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  <front>
    <journal-meta>
<journal-id journal-id-type="publisher">HESSD</journal-id>
<journal-title-group>
<journal-title>Hydrology and Earth System Sciences Discussions</journal-title>
<abbrev-journal-title abbrev-type="publisher">HESSD</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Hydrol. Earth Syst. Sci. Discuss.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1812-2116</issn>
<publisher><publisher-name>Copernicus GmbH</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>

    <article-meta>
      <article-id pub-id-type="doi">10.5194/hessd-12-10921-2015</article-id><title-group><article-title>Experimental evidence of condensation-driven airflow</article-title>
      </title-group><?xmltex \runningtitle{Experimental evidence of condensation-driven airflow}?><?xmltex \runningauthor{P.~Bunyard et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Bunyard</surname><given-names>P.</given-names></name>
          <email>pbecologist@gn.apc.org</email>
        <ext-link>https://orcid.org/0000-0002-2573-003X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2 aff6">
          <name><surname>Hodnett</surname><given-names>M.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Poveda</surname><given-names>G.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-7907-6360</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Burgos Salcedo</surname><given-names>J. D.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Peña</surname><given-names>C.</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>IDEASA, Universidad Sergio Arboleda, Bogotá, Colombia</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Centre for Ecology &amp; Hydrology, Wallingford, UK</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Department of Geosciences and Environment, Universidad Nacional de Colombia, Sede Medellín, Colombia</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Corporación para la Investigación y la Innovación – CIINAS, Bogotá, Colombia</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Facultad de Matemática, Universidad Sergio Arboleda, Bogotá, Colombia</institution>
        </aff>
        <aff id="aff6"><label>a</label><institution>retired</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">P. Bunyard (pbecologist@gn.apc.org)</corresp></author-notes><pub-date><day>27</day><month>October</month><year>2015</year></pub-date>
      
      <volume>12</volume>
      <issue>10</issue>
      <fpage>10921</fpage><lpage>10974</lpage>
      <history>
        <date date-type="received"><day>20</day><month>August</month><year>2015</year></date>
           <date date-type="accepted"><day>5</day><month>October</month><year>2015</year></date>
      </history>
      <permissions>
<license license-type="open-access">
<license-p>This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">http://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions><self-uri xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015.html">This article is available from https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015.html</self-uri>
<self-uri xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015.pdf">The full text article is available as a PDF file from https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015.pdf</self-uri>


      <abstract>
    <p>The dominant “convection” model of atmospheric
circulation is based on the premise that hot air expands and rises, to be
replaced by colder air, thereby creating horizontal surface winds. A recent
theory put forward by Makarieva and Gorshkov (2007, 2013) maintains that the
primary motive force of atmospheric circulation derives from the intense
condensation and sharp pressure reduction that is associated with regions
where a high rate of evapotranspiration from natural closed-canopy forests
provides the “fuel” for cloud formation. The net result of the “biotic pump”
theory is that moist air flows from ocean to land, drawn in by the pressure
changes associated with a high rate of condensation.</p>
    <p>To test the physics underpinning the biotic pump theory, namely that
condensation of water vapour, at a sufficiently high rate, results in an
uni-directional airflow, a 5 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula> tall experimental apparatus was designed and
built, in which a 20 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> body of atmospheric air is enclosed inside an
annular 14 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula> long space (a “square donut”) around which it can circulate
freely, allowing for rotary air flows. One vertical side of the apparatus
contains some 17 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula> of copper refrigeration coils, which cause condensation.
The apparatus contains a series of sensors measuring temperature, humidity
and barometric pressure every five seconds, and air flow every second.</p>
    <p>The laws of Newtonian physics are used in calculating the rate of
condensation inside the apparatus. The results of more than one hundred
experiments show a highly significant correlation, with <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>&gt;</mml:mo><mml:mn>0.9</mml:mn></mml:mrow></mml:math></inline-formula>, of airflow
and the rate of condensation. The rotary air flows created appear to be
consistent both in direction and velocity with the biotic pump hypothesis,
the critical factor being the rate change in the partial pressure of water
vapour in the enclosed body of atmospheric air. Air density changes, in
terms of kinetic energy, are found to be orders of magnitude smaller than
the kinetic energy of partial pressure change.</p>
    <p>The consistency of the laboratory experiments, in confirming the physics of
the biotic pump, has profound implications for current mathematical climate
models, not just in terms of predicting the consequences of widespread
deforestation, but also for better understanding the atmospheric processes
which lead to air mass convection.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p>Atmospheric convection, which leads to air mass circulation, is generally
considered to result from the lower atmosphere acting as a heat engine, with
the kinetic energy for convection deriving from differences in temperature,
according to the general principle that hot air rises and cold air sinks.
However, as Makarieva et al. (2013) point out, when hot air rises in the lower
atmosphere it cools because of expansion and when the same, but now cooler,
air sinks it heats up, such that the overall gain or loss in kinetic energy
is zero. The same cooling and heating happens when air expands and forces
air elsewhere to compress;  there is no net energy gain to do work. In other
words, a strict application of the first law of thermodynamics to the
atmosphere would yield a rate of kinetic energy generation equal to zero.</p>
      <p>Instead, the same authors (2013) present the notion that the potential
energy, derived from an outside source (the Sun), is stored in the
evapotranspiration of water which, on condensing, converts into kinetic
energy, and so drives the process of air mass convection. During daylight
hours closed-canopy forests pump more than double the quantity of water
vapour per square metre of surface compared to the ocean in the same
latitude, the net result being that condensation in cloud-forming over the
forest causes surface air to flow upwards, thereby generating low pressure
at the surface which, in turn, establishes an ocean-to-land pressure
gradient (Makarieva et al., 2013, 2014).</p>
      <p>By means of evapotranspiration, rainforests, whether in the equatorial
tropics or in boreal regions during summer months, feed the lower atmosphere
with water vapour, up to some 3 % of atmospheric pressure, and
thereby provide the source material for cloud condensation. The partial
pressure change, with the corresponding kinetic energy release, drives
convection, according to the biotic pump theory (BPT). From that point of
view, it is the hydrological cycle, including water evaporation and
condensation, which drives convection and therefore the circulation of the
air masses. That is in sharp contrast to the orthodox view of convection and
air mass circulation, which explains the movement of the air mass through
latitudinal differences, helped on by the release of latent heat.</p>
      <p>The proposition that a high rate of evapotranspiration from forested regions
is a prime mover of major air mass convection has remained contentious.
Meesters et al. (2009) rejected the BPT on the grounds that the ascending air
motions induced by the evaporative/condensation force would rapidly restore
hydrostatic equilibrium and thereby become extinguished. In reply Makarieva
et al. (2009) pointed out that condensation removed water vapour molecules from
the gas phase and reduced the weight of the air column. That removal must
disturb hydrostatic equilibrium and make air circulate under the action of
the evaporation/condensation force (Makarieva, 2009).</p>
      <p>The mass of an air column is equal to the number of air molecules in the
column multiplied by their molecular masses. When the number of air
molecules in the column is preserved, its weight remains unchanged and
independent of density. Hence, heating of the air column does not change its
weight. In contrast, condensation changes the number of gas molecules in the
air column and instantaneously reduces the weight of the air column
irrespective of the effects it might have on air density (Makarieva, 2009).
In effect, the BPT states that the major physical cause of moisture fluxes
is not the non-uniformity of atmospheric and surface heating, but that water
vapour is invariably upward-directed as a result of the rarefaction of air
from condensation (Makarieva, 2013).</p>
      <p>The BPT, therefore, maintains that the air pressure sustains its
disequilibrium because of the reduction in total weight of the air column as
condensation occurs, that being a continuous process as the ascending moist
air cools. In fact, when the initial bulk air pressure in the lower
atmospheric levels no longer equals the bulk weight of the air column, the
initial hydrostatic equilibrium of air as a whole is disturbed and an
accelerating upward motion is initiated in the air column. This upward
motion of expanding and cooling moist air sustains the continuous process of
condensation and does not allow the hydrostatic equilibrium of air as
a whole to set in. The motion continues as long as there is water vapour in
the rising air to sustain condensation (Makarieva, 2009). Within the concept
of the biotic pump it is the physical mechanism of condensation which drives
the upward airflow in the lower atmosphere by removing molecules from the
air column, and thus generates the surface horizontal winds, such as the
Trade Winds.</p>
      <p>Evidence in favour of the BPT has come from a number of different sources.
Makarieva et al. (2007, 2013) refer to data showing that precipitation over river
basins which are covered in forest remains as high in the deep interior of
the continent as at the coast, whereas river basins without forest show an
exponential decline in rainfall as one passes from the coast inland.
Spracklen et al. (2012) have shown from their recent pan-tropical study of
rainfall and land-cover, as indicated by the leaf area index (LAI), that
satellite-derived rainfall measurements are positively correlated with the
degree to which model-derived air trajectories have been exposed to forest
cover. Even though Makarieva and colleagues (2014) have some essential
criticisms of the methodology used by Spracklen, they conclude that the
Spracklen results confirm the influence of forest on regional rainfall
patterns.</p>
      <p>In a recent study, Poveda et al. (2014) provide evidence that when the low level
jet streams pass over forested regions, precipitation levels stay high and
constant, whereas over regions which lack forest, precipitation levels
decline exponentially, just as the BPT suggests should happen. Poveda and
his colleagues look at the low level Chocó jet and comment that the
change in direction of the Pacific Austral Trade Winds from Easterlies to
Westerlies just over the Equator at 4<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, may owe their abrupt
switch in great part to the unsurpassed degree of evapotranspiration and
subsequent condensation over the Chocó rainforest in Colombia.</p>
      <p>With more than 380 000 <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> per second of water vapour being brought
in from the Tropical Atlantic Ocean, (Salati, 1987) the Amazon Basin
functions on a far grander scale than the Chocó. It would appear that
evapotranspiration rates are sufficiently high over the rainforest to
increase the volume of the Amazonian atmospheric river in the form of the
South American Low Level Jet Stream as it approaches the western reaches of
the Amazon Basin and is then deflected both upwards and southwards on
encountering the Andes (Marengo, 2006; Poveda, 2014).</p>
      <p>Builes-Jaramillo and Poveda (2015) have now extended their research to look
at possible correlations between the flow of the Northwest Trade winds and
the different seasons encountered over the Amazon Basin. They have found an
inverse correlation between sea surface temperatures (SSTs) in the North
Tropical Atlantic and an increase in the seasonal index of precipitation
minus evapotranspiration (P-E). Whereas the SST has a minimum in February,
the P-E for the Amazon shows a maximum in March. Vice versa the P-E has a minimum in
August followed by an SST maximum in September. Sea surface temperatures are
influenced by the velocity of the surface winds, the Northwest Trade Winds,
and the evaporation of water. The rainy season over the rainforest in March
is associated with dense clouds and condensation. On the basis of the BPT,
intense condensation will lead to stronger surface winds over the North
Tropical Atlantic;  hence their lower temperatures. The corollary is that
reduced cloud formation over Amazonia will lead to reduced surface flow of
the Trade Winds;  hence higher SSTs. These findings have considerable
implications for global climate, indicating that widespread deforestation
could lead to warmer SSTs and therefore presumably to more extreme climatic
events, including hurricanes, over the tropical North Atlantic.</p>
      <p>Overall, the evidence for the BPT is accumulating, but contention will
remain until the physics underlying the convection model and the BPT can be
clearly defined and distinguished. For that reason, this paper describes an
attempt to study the physics in a laboratory setting.</p>
</sec>
<sec id="Ch1.S2">
  <title>Methodology</title>
      <p>To test the underlying physics of the impact of condensation upon airflow,
the idea was conceived of an enclosed structure which would allow
a measurable air circulation to take place under conditions of controlled
condensation. The structure (Fig. 1) consists of two columns, made of
insulated PVC, 4.8 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula> high, with a cross-sectional area of 1.44 <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>,
connected at the top and bottom by “tunnels” 2.4 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula> long with the same
cross-sectional area of 1.44 <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. On account of small leaks some mixing
of the enclosed air with the external air may take place, but the dynamics
of each experiment swamp the impact of any such exchanges, and to all
intents and purposes the structure is leak-proof. However, despite the
insulation, the structure is affected by external temperature and by
differential insolation. The effect of external insolation is measurable by
means of directional airflow and is accounted for in determining the
relationship between the rate of condensation and consequent airflow.</p>
      <p>Access to each column is by means of an insulated PVC door, with double
glazing to allow a view inside. A double-layer of copper refrigeration
coils, 17 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula> in length and 12 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">mm</mml:mi></mml:math></inline-formula> in external diameter, are located 3.4 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula> up the right-hand column, approximately 20 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">cm</mml:mi></mml:math></inline-formula> down from the junction
between the column and the upper tunnel. The total surface area of the
coils, taking a 3.0 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">mm</mml:mi></mml:math></inline-formula> coating of ice into account, is 0.96 <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>;  they
are connected to an industrial compressor located some 3 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula> away on the
floor of the laboratory. The laboratory is contained within a lean-to. The
right-hand column, as viewed from within the laboratory, and as shown in
Fig. 1, is likely to get more insolation, because of its easterly
orientation, than the left-hand column which is shaded from the southerly
sun by beech trees. That difference in orientation results in the “default”
air movement being counter-clockwise, with air rising in the “right” column
and sinking in the “left”.</p>
      <p>Sensors, including thermocouples (T), hygrometers (RH) and barometric
pressure gauges, (BAR) have been judiciously placed, in locations 1, 2 and 3
in Fig. 1, so as to obtain measurements of changing conditions every five
seconds within the columns and tunnels. The Gill 2-D ultrasonic anemometer
(UA), measuring every second, is located 15 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">cm</mml:mi></mml:math></inline-formula> up from the floor of the
upper tunnel and some 5 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">cm</mml:mi></mml:math></inline-formula> from the junction between the tunnel and the
right-hand column. When the airflow in the upper tunnel is direct from the
left-hand column to the right-hand column the directionality is given as
180<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and is close to either 360 or 0<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> when
the flow is reversed. (See Fig. 1).</p>
      <p>Prior to the initiation of an experiment, the entrapped air, having been in
contact with the external environment, displays similar characteristics as
the air outside in terms of temperature, pressure and humidity. However,
once the doors, located at the bottom of each column, are closed the
structure remains sufficiently airtight to permit the changes to
temperature, to humidity and to local pressure brought about during the
course of an experiment to be observed and recorded. The relative humidity
can be reduced to 30 % in the enclosed air through the use of an
industrial dehumidifier. The dehumidifier is always switched off and any
collected water taken away before an experiment is begun.</p>
      <p>Standard physics is applied to the results (Mcllveen, 2010), with separate
calculations for the top tunnel (<xref ref-type="disp-formula" rid="Ch1.E1"/>), the parcel of air affected per second
at the cooling coils (<xref ref-type="disp-formula" rid="Ch1.E2"/>), and the lower section of the right hand column
(<xref ref-type="disp-formula" rid="Ch1.E3"/>). To determine the partial pressure of water vapour at 5 s
intervals, the standard Clausius–Clapeyron equation is used. Since at an
atmospheric pressure of 1013.25 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, water boils at 373 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">K</mml:mi></mml:math></inline-formula>,
represented as <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> it is possible to substitute for <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">and</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and at each temperature, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, to determine the
saturated partial pressure of water, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, for the three locations
(1, 2 and 3). (See Fig. 1, Eqs. 1 and 2).

              <disp-formula id="Ch1.E1" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mfrac><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mfrac><mml:mrow><mml:mi>Q</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula>

        Or

              <disp-formula id="Ch1.E2" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mfrac><mml:mrow><mml:mi>Q</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>⋅</mml:mo><mml:mn>2.303</mml:mn></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>log⁡</mml:mi><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></disp-formula>

        Where <inline-formula><mml:math display="inline"><mml:mi>Q</mml:mi></mml:math></inline-formula>, Latent heat of Evaporation, <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mn>40.65</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">kJ</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">mol</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>, the ideal
gas constant, is 8.3 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">J</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">K</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">mol</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The actual partial pressure of
water vapour, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in the three locations, is given by multiplying the
result by the relative humidity, RH, as measured by the hygrometers, placed in
all three locations (Fig. 1).</p>
      <p>The air density, at that moment in time, is obtained through the use of the
equation of state for ideal gases, namely,

              <disp-formula id="Ch1.E3" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi>R</mml:mi><mml:mi>T</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

        where <inline-formula><mml:math display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> is the barometric pressure (hPa), <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> is the air density in
kg <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is the ideal gas constant, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">J</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">K</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">mol</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>
and <inline-formula><mml:math display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> is the temperature in Kelvin. Since <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> varies with the degree of
humidity in the air, the equation as below is applied, using the values
287 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">J</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">K</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> for dry air and 461 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">J</mml:mi></mml:math></inline-formula>
K<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> for water vapour:

              <disp-formula id="Ch1.E4" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mfenced close=")" open="("><mml:mn>461</mml:mn><mml:mo>⋅</mml:mo><mml:mi>r</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close=")" open="("><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>r</mml:mi></mml:mfenced><mml:mo>⋅</mml:mo><mml:mn>287</mml:mn></mml:mrow></mml:math></disp-formula>

        <inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> is the absolute humidity of water vapour in dry air, hence kg of water
vapour per kg of dry air. The value of <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></inline-formula> the ideal gas constant for moist
air, as water vapour is added or removed, is shown to vary by as much as
1.5, for example, from 288.9 to 287.5 during the course of an experiment.</p>
      <p>To obtain <inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> we need first to obtain <inline-formula><mml:math display="inline"><mml:mi>q</mml:mi></mml:math></inline-formula>, the absolute humidity of water
vapour kg per kg of moist air using (Mcllveen, 2010):

              <disp-formula id="Ch1.E5" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mfenced open="(" close=")"><mml:mn>0.622</mml:mn><mml:mo>⋅</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mtext>wv</mml:mtext></mml:msub></mml:mfenced></mml:mrow><mml:mrow><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi>p</mml:mi><mml:mtext>atmos</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi>p</mml:mi><mml:mtext>wv</mml:mtext></mml:msub></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

        where 0.622 is the ratio of the effective molecular weights of water vapour
and dry air, hence 18/29;  <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mtext>atmos</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the barometric reading at that
moment in time for the three locations and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mtext>wv</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the partial pressure
of water vapour, as calculated at the same time of reading. Then, to convert
<inline-formula><mml:math display="inline"><mml:mi>q</mml:mi></mml:math></inline-formula>, the absolute humidity for moist air, to the absolute humidity for dry air,
<inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula>, the following formula is used:

              <disp-formula id="Ch1.E6" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi>r</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mi>q</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

        To calculate the absolute humidity, <inline-formula><mml:math display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula> (water vapour in grams per cubic metre
of moist air), the values of <inline-formula><mml:math display="inline"><mml:mi>q</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula>, (the air density in kg
<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) are required, as are the values for <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>.</p>
      <p>The air density, <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula>, in kg <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, is obtained using the ideal gas
equation, where the barometric pressure is given in Pascals:

              <disp-formula id="Ch1.E7" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mfrac><mml:mi>p</mml:mi><mml:mrow><mml:mi>R</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">ρ</mml:mi></mml:mrow></mml:math></disp-formula>

        Therefore the humidity in grams per cubic metre of moist air will be
obtained from:

              <disp-formula id="Ch1.E8" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi>h</mml:mi><mml:mo>=</mml:mo><mml:mi>q</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">ρ</mml:mi><mml:mn>1000</mml:mn></mml:mrow></mml:math></disp-formula>

        In order to obtain the kinetic energy values changes in the partial pressure
of water vapour and in air density the following relationship is applied:

              <disp-formula id="Ch1.E9" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="normal">J</mml:mi><mml:mo>=</mml:mo><mml:mtext>kg</mml:mtext><mml:mo>⋅</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mtext>Nm</mml:mtext><mml:mo>=</mml:mo><mml:mtext>Pa</mml:mtext><mml:mo>⋅</mml:mo><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mtext>Ws</mml:mtext></mml:mrow></mml:math></disp-formula>

        Whereby J is joules, N is Newtons, Pa is Pascals and W is Watts. Thereby, the
Ws for both the partial pressure change in the condensing parcel of air and
the change in air density can be calculated. The resulting quantity can then
be converted into the velocity of the airflow (Boyle, 1998):

              <disp-formula id="Ch1.E10" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mtext>Ws</mml:mtext><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>⋅</mml:mo><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>⋅</mml:mo><mml:mi>A</mml:mi><mml:mo>⋅</mml:mo><mml:msup><mml:mi>v</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

        where W is Ws, <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> is the air density in kg <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>v</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> is
the cube of the velocity (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). The area, <inline-formula><mml:math display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>, is taken as the
surface area of the condensing coils, 0.963 <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. Good
correspondence is obtained graphically when the calculated airflow is
compared with the actual measured airflow (see Fig. 26). Equation (10) gives
the ideal relationship between kinetic energy and airflow, as used in
explaining the energy derived from wind turbines (Boyle, 1998). The velocity
to the cube is because the length of traverse of the air depends precisely on
the velocity and therefore adds length to the surface area when calculating
the volume.</p>
      <p>The three variables of temperature, barometric pressure and relative
humidity are all that is required to calculate the partial pressure of water
vapour, using the exponential equation of Clausius–Clapeyron, (Eqs. 1
and 2)
and from that the absolute humidity and air density, (Eqs. 7 and  8) at any
moment in time. It is then a simple task to convert the change in partial
pressure at various points in the structure to kinetic energy in terms of
Watt-seconds (Eqs. 7 and 8). Equally, the changing air densities of the same
parcels of air can be converted to kinetic energy, making direct comparisons
possible between the potential forces (Eq. 9).</p>
      <p>The physics used in the calculations presented here are encapsulated in the
following flow chart, which serves the experimental data as well as the data
from radio-soundings and surface meteorological stations (Bunyard, 2014;
Bunyard et al., 2012).</p>
</sec>
<sec id="Ch1.S3">
  <title>Results</title>
      <p>More than 100 experiments, each lasting approximately 50 min, demonstrate
that sudden changes in the partial pressure of water vapour at the point of
cooling lead to a measurable, clockwise circulation of air, which increases
and decreases according to the rate of change of the partial pressure. The
relationship follows a power law between the rate of change in the partial
pressure of water vapour (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">hPa</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) and the airflow
(<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). It results in a circulation throughout the 14 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula>
length of the experimental structure as air is drawn from the top tunnel into
the area of condensation and then downwards, passing in a clockwise direction
from the right-hand column to the left column and upwards into the upper
connecting tunnel (Fig. 1). In terms of power delivered (kinetic energy as
Ws) the condensation of water vapour, in a chilled parcel of air with
a volume some 430 times smaller than that of the total volume of enclosed
air, is between two and four orders of magnitude greater than that of the air
density change measured for the same parcel of air, the difference in
magnitude corresponding to the relative “dryness” of the air (see Fig. 3
and Eq. 9).</p>
      <p>Through taking account of changes in temperature, relative humidity and
barometric pressure from the strategically-placed sensors (Fig. 1, Eq. 2 to
9), the different forces which come into play can be distinguished, namely:</p>
      <p><list list-type="order">
          <list-item>
            <p>Changes in the partial pressure of water vapour through
condensation, melting and re-evaporation (Experiments 1 to 4, Figs. 4, 6, 8,
10, and 25) and their correspondence to airflow;</p>
          </list-item>
          <list-item>
            <p>Changes in the air density of the chilled parcel air, measured in Watts
as it passes over the cooling coils with comparisons to the kinetic energy of
partial pressure change from condensation (Experiments 1 to 4, Figs. 15, 16,
17, and 18);</p>
          </list-item>
          <list-item>
            <p>The ideal airflow (Eqs. 9 and 10, Figs. 26 and 27) and how the airflow
caused by condensation overcomes the airflow in the counter direction caused
by external differential heating of the two columns (Figs. 4, 5, and 25).</p>
          </list-item>
        </list></p>
      <p>The airflow and condensation profiles for the four experiments shown result
from different internal conditions, including temperature, relative humidity
and differential heating, with the proviso that those internal conditions
are affected over time by external conditions. In particular, small air
exchanges between the external and internal environment take place over the
course of time between experiments, but without impacting an experiment in
course. The internal temperature is measurably affected by the external
temperature and will register differential heating if the sun happens to be
shining on one side of the structure, while the other remains in shade.</p>
      <p>In all experiments, without exception, once the compressor is on and
refrigeration takes place the directionality is close to
180<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and therefore the airflow is clockwise as seen from the
viewpoint of the laboratory. The airflow velocity is determined by two
factors: (a) the directionality of the airflow prior to switching on the
compressor (Experiment 1, Figs. 4 and 5), (b) the rate of condensation as
determined by the rate of change in the absolute (specific) humidity <inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> (Eq. 5
to 8, Figs. 11, 12, 13, and 14). When the initial airflow is
counter-clockwise (Fig. 4 and 5), the airflow resulting from condensation
takes over, and just as a cyclist battles against a headwind, so the
condensation airflow is reduced from what it would be were there no
“headwind”. Hence, accounting for headwind, the airspeed in experiment 1
would be <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn>0.2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>.</p>
      <p>The rate of change in specific humidity for the four experiments is seen in
the following graphs (Figs. 11, 12, 13, and 14).</p>
      <p>By means of applying the equations of state for water vapour and
specifically Eq. (9), the kinetic energies of the rate of change in the
partial pressure of water vapour from condensation and of the air density in
the same parcel of cooled air can be calculated. The resulting curves are
shown in Figs. 15, 16, 17, and 18, and in each instance, at a particular
moment in time, the ratio of air density change to that of partial pressure
change can be determined.</p>
      <p>With airflows of 0.15 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, each parcel of air will take some 0.33 s to
traverse the 0.05 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula> distance from the top to the bottom of the coils.
Empirical evidence of the proper application of physical laws for ideal
gases (Clausius–Clapeyron) is apparent through comparing the weight of
condensed water obtained from the capture of precipitated water, with that
obtained from theoretical considerations of the change in partial pressure
of water vapour and hence in absolute humidity. The “rain” is gathered by
means of a sloping-plane, hard plastic sheet, with a gutter at its lowest
end. Any drops which fail to run into the gutter are mopped up with
absorbent cloths and weighed.</p>
      <p>By measuring (at location 2 in Fig. 1) the changes in humidity <inline-formula><mml:math display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula> per second
taking place in the parcels of air passing through the condenser, a profile of
the changing water vapour content of the air is obtained (Eq. 8). The
experiment of 8  February 2015, when the initial temperature was <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn>1.32</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C and the barometric pressure 1038.85 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula>, gave
a total condensation of 4.45 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">g</mml:mi></mml:math></inline-formula> which agreed with the quantity that
precipitated. For the experiment of 27  July 2015, the accumulated
condensate at 3000 s measured 50 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">g</mml:mi></mml:math></inline-formula> and the amount gathered was 51 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">g</mml:mi></mml:math></inline-formula>.</p>
      <p>In general, the compressor for the cooling coils is switched off 15 min
before the end of the experiment at 50 min. That period allows the
temperature to increase throughout the structure, and in particular in the
section with the coolant coils, such that the ice melts and the liquid water
falls as rain (sometimes as hail) onto the collecting sheet which lies under
the coils at the base of the right-hand column. Calculations of the expected
fallout of rain accord closely to that collected (Figs. 19, 20, and 21).</p>
      <p>When the initial relative humidity is low, i.e. less than 40 %, the
ice-condensate on the coils is found to ablate directly into water vapour
and hence cannot be collected. Calculations of the expected fallout of rain
from an experiment take account of the increase in absolute and relative
humidity resulting from any such ablation. For instance, for Experiment 4,
when the initial relative humidity had been reduced to 31 %, the
quantity of rain collected at the conclusion of the experiment at 50 min
amounted to 2 grams and the calculation of the expected fallout from changes
in the humidity of the enclosed air in the experimental structure was 1.2
grams (Fig. 21).</p>
      <p>When the final relative humidity in the experimental structure is above 60
 % then ablation appears to be minimal and the ice on the coils falls
as rain as seen in Figs. 19 and 20.</p>
      <p>The experimental results make it clear that the key to airflow resides in
the rate of partial pressure change. The latent heat release, of the same
kinetic energy as that from negative pressure change, by warming the air and
making it less dense, tends to generate a counter flow to that from water
vapour condensation. Taking gravitational considerations into account the
air moves downwards to the cooling coils rather than upwards, thus
generating a clockwise circulation.</p>
      <p>Each experiment, under different initial conditions and, during the course of
the experiment generating its own particular conditions, follows the same
pattern in terms of the partial pressure change from condensation and
re-evaporation having a direct impact on the airflow as measured with the 2-D
ultrasonic Gill anemometer. In Experiment 1 and 4, the reduction in pressure,
during the time when the compressor is switched on and refrigeration is
occurring, is indicated by the sensor in location 2, just beside the cooling
coils (Fig. 1). That fall in pressure should be contrasted with the
barometric readings from above the coils, in the upper tunnel at site No. 1
(Fig. 1). The fall in pressure at location 2, while the compressor is
running, can be interpreted as signalling the proximate reduction in pressure
as condensation occurs. The increase in barometric pressure above the
condensation coils in location 1, Fig. 1, could be registering the increase
in air density from a simultaneous drop in temperature and in absolute
humidity (Figs. 22 and 23).</p>
      <p>If all the kinetic energy release from condensation and the reduction in
partial pressure of water vapour were focussed into a single uni-directional
flow, then the ideal flow would be given by Eq. (10), the straight line being
determined by taking the log of both axes (Fig. 24).</p>
      <p>On account of the implosive pressure change as a result of condensation, the
kinetic energy release will be from all angles. Nevertheless, flow
tendencies will result because of other factors, such as gravity or, in the
case of the atmosphere at large, the effect of the upper jet streams on the
columns of air below. As a result, the ideal flow will not be encountered in
the experiment, nor indeed in the atmosphere at large. In the experiments,
the actual uni-directional flow from condensation is found to approximate
one-fifth of the ideal flow. (Figs. 25 and 26). In all experiments, despite the
different initial conditions and the timing and duration of the period of
refrigeration, the close association between the airflow and the rate of
change in the partial pressure of water vapour is to be seen, as shown in
Figs. 4, 6, 8, 10, and 25.</p>
      <p>From the data, the kinetic energy in Watt-seconds can be calculated: (1)
derived from the partial pressure change in water vapour,  (2) from the air
density rate change at the point of cooling,  (3) the latent heat release
(Fig. 27). The results are uniform and unequivocal in that the kinetic
energy release from the imploding parcel of air, subjected to refrigeration,
at an approximate rate of 0.33 s per parcel of volume 0.048 <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>,
when the unidirectional clockwise velocity of air is 0.15 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, is
sufficient to account for the airflow. The kinetic energy release from the
change in air density in the same parcel of air is between two and four
orders of magnitude less than the partial pressure change over the same time
period, the difference depending on the relative humidity at the start of
each experiment (Figs. 3, 15, 16, 17, and 18).</p>
      <p>The correspondence between the airflow (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) and the partial pressure
change (hPa) becomes clear from more than one hundred experiments when
analysed against the rate of change per second of the specific (absolute)
humidity. The relationship between the partial pressure change in water
vapour and the change in specific humidity follows a straight line through
the origin with an <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.9956;  the relationship of the airflow to the
change in specific humidity follows a power law curve with an <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of
0.964 (Fig. 28).</p>
      <p>Meanwhile the relationship between the airflow and the change in partial
pressure of water vapour follows a power law, as expected, with an
<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.9761. The ideal curve of the airflow from the kinetic energy of
the partial pressure change closely follows the trajectory of the measured
airflow (Fig. 29).</p>
      <p>The chilled parcel of air not only has a kinetic energy equivalent to three
orders of magnitude less than that of the change in the partial pressure of
water vapour but the correlation with the airflow is substantially weaker
than is seen with either the change in absolute humidity or the partial
pressure change (Fig. 30).</p>
      <p>Finally, significant correlations are encountered when the changing rate of
partial pressure as a result of condensation is matched against airflow, as
seen in Figs. 31 and 32 for two different experiments.</p>
      <p>Table 1 displays data derived from the right-hand column of Experiments 1 to
4.</p>
</sec>
<sec id="Ch1.S4">
  <title>Discussion</title>
      <p>The highly significant difference in the kinetic energy value of the
observed partial pressure change compared to that of the observed air
density change in the same cooled parcel of air suggests that the notion of
the fundamental importance of water vapour condensation in driving mass air
convection is correct (Table 1). Latent heat release on condensation
dissipates rapidly in the surrounding medium, providing thermal radiation,
and is ultimately lost to the environment. The latent heat release from
condensation in terms of kinetic energy is equal to kinetic energy
calculated for the partial pressure change resulting from the same
condensation (Fig. 27). That confirms the physical relationship between
partial pressure change and the energy involved in the phase transformation
from vapour to liquid and ice, the latter being measurable after it melts
and falls, either as rain or hail. Even though the latent heat is dissipated
to the surrounding air, thus offsetting the cooling from the refrigeration
coils, and in principle tending to cause the air to rise rather than sink,
in a counter-clockwise motion, the circulation still flows in a clockwise
direction.</p>
      <p>Given the ratio between the air density change and partial pressure change
in the same parcel of air, we conclude that the <italic>force majeure</italic> in causing the circulation
is the partial pressure change. Meanwhile, the clockwise directionality in
the experimental structure is the result of the relative mass difference
between the volume of air above the cooling coils compared to that below;
hence more than three times of air mass below compared to above. Given the
experimental set-up, the net result of the difference in air mass above and
below the cooling coils is that the drawing in of air as the partial
pressure reduces will more easily be from above rather than below. Once the
circulation is set in motion it is maintained preferentially by the flow of
air from above which in its turn undergoes cooling and condensation. In
general, at an airflow averaging 0.15 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, three parcels of air of
volume 0.048 <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> should pass over the coils per second. The cooler air
below the coils will increase the likelihood of the flow during condensation
being in the clockwise direction, although as pointed out, the energies
involved are negligible compared to the energies liberated when water vapour
condenses.</p>
      <p>During some experiments, especially when the summer sun was differentially
heating the structure, counter-clockwise flow was observed;  presumably
caused by air density changes, with hot air rising and cooler air sinking
(Figs. 4 and 5). Since each column contains more than 200 times the volume
of air compared to the parcel of air passing over the condensing coils, the
kinetic energy contained in the warmer air is therefore sufficient to drive
the airflow. That airflow, nonetheless, is generally weaker by one half or
more than that obtained when cooling the coil-associated parcel of air, even
though in volume it is 430 times smaller. That finding confirms that air
density changes are considerably weaker in their impact on airflow than that
of partial pressure change brought about through condensation.</p>
      <p>Makarieva (2007) argues that the high rate of condensation over the tropical
rainforest, fed by evapotranspiration, will lead to surface airflow as
a result of the pressure change (1200-fold reduction in volume of each gram
molecule of water vapour condensed). If so, then the experimental findings,
described in the previous section, and all based on the fundamental physics
of ideal gases, can be extrapolated to the wider arena of the earth's
atmosphere inasmuch as the same physics should prevail during cloud
formation and dissipation.</p>
      <p>The energies in evapotranspiration from the rainforest and natural
ecosystems are enormous when totalled for the entire 6 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">million</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of
the Amazon Basin, being equivalent in brute energetic terms to 15 atomic
bombs every second, (each 15 kT of TNT) (Salati, 1987). Equally, the
conventional reason for the reduction in the environmental lapse rate (ELR)
from 9.8 to 5 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C or less per kilometre
altitude when the air is humid refers to the release of latent heat on
condensation, which warms the surrounding air. That is certainly true, but
based on the biotic pump principle, could it be that the rate of cooling
reduces per altitude because warm surface air is sucked upwards at a rate
faster than were it to be dry air which consequently does not undergo
condensation? That being the case, the high rate of condensation over the
rainforest will increase horizontal flow and, as a result, the
transportation of more water vapour from the tropical Atlantic Ocean. The
experimental results provide a clue as to the expected airflow from a given
rate of condensation (Figs. 28 and 29).</p>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <title>Conclusion</title>
      <p>This paper describes a series of experiments, in a specially-designed
structure, to test the physics of condensation and its potential to cause
airflows. The results have provided data for a careful analysis of the
physics involved, showing that condensation and the subsequent release of
kinetic energy from the partial pressure change do indeed account for the
observed airflow. The experimental results therefore provide evidence that
condensation and not buoyancy is the major mechanism driving airflow, thus
lending strong support to one of the main tenets of the BPT.</p>
      <p>The results are significant and unambiguous. At least at the laboratory
scale, using only conventional physics, such as is employed in
climatological studies, the primary force driving convection appears to be
the kinetic energy released in the implosive events which take place during
condensation, with a sudden reduction – <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn>1200</mml:mn></mml:mrow></mml:math></inline-formula>-fold – in the air
volume of one gram-molecule of water vapour (18 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">g</mml:mi></mml:math></inline-formula>) as it transforms to
liquid and ice. Air density changes are shown to be orders of magnitude less
important in convection processes compared to partial pressure changes on
condensation.</p>
      <p>The macro-physics of the experiment is not fundamentally different from that
in the lower atmosphere at large. The same laws apply and are widely used by
hydrologists, meteorologists and climatologists. Those opposed to the biotic
pump theory should therefore re-consider their position and take into
account that the physics underlying the theory may not only be correct, but
that it operates in the atmosphere at large.</p>
      <p>The general implications are that the great forests of the world play
a fundamental role in air mass circulation through providing water vapour via
evapotranspiration, and are therefore the “fuel” for a high rate of cloud
condensation. Airflow circulation is the net result, bringing the rain to
the deep interior of continents. The Biotic Pump theory suggests that the
hydrological role of rainforests is by far their most important climatic
contribution, and that large-scale deforestation may well be as detrimental
in its consequences for the well-being of the planet as are greenhouse gas
emissions. Indeed, it may be that in macro-climatological terms whether
forests are net absorbers or emitters of greenhouse gases is relatively
insignificant compared to their hydrological role.</p>
</sec>

      
      </body>
    <back><ack><title>Acknowledgement</title><p>The experimental structure with its equipment and the actual experimentation
made possible through the bounteous support from the Good Energies
Foundation, Switzerland. Thanks too to Jaymart Ltd for having provided the
matting to cover the flooring of the structure. We are extremely grateful to
Jon Tinker for his comments and suggestions in the preparation of this
manuscript and to Francis Dufort for his help designing the structure.</p></ack><ref-list>
    <title>References</title>

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<table-wrap id="App1.Ch1.T1"><caption><p>Data from Experiments 1 to 4.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{0.8}[0.8]?><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:thead>
       <oasis:row>  
         <oasis:entry colname="col1">Data</oasis:entry>  
         <oasis:entry colname="col2">Experiment 1</oasis:entry>  
         <oasis:entry colname="col3">Experiment 2</oasis:entry>  
         <oasis:entry colname="col4">Experiment 3</oasis:entry>  
         <oasis:entry colname="col5">Experiment 4</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">6 August</oasis:entry>  
         <oasis:entry colname="col3">22 September</oasis:entry>  
         <oasis:entry colname="col4">6 March</oasis:entry>  
         <oasis:entry colname="col5">17 September</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">Initial temperature</oasis:entry>  
         <oasis:entry colname="col2">20.09</oasis:entry>  
         <oasis:entry colname="col3">13.69</oasis:entry>  
         <oasis:entry colname="col4">7.51</oasis:entry>  
         <oasis:entry colname="col5">20.18</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Final temperature</oasis:entry>  
         <oasis:entry colname="col2">19.53</oasis:entry>  
         <oasis:entry colname="col3">13.21</oasis:entry>  
         <oasis:entry colname="col4">8</oasis:entry>  
         <oasis:entry colname="col5">16.64</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Initial RH %</oasis:entry>  
         <oasis:entry colname="col2">73.93</oasis:entry>  
         <oasis:entry colname="col3">90.54</oasis:entry>  
         <oasis:entry colname="col4">97.49</oasis:entry>  
         <oasis:entry colname="col5">31.15</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Final RH %</oasis:entry>  
         <oasis:entry colname="col2">63.21</oasis:entry>  
         <oasis:entry colname="col3">75</oasis:entry>  
         <oasis:entry colname="col4">92.15</oasis:entry>  
         <oasis:entry colname="col5">47.12</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Rate change <inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula>, kg <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> dry air at 1000 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">s</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">0.00006535</oasis:entry>  
         <oasis:entry colname="col3">0.0000567</oasis:entry>  
         <oasis:entry colname="col4">0.000034206</oasis:entry>  
         <oasis:entry colname="col5">0.00003196</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Airflow, m <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>   clockwise <inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> counter</oasis:entry>  
         <oasis:entry colname="col2">0.1<inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>0.09 <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mn>0.19</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">0.18</oasis:entry>  
         <oasis:entry colname="col4">0.06<inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>0.02 <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mn>0.08</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">0.14</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Initial air moisture g <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> air</oasis:entry>  
         <oasis:entry colname="col2">15.95</oasis:entry>  
         <oasis:entry colname="col3">13.89</oasis:entry>  
         <oasis:entry colname="col4">7.614</oasis:entry>  
         <oasis:entry colname="col5">7.14</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Final moisture   g <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> air</oasis:entry>  
         <oasis:entry colname="col2">13.91</oasis:entry>  
         <oasis:entry colname="col3">11.12</oasis:entry>  
         <oasis:entry colname="col4">7.74</oasis:entry>  
         <oasis:entry colname="col5">8.33</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Collected rainfall</oasis:entry>  
         <oasis:entry colname="col2">40</oasis:entry>  
         <oasis:entry colname="col3">25</oasis:entry>  
         <oasis:entry colname="col4">0</oasis:entry>  
         <oasis:entry colname="col5">3</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Calculated rainfall</oasis:entry>  
         <oasis:entry colname="col2">41.4</oasis:entry>  
         <oasis:entry colname="col3">24.26</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>7</oasis:entry>  
         <oasis:entry colname="col5">1.19</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">KE at 1000 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">s</mml:mi></mml:math></inline-formula> rate change ppwv in Ws</oasis:entry>  
         <oasis:entry colname="col2">10.23</oasis:entry>  
         <oasis:entry colname="col3">8.835</oasis:entry>  
         <oasis:entry colname="col4">4.866</oasis:entry>  
         <oasis:entry colname="col5">4.271</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">KE at 1000 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">s</mml:mi></mml:math></inline-formula> air density rate change in Ws</oasis:entry>  
         <oasis:entry colname="col2">0.00083</oasis:entry>  
         <oasis:entry colname="col3">0.000663</oasis:entry>  
         <oasis:entry colname="col4">0.0006497</oasis:entry>  
         <oasis:entry colname="col5">0.0008779</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Ratio of KE</oasis:entry>  
         <oasis:entry colname="col2">12 327</oasis:entry>  
         <oasis:entry colname="col3">13 334</oasis:entry>  
         <oasis:entry colname="col4">7 490</oasis:entry>  
         <oasis:entry colname="col5">4 865</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

      <fig id="App1.Ch1.F1"><caption><p>The experimental structure, showing diagrammatically the positioning
of the sensors, Barometer (BAR), Relative Humidity Hygrometer (RH),
Thermocouple (T), 2-D Ultrasonic Anemometer (UA), the refrigeration coils
(Coils) and the rain-collector. Sensors for RH and T have been placed at each
of the three locations, numbered (<xref ref-type="disp-formula" rid="Ch1.E1"/>) (<xref ref-type="disp-formula" rid="Ch1.E2"/>) and (<xref ref-type="disp-formula" rid="Ch1.E3"/>), and
BAR at locations (<xref ref-type="disp-formula" rid="Ch1.E1"/>) and (<xref ref-type="disp-formula" rid="Ch1.E2"/>). The air is captured from the
outside air at the beginning of each experiment. Changes in temperature,
relative humidity and barometric pressure depend on artificial refrigeration
from the cooling tubes and to an extent, not measured, from the impact of
external wind and insolation upon the insulated (PVC) structure.</p></caption>
      <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f01.pdf"/>

    </fig>

      <fig id="App1.Ch1.F2"><caption><p>A flow chart (Bunyard, 2014), displaying the physics used in the
experiment and in handling radiosounding data as for 24 August 2012; Boa
Vista, Roraima, Brazil.</p></caption>
      <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f02.pdf"/>

    </fig>

      <fig id="App1.Ch1.F3"><caption><p>Ratio of kinetic energy of partial pressure change (ppwv) to that of
air density change, both converted to Ws, as the initial humidity in the
experimental structure is theoretically reduced from 100 % RH (relative
humidity) to 1 %. The <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis gives the derived ratio of the kinetic
energies in Ws and the <inline-formula><mml:math display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> axis indicates the rate at which the specific
humidity reduces because of condensation in kg of water vapour change per kg
dry air (r).</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f03.pdf"/>

    </fig>

      <fig id="App1.Ch1.F4"><caption><p>Experiment 1 (6 August 2015). Profile of condensate change hPa
<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (red and left <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis) and airflow m <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (black
right <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis). The airflow before the compressor is switched on and when
switched off is the result of external differential heating (insolation) of
the two columns. The flow from that heating is counter-clockwise and once the
compressor is switched on the directionality of the airflow changes abruptly
to clockwise as seen in, with a change from 360 to 180<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. The
clockwise airflow from the condensation therefore competes against default
the counter-clockwise flow from differential exposure of the structure to
sunlight. The resultant airflow during condensation is <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn>0.1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The airflow noise is reduced through displaying the
flow with a 10 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">s</mml:mi></mml:math></inline-formula> moving average.</p></caption>
      <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f04.pdf"/>

    </fig>

      <fig id="App1.Ch1.F5"><caption><p>Experiment 1 (6 August 2015). Anemometer reading m <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>
with directionality. The central section, from 600 to 2000 s, when the
compressor is switched on, shows a directionality of 180<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, such that
the flow is clockwise. Before switching on the condenser and equally after
switching it off, the airflow, with directionality circa 360<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, is
counter-clockwise. During the course of the experiment, the changing
directionality is evidence that condensation of a parcel of air, 400 times
smaller in volume than the total enclosed air volume, can overcome the
counter-clockwise circulation derived from the high summer insolation of the
right-hand column. See Fig. 4 for the correspondence between condensation and
airflow.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f05.pdf"/>

    </fig>

      <fig id="App1.Ch1.F6"><caption><p>Experiment 2 (22 September 2015): partial pressure change vs.
airflow. The compressor is switched on at 300 s and switched off at
2200 s. The airflow velocity declines during the time of condensation
as does the rate of condensation owing to the reduction in absolute
humidity. The airflow “noise” is reduced by averaging the flow over a moving
10 s period.</p></caption>
      <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f06.pdf"/>

    </fig>

      <fig id="App1.Ch1.F7"><caption><p>Experiment 2 (22  September 2015). Airflow and directionality.
See Fig. 6 for the correspondence between airflow induced by condensation
and the change in partial pressure of water vapour (hPa <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). In
comparison with the airflow in Experiment 1, the airflow in Experiment 2
exceeds 0.2 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">m</mml:mi></mml:math></inline-formula>, even though the initial starting conditions are similar in
both experiments. Airflow is blue, directionality showing clockwise movement
is brown.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f07.pdf"/>

    </fig>

      <fig id="App1.Ch1.F8"><caption><p>Experiment 3 (6 March 2015). The profile of the inverse
change in the partial pressure of water vapour, hPa <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (red) shows the peaks
corresponding with peaks in the airflow m <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (blue). During this experiment,
because of external low temperatures (<inline-formula><mml:math display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) the
compressor thermostat automatically switched the refrigeration on and off.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f08.pdf"/>

    </fig>

      <fig id="App1.Ch1.F9"><caption><p>Experiment 3 (6 March 2015). The low external temperatures lead
to pulsing of the thermostatically controlled compressor. As seen in Fig. 8,
the pulsing of the compressor corresponds precisely to airflow (blue). The
directionality (brown) is clockwise.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f09.pdf"/>

    </fig>

      <fig id="App1.Ch1.F10"><caption><p>Experiment 4 (17 September 2015). A dehumidifier was used prior to
the experiment to bring the relative humidity down below 40 %. The
airflow during the period of cooling, from 300 to 2000 s, was reduced to
approximately 0.15 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, indicating that the airflow responded
to the reduction in the rate of change of the partial pressure of water
vapour.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f10.pdf"/>

    </fig>

      <fig id="App1.Ch1.F11"><caption><p>Experiment 1 (6 August 2015). The cooling begins at 300 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">s</mml:mi></mml:math></inline-formula>
and finishes at 1850 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">s</mml:mi></mml:math></inline-formula>. The rate of change in the specific (absolute)
humidity reduces sharply in the parcel of air passing over the cooling coils
at the switching on of the compressor (hence showing a “drying of the air”)
but begins to rise during the time during which cooling takes place (showing
that the rate of “drying” is declining). Once the compressor is switched
off the temperature rises and the rate of change in the specific humidity in
the parcel of air begins to approach zero, as it was at the beginning of the
experiment. At 1000 s the rate of change in the specific humidity <inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> is
<inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.00006535 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">kg</mml:mi></mml:math></inline-formula> of water vapour per kg dry air.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f11.pdf"/>

    </fig>

      <fig id="App1.Ch1.F12"><caption><p>Experiment 2 (22 September 2015). The rate of change in the specific
(absolute) humidity reduces sharply in the parcel of air passing over the
cooling coils at the switching on of the compressor. At 1000 s the rate of
change in specific humidity r is <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.000056677 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">kg</mml:mi></mml:math></inline-formula> of water vapour
per kg dry air.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f12.pdf"/>

    </fig>

      <fig id="App1.Ch1.F13"><caption><p>Experiment 3 (6 March 2015). The pulsing changes in the rate of
change in specific humidity, <inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula>, reflect the thermostatically controlled
switching on and off of the compressor. In this experiment, the rate of
change of <inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> in the parcel of air at 1000 s is <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.000063111 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">kg</mml:mi></mml:math></inline-formula>
water vapour per kg dry air. At 1200 s the change in <inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> is
<inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.0000342 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">kg</mml:mi></mml:math></inline-formula> water vapour per kg dry air and the measured airflow
is 0.05 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f13.pdf"/>

    </fig>

      <fig id="App1.Ch1.F14"><caption><p>Experiment 4 (17 September 2015). The dehumidifer has reduced the
relative humidity to below 40 % and, despite initial temperatures <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, the change to <inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> in the cooled parcel of air at 1000 s is
reduced to <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.00003189 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> dry air.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f14.pdf"/>

    </fig>

      <fig id="App1.Ch1.F15"><caption><p>Experiment 1 (6 August 2015). Left-hand <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis is the air density
change <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> in Ws of a parcel of air as it passes through the
condenser (brown). The right-hand <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis is the partial pressure change Ws
of the same parcel (grey) as it passes from the upper tunnel into the
condenser. At 1000 s the ratio between the air density change in Ws and the
partial pressure change in Ws is 14 933.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f15.pdf"/>

    </fig>

      <fig id="App1.Ch1.F16"><caption><p>Experiment 2 (22  September 2015). The respective kinetic energy
of the rate of change in water vapour partial pressure and of air density in
the same parcel of air. At 1000 s the ratio between the two curves is
13 333.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f16.pdf"/>

    </fig>

      <fig id="App1.Ch1.F17"><caption><p>Experiment 3 (6  March 2015). The ratio at 1000 s between
the kinetic energy of the partial pressure change (right-hand <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis) vs.
the air density change (left-hand <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis) is 6544.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f17.pdf"/>

    </fig>

      <fig id="App1.Ch1.F18"><caption><p>Experiment 4 (17 September 2015). The initial reduction in RH to
below 40 % has led to a ratio of 4865 for the respective kinetic energies
of air density change and of water vapour partial pressure change. That
decline in the ratio compared to that calculated in Figs. 15 and 16 fits the
theoretical reduction (Fig. 3) in the ratio as the relative humidity declines
in the enclosed air.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f18.pdf"/>

    </fig>

      <fig id="App1.Ch1.F19"><caption><p>Experiment 1 (6 August 2015). The condensate accumulates as an
ice-coating on the cooling coils during the course of the cooling. Through
the application of Eqs. (1)–(8) the change in the air humidity in each
parcel of air can be calculated (grams per second and grams total). At
3000 s (50 min) the total accumulated is 41.57. That collected as rain
amounted to 40 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">g</mml:mi></mml:math></inline-formula>. The left hand <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis (brown) denotes the
accumulated ice and the right-hand <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis (blue) the inverse profile of the
change in condensate.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f19.pdf"/>

    </fig>

      <fig id="App1.Ch1.F20"><caption><p>Experiment 2 (22 September 2015). The condensate accumulates as an
ice-coating on the cooling coils during the course of the cooling. Through
the application of Eqs. (1)–(8) the change in the air humidity in each
parcel of air can be calculated (grams per second and grams total). At
3000 s (50 min) the total accumulated is 24.26. That collected as rain
amounted to 25 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">g</mml:mi></mml:math></inline-formula>. The left hand <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis (brown) denotes the
accumulated ice and the right-hand <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis (blue) the inverse profile of the
change in condensate.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f20.pdf"/>

    </fig>

      <fig id="App1.Ch1.F21"><caption><p>Experiment 4 (17  September 2015). The condensate in the total
enclosed air (blue) compared to the change in the air from each cooled
parcel (brown). By the end of the experiment (3000 s) the total
moisture in the enclosed volume of air is close to that at the commencement
of the experiment, indicating that ice-condensate has ablated. The rainfall
collected amounted to 3 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">g</mml:mi></mml:math></inline-formula> and that calculated to 1.19 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">g</mml:mi></mml:math></inline-formula>.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f21.pdf"/>

    </fig>

      <fig id="App1.Ch1.F22"><caption><p>Experiment 4 (17 September 2015). Barometric pressure, hPa, in upper
tunnel (before the flow to the coils) (blue) and at the point of cooling
(brown). The Bar sensor (No. 2 Fig. 1, brown) shows a reduction in pressure
of approximately 1 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> during the time of cooling. The Bar sensor in
the upper tunnel (No. 2, Fig. 1 blue), and upstream of the airflow shows an
increase in pressure of approximately 1 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> during the cooling
period.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f22.pdf"/>

    </fig>

      <fig id="App1.Ch1.F23"><caption><p>Experiment 1. Barometric pressures, hPa and partial pressure rate
change hPa <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The Bar sensor (No. 2 Fig. 1, brown) shows
a reduction in pressure of approximately 1 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> during the time of
cooling. The Bar sensor in the upper tunnel (No. 2, Fig. 1 blue), and
upstream of the airflow shows an increase in pressure of approximately
2 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">hPa</mml:mi></mml:math></inline-formula> during the cooling period. That increase in pressure fits the
pattern of cooler, denser, less moist air.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f23.pdf"/>

    </fig>

      <fig id="App1.Ch1.F24"><caption><p>The theoretical airflow resulting from measured rate changes to
the reduction in the partial pressure of water vapour (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">hPa</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) as a result of
condensation (blue). The partial pressure change hPa <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is from location 2,
Both the <inline-formula><mml:math display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis are in a logarithmic scale to base 10.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f24.pdf"/>

    </fig>

      <fig id="App1.Ch1.F25"><caption><p>Experiment (1 March 2015). The partial pressure change (red) is
indicated on the left-hand <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis and the actual airflow (blue) on the
right-hand <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis. The resulting curves should be compared with Fig. 26 in
which the partial pressure change is converted into airflow. The ideal
airflow is some 5 times greater than the actual airflow. The compressor was
switched on at 300 s, off at 800 s and on again at 1200 s to be switched
off finally at 1600 s.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f25.pdf"/>

    </fig>

      <fig id="App1.Ch1.F26"><caption><p>Calculated ideal airflow/5 (red) and actual airflow for 1 March 2015 (blue). Left axis calculated airflow, right axis the actual
measured airflow and <inline-formula><mml:math display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> axis the time in seconds. Counter flow at the
beginning of the experiment was equal to 0.03 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and should be added to the
actual flow measured during condensation of 0.15, thereby totalling 0.18 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The ideal calculated flow, divided by 5 gives a velocity of 0.2 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f26.pdf"/>

    </fig>

      <fig id="App1.Ch1.F27"><caption><p>Experiment 27 July 2015. Cumulative Latent heat release Ws from
calculated per second quantity of condensate (purple) and of partial
pressure change (red). The two curves coincide confirming the two modes of
calculation, one from gram quantity of condensate and the other from
pressure change. The right axis is airflow (brown).</p></caption>
      <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f27.pdf"/>

    </fig>

      <fig id="App1.Ch1.F28"><caption><p>Collected data from 60 experiments with differing initial
conditions. The straight-line curve (blue) left <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis, shows the direct
relationship between the partial pressure change in Ws and the
rate of change in specific humidity, kg/second. The right-hand <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis shows
the measured airflow m <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (brown) with a power law relationship to the rate
of change in specific humidity.</p></caption>
      <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f28.pdf"/>

    </fig>

      <fig id="App1.Ch1.F29"><caption><p>The relationship between airflow and the change in the partial
pressure of water fits a power law. The curve of the actual airflow (yellow)
corresponds well with the curve of the expected theoretical relationship in
relation to the kinetic energy of the partial pressure change in
Ws (blue) <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. Both axes log to base 10.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f29.pdf"/>

    </fig>

      <fig id="App1.Ch1.F30"><caption><p>The relationship between the changing air density of the cooled
parcel of air and airflow. Not only is the kinetic energy of the cooling air
(brown) four orders of magnitude less than that of the partial pressure
change but it shows a poorer correlation. Both axes logarithmic to base 10.</p></caption>
      <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f30.pdf"/>

    </fig>

      <fig id="App1.Ch1.F31"><caption><p>Correlation between partial pressure change hPa <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, and airflow
m <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, during experiment 9  October 2014. <inline-formula><mml:math display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula> axis partial pressure change;
<inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis airflow. Correlation <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, 0.97.</p></caption>
      <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f31.pdf"/>

    </fig>

      <fig id="App1.Ch1.F32"><caption><p>Experiment 5  August 2015, showing significant correlation
between partial pressure change and airflow. Correlation coefficient 0.97,
<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> 0.94.</p></caption>
      <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://hess.copernicus.org/preprints/12/10921/2015/hessd-12-10921-2015-f32.pdf"/>

    </fig>

    </app></app-group></back>
    </article>
