Nitrate leaching from agricultural soils: ecological modelling under different economic constraints

Ecological Modelling 75/76 (1994) 359-369

Nitrate leaching from agricultural soils: ecological modelling under different economic constraints Peter Botterweg

’

‘,*, Lars Bakken

b, Eirik Romstad

’

a JORDFORSK, Centre for Soil and Environmental Research, N-1432 A’s, Norway ’ Department of Soil and Water Sciences, Agricultural Vniuersiiy of Norway, N-1432 A’s, Norway Department of Economics and Social Sciences, Agricultural University of Norway, N-1432 A’s, Norway

Abstract Excess use of fertilizer-N results in leaching of nitrate, which threatens the environment in various ways. Taxes on nitrogen fertilizers have been suggested as a measure to reduce the nitrogen load to the environment. An economic model for predicting the farmers’ decisions regarding fertilizer application, and an ecological model which predicts the nitrate leaching given these decisions is presented. From economic theory it is known that the economic optimal amount of fertilizer is where the value of the marginal product equals the input factor price. Marginal yields are derived from the estimated yield curves and fertilizer-N levels which maximize farmers’ profits. Based on the economic models’ predictions of the profit-maximizing fertilization practice, nitrate losses were predicted by the SOIL-SOILN model. High N-tax levels ( > 200%) are needed to affect the nitrate leaching significantly. However, lower taxes may have an indirect effect on the ecology of farmlands by improving the economics of other measures against nitrogen losses. Key words: Nitrate leaching; Nitrogen fertilizer; N-tax levels

1. Introduction The use of fertilizer-N in agriculture results in leaching of nitrate to surface water German, 1990) and groundwater (Thomassen et al., 1991) and to gaseous N-losses to the atmosphere (Bouwman, 1990). This way the environment is

threatened through deterioration of surface water quality and release of N,O, one of the “climate gases”. Nitrate leaching into the groundwater may result in unacceptable nitrate concentrations in drinking water (Keldstrup et al., 1991).

* Corresponding author. 0304-3800/94/$07.00 0 1994 Elsevier SSDI 0304-3800(94)00002-Y

Science

B.V. All rights reserved

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Thus, the use of fertilizer-N affects both the natural environment and human welfare by polluting drinking water. The farmers' decisions regarding fertilizer levels are based on agronomic and economic considerations. The economic environment sets ultimate limits and probably has the strongest influence on farmers' final decisions. Because modern farming in Europe and USA is an enterprise under economic pressure, means to reduce losses of N have been looked for in the economic sphere. Taxes on nitrogen fertilizers have been suggested as one measure to reduce fertilizer levels, hence nitrogen load to the environment (Simonsen et al., 1992). Other proposals have been taxations based on N-balance, i.e. the difference between N-input and N-output in agricultural products. The objective of this paper is to study the variation in leaching of nitrate from mineral-fertilized small grain crops, as affected by taxes on fertilizer-N. This requires an economic model to predict farmers' decisions regarding fertilizer application, and an ecological model to predict the nitrate leaching given these decisions (Fig. 1). Based on the natural resources available on the farm and the social-economic conditions and constraints facing the farmer, he decides on how to run his farm. Even with the best intentions to minimize the environmental impacts, agricultural activity will influence the environment. When these impacts can be valued and translated into economic terms (Pearce and Turner, 1990; Bakken et al., 1992), new economic constraints may be given to the farmer. Economic ;phere

Joint

sphere Fig. 1. Schematic presentation of the farmers' interactions with the economic sphere and the environment, showing the links between agro-ecology and economics.

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This study is a preliminary result of an interdisciplinary project between economists and ecologists. The aim of the project is to link and integrate the different models describing the processes indicated in Fig. 1. The study presented here concentrates on the role of fertilizer-N in the system.

2. P r o d u c t i o n in e c o n o m i c terms - p r o d u c t i o n f u n c t i o n s

In this study farmers are expected to maximize their returns (profits) from production. One formulation of this decision problem is that the farmers choose the amount of variable inputs that yield maximum profits, ~- (Debertin, 1986; Varian, 1992). To simplify notation we assume one product, y, and one variable input, x. In mathematical terms this problem can be formulated as follows:

x-

(1,

where p denotes the product price, f ( x ) denotes the production function (yield curve), x denotes the variable input, u denotes the variable input factor price, and FC denotes the fixed costs for this production. By differentiating Eq. 1 with respect to x and setting this expression to zero, the first-order condition for profit maximization is obtained: 07r/Ox = 7r f ' ( x ) - v = 0,

(2)

where f ' ( x ) denotes the first-order derivative of the production (the marginal product curve) with respect to x. Let x* denote the value of x that solves Eq. 2. Provided that the second-order condition is also satisfied, i.e. that the second-order derivative of the production function evaluated at x* satisfies f " ( x ) < 0,

(3)

then x* is the profit-maximizing amount to apply of the input factor x (Debertin, 1986; Varian, 1992). To see the expected effect of an increase of the input factor price, u, on the use of the input factor x, take the total derivative of Eq. 2 with respect to x, which yields the following expression: O p / S x f ' ( x ) + p " f " ( x ) - Ov/Ox = 0

(4)

and set Op/Ox equal to zero. This yields the following solution for Ov/Ox: Ov/Ox = p " f " ( x ) < 0

(5)

as f " is negative due to the second-order condition 3. The economic interpretation of Eq. 5 is that if the input factor price, v, increases, the profit-maximizing amount to use of the input factor x decreases. To the producer a tax on an input factor is equivalent to a price increase on that input factor. That is one reason why economists suggest input factor taxes on polluting input factors when monitoring emissions (like leaching) is prohibitively costly (Romstad, 1992; Simonsen et al., 1992). Another, and more important reason, is that such taxes yield a least-cost

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362

y~

y

i

f(x)

~ - ~

f(x)

/

Xt

X*

X

x t X*

X

Fig. 2. The effects of input factor taxes with two different types of production functions: (i) a slowly curving production function, and (ii) a more sharply curved production function, x* is profit-maximizing input factor use without tax, x t is profit-maximizing input with tax.

way of reducing pollution. For a formal discussion regarding the effect of environmental taxes, see Baumol and Oats (1988). In terms of the applicability of input factor taxes, it is clear from Eqs. 1-5 that the shape of the production function, f(x), and in particular the curvature around the profit-maximizing level of the input factor, x*, is important. As can be seen from Fig. 2, the reduction in the profit-maximizing input factor used is much smaller for the production function, which is more sharply curved around the pre-tax optimal point than the less sharply curved function. The effects of an input factor tax is therefore extremely dependent upon the chosen production function. In case of taxes on fertilizer-N it is evident that a correct estimation of the yield curve is mandatory to get good results. On the basis of yield data for the period 1970-1988 for barley with respect to N-fertilization on clay soils in south eastern Norway, the following yield curves were estimated: y = 240.0 + 24.6 x - 0.9 X 2,

VX • [0,8.65 > ],

y = 277.6 + 15.8 x -- 0.4 x 2, Vx ~ [8.65,16],

(6a) (6b)

where x indicates fertilizer amounts (g m-2). The calculated effects of various fertilizer-N taxes using the above yield functions 1 are presented in Table 1. 3. The ecological model The applied model is SOIL-SOILN (Johnson, 1990; Jansson, 1991). The SOIL model is a process-based one-dimensional hydrology model that simulates water

1 The estimated curves have the same slope (first-order derivative) and the same yield at a fertilization level of 8.65 g m -2 making the overall production function for the fertilization interval 0 to 16 g m - 2 continuous and differentiable where they are joined.

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Table 1 Estimated expected fertilizer use as a result of taxes on fertilizer-N Tax percentage on fertilizer-N Expected fertilizer use (g m -2) a

350 7

200 9

80 11

0 12

13 b

15 b

a Rounded off to the nearest integer value in g m -z. b These fertilization levels are not profit maximizing given the product price (0.3 ECU per kg barley) and the base price on fertilizer-N (0.9 ECU per kg), but farmers with incomplete information regarding the yield curve may fertilize at these levels.

and heat flow through a layered soil profile (Fig. 3). Water flow is assumed to be laminar and solved with Richards equation for unsaturated flows. Heat flow in the model is the sum of conduction and convection. Compartments for snow, inter-

Precipit,~ion

Evai)otranspiration

I

t Interceptj°n

I

8o41temperatureu

affectedbythe snowcover I

Evapom-

runoff

V Water uptake by rools

ExternalheaI "91 I~"

(at arbitrarydepth)

I u.=~uI ratedzone satu~ed

Grw inflow

A zor~

source/sink

Net ground ID" water Oow

Grw

heatconvection

T

Maximum

Percolation

Totalrunoff

6o~tmal g0w

he~ convection Fig. 3. Mass balance and heat balance of the SOIL model (from Jansson, 199l).

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P. Botterweg et aL / Ecological Modelling 75 / 76 (1994) 359-369 Fertilizer Deposition

L.)

L)

\) ...So!!.!ayer.above .. ...................................

.i

ill ......iilili.il.

Leaching Fig. 4. A n approximate schematic description o f the nitrogen flows and states o f the soft part o f the S O ] E N model. N denotes nitrogen and subscripts are as follows: f = faeces, Fert = fertilizer, li = litter, N H , = ammonium and N O 3 = nitrate. (From Jansson et al., ]991.)

cepted water and surface ponding are included to account processes at the upper soil boundary. Different types of lower boundary conditions can be specified, including groundwater flow. Weather input variables for the model are daily values for temperature, precipitation, wind velocity, relative humidity, and cloud cover. SOIL has been shown to simulate hydrology satisfactory for a wide range of soil types and vegetation covers in different climate zones (Jansson, 1991). A selection Of the possible output from SOIL is used as input into the SOILN model. Variables used are daily values for water content and temperature for each defined soil layer, the water fluxes between the layers, to drain pipes, to groundwater and from the surface. The SOILN model (Fig. 4) simulates N-transformations in each soil layer and transport of N-fractions with the different water fluxes given by SOIL, denitrification losses, and N-uptake by vegetation cover. 3.1. Model calibration

The SOIL model has been calibrated on a field with clayey soil in the southeastern part of Norway (Botterweg, 1990). The field has been under continuous small grain production, with one growing season a year from late April until the end of August. The field is normally ploughed in October. Measurements of runoff (surface and tile drain) and nutrient losses were available (Oygarden, 1989).

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Table 2 Fertilizer-N levels and levels of maximum N-uptake in plants (MPU) (5 × 5 matrix) that have been simulated for a 19-year period Fertilizer-N level (g m - 2 ) MPU (g m -2)

7 10

9 15

11 20

13 25

15 30

SOILN was calibrated with leaching data from the field measurements, while the nitrogen transformations in the soil have been calibrated against literature. For these reasons it was also chosen not to simulate plant growth, but to simulate a series of five levels of maximum potential N-uptake by plants (Table 2). Maximum potential N-uptake by plants (MPU) can be considered as a parameter describing agricultural management and crop losses by diseases or insect pests. Influences of weather factors on crop production are taken into account via SOIL. A low MPU-value means that the crop is not able to take up available N because oL e.g., diseases, insect damage, bad management, etc.; a high value means the opposite. The amount N actually taken up by the plants was chosen as output variable to represent the N-sink besides leaching. Climate data from a 19-year period (1970-1988) were available from a nearby meteorological station. The mean temperature in the growing season (15th April15th October) is about l l°C and during winter (15th October-15th April) - 3 ° C . Average precipitation is about 800 m m / y e a r .

uptakeby ptants Cs/m2)

N

~u -

MPU - 30 g/m2

N-upUdm by phmts (g/m2) 20

~o s/m2

12.

I

16

...... •

12

8-

4-

""°'"

........ ° ....

- ....

o

-_::-":_

|

|

8

4

O8

12

10

N-leached (l~m2)

14

16 O,

M P U - 10 ~ m 2

6

loJ

8

I0

12

14

N-i~d~d (S/m2) 6'

•

:I

...... ---

6

2

0

0 6

8

10

~1t~

12

N (ll~)

MPU = 30 g/m2

° """

*

.

16

14.

16

" " Z-ZZZ.'~Z:ZZ:2 ......i |

6

222"-'"

8

~

10 ~

-

"

................

12

" ............

14

• ......

..... 16

N ~ )

Fig. 5. Actual N-uptake by plants and nitrogen leached to groundwater and drain tiles, at different levels of N-fertilizer, at maximum potential N-uptake (MPU) of 10 (left graphs) and 30 g m -2 (right graphs), as simultated by SOIL-SOILN for a 19-year period. One asterisk represents sum of one year.

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4. Results A summary of the results for MPU = 10 and MPU = 30 is given in Fig. 5. The results for MPU = 15, 20, and 25 showed the same tendencies as shown for MPU = 30, and are not presented separately. The graphs for N-uptake by plants show that only at the lowest MPU level, MPU is realized as shown by the levelling of the N-uptake curve at fertilizer levels above 14 g m -2. The effect is also shown by the decrease in the variation of actual N-uptake. For the high MPU level,

growing Season

201 N - ~ , ~

~ ~

(~,/~.)

16

12

6

;

li

,o

14

16

8 N4~c~._ (g/m2) 6

!

4

:

2

:

I

0 6

~ , z ~ r N ~m2)

Y~ntsF season

8~

N-1.---~-d ( ~ )

81 4-

*

O.

Fe~llzer N (g/m2) Fig. 6. Actual N-uptake by plants and nitrogen leached to groundwater and drain tiles, during the growing season and the winter season for all MPU levels, as simultated by SO]L-SO]LN for a 19-year period. One asterisk represents sum of one year.

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Table 3 The effect of taxes on fertilizer-N on m e a n yearly nitrate leaching for a situation with low and high m a x i m u m N-uptake (MPU) in the crop, based on a 19-year period of simulation with SOIL-SOILN Taxes (%)

80 200 350

Fertilizer-N (g m - 2 )

15 13 11 9 7

Nitrate leached "Bad farmers" ( M P U = 10 g m -2)

"Clever farmers" ( M P U = 30 g m - 2 1

absolute ( _+STD) (gin 2 y e a r - l )

% reduction

absolute ( _+STD) (gin-2 year-l)

% reduction

8.5(_+2.1) 8.4(_+2.1) 8.4(.+2.0) 7.8 (_+2.0) 6.6 ( + 1.7)

-0.1 0 0.8 7.1 32.2

1.4(.+0.3) 1.2(_+0.3) 1.1(.+0.3) 0.9 (-+0.2) 0.7 ( + 0 . 2 )

-12.7 0 13 25.9 39.0

available N has been less than MPU and the curve for N-uptake by plants only shows the first nearly linear part of the uptake curve before the optimum is reached, and the corresponding leaching curve increases only slowly here. Assuming that the chosen MPU values represent the existing variability in maximum N-uptake among farmers and areas, then a combination of all data may represent a reasonable estimate of average leaching from large areas. Fig. 6 shows that N-uptake by the plants does show a wider spread when all MPU levels are combined, and it increases at higher fertilizer levels. The low N-uptake values at 13 and 15 g fertilizer-N m -2 are for MPU = 10 g m -2. N-leaching is presented for both the growing season and winter time. During the growing season N-leaching varies more than during winter time. The maximum reduction in N-leaching reached is 39.0% for a tax level on fertilizer-N of 350% (Table 3). The absolute differences are up to 2 g m -2 for low MPU and maximum 0.7 g m -e for high MPU. Farming systems reaching a high MPU for the crops will hardly reduce N-leaching by reducing N-fertilizer, but for low-MPU farming systems N-leaching can be reduced in this way when high taxes are introduced.

5. Discussion

This first attempt to estimate a combined yield and N-leaching curve in relation to N-fertilizer level shows the possibility of using process-based ecological models to estimate the curves. It has to be realized that in reality a plant growth model differentiating between total N-uptake in the plant and N in the harvest yield and weight of the yield is necessary for the use in economic models. The farmers' decisions are related to the marked value of the yield and not to the total N-uptake of the plants. But it is reasonable to accept that N-uptake in the plant as used in this experiment gives adequate numbers for quantifying the variation in "yield" and N-leaching. The standard deviations found for N-leaching are about 25% of the mean value. The percentage reduction in N-leaching, caused by taxes

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on fertilizer-N, is near 30%, but absolute values are low. This means that the effect of taxes can hardly be measured in field experiments, because of the variation in leaching caused by variability of the weather between years. Under conditions of good agricultural practice, a high MPU value can be expected, and then unrealistic high taxes on fertilizer-N are needed to reduce leaching of nitrogen, but the effects are minor. Low MPU values, which are equivalent to "bad farming", show leaching values which are high, but sensitive for changes in taxation. Poor agricultural practice is not equivalent with alternative or bio-dynamic agriculture, which has not been simulated in this experiment. Even if taxes on fertilizer-N have hardly any direct effect on N-leaching from agricultural fields, there will be an indirect effect. The higher prices of fertilizer-N increase the economic value of other nitrogen sources in agriculture, like manure and green manure. It will become more economic, e.g., to reduce ammonium volatilization from manure, develop better methods for manure spreading on the field, etc.

References Bakken, L., Botterweg, P. and Romstad, E., 1992. Agriculture and pollution: risky approaches to uncertainties. E c E c / R M A Discussion Paper No. 6, Agricultural University of Norway, As, Norway. Baumol, W.J. and Oates, W.E., 1988. The Theory of Environmental Policy, 2nd edition. Cambridge University Press, New York, NY. Botterweg, P.F., 1990. The effect of frozen soil on erosion - a model approach. In: K.R. Cooley (Editor), Proceedings International Symposium: Frozen Soil Impacts on Agricultural, Range, and Forest Lands, 21-22 March 1990, Spokane, WA. CRREL Special Report 90-1, pp. 135-144. Bouwman, A.F. (Editor), 1990. Soils and the Greenhouse Effect. Proceedings of the International Conference: Soils and the Greenhouse Effect, Wageningen, Netherlands, 1989. John Wiley and Sons, Chichester, UK, 575 pp. Debertin, D.L., 1986. Agricultural Production Economics. Macmillan, New York, NY. Isermann, K., 1990. Share of agriculture in nitrogen and phosphorus emissions into the surface waters of Western Europe against the background of their eutrophication. Fertilizer Res., 26: 253-269. Jansson, P.-E., 1991. SOIL water and heat model, technical description. Internal Paper from Soil Science Department, Swedish University of Agricultural Sciences, Uppsala, 46 pp. Jansson, P.-E., Eckersten, H. and Johnsson, H., 1991. SOILN Model, User's manual. Communications 91:6, Department of Soil Sciences, Division of Agricultural Hydrotechnics, Swedish University of Agricultural Sciences, Uppsala. Johnson, H., 1990. Nitrogen and water dynamics in arable soil. A modeling approach emphasizing nitrogen losses. PhD. thesis, Swedish University of Agricultural Sciences, Department of Soil Sciences, Reports and Dissertations 6, 36 pp. Keldstrup, N., Nielsen, F., Overgaard, K., Rasmussen, E., a n d Villumsen, E., 1991. Nitrate and phosphate in Danish aquifers. In: Nitrogen and Phosphorus in Groundwater, Project Abstracts of the Danish NPo Research Program, Abstracts B. Milj~styrelsen, Copenhagen. Oygarden, L., 1989. Handlingsplan mot Landbruksforurensninger. Rapport No. 6. Utpr~ving av Tiltak mot Arealavrenning i Akershus, GEFO, ~,s, 113 pp. Pearce, D.W. and Turner, R.K., 1990. Economics of Natural Resources and the Environment. Harvester Wheatshaf, Hemel Hempstead, UK. Romstad, E., 1992. Omsettelige krvoter p~ forurensende innsatsfaktorer (Tradeable quotas on polluting input factors). E c E c / R M A Discussion Paper No. 4, Agricultural University of Norway, ,~s, Norway. Simonsen, J., Rysstad, S. and Christoffersen, K., 1992. Avgifter eller detaljregulering? (Taxes vs.

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command and control). Department of Economics and Social Sciences, Report No. 10, Agricultural University of Norway, As, Norway. Thomasson, A.J., Bouma, J. and Lieth, H. (Editors), 1991. EUR 13501 - Soil and Groundwater Research Report II. Nitrate in Soils. Commission of the European Communities, Luxembourg (Office for Official Publications of the EC), 544 pp. Varian, H.R., 1992. Microeconomic Analysis, 3rd edition. Norton, New York, NY.