沙漠研究 24-1, 125-128 (2014)
Ἃ₍◊✲ 24-1, 125 - 128 (2014)
Journal of Arid Land Studies
Journal of Arid Land Studies－ DT11 Refereed Paper －㸫DT11 Refereed Paper㸫

Crop Yield Function and Evapotranspiration Comparison forCrops near Hatch, New Mexico, USA
Blair L. STRINGAM*1) and Kulbhushan K. GROVER1)
Abstract: The state engineer in New Mexico continually evaluates the water rights of many of the water users in the state.
Recently, the state has evaluated the water rights of water users in the Hatch, NM area. To determine water users’ water rights andclaims, this study used crop yield data to determine water requirements using crop yield functions. Average annual crop yields werecollected for alfalfa, silage corn, grain sorghum, onions, and chile. These yields were entered into yield functions to estimate theamount of water or evapotranspiration (ET) that is required to produce these crops. This study compared the ET values from theyield functions to ET values that were determined using 10 years of temperature data for the area. The results indicated that theestimates of crop water requirements based on crop yield functions are comparable to those based on crop ET values. This
comparison only accounts for part of the water requirement because additional water is needed due to irrigation inefficiency. Water
losses in the irrigation process require that additional water is needed to produce the crop yields for this area.
Key Words: Crop water requirements, Crop yield function, Evapotranspiration, Hatch, NM

1. Introduction
Water is an important and often scarce resource which is
the key for the sustainability of agriculture in arid regions
including New Mexico. However, water resources in thisregion are declining at an alarming rate because of drought thathas persisted for the majority of years since 1994 (Gutzler,2013). The majority of water consumption in the arid
southwest is utilized by irrigated agriculture. More than 28
percent of New Mexico’s cropland is under irrigatedagricultureA).
Accurate estimations of crop waterrequirements are important to enhance optimization andefficiency of applied water and subsequently determine
irrigation water requirements and scheduling.
Irrigation application requirements for crops are importantcriteria for water rights negotiation (Blaney et al., 1938;
Schaible and Aillery, 2012). For example, water users in theHatch, New Mexico area recently underwent a water use
evaluation by hydrologists from the New Mexico Office of theState Engineer. Farmers were required to account for theamount of water that they need and use to grow crops in theirarea. They were required to report their crop yields so thatthey could validate crop water needs using a crop yieldfunction.
Researchers at New Mexico State University latercompared the yield data water requirements to ET data. TheET values were determined from an analysis of temperature* Corresponding Author: blairs@nmsu.edu

data for the area. It should be noted that the ET data and theyield function data only account for the water that is required
for the crop production. It does not consider irrigation
efficiencies.
Sammis and Mexal (1999) discussed irrigation in New
Mexico and stated that the majority of irrigation is surface
applied. This means that up to 50% of the water that isdiverted to a field is lost to carriage loss, runoff, deep
percolation, or some other loss that cannot be accounted for.
The Hatch New Mexico area is located in Dona Ana County ofNew Mexico (32°N, 107°W). The major crops grown in thearea include chile, onions, pecans, alfalfa, grain sorghum, andsilage corn. Nearly all of this irrigation is accomplished withflood irrigation practices.
There are two sources of water for this area. A portion ofthis water supply comes from the Elephant Butte and Cabillo
reservoirs via the Rio Grande and Elephant Butte Irrigation
District canal system. The other source of water comes fromgroundwater wells.
Considering that New Mexico has been in a drought fornearly 20 years, researchers and water users are questioning thelong term viability of the water supply (Barnes, 2011; Schaibleand Aillery, 2012). Many ask about the sustainability of theirrigation practices in the area. This is one of the reasons why
the State Engineer has been validating crop water needs.
1.1. Crop production functions
Crop production functions indicate how varying amounts
㸦Received, September 13th, 2013; Accepted, February 10th, 2014㸧

MSC 3Q, PO Box 30003, New Mexico State University, Las Cruces, NM, 88003-8003
1) Department of Plant & Environmental Sciences, New Mexico State University

126of water influence crop yields (Liu et al., 2002). Production
functions are simplified relationships that can be used todetermine crop water requirements for a given crop yield(Hanks, 1974). Yield functions are used for “irrigation
system design and management, agronomic and economicdevelopment, feasibility studies and the benefits of irrigationwater compared with other water uses” (Hanks, 1974).
Yield functions are calibrated for the particular area where
the crop is grown (Sammis, 1981). In this study, therelationship that was used for alfalfa was developed from NewMexico State University research data. Smeal et al. (1992)
developed the following crop production function:
Y=168.035(ET)-2,538.391(1)
Where Y = alfalfa seasonal crop yield (kg ha-1), and ET is cropwater use (cm depth). This equation was converted from its
original form to accommodate metric units. In addition, thisequation is manipulated to solve for required
evapotranspiration depth when a crop yield is entered into theequation. For example equation 1 would take the followingform:
ET=ܻ ൅ ʹǡͷ͵ͺǤ͵ͻͳͳ͸ͺǤͲ͵ͷ(2)For this analysis, it is assumed that a total of seven cuttings ofalfalfa are harvested in the growing season. It is also assumed
that the first crop is grown for 54 days before it is cut. The
next six crops are harvested every 28 days. These are common
time periods for alfalfa in this area.
Kallsen et al. (1983) developed a crop yield function forsilage corn that is grown in New Mexico. This function is:
Y=238.9(ET)-7309(3)
Where Y = silage corn seasonal crop yield (kg ha-1), and ET iscrop water use (cm). Corn is usually planted in the Hatch
area in late April or early May. The crop usually grows forabout 110 days before it is harvested for silage.
Al-Jamal et al. (2000) presented an onion crop waterproduction function:
Y=1,224.2(ET)-35,300.0(4)Where Y = onion seasonal crop yield (kg ha-1), and ET is cropwater use (cm). Onions are planted in Hatch in February andin late September. The February crop grows for about 165
days before it is harvested while the fall crop grows for about
210 days.
Wierenga (1983) developed a crop yield function for green
chile that is grown in southern New Mexico. This function is:
Y=0.5168(ET)-12.1(5)
Where Y = green chile seasonal crop yield (tonne ha-1), and ET
is crop water use (cm). The crop is usually planted in themiddle of April in New Mexico and it grows for about 150
days before it is harvested.

Yield function data are limited in availability for foragesorghum. Saeed and El-Nadi (1998) published some researchon sorghum forage crops. This research does not present ayield function, but it does have graphs from which waterrequirements can be determined. In the Hatch area, sorghum
crops are planted in early May and grow for about 90 days
before harvest.

2. Methods
Recent investigations in the Hatch area used crop
production to determine the irrigation water requirements foraverage crop yields. Average yield data were collected andused to estimate the amount of water required. In order tovalidate these data, temperature data for 10 years (2001 to2010) were collected to estimate crop evapotranspiration.
The Hargreaves equation was used to determine the averagereference ET for these 10 years and subsequently theindividual crop ET was computed.
2.1. Hargreaves ET equation
For this study, an estimate of crop ET water use wasrequired for the entire growing season. This allowed for acomparison to the water use that was estimated from the cropwater yield functions. When all of the weather data areavailable, the Penman-Monteith equation is recommended toestimate crop ET (Hargreaves and Merkley, 2010). However,
only air temperatures were available for this area so theHargreaves equation was used to estimate ET.
‫ ݋ܶܧ‬ൌ ͲǤͲͲʹ͵ܴ‫ ܣ‬ሺܶ ൅ ͳ͹Ǥͺሻξܴܶ(6)Where ETo = reference evapotranspiration; RA = extraterrestrial
solar radiation; T = the mean temperature; TR = the average
daily temperature range. Hargreaves and Merkley (2010)
explain that this equation does not work as well for daily ET
estimation but it provides a good estimate of ET for longer
periods of time. Considering that the crop water use isestimated for the growing season, this equation willaccomplish the goal of this research. The extraterrestrial
radiation has to be estimated for the above equation using a
relationship found in Hargreaves and Merkley (2010).
The crop coefficient (Kc) values and the growth stages thatare used to convert reference ETo to crop ETc estimations arefound in Hargreaves and Merkley (2010). This text presents
a range of Kc values for the various growth stages. Thevalues at the higher end of these growth stages were selected
because of the intense sunlight that is regularly received inNew Mexico.

127

Table 1. Summary of the water requirements to produce the crops
for the Hatch, New Mexico area and the expected ETc forthese crops.
Crop

Average
Yield

Alfalfa
Silage CornOnions
ChileSorghum(kg ha )19,712
9,072
67,20035,840
11,200-1

Yield
Function
Depth (cm)Hargreaves
ETc (cm)

Diff. (cm)

132.7
68.6
83.7
92.8
46.6

140.8
74.5
91.4
93.5
52

-8.1
-5.9
-7.7
-0.7
-5.4

3. Results
The crop yield functions are normally used to determine
the amount of water that is required to produce the recorded
crop yields. In this study the crop yield is already known andthe yield functions are manipulated to determine the required
seasonal water depth for the reported crop yield. A relatively
good agreement is observed between seasonal water depth thatis estimated from Hargreaves ET equation and the seasonal
water use that is estimated by the yield functions for alfalfa,silage corn, onions, green chile, and grain sorghum.
As these data were evaluated, the Hargreaves seasonal
ETc totals could be varied by 2 to 4 centimeters simply byslightly changing the Kc values. While this may have allowed
for a closer correlation of yield function values and ETc values,
the Kc values that are reported by Hargreaves and Merkley(2010), were used to be consistent with using of theHargreaves equation.

4. Discussion
When the yield functions are used to determine the amountof water that would be required to produce the average crop
yields, these values corresponded closely to the crop ET values
determined from the temperature data and the Hargreaves
equation. This indicates that the producers in the area are
harvesting the reported crop yields.
Table 1 shows that there are differences ranging from 0.7
cm to 8.1 cm. These differences are expected for a number ofreasons. First there are errors in the yield function andHargreaves equations.
The yield functions are linear
equations that were determined from a set of data that werecollected for the specific crops. These functions are a best fit
for the entire set of data and do not reflect the year to year
variation that may be realized by the specific crop. As
mentioned earlier, the Kc value can also slightly change theresults. While it is believed that the Kc value is representativeof the crops in the area, there could be slight differences.
Because there is an agreement does not mean that theirrigation for this area is sustainable. These numbers do notindicate the irrigation efficiency. They only indicate theamount of water that is required to produce crop yields.
When efficiency is considered, more water is required for thesame crop yield. Considering the drought that New Mexico
has experienced for the last several years, a sustainableirrigation project needs to increase the irrigation efficiency toprovide enough water to irrigate in the present season and infuture years.
Irrigation management involves applying judicious
amounts of water at the optimum time. Irrigation methods canvary significantly in efficiency. For example, frequent flood
irrigation avoids most water stress to plants and enhances crop
yields, but decreases irrigation efficiency (Sammis and Mexal,1999).
Improved yields can be achieved by using
micro-irrigation techniques such as surface drip, subsurface
drip, and/or micro-spray as well as low pressure sprinkler
systems.
Acknowledgements
We would like to thank Bill Gomez for providing some ofthe data in this work and for his assistance in the data analysis.
We would also like to thank Aaron Beutler fromKeller-Bliesner Engineering for his assistance in the dataanalysis.

NoteA) U.S. Department of Agriculture. (2011): New Mexico Fact
Sheet. Accessed at:
http://www.ers.usda.gov/data-products/state-fact-sheets/statedata.aspx#.Uss9KvuOds
Ehttp://www.ers.usda.gov/data-products/state-fact-sheets/state-data.aspx#. Uss9KvuOdsE (verified Jan. 06, 2014).
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