DOI: 10.31038/GEMS.2023524

Abstract

Shale, a significant rock formation with potential as a source and reservoir rock, presents challenges in drilling due to its unique chemical composition and mechanical properties. To address the instability caused by shale mineralogy, various shale inhibitors are used as drilling fluid additives, interacting with clay minerals to stabilize the clay by neutralizing surface charges. While numerous research groups have extensively studied shale stabilization, clay chemistry, and novel inhibitors, there remains a gap in comprehensive studies that correlate evidence of shale instability from recent literature with clay mineralogy and Zeta potential. This review article fills this gap by presenting pioneering work and recent evidence from literature to provide a clear rationale behind the role of clay mineralogy in shale instability. Notably, a novel correlation has been developed that predicts clay swelling based on Zeta potential for sodium bentonite clay with a smectite percentage ranging from 70-90%. This review work serves as a foundation for future researchers in selecting appropriate shale samples for their shale stabilization studies and estimating clay swelling based on Zeta potential. Ultimately, it presents a more nuanced understanding of the mechanism of shale swelling inhibition, contributing to the advancement of knowledge in this field with a cerebral approach.

Keywords

Clay mineralogy; Shale instability; Shale swelling; Shale hydration

Introduction

Shale is the most abundant clastic sedimentary rock roughly accounting for 70 % of the sedimentary rock type in the Earth’s crust [1]. Shale is a laminated and fissile rock comprising of clay and silt size particles ranging from 0.02 – 0.05 mm in diameter [2,3]. Shales are often located with the layers of limestone or sandstone and typically generate in the environment where silts, muds and other sediments were deposited by the mellow currents followed by the compaction e.g., basins of shallow oceans, payas, river flood plans and floor of deep-oceans [4,5]. The permeability and porosity of shale rocks depend upon the size of the constituent grain particles while their colour is mainly attributed by their composition e.g., the higher the organic content of the clay, the darker will be its colour; purple and reddish colour is due to the existence of hematite and limonite, blackish, brown, and blue hues correspond to the presence of iron ores while calcareous shale are yellowish or light grey [6,7]. Organic shales containing kerogens (a complicated mixture of hydrocarbons generated from animals and plants remains) in substantial quantity, produce oil when subjected to pyrolysis, are called oil shales [8-10]. The term shale oil is also used for the crude oil which is produced from oil bearing shale formations with low permeability and to avoid the confusion with the generic crude oil, the term ‘tight oil’ can be used for shale-oil [11]. The shale oil reservoirs are usually classified by the (Vitrinite reflectance) Ro = 0.6%-1.2%, TOC (Total organic content) > 2% and having complex mineral composition with ultra low permeability (0.001-0.0001) mD and low porosity (<5%) [12,13]. Though, shale is an important reservoir and source rock but drilling through shale formation is a havoc due to its brittle nature. Roughly 70% of the wellbore instability issues are associated with the shale dispersion, swelling and sloughing [14,15]. Wellbore instability issues may arise due to bit balling, pipe stucking, caving and lost circulation which predominantly happens due to shale swelling [16,17]. Shales can undergo through instability mainly due to its chemical composition or mechanical failure [18]. However, in this detailed review, shale instability has been related with the clay chemistry. The pieces of evidence have been collected from the recent literature which directly correlates the clay mineral content with shale instability. Moreover, this review paper also sheds lights on the pioneer work carried out which basically laid the foundation of the role of mineralogy in shale hydration. More importantly, this paper also relates the shale types with its mineralogy and ultimately with instability, paving way for the researchers to choose the suitable candidate for their shale stabilization studies.

Structure of Paper

To begin with, a concise introduction to shale has been presented, followed by an in-depth discussion of clay chemistry and its pivotal role in shale instability, drawing on pioneering research. Next, the impact of clay mineralogy on different types of shales and their resultant instability has been extensively examined. Furthermore, recent literature has been cited to demonstrate the effects of clay chemistry on shale instability. A new correlation, known as the M.H. correlation, has been developed, which establishes a link between clay instability and zeta potential. Finally, the study concludes with a summary of the key findings in the conclusion section.

Clay Chemistry

Understand the Term ‘Shale Instability’

Since, in this section clay chemistry will be discussed in context of ‘shale instability’ thus it is imperative to understand this term before moving forward. The term ‘instability’ is subjective; therefore, it is important to understand this term to make a clear narrative. In context of shale, the shale instability can be depicted by two phenomena: (1) dispersion (2) sloughing. Sloughing or swelling mainly takes place in swelling shale containing expandable clays such as smectite. Generally, cations with high valences are strongly adsorbed to the clay and thus are less prone to swelling as compared to the clay containing low valence exchangeable cations [19]. Unlike swelling, dispersion is mainly the continual disintegration of the shale which is induced when the bonding between clay layers is weakened when it hydrates [20,21]. This leads to the strength reduction of the shale formation which may collapse the wellbore [22].

Clay Mineralogy

Shale is comprised of many mineral grains which are predominantly clay-sized granules. IBorysenko (2009) presented the mineral composition for Pierre shale as: quartz (29%); kaolinite and chlorite (8%); illite, muscovite and smectite (28%); dolomite, albite, orthoclase (13%); and mica (24%) [23]. All these clay minerals can be classified based upon the configuration of alumino-phyllosilicate sheets as 1:1 or 2:1 [24,25]. A 1:1 clay consists of one octahedral and one tetrahedral sheet which are uncharged (neutral) and are bonded by hydrogen bonding e.g., kaolin group (kaolinite, nacrite, halloysite, dickite etc.) [26]. However, 2:1 configure d clay minerals are comprised of an octahedral sheet which is sandwiched between two tetrahedral sheets bonded with cations such as K⁺ (in illite) or Ca⁺/Na⁺ (in smectite) and overall having a negatively charged surface e.g., smectite, illite and chlorite as shown in Figure 1 [27]. Swelling clays have exchangeable cations and layers are always lacking in positive charge due to cationic substitution and thus cations in interlayer are deemed to counter-balance the negative charge in clay layers [28].

Figure 1: 1:1 and 2:1 configuration of clay mineral layers

Shale is composed of various clay minerals [29]. Among these minerals, smectite minerals and smectite/illite mixed layer are deemed to be the main reason behind clay swelling mainly due to their 2:1 configuration and cationic exchange capacity. O’Brien and Chenevert (1973) were one of the pioneers for their significant contribution in qualitatively relating shale swelling and its dispersion behaviour with its mineralogical composition. According to their qualitative study, shales rich in illite/smectite (S/I mixed layer) are more prone to dispersion and swelling. However, illite won’t alone result into sloughing, although it may result into the dispersion of the shale. They also found out that shales rich in S/I (mixed) layers are more prone to dispersion and sloughing. This is because at higher burial depth and certain conditions of temperature, illitization of smectite starts. Firstly, smectite converts to S/I (mixed) layer than to fully illite [30]. Therefore, matured shales hardly contain any smectite content. Table 1 adopted after O’Brien and Chenevert (1973) shows the relation between shale mineralogy and instability issues.

Table 1 shows that shales rich in mixed layer S/I (Smectite/illite) are more prone to dispersion and sloughing. However, shale containing no smectite originally will not undergo through illitization thus no mixed layer will be formed and eventually no prominent shale instability issues will rise [31].

Table 1: Role of clay mineralogy in shale instability

Before discussing the significant shale plays and their mineralogical composition, Table 2 summarizes the properties of various clay minerals which are usually found in the shale followed by a detailed discussion pertaining to all minerals. As a scope of this review, the discussion will be limited to Smectite, Illite, Chlorite and Kaolinite.

Table 2: Surface and chemical properties of problem causing slay minerals

Montmorillonite is a significant member of the smectite mineral comprising silica tetrahedron and aluminum octahedral depicted in Figure 2A. The smectite group has wide spaces between base units and feeble bonding which makes it prone to swelling by intercalation of water cations into the lattice. The swelling can be reduced by substituting the counter-cations such as Ca⁺ and Na⁺. Smectite is mainly found in shallow intervals and at deep intervals it converts to illite which can also show swelling tendency.

Figure 2: Scanning Electron Microscopy results of A) Smectite B) Kaolinite C) Illite [32] D) S/I mixed layer [33].

Illite has lesser tendency to swell in water even though it contains the same base unit as montmorillonite mainly because of strong electrostatic force of attraction and bonding between layers as shown in Figure 2C. Ion exchange may take place at the surface, but the volume expansion caused by this hydration is insignificant as compared to volume expansion in montmorillonite. They are formed by the weathering of muscovite and feldspar and its layers are bonded by poorly hydrated K⁺ ions which keeps it stable against hydration. However, the other type of illite which forms from smectite at HTHP conditions in deep interval has more tendency to swell as compared to the original version.

Chlorite and   Kaolinite, unlike the other clay minerals, do not possess the hydration ability, although kaolinite shows a little dispersive behaviour. Kaolinite clays have lower swelling tendency and show poor ionic exchange capability. Shales rich in kaolinite are brittle in nature and are mainly the subject of mechanical failure in the formation. Not all shales contain every mineral which is responsible for shale instability.

But do shales really swell? It is also very important to mention here that shale doesn’t really swell in in-situ drilling conditions unless there are micro-fractures, exposed internal surface due to overburden or they are already drilled (in the form of cuttings). This above statement has always been a very important topic to debate among various research groups till now. However, the wellbore instability issues, and Non-productive time (NPT) caused by shale dispersion and its sloughing are something that everyone agrees on.

Since, from the pioneer work of O’Brien, it is established that chlorite doesn’t have much to do with the shale instability but infact these are mixed layers (S/I) and Illite which result into shale instability. Now, it is imperative to note if these types of minerals are found in major shale plays around the world. Table 3 presents a few of the major shale plays in North and Central America which depicts illite is usually the common mineral in most of major shale plays. Vermilion and Anahuac shale since is at lower burial depth thus it contains smectite while Atoka and Midway owing to the high burial depth, exhibit the process of illitization in the form of S/I (mixed layer).

Table 3: Mineralogical clay composition of major shale plays in North and Central America [34-36]

Significance of Diffused Double Layer (DDL)

Smectite contains montmorillonite which has the tendency to swell as shown in Table 1, due to weak bonding and 2:1 layer configuration which renders a negative charge on clay surface [37,38]. This negative charge is responsible for attracting water and other cations and thus leading to the swelling of the shale [39]. To understand the swelling caused by smectite mineral in shale, it is crucial to understand how the 2:1 configured negatively charged clay minerals formulate diffused double layer (DDL) or electrical double layer in first place. Clays are predominantly alumino-silicates in which silicon and aluminum ions are continuously being substituted by other cations leaving a net negative charge [21,40]. When clay particles are hydrated (or dispersed in a solution), they are surrounded by thin layer of cations (hydrosphere) from water [22]. Now, an electrical double layer will be formed which includes (i) negatively charged surface, (ii) surrounding cations (Stern layer) and (iii) a thin film of dispersing medium which contains high concentration of counter-ions as shown in Figure 3. Various shale inhibitors alter the DDL and neutralize the charge on clay surface to stabilize the clay against hydration [41,42].

Figure 3: Components of Electrical Double Layer [43,44]

Shale Types and Clay Chemistry

Based upon shale appearance and its response to hydration it can be categorized into various categories to rationalize the swelling mechanism in a more comprehensible way [45].

Brittle Shales

Although they are quite cemented rocks, brittle shales crumble into tiny pieces when exposed to water. However, in the water, these parts don’t swell or get softer [46]. Brittle failure is brought on by: due to hydration of bedding planes and microfracture surfaces, shales first become weak, and clay then fails when surrounded by a matrix of non-swelling minerals like quartz and feldspar [47]. Brittle shales often have a high concentration of kaolinite, illite, and chlorite, all of which are unstable in high-pH surroundings [48]. The shape of cutting and bore hole instability might be severe depending upon the drilling direction (attack angle) with respect to drilling plane and the degree of rock anisotropy [49,50]. A brittle shale may act as a potential source rock for hydrocarbons, particularly gas deposits. Though, the age and brittleness of shales, which are determined by their elastic properties and mineral dominance, are the key factors that determine the success of production under these conditions. Generally, the success of hydraulic fracturing increases with increasing brittleness index [51]. The process includes creating fracture networks in the shale matrix, which would lead to the improvement in recovery factor of these extremely tight formations [52].

Swelling Shales

Although hydration (swelling) and dispersion are linked phenomena, however, the quantity and kind of clays present in the shale’s structure play a significant role in determining when they occur. Osmotic and surface (crystalline) hydrations induce swelling to occur [53,54]. Surface hydration which merely results in a small expansion brought on by the addition of a few water molecules on the surfaces of the clays, is not frequently thought to be of major relevance [55]. In this type of hydration, layers of water molecules form a quasi-crystalline structure between unit layers, increasing the c-spacing, and hydrogen bonds hold the water molecules to the oxygen atoms [56]. On the other hand, osmotic hydration is the main issue that results in the considerable expansion of clays and closure of the borehole [57]. It occurs when cation concentration between unit layers in a clay mineral is higher than those in the surrounding water. Consequently, water intercalates between the unit layers and causes the rise in c-spacing osmotically [38]. Osmotic swellings causes more swelling than caused by surface hydration, but only expandable clays like Montmorillonite can swell on exposure to hydration. Generally, most cations with high valences than those with low valences are more firmly adsorbed. Consequently, low-valence clays without exchangeable cations tend to swell less than clays with exchangeable cations possess high valences [53,58].

High Pressured Shales

Shales can produce abnormally pressured areas when: i) the pore pressure of the surrounding sandstones is slowly transferred over geological time to the shales [59]. When thick shales are compacted, the fluid cannot escape, leading to a considerable increase in pore pressure in deep intervals. ii) Any sandstone formations interbedded with or connected to the shale might produce a pressured zone if it is fully isolated [60]. When drilling through shale at abnormal pressures, shale shakers often show chipped drill cuttings. These small, thin, sharp cuttings are formed when the hydrostatic pressure of the drilling fluid is less than the pore pressure in the shale [61]. Under these circumstances, pore pressure fractures the shale downhole into a long, spalled, concave shape [59]. Hole enlargement from this type of failure would mean complete washout of the hole wall, and unlike hole failure in brittle shale, it does not only occur in certain directions [62]. In the case of stress anisotropy, more faulting could occur in certain directions, but the entire perimeter of the well will still be affected. As mentioned earlier, this failure is caused by incorrect mud weight selection and can be prevented by increasing the mud weight.

Tectonically Stressed Shales

This type of shale is often seen in regions where there is a large-scale deformation of Earth’s crust by natural processes [63]. Shales under these circumstances tend to have bed planes oriented in the direction of the applied stress. This stress, when released, will cause excessive downhole shear failure. The failure severity can increase if the cohesion of the bedding planes decreases due to adsorption of water. The type of cementation e.g. amorphous silica, aluminum or calcium silicate, or organic materials) can also play a critical role in stabilizing or disintegrating shale formations under stress [64]. Tectonically stressed shales usually have low mechanical strength, sub-compaction with a low degree of consolidation, strong tectonic stresses leading to ductile deformation and increasing pore pressure and structural pinnacle for dissolving water and hydrocarbons.

Significance of Clay Minerals in Various Shale Types for Shale Swelling

The above section briefly explains various types of shales usually encountered during exploration and drilling. Brittle shales are well cemented and consolidated, so they don’t tend to swell, however, they are prone to dispersion due to hydration because of the presence of illite and kaolinite which tend to disperse on hydration. Swelling shales usually contain illite, semectite/illite (mixed layer) formulated through illitiization, thus they are prone to swelling as well as disperse. However, in abnormally pressured and tectonically stressed shale; there may be instability due to clay mineralogy, but the main factor for shale instability in fore-mentioned shales is mechanical failure. For such type of shales, only adding shale inhibitors in drilling mud might not be the only solution but sealing the formation, controlling temperature and pressure might be other possible solutions to avoid shale from mechanical failures.

Pieces of Evidence on Clay Chemistry Linking to Shale Instability

From the recent literature, various evidences have been collected which helps in solidify the narrative which was created from the previous discussion. Though, many a research groups have studied shale stability instability but not all of them reported the clay mineralogy in their respective works thus the work summarized is not extensive, but it is enough to establish a clear narrative. Table 4 has been extracted from the available literature and thus has been used to correlate the clay minerals with the shale recovery (dispersion test) and linear swelling results.

Table 4: Pieces of evidence from literature relating shale instability and clay mineralogy

From the above data, the relation between clay mineral and clay dispersion and swellings has been analyzed. Figure 4 shows the higher the content of illite is observed, the more shales are prone to less recovery (more dispersion) because illite tends to disperse. Similarly, the Figure 5 shows the higher the content of the Smectite/illite (S/1) mixed layer is, the higher trend in swelling is observed. The Figures 4 and 5 are in accordance with the discussion carried out above.

Figure 4: Effect of illite content in shale on shale recovery

Figure 5: Effect of (S/1) mixed layer content on shale swelling

Shale Sampling for Stabilization Studies

The most tiresome task for shale stabilization studies is the choice of a proper shale sample especially when the role of any novel inhibitor is being studied. Because it will be useless to perform swelling experiments on shale outcrop which doesn’t have any smectite content or haven’t undergone through illitization [72-82]. Similarly, for shale samples which are low in illite and kaolinite, they shouldn’t be the suitable candidates for shale recovery test because illite and kaolinite rich shales tend to disperse more as compared to chlorite rich shales. Similarly, smectite (montmorillonite) or mixed layer shales tend to swell more as compared to only illite dominant shales. Shales usually have sandstone bedding between them, thus getting the virgin shale cores from subsurface might not be possible. More importantly, shale softens down thus getting consolidated shale cores isn’t really an easy task. Therefore, various researchers prefer bentonite wafers to mimic the effect of shale mainly during linear swelling tests because bentonite is rich in Montmorillonite thus making it a suitable candidate for shale swelling studies. However, for shale recovery test (to measure the extent of dispersion), shale samples which are rich in illite must be used.

M.H. Correlation for Predicting Clay Swelling based Upon Zeta Potential

Based upon the limited data available, a new correlation i.e. M.H. correlation has been developed which can help to estimate the clay swelling in Na-Bt hydrated slurry for the smectite (montmorillonite) content ranging from 70-90%. The data reported in Table 5 is carefully selected for only those research groups where simple Na-Bentonite slurry (with no additives) have been used for clay/shale swelling studies. Therefore, the reported data is limited, however, it helps in making a clear rationale in understanding the relationship between clay swelling and zeta potential. The relationship between zeta potential and clay swelling is complex and highly dependent on various factors such as the type of clay mineral, the properties of the surrounding solution, and the measurement techniques used to quantify zeta potential and swelling. In general, a higher absolute value of the zeta potential indicates a greater electrostatic repulsion between the clay particles, which can inhibit swelling as shown in Figure 6. This is because the repulsive forces between the clay particles prevent them from coming into close contact with each other, which limits the amount of water that can be absorbed into the interlayer space and reduces swelling. Conversely, a lower absolute value of the zeta potential, or a positive zeta potential, can promote swelling by reducing the electrostatic repulsion between the particles and allowing them to come into closer contact with each other. This can increase the amount of water absorbed into the interlayer space and promote swelling. However, the quantitative relationship between zeta potential and clay swelling is not straightforward and can vary depending on the specific conditions but an effort has been made to generalize the relation between clay swelling and Zeta potential as shown in Figure 6, Table 5 and eq. 1.

Shale swelling (%) = 3.25 (Z.P) + 194.3                        (1)

(Where Z.P. is zeta potential in mV and the relation is only valid for Na-bentonite clay where smectite content is between 70-90%).

Figure 6: Relation between shale recovery and zeta potential

Table 5: Relation between Zeta potential and clay swelling

It is also worth mentioning here that the pH and ionic strength of the surrounding solution can greatly affect the zeta potential and swelling behavior of clay particles. At low pH values, the surface charge of clay particles may be positive, which can promote swelling. At high pH values, the surface charge may be negative, which can inhibit swelling. Additionally, changes in the ionic strength of the surrounding solution can affect the zeta potential and swelling behavior by altering the balance of attractive and repulsive forces between the clay particles. Furthermore, the relationship between zeta potential and clay swelling may be affected by the specific measurement techniques used to quantify these properties. Different techniques may yield different results due to variations in the assumptions, models, and experimental conditions used. Overall, while there is a general correlation between zeta potential and clay swelling, the quantitative relationship between these properties is complex and highly dependent on a variety of factors.

Conclusion

This review articles mainly focusses on presenting proofs from recent literature relating clay mineralogy with shale instability. The following conclusions can be drawn from the fore-mentioned discussion

1. Shale instability either due to mechanical or chemical effect, is mainly its dispersion and sloughing (swelling).
2. To foretell, either shale will fail mechanically or will show instability due to its mineralogy, shale types play a vital role. Brittle shales contain illite and are well consolidated, they don’t swell mainly but only disperse when water intercalates between layers and thus weakening the bonding. Swelling shales have S/1 mixed layers which, as the name indicates, makes them prone to swelling. However, abnormally pressured shales and tectonically stressed shales mainly undergo mechanical failures.
3. Bentonite wafers can be used for shale swelling tests as finding a real time consolidated core from deep interval with high smectite content is hard. However, for shale recovery test, shale outcrop samples rich in illite can be used.
4. The recent literature also exhibit the fact that the shales rich in S/I mixed layer will tend to swell more. It is also interesting to note here, that at high burial depth, smectite has already started converting to illite through illlitization, thus the illite formulate through this process also tend to swell.
5. A M.H correlation for predicting clay recovery based upon zeta potential values can be used with limited application of bentonite clay with smectite content of 70-90%.

Recommendations

1. Various shale types can be collected with their mineralogy known and they can undergo swelling and dispersion tests to empirically observe the effect of shale types and clay chemistry on shale instability.
2. The effect of water content and its role on shale swelling can be studied in detail.
3. The study on illitization and its role on dispersion and swelling can be studied.
4. More work on categorizing the shale based upon mechanical failure and instability due to mineralogy can be done.
5. Applications of Machine Learning can be used to categorize shale based upon mineralogy and thus predicting the shale instability behaviour.
6. The combined effect of fracking and swelling can be studied on the shales with expandable clays.
7. Case studies from the field can be collected reporting wellbore failure incidents due to shale instability and thus role of clay mineralogy can be analyzed in all case studies.

Acknowledgement

We would like to pay utmost gratitude to YUPT 015LC0-326 to provide financial assistance for this work.

Declaration Statement

The authors don’t have any conflict of interest to declare.

Authors’ Contributions

Muhammad Hammad Rasool: Writing original draft, conceptualizing, analysis; Maqsood Ahamad: Supervision, investigation.

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DOI: 10.31038/GEMS.2023523

Abstract

The patterns and trends of monthly time series of global atmospheric land based surface temperatures and oceanic surface temperatures, and the combination of the two, from 1850 to 2018, are presented and compared to the overall time series of fossil fuel burning which is shown to be highly correlated with atmospheric carbon dioxide concentrations. Considering only monthly temperature data time series dating back to 1850, and climate factor data in-kind, and by employing an empirical mathematical methodology, we decompose the non-linear, non-stationary, global time series and confirm patterns of frequency and amplitude modulated, discreet internal modes of variability. We find periods of warming and cooling on both the surfaces of the ocean and atmosphere over land with prominent seasonal, annual, inter-annual, multi-year, decadal, multi-decadal, and centennial modes, riding atop overall trends. Our calculated overall rates of global warming differ significantly from the estimates of the Intergovernmental Program on Climate Change (IPCC) 2007 findings, and also with the most recent, 2023 IPCC Report (https://www.ipcc.ch/ar6-syr/). Because the ocean has an enormous heat capacity relative to that of the atmosphere, we find the oceanic warming rate to be less than two-thirds of surface air over land, making the ocean a regulator, a heat capacitor, thus the dominant player in determining global surface temperatures. By employing an econometrics-based statistical formula, we establish a causal relationship between fossil fuel burning and global surface temperatures, which causally links the overall trends in planetary surface temperature rise, to the overall upward trend in fossil fuel burning. Our study also found that there is a 1-year phase lag of global temperatures to fossil fuel burning.

Keywords

Patterns of climate variability, Climate change, Global warming, Climate warming, Global surface atmospheric temperature anomalies, Sea and ocean surface temperature anomalies, Fossil fuel burning, Attribution of anthropogenic influence in climate change

Introduction

The Earth system absorbs the Sun’s incoming short-wave radiation and re-radiates, stores or exchanges it at different rates via natural processes. For a planetary condition of thermal equilibrium, the amount of total outgoing, long-wave radiation would equal the total amount of incoming, short-wave radiation. If outgoing radiation does not equal incoming radiation, then the planet’s global body temperature will vary both spatially and temporally; so, “climate variability”. Many studies have shown that the climate has been warming over the 20^th and into the 21^st Centuries, and they collectively attribute the warming climate to fossil fuel burning. Recent studies have suggested links between fossil fuel burning and climate warming [1-7]. Numerical model studies, such as Millar et al. [8] and Ekwurzel et al. [4], employed global energy-balance coupled climate-carbon-cycle models which attempted to assess global surface temperatures with the emissions of global carbon production. The relationships were visually correlated with causality assumed. However visual correlations of one curve to the next does not in and of itself establish true attribution, and thus “causality”. Herein, our study is based entirely data based, and employs only the global temperature time series and the fossil fuel burning time series. Attribution, by definition, links cause to effect.

In this study, we address the global surface temperature anomalies (GSTA) of the global surface of the Earth, in the upper panel in Figure 1, the global atmosphere surface temperature anomalies above land (GLSTA), in the middle panel in Figure 1, and the global ocean surface temperature anomalies (GOSTA), in the lower panel in Figure 1, from 1850 through the first half of 2018. The reason we limit ourselves to 2018 is that the outbreak and spread of the Covid viral infection globally, may have effected fossil fuel consumption and we will only address more “normal” conditions of greenhouse gas loading of the oceans and atmosphere. We employ documented surface-temperature-anomaly-data. While much attention has focused on the global surface atmospheric temperature record, as greenhouse gases have built up in the atmosphere, far less attention has been paid to the global ocean surface temperature record in-kind. We address that fact. Data are from the Climatic Research Unit and the UK Meteorology Office, Hadley Centre: http://www.cru.uea.ac.uk/cru/info/.

Figure 1: Monthly averaged time series of GSTA (top), GLSTA (middle), GOSTA (bottom) 01 01 1850-07 31 2018.

The climate system, as represented by surface temperature anomaly data, consists of non-linear (NL) and non-stationary (NS) processes, so we utilize an empirical, mathematical, data adaptive technique to decompose the data. Our mathematical decomposition methodology, the Ensemble Empirical Mode Decomposition (EEMD) first presented by Wu and Huang (2009) [1-10] produces internal, intrinsic modes of variability buried within the temperature data time series. We account for the patterns revealed by the internal modes of variability, relate them to naturally occurring physical phenomena and also compute the overall data time series “trends” which we find do not have a natural causal basis. However, we employ a statistical hypothesis test for determining whether one time series, such as fossil fuel burning, can be useful in forecasting another, specifically global surface temperatures, and thus to predict climate warming, past, present and future; thus establishing causality.

Background and Methodology

Wu and Huang (2009) developed EEMD based on the earlier work of Huang et al. [11-17], which employed the Hilbert Transform (the HT) [18,19], in the development of the Empirical Mode Decomposition (EMD) methodology. We employ EEMD in the decomposition of global surface temperature anomaly data time series. It is of note that a mode-mixing problem existed in the EMD decomposition in which successive IMFs were discovered to occasionally mix with or contaminate each other. To address this issue, Wu and Huang (2009) [9,10] added white noise to the various time series, created ensembles, and the mean IMFs were found to stay within the natural dyadic filter windows, preserving their dyadic properties, leading to stable decompositions of frequency and amplitude modulated internal modes of variability in the record length data. The decomposition reveals temporal internal modes of variability (referred to as Intrinsic Mode Functions or IMFs) which are frequency and amplitude modulated, and reveal non-linear (NL) and non-stationary (NS) signals in the data. The IMFs stack from higher to lower frequencies. We also produce data time series “trends”. In discussing the trend of any time series, we first need to consider the definitions and the methodologies of computing a trend. As such, no conventional simple averaging process can be utilized to reflect what information is buried in the multiple temperature time series as they are non-linear and non-stationary to the naked eye (see Figure 1, for example). This underscores the importance of clearly defining what constitutes a trend. Granger [20] presented an insightful definition of a trend as “a trend in mean comprises all frequency components whose wavelength exceeds the length of the observed time series”. For NL, NS datasets, none of these definitions is mathematically applicable leading to employment of the definition based on the EEMD methodology. With EEMD, the non-oscillation “residue”, which is left after the higher to lower frequency IMFs are removed from the time varying decomposition, becomes the trend of the time series.

Global Ocean and Land Based Atmospheric Temperature Anomaly Time Series

Figure 2 shows eleven IMF modes in the GSTA (also true of the GLSTA and GOSTA) with the 11^th being the overall trends of the land-based atmosphere, the ocean surface and the combination of the two. The IMF modes have their respective physical bases. Mode 1 is several monthly variability. Mode 2 is seasonal variability. Mode 3 is the motion of the Earth on its axis of rotation. Mode 4 is the annual signal. Mode 5 is inter-annual variability. Mode 6 is the dominant signal of the El Nino Southern Oscillation (ENSO). Mode 7 is the quasi-Solar Cycle (10-12 years), centered about 11 years. Mode 8 reflects both the North Atlantic Oscillation (NAO) and of the 22-year Solar Cycle. Mode 9, 60-70 years is the Atlantic Meridional Overturning Circulation Belt (MOC), described by Cunningham et al. [21]. Mode 10, 105-110 years represents the Global Thermohaline Circulation Conveyor Belt [22,23]. Mode 11 is the gravest mode or overall trend of the 167-year time series of total data (Table 1).

Figure 2: The EEMD Mode decomposition of the 1850-2017 time series of the GSTA (shown in the Top Panel.

Table 1: Intrinsic Mode Functions (IMFs) shown in Figure 2, in Months (M) or Years (Y)

We note in Figure 2, that for the GSTA, the IMF modes 2, 3 and 10 have amplitudes of 0.4°C, modes 4 and 6 have amplitudes of 0.3°C, modes 5, 7 and 9 have amplitudes of 0.2°C and mode 8 amplitude of 1°C. Mode 11 ranges between +/- 0.5°C. Thus, all the IMF modes contribute to the total time series in temperature amplitudes in a nominally equitable manner across the range of 0.1 to 0.4°C. This finding suggests that the Planet’s internal, natural modes of variability all contribute significantly to surface temperatures and thus cannot be ignored. Thus, periods of relative warming and or cooling occur naturally by the positive and negative disposition of the natural variability, all riding atop overall atmospheric and oceanic trends, and presented in the Table 1.

In Figure 3 (left panel), the trend of the GLSTA shows a record length total rise of 1.22°C and the GOSTA displays a rise of 0.67°C. The collective GSTA rises 0.88°C. The ocean surface temperature has risen at a much slower rate than the atmosphere over land. This is an excellent example of the power of the EEMD IMF decomposition. The full time series of the GOSTA displays an overall beginning to end of the series increase of 0.75°C, the GLSTA shows a rise of 2.91°C and the GSTA indicates an overall increase of 1.25°C. If connecting lines from start to end of the three time series had been drawn, the overall trends would have been greatly overestimated, demonstrating the failing of traditional methods (see IPCC, 2007) [24] of computing a trend, which are to create regression lines. Thus, the IPCC rates of rise of GSTA overestimate the actual rises in temperatures over land by 0.72°C and by a combined air-sea overestimate of 0.37°C. The IPCC straight-line, regression slope estimates are 0.05°C/decade over the full GSTA temperature record, 0.07°C/decade over the prior 100 years, 0.13°C/decade over the previous 50 years and 0.18°C/decade over the latter 25 years of the record.

Figure 3: (left panel) The overall trends of the GSTA (blue), GOSTA (red) and GLSTA (yellow) time series. The GOSTA raw data are shown in Figure 2 and represents the GLSTA and the GSTA (both not shown). (center panel) The time rates of change or 1st derivatives, of the trends of the GLSTA, GOSTA and GSTA time series. (right panel) The fossil fuel burning curves. Atmospheric carbon dioxide concentrations also shown in far right panel Confirming sources are: T. Boden and R. Andres, The Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6290, USA; and G. Marland, The Research Institute for Environment, Energy and Economics, Appalachian State University, Boone, North Carolina 28608-2131, USA.

In Figure 3 (left panel), we present the time rates of our trends and find that the rates of warming from 1850 through 2017 are 0.713°C/Century for the GLSTA, 0.427°C/Century for the GOSTA, and 0.529°C/Century for the combined GSTA. In the Figure 3 central panel, the 1^st derivatives of the trend curves are all positive, and curving upward indicating that the rate of warming is accelerating. From 1955 to the present the overall warming trend of the GSTA (Figure 3) has been ~0.09°C/decade. Clearly, the rate of warming of air over land has globally been 167% greater than that of the surface of the global ocean. In the Figure 3 right panel, we present the fossil fuel burning time, Carbon Emissions (CE) series from 1751-2014, provided via <http://cdiac.ornl.gov/trends/emis/tre_glob.html>. From 1751 until 1850, global CO2 production was from 3 MMTs in 1751 to 54 MMTs in 1850. In the latter half of the 19^th century, carbon emissions increased considerably, with a dramatic upsurge from 1949 to 2014, reaching a value of 950 MMTs and this resulted in the nonlinear rise of atmospheric carbon dioxide concentrations. The CE was essentially flat from 1751 through the mid latter half of the 19^th century when the change of carbon burning began to be spiky. One could proceed here with cross correlations between the CE and GLSTA, GOSTA and/or the GSTA. However, although the temperature curves all display strong visual correlation with the fossil fuel burning curve, visual correlation does not prove a cause-and-effect relationship or attribution.

Granger Causality relating Carbon Burning to Global Surface Temperature Anomalies

We next employ the Granger Causality Test (GCT) [25] to obtain evidence for the strength of the causal relationship between the carbon burning and atmospheric carbon dioxide concentrations and atmospheric carbon dioxide concentrations and the globle temperature time series. GCT statistically tests for determining whether one time series is useful in forecasting another. Generally regressions reflect mere correlations, but Granger argued that by measuring the ability to predict the future values of a time series using prior values of another time series, causality in economics could be tested. A time series X is said to “Granger-cause” Y if it can be shown, through a series of t-tests and F-tests on lagged values of X (and with lagged values of Y also included), that those X values provide statistically significant information about future values of Y. The idea is that if series {x_t} helps to cause series {y_t}, then past values of {x_t} should improve predictions of series {y_t}. This type of causality is established by first modeling {y_t} in terms of the past values of {y_t} through an autoregressive (AR) process, then adding past values of series {x_t} to create a second model. If the second model is statistically better than the first, then one has established causality in the Granger sense. Testing for Granger Causality in global temperatures has been considered by Attanasio et al. [26], Pasini et al. [27-29], amongst others. The above papers consider more time series than those considered here so they can for example separate out anthropogenic forcing and they also allow for non-stationarity in the temperature series. Our approach differs in that we consider only anomaly series {y_t} and one emission series {x_t}, and we find a stationary AR model for the anomalies after appropriately differencing the series and testing for white noise of the residuals?, which we justify our modeling by use of a time series goodness-of-fit test (see Fisher and Gallagher, 2012). One advantage of our methodology is that our final fitted model can be used to predict the impact of current (future) carbon emissions on temperature. We will approach this in a systematic process.

We first consider establishing a causal relationship between the carbon burning time series ({x_t}) and the ocean surface temperature time series GOSTA ({y_t}). Here we model on the monthly scale by taking the average temperature anomaly for each year as y and the average monthly carbon emission created by taking the yearly value divided by 12. Our first model relates GOSTA to past values of GOSTA. Using Akiake’s Information Criterion [30] we select the order of the auto regression to be three, meaning that each year’s GOSTA is related to the values from the last 3 years. The model is fitted using Gaussian maximum likelihood [31]. We use the goodness of fit test [32] to verify that the AR model adequately models the autocorrelation in the GOSTA series; the p-value of 0.9464 indicates that we have found an adequately fitting stationary model for GOSTA model given in Equation (1):

The above model explains the dynamics of the observed series solely from past-observed values. However, to establish the (Granger) causal relationship we instead add the previous year CE value to the model. The resulting model is given by Equation (2):

We can test for statistical significance of each fitted coefficient using the asymptotic normality of the Gaussian maximum likelihood estimators [31]. In particular, we conclude with a p-value of 0.00009 that the coefficient of x_t-1 is non-zero. In other words, the predictive model for GOSTA is significantly statistically better if the previous year CE is included. Model (2) explains the changes in temperature through a combination of autocorrelation (AR) and the impact of CE. We have thus established causality in the Granger sense. In this analysis, we selected the data beginning in 1950, since the warming trend in the latter half of the 20^th century is well established (cf. Figure 3, left panel). However, a similar analysis could be conducted starting at any point in the past. For example, the same analyses beginning each decade in the first half of the 20^th, i.e., in years 1900, 1910, 1920, 1930, 1940, and 1950, resulted in p-values, 0.00005, 0.0002, 0.00002, 0.0002, 0.003, 0.009, for the coefficient of x_t-1, respectively. In each case we conclude the model using the previous year CE is statistically better than the AR (3) model alone; the carbon emission series significantly improves predictions for GOSTA over the model based solely on past GOSTA values. Regardless of starting time, in the 20^th century, one finds statistical evidence of a causal relationship between CE and GOSTA. The coefficient for x_t-1 in model (2) is as follows. For each additional one-million metric tons of carbon emissions (CE), we estimate an increase in global ocean temperature (GOSTA) of 0.0007°C. The average increase in carbon emissions per year for years 1950 through 2014 is about 130 metric tons per year. Our model estimates an increase of 0.007+°C for each 10 metric ton increase in carbon emissions. The highly statistically significant coefficients of x_t-1 for land based atmospheric temperatures and total global surface temperatures are 0.0117 and 0.0087, respectively.

We next employ our fitted models to predict the global sea surface anomaly (GOSTA), the land atmosphere (GLSTA) and combined global surface temperature anomalies (GSTA) for 2015. Figure 4 shows the observed anomalies for years 1950 through 2014. The prognostic values are remarkably accurate. In the plots, we mark the predicted value from our fitted model, the upper and lower 95% prediction limits and the observed value for Year 2015. We conducted multiple-year lag experiments between CE and the surface temperature time series, beginning with 10 year down to 1 year lags (not shown except for the latter). We find that the model, which uses both past values of the anomaly series and the previous year’s carbon emission ( a 1-year lag), provides excellent predictions for the observed anomalies of the ocean surface, atmosphere on land and the combination therein for 2015. This provides further empirical evidence of Granger Causality relating previous year carbon emissions to sea surface, atmosphere on land and the combination temperatures on a global scale. We utilized the 2014 and 2015 data because 2014 is the last year for which we were able to obtain Fossil Fuel Burning data from the website provider at the time that this study was conducted. The results presented above provide a pathway and portend to future increases in global surface temperatures given anticipated increases in fossil fuel burning, GOSTA, GLSTA and GSTA as a function of CE. GOSTA is increasing at the rate of 0.0007°C/ Million Metric Tons of CE. GLSTA is increasing at the rate of 0.00117°C/Million Metric Tons of CE. Thus, the GSTA is increasing at the rate of 0.00087°C/Million Metric Tons of CE. Presently we are on a trajectory to reach 10⁴ Million Metric Tons/year of CE by years 2020 to 2022. These numbers are less foreboding than the straight-line estimates of both the IPCC and NIPCC, but are nonetheless very noteworthy.

Figure 4: Global Surface Temperature Anomalies from 1949-2014 with Granger Causality Predicted (X) versus Actual Temperatures (O) for 2015 and upper and lower 95% confidence limits. (left panel) is for the GOSTA. (middle panel) is for the GLSTA. (right panel) is for the GSTA.

Discussion and Conclusions

Mathematical relationships between fossil fuel burning and surface temperatures in the oceans and over land are presented. The statistical relationship curves reveal strongly that there is a one-year phase lag between global carbon loading via fossil fuel burning and planetary surface temperature rise, different from Ricke and Caldeira [33-41] who proposed that planetary temperatures changed about a decade after burning. In fact, robust relationships are presented between the GLSTA, GOSTA and GSTA, and their past time series, and the CE time series. Via Granger Causality, these surface temperatures are predicted very accurately from fossil fuel burning a year earlier. Thus, the conclusion we reach is that we have proven that there is “attribution” between fossil fuel burning and climate warming. In 2007, the IPCC was awarded a Nobel Prize for its comprehensive analyses of global climate change, including a visual-correlative-comparison of fossil fuel burning and temperature rise. However, a visual correlation does not prove “causality”. In 2003 C.W.J Granger was awarded a Nobel Prize for his work in econometrics theory and applications. We invoked “Granger Causality” to attribute the overall trends in global surface warming to fossil fuel burning and carbon emissions (https://en.wikipedia.org/wiki/Clive_Granger).

Acknowledgement

The authors thank Dr. Thomas S. Malone (former member of the U.S. National Academy of Sciences, now deceased), for having encouraged this study. He observed that cause and effect was necessary to prove attribution. The authors thank Coastal Carolina University for supporting this study.

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DOI: 10.31038/GEMS.2023514

Abstract

The human activities have strongly altered size, age, sex ratio, fecundity, feeding nature and biodiversity of fishes from the freshwater ecosystems over the world especially riverine division. During study period 548 specimens of Cyprinus carpio were collected from February 2019 to January 2020 in fish landing centre at Sirsa from the lower stretch of the Tons River at Prayagraj, Uttar Pradesh, India. The size of fishes varied from 97 to 687 mm (total length). The maximum size of fishes indicated that the stock of C. carpio in the Tons River was in healthy condition. The 251-290 mm size group was most dominated (16.42%) compared to 211-250 mm (14.78%) and 291-330 mm (12.96%) in total exploited stock. The lower size group was maximum exploited with 57.83% from the Tons River at Prayagraj. Higher size group contributed minute proportion with 4.74% in the exploited stock. The exploitation pattern was systematic in all size groups. Current exploitation pattern is systematic and healthy form with environmentally friendly sourcing of food.

Keywords

Size composition, Stock, Exploitation pattern, Ecosystem, Tons River, Cyprinus carpio

Introduction

Fish size composition is an essential component of river and stream ecosystem and represents an evident of structure, function, depth and health of stream/river [1-5]. Mostly large size and perennial rivers has large size of fishes in lotic water bodies [6-9]. The fish exploitation is an economic activity governed by social needs, food security and pressures [10-14]. Freshwater fishing is a chief foundation of income and protein for the riverine populations of most tropical regions [15-20]. Cyprinus carpio (Linnaeus, 1758) or Common carp is an omnivorous and bottom feeder fish species. It is distributed throughout countries in Asian countries as like India, Pakistan, Bangladesh, Burma and Nepal and also globally spread [21,22]. It is economically important fish species from the Tons River and also Ganga River system, and supports an important commercial fishery in rivers, reservoirs, lakes and even in culture ponds [23-25]. C. carpio is a non-native fish species for India. Non-native fishes are helping for homogenization of fish faunas, increasing of diversity and create pressure (example food, space, breeding ground, oxygen, infection and survival of organisms) for indigenous species or native species [26-30]. The fish are often key elements in the environmental planning [31-34]. The present study was thus undertaken to estimate size composition and health of the stock of C. carpio from the Tons River at Prayagraj, Uttar Pradesh, Central India. This study will help in formulating the fishery management policies of C. carpio from the Tons River and to update the knowledge in this field.

Material and Methods

Climate and Characteristics of the River

The climate of this region (Tons River basin) is marked by mild cold during winter and intensive heat during summer. The monsoon season is July to September month. Sometimes winter rainfall is also recorded. The Tons River is essentially a hilly stream arising in the Kaimur hills of the Vindhyan range, Madhya Pradesh, India. The Tons River drains the Bundelkhand geographic region of central India. Bundelkhand lies between the Indo-Gangetic Plain to the north and the Vindhya Range to the south. It is a tributary of the Ganga, which forms confluence at Sirsa near Meja in the Prayagraj district. Tons River lies between latitude 24° 0^’ to 25° 16^’ 54^” North and longitude 80° 26^’ 45^” to 82° 04^’ 57^” East. It banks are lined by deep ravines and the bed is rocky. Agriculture and human settlements were the major land use category in its catchment. During study period 548 specimens of Cyprinus carpio were collected from February 2019 to January 2020 in fish landing centre at Sirsa from the lower stretch of the Tons River at Prayagraj, Uttar Pradesh, India. Size composition (total length) varied from 97 to 687 mm. Drag net, cast net, gill net and hook and line were used by fishers/fishermen to catch the fishes in the river. A total of 548 fish samples (male and female) were collected and analyzed. The total length (mm) from the tip of snout to the end of caudal fin rays was measured by measuring scale. The obtained data from the river was classified into a series of size groups of 40 mm intervals. The number of samples calculated according to size group then converted into percentage.

Result and Discussion

Current exploitation pattern is systematic and healthy form with environmentally friendly sourcing of food. The size composition of C. carpio was varied from 97 mm to 687 mm of total length of fishes with majority between 251 to 290 mm from the lower stretch of the Tons River at Prayagraj, Uttar Pradesh, India (Figure 1). The large size of fishes also recorded in the Tons River in respect of river length. The maximum exploitation was recorded in 251 to 290 mm size group with 16.42%. Minimum exploitation was observed with 0.18% in 651-690 mm size group. Exploitation is an economic activity governed by social needs and pressures. Lower size groups 91-130 mm, 131-170 mm 171-210 mm, 211-250 mm and 251-290 mm were shared in exploited with 5.83%, 8.94%, 11.86%, 14.78% and 16.42%, respectively. Middle size groups 291-330 mm, 331-370 mm, 371-410, 411-450 mm and 451-490 mm were shared in exploitation 12.96%, 8.39%, 7.48%, 5.29% and 3.28%, respectively. Higher size groups 491-530 mm, 531-570 mm, 571-610 mm, 611-650 and 651-690 mm were contributed in exploitation with 2.19%, 1.28%, 0.73%, 0.36% and 0.18%, respectively (Figure 1). The lower size group was maximum exploited compared to middle and higher size groups from the lower stretch of the Tons River at Prayagraj. The experienced mature female fish stock was healthy in the river in monsoon season but very high fishing pressure we observed in this season. On the basis of data, it is observed that lower size group was maximum exploited with 57.83% at Prayagraj. Middle size group was exploited with 37.40%. Higher size group shared sizeable proportion with 4.74% in exploited population (Figure 2). The results also indicated that the exploitation was systematic in lower size group to higher size group. If exploitation is systematic then it is indication of healthy and heavy recruitment in near future. The over exploitation and non-targeted fishing is the biggest problem of riverine fishery [35-37]. The fishing pressure, mesh size, size of nets and fishing technique (example degree) are responsible for increasing or decreasing of total size of fishes and recruitment in the lotic ecosystems [14,38-42]. Fishing pressure changes the biodiversity, size composition, growth rate, age composition, sex ratio, income of fisher and maturation [43-45]. Non-native fishes are also changed selectivity of gear due to nature, dwelling behavior and ecological condition [28,46,47]. The growths of fishes are slightly checked by heavy metals accumulation in the body of fishes [48-50] (Insert Fig 1-2).

Figure 1: Size composition and exploitation pattern of C. carpio from the Tons River at Prayagraj, Uttar Pradesh

Figure 2: Exploitation pattern of C. carpio according to major group-wise from the Tons River at Prayagraj, Uttar Pradesh

Conclusion

It may be concluded that the present research work provides an important baseline study of this fish (Cyprinus carpio). Size composition indicated that the stock of C. carpio from the Tons River was in healthy condition and exploitation was also systematic form. Present condition was recorded due to sustainable exploitation of this species in the river. [20,51,52] stated that the when sustainably harvested or farmed, inland fish can be considered part of the green food movement for more environmentally friendly sourcing of food.

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