Marco conceptual

Evapotranspration as a measure of nutrient uptake

The uptake of chemical compounds dissolved in groundwater by plants is one of the most important factors controlling the dispersion of pollutants in groundwater in an agricultural landscape. In forests, water transpired during the plant growth season makes up more than 90% of the total evapotranspiration (Molga, 1986) because evaporation of water from shaded soil is low. Thus, evapotranspiration in forests can be regarded as a good index of the water uptake by root systems during the plant growth season. Because of sampling problems, it is difficult to have direct estimations of evapotranspiration rates for a total vegetation stand under field conditions. The problem can be solved by taking advantage of a basic physical phenomenon, that solar energy is the driving force for evapotranspiration. Thus, one can estimate the amount of evaporated water if the amount of energy used for this process is known. The heat balance quantifies the partition of intercepted energy, denoted by net radiation flux (Rn), into energy used for evapotranspiration (latent heat flux, LE), heating the air (sensible heat flux, A), soil heating (S) and other processes, which are driven by the small amounts of energy, such as production of plants. Meteorologists deal usually with the three first processes. A model for evaluating the heat balance of a plant stand was recently developed (Kedziora et al., 1987; Ryszkowski and Kedziora, 1987; Kedziora et al., 1989; Olejnik and Kedziora, 1991; Ryszkowski and Kedziora, 1993). The energy fluxes for evapotranspiration, air and soil heating are estimated by empirical equations relating climatological parameters to energy fluxes. The empirical equations were tested under field conditions in special experiments when latent and sensible heat fluxes were directly measured by the mean profile method (Kedzioraet al., 1987; Olejnik and Kedziora, 1991).

Calculation of evapotranspiration from climatological data

Climatological characteristics such as air temperature at 2 m height and soil temperature at 5, 10, 20, 50 cm depth, sunshine, wind speed, vapour pressure, water vapour saturation deficit, precipitation and humidity were measured by standard methods under field conditions. Using these direct measurements the elements of heat balance were estimated using the equations presented below. The daily values of evapotranspiration of the vegetation were calculated from the heat balance equation:

LE = Rn – A – S (1) where:

Rn – net radiation flux (J m-2_day-1₎

LE – latent heat flux (J m-2_day-1₎

A – sensible heat flux (J m-2_day-1₎

S – soil heat flux (J m-2_day-1₎

Having calculated the flux of latent heat, the daily value of evapotranspiration (ETR) was calculated from the equation:

ETR = LE/L where:

L is latent heat of vaporisation equal to 2.448 x 106_{J kg}-1

ETR in this equation is expressed in mm, because one kg of water spread on the surface of one square metre gives a water layer 1 mm thick.

Individual components of heat balance were calculated in the way described below. Net radiation was calculated according to the Penman formula:

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Rn = (1–α) ×Ro ×(0.22+0.54u) –σ(t+273)4×_{(0.56-0.08√e)} ×_{(0.10+0.9u) (2)}

where:

α– albedo of the study surface (dimensionless)

Ro – radiation on a plane surface at the outside of the atmosphere (J m-2_day-1₎

u – relative sunshine (dimensionless) t – air temperature (°C)

e – water vapour pressure (mbar)

σ– Stephan-Boltzman constant equal to 4.9x10-3_{J m}-2_day-1_K-4

The daily soil heat flux during the growing season into soil is very small (Kedziora et al., 1989; Kapuscinski and Moczko, 1990), only a small part of net radiation (from 2 to 7 percent of Rn). Because of difficulties in directly measuring soil heat flux, it was calculated from the following formula:

S = 0.05 ×Rn (3) The sensible heat flux was calculated from the formula:

A = ρa×ca×hs×(Ta–Ts) ( 4) where:

ρa– air density (1.2 kg m-3)

ca– specific heat of air (1004 J kg-1_K-1₎

Ts– temperature of the evaporating surface [K] Ta– temperature at 2 m above the active surface [K]

hs– coefficient of turbulent exchange calculated from the following formula:

hs– v ×k/[{(ln (z–d)/zs)–fs} ×{(ln (z–d)/zo)–fm}] (5) where:

v – wind speed 2 m above the active surface (m s-1₎

k – von Karman’s constant (0.41)

z – height at which measurements were taken (m)

d – zero plane displacement usually equal to 2/3 of the plant height h (m) zo– roughness parameter for momentum transfer (0.13 ×h)

zs– roughness parameter for heat transfer where:

zs= Zo×exp(2) (Kanemasuet al., 1979) (6) h – plant height (m)

fs, fm– stability functions expressing the impact of atmospheric stability on heat and momentum transfer respectively (Kanemasuet al., 1979)

fs= fm= 1–(1-5Ri) when Ri > 0 (7) ln fs= 0.598+0.390 ×ln(–Ri)–0.090 ×(ln(–Ri))2_{when Ri<0 (8)}

ln fm= 0.032+0.448 ×ln(–Ri)–0.132 ×(ln(–Ri))2_{when Ri<0 (9)}

Ri = (g/Ta) ×[(dt/dz) / (dv/dz)2_{] (10)}

where:

g = acceleration due to gravity = 9.81 m s-2

dt/dz; dv/dz = vertical air temperature gradients and wind speed gradients in the measurement layer.

Calculation of the daily values of evapotranspiration from the shelterbelt surface were carried out for the following conditions:

a) The height of trees (hmax) was 15-18 m.

b) At the meteorological station, air temperature (Ti) measurement is carried out at a height of 2 m above the ground surface covered with a few centimetres of short grass. To evaluate the temperature of the active surface (Ts) (the level of active surface depends on plant height), and air temperature at the level 2 m above the active surface (Ta) the following formulae were used:

Ts = Ti– b ×ln(h+c) (16) Ta= Ti– b ×ln(z+c) (17)

Coefficients b and c were established on the basis of the following equations obtained from our own long-term investigations:

b = 0.5 ×{1+sin[(i–104) ×2π/365]} (18) c = 0.6 + 0.4 ×cos[(i–95) ×3.6π/365] (19) where i is ordinal number of day, starting from January the 1st.

The measurement of wind speed (vi) at the meteorological station is carried out at a height of 15 m above ground. Wind speed (v) at a height of 2 m above the active surface was calculated as follows:

v = va×ln[(z–d)/zo] (20) where: va= vi/ln[(z–d)/zo] (21) Calculations of subsurface water flux

The water flux in a layer of soil having the width of 1 metre during a ten-day period may be calculated from the following formula (Drainage Principles and Applications, 1979):

J=10 ×K ×dh/dl ×D (22) where:

J is the ten-day water flux (m3₎

K = hydraulic conductivity (m day-1₎

D = depth of filtration layer (m)

dh/dl = hydraulic gradient of groundwater table (m m-1₎

The values of parameters characterising the water flux in the saturated zone of the studied landscape were as follows:

a) A hydraulic conductivity equal to 0.25 m day-1 _{under pine forest was estimated according to soil}

texture characteristic using methods provided in Drainage Principles and Applications (1979). The hydraulic conductivity under birch forest was estimated by Marcinek et al. (1990) to be equal to 0.5 m day-1_.

b) Mean depth of filtration soil layer is 2 m.

c) Distance between wells P3 (field) and Z4 in the birch forest is 50 m and between wells S2 and S9 (the pine forest) is 56 m.

Calculations of water and chemical compounds fluxes were carried out for a shelterbelt stretch 1 m wide.

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The flux of chemical compound (M) taken up by shelterbelt between two wells during a given ten-day period was calculated by use of the formula:

M = J ×(C1-C2) (23) where:

M – flux of chemical compound (mg m-1×_{ten days}-1₎

J – water flux in ten-day period (l-1×_m-1×_{ten days}-1₎

C1– concentration of chemical compound in (mg l-1_{) under field}

C2– concentration of chemical compound in the forest (mg l-1_).