A Crop Production and Environment Model for Long-term Consequences of Agricultural Production

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NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR

A

CROP PRODUCTION

AND

ENVIRONMENT MODEX FOR LONGTERM CONSEQUENCES

OF

AGRICULTURAL PRODUCTION

N. Konijn

July, 1984 WP-84-5 1

Wo~ki7Lg P a p e ~ s a r e interim reports on work of the international Institute for Applied Systems Analysis and have received only limited review. Views or opinions expressed herein do not necessarily represent those of t h e Institute or of its National Member Organizations.

1NTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS 2361 Laxenburg, Austria

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FOREWORD

The Food a n d Agriculture Program a t IIASA focuses its research activities on understanding t h e nature and dimensions of t h e world's food problems, on exploring possible alternative policies t h a t can help alleviate c u r r e n t problems and prevent future ones.

As a part of t h e research activities investigations of alternative paths of technological transformation in agriculture in t h e context of resource limitations a n d long t e r m environmental consequences a r e being investigated. The purpose is to identify production plans stra- tegies which a r e sustainable. The general approach and methodology has been developed a t I M A and is being applied in several case studies on t h e regional level in different countries with t h e help of collaborating insitutions.

An important element i n this methodology is t h e development of a model t h a t relates soil, climate and genetic properties of crops t o yield input relationships. In addition the changes in soil characteristics t h a t take place a s a consequence of cultivation of crops, inputs applied and culturing practices followed have also to be quantified. The changes in soil affect t h e f u t u r e productivity and t h u s provide a feedback mechan- ism t o explore interactions between soil resources, cultivation technolo- gies a n d environment.

A model developed by Nicolaas Konijn to explore these interactions:

A Crop Production and Environment Madel f o r Long- T e r m Consequences of AgTiCultural e o d u c t i o n . is described by him in t h i s paper.

Kirit S. Parikh Program Leader

Food and Agriculture Program.

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Without t h e information from t h e Centre for World Food Studies (J. Berkhout, P.H. Driessen, H. van Heemst) this paper could not have been written.

1 would like to t h a n k Bob Watts, Martin Parry and in particular Tim Carter who gave their time generously t o reading this paper and making recommendations for improvement.

-Cynthia Enzlberger typed t h e text and equations and never got tired with the many changes required.

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1. Introduction

1

2. The crop production module 2

2.1. Dry m a t t e r production 5

2.2. Water constraint on dry m a t t e r production 9

2.2.1. Soil moisture content 10

2.2.2. Precipitation 11

2.2.3. Irrigation 11

2.2.4. Evapotranspiration 11

2.2.5. Runoff 13

2.2.6. Drainage 17

2.2.7. Solving the water balance 16

2.2.7.1. Water balance during t h e crop season 10 2.2.7.2. Water balance during pre- and post-crop periods 19 2.2.8. Dry m a t t e r production with water a s a constraict 19 2.3. From dry m a t t e r to plant material 20 2.3.1. Respiration and conversion of dry m a t t e r 20 2.3.2. Allocation of dry m a t t e r over plant organs 20

2.4. The n u t r i e n t constraint 23

2.4.1. Soil fertility a n d response t o soil fertilization 23

2.4.2. Organic m a t t e r decay 24

3. The environment module 28

3.1. Water Erosion 29

4. The resource adjustment module 31

4.1. Soil organic m a t t e r 31

4.2. Soil moisture characteristic 3

1

4.3. Soil bulk density 32

4.4. Nitrogen 32

4.5. Phosphorus 32

4.6. Potassium 35

Summary a n d Conclusions 35

References 36

-

^vii^-

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A CROP PRODUCTION

AND ENVIRONMENT MODEL FOR

LONGTEXM CONSEQUENCES OF AGRJCUL'L'URAL PRODUCTION

N. Konijn

1.

Introduction

Most existing crop production models ruffer from a lack of transferability.

Too many changes a r e required to adapt a model to a different physical environ- m e n t . This is often due to an inadequate selection of input characteristics t h a t a r e supposed t o describe t h e physical environment. The model described below attempts to overcome t h i s problem, requiring only limited adaptations t o be widely applicable. Most of t h e selected input characteristics, if not all. a r e usually available.

Such a model, sensitive to t h e i n p u t characteristics t h a t describe t h e physical environment, offers a t t h e s a m e t i m e the possibility of estimating t h e effect of a changing agricultural prod.uction environment on crop yields. Fig- u r e 1 visualizes t h e role of the Crop a n d Environment Model

(C.E.M.)

in relation t o t h e changes in input characteristics because of agricultural production itself. There is a great variety of input characteristics t h a t will determine the crop yield Land classes are determined by a unique s e t of soil, site and climatic characteristics. Beside those c h a r a c t e r i ~ t ~ i c s t h e r e a r e the variable ones which a r e determined by farmer's decisions, which are mainly determined by t h e interpretation of the farmer of the economic situation. They comprise irrigation, fertilizer, and all kinds of other rnanagement characteristics. So for each land class t h e r e might be a considerable number of alternatives, each having its related yield, residue a n d environmental consequences.

Supposing t h a t t h e decision model is able according to a certain criteri.on or certain criteria to choose among t h e generated alternatives, t h e chosen

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alternatives should t h e n be e n t e r e d into t h e updating procedure (resource a d j u s t m e n t module in Figure 1). Only t h e soil c h a r a c t e r i s t i c s require updating in t h e model. Site c h a r a c t e r i s t i c s s u c h as slope c h a r a c t e r i s t i c s a r e affected, but not t o a measurable extent. Characteristics of t h e climate a r e supplied exo- genously, a n d t h e effects of a growing crop and t h e changes in t h e soil on t h e climate a r e n o t considered. Other c h a r a c t e r i s t i c s a r e influenced in t h e future in response t o t h e p r e s e n t year's farmer-decision. This is modelled as p a r t of a decision model which is described m o r e fully in Reneau e t a1.(1981).

The c r o p production a n d e n v i r o n m e n t model (C.E.M.) c a n also be used without t h e i n t e r f e r e n c e of a decision model. In t h a t case t h e r e s o u r c e adjust- m e n t t a k e s place immediately a f t e r t h e C.E.M. estimations, for n o selection among alternatives i s necessary. Instead, t h e production c i r c u m s t a n c e s (e.g.

type of rotation) a r e preset.

To be able t o validate a n d apply t h e model a s visualized in Figure 1, case studies o n a regional level were selected. A regional level being a r e a s of 10.000 t o 100.000 km2. They were i n t e n d e d t o m e e t t h e r e q u i r e m e n t s for both, t h e Crop a n d Environment Model a n d t h e Decision Model.

In t h e following sections we will describe t h e crop production module, t h e environment module a n d t h e p r o c e d u r e for updating t h e i n p u t characteristics t h a t a r e affected by t h e modelled agricultural production.

More detailed information o n t h e functioning of t h e model is available elsewhere: t h e required i n p u t c h a r a c t e r i s t i c s a r e described in detail by Konijn (1983a). a n d t h e way t h e model functions with special reference t o t h e UNIX System of t h e VAX 11/?80 a t IIASA is detailed in Konijn (1983b).

2. The Crop Production Module

In t h e c r o p production module we follow t h e s t r u c t u r e of t h e Physical Crop Production Model of t h e C e n t e r for World Food Studies (1980). Moreover we employ m a n y of the crop product,ion/physical environment relationships on which t h a t model is based. The majority of these relationships have been selected from t h e literature. where t h e y have proved to be generally applicable.

The s t r u c t u r e of t h e c r o p protluction model is shown in Figure 2. It has a h i e r a r c h i c a l s t r u c t u r e : production levels determined a t a higher level can be progressively constrained a t e a c h of t h e lower levels. The model is of a mixed dynamic/static n a t u r e ; estimations of photosynthetic dry m a t t e r production a n d t h e availability of water for plant growth a r e c a r r i e d o u t per t h i r d of a m o n t h t i m e period, while t h e effect of n u t r i e n t s available for p l a n t growth is evaluated on an annual basis.

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Land class characteristics:

p -

Irrigation Fertilizer

(organic, inorganic) Management

(Crop, Planting time, etc.)

+

Crop and

Environmental Module

Figure 1 . Relation between the various modules New Soil

Characteristics

1

for each

Chosen Alternatives

I

4 alternative

I.

b

Resource Adjustment Module

6 m

4

Land clan Crop l rrigation Org

.

Fertilizer Inorg. Fertilizer Main Yield Residue Soil loss N. leached

--- --

Changed Characteristics

+

2

Decision Module

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input characteristics

j dry-; ~

1 m a t t e r

; 1

production

I

¹

i I

n u t r i e n t

constraint

H

I

JI

^I ^I

yield

0

I I I

I

Rgure 2. The

Structure of the Crop Production Module

I

water constraint

I I I I

I I

I

I I I I I

I V I

I I I

I

&Y

m a t t e r allocation

I

-=

I

At

= 10

L days 1

J

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2.1.

Dry Matter Production

Because of t h e pigments they contain plants a r e able t o absorb visible light of wavelengths between 400 and 700 nanometers.* The accumulated energy is used in biochemical reactions during which carbon dioxide is absorbed by t h e plants through t h e i r s t o m a t a (photosynthesis). The products t h a t s t e m from these reactions a r e necessary for plant life. Experiments have shown t h a t t h e r a t e of photosynthesis can be expressed as a function of t h e absorbed radiation.

The absorbed radiation forms a part of t h e global radiation t h a t reaches t h e canopy, t h e global radiation being t h e sum of the direct solar radiation and t h e solar radiation t h a t has been scattered in t h e e a r t h ' s a t m o s p h e r e (diffuse radiation). Global radiation is a frequently measured meteorological characteristic.

The following factors relate t h e global radiation t o t h e absorbed radiation:

The composition of t h e global radiation: cloudy days have relatively more diffuse radiation than clear days. Photosynthesis from diffuse radiation is relatively more efficient t h a n from direct solar radiation, because difTuse light p e n e t r a t e s plant canopies more eflectively.

The inclination of t h e s u n and t h e location of t h e place u n d e r considera- tion: these c a n be described by geometric equations. Information about t h e height of t h e sun is necessary, taking into account t h e annual course of t h e sun. These values a r e integrated over a daily time period, throughout t h e year.

Canopy properties a r e also important. The leaf angle distribution can vary between horizontal and vertical, is crop specific and depends on t h e stage of c r o p growth.

The interception of light depends very much on t h e angle between light direction and leaf angle. The optical properties of leaves and t h e leaf arrange- m e n t in various layers also influence light absorption by plants.

De Wit (1965) related t h e s e aspects of radiation to t h e r a t e of photosynthesis in order to e s t i m a t e photosynthetic d r y m a t t e r production. He showed t h a t t h e leaf angle distribution under normal conditions is negligible. Only for crops with an extremely high leaf a r e a index, growing a t low latitudes (tropical regions) is the effect of t h e leaf angle distribution significant. Such situations a r e rarely e n c o u n t e r e d a n d may be ignored.

At t h e end of t h e 1960's i t was discovered t h a t two main groups of plants with different photosynthetic pathways could be distinguished, one group being m u c h more effective than t h e other in absorbing carbon dioxide (under normal carbon dioxide concentrations). This group of C-4 plants is characterized by t h e first detectable stable product formed when carbon dioxide is fixed: either malate o r aspartate. The less effective plants belong to t h e C-3 group, which

1 nanometer = 10 9 meter

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have phospoglyceric acid as t h e first stable synthesized product a f t e r carbon dioxide fixation. Table l a gives t h e daily total photosynthesis values for a C-3 crop with a spherical leaf distribution for t h e 15th of e a c h m o n t h a n d a t various latitudes, for a c l e a r day a s well a s an overcast day. Table l b shows t h e corresponding values for C-4 crops.

Photosynthesis, a s we have said, also depends on t h e availability of carbon dioxide i n t h e canopy. The consumption of c a r b o n &oxide by plants will decrease i t s c o n c e n t r a t i o n in t h e canopy, a fact t h a t h a s b e e n observed by vari- o u s investigators. In Evans (1963) for example, d i u r n a l a n d a n n u a l cycles of carbon dioxide in canopies a r e reported. To m a i n t a i n t h e r a t e of photosynthesis it is i m p o r t a n t t h a t t h e exchange of CO2 with t h e r e s t of t h e a t m o s p h e r e is maintained a t a sufficiently high level and t h i s i s a function of t h e wind speed. We a s s u m e t h a t wind speeds exceeding 2 m e t e r s p e r s e c o n d a r e suficiently high t o replenish t h e carbon dioxide in t h e c r o p canopy. In o u r case studies t h i s value is usually surpassed. Should wind speed be restrictive, we have to see whether c a r b o n dioxide produced by soil is able t o replenish t h e COZ concentration in t h e canopy t o a sufficiently high level.

Air t e m p e r a t u r e is n o t considered in t h e calculations of t h e C02 assimilation, since it h a s been shown t h a t t e m p e r a t u r e over a wide r a n g e does n o t affect photosynthesis (De Wit, 1965, op.cit.).

To e s t i m a t e dry m a t t e r production t h e values i n Table 1 a r e used (from Goudriaan a n d Van Laar, 1978). Their table is a n u p d a t e d version of o n e produced by De Wit in 1965, incorporating additional information s u c h a s t h e above-mentioned distinction between C3 and C4 p l a n t types.

Table 1 displays d a t a on t h e daily gross dry m a t t e r assimilation for a closed canopy for several d a t e s a n d for various latitudes. Dry m a t t e r production is given for a s t a n d a r d c l e a r day and for a standard o v e r c a s t day. This m a k e s i t possible t o interpolate between these t o s u i t specific c i r c u m s t a n c e s , if ade- q u a t e data exist. The values a r e expressed in kilograms of carbon dioxide per hectare (kg CO2 -ha-').

Before we s t a r t o u r calculations we have to r e p l a c e Table 1 by a table show- ing ten-day values of gross daily dry m a t t e r production. Linear interpolation was adequate t o produce a t a b l e of t h e following form:

tablj,k,~t,rn

(j

=

1.2; k

=

1,8;

A t =

1,36; m

=

1,2) where

j = t y p e o f p l a n t ( C 3 o r C 4 )

k

=

latitude, in g r a d e s from 0

"

till 00

"

A t

=

10 day period of t h e year, t h e first one being I m

=

overcast o r c l e a r day

.I0 January

Knowing t h e l a t i t u d e of our case study a r e a , xlat, we d e t e r m i n e t h e dry m a t t e r production as Follows:

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la Daily gross

C02

assimilation of the closed canopy of a C-3 crop with

a

ppherical leaf angle tbtribution

(kg8 C02/ha),

for two standard sky conditions

- -

North. 15 15 15 15 15 15 15 15 15 15 15 15 lat. jan. feb. m a r . apr. may jun. jul. aug. sep. oct. nov. dec.

C1

=

Clear day Ov

=

Overcast day

Source: Goudriaan a n d Van Laar (1978).

Table lb.

Daily gross

C02 assimilation of

the closed canopy

of a C-4

crop with

a

spherical leaf

angle distribution

(kgs

C02/ha).

for two

standard

sky conditions

North. 15 15 15 15 15 15 15 15 15 15 15 15

lat. jan. feb. mar. apr. may jun. jul. aug. sep. oct. nov. dec.

C1

=

^{Clear day}

Ov

=

Overcast day

Source: Goudriaan a n d Van Laar (1 978)

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Table 2.

Daily total

photosynthetic active radiation for a standard clear day

North. 1 5 15 15 15 15 15 15 15 15 15 15 15

lat. jan. feb. mar. apr. may jun. jul. aug. sep. oct. nov. dec.

All values in ~ a l - c m - ~ - d a ~ ' l

Source: Goudriaan andVan Laar (1978).

Table 3.

Soil

Texture and

Soil

Parameters

Soil t e x t u r e

p or o-

sity %

k,

cm.day'' coarse s a n d

fine sand

loamy fine sand sandy loam silt loam loam clay loam light clay basin clay

Source: Centre for World Food Studies (Personal Communication)

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( j

=

1.2; At

=

1.36; m

=

1.2) with

dm

=

gross daily dry m a t t e r production, kg C 0 2 .ha-lday-l k l

=

latitude, s o t h a t k l

s

xlat a n d k1+ 10

>

xlat

j, A t , m

=

s e e above

For t h e estimation of t h e potential dry m a t t e r production, t h a t is t h e dry m a t t e r production based on global radiation, an interpolation between t h e production on a c l e a r day a n d on a n overcast day h a s t o be c a r r i e d out. The radiation on a n overcast day is a s s u m e d t o be o n e fifth of t h e radiation of a s t a n d a r d clear day.

where

dm ⁼

potential dry m a t t e r production, kg C 0 2 *ha-2 .day-1 globra

=

value for global radiation, c a l .cm4 -day-1

c l e a r d

=

s t a n d a r d radiation value for a clear day, cal -cm-2 -day-1 m l

=

overcast day

m 2

=

c l e a r day j, A t

=

as before

For t h e s e calculations we n e e d t o know t h e radiation value for a s t a n d a r d clear day. Table 2 p r e s e n t s d a t a on a s t a n d a r d c l e a r day radiation for each m o n t h a n d latitude interpolation c a n be applied accordingly a s for Table 1:

(symbols a s Eq. ( 1) a n d (2)))

Tables 1 and 2 a r e for t h e n o r t h e r n hemisphere. For t h e s o u t h e r n herni- s p h e r e t h e year s t a r t s with July instead of January.

2.2. Water Constraint

on

Dry Matter

Production

Few a r e a s a r e never affected by drought. Precipitation p a t t e r n s change from y e a r t o year a n d even within a year during t h e cropping season shortage of water m a y r e s t r i c t yields. Prediction of precipitation a n d yield can only be based on statistic a1 i n t e r p r e t a t i o n of col.lected data.

We will work u n d e r t h e assumption t h a t plant transpiration i s proportional t o t h e C 0 2 assimilation of plants. This m e a n s t h a t if transpiration drops because of a d e c r e a s e i n a t m o s p h e r i c demand for water o r because of r e s t r i c t i o n s in plant available w a t e r in t h e soil, t h e dry m a t t e r production will drop as well.

To d e t e r m i n e t h e availability of water for plants t h e water balance c a n be expressed a s follows:

%+At,l,c

- -

't,l,c ⁺P ~ t , l ⁺IAt,l,c

-

E ~ t , l , c

-

R ~ t , l , c

-

D ~ t , l . c (4) ( t

=

1.36; 1

=

1.1; c

=

1,c)

where

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S =

soil m o i s t u r e c o n t e n t of t h e root zone, c m P

=

precipitation, c m

I

=

irrigation, c m

E

=

evapotranspiration, c m

R =

runoff, c m D

=

drainage, c m

1

=

land class, t h e n u m b e r of land classes depending on t h e case study

C

=

c r o p

At

=

time period

The water balance d e t e r m i n e s t h e soil moisture c o n t e n t a t the e n d of t h e time period

A t

given t h e initial moisture c o n t e n t a n d quantities of t h e o t h e r variables for t h e t i m e period concerned. Each of t h e components of t h e water balance is described below.

2.2.1.

Soil Moisture Content

(S)

The soil moisture c o n t e n t is a n important e l e m e n t i n t h e calculation of t h e water balance. I t is related t o soil moisture tension which expresses t h e energy s t a t u s of t h e water i n t h e soil. It tells us whether o r not water is available for plants. If t h e tension r e a c h e s a c e r t a i n critical value, \kc,, the plant closes i t s stomata a n d transpiration will be reduced. This critical value varies with type of crop.

The following equation describes the relationship between moisture con- t e n t and moisture tension.

with

9 =

soil m o i s t u r e tension, c m

H20

vo

=

maximum soil moisture content, which is equal t o t h e soil porosity, volumetric %

v*

=

soil moisture c o n t e n t , vol. %

y =

soil specific p a r a m e t e r

The g a m m a ( y ) is soil specific constant. I t can be determined by regres- sion analysis of t h e soil moisture tension and soil m o i s t u r e content. Values f o r y a r e given in Table 3, a n d observations in t h e Netherlands suggest t h a t soil texture is a good indicator of soil moisture characteristics (P.M.Driessen, personal communication). To convert from soil moisture tension t o moisture con- t e n t we m a y need:

symbols a s before

I t should be noted t h a t t h e water balance applies to t h e rooting zone s u c h that:

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where

S

=

soil m o i s t u r e c o n t e n t , crn.

r d

=

rooting zone depth, c m .

Rooting development a n d rooting d e p t h a r e c r o p specific, one r e a s o n why s o m e crops a r e m o r e drought r e s i s t a n t t h a n others. In t h e model rooting depth depends on t h e s t a g e of c r o p development.

2.2.2. Precipitation

(P)

S t a n d a r d precipitation d a t a a r e r e q u i r e d a s o n e c o m p o n e n t of t h e water balance. The interception of precipitation by t h e c r o p is t a k e n i n t o a c c o u n t while estimating t h e runoff.

2.2.3. Irrigation

(I)

Under c e r t a i n climatic conditions i r r i g a t i o n water is r e q u i r e d for optimal p l a n t growth. The model responds t o t h e following i n p u t variables:

t h e a m o u n t of available water over t h e whole growing s e a s o n

8 t h e a m o u n t of water available a t t h e t i m e of application

a soil water c o n t e n t threshold value below which irrigation i s r e q u i r e d t h e kind of irrigation s y s t e m

t h e efficiency of the irrigation

A t p r e s e n t o u r i n t e r e s t lays only i n t h e irrigation efficiency a f t e r t h e w a t e r h a s r e a c h e d t h e field. Efficiency in t h e field is m a i n l y d e t e r m i n e d by t h e type of irrigation a n d t h e soil type, assuming ideal m a n a g e m e n t by t h e f a r m e r .

2.2.4. Evapotranspiration

(E)

Evaporation from a free water s u r f a c e can b e approximated by t h e Penman-formula (Penman, 1948):

where

E,

=

evaporation from a f r e e water surface, c m -day-'

R, ⁼

n e t radiation, cal .cm-2 .day'' G

=

soil h e a t flux, cal . c m 4 .day-'

A =

r a t e of ~ h a n g e of t h e s a t u r a t i o n vapor p r e s s u r e with t e m p e r a t u r e , m b a r ."C-

y

=

psychrometric coefficient, "C ambar-' e,

=

s a t u r a t i o n vapor p r e s s u r e , rnb e

=

a c t u a l vapor p r e s s u r e , m b fru)

=

wind speed function, rn

-set-'

L =

l a t e n t h e a t of vaporization of liquid water, cal -grn-l

The soil h e a t flux is negligible over t h e 10-day model t i m e steps. The s a t u r a t i o n vapor pressure a t a i r t e m p e r a t u r e (T) c a n be d e t e r m i n e d with t h e

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following equation (Goudriaan, 1977):

with

T =

air t e m p e r a t u r e , centigrade

The slope of saturation vapor pressure

(A)

curve can be estimated by:

( t h e symbols before)

The n e t radiation can be m e a s u r e d directly, b u t this is not often done.

However, because of derived empirical relationships, related m e a s u r e m e n t s can help us in detorrnining t h e n e t radiation. Angstrijm (1924) related t h e hours of sunshine t o the solar radiation, while Prescott (1940) gave this relationship more practical applicability by replacing standard clear day radiation by extra- terrestrial radiation. Excluding reflection and longwave terms, this relationship can be expressed as:

where

R, =

e x t r a terrestrial radiation or angot-value, cal .cm-2 -day-'

r =

reflection of water surface a,b

=

climate dependent c o n s t a n t s n

=

actual hours of sunshine, hr

N =

max. possible hours of sunshine, hr.

lw

=

longwave radiation, cal -day-l

The long wave radiation (lw) lost by t h e e a r t h surface can be approximated by:

with

u =

Stefan-Boltzmann constant (11.69*10-~ -cal - ~ m - ~ - o c - ~ -day-])

=a

=

actual vapor pressure, mbar c,d,e & f

=

climate dependent constants

This procedure for estimating n e t radiation requires m e a s u r e m e n t s of vapor pressure and hours of sunshine. If t h e hours of sunshine a r e replaced by observations of global radiation, increased accuracy can be e x p e c t e d

In situations with agricultural production a t altitudes considerably different from sea level, a correctiori for t h e psychrometric coefficient will be necessary:

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where

C~

=

specific h e a t of a i r a t c o n s t a n t pressure cal egm-' -mbar-'

=

a i r p r e s s u r e a t altitude h , m b a r

=

l a t e n t h e a t of vaporization, cal Sgm-'

=

r a t i o of.molecular weight of water over molecular weight of air, i.e.

mixed ratlo

The a t m o s p h e r i c p r e s s u r e a t altitude h c a n be d e t e r m i n e d by t h e a l t i m e t e r equation:

where

g

=

gravitational acce1eration.m .sec2 p,

=

barometric p r e s s u r e a t s e a level, m b a r

R =

gas constant, J mol-l

. "c-'

h

=

altitude, m e t e r s above s e a level

To calculate t h e potential evapotranspiration (Ep) t h e reflection of a water surface (equation 11) should be replaced by t h e reflection for a c r o p canopy.

Although t h e reflection may change f r o m crop t o crop, a n adequate r e p r e s e n t a - tive value is 0.25 (Monteith,1973).

Potential evapotranspiration can be converted to c r o p evapotranspiration by:

E

=

kc,,, E~

with

E =

c r o p evapotranspiration k c

=

c r o p coefficient

C

=

c r o p

s

=

s t a g e of crop development

The crop coefficient (kc) depends mainly on t h e s t a g e of crop development.

Values for different types of crops a t t h e i r different s t a g e s a r e t a k e n from FA0 (1977).

2.2.5.

Runoff

(R)

Not all t h e precipitation becomes runoff, because of t h e r e c h a r g e capacity of t h e soil. The recharge capacity or I-etention is determined by:

t h e interception of rainfall by c r o p cover

t h e ponding on t h e soil surface because of limited infiltration and irregu- l a r i t i e s on t h e surface.

a m o u n t of water intake by t h e soil.

The p a r t of t h e infiltration in excess of t h e m i n i m u m infiltration (Table 4), t h e interception by t h e c r o p cover, and t h e pondirig together form what is known a s t h e initial abstraction.

The relationship between runoff (R) a n d precipitation (P) is illustrated if Figure 3 a n d may be expressed a s follows (Soil Conservation Service, 1964):

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Kgure 3. Rainfall/ Runoff relationship

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mure

4. Schematic presentation of the water balance estimation Estimation of

@ R, D

St+l =

S' =

st

+ A t

St+P-E-R-D

A

St

+

at

N o

co.01

Solution St + d t

(20)

Table

4. CuRe Number for Various Minimum Indltration Cover-Combinations.

Cover Minimum Infiltration cm/hr

land use treatment or hydrologic 0.95 0.6 0.25 0.06

practice condition

fallow straight row

--

row crops8 straight row poor

row crops8 straight row good

row crops* contoured poor

row crops8 contoured good

row crops* contoured & terraced poor row crops* contoured & terraced good small grain** straight row poor small grainL* straight row good

small grain** contoured poor

small grainee contoured good

small grain** contoured & terraced poor small grain** contoured & terraced good

close straight row poor

seeded straight row good

legumes contoured poor

or contoured good

rotation contoured & terraced poor meadow contoured & terraced good

pasture poor

or fair

range good

pasture contoured poor

or contoured fair

range contoured good

meadow good

woods poor

fair good maize. sorghum, soybeans, sugarbeets wheat, oats, barley,

flax

Source: W.S. Soil Conservation Service (1972)

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where

R

= a c t u a l r u n o f f , c m P

=

precipitation, c m S t

=

r e c h a r g e capacity, c m I,

=

initial abstraction

The maximum r e c h a r g e capacity, St,,, will be r e a c h e d if t h e soil is in a dry condition. This m a x i m u m r e t e n t i o n c a n be e s t i m a t e d from t h e s o called curve number ( c n ) for a dry soil condition.

The curve n u m b e r s have been experimentally d e t e r m i n e d a n d Table 4 shows t h e i r value for various surface conditions. For a given soil i t i s t h e m i n i m u m infiltration, in addition t o i t s land use t h a t co-determine t h e curve number. The kind of l a n d use also influences t h e c u r v e n u m b e r ; a " g o o d rotation is one with a t least 2 years of meadow o u t of 4 years, a n d a "poor" one, h a s n o meadow a t all in t h e rotation (Table 4). Knowing t h e soil porosity and t h e a c t u a l soil moisture c o n t e n t , we a r e able t o calculate t h e a c t u a l r e c h a r g e capacity (St):

S t

=

St,, (v,

-

v*) (symbols as before)

Finally we n e e d t o know t h e initial abstraction I,. This value is normally close t o 0.2 (Soil Conservation Service, 1964), b u t i t may b e useful t o validate t h i s by means of locally collected data.

2.2.6.

Drainage (D)

If t h e soil m o i s t u r e c o n t e n t r e a c h e s a level such where capillary forces a r e no longer able t o withhold t h e water against t h e gravitational force, drainage will take place. This will happen if t h e moisture c o n t e n t is g r e a t e r t h a n field capacity. Profiles with a d e e p g r o u n d water level r e a c h field capacity at a soil moisture tension of approximately 1 bar. Thus whether drainage t a k e s place o r

9

n o t c a n be described by:

where

S

=

initial soil m o i s t u r e c o n t e n t in root zone, cm

P =

precipitation, c m R

=

runoff, c m

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vtc

=

soil m o i s t u r e content a t field capacity, vol%

r d

=

root zone depth, c m

However, over t h e period concerned, evapotranspiration will also occur t h u s reducing t h e possible drainage, giving:

If D

s

0 no drainage will take place.

2.2.7. S o w

the

Water

Balance

The water balance is solved per land class (1) and per crop (c). Three different periods of crop production a r e recognized: a pre-crop period, the cropping period a n d t h e post-crop period. The first- a n d last-mentioned periods require slightly different methods of solving t h e water balance. However, basi- cally in each period we solve t h e water balance per 10 day intervals. We first describe t h e water balance during the cropping season.

2.2.7.1. Water Balance during

the

Crop Season

Solving t h e water balance gives us the soil moisture content a t t h e end of the time interval concerned- This value serves a s t h e initial value For the next time interval.

One complicating factor is t h a t we need to know t h e e n d moisture content beforehand in order t o be able t o estimate t h e value of t h e drainage and runoff t e r m s in the balance. For t h e evapotranspiration we need t o know St+At only if t h e critical value,

+,,,

t h a t will restrict water uptake by plants is surpassed

If C

< +,,

we solve t h e water balance as is shown by t h e flow c h a r t of Figure 4. Giving an initial soil moisture content, we make a first approximation of St+At, which is called S'. With this value we estimate t h e drainage and runoff.

This enables us t o improve t h e St+At value. If the last value still differs considerably from

S'

we replace i t a n d go through the calculations again.

If, during t h e time interval concerned,

+

becomes g r e a t e r than q,, then we have to split o u r time interval ( At) into two parts. Therefore we have to know t h e critical moisture c o n t e n t

+,,.

This value is crop dependent, some crops show wilting a t lower soil moisture tensions t h a n others. In t h e following equation we e s t i m a t e t h e fraction O F the total amount of available water a t which stornatal closure will reduce evapotranspiration (F.A.O., 1979).

where

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p t

=

fraction of available water

p5

=

fraction of available water a t s t a n d a r d value Ep

=

potential evapotranspiration,mm -day-l

Table 5 shows t h e s t a n d a r d values for p5 of various crops. The c r i t i c a l soil m o i s t u r e c o n t e n t c a n be e s t i m a t e d a s follows:

a n d t h e critical soil m o i s t u r e tension, from (5) is :

with

"fc

=

soil m o i s t u r e c o n t e n t a t field capacity

"P

w =

soil m o i s t u r e c o n t e n t a t p e r m a n e n t wilting point

"cr

=

c r i t i c a l soil m o i s t u r e c o n t e n t + m

=

critical soil m o i s t u r e tension

With

.kc,

known we c a n c a l c u l a t e t h e p a r t of t i m e interval A t r e q u i r e d t o r e a c h t h a t value:

where

A t

=

t h e original t i m e interval

d =

t i m e interval a t which t h e critical soil moisture is r e a c h e d (other symbols a s i n Eq. 4)

2.2.7.2. W a t e r Balance during

Pre-

and Post-Crop Periods.

We follow t h e calculation procedure described above, however t h e evapotranspiration should be replaced by t h e evaporation when no c r o p is grown. The estimation of t h e evaporation h a s b e e n described in section 2.2.4.

2.2.8. Dry Matter Production

with

Water as a Constraint

By solving t h e water balance we obtain values for evapotranspiration p e r t i m e interval:

Only if those values a r e equal t o t h e potential evapotranspiration i s potential dry m a t t e r production possible. When r e a l evapotranspiration shows plants t o be water stressed t h e n dry m a t t e r production will be r e d u c e d The r e d u c t i o n in production will be proportional t o t h e reduction i n evapotranspiration.

(24)

where

w d m = dry m a t t e r production i n c l u h n g water constraint, kg -ha-1 pdm

=

potential dry m a t t e r production, kg .ha-'

E

=

real evapotranspiration 6,At

=

time interval

j = t y p e o f p l a n t 1

=

land class c

=

crop

2.3. Prom

Dry

Matter to Plant Material

The dry m a t t e r production is composed of a g r e a t variety of components t h a t can be chemically distinguished. We have already expressed the photosyn- thetically produced assimilates a s kg C 0 2 per ha. In order to make a chemical distinction, t h e dry m a t t e r t e r m is reexpressed as a quantity of carbon dioxide, and we consider plant material t o be a product of t h e physiological functioning of t h e plant. This functioning includes t h e allocation of the dry m a t t e r between the various plant organs, respiration and conversion of t h e fixed carbon dioxide during plant growth.

2.3.1. Respiration and Conversion of Dry Matter

In order to maintain a functioning metabolism during growth, plants m u s t respire, a process involving t h e consumption of a proportion of t h e stored assimilates. The r a t e of respiration is dependent on temperature, being about 1.5% of t h e standing dry m a t t e r a t 25 "C. The respiration rate approximately doubles with an increase in t e m p e r a t u r e of 10 " C (

Q,, -

^2).

During growth t h e fixed carbon dioxide is converted t o chemical compounds such a s carbohydrates, proteins and lignin. The efficiency of t h e conversion is independent of t e m p e r a t u r e and values for this efficiency a r e given in Table 6 (Penning de Vries, 1975). In this table the photosynthesis sub- s t r a t e has been expressed in g r a m s of glucose ( C6H1206 ), requiring t h e conversion from carbon dioxide t o glucose. The production in plant material is described in t h e following way:

where

wpm= produced plant m a t e r i a l kg .ha-1

com

=

efficiency of conversion from dry m a t t e r t o plant material w d m = dry m a t t e r production a f t e r water constraints, kg -ha-I maint= respiration coefficient

t = C A ~

2.3.2. Allocation of

Dry

Matter over Plant Organs

The distribution of plant material between t h e various plant organs is dependent on t h e stage of crop development (Figure 5).

The distribution ratios a r e specified after t h e conversion into t h e various plant compounds h a s taken place. We may describe t h e allocation by:

(25)

Table 5.

fhndard

Values for Rac tion of Available Water for some Crops

Crops ~5

spinach peppers lettuce clover groundnut sunflower maize wheat sorghum sugarcane sisal

Source:

FA0

1977. Crop water requirements.

FA0

irrigation and drainage paper No. 24.

0 .O 0.5 1 .O

Relative Plant Age

Rgure

5.

Relative pnrtioning over plant organs

(26)

Table 8. Values for the Conversion of Glucose into the

Main

Chemical Rac- tions of Plant MateriaL

Chemical Fraction gr product/gr CHzO

Nitrogenous compounds (normal mix of amino acids, proteins and nucleic acids)

from N O T from NH, Carbohydrates Organic acids

Lig

nin

Lipids

Source: Penning de Vries (1975)

Yield ( Y )

Y(-P)

N-Uptake

N -Appl ied

Rgure (I. Graphical presentation of response

to

chemical fertilizers

(27)

wpmj,l,c,~t

=

wpml,c,~t ' "locj with

alloc= relative allocation factor j

=

plant organ

(other symbols as before) 2.4. The Nutrient Constraint

While estimating t h e effect of water availability on t h e yield we assumed t h a t no plant nutrients were limiting to growth. However, many nutrients are essential for plant growth and their depletion o r absence may restrict plant production. The reason may be imbalanced soil n u t r i e n t availability or simply a n u t r i e n t deficiency.

In general nitrogen and phosphorus a r e t h e most widespread deficient nutrients. Because of t h e relatively large amount of t h e s e nutrients required.

commercial fertilizers a r e needed t o replenish t h e n u t r i e n t s taken away when t h e marketable product is removed. The soil itself is usually not able t o mineralize sufficient n u t r i e n t s from organic m a t t e r or through weathering of soil minerals t o replenish losses.

In some situations potassium may limit growth as well, but potassium . requirements a r e more site- and crop-specific. We first describe the effect of nutrition on plant growth (2.4.1) and t h e n we emphasize t h e role of organic m a t t e r , by describing how decay of organic m a t t e r takes place and how it sup- plies n u t r i e n t s (2.4.2).

2.4.1. Soil Fertility and Response t o Soil Fertilization

The effect of n u t r i e n t s on crop yields is shown in Figure 6 (van Keulen, 1982). The top-right hand quadrant shows t h e relation between nutrient uptake a n d t h e marketable yield The yield/nutrient uptake ratio (a) is approximately constant a n d is determined by t h e crop and t h e n u t r i e n t concerned.

If no fertilizers a r e applied t h e yield

(Yo)

depends on t h e nutrient s t a t u s of t h e soil;

Ui

is t h e amount of n u t r i e n t mineralized f r o m t h e organic matter. The maximum yield can only be reached through t h e application of organic and/or inorganic fertilizers.

The bottom-right hand quadrant of Figure 6 shows t h e relationship between t h e n u t r i e n t uptake and the applied nutrient. This relation is determined by t h e efficiency of t h e fertilizer (

8

). This efficiency depends on the chemical properties of t h e fertilizer. t h e way i t is applied, a n d t h e behavior of t h e fertilizer in t h e soil. The crop itself has a role as well, because the rate of growth of t h e roots a n d t h e root distribution through t h e soil codetermine how efficiently t h e n u t r i e n t s a r e taken up.

In t h e top-left hand quadrant of Figure 6 we find a direct relation between t h e fertilizer applied and t h e yield. This is t h e conventional way of presenting

(28)

fertilizer trial information.

We can express t h e response to fertilizers as follows:

YF

=

YP ⁺a ~ ^',&,F ~

.

VF with

Y

=

marketable yield, kg .ha-1

Yo

=

yield based on natural fertility, kg .ha-1 V

=

a m o u n t of fertilizer applied, kg .ha-1 a

=

n u t r i e n t uptake coefficient

B =

fertilizer efficiency coefficient c

=

crop variety

F =

kind of fertilizer

One of t h e oldest concepts in soil fertilization s t a t e s t h a t no response to a fertilizer is possible if another nutrient limits the production. Although some contradictory evidence exists we will apply t h e concept here, being convinced t h a t it describes reality well enough. Combining this with t h e characteristics already mentioned, namely plant composition, uptake of nutrients and t h e efficiency of fertilizers gives us a r a t h e r simple description of response t o nutrients, expressed as a minimum law:

YF

=

min [ Y #

+

a , , ~

-

^*

Knowledge about t h e fertilizer efficiency coefficient and soil analysis a r e crucial in t h e determination of the response to fertilizers. The kind of data required for their determination a r e described elsewhere (Konijn, 1983a)

2.4.2.

Organic Matter Decay

Among t h e solid parts of t h e soil, organic m a t t e r undergoes t h e quickest transformations. The r a t e s of the transformations a r e such t h a t their effects a r e noticeable even within t h e cropping season. They operate concurrently with t h e mineralization and fixation of plant nutrients, of which nitrogen is by far t h e most important. But the role of organic m a t t e r is not restricted to t h e chemical fertility of t h e soil. Changes in organic m a t t e r content bring about changes in s t r u c t u r a l stability and affect t h e soil moisture characteristics of t h e soil. The l a t t e r will be dealt with when we describe t h e resource adjustment;

here we r e s t r i c t ourselves to t h e "weal a n d woe" of t h e organic m a t t e r as h a s been developed by P. Driessen (CWFS, Wageningen, personal communication)

Due t o t h e heterogeneity of the organic m a t t e r , six fractions have been distinguished They a r e assumed to be universal: proteins, sugars, cellulose, lignin, humic substances and i n e r t material. Each of t h e m is subject to decay because of their use as nutrient and energy source by the various soil organ- isms. The r a t e of change of decay is a function of the amount of material in t h e particular fraction:

(29)

dfr .

A = + . d t f r j with

f r

=

a m o u n t in fraction k

=

coefficient of decay j

=

t h e fraction

The coefficient of decay will however change with time. This is d u e t o t h e change in heterogeneity (q) of e a c h of t h e fractions.

Values for heterogeneity a n d decay r a t e s a r e given in Table 7. The r a t e of decay is also affected by t h e soil environment: soil acidity, soil t e m p e r a t u r e and soil moisture content. Moreover, t h e quality of t h e organic m a t t e r , which is d e t e r m i n e d by t h e carbon/nitrogen r a t i o (C/N-quotient), plays a role. Each fac- t o r may c a u s e a reduction in decay r a t e , t h e most limiting d e t e r m i n e s t h e a c t u a l r a t e of decay.

with

k(ac)= a c t u a l decay r a t e r c

=

reduction factor j

=

fraction

The transformations of organic m a t t e r a r e schematized in Figure 7. Each of t h e fractions follows t h e conversions illustrated and t h e r a t e s of those conversions a r e controlled by t h e above-mentioned factors affecting decay rate.

The dead plant m a t e r i a l (primary m a t e r i a l ) undergoes a biochemical degradation. The primary m a t e r i a l is only partly decomposed, a n i n t e r m e d i a t e product is formed t h a t will be u s e d by microorganisms a s a s o u r c e of nitrogen a n d carbon. This leads t o the formation of secondary products which is accompanied by losses in liquid and gaseous form. With each t i m e s t e p a p a r t of t h e s e secondary products (intermediate product 2) forms t h e basis for condensation, t h a t is, synthesis of various organic products t h a t are grouped a s t e r t i a r y products.

Their formation is again accompanied by losses in liquid a n d gaseous form. P a r t of t h e tertiary products will undergo t h e fate of i n t e r m e d i a t e products 1.

These transformations a r e repeated from t i m e interval t o t i m e interval a n d if t h e r e i s n o r e p l e n i s h m e n t by m e a n s of fresh organic m a t t e r , i t is obvious t h a t a gradual loss of organic m a t t e r takes place over time. By adding up t h e primary, secondary a n d t e r t i a r y m a t e r i a l a f t e r each t i m e s t e p we a r e able t o follow t h e changes in organic m a t t e r c o n t e n t . However, n o t only t h e organic m a t t e r c o n t e n t changes over time; soil acidity a n d t h e mineralization of nitrogen will change as well.

The soil acidity is d e t e r m i n e d by t h e cation exchange capacity. It is described by a n empirical relation:

(30)

Biochemical Degradation

Condensation,

\ -

Losses

(3

Rgure

7. ' h e decay of

organic material

(31)

Table

7.

Ractions of

^Organic

Matter. their Decay Rates

and

Heterogeneity

Fraction heterogeneity decay r a t e

9 Per day per 365 days

Proteins 0.0008 0.23 0.17

Sugars 0.0035 0.17 0.05

Cellulose 0.00'71 0.05 0.003'7

Lig nin 0.0015 0.0023 0.00 13

Humic substances 4.5

x

lo4 1.2

x

lo4 1.2

x

lo4

0 1

00 200

Days

from

Planting (Cotton)

mure

8.

Relative nitrogen

uptake during

the growing season

(32)

( c e c t

-

cect,,) (17.6

-

^{pH -50)}

APHA~

=

(280

.

depth

+

17.6

-

^cect)

where

APH

=

change in soil acidity

c e c

=

cation exchange capacity of organic m a t t e r meq. .ha'1 depth

=

thickness of horizon with organic m a t t e r , c m

t =

^{t i m e}

At

=

t i m e s t e p

During t h e transformations nitrogen is mineralized. Depending on t h e nitrogen r e q u i r e m e n t by t h e crop, the soil environment (pH, T. v ) and t h e quality of t h e organic m a t t e r , all o r a p a r t of the nitrogen will go to t h e plant.

Depending o n t h e crop, t h e r e a r e certain potential u p t a k e p a t t e r n for n u t r i e n t s , which normally follows a sigmoid p a t t e r n (Figure 8 ) . This potential uptake may not be r e a c h e d because of t h e factors mentioned above. Here again, t h e most limiting f a c t o r will determine t h e reduction on potential uptake t h a t will take place:

where

U

=

uptake of N for c r o p c

u!g =

potential uptake

r f

=

reduction due t o soil environment or organic m a t t e r quality

A t =

t i m e period

For t h e o t h e r n u t r i e n t s potassium and phosphorus we follow the s a m e procedure, although t h e quantities involved a r e considerably smaller t h a n for nitrogen.

3.

The Environment Module

Although t h e environment module is described separately, i t s processes also take place during t h e growing season, i t is logical t h a t intermediate output from t h e c r o p production module should be used in determining the environ- m e n t a l consequences.

With regards t o agricultural production we distinguish between two kinds of environmental effects.

t h e on-site effects: t h e y a r e mainly comprised of changes in soil properties t h e off-site effects including the occurrence of soil sediments in surface waters a n d nitrogen in g r o u n d water.

These a r e t h e r e s u l t of various processes t h a t a c t upon t h e land during agricultural production. The importance of the processes is s i t e determined and, although fully recognizing t h e importance of t h e o t h e r processes, we will r e s t r i c t ourselves for t h e m o m e n t to water erosion.

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3.1. Water

Erosion

We will use t h e Universal Soil Loss Equation (U.S.L.E.) which was developed by t h e U.S.D.A. (Wischmeier and Smith, 1978). Estimated soil loss, using t h e USLE, is given as:

where

A

=

soil loss

R

=

rainfall erosivity factor

K =

soil erodibility factor L

=

slope length factor

S =

slope grade factor

C

=

crop and management factor P

=

practice support factor

l,c,At= resp. land class, kind of crop and time period

For standard conditions all t h e factors except t h e rainfall erosivity and soil erodibility become equal unity. Information from a large number of field trials have led to t h e possibility of estimating these factors when deviating conditions occur.

Each of the t e r m s of t h e USLE may briefly be described a s follows:

Rainfall Erosivity

In principal erosivity should be determined through the analysis of rainfall data. Therefore t h e rainfall has to be registered continuously, for example a s pluvigrammes. Empirically, t h e maximum 30 minutes intensity of each rainstorm multiplied by t h e total rainstorm energy gives the best fit with t h e soil loss under standard conditions for a certain kind of soil. The accumulated values for t h e erosivity per month should be determined to be able to make a good estimate for t h e cover and management factor (explained below).

Soil Erodibility

The following relation determines t h e erodibility (K) based on information about soil texture, soil organic matter, soil structure, and permeability (Wischmeier and Smith, 1978).

K1 =

[2.1.

h i " ' - lo-" -

⁽¹²

-

^{a l )}

+

3.25 n(a2-2)

+

^2.5

.

(a3-3)) / 100 (37) with

M =

% silt

.

(100

-

% clay ) a 1

=

percent organic m a t t e r

a2

=

soil s t r u c t u r e code used in soil classification a 3

=

profile

-

permeability class

Slope Length and Slope Grade

(34)

The slope length and slope grade factors a r e determined jointly in the following formula:

.

(65.41

.

sin2$

+

^4.56

.

sin$

+

^0.065)

where

A

=

slope length in meters a n d

$

=

slope angle in degrees

m

=

a slope dependent "constant"

Cover and Management

Like erosivity, t h e value for t h e cover and management factor changes over the year. During t h e year such events as land preparation and crop development bring about changes i n plant cover. Therefore information for a complete year with all its agricultural activities is required (see Konijn, 1983a).

Support Practice

This factor requires information on s u c h practices a s terracing, contour plowing etc. For details, s e e Konijn (1 983a).

Some of t h e above input characteristics a r e similar to those required for the crop production module; o t h e r s , especially the site characteristics exclusive t o t h e erosion estimation. There is also a technology input and finally, some input h a s been c r e a t e d as output from t h e crop production module. The result i s t h e soil loss for various periods of the year (At) which, when accumulated, give the annual soil loss.

As we will see in Section 4, t h e soil loss i s used as a basis for t h e estimation of changes in some soil properties (on-site effects). To evaluate t h e off-site effects we have to estimate which p a r t of t h e soil loss will be transported into t h e surface waters. This will require a more geographical interpretation of the a r e a under study. Catchment areas have to be recognized, a n d assumptions on t h e division of the c a t c h m e n t a r e a into various lands of land use a r e required.

They allow us to make a rough estimate of t h e amount of sediment t h a t can be expected in t h e surface water.

with

A

=

soil loss, metrictons .year-1

0

=

a r e a of specific land class/crop combination a

=

catchment a r e a

1

=

land class

C

=

crop

At

=

time period

The sediment delivery ratio (sdr) is a function of t h e size of t h e c a t c h m e n t a r e a

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sdra

=

f(Oa)

Therefore the sediment in t h e surface water leaving the area is:

'a,At

=

^sdra ^'*a,At

4. The Resource Adjustment Module

Some of the soil characteristics a r e subject to gradual changes over the year because of agricultural production. Of these characteristics some have to be updated a t t h e e n d of t h e year. This is t h e consequence of t h e way we apply the hierarchical system (section 2). Estimations a r e not carried out p e r time step through all t h e hierarchical levels, but per hierarchical level for t h e whole year.

A

characteristic used a t a higher level but affected by a characteristic t h a t changes during crop production a t a lower level can only be updated a t t h e end of t h e year. Only those characteristics t h a t a r e updated a t t h e end of the year a r e described below.

4.1. Soil

Organic Matter

As a result of decay during t h e year, loss in organic m a t t e r takes place throughout the whole topsoil horizon. A description of t h e decay of t h e organic m a t t e r is given in paragraph 2.4.2. In contrast, erosion does not affect the whole topsoil horizon, acting upon only t h e soil surface. Knowing t h e soil loss and t h e bulk density of t h e soil we a r e able to calculate t h e loss in topsoil thickness.

sllnC

.

^10-2

tsl,,,

=

bdl with

tsl

=

topsoil loss, c m

sl

=

soil loss, me trictons-ha'l bd

=

bulk density, gm-cm5 1

=

land class

C = c r o p

Depending on the module, we need to know t h e organic m a t t e r expressed in different dimensions. For t h e total amount of organic m a t t e r per h e c t a r e we simply use t h e soil loss per h e c t a r e multiplied by t h e percentile c o n t e n t of organic matter. For other conversions we need t o know t h e thickness of t h e topsoil horizon and t h e bulk density.

4.2. Soil Moisture Characteristic

The soil moisture characteristic concerns the relation between t h e soil moisture content ( v ) and soil moisture tension (+ ) (see Section 2.2.1., equation 5).

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This relation is affected by a change in organic m a t t e r content (Figure 9).

This in t u r n affects t h e pore size distribution: a decrease in organic m a t t e r means a decrease i n porosity and t h e value of vo will change. The porosity can be expressed as a function of t h e specific soil density a n d t h e soil bulk density.

-

¹⁰⁰

.

(sd

-

bd)

v o

-

_sd

where

sd

=

specific soil density, gm - ~ r n - ~ bd

=

soil bulk density, g m - ~ r n ' ~

The change in soil density with organic m a t t e r c o n t e n t is described in t h e next section.

4.3. Soil

Bulk Density

Both t h e specific density and bulk density a r e Functions of t h e composition of t h e soil, t h a t is its mineral and organic parts. Because of its low specific density, relatively small changes in organic m a t t e r c o n t e n t have a considerable effect on t h e soil bulk density.

loo '

and bd

=

¹⁰⁰

where a and b express t h e percentages For each of t h e soil components (i):

x

^ai

⁼

^{100 and} ^bi

⁼

¹⁰⁰

i i

The pore distribution in t h e soil is a s s u m e d t o be constant, which m e a n s t h a t t h e soil constant

y

will not be affected.

4.4.

Nitrogen

Nitrogen in t h e various fractions, in t h e soil a n d taken up by t h e plant c a n be calculated a s well. For t h e moment n o interaction between t h e soil's organic m a t t e r and applied nitrogen is assumed t o exist, a n d no carry over OF fertilizer nitrogen from one year t o t h e next is supposed to be possible. This means t h a t we assume complete loss of nitrogen through s u c h processes as leaching and denitrification.

This is clearly a provisional solution a n d will require a more realistic approach in t h e near future.

4.5.

Phosphorus

Phosphorus applications are known for t h e i r inefficiency. I t has been observed t h a t t o maintain yield a t its maximum level regular annual applications are required. This is due t o t h e fixing capacity of most of t h e soils. How- ever although t h e efficiency within the cropping season is low, t h e r e is a clear

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residual effect of t h e applied phosphorus fertilizer. This m e a n s t h a t t h e crop yield in t h e second year without phosphorus application will be higher t h a n they would have been with no application in t h e first year.

Our concern h e r e is t h e carry-over from year t o y e a r of t h e soil phosphorus, with or without fertilizer application.

Figure 10 shows t h e relationship between t h e soil analysis a n d yield. We consider a linear relationship t o be a close approximation.

where

y

=

yield

p

=

soil t e s t coefficient a

=

crop uptake coefficient s a

=

soil analysis

In case no crop is grown, t h e r a t e of change of t h e residual effect of phosphorus fertilizers is approximately proportional t o t h e a m o u n t applied.

The soil analysis (sa) c a n be used for t h i s purpose because we assume t h a t t h e efficiency of t h e applied phosphorus fertili.zer does not differ from the phosphorus already in t h e soil.

If a crop is grown a part of t h e available P is removed. For a linear uptake over t h e growing season then:

which would give us the following analytical solution.

where

s a

=

soil analysis a t t i m e

t

sa,

=

soil analysis a t t i m e t, t

=

t i m e

a

=

crop specific c o n s t a n t b

=

soil specific constant

If no crop is grown t h e residual effect becomes:

The values for q and b should preferably be derived from local information.

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0

10

20 30

40

50

Soil Moisture Content, Vol.%

Kgure

9: Soil moisture retention curve ^as

determined by organic matter content

Yield ( Y )

4

^I

I I Uptake Phosphorus

I

(Sa)

Figure 10:

Response to fertilizers bazsed upon soil

analysis