By Gary Abernathy

This article was originally published at The Empowerment Alliance and is re-published here with permisson. 

The Trump administration’s impressive efforts to reboot traditional, reliable energy in the U.S. are a godsend not only for Americans but for people around the world. Whether reversing Biden-era prohibitions against offshore drilling or fast-tracking permits for natural gas exploration and extraction, President Trump’s devotion to utilizing the most abundant and affordable energy sources on earth will keep Americans prosperous, healthy and free.

But breathing new life into tried-and-true energy resources is only half the battle. Just as important is putting the brakes on the disastrous expansion of so-called renewables like wind and solar when their existence depends on subsidies and other life-support measures. The vaunted “all of the above” approach to energy is reasonable only when “all” are able to compete on a level playing field and demonstrate they are reliable and profitable.

To be sure, there are instances where alternative energy is effective and economically sustainable – particularly at the micro level. Many homeowners have chosen to install rooftop solar panels to assist in their household power needs. Micro wind turbines are being utilized in limited capacity to perform such tasks as pumping water or charging batteries. In both cases, the technology is cost-effective for the intended limited purposes.

But the large-scale wind and solar farms that have sprouted up across the country are almost wholly supported by government subsidies and tax credits. As noted in January by the Institute for Energy Research, “Treasury Department figures show that subsidies for wind and solar dwarf all other energy-related provisions in the tax code, costing $31.4 billion in 2024, and are expected to cost taxpayers $421 billion more between 2025 and 2034 based on the subsidies in the Biden-Harris climate bill.”

The report added, “Federal tax expenditures for the investment tax credit (ITC) and production tax credit (PTC), which are the primary drivers behind the deployment of wind and solar energy, are, by far, the most expensive energy-related provisions in the federal tax code. Between 2025 and 2034, the ITC and PTC will account for more than half of all energy-related tax provisions.”

Those ballooning subsidies and credits are at odds with a government dedicated to shrinking the size of the federal bureaucracy, and they create an unbalanced and non-competitive energy marketplace. To that end, Trump presented a budget outline in early May that slashed subsidies for alternatives and cut billions from “climate change” programs favored by his predecessor.

According to Reuters, in addition to ending most subsidies, the energy budget proposal “cancels more than $15 billion in carbon capture and renewable energy funding” from President Biden’s misleadingly named Inflation Reduction Act of 2021. Also ended would be about $1.3 billion in grants issued by the National Oceanic and Atmospheric Administration for “climate-dominated research.”

The story added, “The plan reorients Energy Department funding toward research and development of technologies that could produce an abundance of oil, gas, coal and critical minerals, nuclear reactors and advanced nuclear fuels, the White House said without further details.”

As of this writing, a battle is raging in Congress about the alternative energy cuts included in Trump’s “big, beautiful” bill. Some Senate Republicans want to extend the length of time before energy credits sunset. As reported by The Hill, the Senate version allows solar and wind farms that begin this year to receive the full credits.

“Before, when the bill was in the House, it demanded that those projects start only 60 days after the bill passed, essentially leaving no time for new clean energy investments,” The Hill reported. “The Senate is also allowing projects that begin construction in 2026 to receive 60% of the credit, in 2027 to receive 20% and in 2028 to receive no credits.”

Trump’s reaction to the more lenient Senate provisions has been unequivocable. “I HATE ‘GREEN TAX CREDITS’ IN THE GREAT, BIG, BEAUTIFUL BILL. They are largely a giant SCAM,” he posted on social media. “Windmills, and the rest of this ‘JUNK’ are the most expensive and inefficient energy in the world, is destroying the beauty of the environment, and is 10 times more costly than any other energy. None of it works without massive government subsidy (energy should NOT NEED SUBSIDY!). Also, it is almost exclusively made in China!!! It is time to break away, finally, from this craziness!!!”

Trump’s bombastic style aside, it’s hard to argue with his main points. Still, political realities – lawmakers worrying about curtailing jobs in their states already underway or in the pipeline – mean a final bill will probably include more subsidies for more years than Trump would prefer.

But even if it’s not ideal, the bill that comes out of the current Congress will still represent a comparative about-face from the draconian mandates, subsidies and credits for alternatives foisted upon us by the Biden administration. However imperfect the coming budget bill might be, our energy future will indeed be big and beautiful compared to what could have been.

Gary Abernathy is a longtime newspaper editor, reporter and columnist. He was a contributing columnist for the Washington Post from 2017-2023 and a frequent guest analyst across numerous media platforms. He is a contributing columnist for The Empowerment Alliance, which advocates for realistic approaches to energy consumption and environmental conservation. Abernathy’s “TEA Takes” column will be published every Wednesday and delivered to your inbox!

This article was originally published by RealClearEnergy and made available via RealClearWire.

From Climate Etc.

By Joachim Dengler

Are the natural carbon sinks failing?

For a long time, the discussion about the relation between temperature and CO₂ concentration has been focused on the greenhouse effect and its possible feedback mechanisms, captured by the concept of sensitivity.

Here, I would like to shift the focus to the other side of the story: the possible causal influence of global sea surface temperature on the growth of CO₂ concentration. Some readers may see this as a contradictory paradigm to the greenhouse effect; others may see it as one of the feedback mechanisms of the greenhouse effect.

The motivation for the investigations constituting the background paper of this post, “Evaluating the Effectiveness of Natural Carbon Sinks Through a Temperature-Dependent Model”, was published in the mainstream media like the Guardian, claiming that “Trees and land absorbed almost no CO₂ last year. Is nature’s carbon sink failing?“. A closer examination of all the articles published on this topic revealed that they all refer to a single publication. The scientific basis and trigger for the discussion had been a preprint of this article: “Low latency carbon budget analysis reveals a large decline of the land carbon sink in 2023”.

To find an appropriate answer to this, it is necessary to take a closer look and use original data to examine how the changes in CO2 concentration develop. In a scientific paper, it is legitimate to state, even guess, a model of a given form and relate this to measurements. This is what I did in the background paper by setting up a sink model that depends on both CO₂concentration and temperature. I underestimated the consequences of decades of debates about the relationship between CO₂ concentration change and temperature change. Before evaluating the interesting implications of the temperature-dependent model, I found myself confronted with fundamental doubts and prejudices. Therefore, I deviate from the structure of the published paper and begin with a visual introduction to the subject.

The effective monthly CO2 sink capacity is measured as the difference between the monthly anthropogenic emissions and the growth in concentration:
<sink capacity> = <anthropogenic emissions> – <concentration growth>     (1)
To measure concentration growth independently of seasons, growth is defined as the difference between the current concentration and the concentration 12 months prior.

Figure 1: Anthropogenic emissions (blue), CO₂ concentration growth (orange), and sink capacity (green). The Sink effect has a negative sign (for display purposes only).

From the continuity equation, it follows that the sink capacity is also the difference between global absorptions and natural emissions:
<sink capacity> = <global absorptions> – <natural emissions>            (2)

Anthropogenic emissions, concentration growth, and sink capacity are displayed in Figure 1.

Motivating the temperature-dependent model with Henry’s Law

Henry’s law describes the exchange of gases, here CO₂, between a liquid, where the gas is dissolved, and the gas phase, here in the atmosphere. In the equilibrium, the concentration  C  of the dissolved CO₂ is related to the partial pressure P of CO₂ in the atmosphere by C = k^.P, where k is Henry’s law constant (mol/(L·atm), specific to CO₂ and temperature, C is measured in mol/L, and P is measured in atm. The numeric value of the partial pressure P corresponds to the CO₂ concentration, measured in ppm, because the total atmospheric pressure is assumed to be 1 atm.

Henry’s law constant k is influenced by temperature, salinity, and pH. Given the actual measured conditions of the Earth’s oceans, temperature is the dominant factor influencing k and thus CO₂ solubility. Its large spatial variability (0–30°C) drives significant regional differences in air-sea CO₂ flux, with cold polar waters acting as CO₂ sinks (higher solubility) and warm tropical waters often acting as sources (lower solubility). For example, the solubility of CO₂ in polar waters can be more than double that in tropical waters due to temperature alone. The temperature dependence of the solubility on k is displayed in Figure 2. Despite the complex, nonlinear mathematical form, the temperature dependence of solubility is close to antilinear, getting smaller with growing temperature.

Figure 2: Temperature dependence of Henry’s law constant (solubility).

The downwelling flux of CO₂, the sink effect, is proportional to the difference between the equilibrium concentration k^.P  and the actual concentration C of the dissolved CO₂.
Without diving here into the details of the computation, this suggests that the ocean sink effect not only depends on the CO₂concentration via the partial pressure P, but also on temperature, which dominantly determines Henry’s law constant k.
This is visualized in Figure 3, taken from the publication “Uptake and Storage of Carbon Dioxide in the Ocean: The Global C02 Survey“

Figure 3: Ocean net CO2 flux map.

Although the authors state that rising emissions due to higher temperatures are compensated by reduced dissolved CO₂ concentration from increased biological activity of phytoplankton, the map indicates that areas of net absorption are near the poles, and regions of net emissions are near the equator. The map clearly shows that higher temperature implies higher emissions, respectively, lower absorption. Phytoplankton therefore reduces the temperature-dependent increase of natural emissions, but it does not fully compensate for it.

Similarly, the decay of biological matter and organisms is related to van’t Hoff’s rule, which states that an increase in decay rate and, thus, natural emissions scale with an increase in temperature. Of course, the sustainable availability of decayable substances depends on photosynthesis. Photosynthesis also scales with sunlight hours and temperature up to 30 °C, besides scaling with CO₂ concentration. CO₂ fertilization dominates the greening of the Earth, which has been more than 30% since 1900. So, it is logical that absorption dominantly scales with CO₂ concentration, while biological decay, implying natural emissions, scales with temperature. When both are correlated as they have been for the last 65 years, a balanced growth of both is expected.

The temperature-dependent model

We recognize from Figure 1 that CO₂ concentration can change very fast. Therefore, the input data are monthly time series of CO₂concentration and sea surface temperature.

Because it takes time to heat the ocean in summer and cool it down in winter, we allow several months of time lag between sea surface temperature changes and subsequent sink changes.

The simplest sink model with the dependency on CO₂ concentration and temperature is a linear model
<sink capacity> =     a^.<concentration> + b^.<temperature> + c      (3)

This model has been presented before; new insights are gained by changing the data granularity to months and optimizing the time lags between concentration growth and temperature.   Independence from seasonality and noise reduction is reached by averaging the measured data over 12 consecutive months. Nevertheless, the time lag is computed with a monthly resolution.

When estimating the optimal parameters a,b,c of equation (3) for a measured sink capacity according to equation (1), the explained variance (R² value) depends on the time shift between the temperature measurement and the subsequent CO₂ sink capacity.  This is displayed in Figure 4.  With a 4-month time lag, the model explains 80% of the data variance, compared to 57% when a sink model without temperature dependence is applied, i.e., when b=0.

Figure 4: Explained variance of the concentration and temperature-dependent sink model

This is reflected in the quality of approximation of the measured smoothed sink capacity, as displayed in Figure 5. While the concentration-based simple model explains the trend, the new model, including temperature, also explains most of the short-term variations.

Figure 5: Measured sink capacity (blue), approximation with simple sink model (green, only CO2 concentration), and temperature-dependent model (orange).

There is only one significant outlier. The sink capacity between 1991 and 1994 is considerably larger than predicted by the model. Roy Spencer explained this as a consequence of the Pinatubo eruption in 1991, where the dust-induced increased diffuse light increased photosynthesis considerably.  Otherwise, the predicted value of the actual concentration growth is remarkable, as shown in Figure 6. Again, for comparison, the prediction of the simple sink model without the temperature term is shown as the green graph. The fact that the green graph clearly shows a consistent declining trend since 2013 indicates that the concentration-dependent causes for sink capacity are more likely to have increased instead of decreased.   The details of the concentration growth are remarkably well predicted by the sea surface temperature. In particular, the sharp rise in concentration growth since 2023 is entirely temperature-based.

Figure 6: Monthly concentration growth (blue), modelled with concentration only (green) and additionally with temperature (orange).

Intuitive understanding of model parameters

Looking at the graphs, the introduction of temperature dependence seems to influence only short-term data variability. But temperature has a trend. This has severe consequences on the resulting parameters, shown in Table 1.

Table 1: Regression results of simple and extended sink model

In the simple, temperature-independent model, the absorption is only about 2% of the concentration, whereas the temperature-dependent model implies 5%. This is a severe discrepancy that deserves attention.  The mathematical explanation of the discrepancy can be found in section 5 of the 2024 publication.  If, in reality, sink capacity depends on temperature and temperature is strongly correlated with CO₂ concentration (which is the case), if you then offer a mathematical model that contains only CO₂ concentration as a parameter, then the CO₂ parameter will also take the role of the missing temperature.

Figure 7 conveys an intuitive understanding by assuming that down-welling absorptions are controlled by CO₂ concentration (green arrow), while natural emissions are controlled by temperature (blue arrow). By definition, their difference is the measurable sink effect (red arrow). When temperature is essentially a linear function of CO₂ concentration (which is the case since 70 years), then in the long term, the concentration trend cancels the temperature trend. In the sink capacity, therefore, only the short-term variability of temperature is visible.

Figure 7: Intuitive explanation of apparent model discrepancy.

Validating the model with ¹⁴C decay after the bomb test ban treaty

The nuclear bomb tests beginning in the 1950s stopped rather suddenly in 1963 with the Nuclear Test Ban Treaty. This provides a close-to-ideal identifiable carbon emission pulse of ¹⁴C that has been thoroughly investigated for more than 40 years. The data series is the global data sequence from 1950 to 2019 from the supplements of the article “Atmospheric Radiocarbon for the Period 1950–2019“. The relative deviation from the preindustrial zero level of ¹⁴C concentration, Δ¹⁴C, is displayed as the blue graph in Figure 8.

Figure 8: Relative deviation from preindustrial ¹⁴C level (blue), adjusted relative deviation of ¹⁴C level by setting pre-1963 level to 0 (orange).

Why is this concentration decay representing “pure” absorptions? The CO₂ emissions from the oceans have the much lower ¹⁴C concentration of the long-term equilibrium before the bomb tests; therefore, the upwelling ¹⁴C can be neglected.
This decay includes both the decay of ¹⁴C concentration into the long-term sinks, but also the Suess effect due to the atmospheric concentration change of ¹²C by anthropogenic emissions. For the determination of the Suess effect, the 25-year interval from 1965 to 1990 with a good ¹⁴C decay signal was taken. The upper bound of the diluting Suess effect due to fossil fuels is obtained by pretending there is no sink effect, thus adding the cumulative emissions of 60 ppm (=127 GtC) between 1965 and 1990 to the 1965 CO₂ concentration of 320 ppm.  This results in a Suess effect contribution of 0.69% per year to the decline of the relative ¹⁴C concentration. With a value of 0.058 for the decay constant of the uncorrected data, the reduction by 0.0069 results in 0.051, the actual absorption constant of ¹⁴C. Considering the 95% confidence interval [0.047,0.055], this is a perfect confirmation of the concentration-dependent absorption constant of the extended sink model.

Validating the model with soil respiration

Photosynthesis is the primary driver of the following processes of plant decay and soil respiration. Net Primary Production (NPP) during the time interval from 1982 to 1999 was investigated. They found a yearly increase of 3.4 GtC of NPP over 18 years. During this time, the temperature increased by 0.25 °C. This would imply a 13.6 GtC increase of bound carbon per °C and year. According to the article, this was not only due to the increase of CO₂ fertilization but also, to a large degree, to the reduction of cloud cover over the Amazon rainforest and an increase in solar radiation, which directly influences photosynthetic processes more than CO2 concentration and temperature. A later reported decline of yearly NPP by 0.55 GtC in the years 2000–2009 adjusts this exorbitantly high yearly number to 2.85 GtC/0.5 °C = 5.7 GtC/°C.

During the 19 years from 1989 to 2008, the natural emissions from soil respiration 𝑅𝑆 have risen by 0.1 GtC per year, i.e., 1.9 GtC during the whole investigation period. During this time, the global temperature has increased by 0.3 °C. Therefore, we have a soil respiration temperature dependency of 6.33GtC/°C. The temperature coefficient of the extended model, is 3.6 ppm/°C = 7.7 GtC/°C with the 95% confidence interval [5.9, 9.5] GtC/°C. This can be considered a sufficiently good match with the evidence from soil respiration.

Other Approaches relating Temperature to Sink Effect

I am aware of two other approaches to deal with the temperature dependence of the sink effect. Both have in common that they do not use temperature itself as a predictor, but a variable derived from temperature, which does not have a long-term trend.  The obvious reason for this approach is the known fact that the measurable sink effect does not show any long-term trend.  As I discussed above, this is a superficial conclusion from the observations; it ignores the fact that due to the large correlation between concentration and temperature, actual temperature effects might be hidden.

Ferdinand Engelbeen has suggested that the sink effect and, as a consequence, the concentration growth, should depend on the time derivative of temperature instead of temperature itself. Indeed, the derivative of temperature does not have a trend.  And the numerical explanation value of the data variance is also 0.8 for his model, the same as for the model described here. Nevertheless, I do not consider taking the derivative of temperature as a predictor for the sink capacity or concentration growth, respectively, a good idea.

Both mentioned natural laws, Henry’s law and van’t Hoff’s rule,  relate natural emissions to temperature and not to its derivative. Also, a simple thought experiment rules out the derivative: Let us assume a single temperature jump of 1 °C at the sea surface, then the temperature is assumed to remain at the elevated level for a long time. If the temperature effect depended on the time derivative of temperature, there would only be a single pulse of natural emissions during the very first time interval. But in reality, temperature is a thermodynamic state variable. This implies increased natural emissions at all times following the temperature step (under ceteris paribus conditions).

Roy Spencer has related the short-term variability of the sink effect to the Multivariate ENSO index (MEI).  MEI is also a trend-free variable, where two of the five components of the MEI are regional sea surface temperature and regional air temperature anomalies. The anomalies are determined by subtracting the 30-year average from the temperature. This removes the trend from the temperature, but preserves the short-term variability.

To understand the relation of these approaches to the temperature-dependent model described here, temperature is decomposed into a linear function of CO₂ concentration, containing the temperature, and a residual temperature. This is displayed in Figure 9.

Figure 9: Monthly sea surface temperature (blue), temperature from linear model of CO₂-concentration (orange), residual temperature (green)

The residual temperature is a residual of a regression model and, therefore, by definition, zero-mean and trend-free. When the residual temperature replaces temperature in the extended model, the results for absorption coefficient a and the constant c are identical to those of the simple model (without temperature), the temperature coefficient b is identical to that of the temperature-dependent model (see details in previous publication). The model reconstruction of the concentration growth is identical to that of the temperature-dependent model.

Comparing the residual temperature with the Multivariate ENSO Index (MEI) and the derivative of the temperature, it becomes clear why all three lead to similar results. All three time series are displayed in Figure 10, slightly smoothed to keep them visually identifiable.

Figure 10 Comparison of Residual Temperature (blue) with the Multivariate ENSO Index (orange) and the Derivative of Sea Surface Temperature (green)

The residual temperature has structural similarities with the MEI signal. When sea surface temperature is indeed a physical driving force of the sink effect and CO₂ concentration growth, it can be expected that MEI has a significant influence on the sink effect. In that case,  I expect that the model based explicitly on sea surface temperature explains the observed data better than the model with the complex MEI index. I invite Roy Spencer and others to determine the R² value when MEI is used besides CO₂ concentration as a predictor.  The first temperature derivative is also quite similar to the residual temperature, but appears time-shifted. This is because the derivative of a periodic function is a phase-shifted version of that function.  Empirically, this is reflected in the fact that the optimal fit requires the derivative of the temperature to be shifted by 9 months instead of 4 months as with the residual temperature.   In contrast, the peaks of the MEI signal coincide with those of the residual temperature; both are essentially the difference between the temperature and its temporally smoothed version.

My reason to prefer the model with the actual temperature is physics.  The elementary sink processes only experience the state variable temperature, not complex derivations of it.

Conclusions

The continuity equation, together with the observed consistent decrease in the ¹⁴C concentration in the atmosphere after 1963 and the observation of temperature-dependent natural emissions, are powerful tools for evaluating observations.

One purpose of this article is to explain the recent rise in concentration growth as a consequence of rising sea surface temperatures instead of a hypothetical unobserved decline in absorption by oceans or plants. While the rise in concentration growth is real, the cause is not a failure of sinks but a larger rise in temperature beyond the trend that corresponds to the CO₂ level rise.

It should, therefore, not be off-limits to consider temperature as a “normal” cause of CO₂ concentration changes in the public debate, as an influencing factor instead of speculating about the absence of sinks without evidence.

This does not exclude causality in the other direction; the greenhouse effect, the rather large temperature coefficient on natural CO₂ emissions, certainly limits the possible climate sensitivity.

The temperature-dependent model makes it possible to better separate the actual anthropogenic origin of CO₂ changes and the natural causes, among which temperature is a very important one. Many people were confused when, in 2020, no effect of the anthropogenic emission reduction could be seen in the concentration growth. When the temperature effect is removed, as is the case in the simple model, then the effect of the lockdown-caused emission reduction can be seen, e.g., the green curve in Figure 6.

The most important contribution is that it became possible to separate downwelling absorptions from upwelling natural emissions. Through the evaluation of the bomb test ¹⁴C time series and by the Suess effect correction, we have a reliable estimate of the yearly absorption rate of 5% of the CO₂ concentration. Together with the precise CO₂ concentration measurements on Mauna Loa and the accepted measurements of anthropogenic emissions from the International Energy Agency (IEA), the continuity equation constrains the yearly net natural emissions. Together with the extended model, we also have an understanding of their temperature dependency.

Richard Willoughby

Summary

This article begins with observations of top of atmosphere radiation balance over a moored buoy located in the middle of the Bay of Bengal in conjunction with surface data from the moored buoy for the same time.  It progresses into more recent observations of daily OLR emission from above all ice free ocean surface to establish that the average effective emission temperature for every location across the global oceans is below the freezing temperature for water.

A model for broad spectrum transmission of OLR to space through the atmosphere over a warm pool is explained and sequenced through a series of time intervals to appreciate how ice forms as a consequence of long wave radiation heat loss at altitude.

The article concludes by making the case for convective overshooting playing a key role in the observed SST regulating process.

Introduction

The Bay of Bengal is one of the best locations across the oceans to observe the development of convective instability.  The solar intensity at 15N exceeds 425W/m² from the time the solar zenith moves north of the Equator in March to the time the zenith moves south of the Equator in September.  That means there is sufficient solar intensity to reach and maintain the ocean surface temperature (SST) at its sustainable limit of 30C for almost 6 months.  Chart 1 provides monthly data from CERES top of atmosphere (ToA) observations available from NASA NEO showing the radiation balance at 15N and 90E for 2017.

Chart 2 provides surface based data collected from the moored buoy at 15N, 90E at daily time resolution from the same location as Chart 1 for the same period. 

The SST is observed to rise from day 16 to day 100 when a cyclone passed over the moored buoy then again increases to overshoot the sustainable temperature of 30C till cyclic instability sets in with associated rainfall from day 150.  By day 300, the solar zenith moves south of the Equator and the solar intensity at 15N is insufficient to maintain the cyclic instability and the temperature declines. 

Combining observation displayed in Charts 1 and 2 enables the conclusion that the regulating process has moisture convergence from surrounding ocean to the vicinity of the moored buoy because the Net radiation averages 100W/m² while the SST tracks between 28.5 and 30C.  So despite the net heat flux to the atmosphere, there is no corresponding increase in surface temperature.  The additional heat input is the result of local precipitation exceeding evaporation.

Chart 3 combines daily surface and ToA data for July 2017 to improve the time resolution over Chart 1.

An important observation of Chart 3 occurs on 21^st July.  Here there is intense rain indicative of convective instability centred in the vicinity of the moored buoy but it coincides with low reflected short wave (SWR) and high outgoing long wave radiation (OLR).  This indicates that the cumulonimbus anvil associated with monsoonal rain does not contribute significantly to daily short wave reflection.  It also indicates that the OLR is emitting from higher temperature during and immediately after the instability than during the development of convective potential.

Here it is worth plotting the correlations between SWR and OLR and surface sunlight to OLR per Chart 4.

The result that the SWR is negatively correlated to OLR with a coefficient greater than unity demonstrates the cloud effect over warm pools produces radiation cooling rather than heating.

The Role of Ice in the Atmosphere

Chart 5 expands the observation of OLR to all ice free ocean surface and comes forward in time to 20 March 2025 when the solar zenith is over the Equator.

The effective radiating temperature for OLR emissions over oceans for 31,800 grid cells is shown in Chart 6.

The effective emission temperature over oceans ranges from 216K to 272.6K.  Given that molecules capable of emitting OLR will be losing heat, the H₂O molecules in the atmosphere with temperature below 273K will be solidifying to ice.  Accordingly the vast majority of OLR emissions above ocean surface will be from ice.  The ice will be at high altitude over warm pools at 303K.

OLR Emissions above Ocean Warm Pools at 303K

Ocean warm pools exhibit cyclic convective instability over a period of a few days.  Chart 3 above exhibits 5 to 6 cycles in a month or averages a cycle every 5 to 6 days.  In the location where the instability is initiated, the convective plume transports heat from low altitude to high altitude resulting in intense rainfall as the expanding air cools at altitude.  After instability there is an initial period of clear sky with close to saturated conditions.  In reality, the column will rarely be fully balanced but ranges from water deficit to super-saturated.  Chart 7 shows the atmospheric profile for water vapour and temperature under perfectly saturated conditions over 303K surface.

For the purpose of this analysis, the modelled column has 200 layers of 100m thickness.  This results in the bottom layer having a total of 3mm of water.  There is very little water above 15,000m and negligible emissive power above 18,000m so the temperature is almost constant; just below 200K.  Water dominates the OLR emissive power of the column so when there is little to no water, the emissive power is negligible.

Chart 8 examines the broad spectrum OLR absorption up the column based on a water vapour OLR absorption constant of 10% per mm.  The OLR fraction transmitted to space is based on working down the column applying Beer’s Law.

It becomes apparent that nearly all OLR emitted below 3000m is reabsorbed while OLR to space progressively increases above 5,000m to reach its maximum above 15,000m

Having established the OLR absorption and transmission profile for the saturated column, it is now possible to determine the OLR transmitting power of the column and the rate of heat loss at altitude per Chart 9.

These calculations apply Kirchhoff’s Law of Radiation with the simplifying assumption of bulk absorption for the OLR spectrum such that there is just one value for absorption or emissivity at each layer.  This then enables using the Stefan Boltzmann equation for OLR transmission up the column and to space, which is assumed to be at 0K.  The resulting radiating power is 275W/m², which corresponds to an effective radiating temperature of 263K.  However it is clear that there is heat being lost from the column below freezing and noteworthy that there is OLR radiation heating below 2,400m.

The loss of heat at altitude results in ice and condensate production over time as shown in Chart 10.

A time step of 2500 seconds has been chosen to simplify the mass flow of ice cascading down the column with time.  The terminal velocity of sub 100 micron ice particles is taken as 4cm/s so they will fall 100m (one layer) in 2500 seconds.   Chart 11 shows the transmitting power and rate of heat loss at 2500 seconds after saturated state taking the absorption coefficient for water condensate as 50% per mm and ice at 90% per mm.

The transmitting power has reduced slightly to 271W/m² but there is not much change in the altitude or amount of heat loss.  After seven iterations, the development of the ice and its influence becomes clearer as shown in Chart 12.

After 17,500 seconds, the transmitting power is down to 253W/m² and it is now apparent that the heat loss is occurring at higher altitude while less heat is being lost below the 273K altitude.  Also the altitude of radiation heat gain has increased to 2,900m.

This simple model is only valid for overnight analysis or 19 iterations; shown in Chart 13.  It is not valid for sunlit atmosphere where short wave absorption plays a significant role in the development and dissipation of the ice along with other complicating factors.

So after 13 hours of overnight heat loss following late afternoon convective storm over 303k ocean, the OLR transmission is down to 226W/m² and heat loss is centred around 11,000m with very little heat loss from water condensate or water vapour.  There is now long wave heat gain up to 3,800.  The ice accumulation at various time iterations is shown in Chart 14.

After 13 hours without sunlight, there is a total of 2.8kg of ice per square metre and it dominates both the OLR transmission and solar EMR thermalisation.  A sunlit model results in greater complexity and a story too long for this article.

Discussion

This overnight example gives insight into the initial ice development.  Through the daylight, solar EMR is absorbed by the ice and some sublimates during the peak daylight but there is insufficient heat input to induce upward mass flow.  Over a few nights and days of cycling heat loss and heat gain, the ice becomes layered but with continual descent of ice or associated water vapour.  The column becomes increasingly unstable as the ice and water condensate descends and the region above the level of free convection (LFC) deflates to increases in density while the region below the LFC gains energy with reducing density. 

The water condensate that falls below the LFC is vaporised by the heat gain from absorbed solar EMR and OLR from lower altitudes.  The column also gains water vapour from the surface insolation.  It takes upward of five days to reach the maximum convective potential.  A column above 303K SST with maximum convective potential is devoid of cloud so there is usually clear skies ahead of instability occurring.  The SWR is high immediately after instability then gradually reduces as the high altitude ice develops.  SWR is usually low before instability occurs.

The full sunlit ice development model, reasonably tuned to observations, achieves a balance in heat gain below the LFC equal to the loss of heat above the LFC.  This only occurs when the SST is at 303K.  When the SST is lower, there is not enough energy below the LFC to fully saturate the region above the LFC during instability.  If the SST was able to exceed 303K and the region below the column was in equilibrium with the surface, then instability will cause convective overshooting with very high altitude ice that remains persistent due to its small size having very low terminal velocity.  Going back to Chart 2 it is apparent that convective overshooting occurred at the onset of the instability when the temperature dropped from above 31C to below 30C in two days.  The OLR for the 1^st June averaged 147W/m² (225K), which is only possible starting from convective overshoot.

In looking at convective overshooting, it is regularly observed above tropical cyclones where daily OLR can be less than 100W/m² (204K).  One of the more unusual places that experiences convective overshooting is Missouri.  Here it is associated with similar atmospheric instability but the instability is caused by the mixing of high altitude dry air stream and moist mid altitude air stream to produce tornados.

Conclusions

Efforts to understand the inherent stability of Earth’s climate and the basis of climate trends without a deep understanding of ice accumulation and loss from land; sea ice growth and all ice melt on oceans and ice nucleation, sublimation and terminal velocity in the atmosphere are doomed to fail.  Ice dominates Earth’s radiation balance by orders of magnitude over any gas including water vapour.

I, and others long before me, recognised that ocean atmospheres exhibit an SST regulating process that prevents temperature sustaining more than 30C (303K).  Prior to this analysis I had mentally pictured the regulating process as a fuel regulating governor with fine control that progressively reduced the fuel (surface sunlight) until 30C was reached.  The analogy is now changed to one where the engine can be flooded and sputters when the throttle is opened too fast.  It is possible to overfuel the engine with more heat below the LFC than needed to rebalance the heat loss above the LFC. 

Earth’s atmosphere over tropical oceans can be viewed as a finally tuned engine reaching peak performance, in terms of heat uptake when SST is at 303K.  Convective instability is similar to ignition in the Carnot cycle.  If the engine fails to fire at the right time and the surface temperature overshoots then any ensuing convective instability will overshoot and the surface will cool below 303K before it reaches instability again.

As a consequence of this analysis, I have elevated the significance of convective overshooting on my list of climate control factors.

The Author

Richard Willoughby is a retired electrical engineer having worked in the Australian mining and mineral processing industry for 30 years with roles in large scale operations, corporate R&D and mine development.  A further ten years was spent in the global insurance industry as an engineering risk consultant where he developed an enduring interest in natural catastrophes and changing climate.