DESCRIPTION OF EVAPOTRANSPIRATION (ET), REFERENCE ET, AND THE CROP COEFFICIENT

Evapotranspiration (ET) is the amount of water that moves from the ground (and plants on the ground) to the atmosphere through both evaporation and transpiration. It is primarily important to people who are monitoring plant growth and associated water usage. Measuring actual ET for a given location requires the measurement of weather variables at different heights at the same location and is beyond the capabilities of the current Davis weather stations. Instead, a single set of weather data measurements (described in detail below) are used to calculate a Reference ET (ETo). ETo is the amount of ET that is expected at a location with specified reference conditions under the actual weather conditions. The two most common reference conditions used for agricultural purposes are the grass reference – well watered grass that completely shades the ground, is uniformly clipped to a few inches in height – and the alfalfa reference – similar to the grass reference with alfalfa instead of grass, and a different height. The Davis ET calculations all calculate ETo for a grass reference. To determine actual ET from a reference ETo, multiply the ETo by a crop coefficient (Kc). The crop coefficient accounts for the type of plant, the maturity of the plant, and may include local factors such as soil type (it is up to the individual user to determine what Kc is appropriate. See below for a list of some sources.) It is very important, when selecting Kc to make sure that the coefficient is for use with a grass reference. Do not use coefficients that were derived from alfalfa referenced ETo.

DATA SAMPLING AND VARIABLES REQUIRED FOR CALCULATION

The console calculated ETo using samples of Temperature, Humidity, Wind Speed, Solar Radiation over a one hour period. This sampling is independent of sampling undertaken for the creation of archived data records. At the end of the hour, the arithmetic mean is calculated for each value by dividing the sum of the sampled data values by the number of samples taken. The number of samples is tracked for each sensor independently in case some sensors are not connected for some part of the period. The value of the saturation vapor pressure and actual water vapor pressure are calculated from the current values of temperature and humidity and sampled. These vapor pressure values (in kPa) are used to compute the average saturation vapor pressure and the average water vapor pressure for the hour.In addition, the raw Barometer value (i.e. not corrected for altitude) at the end of the hour is read. The temperature is calculated in tenths of a degree F, the humidity is calculated in tenths of a percent, wind speed is calculated in miles per hour, solar radiation is calculated in watts per square meter, and atmospheric pressure is read in thousandths of an inch of mercury. All arithmetic is in integers. Values that use fractions are represented by multiplying by an appropriate value. The formulas given below that use functions more complicated than addition, subtraction, multiplication, and division are calculated with table lookups with linear interpolation where appropriate.

NET RADIATION

Solar radiation is the primary source of energy that drives evapotranspiration, but what is important is the net radiation, incoming radiation minus outgoing radiation, at all wavelengths. The Davis solar radiation sensor measures incoming radiation in the visible portion of the spectrum. From this we must subtract out the component that is reflected off the plant leaves. This value is called the albedo. In addition to the radiation in the visible spectrum, we must also take account of the longer wavelength thermal radiation. This is modeled as black-body radiation coming from three sources at the measured air temperature. The first source is the portion of the sky that does not contain clouds, the second source is the portion of the sky containing clouds, and the third source is the ground radiating into the sky. The first two sources are incoming radiation and the third is outgoing radiation. In order to determine the relative contributions of source one and two, we need to calculate the percentage of the sky that is covered by clouds. The cloud cover fraction is estimated by comparing the actual mean solar radiation received against the amount we would have received if the sky was clear. In order to calculate the clear sky radiation, it is necessary to calculate the height of the sun above the horizon (solar altitude angle). The altitude of the sun depends, in turn, on the latitude, longitude, day of the year, and time of the day. The net radiation equation cited in the reference section does not represent the exact method that Davis weather stations use to calculate net radiation.

ACCURACY

These equations were modeled after the ones used by the California Irrigation Management Information System (CIMIS), a program run by the California Department of Water Resources. Therefore, the accuracy of the Davis ETo calculations are made against the ETo calculations made by CIMIS. Some of the differences between Davis and CIMIS ETo calculated values are due to differences in resolution, rather than accuracy.

There are two major factors that cause differences between Davis and CIMIS ETo calculations: differences in sensor measurements, and differences in net radiation values.

The Vantage Pro measures wind speed in one mile per hour increments, but maintains a higher resolution for hourly averages. As explained above, there are several different ways to calculate a hourly average vapor pressure and saturation vapor pressure values. The CIMIS method is to calculate and sample the vapor pressure value as described for the Vantage Pro. However, the saturation vapor pressure is calculated from the average temperature. This method will produce a saturation vapor pressure that is equal or lower than the average of the sampled saturation pressures.

REFERENCES

General reference on ET

Jensen, M .E., Burman, R. D., Allen, R. G., Editors (1990) “Evapotranspiration and irrigation water requirements.” ASCE Manuals and Reports on Engineering Practice No 70.

Paper describing CIMIS’ equations and methodology:

Snyder, R. L., Pruitt, W. O. (1992). “Evapotranspiration Data Management in California”

Irrigation & Drainage Session Proceedings/Water Forum ’92 EE, HY, IR, WR, div/ASCE

Paper describing net radiation:

Dong, A, Grattan, S. R., Carroll, J. J., Prashar, C. R. K. (1992). “Estimation of net radiation over well-watered grass.” J. of Irrigation and Drainage Engineering, Vol. 118, No. 3 ASCE

Web sites with useful information

CIMIS home page

http://wwwdpla.water.ca.gov/cgi-bin/cimis/cimis/hq/main.pl

Provides some guidelines for water requirements for growing landscape plants in California

http://wwwdpla.water.ca.gov/urban/conservation/landscape/wucols/index.html