Optimisation of the Use of Water Reserves in Agriculture from the Modelling Water-Soil-Crop System

VII

WATER RESOURCES AND AGRICULTURE

Copyright © IFAC g, System Approach for Development Rabat, Morocco, 1980

OPTIMISATION OF THE USE OF WATER RESERVES IN AGRICULTURE FROM THE MODELLING WATER-SOIL-CROP SYSTEM G. Bel*, C. Maertens** and

J.

Puech**

*C.E.R . T., Automatic Control Department, Post Box 4025, 31055 Toulouse, France **I.N.R.A., Toulouse Research Center, Post Box 12, 31320 Castanet, France

Abstract. The aim of the study is the modelling of the water-sail-corn system from experimental data, which have been measured in full size expriments on various cultures over a period of ten years by the Agro station, in order to improve water use in agriculture. For various plots and several years, series of soil humidity at several depths (every 10 cm down to 1.6 m) have been gathered at various instants of the year (about 20 for each plot every year) .The application of systematic techniques of modelling and id en tific a tion to this system allowed the build up of a model simulating the time histories of the hydrous state of a soil farmed in corn. The problems encountered lead to back up the classical model error identification method by statistical data analysis methods. Good results for the specific application ~onsidered (precision better than 10%) have been obtained by alternate and iterative use of both kinds of methods, It is then possible to calculate the detailed hydrous state of the soil (every 10 cm) from easily measured data, namely rain, potential evapotranspiration and some parameters characteristic of the soil and culture. This is particularly useful for the precise forecast of the days and volumes of irrigation for a better use of the available water, Keywords. Agriculture, data reduction and analysis, Ecology, Identification, Modelling, Moisture control, Optimisation, system analysis

INTRODUCTION

rim.ental m.oisture !"esure!'1ents :"'or soil producing various crops.

During the last few years, important progress has been made in agronomy in the areas of ge netics, fertilization, crop protection and more generally in overal cultivating techniques .

The goal of the present study is the modelling of the water - soil- crop system from this experimental data . The use of systematic modelling and identification techniques has permitted us to perfect a model that simulates the evolution in time of the hydrous state of soil yielding a corn crop . The choice of plant for this exprimental modelling was determined by its economic importance , its future development and its high sensitivity to irrigation .

Water, in subhumid regions, has terefore become one of the principal factors in determining vegetable production , especially for summer crops (various types of fodder, corn, sunfl ower , fruit trees".) However this water is relatively rare in agriculture and if provided by irrigation , its cost if fur from negligible in relation to other crop production costs .

So as to be easily used in sites outside the experimental one , the model must only need easily measurable data to be put into practice : daily meteorological data and certain soil and crop characteristics . It then permits one to calculate the hydric state of the different layers of soil occupied by its roots each day of the plant ' s life. The quantity of water necessary to satisfy the plant 's needs can then be determined and,as a result/better productivity will be obtained ,

Its val orization is consequently a general problem which presupposes a better quantitative knowledge of the ecophysiological phenomena relating to the plant ' s water needs and to its manner of food intake through the roots, A better knowledge of agronomical phenomena is also necessary in order to determine the most appropriate irrigation methods. In the pur'pose of meeting these ojectives , the National Institute of Agricultural Research's Agronomy Station at the Toulouse Research Center has been dedicated to the study of such hydrous problems for a period of almost ten years. Thanks to fieldwork exprimentation carri ed out over an area of 20 hectares , we were able to gather a considerable number of expe-

DESCRIPTION OF THE EXPERIMENTAL AREA EMPLOYED AND OF THE MEASUREMENTS SELECTED a) Experimental area Situated np-ar Toulouse (in south west France) the 20 hectares surface of dark br own earth., resembling I'terrefors "permits a global study, 317

G. Bel, C. Maertens and J. Puech

318

respectively calculated on the day j-1. The model permits us to determine the physblogical development and hydrous state on day j. Moisture (t) at various depths Plants physiological development

Rainfall (t) Meteorology Irrigation(t)

P(t):rainfall at time t I(t):irrigation at time t PET(t):potential evapo transpiration at time t CC : field capacity of layer i i PF42i PF 4 . 2 of layer i X2 ••• X9 parameters to be identified Given the differential system

Xl,

~~(t) Soiltype

Variety density

Of the various available meteorological data influencing the plant's exchanges with its exterior environment, we have chosen the potential evapo-transpiration as the model's input. Determined from evaporation levels in a (Piche) tank and from the consumption of a reference plant cover (evapo transpirometer) the PET synthesizes the effects of wind, sun and temperature.

DESCRIPTION OF THE

~IODEL

From acquired knowledge of the phenomena it was by induction that the INRA agronomists carried out research on the best structure to be employed for this spacio-tempore~non­ linear/deterministic model. Among the various types of possible structures was chosen one that would allow the best adaptation of the parameters to measurements. This model is composed of the diverse sub models described below :

=P(t)+I(t)-RETI(HI,PET(t),t)-DRI(HI)

dHj(t) = DR. 1(H. 1)-DR.(H.)-RET.(H.,PET:t),t) dt lll l l l dHdnt(t) =DR

n-

1(H

n-

1)-DR (H )-RET (H PET(t),t) n n n rr

with

(1. (H. (t)-CC.) if H. (t» .. Xl l l l

DR.(H')::l0 if PF42i~ l l 1 (PF42.-H. (t))if H. (t)< l l l

CC. l

Hi(t)~

CC.

PF42.

l

l

X2

We may note that the existence of pronounced interhorizon coupling and strong non linearities complicates identification.

3/ . Plant equations In order to calculate the plant's wa.ter consumption, one must first determine its maximum evapo-transpiration whose value is in funtion of the foliar index and the varying vegetative stages. The general law of water needs evolution for various plant covers is shown below :

1/ The soil model The soil is modelled as a serles of cascading linear, run-off reservoirs over a threshS·l la. called field capacity FC. The reservoirs conditions are characterized by their stock or humidity expressed in millimeters of water. The plant's roots take water directly from these reservoirs, the number of which depends on the soil in study (these are 16 in the majority of plots studies). Each reservoir corresponds to a 10 cm soil layer

,l ~

16

I

CC

Ocm pF42

DEPTH!

~?1)L Real ~vap~-trans-

______ ~

-.:;:??f ~~

20 :;

1

plratlon

L

:~2H-'

•

2/ Hydrous soil condition equations The soil layers are numbered from 1 to n from the soil surface downwards. All the hydrous variables are expressed in mm of water. let : H.(t) : hydrous state (or moisture) of layer l i (or reservoir) at time t DR. (t):drainage of soil layer i into layer l i+1 at time t RET.(t):plants water intake of soil layer i l at time t

Number

~

days

following emergence This law is characterized by an equation with two parameters (X3 and x 4) which permit one to wary respectively the date of the maximum MET/PET relation, the width of the corresponding hump and the value of this maximum, which can exceed the value 1 MET = PET f(t,

X3, X4)

The real consumption of the plant (RET) depends therefore not only on on its needs (MET) but also on the soil's hydrous condition and climatic demands. In fact /1/ a determined hydrous reserve and the soil's transfer capacity is influenced by its moisture content and the speed of its natural drying-up process. Consequently for given climatic conditions the plant's use of soil reserves over a certain threshold brings about a decrease of water consumption and has repercussions on consumption rhythms. Whatsmore, it has been noted /1/ and /10/, that the intensity of this demand has an important influence on the soil's possibilities of water transfer to the crop and eventl.laly cuts down the using up of the soil's water reserves during years of strong hydrous deficit. Our model provides a rough analysis: in the following series of curves /10/, the relation consumption RET need

MET

Optimisation of the Use of Water Reserves in open fields with real crop rotations, thereby comming as cl ose as possible to large scale farming and to diverse methods of dry or irrigated cultivation . The area is divided into 196 plots of 200 m2 each. Every year, certain plots produce the principal regional crops/some i:rigated / ot~ers not. Other p~ots produce exprlmental serles of crops for lno. teryearlyassessment and irrigation policies.

b) Moisture measurements The soil's moisture measurements (hydric profile) are taken each year, for each plot, in accordance with the periodicity adapted to each study ' s plan . These measurements are taken at periodic depths (every 10 cm down) by means of a neutron humidimeter.

c) r·leteoro 1ogy s tati on A meteorology station situated on the experimental area permits the gathering of classi cal meteorological parameters : temperature humidi ty , sunshine , wind , evaporation and global radiation.

d) Cultivating processes The cultivation methods employed are similar to those of a good farming concern . The end of season yield is assessed from representative surfaces (minimum 25 m2 )

e) The soil At the beginning of the experiment , the different types of soi l of each plot , are determined by a physico-chemical analysis and by structural stability tests .

f) Available data At the beginning of our re search we had at our disposal the 1971 t o 1976 hydric and meteorological informations for twelve different plots As corn is not cultivated on each of these plots every year , 2 1 series of hydric profiles corresponding to the various plots were available to us. It is this collection of exprimental data ,ex-::eptional in the field of agriculture, that was put into use.

DESCRIPTION OF THE SYSTEM AND METHOD EMPLOYED The following diagram portrays one manner to descri be the water- soil·crop system

319

Various "loops" are noticed which emphasize the plant's possibilities to adapt to c limatic conditions and also the modelling difficulties. - The plant's water needs depend on its physiological development which in turn result from the satisfying of its water needs . The plant can thus reduce its consumpt i on and growth if the climatic conditions are harsh or if the moisture available in the crop r oot zone is insufficient (2nd l oop) . - Root growth depends on the physiological development of the plant but also on the so il's water pressure. The easier it is to extract water from the near surface layers . , the 'le sser will be the plant ' s tendency to plunge its roots deep into the earth. Consequently we can observe that , with irrigated crops thellieful roots remain c l ose to the surface while with non irrigated crops, the roots go very deep . To make a model of this system, we used the cybernetics systems approach , or more specifically the model error identification method. Although this method may be a classical one for use in process analysis it is much less so in the field of agronomy . These already exist a certain number of arti cles relating t o models of the water- soilcrop system. The se are, either very detailed models connected with exprimental crops in the l aboratorY, or very r ought models not concerned with in-depth moisture distribution, which are thus used on a site in accordance with the periodic measurements taken . Our approach is half way between these two methods, our aim : to find a gl obal model one that is spacio - temporal or dynamic (with ti med humidity variation) of the grey box type. We wLll not endeavour to neatly copy r eality , but rather t o reproduce its effects by linking them to exterior causes. The following diagram depicts the model's precise input and output points. At the start we know the date and density of seeding , the soil type and the plant variety. For every day j , we know the values f or rainfall, irrigation and meteorology as well as the plant ' s deve lopment and the soil ' s hydrous condition as

G. Bel , C. Maertens and J . Puech

32 0

depends not onl y on the average soil moisture but also on the potential evapo t r anspi r ation (PET) cl imate RET

.!:1!T_ ..

horizon; sum of the~uare of the differences at certain critical dates . .. ) the model's parameter values were determined with the aid of Powell ' s Algorithm of Optimisation and by means of the following classical diagram M. (t) l

Soil moEture

Entry _ Rainfall PET Irrigation

+

The above series of curves lS depicted by an equation with~arameter x5 If H

mean

n

=

(t)

."_ 1' H. (t) l -

l

n

= number

of sections in the root area on date t - 1

= MET

RET

g(H (t) , PET , x ) mean 5

We must next see how this demand is distributed among the various soil layers in order to solve the differential system. The first step is to determine the plant's root depth . A measurement analysi s gives us the following curve of useful root depth :

70

50

Number of days emergence

after ~

r ~

depth

The intake distribution between layers is then inverely proportional to the depth so as to take into account the small est degr ee of possibility fo r water transfer to the very ~epths . Let s ( ~, x ) a f unction of the iX, or e l X, type. Glven 7 : kRET(t) RET. (t) l s(i , x ) 7 also

n

k

L

i =1 Therefor e k n

~ s(i , x )

7 l= 1 Thus having knowl edge of the RET.(t) we have all the el ements necessary to solve the di f ferential system r el ative to hydrous equat i ons of the soil and so determine the hydrous conditions immediately f Ollowi ng .

IDENTIFICATION OF PARAMETERS On the goal of Obtaining the most realistic r esults for cer tain c r iter ia (differences between measured moisture and calculated moistur ~ sum of t hese diffe r ences fo r a given depth or

The problem dealt with various criteria , yet we decided to accept the slight deterioration of one of the criteria if this permitted the appreciable amelioration of others,notably during the critical plant growth period.

SPATIAL EVOLUTION OF PARAMETERS After the identificati on phase , we had available the Xi parameter values producing the most realistic result s for each plot . In order to facilitate the model ' s future realization on other areas , a study of the evolution of identified parameter values in relation to the various plots was carried out . The goal : - to regroup parameters and similar plots - to link the model ' s Xi parameters to easily measurable qi physical characteristics (soil composition , planting density , corn variety .. ) The method employed was that of multivariate statistical analysis : the "princi pal component factoral analysis method" which allowed us to underline , the connections that exist between the model ' s parameters and certain physical characteristics . These relations enable one to obtain a model whose parameters are physi cal characteristics measurable once and for all on the site itself , before the CUltivating season.

VERIFICATION OF MODEL'S VALIDITY To determine the validity of the r esults obtained from the use of such models concerned uniquely with the soil and crop ' s physical characterist ics we set up a simulation for each plot year. We were thus able to obtain very good results which are highly sat i s facbor) on the agronomic point of v iew . To clarify , we may add: - ave r age errors in layer ' s moisture are gene rally in the area of 2 mm for measurements of approximately 15 to 30 mm , and are never superior to 4 mm . This is ~ually the case for near surface sections where the majority of water movements take place (there are the most difficult to modelize) , and for deep sections . - Global moisture errors , accumulated on the entire hydrous profile for one day of measure ments are , on average , less than 20 mm , f or profiles corresponding to 500 mm of water . The maximum global moisture error value of all the various plots studied does not surpass 66 mm .

Optimisation of the Use of Water Reserves These few, but partial figures show.t~at t~e information obtained is indeed sufflclent ln view of the fact that in a given field the soil' s lack of homogeneity scarcely per mits a more accurate spatial measurement evolution. Bel ow you will find examples of results obtained from two differents plots : plot·E2073· non irri gated of the'Pioneer 3567' corn variety and plot ":F0974 " irrigated of the "INRA 400" corn variety. The curves represent on the one hand the model's calculated humidity evolution and on the other hand , the different measurements shown by small points. The individual curves correspond to various 10 cm soil layers taken

321

at periodic depths. The peaks represent rainfall or irrigation. The figures on the left show the average error between the model and the measurement fo r each depth level in millimeters of water . We may note that,especially during the critical phases , the results provided by the model based on parameters calculated from physical characteristics/are very close to the ori ginal measurements.

----~----------------------------------------------------------------------------------------CONCLUSION Systematic modelling methods are rather rarely applied to the field of agriculture these days. New problems encountered during the course of this ecosystems modelling study have led us to the simultaneous use of the "model method" classical in this type of study and methods relating to multivariate stat i stical. I t is the methodology that callS for a successive and repeated use of the two above methods: that permitted us to obtain reliable results. It is therefore with confidence that we can look Iorwalrlto other applications of modelli ng in this field. In particular , the corn model can be carried on in two directions : CSA D - 0

-ll real time" use : model simulation replaces a moisture captor , making it possible to cal culate the soil ' s daily hydrous condition . This could bring about: • an improvement in functioning or planned irrigation systems .the de termining of pseudo optimal irrigation policies in open loops. With knowledge of the soil ' s hydrous condition and the pl ant ' s water needs (known by agronomists), one can determine irrigation dates and water quantities that will satisfy the plant 's needs all of which will lead to better water management, so often rare and expensive (the profit yield of irr igated water is presently estimated at approximatel y 40%) . • the possibility of carrying out an automatic irrigation system that will independently start and stop water flow.

G. Bel, C. Maertens and J. Puech

322

- provisional use. In this case by means of past meteorological data, one can determine the grounds for carrying out an irrigation program by calculating the level of water deficit, the time taken and the profit loss suffered. An estimate of the various necessary dimensions of irrigation facilities can likewise be reached by simultating the different irrigation policies provided by these various facilities (irrigation periodicity possible, quantity of supplied water). With the use of other ex~erimental data, the model's eventual applications to other types of crops can also he forseen. The advantage of such models will depend on the water sensitivity of the crops chosen. These excellent results obtained with corn, a plant highly sensitive to water, provide a good example of what can eventually be achieved.

BIBLIOGRAPHIE /I / Station d' Agronomie de Toulouse (INRA)_ Plante sol climat et irrigation. Le point de 8 annees de recherches sur l'alimentation hydrique des plantes et la valorisation de l'eau - INRA, 136 pages, 1973 /2/ Maertens C., Blanchet R., Rellier J.P. Influence de la nature des sols et de leur exploitation racinaire sur l'evolution des profils hydriques - Agrochimica XVIII n03, pp 259 265, Xeme symp. Int. d'Agronomie, Bari, 1974 /3/ Maertens C, Blanchet R., Puech J. Influence de differents regimes hydriques sur l'absorption de l'eau et des elements mineraux par les cultures. Regimeshydriques systemes racinaires et modalites d'alimentation en eau - Ann. Agro., 25(4)pp 575586, 1974 /4/ Puech J., Haertens C., Efficience de l'eau consommee de quelques cultures placees dans differentes conditions ecologiques Agrochimica XVIII n03, pp 223 230, Xeme Symp. Inter. di Agrochimica "I problemi dell acqua in agricoltura" Bari, 1974 /5/ Yu 0., Gintzburger G., Gounot M., Hodele de fonctionnement d'un peuplement de dactyle en phase vegetale. Approche morphogenetique. Oecol. Plant, 107 139, n02, TIO, 1975

/6i INRA Toulouse - Avertissements irrigation (1967-1975) Collaboration avec quatre departements, les chambres d'agriculture et les SUAD (Service Unite Agricole et De-veloppement). /7/ Jensen, Robb, Franzcy, Scheluding irrigations using climate crop sol data - Jnl Irrigation and Drainage Dsion ASCE, 70 /8/ J.C.Flinn, The simulation of crop irrigation systems, Systems Analysis in Agricultural Management, John Wiley, 1971

/9/ Hall and Dracup, Water ressources systems, Engineering MacGraw Hill, 1970 /10/ Denmead, Shaw, Availability of soil water to plants on affected by soil moisture content and meteorological conditions Agronomy Journal, vol 54, pp 385 390, 1962 /11/ Fogel, Duckstein, Kisiel, Optimum control of irrigation water application. Automa tica, vol 10, 1974 /12/ Dudley, Howell, Husgrave, Optimal intraseasonal irrigation water allocation, Water Resources Rs., 7 (770 778), 1971 /13/ Rambal, Romane, Aguilar Martin, Modelisation de la production de biomase vegetale de la steppe sud tunisienne par une methode globale d'estimation des parametres et par filtrage non lineaire. Congres AFCET "Al\alyse des systemes" Versailles, 1977 /14/ Rawse, Stone, Gerwitz, Simulation of the water distribution in soil. Plant and Soil, 517-550, 1978