The Bowen Ratio Method and PAN Evaporation Explained

Bowen Ratio Method
Bowen Ratio Method

Energy Balance and The Bowen Ratio Method Explained

During the Evapotranspiration process, energy is used to convert water from liquid to vapor and transfer the vapor to the atmosphere. The Bowen-ratio method, which were used to estimate ET, are based on characteristics of the energy budget associated with atmospheric fluxes.
Bowen Ratio Method
Bowen Ratio Method


  • two solid-state temperature and relative-humidity probes mounted on an exchange mechanism.
  • two anemometers to measure wind speed.
  •  a net radiometer to measure net radiation.
  •  a set of soil-heat flux plates, thermocouples, and a water-content reflectometer to compute the subsurface-heat flux.
  • two infrared temperature sensors to measure plant-canopy and soil temperatures.

Energy budget equation

The balance between incoming and outgoing energy fluxes can be mathematically expressed by the one-dimensional form of the energy-budget equation.

Rn = G + H + E


Rn   = Net radiation absorbed by the land

G = Subsurface heat flux

H = Sensible heat flux

= Latent heat flux


  • Energy terms related to biological processes, such as photosynthesis and the storage of heat in plant biomass, are considered negligible, thus are not included in the energy budget.
  • Energy terms related to the horizontal transfer of heat also are not included.

Net radiation, which depends on the temperature and reflectivity of the surface exposed, is the sum of all incoming and outgoing radiation at the surface of the Earth, and is considered positive when the sum of incoming radiation exceeds the sum of outgoing radiation.

The subsurface-heat flux is the amount of energy stored in the soil or water column.

Sensible-heat flux is the amount of energy that heats the air directly above the soil, plant canopy, or water surface .Sensible-heat flux is temperature-driven and directly relates to the turbulent transfer of heat.

Energy that is consumed by ET is the latent-heat flux, which is related to the vapor-pressure gradient and the turbulent transfer of vapor.

At the Earth’s surface, the difference between net radiation and subsurface-heat flux is the energy available for sensible- and latent-heat fluxes (often called turbulent fluxes).

Ea = Rn – G

Empirical formulae REFER PPT


  • Net radiation and subsurface-heat flux can be measured in the field using available instrumentation.
  • Sensible-heat and latent-heat fluxes are not easily estimated because turbulent transfer coefficients (kh and kv ) are difficult to determine.
  • However, Bowen determined that if the transfer coefficients are assumed to be equal, the ratio of sensible-heat flux to latent-heat flux is proportional to the ratio of the vertical gradients of temperature and vapor pressure above the surface and can be approximated from measurements of air temperature and relative humidity at two different heights.
  • Bowen ratio = (H / λ E) = [(P Ca) / ( λε)] [(Tl – Tu) / (el – eu)]
  • The ratio of sensible-heat flux to latent-heat flux was used in a modified form of the energy-budget equation along with micrometeorological data to compute ET at the four Bowen-ratio sites in the refuge.
  • Evapotranspiration, ET = [Ea /( λpw)][(P Ca)/(λε)] [(Tl – Tu) / (el – eu)+1]

Significance : bowen ratio

the Bowen ratio is used to describe the type of heat transfer in a water body either as sensible heat or latent heat.

when the magnitude of B is less than one, a greater proportion of the available energy at the surface is passed to the atmosphere as latent heat than as sensible heat, and the converse is true for values of B greater than one.


Under certain conditions, the Bowen ratio approaches -1 and application of the method is invalidated. It occurs during periods of low ET and probably had little effect on the daily ET computation.

When this happens, the calculated value of latent heat flux loses numerical meaning.

PAN Evaporation

The evaporation rate from pans filled with water is easily obtained.

In the absence of rain, the amount of water evaporated during a period (mm/day) corresponds with the decrease in water depth in that period.

Pan evaporation is a measurement that combines or integrates the effects of several climate elements like:

  • Temperature
  • Humidity,
  • Rain fall
  • Drought dispersion
  • Solar radiation and
  • wind.

PAN Evaporation

  • Although the pan responds in a similar fashion to the same climatic factors affecting crop transpiration, several factors produce significant differences in loss of water from a water surface and from a cropped surface.
  • Reflection of solar radiation from water in the shallow pan might be different from the assumed 23% for the grass reference surface.
  • Storage of heat within the pan can be appreciable and may cause significant evaporation during the night while most crops transpire only during the daytime.
  • Evaporation is greatest on hot, windy, dry days; and is greatly reduced when air is cool, calm, and humid.
  • Pan evaporation measurements enable farmers and ranchers to understand how much water their crops will need.

Calculating Evapo-transpiration(ETo)

The use of pans to predict ETo for periods of 10 days or longer may be warranted.

The pan evaporation is related to the reference evapotranspiration by an empirically derived formula.

ETo = Kp Epan


ETo reference evapotranspiration [mm/day],

Kp pan coefficient [-],

Epan pan evaporation [mm/day].

Pan coefficient (Kp)

It depends on



Position of the pan

Ground cover in station

Pan’s surrounding environment

These above factors have significant influence on the measured results.

The siting of the pan and the pan environment also influence the results. This is particularly so where the pan is placed in fallow rather than cropped fields. Two cases are commonly considered: Case A where the pan is sited on a short green (grass) cover and surrounded by fallow soil; and Case B where the pan is sited on fallow soil and surrounded by a green crop. Depending on the type of pan and the size and state of the upwind buffer zone (fetch), pan coefficients will differ. The larger the upwind buffer zone, the more the air moving over the pan will be in equilibrium with the buffer zone. At equilibrium with a large fetch, the air contains more water vapour and less heat in Case A than in Case B.

Class Apan

  • Diameter 120.7 cm
  • Deep 25 cm
  • It is made of galvanized iron or Monel metal.
  • The pan is mounted on a wooden open frame platform which is 15 cm above ground level.
  • The soil is built up to within 5 cm of the bottom of the pan.
  • The pan must be level

It is filled with water to 5 cm below the rim, and the water level should not be allowed to drop to more than 7.5 cm below the rim. The water should be regularly renewed, at least weekly, to eliminate extreme turbidity. The pan, if galvanized, is painted annually with aluminium paint. Screens over the pan are not a standard requirement and should preferably not be used. Pans should be protected by fences to keep animals from drinking.

Pan readings are taken daily in the early morning at the same time that precipitation is measured. Measurements are made in a stilling well that is situated in the pan near one edge. The stilling well is a metal cylinder of about 10 cm in diameter and some 20 cm deep with a small hole at the bottom.

Colorado sunken pan

  • Pan is 92 cm (3 ft) square.
  • 46 cm (18 in) deep.
  • made of 3 mm thick iron,
  •  placed in the ground with the rim 5 cm (2 in) above the soil level.
  • Also, the dimensions 1 m square and 0.5 m deep are frequently used.
  • The pan is painted with black tar paint.
  • The water level is maintained at or slightly below ground level, i.e., 5-7.5 cm below the rim.

Measurements are taken similarly to those for the Class A pan. Siting and environment requirements are also similar to those for the Class A pan. Sunken Colorado pans are sometimes preferred in crop water requirements studies, as these pans give a better direct estimation of the reference evapotranspiration than does the Class A pan. The disadvantage is that maintenance is more difficult and leaks are not visible.

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About Anand Paul 253 Articles Engineer and Tutor. Anand Paul is a bridge engineer at ch2m Global Design Center, Hyderabad. He is responsible for regional and local design projects. Committed to quality and timely delivery, he has been assigned multiple domain projects in Middle and India. Being a programmer, he is leading in-house spreadsheet development team. Apart from his routine, he runs, an exclusive Civil Engineering website.

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