June 30, 2024 was a day of huge evaporation! Will June 30, 2025 be a repeat?
Richard Williams
Principal of Phaethon Research for Clean Energy and Arethusa Investing In Clean Water
Abstract
On June 30, 2024, 9.24 millimeters (.364 inches) of canal water evaporated in West Haven, Utah. The Penman Equation with the 20-step procedure developed by the University of Florida is the method used for calculating evaporation with a combination of satellite data on radiation from NEON and weather data from Utah State University’s Climate Center https://edis.ifas.ufl.edu/publication/AE459 https://climate.usu.edu/ https://data.neonscience.org/data-products/DP1.00024.001 ?
The historical averages for June, and July, were 6.9 mm/day and 7.93.mm/day respectively for West Haven. Evapotranspiration and Precipitation Data for Calculating Irrigation Water Requirements in Utah??https://extension.usu.edu/irrigation/research/evapotranspiration-and-precipitation-data The method of computation for Utah’s historical evaporation is unknown thus precluding a direct comparison.
However, it is clear from the following weather and meteorological data, that June 30 had nearly ideal conditions for evaporation! The humidity range of 42 t0 51, is evidence that air had capacity to become saturated with vapor. There was a rapid rise in water temperature, 21.4 degrees Celsius at 8:30 am to 23.4 degrees Celsius at 7:00 pm., A high average air temperature 30.05 degrees Celsius (86 Degrees Fahrenheit) easily explained the rise in water temperature. Finally, a moderate breeze prevailed at 6.53 meters/second (14.6 miles per hour).
12:30 pm, was the peak moment of evaporation! The temperature was 36.67 Celsius (98 degrees Fahrenheit) and wind velocity of 10.73 meters/second (24 miles per hour). ??With focus upon this peak, this paper addresses the question “Will June 30, 2025 be a Repeat?” To answer this question, we posit a rectangular prism of 1 square meter with a depth of one millimeter at 12:30 pm on a canal in West Haven, Utah June 30, 2024. The canal is 7.56 kilometers (4.7 miles) away. The prism travels at velocity of 1.176 meters per second (2.5 miles/hour). ?It covers a distance of planned canal top photovoltaic project, 426.72 meters (1400 feet) in 362.34 seconds!
A range of likely and possible interactions between the prism and five evaporation agents are explored. These evaporation agents are set forth below:
1 Wind
2 Direct Normal Irradiance,
3 Diffuse Radiation
4 Air to Canal heat transfer,
5 Thermal Diffusion
The agents evaporate four types of molecules. The molecules are classified by buoyancy, phase, and level of energy. Together the agents and the molecules comprise the evaporation task force!
Our findings are the wind generates 70.54 newtons at an average velocity,10.73m/s. It can displace a rectangular prism with 1-meter x 1-meter x 7 mm. dimensions, At a depth of 7mm., there are number of molecules with negative buoyancy that can be evaporated! 70.54 newtons can easily break the bonds of surface tension .742 n/meter.
The convective heat transfer coefficient increases by 21.2% when the wind speed increases by each 5 m/s increment. Given the coefficient is 100 watts/m^2 kelvin at wind velocity of 4m/s, the coefficient increases to a range between 122 and 150 watts/meter^2 Kelvin. The high velocity also means more air molecules per second transfer heat to the prism.
The canal temperature increased from 21.4 Celsius at 7:30 am to 23.4 Celsius at 7:00 pm. As a result, buoyancy of water molecules within 2 millimeters of the surface increased. Also, the rate of vaporization, and amount of heat transferred by diffusion rose!
The last findings pertain to planned Canal Top PV. First, visual inspection of some of the canal top structures in India and artists’ rendering of structures in Arizona and California reveals possible low-pressure areas. These areas present a risk of increasing wind velocity via the Venturi effect! Second, 362.34 seconds of interception of sunlight is unlikely to affect the daily evaporation rate! Third, management of the wind is vital to averting a repeat of high evaporation on June 30, 2025!
Introduction
Any discussion of evaporation starts with the Sun, the Earth, and The Second Law of Thermodynamics: a system seeks to achieve its lowest energy state. The Sun, the most important actor, distributes on average 1361 watts per square meter to top of Earth’s atmosphere. AI Google
A net of about 1000 watts per square meter makes its way past clouds into atmosphere. Air molecules absorb a portion of the incoming radiation. The Earth on average receives 340 watts /square meter. Google AI The Sun’s uneven distribution of heat causes some parts of atmosphere to be heated to a greater extent than the others. The movement of air from colder high-pressure parts of the atmosphere to hotter low-pressure areas is wind. The movement is the first application of the Second Law of Thermodynamics: movement to lowest energy state.
The Earth has sufficient mass for gravity to hold onto an atmosphere. The atmosphere takes its place as furthest from the earth as the least dense phase of matter. As the distance of the Sun changes relative to the Earth on yearly and daily basis, water liquid and water vapor molecules gain or lose energy.
Evaporation is another application of The Second Law of Thermodynamics. Rising Molecules are described as possessing positive buoyancy! When the molecules stop rising they achieve neutral buoyancy and their lowest energy state. Conversely, molecules that have negative buoyancy fall. They keep falling until they reach neutral buoyancy. The Second Law of Thermodynamics also dictates the movement of heat in the water. The heat moves from warmer areas to cooler areas.
The Penman equation and its various permutations, is the most widely accepted formula for computing evaporation. The best data collection method for the Penman equation is Eddy covariance. This method entails measurement of change in atmospheric fluxes in real time with use of sophisticated instruments placed at distances from each other!
?The 20-step procedure of the University of Florida is a significant step down in accuracy from Eddy Covariance. Thus any Penman Method?computation should have a large range of uncertainty. Based on literature in the field plus or minus 30% is appropriate. ??Researchers study true scale of evaporation at Lakes Mead, Powell By Henry Brean Las Vegas Review-Journal April 19, 2019 https://bouldercityreview.com/news/researchers-study-true-scale-of-evaporation-at-lakes-mead-powell-51822/ Thirty percent reduction of 9.24 is 6.48 while 30% increase is 12.02. After considering all the data, 6.48 mm to 9.24 mm is the most likely range for evaporation!
6.05 of 9.24 millimeters/day of evaporation were due to radiation. According to Penman equation, wind function for evaporation is dependent upon wind velocity, temperature, ratio of vapor pressure to latent heat of vaporization and slope of vapor pressure curve! Plugging these factors into the Penman equation, Wind accounts for 3.193 millimeters. While the aggregate evaporation of 9.24 mm/day is not in dispute, the allocation between radiation and wind is!
After reviewing the following recent literature, and preparing this paper, it is our belief the amount of evaporation attributable to the wind should be substantially higher than 3.193mm/day [ See Wind-Driven Interfacial Evaporation from Cold Water Binglin Zeng, Shane Stark, Edward Yan, Mohammad Jadav Palim, Tanay Kumar,[Hassan Hamza,? Hongying Zhao Xuehua Zhang https://arxiv.org/html/2406.12522v1.andThe Impact of Wind Speed on the Rate of Water Evaporation in a Desalination Chamber Journal of Advanced Research in Fluid Mechanics and Thermal Sciences Ristanto Wirangga1 , Dan Mugisidi1,* , Adi Tegar Sayuti1 , Oktarina Heriyani, https://repository.uhamka.ac.id/id/eprint/25939/1/Ristanto%20Wirangga%20-%20The%20Impact%20of%20Wind%20Speed.pdf Using Windbreaks for Decreasing Lake and Reservoir Evaporation: A Case Study from Iran Seyed Arman Hashemi Monfared 1Mehdi Rezapour 2Tahmineh Zhian 1https://www.pjoes.com/Using-Windbreaks-for-Decreasing-Lake-and-Reservoir-Evaporation-A-Case-Study-from,89984,0,2.html}
Our final points are that some structures with panels designed to reduce evaporation may do the opposite by creating a wind channel and that time in which a canal is shielded must be significant portion of the day in order to reduce evaporation.
The structure of this paper will be as follows:
??1????Characteristics of the Rectangular Prism of Irrigation Water on June 30, 2024;
??2???Five Agents of Evaporation and Four Types of Water Molecules as The Task Force
3 Comparison of Five Agents on June 30 through 24 hours with performance at 12:30 pm;
4? Length of time Sun is Blocked Must Be Sufficient;
?5 ?Inadvertent Wind Channels May Cause the Venturi effect;
?6?? ?Conclusion.
Characteristics of the Rectangular Prism of Irrigation water On June 30, 2024
Let’s examine a model of portion of the irrigation canal! The canal is in West Haven, Utah. 41.2030° N, 112.0511° W. Imagine a square meter of water receiving sunlight with a depth of millimeter at 12:30 pm on June 30, 2024. The depth of one millimeter is sufficient to hold .3 to 1-micron long strands of longwave and shortwave radiation absorbed from the sun, transferred by convection from the air and water or received through diffusion of heat.
The water in this hexagonal prism contains one kilogram of water. 4184 joules are needed to raise 1 kg of fresh water, one degree Celsius. Given the average number of watts or joules/sec is 340, only 8.12% of the water molecules in the prism can have their temperature raised by one degree! But heat energy received is not exclusively used for increasing temperature! Some will be involved in conversion of water to vapor. Still other joules will be distributed to cooler areas.
The prism is part of an irrigation canal that has 182.88 centimeters (6 feet) depth, 16.76 meters (55 feet) is the average width., But of the 16.76 meters, it appears from visual inspection of the above photograph that only 9.14 meters (30 feet is water! 5.95 km (3.7 miles) is its length of the canal.
The canal is fed by the Weber River 16.01 kilometers away The Weber River is 160.93 Kilometers (100 miles). The river's primary source of water is mountain snowmelt. In early June there were reports of snowmelt still feeding the river. Thus the temperature of 23.3 Celsius on June 30, 2024 at 7:00 pm. is a remarkable rise from May 31, 2024 pm where temperature was 13.3 Celsius. https://waterdata.usgs.gov/monitoring-location/10141000/#parameterCode=00065amp;period=P7Damp;showMedian=falseT
The velocity of water in canal is 1.176 meters/second. The Ogden Hinckley airport is 7.56 kilometers (4.7 miles) away. The temperature of the river and weather data of the airport will be treated as data for the temperature of the canal and weather conditions in West Haven, Utah! This prism of water is moving at velocity of 1.176 meters/second. or 2.5 miles/hour. Normal walking speed is 1.176 to 1.788 meters /second (2.5 to 4 mph)
We assume the portion of the canal in the photo is the beginning of the (1400 feet) which will be covered by PV in 2025. In order to model the effect of covering 1400 feet, we will determine first how long it takes for this cube of water to travel 466.67 meters or 1400 feet. It takes 362.34 seconds.
Here the irrigation canal is flat relative to the Earth. Its declination angle is a mere few minutes above 0-degree angle! The value of the cosine is .9986. The declination angle is the angle of orientation of the object receiving sunlight relative to the horizontal.
The temperature was 36.67 degrees Celsius or 98 degrees Fahrenheit. The wind velocity clocked in at 10.73meters/ second or 24 miles/hour. Pressure was really high at 1756.78 millibar or 25.46 psi! https://climate.usu.edu/
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Below is a diagram of water vapor in large and small bubbles. The vapor in each bubble has positive buoyancy. The Type A bubbles are larger because they have more energy and exert more force against the bonds of surface tension.
The surface tension bonds strength equal .742 Newton/meter. They are a major barrier to evaporation.
Another hurdle is the latent heat of evaporation requirement that 2.26 joules or energy are needed to convert 1 milligram of water to vapor. Given the prism contains 1 million milligrams and that Earth receives on average only 340 watts/meter^2, only150 milligrams of water could be converted into vapor, assuming that all the energy received is used for this purpose.
Five Agents of Evaporation and Four Types of Water Molecules as the Evaporation Task Force
Direct Normal Irradiation (DNI) is only one of five evaporation agents. There is diffuse radiation, wind and convective heat transfer from air and convective heat transfer by diffusion. Diffuse sunlight is direct sunlight that has been reflected and partially absorbed. it carries a fraction of energy of direct sunlight which has at most 70% of DNI. The agents work in concert to take four classes of molecules set forth below out of the water and put them into the atmosphere!
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The water molecules are depicted in the diagram above. Their characteristics are as follows.
The agents in their quest to liberate molecules from the canal either in the former of buoyant water vapor or windborne droplets resemble an aircraft carrier task force in combat in the air above the canal, on and below its surface. Moreover, each of the agents resemble a specific type of warship. This we have coined the name Evaporation Task Force for Agents and the four type of water molecules.
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The Direct Normal Irradiation is a cruiser with a few Type A molecules -helicopters and missiles, that have been fortunate to aggregate energy from direct sunlight, reflected sunlight, the air and diffused heat to break surface tension and ascend into the atmosphere. Maintaining buoyancy is heat dependent. Therefore, helicopters or missiles cannot operate at low temperatures in cold ambient conditions. It also can fuel Type B, C and D molecules
The Indirect sunlight and air heat transfer are destroyers with no ability to launch molecules on their own. They can only assist in fueling molecules. The diffusion of heat is a slow moving submarine that can assist in fueling molecules in the prism, and molecules in other parts of the canal.
The wind is the carrier with a catapult that can launch any molecule regardless of state of buoyancy and within a broad range of ambient air temperature. As a carrier it also has bombers, devoted to destroying surface tension bonds. Missiles from carrier based jets hit the water and displace the prism into the air.
The wind also has a fighter wing which clears the air of water vapor. This aspect of the wind is major indictment of Penman Equation's estimate of the impact of wind upon evaporation. designated Et wind!
The relationship of ET wind is improperly characterized as dependent variable with respect to PT, and Ea as two of its independent variables. because PT, and Ea are also dependent upon the ET wind!
Lincoln Zotarelli, Michael D. Dukes, Consuelo C. Romero, Kati W. Migliaccio, Kelly T. Morgan
Ea variable, actual vapor pressure is changed as the low pressure moist air is displaced by drier high pressure air. In the denominator of PT equation Δ, the psychometric constant in Equation computing PT This constant assumes constant pressure! However when the wind blows, the pressure changes as High pressure moves to low pressure. Thus Δ, the psychometric constant changes!
Lincoln Zotarelli, Michael D. Dukes, Consuelo C. Romero, Kati W. Migliaccio, Kelly T. Morgan
The relationship of ET wind to PT Δ, and Ea is co-dependent.. The upshot is that wind ensures that the saturation of the air never reaches the 100% limit and thus always creates more space for water vapor!
Perhaps even greater reason for skepticism about the impact of the Δ,and Ea, is that the current wind is a result primarily of past of activity of the Sun heating air unevenly. The wind variable has autocorrelation with past activity of the sun!
The last analogy of the wind to a vessel is the wind acts as a speedy transport for air molecules that can enhance their heat exchange with the prism. When the air is warmer than the water, the heat exchange occurs day and night!.
Comparison of Five Agents on June 30 through 24 hours with performance at 12:30 pm
The wind is the greatest source of energy by far 743.761 watts of the 5 evaporation agents. It generates 70.54 newtons at an average velocity,10.73m/s. If we compare the average force of the wind 6.53 meters throughout day, only 21 newtons of force is generated. This enough to move 2 kilograms, a rectangular prism of only 2 millimeters in depth. 70.54 Newtons of force strike 7 kilograms of water or square meter of water 7 millimeters. As a result, Type A, B, C and D molecules hurtle as if they are catapulted off an aircraft carrier. High velocity winndborne air increases the heat transfer coefficient to a range of 122 to 150 watts/meter^2 Kelvin. Analysis of the Influence of Convection Heat Transfer in Circular Tubes on Ships in a Polar Environment MDPI
The wind acts as transport for air that engages in convective heat transfer with the canal surface. The wind is a fighter jet clears the vapor from over the surface of the canal which increases saturation capacity of air to absorb more water vapor!
At 70.54 newtons , the wind can easily break the bonds of surface tension .742 n/meter in the manner of ordnance from a bomber. However even if the wind moves at a snail’s velocity of 1.15 m/s, it has .8103 newtons. there is enough force to break surface tension.
The alternate method of breaking surface tension is the applying force of shortwave or longwave radiation at single point or area of contact. This second option is almost infinitely less likely for the following reasons.
Assuming the second before 12:30 arrives only one more strand is needed of radiation is needed to arrive at specific location where there are other strands to break a bond, the chances are unbelievably low for a strand to reach this location! The number of photons or strands of short wave radiation needed to equal the strength of surface tension is 216,216/meter assuming each strand is 3.43 x 10^6 joules/m^2. if Long wave radiation is used 13,086,420 strands/meter are needed because long wave radiation is 5.67 x 10^-8 joules/m^2.
The .742 newtons/meter is a ratio. Thus bubbles with the length of a millimeter would require only 1/1000 of the strands of radiation to equal the force of surface tension in that location. Even given this reality, the diminutive size of radiation relative to the size of the space in ! meter x 1 meter x1 millimeter and number of possible locations makes accumulation sufficient so daunting!
The size of the short-wave radiation are .3 to 1 microns and longwave .7 to 1 micron, respectively . It has to land in an area of 4 square microns. The 1 meter x 1 meter area of the prism is 10^6 microns x 10^6 microns. While 10^12 is 1000 times the number of squares in the below diagram, the diagram presents a visual of how the huge odds against a single wave landing in the blue circle where there are 216,216 strands! Now if one argues that billion strands of radiation are released, the chances of hitting the blue dot does not improve as the release of each strand is an independent event.
If one argues that there are numerous points where the addition of one more wave can land where there are sufficient numbers to break the surface tension bond, then the temperature must approach 100 degrees Celsius at atmospheric pressure. But this is not the case as temperature is 36.667 Celsius!
If on the other hand one posits a line of photons are oriented in a series like (a) and (b) below, then the question arises what is the effect of absorption of some of the photons by clouds and air molecules upon the line. ?Also, what is the effect of forces like interference from other waves and air resistance upon direction of the waves and fact they are of differing velocities. collisions are inevitable that disrupt the line and scatter the waves. The answer to both questions is that their effect is to disrupt the line and directions of the waves not absorbed or reflected and make it virtually impossible for the line to remain intact!
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In sum, the ease at which wind can break surface tension relative to difficulty of accumulation of energy at temperatures of 36.37 degrees Celsius is compelling support for the proposition the wind is the agent that breaks surface tension!
Length of Time Sun is Blocked Must Be Sufficient
?There are projects in the United States that will entail erection of photovoltaic panels over a segment of irrigation canals in Arizona, California and Utah. The segments are 2700 feet in Arizona, 1.6 miles in California and 1400 feet in Utah, respectively! There is no evaporation savings projection for Project Nexus in Merced, California! However, the project manager for the Gila River site in Arizona said that he expected 50% reduction. Weber Basin has projected 1.2 million gallons/year in evaporation savings at West Haven, Utah.
The length of time the Sun is blocked has to be a significant portion of the day in order for blocking solar radiation to be effective. As noted earlier, the West Haven project will block the Sun for 362.34 seconds. Assuming identical water velocities, the Gila River project which is roughly double length of the West Haven project will block the sun for little less than 724 seconds. In Merced, California Project Nexus blocks a prism in the the canal for 36 minutes! These periods are just too small relative to hours of the day and hours of solar radiation!
Also for any partial covering of a canal, The thermal diffusion ,the submarine, in our task force analogy, will cause heat to migrate from uncovered areas of the canal to the covered areas at .0149 meters per second. This diffusion mitigates the effect of blocking sunlight!
Inadvertent Wind Channels May Cause The Venturi Effect
The Venturi effect is defined as the drop in static pressure of a fluid as it flows subsonically through a constricted area of a pipe.?
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A labeled diagram is set forth above. The area labeled A1 and A2 lay the essence of the problem; A1 is low pressure A2 is high pressure. When air from high pressure moves through low pressure, the velocity increases.
In looking at the two photos below, there is a possibility that pv is acting like A2, the point of smaller area and low pressure! Because these situations do not involve a pipe, they are better characterized as wind channels.
Given the prominent role of the wind in evaporation, increasing its velocity can hugely offset the benefit of reducing radiation.
CONCLUSION
To avert a repeat of 9.24 mm/day evaporation loss in June 2025 with solar pv placed on the irrigation canal, the design should maximize shading, impede the velocity of the wind and avoid creating wind channels.
The wind function in Penman contains psychrometric constant and vapor pressure, variables that are codependent variables that do not limit evaporation. The wind's velocity and placement is attributable to the Sun! The wind's ability to evaporate is not constrained with 42 to 51 relative humidity range!
Somehow the effect of shading the canal for 5 minutes needs to be extend to where there is significant effect during a 24 hour period. In addition, the supplemental measures need to be taken to reduce the energy in the canal and enhance the natural barriers or place artificial barriers to impede the departure of water vapor.
Principal of Phaethon Research for Clean Energy and Arethusa Investing In Clean Water
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