Toward a Deterministic Model of Cloud Development over Ocean Warm Pools – Watts Up With That?

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.

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