International system of units (SI): Application
to crop science1
J. J. Vorst, L. E. Schweitzer, and V. L. Lechtenberg2
ABSTRACT
The adoption of the International System of
Units (SI) has been recommended as a uniform
method of reporting quantitative measurements.
While many measurements currently being used
by crop scientists are consistent with SI notation,
some measurements are expressed using other
methods of notation. Examples of SI units suggested for use by crop science teachers and researchers are presented. To show the relationship
of SI notation and other frequently used methods
of expression, sample conversions between some
commonly used units and preferred SI units are
listed.
Additional index words: SI, International Units,
Standard units, Crop Science nomenclature.
A
S reported by Thein and Oster (1981) ASA committee 321.4 has recommended adoption of SI
units as a uniform method of reporting quantitative)
measurements. Many terms currently in use in crops
teaching and research are consistent with SI notation.!
The objective of this paper is to list some common SI
units which are important to crop scientists, and to
show how these units relate to other frequently used
methods of expressing crop responses.
SI Units Important to Crop Science. Table 1 lists SI
units which are suggested for use in crop science teaching and research (Anonymous, 1981). While this list is
not meant to be all inclusive, it includes examples of
units for several common measurements. Sample conversions between some commonly used units and preferred SI units are listed in Table 2.
Area. The basic SI unit for area is the square meter
(m2). Crop scientists frequently express leaf area in
terms of cm2 or dm2. Use of cm2 or dm2 for expressing
leaf area is acceptable, however derived units such as
mg«dm"2 are unacceptable. The accepted method of expressing measurements such as mg«dm~ 2 is mg«m~ 2 .
Concentration. The use of percent in expressing concentration is discouraged because of possible ambiguities. For example, a 10% sucrose solution may mean a
solution that is either 10% sucrose by weight or by
volume. Concentration is also often expressed by direct
ratios, such as parts per million. Frequently different
methods of expressing concentration may be found in
the same paragraph or sentence (Incoll et al., 1977). For
substances of known molecular weight, concentration in
liquid media is moles per cubic meter (moNrrr3), or
moles per liter (mol«L~'). Grams per cubic meter
(g«m~3) or grams per liter (g«L~') are recommended for
the expression of concentration for substances of unknown molecular weight. The recommended expression
of concentrations (known molecular weight) in fresh or
dry plant material is moles per kilogram (moNkg"1).
Concentration in plant material when molecular weight
is unknown is to be expressed as grams per kilogram
(g-kg-).
The concentration of ions in which the source of
charge is known can be expressed as moles of positive or
negative charge per liter (mol( + )«L~ l , mol(-)«L"')- A
conversion from percent (solute) to moles per liter or
moles per kilogram cannot be accomplished without
knowledge of the gram formula weight.
' Contribution of Dep. of Agronomy, Purdue School of Agriculture
Journal Paper no. 7.
'Associate professor, Assistant professor, and professor, respectively, Purdue Univ., West Lafayette, IN 47907.
SI UNITS IN CROP SCIENCE
Table 1. Examplesof preferred units for expressing
plant sciencerelated quantities
Quantity
Application
Area
ConcentrationS"
Leaf area
Meter squared
In liquid media
molecular weight
Moleper liter
known
molecular weight
Gramper liter
unknown
In plant material
molecular weight
known
Mole per kilogram
molecular weight
unknown
Gram per kilogram
Ion uptake
Moleper liter
Evapotranspiration rate
Elongation rate
Plant
Plant
lon transport
Ion uptake
Velocity
Plant
CO2mass flux
density
Length
Photosynthetic
rate
CO2 amount of
substance flux
density
Photon flux
density
Radiation
Unit
Symbol
goL-’
-~
mol. kg
g,kg -~ (mg.kg
-~
mole,L
-~)
(mol,m
mol(+),L-’
mol(-),L-’
Meter per second
Meter per second
Millimeter per
second
Meter per day
Mole per kilogram
per second
Mole per second
Meter
Milligram per meter
squared per
second
Micromole per meter
squared per
second
Mole per meter
squared per
second
Second per meter
Milligram per meter
squared per
second
m-s"
m,s-’
Stomatal
H20 mass flux
density
Water relations
Potential (~k mass
Joule per kilogram
basis)
Pressure (6
volumebasis)
Pascal
Grain or forage
Megagram per
hectare
Gram per meter
squared
Mass of plant
Gramper plant, or
per plant parts
Gram per meter
Plant
squared
Specific leaf
weight
mol
Mole of charges
per liter
Resistance
Transpiration
rate
Yield
2m
mm-s-’
-~
m.d
mol. kg-~¯ s-~
mol-s
m
-1
mg-m-2,s
-’
#mol,m’2,s
-t
mol-m2-s
s,m-’
mg,m-~ ¯ s-t
71
Evapotranspiration
Rate. Evapotranspiration
rates
are frequently expressed as millimeters or decimenters
of water lost per day, week, or growing season. SI units
recommended for the expression of evapotranspiration
are .nanometers per second (nm.s -~) and millimeters per
day (mm.day-’).
For example, an evapotranspiration
rate of 600 mmof water occurring over a 120 day grow-’.
ing season would be reported as 5 mm.day
Elongation Rate. Rates of increase in plant height, or
length of stems, roots, or other plant parts frequently
have been reported in units of centimeters elongation
per hour or per day. Consistent
with SI notation,
elongation rates may be expressed as millimeters
per
second (mm.s-~), or meters per day (m.day-t). For
ample, stem elongation rate may be expressed as .02 m
per day, 0.231 micrometers per second (#m.s-t), or 231
nanometers per second (nm. s-’).
Ion Transport. The SI unit for measuring ion uptake
by plant roots fs micromoles per kilogram of fresh or
dry root mass per second (#mol.kg-~.s-~).
Since ion uptake is frequently expressed as micromoles per kilogram
root tissue per hour, converting this measurement to SI
notation involves changing hours to seconds, as noted in
Table 2. SI notation for the expression of ion uptake
velocity is moles per second (mol.s-’).
Length. As noted in Table 2, the meter has been prescribed as the SI base unit for length measurements. An
example of acceptable $I length notation, therefore,
might be row width expressed as 76 cm, or as 0.76 m,
and plot length expressed as 20 m.
J- kg-’
Pa
Mg,ha-’
-2
g¯m
g. plant, or
g-plant part
-a
g. m
Apparent Photosynthesis.
Apparent photosynthetic
rates are currently
expressed as CO2 mass flux for a
given tissue surface area (mg.CO,.dm-’.hr-’).
In adapting the expression of apparent photosynthesis
to SI,
similar convention applies. Appropriate SI expression
of apparent photosynthesis
is milligrams of CO2 per
meter squared per second (mgCO,.m-2.s-t).
As noted
-t to
Table
2, conversion
from mg.dm-2.hr
While the liter is not a base unit in S1, the ASA,CSSAand SSSAwill accept
the liter as a unit of measurement.
Table 2. Conversionfactors to preferred units from somecommonly
used units for expressing
plant sciencerelated quantities
Multiplication
factor for
conversion of
Column1 to 2
1. Area
2. Elongation rate
3. Ion transport
4.
5.
6.
7.
8.
lrradiance
Apparent photosynthesis
Photon flux density
Stomatal resistance
Transpiration
9. Water potentiai (volume basis)
(mass basis)
10. Yield (grain and forage)
12. Specific leaf weight
0.0001
0.116
0.00028
697
0.0278
1.00
100
180.2
10000
27.7777
100
100
0.001
0.1
10000
Colume I
Commonexpression
2cm
-t
cm,day
#mol,kg-’,hr-’
Column 2
SI units
2m
-t
#m,s
-’
cal.cm-~.min
mg.dm-’.hr-’
-’
#E-m-2-s
#mol-kg-’,s-’
-t
#mol.m.s
#mol. kg
-~
W.m
-’
mg.m-~.s
-’
/~mol.m-~.s
s,cm-’
-’
#mol,cm-2,s
-t
mg.cm-a,s
-’
g.dm-Z-hr
bars (6 volumebasis)
bars (6 massbasis)
kg,ha-’
kg-ha-’
-a
g,cm
s,m-’
"’
mg,m-a,s
-t
mg,m-a,s
-j
mg-m-~oS
-J
MJ om
J,Kg-’
-t
Mg,ha
-2
g,m
-~
g,m
Multiplication
factor for
conversion of
Column2 to I
10000
8.64
3600
0.00143
36.00
1.00
0.01
0.00555
0.0001
0.036
0.01
0.01
1000
10
0.0001
72
JOURNAL OF AGRONOMIC EDUCATION, VOL. 10, 1981
mg«m"2«sec"' requires multiplication by the factor
0.0278. Photosynthetic rates of 40.000 mg-dnT 2 «hr" 1
and 1.112 mg»nT 2 «s"' are therefore equivalent.
Light. The quantification of light in visual terms
(candela) in general lacks sensitivity in photosynthetically active portions of the electromagnetic spectrum
(Incoll et al., 1977). As an alternative, light (irradiance)
may be described in energy terms such as calories, ergs,
watts or joules. Accepted SI notation for irradiance
(total light energy per area incident) is watts per square
meter (W-nr2).
Plant scientists concerned with the photochemical
photosynthetic reaction must quantify light in terms of
photon content, rather than total energy. To meet this
need, photon flux density is used to describe the number
of photons incident per unit area over time. Incoll et al.
(1977) note that one mole of photons (Avogardro's
number of photons) has been equated directly with one
einstein (E) in the calibration of commercially available
sensors. Thus, a common expression of photon flux
density is fi einsteins per square meter per second
OtE'iir^s"1). While the einstein is not recognized as a
base unit in SI, the continued use of currently available
sensors will require no recalibration. Within SI, photon
flux density is to be expressed using mole quantities of
photons. Therefore, a flux density of 1500 micro
eisteins per square meter per second (nE«m'2«s"') may
be converted directly to SI expression as 1500 micro
moles per square meter per second (|tmol«m"2«s"')Stomatal Resistance. Currently, stomatal resistance
to diffusion is most often expressed as seconds per centimeter (S'cm"1). Adaptation of this expression to SI will
require only the incorporation of the SI base unit for
distance, the meter. For example, stomatal resistance to
the diffusion of water vapor through stomates (i.e.,
transpiration) might be expressed in the range 50 to 500
S'nr1, rather than the current .5 to 5 s-cm"1).
Transpiration (H2O Mass Flux Density). A wide
variety of units are currently in use for the expression of
water vapor loss from leaf area (i.e., transpiration).
Common units include /tmol HzOcm-^min"1, mg
H 2 O«dm" 2 «min"', and g H2O dm~ 2 'hr~'. In SI notation
transpiration may be expressed as milligrams H2O per
meter squared per second (mg'nr^s"1). For example, a
transpiration rate of 5 ^g«cm"'«s"1 would, in SI units, be
expressed as 0.5 mg'irr^s"1.
Water Relations. As plant scientists, agronomists are
concerned with the precise description of water status in
the soil-plant-atmosphere continuum. Currently,
several terms are utilized to describe water status. The
SI unit used to describe water concentration in the
atmosphere is grams per cubic meter (g-m~3).
The bar is widely used at present to describe water
(chemical) potential. However, while conceptually clear
in use for plant scientists, the bar presents interpretive
difficulties for members of other disciplines. The SI unit
for pressure is the pascal (Pa). While pascal is the SI
unit for pressure, joules per kilogram (J»kg"') is the appropriate unit for expressing water potential (1 Pa = 1
J«nr3). Within this system, water potentials previously
expressed as 0 to 15 bars would be expressed as 0 to 1500
joules per kilogram (J»kg~').
Yield. Expressions of grain and forage yield, using SI
units, are kilograms per hectare (kg«ha"')> megagrams
per hectare (Mg«ha"'), or grams per meter squared
(g«m"2). Current expressions of yield which include
imetric tons are not acceptable in SI notation.
In SI notation, plant mass is expressed as grams per
plant or plant part (g« plant"1; g« kernel"1). Expressions
of seed mass, for example, as g«100 kernels, is discouraged. Milligrams per kernel (mg« kernel"1) is appropriate.
Specific Leaf Weight. Specific leaf weight is frequently expressed as grams per centimeter squared (g«cm~ 2 ).
Since the centimeter is not a base unit in SI, specific leaf
weight is appropriately expressed as grams per meter
squared (g.tn"2).