By Richard Willoughby

May 2021

(The author appreciates the availability NASA’s Earth Observations satellite data sets used in this analysis.)

This is a three part series that analyses the role of atmospheric water in regulating Earth’s thermal balance.

Part 1 An analysis of the temperature of tropical ocean warm pools and the temperature limiting processes

Part 2 Discusses the mechanism of deep convection concluding with the persistency of clouds over ocean warm pools.

Part 3 Examines the global ocean energy balance over an annual cycle month-by-month to identify the role of atmospheric water in regulating the energy balance.

Part 2:  Deep Convection and Development of Convective Potential Energy

Water in the atmosphere behaves differently to the other gases.  Water vapour has the lowest density of the common constituent gasses.  Water exists in the atmosphere as a gas, liquid and solid.  All three phases are effective emitters of long wave radiation and ice in the atmosphere forms highly reflective cloud.

The unique properties of water in the atmosphere create convective instability that is observed to limit the ocean surface temperature in tropical warm pools to an annual average of 30C, detailed in Part 1 above.  The primary cause of convective instability that drives deep convection is the buoyancy of water vapour.  The development of convective potential relies on the ability of atmospheric water, in all phases, to cool by radiated heat transfer.

Level of Free Convection

Convective instability can only occur when the mass of water vapour in the atmosphere exceeds 30kg/sq.m; equivalent to 30mm water vapour.  Once the level of water vapour exceeds 30mm, the atmosphere can partition into a zone of free convection in contact with the surface and an upper zone that is not involved in the surface vertical convection current.  The upper altitude of the surface mixing zone is termed the Level of Free Convection (LFC).

To better appreciate how the LFC develops, it is useful to examine the conditions of a saturated air column over a surface at 300K (27C).  Such conditions are observed over ocean surfaces at the onset of the deep convective cycle.  Figure 10 compares the density of air with altitude and the density of water vapour with altitude. 

Figure 10:  Variation of moist air density with altitude and water vapour density with altitude in saturated column above 300K surface

With reference to Figure 10, it is observed that the density of the water only makes a small contribution to the total air density and falls off rapidly with altitude such that water has negligible mass above 14,000m.  Moreover, this is for a saturated column but water vapour can be present over a wide range of relative humidity at any altitude from zero up to the saturated level.  Figure 11 compares the density change of moist air with altitude and the density contribution of water in saturated air.

Figure 11:  Formation of level of free convection in saturated air column above 300K surface

With reference to Figure 11, it is observed that the density of water with elevation is greater at ground level than the change in density of air with elevation.  At 5000m and 6g/Cu.m, the density of the water vapour reduces faster than the density change of the total mixture with altitude.  That transition creates the condition where dry air will be supported by a moist air column below.  Similarly, a rising air column, under thermal equilibrium, will not rise above the LFC.

An LFC can exist in any air column where the total water column exceeds 30mm irrespective of relative humidity.  The free convection zone below the LFC will increase in water vapour above a warming ocean surface while the water vapour above the LFC is solidifying or condensing as it cools via radiated heat loss.  Given sufficient time, the water vapour above the LFC solidifies and condenses to leave dry air while the zone below the LFC becomes saturated.  This condition can be better appreciated with reference to Figure 12 for the atmospheric conditions above a 303K surface.

Figure 12:  Developing convective potential over a 303K ocean surface

The atmospheric temperature profile will follow a saturated adiabat from the surface to the LFC then progress upward along the dry adiabat that passes through the LFC.  Under these surface conditions and relative humidity, the LFC is at 6300m where the temperature is just above freezing at 276K. 

Convective Available Potential Energy

The partitioning of the atmosphere above and below the LFC can exist while the column is in thermal equilibrium.  If there is a disturbance that causes a small parcel of moist air to penetrate into the dry zone, its lower density and, therefore, buoyancy will cause it to rise and it will be followed by more moist air until the zone above the LFC becomes supersaturated.  This is the process of cloudburst whereby moist buoyant air bursts into the upper dry zone once the thermal equilibrium is upset and convective instability ensues.  The supersaturated air above the LFC gives rise to local precipitation that can grow to intense rain if moist air converges laterally from more stable zones.

With reference to Figure 12, the work done by the rising moist air during cloudburst is determined by the area on the chart between the moist adiabat and the dry adiabat above the LFC.  The low level of moisture above 14,000m or 220C means this condition limits the development of convective potential to below this altitude above ocean warm pools limiting at 303K.  The maximum possible Convective Available Potential Energy (CAPE) above a surface at 303K is 6000J/kg.  This requires the CAPE to be fully developed before instability occurs.  Observations above tropical warm pools indicate the convective potential rarely exceeds 4000J/kg in these regions.  The maximum updraft velocity during cloudburst is the square root of the CAPE*2.  A CAPE of 4000J/kg would consequently create a maximum updraft velocity of 98m/s.

Convective Instability and Cloud Cover

The atmospheric column becomes supersaturated during cloudburst.  Water vapour can extend to at least 14,000m during cloudburst and produces high level cumulus cloud that effectively blocks surface insolation at the onset of the convective cycle and each subsequent cloudburst.  The outgoing long wave radiation is absorbed by the water vapour, water condensate and, finally, the ice high in the atmosphere that will have a radiating temperature as low as 220K with a corresponding OLR radiating power of 130W/sq.m with average outgoing long wave power of 210W/sq.m over 30C warm pools.  By contrast, the peak reflective power can be as high as 1000W/sq.m in peak insolation as observed at the tropical moored buoys. 

The precipitation following cloudburst subsides leaving the zone above the LFC saturated but set to again develop convective potential.  During this stage, most long wave radiation from tropical warm pools exits above the LFC to solidify the water vapour thus forming persistent cirrus cloud that deepens during the CAPE development phase.  

The persistency of the cirrus cloud is better appreciated with reference to distribution of water vapour above the LFC and the level of freezing for stated surface temperature as set out in the following Table 1.

Table 1:  Distribution of water vapour above the LFC and the level of freezing under saturated conditions for nominated surface temperature

The table sets out the limiting conditions but only for the CAPE development phase when cirrus cloud deepens and then thins before the cycle repeats.  At 300K, the clear sky conditions can persist for approximately 37% of the CAPE development phase if the divergence does not disrupt the cycle.  The ice forming the cirrus cloud melts as it descends below the level of freezing and continues to descend below the LFC as water condensate.  The cirrus cloud dissipates while the exiting OLR is condensing the water vapour below the level of freezing but above the LFC.  Usually the air above 300K water surface diverges to air over warmer water and this disrupts the regular convective cycle such that clear sky persists for longer than 37% of the time.  On the other hand, convergence of moist air to warm pools at 303K, where clear sky would be expected 24% of the CAPE development stage, reduces the proportion of clear sky to a level where the surface heat fluxes, including cooling precipitate, are balanced and 303K is the upper temperature limit.  Without convergence playing a role, the radiated heat fluxes balance when the surface reaches 305K with clear skies 17% of the CAPE development stage.  A surface temperature of 306K has not been observed in open ocean warm pools.  At this temperature, the sky above the ocean would maintain persistent cloud, cycling from cumulus to thickening cirrus then thinning cirrus but no clear sky before the next cloudburst.

The location of the warmest pool experiences convergence of mid-level moist air and cooler adjacent zones experience corresponding divergence.  This results in the warmest pool experiencing precipitation of up to 15mm/day, twice the daily rate of condensate production, while adjacent locations 2.5mm/day, under half the daily condensate production.

Typical long wave radiating power over a tropical warm pool is 210W/sq.m.  This corresponds to water vapour solidification/condensing rate of 7.3mm/day.  Hence, above a warm pool of 303K (30C), it takes a maximum of 45 hours for a convective cycle to solidify/condense 13.8mm of water vapour if it is not disrupted by divergence of moist air and shorter if it reaches instability before the CAPE reaches full potential.  Observed convective cycles rarely run to full potential.

The Persian Gulf

The surface temperature in the Persian Gulf has been observed to reach 307K in August but examining the atmospheric profile shows the mid-level moisture content is too low to create the LFC needed before deep convection can develop.  The Persian Gulf experiences high rates of evaporation but the prevailing dry north-westerly winds transport the high level moisture laterally to the Arabian Sea.  Cloudbursts are rare events in the Persian Gulf.

Data Sources

I have used many months from these sets.  All the charts and images are independently produced meaning not copied images from these links.

There is also data from the moored buoys that I refer to:

via Watts Up With That?

May 24, 2021