It is stated that about 90 percent of the infrared heat reflected upwards by the earth’s surface after absorbing sunlight is then absorbed by atmospheric greenhouse gases (GHGs) and radiated back to the earth’s surface [1]. This is referred to as “heat trapping” or greenhouse effect. Human activities have increased atmospheric GHGs by over 48% since industrialization, which is believed to expand the greenhouse effect. It is also stated that “there’s a better than 95 percent probability that human-produced greenhouse gases such as carbon dioxide, methane and nitrous oxide have caused much of the observed increase in Earth’s temperatures over the past 50-plus years” [1]. From these, it seems that GHGs are the culprit and solar energy is the only energy source that GHGs trap and reflect back to the earth’s surface in the form of infrared radiation, leading to the warming, but neglects the fact that waste heat (including residual heat) enters the environment from human activities in the context.

Although the mainstream perceives that GHGs should be held accountable for the warming based on the assumption that they form a “blanket” covering the earth, exerting greenhouse effect and preventing heat radiations from escaping to outer space, thus triggering global warming, this doesn’t seem to be supported by the facts: 1) GHGs only share about 0.04%, a very trace amount, in the atmosphere; 2) GHGs have different specific gravities (air = 1, CO₂ = 1.5189, CH₄ = 0.5537, N₂O = 1.530, O₂ = 1.1044 [2]), randomly distribute in the atmosphere spatially with CO₂ and N₂O mostly staying at the ground level, meaning that they cannot form a “blanket” at a certain level with such a trace quantity; 3) absorbing and reflecting infrared radiations and other wavelengths of light are not the unique characteristics of GHGs, everything with absolute temperature over zero degree can absorb and emit radiations at certain wavelengths. Therefore, other compositions in the atmosphere can also absorb and reflect radiations. Additionally, GHGs should also absorb certain wavelengths of solar radiations. They then emit and reflect radiations equally upwards and downwards because of their statistically symmetrical distribution in the atmosphere, thus the solar energy reaching the earth’s surface should be reduced after GHGs absorb its infrared, causing a cooling effect eventually, if the theory were valid i.e., GHGs trap and reflect heat.

Further, if GHGs were responsible for the warming, they would articulate quantitively the warmth in surface air, in land surface and sea surface as well as the sea level rise, i.e., a unique relation Δt_gw (or ΔL_s) = f(C_ghg) could exist between the atmospheric GHG concentration (C_ghg) and the global (air, land, ocean) warming (Δt_gw) as well as sea level rise (ΔL_s). However, the fact is that no single model can well simulate the air temperature changes, thus assembling all “satisfactory” models’ simulations together, and taking their mean become an approach, although such an approach doesn’t make common scientific sense (because if variables x and y correlate, theoretically only one relationship y = f(x) exists), the simulated results still cannot align well with the observations (refer to Figure 9.8 in Reference [3]). Quantitatively explaining the temperature changes in land surface and sea surface as well as sea level rise faces more challenges.

On the other hand, exploring the relation between CO₂ concentration and the surface air temperature anomalies finds that no correlation exists based on the datasets from [4] [5] as shown in Figure 1, which exhibits the CO₂ concentration (in ppm) and annual mean air temperature anomalies from 1880 to 2011.

The time span between 1880 and 2011 can be divided into four periods according to the changes in annual mean anomalies: 1) 1880-1909 anomalies decreasing period; 2) 1910-1944 anomalies slight increasing period, 3) 1945-1964 anomalies very slow increasing period and 4) 1965-2011 anomalies rapid increasing period as shown in the embed small figures on top of Figure 1. Clearly, the air temperature anomalies and atmospheric CO₂ concentration don’t correlate. However, a strong pseudo-relation does exist in the last period since 1965. This finding is similar to Gosselin’s analysis [6]. Therefore, it is unlikely that there is a single cause-effect between CO₂ (also GHGs) and the global warming, and even just from the pseudo-relation during the last period since 1965 to draw that CO₂ has incurred the warming is farfetched because CO₂ is a concurrent by-product with waste heat from the increased fossil fuel combustions. Adversely, CO₂ and waste heat should correlate well (their relationship will be explored later). The strong pseudo-relation between annual mean anomalies and CO₂ since 1965 implies that waste heat may correlate to the air anomalies and may be the real contributor to the temperature changes, or the global warming.

The GHG-based climate change theory has been facing strong challenges, although a large number of models have been developed.

In addition, water vapor is a far more concentrated gas than GHGs in the atmosphere, it retains or traps much more heat than GHGs due to its greater specific heat capacity (SHC). Water on the earth and its vapor in the atmosphere largely regulate the temperature of the environment we live in.

The climate system consists of four components: air, land, oceans, and ice. In the previous study [7] [8], though sea ices are taken into consideration by retrieving their melted quantity from reported sea level rise, it is better to accurately contemplate sea level rise reversely from ice melting.

Global warming is a basic thermodynamic phenomenon. Waste heat from human activities can induce direct warming and ice melting. There should be unique determinative relations between the waste heat and the warming in the air, land, oceans, and ices melting as well as the sea level rise.

According to the Law of Conservation of Energy or the First Law of Thermodynamics, energy can be transformed from one form to another or others (e.g., coal through combustion to heat, electricity, and chemical energy contained in new products), but cannot be created nor destroyed. It is obvious that while being used, part of the energy is inevitably transformed into a non-useful form as residual or waste energy that dissipates into the environment.

Usually, we only consider how and how much energy is used, but are less concerned about where the energy goes eventually. In fact, in every energy application, it experiences a form transformation: from one form to another or others. For example, when burning coal to boil water, the energy released from combusting coal is converted to: 1) heat energy that heats up and boils the water, 2) heat energy that heats up the boiler case that eventually escapes into the environment and 3) the energy that disperses into the environment along with flue gas and water vapor. Among these three parts, the last two are obviously a kind of waste heat (or waste energy) that is useless. Even for the first part, the heat energy retained in the hot water is eventually released into the environment too as residual heat, whether it is used for heating or for drinking. Thus, all these three parts enter the climate system, and are referred to as waste heat.

Similarity exists in burning natural gas in the furnace, running air conditioners, cooking/baking, etc. in residential and commercial sectors from which the amount of waste heat is almost the same as the amount of energy consumed [7] [8].

In transportation, only a small part of consumed energy is used to move loads and vehicles themselves for useful work, whereas the rest is dispersed into environment through friction (which is then converted to heat) and sensible waste heat from radiator, hot hood, and tail gas, etc. It’s estimated that about 75% of the used fossil fuel energy in transportation is dispersed into the environment as waste heat [7] [8].

In industries, the energy consumed is converted to several forms such as electricity, chemical energy retained in products and heat in addition to waste heat.

The widely used concept of energy efficiency cannot tell exactly how much energy is ultimately converted to useful work or retained in products, it only indicates how much of the input energy can be produced out during a process. For example, when boiling drinking water using a modern kettle with an efficiency of 90% (obviously it is very efficient), 90% of the consumed energy is used to heat the water. However, it is unclear how much energy will be still contained in the boiled water at its final state. Few people realize that almost all of this very 90% of the consumed energy is also released into the environment eventually, in addition to the 10% already entered the environment even during the boiling process. Cooking is another similar example. Thus, a new concept to describe how much of the consumed energy is really converted to useful work or energy retained in products is necessary, which is referred to as energy’s effective conversion efficiency (EECE) [7] [8]. It is the EECE that can clearly tell how much consumed energy is dissipated to the environment during a process.

As analyses shown in [7] [8], in the residential and commercial sectors, almost all the energy consumed is eventually dissipated into the environment. In transportation, only about 25% of the consumed fossil fuels is converted to useful work by considering the different levels of technologies across the world, and the rest, i.e., 75%, is wasted into the environment through friction and sensible heat. In industries, it is assumed that the entire EECE is about 30% across all sectors.

According to BP [9], industries consume about 51% of the global energy, residential and commercial 29% and transport 20% (these shares may vary from time to time, but the variance should be reasonably small). Thus, it is estimated that the global EECE is about 20%, which means about 80% of the energy consumed globally enters the environment as waste heat [7] [8]. This is reasonable if considering the different technology levels in the world, and even in the USA with the most advanced technologies, the waste heat is reported to be about 67% of the consumed energy because of the inefficiencies in energy application processes, equipment [10].

BP has adjusted its estimate of a standard power plant’s thermal efficiency from 36% in 2000 to 40.4% in 2019 [11] [12] in the last two decades, while remaining 36% for the period of 1965-2000, to reflect the technology advancements. Nevertheless, from the perspective of global energy application, this adjustment would not affect much on the global EECE since the basics of the energy application processes have not been changed radically. Therefore, assume the EECE is 20%, although during earlier years (say, 1965 to 1979, only after that point climate change has become more recognized) a lower EECE might exist because of less advanced technologies, especially in developing countries.

Besides, countless flaring and spontaneous firing of surface coal and methane from the natural reservoirs, volcanic eruptions, forestry wildfires and various chemical fuel applications (such as space explorations, military activities, etc.) also send a huge amount of heat to the climate system, contributing to the global warming.

Equivalent Climate Change Model (ECCM) has been developed to explain the warming phenomena, consisting of respective equivalent climate change boundary layers to simulate temperature changes in surface air, land surface, and seawaters surface [7] [8]. The results show that the simulated temperature changes are well consistent with those observed anomalies in air, land, and oceans, respectively. However, ice melting was not considered in the same way, instead, it was considered through the observed sea level rise based on NASA’s assumption that one-third of the rise is from sea water warming and two-thirds are from ice melting [15] [17]. In fact, this is not an appropriate approach and cannot fully explain how ices respond to human activities and how ices melt and contribute to sea level rise.

In the present study, melting of both ices (glaciers, icebergs, and ice shelves) and sea ices (i.e., ice sheets and covers) is considered thermodynamically based on the SHC and latent heat of fusion. Incorporating this into the existing ECCM [7] [8] constitutes a new climate change thermodynamic model (CCTM) that includes a thermodynamically equivalent climate change surface air layer (or column), a thermodynamically equivalent climate change land surface layer, a thermodynamically equivalent climate change seawaters surface layer, and the melting of glaciers and sea ices. They absorb the waste heat from human activities according to their respective SHC.

The temperature change in surface air:

Δ t a = 3 Δ H a 4 π [ ( R 0 + h ) 3 − R 0 3 ] ⋅ ρ a ⋅ C p a (2)

The temperature change in land surface:

Δ t l = Δ H l S l D l ρ l C p l (3)

The temperature change in seawaters surface:

Δ t w = Δ H w S w D w ρ w C p w (4)

The amount of sea ices melted due to the absorbed heat:

M s i = Δ H s i L p s i (5)

The amount of glaciers melted due to the absorbed heat:

M g l = Δ H g l L p g l (6)

where,

R₀ Earth radius, 6371 km

h The depth of the surface air layer in atmosphere from the earth surface

S_w Seawaters surface area, 361,800,000 km²

D_w The depth of the seawaters surface layer

ρ_a Air density under normal pressure

C_pa Air SHC under normal pressure, or the isobaric heat capacity

∆H_a The heat absorbed in the surface air layer corresponding to the temperature change ∆t_a

∆t_a The temperature change in the surface air layer after experiencing heat change ∆H_a

ρ_w The seawaters density

∆H_w The heat change in seawaters surface layer corresponding to the temperature change ∆t_w

∆t_w The temperature change in the seawaters surface layer after experiencing heat change ∆H_w

C_pw Seawaters SHC under normal pressure

ρ_l The land (soil) density

∆H_l The heat change in land surface layer corresponding to the temperature change ∆t_l

∆t_l The temperature change in the land surface layer after experiencing heat change ∆H_l

C_pl Land (soil) SHC under normal pressure

S_l Land area on the earth surface

D_l Depth of land surface layer

M_gl Annal amount of melted glaciers (i.e., pure ice)

C_pgl Glaciers (i.e., pure ice) SHC under normal pressure, 2.11 kJ∙kg⁻¹∙K⁻¹

L_pgl Glaciers (i.e., pure ice) latent heat of fusion at constant pressure, 333.4 KJ∙Kg⁻¹

M_si Annual amount of melted sea ices

∆H_si Annual heat amount absorbed by melted sea ices

C_psi Sea ices effective SHC

L_psi Effective latent heat of fusion of sea ices at constant pressure.

Glaciers, including icebergs and ice shelves floating on oceans but originated on land [18], and the landfast ice, formed from pure water, melt at zero degree Celsius (0˚C), have a SHC of 2.11 kJ∙kg⁻¹∙K⁻¹ and latent heat of fusion of 333.4 KJ∙Kg⁻¹ [19] .

As described in [7] [8], the feature of this study is using SHC to allocate heat entered the climate system from human activities to the components: air, land, oceans, sea ices and glaciers.

Sea ices (including ice sheets and covers) behave very differently than pure ice because they contain brine and salts. They melt at different temperatures than they form. Seawaters freeze at about −2.0˚C [20] - −1.8˚C [21] to form sea ices due to the salinity. The resulting ices trap brine that either precipitates or drains out of the ice crystal lattice [22], forming brine pockets and eventually flowing into the oceans again. As a result, the bulk salinity in sea ices is much lower than that in seawaters (34 - 35 parts per thousand, i.e., ppts). For old and matured sea ices it is estimated the salinity ranges from 4 to 12 ppts (4 ppts is widely used for bulk sea ices) although some have lower or greater values, while for new ices or those at the bottom of ice sheets (or covers) the salinity may be greater, for example, new ices can be of between 12% - 20% [23] when growing from seawaters with normal salinity of 32 - 35 ppts or greater. Further cooling during winter reduces salinity. Therefore, it is reasonable to consider that the salinity of sea ices melted during the melting season has reduced gradually from early years when more new ice was formed around the matured ones, and the amount of new ice reduces recently as the global warming proceeds.

Similar to pure ice, sea ices are resistant to melting because it needs more heat (i.e., latent heat of fusion) to go through the phase transformation. Because of very limited knowledge and data on sea ices behavior and physicochemical properties, details of the formation and ablation are not very clear yet, and much less is known about how sea ices melt in the real ocean environment, however the process is very complicated. Sea ices melt at distinguishingly higher temperatures than the freezing points (−2.0 [20] - −1.8˚C [21]). From Spring to Autumn seawaters and surface air over them become warmer, it is hypothesized that when the in-situ temperature in the bulk sea ices exceeds a point at which the ice - brine pocket remains at microscopic level equilibrium at the interface [19], the melting process initiates, meltwater diluting the brine solution in the pocket, enlarging the brine flux channel and accelerating the ice melting, as a result, increasing sea ices melt. Towards summer, temperature becomes higher and the melting speeds up. Sea ices can melt completely at a temperature (T_f) determined by the following equation [19],

T f = m m ∗ S s i (7)

For example, the potentially complete melting temperature is about ?0.22˚C when the salinity (S_si) is 4 ppts and enough heat energy is available. However, due to the vast volume of sea ices and relatively limited heat availability, only a part of the ices can melt before getting into winter to re-form ices.

As such, it is anticipated that no evident phase transformation (or fusion) from sea ices to seawaters can be observed, at a certain temperature, that can be expected by a certain value of latent heat of fusion, instead, a transitional process exists that merges the phase transformation into a melting process. Under such a situation, using sea ices’ effective specific heat capacity (ESHC) [19] [22] is more appropriate. ESHC includes the latent heat for phase transformation (i.e., fusion) that accompanies temperature change in sea ices [19]. Furthermore, the latent heat of fusion is a function of salinity and temperature [19] [22] [24].

According to Ono [24], sea ices’ ESHC can be expressed as below:

C p s i = ( 0.505 + 0.0018 T + 4.3115 S s i T − 0.0008 S s i + 0.00002 T S s i ) ∗ 4.1868 (8)

Similarly, using effective latent heat of fusion to describe sea ices heat requirement during phase transformation is advisable. Sea ices’ effective latent heat of fusion can be expressed as below according to Petrich et al. [19]:

L p s i = L p g l − C p g l T + C p g l m m S s i − m m L p g l S s i T (9)

Or simply,

L p s i = 333.4 − 2.11 T − 0.1142 S s i + 18.0403 S s i T (9a)

where,

m_m Water’s freezing point depression as a function of salinity S_si, −0.054 K/ppt,

S_si Salinity of sea ices, in parts per thousand (ppts),

T Temperature of sea ices in degrees Celsius (˚C), T < 0˚C.

Assuming the values of salinity of sea ices are as indicated in Table 1 for this study period concerned, where they are decreasing gradually due to less formation of new sea ices, and this decrease escalates in recent decades as warming accelerates.

Meanwhile, the ESHC of sea ices at −2˚C (the most conservatively highest temperature at which it is in a steady state), the melting point temperature for potentially melting completely as well as the latent heat of fusion at the melting point that are calculated from Equations (7)-(9a) are also included in Table 1.

For air, its SHC depends on the temperature and the moisture content, and the latter can be derived from relative humidity. Air SHC is calculated by the equation in [25] with the procedures prescribed in [8], i.e., obtaining the absolute humidity from relative humidity and then water vapor’s SHC at the corresponding temperature. Table 2 shows the surface air’s temperature, relative humidity, absolute humidity, water vapor’s SHC and finally the air’s SHC. The water vapor’s SHC at 20˚C is obtained by simple linear interpolation between 2˚C (i.e., 275 K, 1.859 KJ∙Kg⁻¹∙K⁻¹) and 27˚C (i.e., 300 K, 1.864 KJ∙Kg⁻¹∙K⁻¹) [26]. The global average of air relative humidity and temperatures are obtained from the respective datasets [27] and [28] on an annual basis.

For seawaters, its SHC is determined by its surface temperature that is averaged from the datasets [29] annually, and the corresponding SHC is about 4.004 KJ∙Kg⁻¹∙K⁻¹ at the corresponding temperature range of 13˚C - 14˚C [30] as shown in Table 3.

The land’s SHC is assumed to be 0.83 KJ∙Kg⁻¹∙K⁻¹ from [31].

Therefore, the relative strengths of SHCs (or simply SHC shares) of air, seawaters, land, sea ices, and glaciers in the climate system are summarized in Table 4 for the study period, which determines how much heat will be allocated to each component respectively.

Air temperature changes calculated by using Equation (2), the allocated waste heat energy entered the surface air boundary layer, the air density, and SHC in Table 2, are shown in Figure 3 at different layer depths, in which NASA’s annual mean of observed anomalies and 5-year moving Lowess smoothing [33] are

also exhibited.

From Figure 3, it is clear that in most of the time, especially the last four decades, the observed anomalies are very consistent with the calculated results at the surface air boundary layer depth between 20 - 30 meters, and the Lowess smoothing anomalies [33] are much closer to that calculated at the depth of 25 meters.

Therefore, it is reasonable to draw that a surface air column with a depth between 20 - 30 meters can be considered equivalent in simulating its warming trend, with a 25-meter depth being a representative. However, before late 1970s this is not true, observed anomalies are much less than those calculated.

Plotting the calculated results of air temperature changes at the surface air boundary layer depth of 25 meters, NASA Annual Mean and Lowess smoothing values [33] with the energy entered the surface air obtains the left in Figure 4, in which the corresponding trend lines are also exhibited. The black solid line on blue dots represents the strongest relation between the simulation results and the energy entered the air with a correlation coefficient of 1, which is understandable. The green triangles and dash line represent NASA’s annual mean anomalies, the red squares and dot line represent Lowess 5-year smoothing values. It is noticeable that the red dot line and the green dash line are almost overlapped, with their respective correlation coefficients being 0.9361 and 0.8769 (Figure 4, Left), advising that the correlations between these observational values and the energy quantities are very strong. Furthermore, these trend lines of observational values are also very close to that of the simulations.

As indicated earlier, obvious differences exist between the observations and the simulations until late 1970s. Excluding these data points and only taking the rest points since 1980 is indicated at the right in Figure 4. It can be seen that while the simulations with the energy entered the surface air still show the strongest relation with the correlation coefficient of 1, NASA’s-Annual Mean

and NASA’s Lowess smoothing against the energy entered the air still exhibit respectively strong relations with big correlation coefficients of 0.8669 and 0.9618, and their trend lines are much closer to that of the simulations, and even they almost overlap each other, compared to those in the left figure for the period of 1965-2019. This is not by accident.

All these suggest that the temperature changes or anomalies in the surface air are strongly linked to the extra energy (i.e., waste heat here) entered the air, providing direct evidence that energy beyond the earth’s energy budget balance entered the surface air caused the air temperature increase. This approach can be used to predict the future surface air temperature rises.

Simulations of land surface temperature changes by using Equation (3) and the energy entered the land in Table 5 are shown in Figure 5, in which NASA’s annual mean and 5-year Lowess smoothing of observed land temperature anomalies [33] are exhibited as well.

Clearly Figure 5 shows the similar trends to surface air temperature changes as seen in Figure 3. Before late 1970s the observed anomalies deviate obviously from the simulations, with more negative anomalies; during the 1980s and 1990s the observed anomalies fluctuate between the simulations at a boundary layer depth of 0.015 and 0.15 meters, while in the last two decades the observed anomalies fall within the simulations between boundary layer depths of 0.0175 and 0.03 meters, and a depth of 0.025 meters can be a good representative since 1980.

These variations may have reflected the changes in methods and technologies of measurements as well as in natural conditions on the land surface such as vegetation covers as well as the effect of ice melting (the land is the most susceptible to any heat changes because of its smallest SHC among the components).

Plotting the simulation results at the boundary layer depth of 0.025 meters, observed anomalies (NASA_Land_Annual_mean and NASA_Land_Lowess) against the energy entered the land surface are shown in Figure 6: Left―the data from 1965-2019 and Right―the data from 1980-2019, revealing clearly that strong relationships exist either for the NASA_Land_Annual_mean vs the energy or the NASA_Land_Lowess vs the energy, and both have big correlation coefficients, while the simulation’s correlation coefficient is 1.

Again, after excluding the data before 1980, the observational trends (NASA_Land_Annual_mean and NASA_Land_Lowess) in the right figure of Figure 6 are much closer to the simulations than shown in the left. All these indicate that strong relationship exists between the land surface temperature change and the energy absorbed. This approach can be used to predict the future land surface temperature rises.

Simulations of sea surface temperature changes by using Equation (4) and the energy entered sea surface waters in Table 5 are shown in Figure 7, in which NASA’s annual mean and 5-year Lowess smoothing of observed sea surface temperature anomalies [33], NOAA’s annual anomalies [35] are exhibited too.

Similarly, before late 1970s the observed anomalies deviate obviously from the simulations, with more negative anomalies. During 1980s and 1990s the observed anomalies fluctuate between the simulations at boundary layer depth of 0.03 and 0.1 meters, while in the last two decades the observed anomalies fall

within the simulations between boundary layer depth of 0.04 and 0.08 meters, and a depth of 0.06 meters can be a good representation since 1980. These variations may have reflected the changes in methods and technologies of measurements, in natural conditions of the sea surfaces such as the chemical and physical properties of surface seawaters as well as the effect of ice melting.

Plotting the simulation results at the seawaters boundary layer depth of 0.06 meters, observed anomalies (NASA_Ocean_Annual, NASA_Ocean_Lowess and NOAA_Ocean_Annual) against the energy entered the seawaters are shown in Figure 8: Left contains the data from 1965-2019 and Right contains data from 1980-2019, revealing clearly that strong relationships exist either for the NASA_Ocean_Annual vs the energy or the NASA_Ocean_Lowess vs the energy, or NOAA_Ocean_Annual vs the energy. All these observed anomalies trend lines have big correlation coefficients (about 0.80 or greater), and the simulation’s correlation coefficient is 1.

Additionally, it is very interesting that the NOAA_Ocean_Annual trend line is almost parrallel to the simulation one (cf. their slopes), which is important and supports that the temperature changes are due to the contribution of energy. In general, all these indicate that strong relationship exists between the sea surface temperature changes and the energy absorbed.

This approach can be used to predict the future sea surface temperature rises.

In this study, the relationship between sea level rise and the intake energy associated with ices melting and seawaters warming has been explored. The ices include sea ices (i.e., ice sheets and covers), glaciers (including landfast ices).

Based on energy absorbed respectively by sea ices and glaciers as listed in Table 5, the amounts of melted sea ices and glaciers by Equations (5) and (6) are shown in Figure 9.

Sea level rise consists of the following: 1) added depth from melted ices (or meltwaters), 2) added depth from meltwaters due to thermal expansion from melting point to the average of global sea surface temperatures, 3) added depth of meltwaters due to thermal expansion from seawaters warming and 4) added depth due to thermal expansion of bulk seawaters warming.

Specifically, the contribution from sea ices melting can be calculated as below:

1) added depth from melted sea ices;

2) added depth from melted sea ices due to thermal expansion from melting point (Table 1) to the average of global seawater surface temperature. The average seawater surface temperature during the melting season (May ~ Sept) is determined from the NCEI’s ERSST V4 datasets [29] as shown in Table 3;

3) added depth from melted sea ices due to thermal expansion from the surface seawaters warming, i.e., seawater surface temperature rising as discussed in the foresaid section “Sea Surface Temperature Change”. The value of temperature rising is that calculated at the sea surface boundary layer depth of 0.06 meters.

The contribution from glaciers can be calculated as below:

1) added depth from melted glaciers;

2) added depth from melted glaciers due to thermal expansion from melting point (i.e., 0˚C) to the corresponding global average seawater surface temperature (Table 3). The corresponding average seawater surface temperature at the melting seasons (May ~ Sept) is determined from the NCEI’s ERSST V4 datasets [29];

3) added depth from melted glaciers due to thermal expansion from the surface seawater warming, i.e., seawater surface temperature rising as discussed in the foresaid section “Sea Surface Temperature Change”. The value of temperature rising is that calculated at the seawater surface boundary layer depth of 0.06 meters.

Seawaters (including the deep waters) are subject to thermal expansion due to the cumulated entrained heat energy. According to Luann D. and Rebecca L. [36], “the 1993-2020 heat-gain rates (in oceans) were 0.37 - 0.41 Watts per square meter for depths from 0 - 700 meters, depending on which research group’s analysis you consult. Meanwhile, heat gain rates were 0.15 - 0.31 Watts per square meter for depths of 700 - 2000 meters. For depths between 2000 - 6000 meters, the estimated increase was 0.06 Watts per square meter for the period from June 1992 to July 2011”, the average temperature rise due to this heat gain is estimated about 3.23446E−05˚C per year for the full ocean depths. Suppose this temperature rise applies to the entire period of this study and a depth of 2000 meters is taken as a representative for the entire ocean depths, seawaters’ thermal expansion coefficient is 1.57E−4 K⁻¹ under the pressure of 2000 decibars (in oceans one meter depth is about equivalent to 1 decibar) and 5˚C at a salinity of 35 ppts [37].

The simulated global sea level rise (GSLR) that accumulates annually is shown in Figure 10, where the measured global mean sea level rise (GMSL, mm) [38] is also exhibited. Clearly, they have similar trends. Since the GMSL is an accumulated record since 1880, and in 1965 its value is 86.8 mm, adjusting the GMSL by subtracting 85 mm can easily compare with the simulations which start from 1965. The adjusted GMSL (i.e., GMSL-85) is also shown in Figure 10. Clearly at an early time the simulation is very close to the measurements, however, an increasing departure from the simulation appears with time especially in the last two decades. The potential reasons for this departure may be attributed to 1) volcanic eruptions, wildfires, coal fires [39], natural gas fires and explosions [40] [41], flares as well as various chemical fuels used in military and space explorations, etc.; 2) increase in the amount of melted multiple-year sea ices in which salinity is very low and even close to zero (0), compared to simulations with higher salinity.

Increased volcanic eruptions have been reported since 2000 [42], although the actual number may be greater and possibly remain unchanged due to inaccessibility and technological difficulties. Volcanic eruptions eject substantial energy into the climate system that can change the climate, for example, the eruption of Mount St. Helens in 1980 released 24 megatons of thermal energy, equivalent to 1600 times the size of the atomic bomb dropped on Hiroshima [43], that is about 0.1E+15 KJ. However, huge amount of volcanic dust, etc. may also shelter solar radiations, leading to a decrease in the temperature in the system afterwards.

Additionally, wildfires occur recently more frequently and intensively such as those in California and Australia. According to Jonathan [44], the annual energy released from wildfires in Western United States is about 1.4E+15 KJ. Although these wildfires are fueled by the biomass that is included in the earth’s energy budget balance during a long growing time, the concentrated burning and

release of this cumulated energy in a short time will impact the system’s behavior.

These compounding effects are significant on the system.

Figure 11 plots the sea level rise (both simulated sea level rise, i.e., cumulated calculated GSLR and GMSL-85) against the energy associated with ice melting (i.e., the sum of the energies melting sea ices and glaciers respectively). Polynomial regressions show clearly that both the measurements and the simulations have strong correlations with the energy.

According to the regression of GMSL-85 in Figure 11, the energy that melted ices (i.e., sea ices and glaciers) in 2019 should be 339.84E+15 KJ, compared to the allocated waste heat of 324.02E+15 KJ, the difference of 15.82E+15 KJ could be the extra energy coming from those forementioned energy sources. It is known that in 2019 the energy allocated to melting sea ices and glaciers is about 78.65% of total waste heat entered the climate system, thus this extra energy melting the ices corresponds to a total extra energy of 20.12E+15 KJ. That would contribute to extra temperature rises in air, land, and oceans of about 0.021˚C (depth: 25 m), 0.028˚C (depth: 0.025 m) and 0.014˚C (depth: 0.06 m), respectively. These correspond to adjusted simulation results of 0.97˚C, 1.34˚C and 0.67˚C, being much closer to their corresponding observations: 0.99˚C, 1.44˚C and 0.68˚C [33].

Furthermore, Figure 12 shows the contributions to sea level rise of sea ices melting, glaciers melting and bulk seawaters warming on an annual basis (top) and cumulated basis (bottom) when sea ice salinity changes from 12 (1965) to 4 ppts (2019). Clearly, on an annual basis (top), the melting of sea ices is the dominant contributor to sea level rise, sharing about 90.2% - 95.6%, and glaciers contributing about 3.6% - 9.5% while bulk seawaters warming only contributes about 0.4% - 1.2%.

On the cumulated basis (bottom), the melting of sea ices still dominates the sea level rise, with its contribution ranging from 93.6% - 95.5%, glaciers melting contributes about 3.6% - 5.8% and bulk seawaters warming only shares about 0.5% - 1.2%.

We can therefore forecast future sea level rise if the salinity in sea ices and the global EECE as well as global energy consumption, etc. are known.