106 J. Olejnik et al. Agricultural and Forest Meteorology 106 2001 105–116
and Van Ulden 1983; Morton 1983; McNaughton and Spriggs 1985; Sellers and Dorman 1986; Ko-
vacs 1988, Holtslag and De Bruin 1988; Olejnik 1988a,b; Van De Griend and Van Boxel 1989;
Olejnik and Kedziora 1991; Beljaars and Holtslag 1991; Olejnik 1996; Wegehenkel 1997a. These
models can be applied at different scales: from a field to regional scale, but with the increase in scale some
important problems occur i.e. availability of input data such as soil moisture for large areas. One of
the most important problems during the procedure of modelling the water balance is coupling atmo-
spheric and land surface processes. The characteristic length of atmospheric processes is said to be 100 km
Kundzewicz, 1990, while the characteristic length of surface processes is smaller by many orders of
magnitude down to cellular scale for many biologi- cal processes. Land surface processes are too small,
too fast, too numerous and too heterogeneous to be represented explicitly in models, and therefore, the
parameterisation of these processes is necessary.
Recently, at
ZALF Institute
of Landscape
Modelling the THESEUS model was developed Wegehenkel, 1997a, 2000. Using this model, it
is possible to estimate the evapotranspiration of a chosen agricultural field or landscape with a one
day time step. To evaluate the results obtained using THESEUS i.e. toolbox for hydro-ecological simu-
lation and evaluation utilities model, measurements of evapotranspiration were made in some selected
fields in the eastern part of Germany and the western part of Poland. To estimate evapotranspiration, the
heat balance components of the selected fields were measured using the modified Bowen ratio method.
2. Investigation sites
The measurements were carried out in the neigh- bourhood of Müncheberg, state Brandenburg, East
Germany, and Turew, state Wielkopolska, West Poland 52
◦
35
′
N, 14
◦
10
′
E and 52
◦
30
′
N, 17
◦
00
′
E, respec- tively. The elevation of both sites is about 80 m. In
Turew and Müncheberg, the climate is transitional between continental and marine, with moderate tem-
perature 8.3
◦
C — annual average and air humidity 78 and 81 in Turew and in Müncheberg, respec-
tively, low measured precipitation annual 530 mm in both sites. Relative sunshine is moderate in summer
42 and 45 in Turew and Müncheberg, respectively and low in winter 18 and 19. Global radiation
differs a little between these two sites, reaching dur- ing a year 3600 MJ m
− 2
in Turew and 3700 MJ m
− 2
in Müncheberg, while net radiation is near the same about 1470 MJ m
− 2
at both sites. Soils in Turew and Müncheberg are mainly light to moderate textured
sandy loam and loamy soils with moderate organic matter content. Ground water level ranges between
0.5 and a few meters below the ground surface. The soils have low sandy soil to moderate water reten-
tion. Intensive agriculture and many forests create a mosaic landscape.
3. Methods of modelling and measurements
3.1. The THESEUS model The modelling system THESEUS from Wegehenkel
1997a, 2000 was used in this study. This modelling system consists of different sub-models for the atmo-
sphere, plant and soil, which can be combined to build an appropriate simulation model for a wide range of
purposes and data bases in the context of water bal- ance and crop production modelling. A overview of
the modules in THESEUS is given in Table 1.
The THESEUS is the modelling system that in- tegrates various complex model components for the
purpose of water balance modelling and crop growth simulation. These components are modules for cal-
culating potential and actual evapotranspiration, crop growth and soil water balance. A simulation procedure
is created by selectively coupling appropriate modules from a library within a simple user interface to create
a suitable model for the desired application accord- ing to user needs and expectations. The selection of
appropriate simulation modules from the THESEUS modelling system enables the user to accommodate
the simulation model taking into account the follow- ing criteria: objectives of the proposed study, amount
of model outputs which are necessary to draw well-founded study and data availability. However,
the THESEUS is still under developing procedure the commercial version is expected in the near future,
the system in which the user may decide on the com- plexity of model description leads to tools that may be
J. Olejnik et al. Agricultural and Forest Meteorology 106 2001 105–116 107
Table 1 Components of THESEUS model Wegehenkel, 2000
a
Model section and its output Model equation
Input data requirements Atmosphere modules
ETP According to Haude 1955
D , k
ETP According to Turc 1961
R
n
, T ETP
According to Penman 1948 R
n
, T, D, u ETP
b
According To Wendling et al. 1991 R
n
, T, D, u ETP
According to Penman–Monteith Monteith and Unsworth, 1990
R
n
, T, D, u Plant model modules
ETR Specific crop type correction coeffi-
cient ETPETR according to Spon- agel 1980
Crop type Plth, R
t
, Sdg, INT, TR, ETR
b
Plant model according to Koitzsch and Günther 1990 in combination
with sum of effective temperature Crop type, T
Plth, R
t
, Sdg, INT, TR, ETR, LAI, Biom Plant model according to Stenitzer
1988 in combination with Penman–Monteith approach
Crop type, T, plant data Soil water dynamics modules
EVP, Perc, next day θ One layer dimension
plate-theory model according to Renger et al. 1974
Initial values of P, θ , FC, PWP EVP, Perc, next day θ
b
Plate-theory model in combination with nonlinear storage routing Glugla, 1969;
Wegehenkel, 2000 Initial values of P, θ , FC, PWP
EVP, Perc, Inf, CAP, I, next day θ Darcy-model SAWAH
Ten Berge et al., 1995 Initial values of P, θ , pF, K
a
Biom: biomass kg ha
− 1
; CAP: capillary rise mm per day; D: saturation water vapour pressure deficit g cm
− 3
; ETP: potential evapotranspiration mm per day; ETR: actual evapotranspiration mm per day; EVP: actual evaporation mm per day; FC: field capacity
vol., mm dm
− 1
; pF: soil water retention function; I: infiltration mm per day; INT: interception mm per day; K: soil hydraulic conductivity m per day; k: plant specific coefficient; LAI: leaf area index m
2
m
− 2
; P: precipitation mm; Perc: percolation mm per day; Plth: plant height cm; PWP: permanent wilting point vol.; R
n
: net radiation J cm
− 2
; R
t
: rooting depth cm; Sdg: soil covering degree ; T: daily average air temperature
◦
C; TR: actual transpiration mm per day; u: wind speed m s
− 1
; θ : soil water content vol..
b
Modules which have been used in modelling procedure described in this paper.
sufficient from a scientific as well as from a manage- ment point of view. This corresponds to a potentially
wide range of applications. Each modelling approach has its specific restrictions taking into account the dif-
ferent demand of input data and the range of different simulation results. Therefore, THESEUS can be ap-
plied not only in different land-use conditions but also in different climatic conditions. The important advan-
tage of the model is the possibility of application in different scales-from a field to regional scale.
In our investigations, the following modules of THESEUS were used Table 1, footnote b:
1. ETP calculated with the Wendling formula; 2. Determining transpiration, evapotranspiration and
interception based on the semiempirical plant model according to Koitzsch and Günther 1990;
and 3. Soil water balance with a multiple layer model
combined with a nonlinear storage routing tech- nique according to Glugla 1969 Wegehenkel,
2000. The soil profile is divided into layers of 10 cm thick-
ness down to a depth of 90 cm. The texture classes were determined in the field. The required input pa-
rameters for the soil water module such as water con- tent at field capacity and at wilting point are derived
automatically within the modelling system THESEUS from soil texture class of the corresponding soil layer
modified by organic mater content, hydromorphic pat- terns and bulk density class.
108 J. Olejnik et al. Agricultural and Forest Meteorology 106 2001 105–116
To control values of modelled soil moisture during the measurement periods the time domain reflectome-
try TDR method was used Topp and Culley, 1989. It integrates the volumetric water content of a soil pro-
file along the length of a pair of metal rods anten- nas that must be driven into the ground. The method
produces reliable and comparable results to gravimet- ric measurements Jenkins, 1989 in soils low in clay
content and electrolytes as in this study. Simulated by the model soil moisture content agreed closely with
time domain reflectometry measurements and during the measurement periods there were not need to do
corrections.
The time resolution of the THESEUS model is 1 day, and therefore, it needs as inputs standard meteoro-
logical data air temperature, precipitation, etc. with the same time resolution.
3.2. Heat balance components measurements 3.2.1. Description of the measurement system
To measure the radiation fluxes, the CNR-1 sensor is used. The CNR-1 consists of upward and downward
facing pyranometers and upward and downward facing pyrradiometers, which are used to measure incoming
and outgoing short- and long-wave radiation fluxes, respectively.
Soil heat fluxes were measured using commercial soil heat flux plates, 10 plates were placed at the depth
of about 0.03 m. Five psychrometers were used to measure the pro-
files of air temperature and water vapour pressure using quartz crystal thermometers Olejnik, 1988b,
1996. The oscillation frequencies of the quartz crys- tal depends only on temperature and can be measured
over long distance of signal wire.
Electrical signals from all sensors are measured by milivoltmeter or frequencymeter installed inside the
data logger via channel selectors. The data logger is also responsible for channel selectors control and dur-
ing the measurement procedure all data are stored in data logger memory. The end task of the data logger
is to control the ventilation system of the psychrome- ters. Five commercial aspirators are used which start
to work 3 min before the measurement cycle begins.
All measurement conditions time of data collec- tion, numbers of sensors, etc. can be changed by the
operator using the main computer PC. The standard measurement cycle consists of: 60 measurements of
dry- and wet-bulb temperature measurements at five levels, 60 measurements of short- and long-wave radi-
ation and 60 measurements of soil heat flux. One mea- surement cycle takes about 25 min, and in standard
mode, is repeated every hour of the day 24 times. After the measurement procedure, the collected data
are stored on PC hard disk. The whole system needs 12 V power supply.
3.2.2. Description of calculation methods The energy balance equation can be written as fol-
lows: R
n
+ LE + S + G =
1 where R
n
is the net radiation flux density, LE the la- tent heat flux density L is the heat of water vapor-
isation and E the evapotranspiration, S the sensible heat flux density and G the soil heat flux density all
fluxes incoming to the active surface are positive and all outgoing are negative.
The Bowen ratio is defined as follows: β =
S LE
2 Using Eqs. 1 and 2, it is possible to calculate the
latent and sensible flux density using the so-called Bowen ratio method:
LE = − R
n
+ G
1 + β 3
and S = −
R
n
+ G
1 + 1β 4
where E, the evapotranspiration rate, can be calculated from dividing LE value by L.
It is known that latent LE and sensible S heat flux densities are proportional to water vapour and air
temperature gradients, respectively Monteith, 1975, as follows:
LE = K
V
ρc
p
γ
− 1
∂e ∂z
5 S = K
H
ρc
p
∂T ∂z
6 where γ is psychrometric constant, e the water vapour
pressure, T the air temperature, ρ the air density,
J. Olejnik et al. Agricultural and Forest Meteorology 106 2001 105–116 109
c
p
the specific heat of air and K
V
and K
H
the eddy diffusivities for water vapour and heat, respectively.
From Eqs 2, 5 and 6 and assuming that K
V
≈ K
H
, the Bowen ratio can be expressed as follows: β = γ
δT δz δeδz
7 In measurement practice, the gradients in Eq. 7 are
replaced by differential quotients Black and Mc- Naughton, 1971; Monteith, 1975
∂e ∂z
= 1e
1z =
e
2
− e
1
z
2
− z
1
8 ∂T
∂z =
1T 1z
= T
2
− T
1
z
2
− z
1
9 where e
1
and e
2
are water vapour pressure measured at two levels 1 and 2, T
1
and T
2
the air temperatures measured at two levels 1 and 2, and z
1
and z
2
the height above the ground of two measurement levels 1 and 2.
The Bowen ratio method of LE and S estimation described above, is commonly used by many inves-
tigators Spittlehouse and Black, 1981 and there are even commercial measurement units, based on this
method. Unfortunately, using only two measurement levels there is a possibility of errors when measure-
ments are carried out in a patchy landscape. Tem- perature and water vapour sensors must be located
within the internal boundary layer characteristic of the ecosystem under investigation fetch. The only way
to meet the fetch requirements, using only two layers of measurement, is to carry out the measurements of
latent and sensible heat fluxes above relatively large fields. In Middle Europe the landscape is often very
patchy and it is hard to meet the fetch requirements. Therefore, the modification of Bowen ratio method
was proposed by Olejnik, 1996 in which, air temper- ature and water vapour are measured at five heights.
The advantage of several measurement heights is that height of the adjusted surface layer or internal bound-
ary layer can be identified. Having the data on air tem- perature T
z
and vapour pressure e
z
at five levels it is possible to estimate both as a function of height as
follows: T
z
= f
1
z 10
e
z
= f
2
z 11
where z is height above the ground. In Eqs. 8 and 9, the differential quotients can be
replaced by the derivatives of functions described in Eqs. 10 and 11 i.e. df
1
dz and df
2
dz. The calculation of latent LE and sensible S heat
fluxes by the use of modified Bowen ratio method is shown on the basis of one selected measurement
cycle of air temperature and vapour pressure profiles Fig. 1. Using the psychrometric equation the water
vapour data are calculated on the basis of dry- and wet-bulb temperatures at five levels. The results of the
calculations for 40 profile series during one measure- ment cycle is shown in Fig. 1a. On the basis of these
profiles, mean values of air temperature T and wa- ter vapour pressure e at five levels were calculated
Fig. 1b. Using statistical and numerical methods, the air temperature and vapour pressure, as functions of
height, can be found Eqs. 10 and 11, solid line in Fig. 1b. The result of calculations of LE and S are
shown in Fig. 1c.
After determination of all four components of heat balance equation Eq. 1, evapotranspiration can be
calculated from latent heat flux density. These values obtained from measurements were then compared with
evapotranspiration simulated by THESEUS.
3.3. Measurement periods and types of surfaces The measurements were carried out during 8 pe-
riods in the fields near Turew and Müncheberg. In Turew, measurements were made in alfalfa and sugar
beet crops as well as a bare soil, while at Müncheberg, measurements were made in oat, wheat and sun-
flower crops. Measurements during period from 1–4 were carried out in Turew and periods from 5–8 in
Müncheberg. The lengths of measurement periods varied from 7 days periods 6–8 in Müncheberg
to 16 days periods 3 and 4 in Turew. The whole measurement set consisted of 81 days.
4. Results and discussion
