0038-075X/08/17306-401–407
Soil Science
Copyright * 2008 by Lippincott Williams & Wilkins, Inc.

June 2008
Vol. 173, No. 6
Printed in U.S.A.

USING THE TRANSPIRATION REGIME TO ESTIMATEBIOMASS PRODUCTION
Viliam Novák1 and Martinus Th. van Genuchten2
The design and implementation of a new or improved irrigation or
drainage system should be preceded by a study of the soil water regime(SWR) to define the need for such a system and to optimize its design.
This requires estimates of appropriate parameters characterizing thelong-term (multiyear) dynamics of the SWR and its relation to biomass
production. Parameters that could be used for this purpose are the watercontent or pressure head at one or several points in the soil root zone or
the average water content of the root zone, as affected by precipitationand evapotranspiration or other variables. Because these variables
change from year to year, it is necessary to characterize somehow
statistically the SWR during a relatively long period. Because the watercontent is not easily related directly to biomass production, we used thecalculated seasonal transpiration rate as an indirect characteristic of the
canopy water regime. This article presents a method for estimating plant
production as a function of the seasonal transpiration rate as calculated
retrospectively with the HYDRUS-ET software package. New in our
approach is the use of an empirical relationship between seasonaltranspiration and yield. The cumulative frequency distribution ofseasonal transpiration was chosen as the basic characteristic of the
SWR as a source of water for plants. The approach allows one toestimate cumulative frequency curves of actual and potential yields. The
difference between these two curves is the cumulative frequency
distribution of yield to be optimized by the irrigation system. The
method permits a better cost-benefit analysis by comparing expected
yield increases with the investment and operational expenses of the
newly designed irrigation system, or of newly invoked water management practices. The approach is illustrated using a 31-year time series ofdata for a corn crop (Zea mays L.) grown on loess soil in Slovakia. (Soil
Science 2008;173:401–407)
Key words: Soil water regime, transpiration, biomass production,yield, HYDRUS-ET.

term soil water regime (SWR) is
generally understood to refer in some way
to the soil water content, often of the root zone,
and its changes with respect to time. Several
parameters could be used to numerically characterize the SWR, such as various statisticalTparameters of the soil water content during thegrowing season (e.g., mean, variability, temporalcorrelation, trend, and persistence). Because soil
is an inherent part of the soil-plant-atmosphere
continuum, the SWR is influenced by manyfactors such as the physical properties of the soil
itself, climatological parameters (e.g., precipitation and evapotranspiration), and possibly depth
to groundwater.
Most or all of the previously mentioned
processes and parameters affecting the SWR are
variable in time and across seasons. To properly
characterize the SWR, it is therefore necessary

HE

1Instituteof Hydrology, Slovak Academy of Sciences, Rac̆ianska 75, 831 02
Bratislava 3, Slovakia. Dr. Novák is corresponding author. E-mail: novak@uh.savba.sk

2U.S. Salinity Laboratory, USDA, ARS, 450 W. Big Springs Rd, Riverside, CA
92507.

Received Oct. 9, 2007; accepted Mar. 19, 2008.
DOI: 10.1097/SS.0b013e318178e739

401

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NOVÁK AND VAN GENUCHTEN

402

to account for the long-time variability of theseparameters, which are necessary input to thedesign and implementation of improved irrigation and drainage practices, and for optimizing
the SWR for plant production. As such, theSWR can be compared in many ways withclimate in that the variability in meteorologicalcharacteristics is often smoothed to produce
some characteristic climate.
An early hydrological classification system
for the SWR was suggested by Vysockij (1906),
and later revised by Rode (1965). A key
characteristic of their classification was the
direction of the dominant water flux in the soil
root zone. Based on the main flow directions,they divided the SWR into percolative, nonpercolative, periodically percolative, and evaporative schemes. A more ecologically based
scheme was proposed by Kut<lek (1978), whoclassifies the SWR according to the moisture
content of the soil root zone, being in somerange between such limits as the permanent
wilting point (the water content at a pressure
head of j15,000 cm), the point of limited
availability of soil water to plants (at j2500 cm),and field capacity (traditionally assumed to be atabout j300 cm). Closely related to this is theconcept of available water, generally understood
to be the difference between the water contents
at field capacity and the permanent wilting
point, although all of this water may not
be equally available to plants (e.g., Letey, 1985;
Kirkham, 2005).
Although the approach and related definitions of available water by Kut<lek (1978) doallow one to estimate the suitability of the SWR
for plant growth on a more general quantitativebasis, these methods still are static schemes inthat many transient soil and climatologicalfactors are neglected. The aim of this contribution is to propose a method for estimating plant
production based on the relationship between
seasonal transpiration rate of a particular canopy
and biomass production (yield).
THEORETICAL
Rather than using such indirect proxies as
the soil water content or pressure head, we
assessed the relationship between biomass production and the SWR in terms of the flux ofwater through the plant (i.e., the transpirationrate). Budagovskij and Grigorieva (1991) previously proposed the transpiration rate (daily orseasonal) as the basic characteristic of soil water

SOIL SCIENCE

when viewed as a source for the biosphere.
They used the ratio (p of actual transpiration(Et) to potential transpiration (Etp) to quantify
the degree of availability of soil water for a crop
canopy as follows:
)p ¼

Et
Etp

ð1Þ

This criterion is based on the assumptionthat only the water flux through the plant will
participate in the biomass production process.
Although soil water is the source of most waterused by the biosphere and can be exploited byplants, its presence as such in the soil does not
imply its immediate or even eventual use forbiomass production.
A quantitative assessment of the influence ofsoil water in the soil root zone on biomass
production can be made using well-known andwidely accepted empirical relationships between
biomass production (yield) and total transpiration during the growing season of a given crop
(Hanks and Hill, 1980; Vidovi* and Novák,
1987; Feddes et al., 1999; Kirkham, 2005).
These relationships, generally thought to beapproximately linear, are valid for a particularplant (canopy) at a particular site subject tostandard tillage and nutrition conditions. The
only transient characteristic is the transpiration
rate as influenced by local meteorological conditions and soil water. The relationship between
biomass production (yield) and the seasonaltranspiration rate can be expressed by the linear
equation:
Y ¼ kt Et  Y0

ð2Þ

where Y is dry biomass produced per unit area(t haj1), kt is the slope of the relationship (t haj1
cmj1), referred to as the crop water use
efficiency by Hillel and Guron (1973). Et is thetranspiration total over the growing season of
the particular canopy (cm), and Y0 denotes
the intersection of Eq. (2) with the vertical axis(t haj1).
Having Eq. (2) for a given site, and knowing
the transpiration total of the particular canopy
for each growing season as calculated retrospectively for a reasonably long period (cf, climatological studies usually cover at least 20 years), it
is possible to calculate cumulative frequency
curves of both potential and actual yield. The
difference between these two curves is thepotential increase in yield that could be realizedby optimizing the SWR through irrigation.

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VOL. 173 ~ NO. 6

TRANSPIRATION REGIME ESTIMATES BIOMASS PRODUCTIONAPPLICATION
Eq.(2) was applied to a large database of
information obtained for the Most pri Bratislave
site located 5.5 km east of the city of Bratislava(48- 08¶ N, 17- 16¶ E) in the northwestern part ofthe „itn] ostrov region of Western Slovakia. The
loamy soil in the area, classified as a chernozem(Food and Agriculture Organization classification),is relatively homogeneous in the upper 1.5 m. A
thick layer of Danube-originated gravel is locatedbelow this soil layer. This and the fact that the
groundwater table generally oscillates between 6
and 8 m below the soil surface indicate thatcapillary rise did not influence the water content
in the root zone. This section gives a brief synopsis
of the model and data used in our study.
Retrospective Modeling
Long-time series of the SWR were estimatedby retrospective modeling. The simulations werecarried out assuming constant plant and soil
properties, with only the meteorological data
allowed to change. We used the Windows-based
HYDRUS-ET software package (wimﬂnek et al.,1997) for our modeling. HYDRUS-ET is anearly modification of the HYDRUS-1D code of
wimﬂnek et al. (1998), but with more flexible
provisions for calculating root water uptake andtranspiration. The code uses the Richards equation to simulate water flow in variably saturated
systems, whereas convection-dispersion–typeequations are used for both heat and solutetransport. The evapotranspiration rate and its
components (transpiration and evaporation) in
HYDRUS-ET are calculated with the modified
Penman-Monteith equation (Novák, 1995;
Allen et al., 1998) using standard meteorological
data and specific information about different
types of plant canopies. Potential transpiration
rates were estimated first, after which actual rates
are calculated from soil actual water content
distributions as described in the user manual(wimﬂnek et al., 1997). Transpiration was further
used to estimate root extraction patterns,
expressed by means of a sink term in the Richards
equation. The HYDRUS-ET also contains
procedures for calculating the interception byplants of rainfall and/or irrigation water. Details
are in the HYDRUS-ET user manual (wimﬂnek
et al., 1997).
Site Description and Soil Properties
The soil profile at the Most pri Bratislave
site was sampled at depths of 10, 20, 30, 50, 70,403

and 100 cm below the soil surface using metal
cylinders of 100-cm3 volume each. Altogether,
33 vertical profiles were sampled involving
three profiles at each of 11 sampling events tocharacterize spatial variability in the soil
hydraulic properties. Basic soil characteristics
were determined in the laboratory. They
included soil water content distributions versus
depth and saturated hydraulic conductivities
using the falling pressure head method. Desorption branches of the soil water retention
curves relating the water content (E ) and thepressure head (h) were measured using standard
pressure cell methods (e.g., Dane and Hopmans,
2002). The measured E(h) data were subsequently fitted with the retention equation of
van Genuchten (1980), whereas unsaturated
soil hydraulic conductivities were calculatedusing the Mualem model (Mualem, 1976; van
Genuchten, 1980). Soil hydraulic parameters
used in the HYDRUS-ET calculations are listed
in Table 1.
Meteorological Data and Plant Characteristics
Meteorological data for the simulations
were obtained at a meteorological station near
the experimental site. The soil water dynamics
at the site (soil water contents, pressure heads,
daily evaporation, and transpiration rates) wasmodelled for three crops: corn (Zea mays L.),
winter wheat (Triticum aestivum L.), andspring barley (Hordeum vulgare L.), which were
the representative crops during the growing
seasons of 1971 through 2000, and 2003. The
various field measurements were carried out
only in 2003.

TABLE 1
Soil characteristics for the loess soils at the Most pri Bratislave
site, Slovakia
Soil hydraulic parameters

Ev, cm3cmj3Ela, cm3cmj3
Efc, cm3cmj3
Es, cm3cmj3
Ks, cm dj1!, cmj1
n

0.18
0.28
0.35
0.40
4.86
0.05771.30

Ev: water content at the wilting point (j15,000 cm); Ela: watercontent corresponding to the point of limited availability ofsoil water to plants (j2500 cm); Efc: water content
corresponding to field capacity (j300 cm); Es: saturated
water content; Ks: saturated hydraulic conductivity; " and n:
van Genuchten water retention coefficients.

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404

NOVÁK AND VAN GENUCHTEN

The growing seasons of the crops, assumed
to be identical to the transpiration periods, were
defined as the period between appearance ofthe first green part of the plant and physiological maturity. Corn (for which the method
will be demonstrated here) transpired between
May 5 and September 16 for the climaticconditions of southern Slovakia. The exacttranspiration time depends in general on thelocal climate conditions (precipitation, air temperature, air humidity, sunshine duration, windvelocity). The average air temperature of thegrowing season was 18.3 -C. The site was foundto be very suitable for corn production.
HYDRUS-ET Input Data
The Hydrus-ET model input data were as
follows:
Meteorological Data
Average daily air temperature, water vapor
pressure of the air, wind velocity (at 2-m height),
daily precipitation rates, and daily sunshine
duration, all measured at standard height.
Plant Characteristics
Plant (canopy) height, leaf area index,
rooting depth (as a function of time), canopy
roughness, canopy albedo. All of these data were
measured directly in the field.
Soil Characteristics
The initial water content distribution wasmeasured at the beginning of the growing
season in 2003. We assumed the same initial
distribution for all 30 simulated seasons. The soil
profile was assumed homogeneous. We used the

SOIL SCIENCE

desorption branch of the water retention curve
because this gave soil water content distributions
close to the measured values (Novák and
Gallová, 1998). Calculated water content profiles obtained with HYDRUS-ET during 2003
compared well with observed values (results notfurther shown here).
RESULTS AND DISCUSSION
Retrospective modeling with HYDRUSET produced daily average values of the soil
water content and pressure head at selected
depths in the soil profile. Figure 1 shows seasonal
distributions of 5-day average soil water pressure
heads at a depth of 50 cm for the corn crop during
different seasons. For completeness, we also included the pressure heads at field capacity(j300 cm) and the limited water availability(j2500 cm). The seasonal distributions of thepressure head showed considerable variability
among the seasons, thus illustrating the need tocharacterize the long-time SWR in statistical terms.
The year 2003 was an especially very dry year.
As discussed earlier, actual biomass production (yield) can be estimated by using theempirical relationship Y = f (Et ), and potential
yields (i.e., yields where soil water is not
limiting the transpiration rate) using Yp =f (Etp), where Yp is the potential yield, and Etp
is the potential transpiration total during thegrowing season. For the corn canopy at Most pri
Bratislave (Fig. 2), we obtained the following
relationship for Y = f (Et ).
Y ¼ 0:71 Et  2:4

ð3Þ

Eq.(3) is valid within the range of calculatedseasonal transpiration rates (7.5 G Et G 17.1 cm)
for the 31 growing seasons. Corresponding

Fig. 1. Seasonal courses of the soil water pressure head h (cm) at 50-cm depth as calculated with HYDRUS-ET for acorn crop grown at the Most pri Bratislave site in southern Slovakia. Results are presented for six seasons, witheach data point presenting 5-day averages. The solid (j300 cm) and dashed (j2500 cm) lines represent limits of
the range of limited availability of soil moisture for plants.

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VOL. 173 ~ NO. 6

TRANSPIRATION REGIME ESTIMATES BIOMASS PRODUCTION

Fig. 2. Plot of the mass of corn grain yield (Y) versus
transpiration total (Et) during the growing season at the
Most pri Bratislave site in Slovakia. The empirical
relationship represents six seasons within the period
1971–2000 and 2003.

measured grain yields (for 6 seasons only) ofcorn were 4.0 G Y G 9.7 t haj1. Considerable
care should be taken when extrapolating outsideof these ranges. Seasonal transpiration totals
substantially below the lower limit of themeasurement range may well lead to very
unrealistic estimates of plant yield.
Figure 3 shows exceedance curves of thecorn canopy seasonal transpiration total (Et ) andthe potential transpiration total (Etp), as well as
the difference ($E), for the years 1971–2000 and
2003. Application of Eq.(3) to the data in Fig. 3
leads to estimates of the actual corn grain yield

405(Y) and the potential yield (Yp), and of thecorresponding difference ($Y ). This differenceis the maximum increase in grain yield that canbe expected by optimizing the SWR to cause
corn to transpire at the maximum (potential)
rate for the given meteorological conditions.
The resulting exceedance curves of the corngrain yield are plotted in Figure 4. The differences between the potential and actual transpiration (Fig. 3) and yield (Fig. 4) totals weregenerally relatively small, except for the 2003
season, which was extremely hot and dry. The
local climate hence was relatively stable over the
31-year period of study, except for 2003.
The average corn grain yield (Y) was
estimated to be 7.64 t haj1, and the averagepotential yield (Yp) was 9.03 t haj1. This meansthat the difference was $Y = 1.4 t haj1, which
represents 18% of the average yield. The
question now arises whether it would bereasonable (cost-effective) to design and operate
an irrigation or drainage system that will
optimize the SWR, such that the dry grain
yield increases by some or all of the 1.4-t haj1
difference. We note that our method is illustrated here using an example involving
relatively favorable climatic conditions. Moresignificant differences between Y and Yp are to
be expected for drier climates and for soils
having lower water-holding capacities (coarsetextured soils).
Alternative approaches to characterize soil
water availability to plants may be based onlong-time field measurements or by using
models for crop growth. Direct field monitoringis probably too cumbersome and expensive formost applications. Crop growth modeling may
well be a viable alternative, provided that thegenerally large number of input parameters

Fig. 3. Exceedance curves of the seasonal transpiration total of the corn canopy (Et) and the potential
transpiration rate (Etp), and the difference ($E), for the years 1971–2000 and 2003 at the Most pri Bratislave site,
Slovakia.

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406

NOVÁK AND VAN GENUCHTEN

SOIL SCIENCE

Fig. 4. Exceedance curves of the corn grain yield (Y) and the calculated potential yield (Yp), and the difference($Y), for the 1971–2000 and 2003 growing seasons at Most pri Bratislave, Slovakia.

needed for such models can be quantified
properly. By comparison, our method is relatively simple, needs only standard input data,and can be used in combination with any modelthat calculates the transpiration rate. Hence,
rather than HYDRUS-ET, one could use suchother models as GLOBAL (Majer*ák and Novák,1992) or SWAP (Huygen et al., 1997) for thispurpose. The method allows one to compare
design, construction, and operational expenditures with additional income from the increase inpotential yield, and hence to evaluate potential
profits or losses. Thus, the question becomes an
economic one: Is the additional income of the
expected yield increase sufficient to cover theincreased design and operational expenses?
CONCLUSIONSThe proposed method for estimating biomass production depends on seasonal transpiration totals as calculated retrospectively with amathematical model. The method is based on
the widely accepted empirical linear relationshipbetween biomass production (yield) and theseasonal transpiration total of the canopy being
considered. The procedure should be applicable
to any given canopy, site, and invoked setof agricultural management (e.g., tillage andnutrient) practices. The proposed approach was
illustrated using a corn canopy grown on a loesssoil but should be applicable to any canopy andsoil combination.
Using cumulative frequency curves for theseasonal transpiration total, the cumulative frequency curves of actual and potential biomass
production can be evaluated using Eq.(2).
Potential increases in yields as a result of
optimizing the SWR can subsequently be
estimated. We note that the methodology holds

for a given canopy because transpiration rates
will be different for different canopies mainly
because of differences in the length of thegrowing seasons involved and the different
periods during which the crops are grown in aparticular year (winter cereals, corn, alfalfa[Medicago sativa L.]). The method allows one
to compare the design, construction, and operational expenditures needed to optimize transpiration so as to reach potential yields, thus leading
to estimates of the increase in income and of
potential profits or losses associated with the
new irrigation system.
ACKNOWLEDGMENTS
The authors thank the Slovak Grant Agency
VEGA (Grant No. 2/4066/24) and APVV (No.
51-030205) for partial support of this work. This
article is further based on work supported in partby Sustainability of Semi-Arid Hydrology andRiparian Areas under the STC Program of the
US National Science Foundation (Agreement
No. EAR-9876800).
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