt}_atm represents the net depletion rate of O₂ in the atm. It is the difference between the O₂ used by FFLU and the O₂ produced by biomass.

The RQ_Glob depends on RQ_FF, RQ_LBM, RQ_OWBM, combined Land and ocean water biomass RQ_LOWBM, annual energy release, CO₂ sources, and CO₂ sinks. Expanding the relationship for RQ_Glob,

$$R{Q}_{Glob}=\frac{{\dot{N}}_{C{O}_2,atm}}{{\dot{N}}_{O_2,atm}}=\frac{{\dot{N}}_{O_2,FFLU}\ast R{Q}_{FFLU}-{\dot{N}}_{O_2,LOWBM}R{Q}_{LOWBM}-{\dot{N}}_{C{O}_2,st,Ocn}}{{\dot{N}}_{O_2,FFLU}-{\dot{N}}_{O_2,LOWBM}}=\frac{R{Q}_{FFLU}-x\ast R{Q}_{LOWBM}-y}{\left(1-x\right)}$$

(29)

where ${\dot{N}}_{O_2,FFLU}$, O₂ consumed by FFLU, $x=\frac{{\dot{N}}_{O_2,LOWBM}}{{\dot{N}}_{O_2,FFLU}},y=\frac{{\dot{N}}_{C{O}_2,st,Ocn}}{{\dot{N}}_{O_2,FFLU}}$, and ${\dot{N}}_{O_2,LOWBM}$ O₂ produced by both the land and ocean biomasses. Solutions for “x” and “y” are presented in Part II [86]. Since RQ _FFLU = 0.78 and RQ_LOWBM ≈ 1 and approximating RQ _FFLU ≈ RQ_LOWBM,

$$R{Q}_{Glob}\approx R{Q}_{FFLU}-\frac{y}{\left(1-x\right)}$$

(30)

It is apparent from Equation (30) that the greater the storage of CO₂ by the ocean {term: y/(1 − x)}, the lesser is RQ_Glob < RQ_FFLU.

As an example, consider the year 2006, for which the annual energy release is known as 460 Exa J/year (which includes FF and LU). With constant HHV_O2, the O₂ consumed from the atm is given as 1.03 Peta mols/year and with RQ_FFLU = 0.778, the CO₂ released is 1.03 ∗ 0.78 = 0.8 Peta mols/year. The CO₂ added to the atm in ppm = 0.8/0.177 = 4.51 ppm since 1 ppm CO₂ added to the atm is equivalent to 0.177 Peta mols added to the atm. Similarly, O₂ removed from the atm in ppm = 1.03/0.177 = 5.8 ppm. If there were no biomass and no oceans, RQ_Glob = RQ_FFLU = 0.778. If the planet has only biomasses, they serve as CO₂ sinks and O₂ sources. Assuming % CO₂ sink by biomass to be 0.32 {Part II}, CO₂ sink by biomass = 1.46 ppm, and hence, net CO₂ added to the atm = 4.51 − 1.46 = 3.05 ppm. The O₂ added by biomass = 1.46 ppm. Thus, net O₂ removed from the atm is 5.8 − 1.46 = 4.34 ppm, assuming RQ_LOWBM ≈ 1. Now RQ_Glob RQ = 3.05/4.34 = 0.7 and not much change from RQ_FFLU of 0.778. When ocean CO₂ storage of 23% of CO₂ from FFLU {Part II} is included, CO₂ as stored in the ocean = 0.23 ∗ 4.51 = 1.04 ppm, and hence, net CO₂ added to the atm = 3.05 − 1.04 = 2.01 ppm, close to Keeling’s slope: d[CO₂]/dt = 2.02 ppm/year/ Now RQ_Glob = 2.01/4.34 = 0.46 ≈ 0.47< RQ_FFLU. Hence, the slope {d[CO₂[/dt}atm is affected more by the amount of CO₂ stored in oceans than by the extent of CO₂ sink by biomass. The higher the storage of CO₂ by oceans, the lower the RQ_Glob for given {d[O₂]/dt}atm and the higher the acidity of the ocean.

The RQ_Glob of 0.47 (<RQ_FFLU = 0.78) is interpreted as the global respiratory quotient of “hypothetical single fossil fuel (HSFF)” releasing 0.47 net moles of CO₂ {=CO₂ released from combustion of FFLU-CO₂ sink via BM and CO₂ storage in oceans} for every O₂ mole depleted (=O₂ consumed by FFLU-O₂ produced by LOWBM) from the atmosphere, as though this fictitious power plant is located on a barren earth without ocean water and chlorophyll on the planet. The number 0.47 multiplied by 12.01/44.01 = 0.273 indicates the net amount of moles of C depleted from the reserves of C on the planet. Figure 10 illustrates the difference between the green planet with oceans and the barren planet. Figure 10a represents the earth, with power plants burning FF or FFLU serving as a CO₂ source, biomasses undergoing PS with a CO₂ sink and O₂ source, and oceans serving as CO₂ storage. Figure 10b is a fictitious planet somewhat analogous to the metabolism in humans since the “fictitious” barren earth, without chlorophyll and oceans, does not have any mechanism to produce O₂ or provide a CO₂ sink.

Other consequences of Keeling’s data and RQ_Glob are as follows: (i) Keeling’s data indicate that the oxygen depletion rate in the atm is 4.48 ppm per year [Magnitude of slope of {d[O₂]/dt}_atm} and the CO₂ addition rate to the atm is 2.082 ppm/year [slope of {d [CO₂]/dt}_atm}. The normal atmospheric O₂ concentration in 1991 was 210,000 ppm. Thus, the depletion rate is extremely small compared to the initial oxygen concentration. However, it is well known that cells of BS do not receive oxygen when the O₂ % in atm falls below 16.5 16.5 % or 165,000 ppm [87]. Hence, O₂ will reach 165,000 ppm in about 12,000 years with linear fit of O₂ data (about 3000 years with quadratic fit) for human extinction or be depleted completely in about 47,000 {=210,000/4.48} years. (ii) The RQ_Glob of 0.47 indicates that 0.47 net moles of C were removed from the earth {C mined-C stored by ocean water-C removed biomass} and added to the atm as gaseous CO₂ per mole of O₂ depleted from the atm. Keeling’s data indicate that with 4.3 ppm/year (Column 3 of Table 2) or 0.76 Peta mols of O₂/year, the annual loss of C(s) from earth is estimated as 4.3 GT, which presumes that (i) FF can be represented by C-H-O and no sequestration of CO₂. Alternately Keeling’s data with linear fit indicates CO₂ gain tin atm to be 2.08 ppm or Carbon converted into gas as 2.08 ∗ 0.177 ∗ 12.01 = 4.4 GT/year (ii) All H in fuel gets converted into H₂O, which stays on the land/ocean. The C mass loss after 47000 years is estimated at 202,000 GT, {which includes C from coal, oil, and gas} or a decrease in earth’s mass of 202,000 GT, which is negligible compared to the initial earth’s mass of 5.97 ∗ 10¹² GT (iii) With CO₂ sequestration, the mass loss rate is almost zero. (iv) For the physiological effects of decreasing O₂ concentration, see Ref. [88]. (v) The atmospheric pressure is due to the weight of the air over the unit area. Once oxygen is depleted, the weight of the air column decreases, and hence, the atmospheric pressure will decrease due to the depletion of O₂. If CO₂ addition is ignored or sequestered using underground storage, the atmospheric pressure decreases to 79,000 Pa with 100% N₂ in the atmosphere. (vi) If CO₂ is not sequestered and continues to be at the current rate, it increases pressure above 79,000 Pa. Now the atm pressure is by both CO₂ and N₂, and it is estimated at 89,000 Pa {CO₂: 11% of N₂: 89%}. If all plants, trees, and PP cease to exist, the oxygen production stops [89] and if humans continue to use power plants, oxygen depletion rate due to FF will be 5.8 ppm per year and planet will run out of oxygen in 36,200 years !

4.5.3. RQ_Glob and Rationality for RQ_Glob < RQ_FF

RQ_Glob is around 0.48 in 1991 to and it decreases to 0.46 in 2021 when a quadratic fit is used (Figure 11) with an average of 0.47 and the RQ_Glob is constant at 0.47 with a linear fit.

Figure 11 shows decreasing RQ_Glob with a quadratic fit, revealing increased storage of CO₂ in oceans. Furthermore, the increasing ocean surface temperature may release O₂ into the atm, thus lowering the RQ_Glob. [58]. It is seen from Equation (30) that increasing the storage of CO₂ in ocean water {term y, Equation (30)} lowers the RQ _Glob, which decreases the rate of increase of CO₂ in the atm, but at the cost of increasing the acidity of oceans. The website mentioned in Ref. [90] manages “ocean carbon and ocean acidification data”, and the website confirms the increasing acidity of ocean water [91].

Unlike BS, which does not have any mechanism for O₂ production within the body, and hence, 0.7< RQ < 1 (without accounting for glycolysis), the breathing planet has a mechanism for O₂ production on land and OWBM. Ignoring CO_{2,st, ocn,} the RQ_Glob is always less than RQ_FFLU for any x < 1. For a linear fit, the RQ_Glob is constant at a₁/b₁ = 0.47, but for a quadratic fit, RQ. Thus, the RQ_Glob average for 1991–2018 is about 0.47. Ideally, planet earth needs the RQ_Glob close to zero to maintain CO₂ at a constant value.

4.5.4. Predicted Saw-Tooth Pattern of O₂ Given CO₂ Data and RQ_Glob

Given the saw-tooth pattern of CO₂ data and RQ_Glob = 0.47, one can predict the O₂ pattern RQ (See Appendix A.2 ad Figure A1 for details). Suppose the first data i was on 19 January 1991 (day 1). Then there are a series of readings on several dates: 14 January 1991, 4 April 1991, 18 April 1991 … 18 April 1991 … 30 December 1994. The established O₂ in ppm (4 April 91) = O₂ in ppm (14 January 91), set at 209,474.2 ppm + {CO₂ data in ppm on 4 April 91- CO₂ in ppm 14 January 91}/RQ_Glob, estimated O₂ in ppm (18 April 91) = O₂ predicted (4 April 91) + {(CO₂ data in ppm on 18 April 91) − CO₂ in ppm 4 April 91)}/RQ_Glob, …. Figure 12 shows the saw-tooth pattern for CO₂ and O₂ (from data) and a comparison of data for O₂ with estimated O₂ using RQ_Glob for the period 1991–2020. Since distinction is not clear, Figure 13 shows the blown-up version of the comparison for a short period (1991–1994). It shows data on CO₂ and O₂ for 1992, 1993, and 1994, predicted O₂ (solid line) using R_Glob vs. days/10, where days are counted since 19 January 1991. Since the O₂ estimate uses CO₂ data, the estimated O₂ also reveals a saw-tooth pattern. The pattern and prediction of O₂ are explained as follows.

The solar input in FW is about 715 kWh/m² (over 6 months), while the input in SS is about 1130 kWh/m² (over 6 months), and hence, 57% more for solar input in SS compared to FW. Further, RQ_SS may be different compared to RQ_FW., i.e., the BM, a “mixture” of different types of trees and plants in SS and FW {e.g., live oak, which does not shed leaves, vs. post oak, which sheds leaves in FW), may be different in SS and FW, and as such, RQ’s for BM may be different. Further, at the end of FW, the CO₂ may also be released by the oxidation of dead leaves by microbes, or the CO₂ sink in FW may be less compared to the CO₂ sink in SS. The O₂ production term due to biomass in Equation (29) for FW < O₂ production for SS. There is more depletion of O₂ in FW, and hence the slope of {d[O₂]/dt} in at _FW in FW is also higher. Arguments could be repeated for SS, where CO₂ sink increases (numerator term in Equation (29)), lowering CO₂ in the atm by BM in SS. But it also increases the O₂ production term in the denominator. Thus, compensating effects are present both in SS and FW, so RQ_Glob may be about the same in both FW and SS {see future work in the manuscript}, as the author assumed. But it is of concern whether the amplitude of variation in CO₂ by 6 ppm decreases with more annual energy consumption, which results in a higher release of CO₂ but not enough CO₂ sink in SS, thus decreasing the amplitude [92]. Keeling’s data are for the northern hemisphere, and the data are not affected by the southern hemisphere (where the seasons are reversed) since the mixing time between the two hemispheres is of the order of one year [92].

4.5.5. Death of BS vs. Death of Green Planet Earth

The BS can live when the RQ (0.7 to 1) and the oxidation reactions deliver the required energy for maintaining life-sustaining functions. However, those reactions involve electron transfer, resulting in the creation of a few radicals that cause damage to cells, thus resulting in the aging of the body and the eventual creation of a birth–death cycle. So, in order to live, the BS must eventually die. A faster oxidation reaction per unit mass of body (i.e., more energy release rate per unit mass, e.g., ants) results in a shorter life span [65]. Green planet earth consists of BS and NBS (e.g., sand, rocks, etc.) that breathe in oxygen and release CO₂ with an RQ of 0.47 to support mechanical and leisure life and to live comfortably. In doing so, the terrestrial system undergoes a self-destruction of ecosystems with increasing CO₂ in the atm, which results in global warming, the acidity of ocean water, and hence, the slow death of the green planet.

4.5.6. Earth Tilt Angle and Mining and Drilling of Fossil Fuels

The normal tilt angle of the earth is about 23.5 degrees. Earth has been shown to be tilted 80 cm (80 cm or 31.5”) farther east over the last 30 years [93,94]. The tilt is attributed to pumping a large mass of water {2150 GT, 1993–2010 with a total of 17 years, 126 GT/year} from the reservoirs containing 2.0 ∗ 10¹² tons of water and a tilt of about 4.4 cm/year due to a shift in water masses. The tilt rate per unit mass of water shift is 0.037cm per GT. Similarly it was shown that mining fossil fuels at locations farther from axis of rotation affects the mass distribution and can result in change in moment of inertia affecting earth’s tilt; i.e., the tilt tangle is affected by pumping or, in general, removing a large amount of solid and liquid masses and converting them to gas and thus affecting mass distribution around the globe [94,95]. If so, then one could speculate that the tilt tangle may also be affected by pumping large amounts of oil and gas and mining coal out of the ground or, in general, removing a large amount of solid and liquid masses and converting them to gas and thus affecting mass distribution around the globe. Unlike the pumping of water, where water undergoes a cyclic process of pumping of water and recovery on land and ocean moderating tilt, the “pumping” of FF converts solids into gas in the atmosphere; as such, the problem of tilt may be more severe! In Section 4.5.2, it was determined that the C mass loss rate from the earth is 4.3 GT/year, and hence, for a period of 17 years, the total mass moved out is 73 GT. Apart from groundwater tilt, it is speculated that there could be an additional tilt of 73 ∗ 0.037 = 2.7 cm over 17 years!

4.5.7. Effects of Presence of CH₄ in the Atmosphere

In addition to CO₂ and CH₄, other global warming gases include H₂, N₂O, and SF₆. The CH₄ in the atm increases at a rate of 7.87 ppb/year (not shown) along with CO₂ at 2.08 ppm/year or a CO₂ total of 2.08 + 10 ∗ 7.87/1000 = 2. 16 ppm/year. Note that the GWP of CH₄ is about 10 times that of CO₂. O₂ typically decreases at a rate of 4.44 ppm/year. Thus

$$R{Q}_{Glob,C{O}_2+C{H}_4}=\frac{\left(2.39 \mathrm{ppm}+7.87\mathrm{ppb} \ast {10}^{-3}\left(\frac{\mathrm{ppm}}{\mathrm{ppb}}\right) \ast 10.4\right) \ast {10}^{-6}\left(\frac{\mathrm{moles}}{\mathrm{ppm}}\right)}{4.44 \mathrm{ppm} \ast {10}^{-6}\left(\frac{\mathrm{moles}}{\mathrm{ppm}}\right)}=0.556,\mathrm{GWP}\mathrm{for}C{H}_4=10.4$$

(31)

Thus addition of CH₄, is equivalent to a total of 17 GT of CO₂ added to the atm.

4.5.8. RQ_Glob and CO₂ in Giga Tons per Exa J

When Equation (26) is used in Equations (8) and (9), the relation does not yield GT per Exa J of energy release but yields net GT of CO₂/year {i.e., CO₂ source—CO₂ sink via BM and storage} per Exa J of net energy release {=difference between the energy release from FFLU and energy input via solar energy during PS processes}. When the energy difference is divided by the average heating value of biomasses, it provides the mass of potential FF depleted from planet earth. Part II will introduce fossil energy-based RQ_Glob,En, which will provide CO₂ release per unit Exa J of energy release from FF so that a direct relation between annual FF energy and CO₂ in GT per Exa J can be provided.

5. Conclusions

The RQ concept borrowed from biology literature is adopted in engineering literature, and it provides a relation for CO₂ in GT per Exa J as 0.1 ∗ RQ and CO₂ in million tons per MMBtu as equal to 0.116 ∗ RQ. For biomasses that serve as CO₂ sinks and O₂ sources, CO₂ sink in GT per Exa J energy input for biomass growth = 0.1 ∗ RQ. Instead of RQ, the PS literature uses the following terms: ExR, RR, PQ, and RR which are equal to the inverse of RQ. Keeling’s annual data on CO₂ and O₂ (1991–2018) are used to obtain the global RQ (RQ_Glob) as RQ_Glob = 0.47, which implies that net CO₂ moles added to the atm (after accounting for CO₂ sink by oceans and biomasses= 0.47 per unit ) net mole of O₂ removed from the atmosphere RQ. The power plants on earth use natural gas (RQ = 0.5), oil (RQ = 0.7), and coal (RQ = 1) as FF. Based on CO₂ and the energy data, RQ_FF ≈ 0.78. The global RQ for FF satisfies the inequality 0.5 < RQ < 1. While RQ_FF or RQ_BM are properties of fuels and biomasses, RQ_Glob = is not a property and it depends on CO sink in atm, biomass and oceans. The global RQ is lower than 0.78 since the global RQ is affected by O₂ production and CO₂ sink in addition to CO₂ source and O₂ sink by FF, and hence the RQ_Glob of 0.47 < 0.78. The FF with a lower RQ must be selected and biomass with high RQ is desired in order to reduce CO₂ added to the atmosphere. The saw-tooth pattern of O₂ is predicted with data on CO₂ and the global RQ.

6. Future Work

Future work must include the creation of genetically engineered biomasses with high RQ values greater than >1. The RQ concept, along with CO₂ and O₂ balance equations, may be used for estimating the CO₂ distribution in GTt/year and % distribution of CO₂ in the atm, land, and ocean, as well as storage in ocean water. The results must be validated by comparing the RQ-based results with those obtained from detailed computer models developed for CO₂ stored in the atm, land, and ocean water (Part II). Knowledge of the RQ for SS and FW is required in order to predict the saw-tooth patterns of CO₂ and O₂ concentrations. Data are needed for studying the effects of (a) oxygen depletion, (b) CO₂ addition, and (c) sequestration on the barometric pressure. Since water pumping seems to affect the earth’s tilt angle [93], similar studies are needed on the effects of mining oil and solid fuels from the ground.