Transport modelling in watersheds

Ecological Modelling, 52 (1990) 135-179

135

Elsevier Science Publishers B.V., Amsterdam

Transport modelling in watersheds B. Caussade and M. Prat Institut de Mdcanique des Fluides, U.R.A. au C.N.R.S., Avenue du Professeur Camille Soula, 31400 Toulouse (France) (Accepted 22 January 1990)

ABSTRACT Caussade, B. and Prat, M., 1990. Transport modelling in watersheds. Ecol. Modelling, 52: 135-179. We show, giving relevant examples, how the modelling of principal phenomena taken into account in the transport models in watersheds is treated. We next present, in diagram form, the main models proposed in the last 15 years, especially in the U.S.A. Two models developed at the Fluid Mechanics Institute in Toulouse help to illustrate the advantages and weaknesses of this type of approach. In the last part, lessons are drawn from this piece of research and we attempt to broaden lines of thought to improve the weak chain in these models, i.e. the simulation of the water cycle.

1. INTRODUCTION

At the watershed level two kinds of pollution occur: (1) On the one hand 'point' pollution, either of agricultural origin (agricultural cooperatives, husbandry etc.) or of urban origin (town waste, slau.ghterhouses) or of industrial origin (factories, mines etc.); these are easily localised and their control does not usually present any problems apart from financial ones, (2) On the other hand there is 'non-point' pollution. This is much more difficult to pinpoint because of the fact that it is widespread throughout the environment. The force of its effect can only be calculated in the long term and thus it generally leads to an examination of fundamental problems at the level of the ecosystem involved. The treatment of this type of non-point pollution is almost impossible a posteriori, and depends on being controlled at source. It is in this case that modelling can be a very useful tool, both for the researcher in terms of understanding the p h e n o m e n a at stake whose com0304-3800/90/$03.50

© 1990 - Elsevier Science Publishers B.V.

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plexity can easily be imagined as soon as all these factors are in close interaction, and for the manager who may use it as an aid to decision-making in his research into the necessary coexistence between a 'reasonable' type of pollution, based on the self-purifying capacity of the environment and the economic factors tied to a prosperous agricultural policy. All the investigations show that agricultural practices play a major part in the deterioration of water quality; the essential elements are: suspended matter linked to the p h e n o m e n o n of erosion due to run-off; nutrients (nitrogen and phosphorus) generally input by fertilizers; pesticides; the climate; and the site. A watershed model should therefore describe as realistically as possible the effects, on the environment concerned, of transport and transformations of products liable to contribute to its degradation and of other contributing factors. The first models were developed in the 1970's in the U.S.A. and, as will be seen, there is active research in this field. 2. FUNCTIONING OF AN AGRICULTURAL WATERSHED The principal vehicle of pollution at the watershed level is water. Rainwater run-off carries away earth; the resulting erosion, as well as dissolved substances (nutrients, pesticides, salts) flows towards the receiving environment, which is generally a river but can also be a reservoir, lake, lagoon or the sea. Some of this water infiltrates, and can contaminate the phreatic water and reappear in the surface water through sub-surface and underground run-off. These p h e n o m e n a are, of course, accompanied by biochemical transformations as soon as the products involved are non-reactive. An agricultural watershed is generally a site which fits in with the hydrologic definition of a watershed (all water forced into the interior of the site joins the hydrographic or hydrogeological network of the site, which network allows only one outlet) whose water quality will depend on the climate (rainfall, evaporation, temperature), on the economic system which draws on h u m a n activity therefore agricultural techniques and farming practices, and on the vegetation. These four elements (site, climate, economic system, vegetation) are more or less intertwined. 3. MODELLING 3.1

Problemsposed by modelling

It is easy to understand that the modelling of the functioning of a watershed submitted to a whole series of necessary influences will be a difficult task whose approach will, of necessity, be multi-disciplinary.The

TRANSPORTMODELLING1NWATERSHEDS

INPUT

137

PRINCIPAL PROGRAMME

OUTPUT~

~--

~ DATA READINGIN NUTRIENTS ~OUTPUT SPECIFICATION

HYDROLOGIC CYCLE

EROSION

~

PESTICIDES "~

YES

I ADSORPTIONTRANSFERAND

NO

TRANSFORMATION AND I TRANSFERS

YE~

~ NUTRIENTS

IDEGRADATION

NO

Fig. 1. Structure of watershed type model (according to Donigian and Crawford, 1979).

only possible way, at the present time, of tackling the problem is to proceed by successive stages, i.e. to conceive the development of a general and complete model as the juxtaposition or overlapping (with more or less close link's) of sub-models, each being responsible for a particular phenomenon; in all cases the frame of the model remains the hydrologic model. This approach which is, moreover, not without influence on the expected result, is also made necessary by the variability of spatio-temporal scales connected with the different simulated phenomena. Figure 1 shows, in diagram form, the principle of the structural organisation of such a model. On the conceptual plan, a problem arises with regards to the models' capacity of simulating the functioning of watersheds of very different sizes. This, of course, is linked to the models' capacity to take into account the variability of the four elements already mentioned, which are: site, climate, economic system, and vegetation. This problem is vital to the extent that this

138

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A N D M. P R A T

greater or lesser capacity will have bearings on the areas of application and, as a result, on the more or less general character of the model. Another aspect involves the kinetics of transformation and of the transfer of elements concerned. It may seem delusionaly, for example, to wish to simulate, using the same model, the development of a phytosanitary product whose retentivity effects might be felt after 4 or 5 years, and the development of nitrogen on the scale of one season. In any case, whatever the degree of complexity of the model or its level of generality, the calibration will remain the most delicate problem. In this case we will learn that the drawing-up of a model will be based on the research of a good degree of tolerability between the complexity level of the modelled p h e n o m e n a and the classic observation of sites. Before discussing the principal models proposed by previous research, we will see in what way the modelling of the three main functions of a watershed is generally dealt with: water-cycle; erosion; biochemical transformations. This will allow us to show how difficult the task is, as well as to better understand, in the absence of explanations, the choices and compromises made necessary on the one hand by the advanced state of research and, on the other hand, by the type of application aimed at. It would be unrealistic to want to develop a model if the classic observation of sites does not allow the proper undertaking of this operation for all the phenomena to be considered. In the same way, the application of a model implies that the user possesses all the chronological data necessary to set it up. This supposes that the manager interested in a given watershed knows its 'history'. If this is the case, especially in Europe and in the U.S.A., for hydrologic parameters there are, on the other hand, great lacks with regard to chemical and biochemical parameters. The reason for this is that interest in water resources has always been from a quantitative point of view, and only since the 1970's, from a qualitative one. 3.2

Modellingof the water-cycle

There are two possible ways of describing the transfer of water into the soil. One way consists of taking as a base the concepts of transfer physics in a porous environment; a porous environment is usually defined as a rigid solid of complex form and includes voids termed 'pores'. These voids m a y intercommunicate, and may be of several phases liable to flow and, eventually, the exchange of matter and energy. In the case of pores big enough relative to molecular dimensions, the porous environment can be considered as a set of closely interwoven continuous environments; thus the transfers can, in theory, be accurately described by so-called microscopic (i.e. on the pore scale) equations of continuous-environment dynamics. In reality, given the geometrical corn-

TRANSPORT MODELLING IN WATERSHEDS

] 39

TABLE 1 Twin system of equations of partial derivatives translating the heat and mass transfers to the porous environment

Oo~/Ot=v.[D,~V~O+DTVT]-V. ~K Vz

]

.OT (pC)

D~ DT Dv DvT K

Lv T t

X* (pC)* p

~ - = V ' [ ( ~ * + L v P D ~ T ) V T ] + V ' ( L ~ o D ~ Vco) Isothermal diffusivity coefficient of mass (m2 s 1) Non-isothermal diffusivity coefficient of mass (m2 s 1 o C-l) Isothermal diffusivity coefficient of mass in vapor phase (m2 s 1) Non-isothermal diffusivity coefficient of mass in vapor phase (m 2 s-1 o C 1) Hydraulic conductivity (m s-I) Latent heat of vaporization heat Temperature ( o C) Time (s) Apparent thermal conductivity (W m- 1 o C - l ) Ponderal water content (kg kg-i) Equivalent thermal capacity of the porous environment (J m- 3 o C 1) Density of water (kg m- 3) Density of dry material (kg m 3)

plexity of the pore space, microscopic equations c a n n o t be solved directly. In order to o b t a i n workable equations, a change of scale is carried out whose aim is to consider the porous e n v i r o n m e n t as an equivalent fictitious c o n t i n u o u s e n v i r o n m e n t (we try to base our reasoning on m e a n values defined f r o m a 'representative e l e m e n t a r y volume', comprising several pores). F o r more details, refer to Bories (1985). In fact, in m a n y cases a n d especially in the case of n u m e r o u s types of soils, it is possible to establish so-called macroscopic equations which take into a c c o u n t the evolution of m e a n values (temperature, water c o n t e n t . . . ) within the porous e n v i r o n m e n t . As an example, Table 1 represents the set of e q u a t i o n s which takes into a c c o u n t coupled transfers of heat a n d mass in a porous e n v i r o n m e n t which c a n n o t be deformed, is h o m o g e n e o u s , accurately divided, a n d w i t h o u t chemical reaction. We notice that the change of scale does n o t take place w i t h o u t some loss of i n f o r m a t i o n , which results in the a p p e a r a n c e of a n u m b e r of p h e n o m e n o logical coefficients, usually m a r k e d l y non-linear, which are often d e t e r m i n e d by specific experiments (Crausse, 1983). This type of modelling was successfully applied to the s t u d y of n u m e r o u s transfer p r o b l e m s in p o r o u s environm e n t s (cf. Crausse et al., 1981; Recan, 1982; Crausse, 1983) a n d can be

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extended to the case of the transfer of reactive products in soils (Caussade and Prat, 1984). It is possible, with the help of this formulation, to model nitrogen transfer in the soil, taking into consideration the different stages of its cycle in the soil as well as the rhizosphere's action (Caussade and Prat, 1984). From the beginning a number of limitations appear concerning this type of modelling, especially with its perspective application in situ. Firstly we note that, contrary to the hypotheses which determined the drawing-up of the model, soils are not usually either homogeneous or nondeformable (clay soils in particular). This poses the question of the sturdiness of the model with regard to a divergence, with respect to the hypotheses for a given objective (the fact that a soil is not homogeneous might not, for example, be influential if the objective is the estimation of water storage; but the same fact cannot be disregarded if it is a question of studying the evolution of a water-content profile). To these problems might be added particular phenomena which destroy the predictive capacities of models for certain catastrophic situations if they are not specially taken into account (for example, very fine surface fissuring). Another series of problems arises from the deduction of phenomenological coefficients and, also, from the solving of equations which, given their markedly non-linear characteristics, can only be done numerically (as a result, the cost of calculations makes this approach more adapted to simulations over short periods, from several days to a month, rather than over a year). These precautions, however, do not mean that the approach based on the concepts of continuous-environment mechanics is at a dead end. Quite the opposite, their aim is rather to underline the necessity of finding the balance between the desired objective, the modelling most adapted to reaching this objective and the available data. For example, it will be quite useless to retain the terms of thermomigration (terms D v, Dv-r in Table 1) if elsewhere the coefficients of isothermic mass scatter are not well known for the soil under study. In the same way, it will be irrelevant to incriminate the transfer model when, at the same time, we have to deal with particular biological processes not taken into consideration by the model (for example, characteristics of the nitrogen cycle). A second method of describing the transfers of soluble products in the soil consists of relying on hydrologic models. We shall have a quick look at the general basic principles. Any rain which falls on a watershed plays a part in the surface flow, in soil infiltration and in a certain amount of evaporation. These various phenomena differ according to the weather and the site. However, for a given moment and for a given control volume it is possible to set down the input-output balance of the water mass.

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TRANSPORT MODELLING IN WATERSHEDS

×,

¥,.,, ×*

5'1 ¥2 Yl

W1

W2 ~

>

Wl W2

I2

Fig. 2. Schematic figure showing the different elements which m a k e up the b a l a n c e of water mass in a watershed (Chebotarev, 1966).

Let us look at a cylindrical control volume restricted above by surface F, below by a surface at a certain depth, and on all the sides. Everything which goes into and comes out of the balance is carried over to the surface unit F and time unit T. The elements of this balance are the following (Fig. 2): rainfall X; condensation Z~; evaporation (or evapotranspiration) Z2; water inputs and outputs by way of rivers Y~ and Y2; water inputs and outputs by way of subsoils, 11 and 12, respectively; water inputs and outputs through lateral surfaces, W1 and W2, respectively; surface and soil water storage from the beginning to the end of the time-interval T, U1 and U2, respectively. The general equation balance in a simplified form would be expressed as follows: X= Y+Z+

W+U+I

The components X, Y and Z are positive by definition; the others can be either positive or negative. The fourth term of the right-hand part of the balance shown represents the variation of the a m o u n t of stored water in the elementary volume, and can be divided into three parts:

u = uG+ Uy+ Us UG represents the variation in the amount of stored water between the lower and upper parts of the section of ground of the control volume, UN the variation in the amount of stored water at the snow-cover level, and Us the variation in the amount of stored water by way of rivers and dams.

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B. C A U S S A D E A N D M. P R A T

If we admit these principles, it remains to mathematically model the transfer of water to the watershed, i.e. to establish the link rain-runoff. Very m a n y researchers have taken an interest in the mathematical modelling of the transfer of water to watersheds (Crawford and Linsley, 1966; Roche, 1971; Girard et al., 1972). Models can be classified into certain types (for a more complete list see Oberlin (1973) and Ambroise (1980)): statistical models which look on the watershed as a black box (Ciriani et al., 1977); and global conceptual models (Crawford and Linsley, 1966) which regard the watershed as a collection of reservoirs. F r o m the spatial viewpoint they are global, and do not take account either of the heterogeneity or of the structure of the watershed; they require parameter calibration. Spatialized conceptual models have also been elaborated (Girard et al., 1972). These models are very like global conceptual models, but the watershed has been divided up into homogeneous units. They also call for parameter calibration techniques, and need a much greater amount of data. The last model type is made up of spatialized and physical models (Beven and Kirkby, 1979). These are the most satisfactory models, since they take into account watershed heterogeneities and are based on the measurement of a certain number of watershed characteristics. They require a great n u m b e r of measurements on the site itself. Despite the difficulties which arise, these two approaches are complementary. First of all, we will note a complementarity on the time-scales. The hydrologic approach is more adapted to simulations on an annual scale, whilst the approach based on the mechanic concepts is more suited to simulations of p h e n o m e n a over a period of several days (up to a month). To these differences, on the time-scales, are associated space-scale differences (large scales for the hydrologic models, small scales for the physical models) and the delicacy of the considered phenomena. It is at this level that the real complementarity of the two approaches is to be found. F r o m the local approach we obtain a fine simulation of transfers and the associated processes (cf. transfer of reactive products; Caussade and Prat (1984)) and, thanks to a sensitivity study, we can as a result make a difference between the p h e n o m e n a which, on a spatio-temporal scale like that of the watershed, must be taken into account (example the role of vegetation) from these which can be left aside (example: the influence of thermic gradients on mass transfer). In short, we expect a hierarchicization of the p h e n o m e n a and, through that, an aid to modelling on the hydraulic scale. In addition to this hierarchicization, the interest of a twin approach involves a greater integration of physical processes in hydrologic models. As we pointed out in Section 3.1, we can see the time when the approaches of the conceptual type and of the soil physics meet up is still far ahead, but it is from this meeting that we can expect substantial improve-

TRANSPORT

MODELLING

143

IN WATERSHEDS

ments in the water-cycle simulation in the soil. Concerning this subject, the reader interested in a detailed discussion on these two approaches can refer to the article by Brutsaert (1986). 3.3

Modelling of soil erosion

As we said previously, the putting into practice of a model of water management of surface waters demands that we have a good understanding of the transport processes of agricultural pollutants. To achieve this, one must be able to calculate the soil loss through erosion which, as can be imagined, will be closely linked to the hydrologic cycle. Sediments are a potential water pollutant, but they also transport most of the pesticides and phosphorus in an adsorbed form. At the present time, two approaches proposed by American researchers are used quite systematically. The first is based on the use of the universal equation of soil loss USLE, the Universal Soil-Loss Equation (Wischmeier and Smith, 1978); this is an approach of the empirical type. The second approach is based on the use of a model proposed by Negev (1967). This last approach, much more fundamental, requires the calibration of a certain number of coefficients which allows the 'adaptation' of the model to particular conditions of the site under study. The use of the USLE poses a problem linked to the fact that its parametering was carried out only from data obtained on soils in the U.S.A., which corresponds to particular conditions unlike these found, for example, in Europe. 3.3.1 Model of the empirical type The universal soil-loss equation was established in the 1950's and several modified forms have been subsequently suggested, mainly in order to take into account occasional phenomena linked to rainy episodes of the shower

IEROSIONOPENOSONI CAPACITYOF I . . . . . . . . EROSION

AND . . . . . . .

~

CAPACITYOF ERODING AGRICULTURAL

RAIN ENERGY

I

MANAGEMENT

PHYSICAL

C.~ACTE.ICT~CS ~ SOIL MANAGEMENT

I I PLANT MANAGEMENt

A:R-K'LS'P-C Fig. 3. Structure of the universal equation of soil loss (according to WMO, 1983).

144

B. CAUSSADE A N D M. PRAT

type which indicate the beginning of the critical phase of soil erosion (Onstad and Foster, 1975; Williams, 1975; Wischmeier and Smith, 1978). It is based on the observation of a great n u m b e r of sites representative of soils existing in the U.S.A. and which concern, in particular, the run-off and the soil quantities lost. This equation translates the fact that erosion is dependent on the erosive capacities of physical agents, i.e. rain and run-off, as well as the eroding of soils which depends on their type. Figure 3 illustrates the structure of this equation, which is described as follows (Onstad and Foster, 1975): A = ( EKPCSX

15 )/185.58

where A is soil loss, E energy factor, K eroding factor of the soil, C agricultural practice factor, S slope factor of the soil surface, and X length of the slope. The energy factor is expressed by the relation: E = 0.5R + 1 5 Q q ~/3 where R is erosive capacity factor of the rain, Q run-off volume, and q m a x i m u m flow. The slope factor of the soil is calculated from a simple law of the parabolic type: S = asZ + bs + c

where a, b and c are constants to adjust, and s is the slope of the soil. This equation applies for each sub-watershed and one can, as a result, calculate a rate of soil detachment for each c o m p a r t m e n t of watershed under study by the following relation: D = aA/Ox

where x is the abscissa calculated following the slope of the soil. The model can be a sophisticated one, depending on the variability of the erosion p h e n o m e n o n in the w a t e r s h e d u n d e r study, for the water run-off encourages the forming of furrows on the soil surface, which will cause greater sediment washing away than erosion between the furrows. Here, too, the laws obtained are quite empiric and not easily transposed. The assessment of the transport capacity of the system is next established from the universal equation of soil loss and, depending on the value of the detachment capacity, one can deduce from this the sediment quantities and those exported at the sub-watershed-scale up to the watershed outlet. As mentioned previously, this type of model, given parameters from data on U.S. soils, would appear difficult to transpose to other countries, but it must be admitted that it has produced quite acceptable results in H u n g a r y and Belgium. The main advantage of this formulation is that it does not require chronological site data as is the case with so-called fundamental

TRANSPORT MODELLING IN WATERSHEDS

145

models; another advantage is that it takes into account agricultural practices. 3.3.2 Model of the fundamental type This type of approach was introduced based on research by Negev (1967) at the Stanford University and completed by research by Meyer and Wischmeier (1969), Onstad and Foster (1975) and Fleming and Fahmy (1973). Although Negev's model simulates all the compartments of the erosion process to all purposes we only take into consideration the detachment of soil particles through raindrops and their transport through run-off. In particular we do not take into consideration the p h e n o m e n o n of sedimentation and distribution of the particle sizes. As an example, this type of approach leads to the algorithms shown in Table 2. These allow us to calculate the amounts of particles detached through erosion and the amounts of particles washed away. As can be seen, these algorithms attempt to show the most important processes, and it is especially valid in the case of the impact of agricultural practices - surfaces covered by vegetation, the date of harvests and of ploughing.

TABLE 2 Algorithms of simulation of soil loss (Donigian and Crawford, 1979) - Detachment of particles RER(t) = (1--COVER(T))KRERPR(t) . . . .

- Transportation of particles SER(t) = (KSEROVQ(t)SRER(t). . . .

where RER(t) COVER(t) KRER PR(t) JRER

SER(t ) JSER KSER SRER(t) OVQ(t)

for SER(t) ~ SRER(t)

amount of detached particles during the time t ( t / h a ) fraction of soil covered by vegetation at given time T, during the growth season of plants coefficient of detachment (given soil properties) rainfall during time t (mm) exponent amount of particles transported through run-off ( t / h a ) exponent transport coefficient amount of transportable particles at the beginning ( t / h a ) run-off during the time t (mm)

t, metric tonne = 1000 kg.

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B. C A U S S A D E A N D M. P R A T

In the most sophisticated models, we also suggest taking into account the more or less great 'availability' of the particles in playing a part in the erosion phenomenon, depending on the linking forces between particles which encourage their binding together, and which depend on soil characteristics, meteorological conditions and cultivation practices. This type of model can, of course, be extremely complicated, as soon as the observation data allow and the systematic tests are possible. One can always wonder if, from a practical standpoint, it would be reasonable (advisable) to go beyond a number of several parameter units to be calibrated; nevertheless, the fact remains that this is a very good way of better understanding the various processes involved in the phenomenon of soil erosion. 3.4

Modellingof biochemical transformation

In every terrestrial ecosystem, the biogen elements are incorporated one after another into the different living constituent parts (plants, animals, microflora), then liberated, there is termed element renewal. These cyclical transformations undergone by the elements make up the matter cycle. Here, we are not concerned with the cycles of these different elements but only with the nitrogen and phosphorus cycles. We will also touch on the phytosanitary products which are widely used at the present time in cereal cultivation. As we shall see, the cycles of these products are little known in that the side effects caused by the retentivity of certain substances only appear after a few years. 3.4.1 Modellingof the nitrogen cycle The atmosphere constitutes the main reserve of nitrogen used by the biosphere. Atmospheric nitrogen, however, cannot be used as it is by most living organisms which need compound mineral or organic nitrogen. Since plants can only use compound nitrogen in nitric or ammoniacal form, it is necessary for soil nitrogen which, with the exception of mineral fertilizers, is mixed with it almost exclusively in fresh organic-matter form, to be enriched with minerals beforehand. This mineral enrichment is made up of two stages, ammonification and nitrification. Concurrently, a fraction of the microorganisms rivals with the plants for the consumption of the mineral nitrogen of the soil; this is the process of immobilization. The nitrified nitrogen can be reduced to N and N20 by the microorganisms of the denitrification, and the gaseous nitrogen thus formed joints the pool of atmospheric nitrogen. These different microbial transfomations play a part in the enriching or the deterioration in nitrogen of the earth-vegetation ecosystem.

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T R A N S P O R T M O D E L L I N G IN W A T E R S H E D S

These biological processes are superimposed on the non-biological processes: input by rain or irrigation, fertilizer and seeds, adsorption of atmospheric ammonia; losses through ammonia volatilization and chemical reactions of denitrification, output through harvests or fires, leaching or erosion; and temperature influence. Looking at information on the subject, we notice more or less essential differences at the level of schematic representation. These differences usually stem from the way the organic matter is considered. Since the aim of modelling is to establish a 'working model', i.e. a model able to be used for simulation in real cases, we should therefore examine the representation of the nitrogen cycle in the light of information usually available, even if that means making the model complicated at a later stage. In the soil in general there are mineral nitrogen concentrations of total N and sometimes of organic N. Except for a specific piece of research (i.e., laboratory experiments) there are no data on the composition of organic N or on the biomass. In the light of available information it would appear useless to differentiate several forms of organic N. The scale of time suggested for the simulation goes from a week (e.g. for a field model) to a year (for a watershed). Thus we can only plan to include in the model a stock of organic matter which is easily enriched in minerals. We thus end up with simplified representations (see Tanji and Gupta, 1978; Donigian and Crawford, 1979; Iskandar and Selim, 1981) in which fixation of atmospheric nitrogen is ignored and volatilization is not taken into account. Differences on the level of the nitrification are also noted. As far as the reactions of NH~- desorption-adsorption are concerned, some authors accept the hypothesis of a local immediate balance between the dissolved form and the absorbed form. The research we have devoted to this problem led us to adopt a cycle very close to that proposed by Iskandar and Selim (1981), which is shown in Fig. 4. This representation is, by means of a system of ever possible simplifications, the most flexible and the easiest to adapt to the case in study. We thus

tog IAnqnRnrn~_~lN THESOLUTION~ L ........I cs -IOF THE SOIL I CAM

ORGANIC

~IN

THE SOLUTION

CN~ ~ T H E

SO~

N ~J LEACHING

Fig. 4. Simplified cycle of nitrogen: Model of biochemical transformations (Caussade and Prat, 1984).

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B. C A U S S A D E

A N D M. P R A T

TABLE 3 Twin system of differential equations for nitrogen transformations

Organic nitrogen d [ N - O R G ] / d t = CIM[N-NO3] + CAM[N-NH4~] -- c M [ N - N O R G ]

Ammonia in solution d[N-NH4sl/dt=cs[N-NH4~] + c M [ N - N O R G ] - [CAM+ CAD + cYl ] [ N - N H a s ] Adsorbed ammonia d[N-NHG]/d/=

CAD[N-NH4~ ] - c s [ N - N H 4 . ]

Nitrite d [ N - N O z ] / d t = CNI[N-NH4~ ] + cNZ[N-NO3] --[C6 + CNA][N-NO2]

Nitrate d [ N - N O 3]/dt = CNA[N-NO 2 ] -- [CIM + CIM CAM CM cs CAD cyl CN2 CO CNA

rate rate rate rate rate rate rate rate rate

of of of of of of of of of

C N 2 ] [N-NO3]

immobilization ammonification mineralization liberation retrogradation nitration nitrition denitrification nitration

limited the cycle to purely biochemical angles, which is usually adequate in the case of the watershed approach. Classically we adopt the laws of first order for the kinetics. As an example, and with reference to Fig. 4, the equation for each form of nitrogen leads to the system of differential equations shown in Table 3. At this stage it is useful to not forget that the dynamics of nitrogen in the soil are influenced by a certain n u m b e r of factors, linked to the climate and which play a part as forcing variables of the model (humidity and temperature), or linked to the soil, these factors being considered stable at the scale of the simulation time. We will not dwell further on these problems because our aim here is confined to underlining the range of questions challenging the modeller faced with the reality of the area under study, and who is careful to establish a model fitting the concepts we have mentioned above. 3.4.2 Modellingof the phosphorus cycle Phosphorus is used to make up protide and lipidic organic combinations (especially nucleic acids), and a phosphorus cycle is set up between mineral

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MODELLING

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IN WATERSHEDS

reserves and living beings. Although phosphorus does not exist in different forms, as does nitrogen, phosphorus compounds undergo transformations which are of importance to agriculture. Phosphorus can be enriched in inorganic phosphates and, under certain conditions, the reaction can be reversible, i.e. inorganic phosphates are transformed into organic phosphorus; this is the immobilizing stage. The inorganic phosphates are either heavily adsorbed by clay particles or present in the form of insoluble phosphates of calcium, magnesium, iron or aluminium. The concentrations of soluble phosphates rarely exceed 0.2 mg/1. In this way the main mechanism of loss of phosphorus compounds is soil erosion. In the same way as for nitrogen, numerous simplified phosphorus cycles have been written about. We can take as examples Selim et al. (1976) and

I

KAS

[

PO 4 - A

L

P

-

PLANT

t -I

PL

PO 4 - S

KSA

KIM

L

V--"

;l

P - ORG

KM

I

Fig. 5. Simplified phosphorus cycle (Donigian and Crawford, 1979).

TABLE 4 Twin system of differential equations for phosphorus transformations (Donigian and Crawford, 1979)

Organic phosphorus d/dt [ O R G - P ] = - KM[ORG-P] + KIM[PO4-S ] Phosphates in solution d/dt [PO 3-S] = KM[ORG-P] -- (KIM + KSA+ KPL) [PO4-S] + KAs[PO4-A] Adsorbed phosphates d/at [PO 4 - A ] = KsA[PO4-S] -- KAs[PO4 - A ] Phosphorus taken through plants d/dt [PENT-P] = KPL[PO4-S] KM I~IM KSA KPL KAS

rate rate rate rate rate

of of of of of

mineralization immobilization adsorption sampling through plants desorption

]50

B. CAUSSADE AND M. PRAT

Donigian and Crawford (1979). Donigian and Crawford's (1979) example does not take into account mineral phosphorus, quite justified for most watersheds. Here too, the kinetics are drawn by the laws of first order. With reference to Fig. 5 the equation for each form of phosphorus leads to the system of differential equations shown in Table 4. It is understood that, like nitrogen, the dynamics of phosphorus are influenced by different factors such as temperature, humidity, etc., which, of course, will complicate the modelling. It will thus be a good idea to bring a certain realism to the model based on the concepts we have just mentioned and on available information. 3.4.3 Modelling of transfer and transformations of pesticides We have always been concerned with the relative toxicity of phytosanitary products used to destroy noxious animals and plants. Checking their use, however, has turned out to be very difficult thus leading to the risk of pollution in natural environments. Pesticides' way of functioning depends on the nature of the organisms to be destroyed, and so their chemical composition is very varied. About thirty groups of them have been listed. In water or in the soil pesticides undergo chemical and microbiological damage under the action of bacteria, algae and lung; abiotic chemical reactions also transform pesticides. They can be dissolved in soil solutions and carried slowly towards underground water despite their more or less strong fixation on soil components. In the face of problems posed by the use of these "synthetic molecules", one has to best define their harmlessness from both a toxicological and an ecological point of view. It is an accepted fact at the present time that persistence of pesticides in the soil poses real problems for successive cereals and for contamination of the environment. Also, given the range of products available in agricultural practices, one can easily imagine the difficulties of transfer modelling and of the degradation of these products, as certain vital processes are little or ill-known. Today, research is very active in this field. The algorithms used for the modelling take the following form: X/M

= K C 1/N +

F/M

with X / M is adsorbed pesticides per soil unit, F / M pesticides adsorbed and fixed permanently per soil unit, C balance concentration of pesticides in solution, N exponent, and K coefficient. Considering what has been said above, this type of algorithm, which is founded upon the empirical separation of quantities of pesticides transported in solution and through sediments, is far from being representative of the reality as we understand it at the present time, for it does not convey the

TRANSPORT

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IN WATERSHEDS

151

phenomenon of hysteresis observed in the adsorption-desorption process (Davidson and McDougal, 1973), and the more or less empirical formulae which have been suggested to take the hysteresis phenomenon into account are not easily applied because of the numerous parameters needed to calibrate and, more importantly, lack generality. This brief look at the problems posed by transfer modelling and of the deterioration of pesticides illustrates how a lot of effort is still to be made at the chemical and biochemical levels of these products before being in a position to suggest sufficiently reliable predictive models. 4. P R I N C I P A L S I M U L A T I O N M O D E L S

We now review the ten main simulation models suggested, in chronological order since 1975. In general they are models of the 'research' type, i.e. designed to test ideas and algorithms; they are complex and expensive and have rarely been tested in real cases. Their main aim is to estimate the concentrations of different dissolved and particulate organic chemical substances at the watershed's outlet. In the Appendix, we present these models in the form of synthetic plates where the reader will find systematically the model's name, the bibliographical references, the aims of the modelling, the organisation method of the model and the techniques and algorithms used; at the end are a few remarks of general interest necessary for judging the model's limits. The examination of these charts provides information on important points. Indeed we note, firstly, that the organisation of the models is always the same and is based on the use of sub-models working in series, secondly, that the model intended to simulate erosion is usually founded on the universal equation of soil loss, and lastly, that all these models have either never or rarely been systematically used to estimate their performances. Next - and this is an extremely important point for researchers in fluid mechanics - we note that the subroutine intended to simulate the hydrologic cycle, this being the cornerstone of the model, is the one which creates the most diversity as to the type of approach suggested. We thus touch on one of the most important problems of transport modelling in the watershed: the modelling of the water cycle. 5. R E S E A R C H C A R R I E D O U T BY T H E F L U I D M E C H A N I C S I N S T I T U T E O N T H E MODELLING OF NITRATE TRANSFER

Brief accounts of two pieces of research recently carried out by the Fluid Mechanics Institute in Toulouse will illustrate the contribution of modelling towards understanding of nitrate transfer, on the one hand on the cultivated

152

B. CAUSSADE AND M. PRAT

field scale and on the other hand on the scale of the small polycultivation watershed; they also show how these models can be used to test the influence of cultivation practices on water quality. It also serves to show how the function of transfer is organised in both cases, i.e. to highlight the dual 'mechanistic approach'-'systemist approach'. In the first case, the modelling is founded on partial derivative equations expressing the balances (of mass, momentum and possibly of energy), in the second case it is founded on analytical relations deduced from conceptual approaches on domains on a large scale. 5.1

Field model

The example chosen corresponds to the distribution of nitrate fertilizers on wheat fields in south-west France. The notion of a non-preservative product in solution in the soil must be studied, if we wish to be realistic, taking into consideration the transitory phase of water run-off into the non-saturated zone. The one-dimensional vertical transport of such a product is governed by an equation of the dispersion-convection type. The transport of aqueous solution depends, of course, on water content and on

K(e), h(O), ~(O), C*(e)

l E.T.P. RAIN, SURFACE TEMPERATURE I

D(O), CC, PF4.2, WD, WN Crop coefficient Root density Root depth

Mass Transfer fl f

I

Rain, N-NO, in the rain, E.T.P. Fertilizer

I l

4,

Transformation Transfer

Heat T r a n s f e r

@, T, K, h Kinetics Root density

~ i

Root length Absorption rate by the plants

t

I ,

I

I I I II

II II

J N-NO3(z) , N-NO2(z N-NH~(z)

N-NORG Fig. 6. Block diagram of the interdependence of modelled processes in the field model.

TRANSPORT

Woter

MODELLING Content

020

153

IN WATERSHEDS

8(crn3/cm3 } 025

O.30

0

N i ..C

50

n

10O

>

Fig. 7. Validation of the field model: profiles of water content.

temperature. The equations used in modelling these phenomena are given in Table 1; they can be simplified by taking into consideration the specific characteristics of a field of application. The inputs and withdrawals of nitrogen connected with the exchanges at the level of cultivated soil can be illustrated in a diagram, as Fig. 4 shows. The entry of conservation equations for each form of nitrogen allows us to propose the system of differential equations in Table 3. As far as the absorption of nitrogen and water by plants is concerned, the two processes are treated independently from each other. To model nitrate absorption we have chosen an approach of the Michaelis-Menten type, and for water absorption we have chosen a model of the macroscopic type according to Moltz and Remson (1972). As a guide, Fig. 6 shows a concise diagram of the interdependence of modelled processes. For the conditions of model validation, refer to Caussade and Prat (1984). A good degree of adequacy between the simulation and the experiments in the case of water content is to be noted (see Fig. 7). The adequacy is not as good for temperature, mainly because of the conditions at the lower limit (z = 0) because the measurements of surface temperatures are sensitive. In the case of the nitrates, the divergence between the experimental and simulation results strike us as being compatible with the measurement errors (see Fig. 8). As far as the sensitivity study of the model is concerned, a pronounced sensitivity to the kinetics of biochemical transformations is to be noted. We have observed a strong influence of the nitrate environment on the storage

154

B CAUSSADE

A N D M. P R A T

N-NO~ Concentration (~g/cm 3) 10

20

30

so I.C, r m t l a t C o n d i t i o n s • ~ Measured ¢%

--

Simulated

100

Fig. 8. Validation of the field model: N - N O 3 profiles.

capacities. Taking this into account, we see that a better knowledge of kinetics is necessary in order to obtain a better representation of reality. As for practical application, Figs. 9 and 10 sum up the results obtained in a fertilization experiment which was carried out as follows: having taken into account the climatic conditions we simulated wheat fertilization in one input

N-NO~(ug/cm3) 0

100

I

__~2

_ __;3'

200

...Jr,

5C

'7

]00

Fig. 9. Fertilization simulation with the field model: nitrate profiles. - days: input 1 time. - . . . . . 2, Profile after 14 days: input 2 times. conditions: input 2 times. - 4, Initial conditions: input 1 time.

1, Profile after 14 3, Initial

TRANSPORT MODELLING IN WATERSHEDS

155

p.,2 C xx

///

i

Eu x /, c 1

~z I/I -J u_

3I

1

5

71

'

9

I

11

113

Time (days) Fig. 10. ...... (NO z ~ 2 times.

F e r t i l i z a t i o n s i m u l a t i o n w i t h t h e field m o d e l . • . . . . 1, F l u x a b s o r p t i o n b y t h e p l a n t s . 2, N i t r i f i c a t i o n flux ( N O 2 ~ N O 3 ) : i n p u t s o n 2 t i m e s . - 3, N i t r i f i c a t i o n flux N O 3 ) : i n p u t s o n 1 time. - . . . . . 4, I m m o b i l i s a t i o n flux ( N O 3 ~ N - O R G ) : i n p u t s o n - 5, I m m o b i l i s a t i o n flux ( N O 3 ~ N - O R G ) : i n p u t s o n 1 t i m e .

only (95 k g / h a ) then fertilization in two inputs within a week of each other (47.5 kg/ha). In both cases we presumed that the spreading would concern the first 10 centimeters. Given the duration of the simulation and of the hydrodynamic characteristics of the soil, there is no difference to be seen between the two methods at the flux levels at 60 cm and below (Fig. 9). On the other hand, the rapidity of nitrification (Fig. 10) is to be noted, as well as the distinct tendency of a part of the nitrogen input to be immobilised (curve 4, Fig. 10), which conveys the plant microorganisms competition to the level of nitrogen management. Examination of the profiles (Fig. 9) conveys the influence of pluviometry on leaching. The most important migration takes place where there is input on two occasions, the second input taking place just before a heavy rainfall. However, this effect is masked by the storage p h e n o m e n a just mentioned. This illustrates the type of application of such a model. 5.2

Watershed model (MB V)

The main outlines of this model are given in the Appendix in the form of a chart. The model's architecture clearly brings to the fore the different sub-models, their hierarchical importance and their interdependences.

156

B. CAUSSADE AND M. PRAT

The water-cycle model was chosen with the intention of drawing up an easily usable model. This is the reason why we adopted a model of the global conceptual type, the C R E C model (Guilbot, 1975). This model, shown in diagram form in Fig. 11, is based on assumed knowledge of the water cycle in the watershed. Rainwater (P) plays a part in counteracting the humidity lack in the soil (this is a quantity of water which is therefore 'lost' since it is not to be found at the outlet), the surface discharge QS, the sub-surface discharge QH (non-saturated zone of the soil), and the underground or base discharge, QG. The discharge at the outlet, i.e. the river, is thus the sum of the discharges, giving: Q = QS + QH + Q~ The principle of the model is as follows: the question is to find out, depending on the state of humidity of the soil, the fraction of water which plays a part in the run-off (production function), then to transfer this water (transfer function) to the outlet by means of a system of filling and draining reservoirs which represent the different functions of the cycle; the laws of draining depend on a series of parameters whose calibration is assured by comparing calculated and observed discharges. The biochemical transformation model is that shown on Fig. 4 and Table 3. The transfer model is established on the basis of two hypotheses: (a) that the watershed is 'well drained', i.e. on average the water contribution of the suit of each type of crop take the same time to reach the outlet; (b) the water content is the same over the whole watershed. This water content is brought under control at the reservoir level, which represents the non-saturated zone. We can thus say:

j=I(Sj) with q~j the average water content of the non-saturated zone, Sj the reservoir's level, j time, and f function generally linear. If we define A as the total area of the watershed, A' the area occupied by the crop i, and Nj the N - N O 3 - , concentration in the soil occupied by the crop, we deduct the average Cj concentration in N - N O 3 - in the water of the soil occupied by the crop i, or: Nj.t

q-i(s,) The balance equation for the non-saturated zone over a space of given time (in our case 1 day), can be written for the crop i with reference to the

E, = l,

no

! .......

recharge of the humidity deficit

_L~ ......

I

linear transfer

I~\\\\\\\\\~ turbulent flow

~1~~1

31SCHARGE

underground zone

I /I Gj= [(H - x,)/x~] I

~pper horizons

surface run-off

Fig. 11. Diagram illustrating the model's functioning(according to Guilbot, 1975).

.. .........

I

/, > .

,4 Sj = E~[x3exp(x,S,. ~)]"

I

I ETR, = ET~,E' - ex0/-~,Jx,II I

E, = P,

yes~P,~

4-

I, = x. - x, ~ ]

! Q1 = Q7 + Q,"

= (x,H)2~._._--

L*h "-4

I am

RALNFAU-

J

-1

.~ - ~

NO2 ~

]

I

P~S I

PLANTS

I

F

UNDERGROUNDRESERVES.J~I~O underground

ENTRYVARIABLES (CROPS,FERTILIZERINPUT)

NHI, ~

/

Fig. 12. Diagram of the organisation of the M B V model.

-

NN ~

~ ADSORPT,ON

t

I

F-~ SEEPAGE

t

EVAPORATION

CLIMATICVARIABLES

p ~/11~ O surface ATI | NON-SATURATED ZONE: I RAIN-DISCAHRGE| RECHARGEOF HUMIDITY MODEL(CREC) [ DEFICIT /~1P Q sub-surface

[ TEMPERATUREJ

]

4Jin underground run-oil

1

i..o concen,aio~ at the outlet

ll

IN-NOconcentration ~I ""

~

N-NQ concentration IN-NO 3concentration I~in sub-sudace in non-saturated run-off zone

'I N-NO concentration in surtacerun-off

Z

B1

>

t~ >

DO

C.

TRANSPORT

MODELLING

159

IN WATERSHEDS

notes for Fig. 11:

f( Sj )

C)+I=Cjf(Sj+,)

AHj C;

Ej6P

FTC

Lf(Sj+I) + Lf(Sj+I) +- f(Sj+l) I

II

III

FP

f(g+l) IV

I losses through sub-surface run-off of discharge QH and seepage towards the underground zone (see Figs. 11 and 12) II rain input III production-consumption by the biochemical cycle Iv consumption by the plants with AHj the sheet of water taking part in the transfers (sub-surface and underground), Ej the efficient height of rain, Cp the N - N O 3 concentration of the rain, FTC flux due to the biochemical transformations, FP flux due to the absorption by the plants, L the thickness of the soil (in our case 0,40 m), and j, j + 1 day j and day j + 1 The average concentration of the non-saturated zone, C s, is then: p

Ai

c;+1= Y'. c;+17 i=1

with p number of crops. As far as the transfer by sub-surface run-off is concerned, we presume that it takes place in two stages. Two transfer parameters Y1 and Y2 are introduced; they convey the progressive lessening of concentration observed between the water under cultivation and the outlet. There results: c.'+,1 =

HZ'

611,+1qsvl

c#,

_

Hff_Ca + (AH/A)H~a I

H

(A /AIH/+H 11 II

i input from the non-saturated zone II losses towards the second transfer reservoir

A /A)Hj+ 1 I

(AH/A)HZ21

(AH/A)Hj ,

II

III

I input of the first sub-surface reservoir seepage m losses in the river with C 14, and C H2 the N - N O 3 concentrations in the reservoir's water, 1 and 2 representing nitrogen transfer at the sub-surface run-off level, H 1 and H 2 II

B. CAUSSADEAND M. PRAT

160

the corresponding levels of the reservoirs, A H the area relative to the sub-surface run-off, and QH the discharge of sub-surface run-off. For the reservoir representing underground run-off we write: H?

cJc+, = c~ Hj~+I

(3 H~ ajcj

oGcG _

( A~/A ~-'J )j HjG+I

+

(AG/A)HjO+I

I

II

I losses in the river II input of the second sub-surface reservoir with C G the N - N O 3 concentration in the underground run-off water, H G the level of the reservoir representing underground run-off, QG underground run-off discharge, AG the sheet of water supplying the underground zone, and A G the area relative to underground run-off. The N - N O 3 concentration of the water reaching the outlet is thus given for the following relation: [~s

t,",Ru

H

Cj R I = ~ ; j + P - J + I + Q f + l C j + l

I')G

~G

-'~ ~ j + p - ~ j + l

with C R the N - N O 3 concentration at the outlet, and C Ru the N - N O 3 concentration of run-off water. The N - N O 3 concentration of run-off water is presumed to be equal to that of the rain in the summer floods. When the flood involves water from the soil (in the case of winter floods) and transport of suspended matter, we admit that the concentration in the superficial run-off is proportional to the concentration in the non-saturated zone. In the river, we make the supposition that the nitrates are preserved up to the watershed's outlet (rapid transfer). The whole organisation of the model is shown in Fig. 12. The use of the CREC model on the Watershed gave good results (see Fig. 13). Certain characteristics of the watershed and of year simulated have underlined the model's weaknesses, which have moreover been pointed out in other applications (Guilbot, 1972). These weaknesses relate mainly to the flood simulation and to the non-permanent rivers. Another type of difficulty comes from the wide divergence between the watershed's reaction time (6 h) and the space of time of the simulation (24 h), a divergence which creates difficulties in the frequency of rainfalls and flood simulation. Finally, the parameter's value at the end of calibration shows the importance of subsurface run-off in this type of steep watershed. As for the 'nitrogen' model, it gives good results knowing that we presumed that the watershed was covered by only four types of crops: wheat/barley; Indian-corn/Indian-millet; permanent grassland; and temporary-grassland/heath. This can be

TRANSPORT

MODELLING

161

IN WATERSHEDS

2.0

1.S

E Ld (D i u u~ o

0.5

--" -:- "'--"T , - OCT NOV DEC JAN

"

~ FEB

Fig. 13. Daily discharges:., measured;

l MAR

APR

~ h ' ' ' ~ MAY JUNE' JULY' AUG

' SEP

, simulated.

observed in Fig. 14, where one can see the experimental points and the results of the simulation for data of the area of countryside under study. The evolution of the mean nitrate content in the root zone under different crops matches the nitrogen description in the field. We observe the period of reorganisation after the harvest, followed by an autumnal mineralization period. The period of intense leaching and of the end of biological activity is quite visible (December, January). The period of active vegetation is marked by an increase in content due to spring mineralization and to fertilization. The decrease in content at the end of the period is mainly linked to the rhizospheric effect and to the absorption by the plants. As for the simulation of concentrations at the outlet (Fig. 14), we note that two periods are less well represented. These are the period of active vegetation of winter crops and their fertilization, and the low-water period (August). It is to be remembered that the hypothesis of nitrate preservation in the river is made during its transfer to the outlet. Now, the period under study is often favourable to the phenomena of algae consumption or denitrification, which may explain in part the difference between the experimental and simulation results. Considering that the model satisfactorily accounts for the nitrate transfer at the watershed level, the calibration results can represent a basis for

162

B. CAUSSADE A N D M. PKAT

10.

%

1" E

¢'3 0

,%4 0 Z

I

Z

/..

•o

O0

|

,

,

DEC JAN ' FEB 'MAR 'APR 'MAY 'JUNE 'JULY 'AU6 'SEP , simulated. Fig. 14. Daily nitrate concentrations: O, measured; - OCT

NOV

12

,,r',x

t

'% '\ ,,

i!

!,

E ,:,,

i~ '

o

6

~?/,".:

.

"I

~

,'"1I~ .,~

x

?"

':',,

!'7" i ,tj :

..

]HI. ,

MONOCULTI VATION INDIAN CORN

,

"

f

....:.,'

",,.-,.,_ :'-'-,

!! ,

,---~ ~

MbNOCULTI VATI ON

~

wHEAT

i:

~

............ "~'----'

:,,

POLYCULTI

0 OCT NOV DEC JAN FEB MAR APR MAY JUNEJULYAUG SEP Fig. 15. Evolution of nitrate c o n c e n t r a t i o n s at the outlet. C o m p a r i s o n s between the actual situation (polycultivation) a n d the simulation o f one type of cultivation over the whole watershed.

TRANSPORT

MODELLING

163

IN WATERSHEDS

10

%

E

O Z

~

•

I

OCT

• 'o

I

NOV

I

DEC

I

JAN

I

FEB

I

MAR

I

APR

I

NAY

I

I

J U N E JULY AU6

I

SEP

Fig. 16. Influence of agricultural practices on nitrate losses. Simulation of inputed fertilizers at different periods: 1, input on one occasion: 15 February. 2, input on two occasions: 15 February, 25 March. 3, input on one occasion: 25 March.

comparison which can be referred to study, from the simulation of hypothetical situations, the role played by the climate, agriculture and its practices in the worsening of the quality of surface water. As an example, the simulation of watershed use by one type of crop (Fig. 15) clearly shows that the growing of Indian corn, which leaves the soil bare for a long time (no absorption by the plants, non rhizospheric effect during the spring rain period), is the most polluting. According to the model, fertilization plays an important part in the water quality. This influence was studied in a more detailed way by comparing the simulation results obtained during fertilization of winter cereals ( w h e a t / b a r ley) in just one input on 15 February, and in one input on 15 March (curves 1 and 3, respectively, in Fig. 16); we remind you that the model's calibration curve (curve 2 in Fig. 16) corresponds to a wheat and barley fertilization in two inputs: 15 February and 25 March; in the three cases the quantity of imported fertilizer was 110 k g / h a . We note that the least-polluting agricultural practice was, that year, the input in one, on 25 March. The putting into practice of such a model encourages several comments on the functioning of the 'agricultural watershed' ecosystem. The most important nitrogen losses, which are linked to the highest concentrations, took place during the period when the earth was bare during rainy periods in January. For the following period, the key factors which

164

B. C A U S S A D E

A N D M. P R A T

explain the flux at the river are fertilization and type of cultivation. The most polluting fertilization is that which takes place during the drainage period. From the point of view of water quality the type of cultivation most suitable would be that which gives an early vegetable cover but is associated with late fertilization. 6. C O N C L U S I O N S A N D PERSPECTIVES

From the examples we have shown we can draw several lessons. We have shown: The importance of physical mechanisms and, as a result, the need to develop local research to help to understand phenomena and modelling on a greater scale. The interest of numerical simulation, even at the cost of greatly simplifying certain processes (in particular biological processes), which allows a better understanding of the ecosystem by taking all the phenomena into account. The integration of all these processes into a model allows a better overall comprehension of a minimum of information in order to obtain a correct study of the ecosystem. The necessity to well adapt the model to the spatio-temporal scale of investigation. The necessity to improve the models of nutrient transfers at the watershed scale. This means improving the hydrologic models (to be convinced of this it is enough to observe the leading role of mass transfer in local models) with the need to go on to spatialized and specialised models (not only focussed on the reconstitution of the discharges but on the reconstitution of certain parts of the hydrologic cycle, depending on the application in mind) integrating the maximum of physical processes. We are going to give our attention to the last point since it is the Fluid Mechanic scientist speaking. We saw that the transfers in watersheds could be understood by following two quite different approaches. In fact these approaches are complementary and pose the problem of spatial growth from the approach of 'mechanics of continuous environments'. A first difficulty arises when we use models such as that in Table 1 when we noted that within one and the same plot the hydrodynamic characteristics (coefficients D and K in Table 1) can vary in magnitude (Vauclin et al., 1981). As a result, we have to take into account the stochastic nature of these parameters. The consideration of this very great spatial variability can be made relatively simply when we can admit a geometrical similarity between the different environments making up the plot. We can then show that the hydrodynamic characteristics for two similar environments can be

T R A N S P O R T M O D E L L I N G IN W A T E R S H E D S

165

very simply differentiated from each other by means of a similarity ratio; this ratio is called the scale factor (Brunet et al., 1985; Luxmoore and Sharma, 1980). It is enough to know the distribution of the scale factor (log-normal, usually) and the characteristics of the associated relevant environment to study the effect of spatial variability on the transfers (this does not seem to have been done in the case of nitrogen transfer). By this means we can thus simulate the average behaviour of the soil. Nevertheless, to carry this out we must make enough calculations which correspond to a sufficient number of values of the scale factor. This obviously makes the procedure heavier. At this stage, theoretically nothing prevents us from applying the spatial extension to the small watershed by defining enough elementary plots, by describing the connecting conditions between the plots and by taking into account, in all their complexity, the conditions at the boundaries (transfers between the plot's surface and the atmosphere, connections between zones, saturated zones followed by hydrologic and hydrogeological networks, etc.). However, such modelling requires an amount of information usually impossible to collect. Moreover, the cost of the calculations would very quickly limit the interest of such an approach. In fact we are faced with a situation similar to that which led to the drawing up of macroscopic equations. In other words, we know the equations which govern the phen o m e n a at the plot scale but to hope to solve then we are unable to describe with enough precision the conditions at the boundaries and of the connections between the plots. Unfortunately the similarity does not go any further and there is no theory which allows us to deal with this new change of scale. For we are no longer confronted with a case of local lack of homogeneity as in the previous case (i.e. at the level of the pores) but with lacks of homogeneity on different scales up to the scale of the level of description aimed at. However, when the scale of observation is the watershed, we usually take less interest in the details of the transfers between the various levels of reference (watershed area, underground water, h y d r o d y n a m i c networks, o u t l e t . . . ) than in the fluxes exchanged at each level. This wish to simplify leads us to look for laws which allow us to avoid direct formalization of p h e n o m e n a by means of equations as complex as these in Table 1. Let us look at, for example, the case of monodimensional mass transfer in a homogeneous soil. If we integrate the simplified equation deduced from Table 1 accounting for this transfer between level z -- 0 and z = 1 we obtain the following equation: pl O ( W ) / O t

= E-

S

where E is the density of mass flux at the level z = O, S is the density of mass flux at level z = 1 and ( W ) is the average water content between the

166

B C A U S S A D E A N D M. P R A T

levels z = 0 and z = 1, and that a flux density (quantity of water per surface unit and per time unit) is counted positive following o z by convention. For a time interval At, we thus obtain: ( W ) ' + ~ ' = (W)t + ( E A t - S A t ) / ( p t ) The idea is then, for example, to join the value of S at the m o m e n t t to the values of ( W ) and E at the previous moments by as simple a law as possible. This method produces the appearance of a certain n u m b e r of parameters that have to be defined as well as possible. [In Brunet et al. (1985) examples of this type of parametering can be found.] It can be seen that this approach is very close in spirit to the ideas used to draw up conceptual models. Moreover it is a pity that the possibility of joining-up the approaches of the conceptual type and of the physical type of the soil has not been better used, as far as we know, with a view to founding parametering while at the same time solving the corresponding differential equations. [However, see Luxmoore and Sharma (1980) for example where this type of comparison is made to validate the infiltration algorithm.] We have just seen how the path towards the small scales can be followed. As far as the extension of conceptual models towards the large scales is concerned, it can only be done at the cost of a certain spatialization by trying to subdivide the watersheds into sufficiently homogeneous parts where a type of modelling such as that described above can be attempted. If modelling on a large scale has to involve a certain spatialization, real progress is to be expected, in our opinion, when substantial improvements will have been carried as far as the hydrologic models themselves are concerned. We would like to remind you that, even if at the present time the conceptual models appear to be the most suitable for the modelling of nutrient transfers on the watershed scale, they include a certain n u m b e r of parameters of little physical meaning which must be calibrated. This calibration is carried out in comparison with only the discharges at the outlet and because of this it is hopeless to expect an accurate simulation of the other parts of the cycle (evapotranspiration, infiltration, e t c . . . ) . However, these other parts are the most important to master with a view to simulating the nutrient transfers. As we have already said, as well as this hierarchization, the interest of a dual approach involves a greater integration of physical processes in hydrologic models. Interesting attempts have been made; see for example Luxmoore and Sharma (1980) where a hydrologic model, indeed applied to small-sized watersheds (ten hectares) integrates equations of the physical type of the soil and the concept of spatial variability from the notion of scale factor.

T R A N S P O R T M O D E L L I N G IN WATERSHEDS

] 67

Improvements of this type obviously add to the amount of information available and necessary for the drawing-up of models and, even more than in the case of conceptual models, its formulation can only reasonably be attempted within the framework of pluridisciplinary research. 7. REFERENCES Ambroise, B., 1980. Principaux types de mod61es math6matiques de bassin versant. Bull. Assoc. Geogr. Fran~. Paris 468, 31 pp. Arnold, J.G. and Williams, J.R., 1985. SWRRB a simulator for water resources in rural basins. Volume 1. Model documentation. USDA Agricultural Research Service, Temple, TX, 66 pp. Beven, K.J. and Kirkby, M.J., 1979. A physically based, variable contributing area model of basin hydrology. Bull. Sci. Hydrol., 24: 43-70. Bodes, S., 1985. Fragment de description de la physique des transferts thermiques dans le sous-sol. Houille Blanche, 3/4: 211-220. Brunet, Y., Vauclin, M. and Vachaud, G., 1985. Thermohydraulique de la zone non satur6e en relation avec les 6changes sol-atmosph+re. Houille Blanche, 3/4: 227-238. Brutsaert, W., 1986. Catchment-scale evaporation and atmospheric boundary layer. Water Resour. Res., 22: 395-455. Caussade, B. and Prat, M., 1986. Small watershed models: results and perspectives. In: J. Lauga, H. Decamps and M.N. Holland (Editors), Proc. Toulouse Workshop, MABUNESCO/PIREN-CNRS, pp. 141-164. Caussade, B. and Prat, M., 1986. Les modules petits bassins versants: enseignements et r6flexions prospectives. In: Workshop Land Use Impacts on Aquatic Ecosystems: The Use of Scientific Information, Toulouse. Caussade, B., Pierre, D. and Prat, M., 1984. Mod+le d'6tude et de gestion de la teneur en azote des eaux de surface dans un bassin versant sous culture. J. Hydrol., 73: 105-128. Chebotarev, N.P., 1966. Theory of Stream Runoff. Israel Program for Scientific Translations, Jerusalem, 464 pp. Chow, V.T., 1964. Handbook of Applied Hydrology: A Compendium of Water Resources Technology. McGraw-Hill, New York, 1400 pp. Ciriani, T.A., Maione, U. and Wallis, J.R., 1977. Mathematical Models for Surface Water Hydrology. Wiley, New York, 423 pp. Crausse, P., 1983. Etude fondamentale des transferts coupl6s de chaleur et d'humidit~ en rfiilieu poreux non satur& Th~se de Doctorat d'Etat, INP, Toulouse, 209 pp. Crausse, P., Bacon, G. and Bories, S., 1981. Etude fondamentale des transferts coupl6s chaleur-masse en milieu poreux. Int. J. Heat Mass Transfer, 24: 991-1004. Crawford, N.H. and Linsley, R.K., 1966. Digital simulation in hydrology: Stanford watershed model IV. Tech. Rep. 39, Stanford University, Stanford, CA, 210 pp. Davidson, J.M. and McDougal, J.R., 1973. Experimental and predicted movement of three herbicides in a water-saturated soil. J. Environ. Qual., 2: 428-433. Donigian, A.S. and Crawford, N.H., 1976. Modelling pesticides and nutrients on agricultural lands. EPA-600/2-76-043, Environmental Research Laboratory, U.S. Environmental Protection Agency, Athens, GA, 317 pp. Donigian, A.S. and Crawford, N.H., 1979. Water quality model for agricultural runoff in modeling of rivers. In: Hsieh Wen Shen (Editor), Fort Collins, CO. Donigian, A.S., Imhoff, J.C., Bicknell, B.R. and Little, J.L., 1984. Application guide for

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A N D M. P R A T

hydrological simulation program-fortran (HSPF). EPA-600/3-84-065, Environmental Research Laboratory, U.S. Environmental Protection Agency, Athens, GA, 177 pp. Fleming, G. and Fahmy, M., 1973. Some mathematical concepts for simulating the water and sediment systems of natural watershed areas. HO-73, Department of Civil Engineering, Strathclyde University, Glasgow, 26 pp. Fr6re, M.H., Onstad, C.A. and Holtan, H.N., 1975. ACTMO: an agricultural chemical transport model. ARS-H-3, USDA Agricultural Research Service, Hyattsville, MD, 54 pp. Garner, W.R., 1965. Movement of nitrogen in soil. In: W.A. Bartholomew and Clark F.E. (Editors), Soil Nitrogen. American Society of Agronomy, Madison, WI, pp. 103-122. Geng, Q.Z., 1988. Mod61isation conjointe du cycle de l'eau et du transfert des nitrates dans un syst6me hydrologique. Th6se de Doctorat, Ecole Nationale Sup6rieure des Mines, Paris, 226 pp. Girard, G., Morin, G. and Charbonneau, R., 1972. Mod61e pr6cipitations - d6bits discr6tisation spatiale. Cah. Off. Rech. Sci. Tech. Outre-mer (ORSTOM) S6r. Hydrol., 9 (4): 35-62. Girard, G., Ledoux, E. and Villeneuve, J.P., 1980. Mod61e int6gr6 pluie-eau de surface-eau souterraine. Houille Blanche, 4/5: 315-320. Green, W.A. and Ampt, G.A., 1911. Studies on soil physics. The flow of air and water through soils. J. Agric. Sci., 4: 1-24. Guilbot, A., 1972. Application d'un mod61e conceptuel de liaison pluie - d6bit aux donn6es du bassin exp6rimental de Gapeau. A. Le bassin de Sainte Anne. Rapp. 38, Laboratoire d'Hydrologie Mathematique (LHM), Universit~ des Sciences et Techniques du Languedoc, Montpellier, 33 pp. Guilbot, A., 1975. Mod61isation des 6coulements d'un aquif+re karstique. Th6se, Universit6 des Sciences et Techniques du Languedoc, Montpellier, 117 pp. Hagin, J. and Amberger, A., 1974. Contribution of fertilizers and manures to the N- and P-load of waters. A computer simulation. Final report submitted to the Deutsche Forschungs Gemeinschaft from Technion, Haifa, Israel, 123 pp. Haith, D.A., 1982. Models for analyzing agricultural nonpoint-source pollution. Res. Rep. RR-82-17, International Institute for Applied Systems Analysis. Laxenburg, Austria, 29 PP. Haith, D.A. and Loehr, R.C., 1979. Effectiveness of soil and water conservation practices for pollution control. EPA-600/3-79-106, Environmental Research Laboratory, U.S. Environmental Protection Agency, Athens, GA, 474 pp. Holtan, H.N. and Lopez, N.C., 1971. USDAHL-70 model of watershed hydrology. Tech. Bull. 1435, USDA Agricultural Research Service, Washington, DC. Holtan, H.N., Stiltner, G.J., Henson, W.H. and Lopez, N.C., 1974. U S D A H L - 74 revised model of watershed hydrology. Plant Physiol. Inst. Rep. 4, USDA Agricultural Research Service, Washington, DC. Iskandar, I.K. and Selim, H.M., 1981. Modeling nitrogen transport and transformations in soils: 1. theoretical considerations. Soil Sci., 131: 223-240. Knisel, W.G., 1980. CREAMS: a field scale model for chemicals, runoff and erosion from agricultural management systems. In: W.G. Knisel (Editor), Conserv. Res. Rep. 26, U.S. Department of Agriculture, Washington, DC, 643 pp. Ledoux, E., 1975. Programme N E W S A M . Principe et note d'emploi. Rapport LHM/RD/75/ll, Ecole Nationale Superieure des Mines de Paris, Centre d'Informatique Geologique (ENSMP-CIG), Laboratoire d'Hydrologie Mathematique. Ledoux, E., 1980. Mod61isation int6gr6e des 6coulements de surface et des 6coulements

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MODELLING

IN WATERSHEDS

169

souterrains sur un bassin hydrologique. Th+se de Docteur Ingrnieur, Ecole des Mines de Paris/Universit6 Pierre et Marie Curie, Paris VI. Ledoux, E. and Tillie, B., 1987. Programme NEWMAN. Principe et notice d'emploi, version 1987. Rapport L H M / R D / 8 7 / 4 0 , Ecole Nationale Superieure des Mines de Paris, Centre d'Informatique Geologique (ENSMP-CIG), Laboratoire d'Hydrologie Mathematique. Lorber, M.N. and Mulkey, L.A., 1982. An evaluation of three pesticide runoff loading models. J. Environ. Qual., 11: 519-529. Luxmoore, R.J. and Sharma, M.L., 1980. Runoff responses to soil heterogeneity: experimental and simulation comparison for two contrasting watersheds. Water Resour. Res., 16: 675-684. Mehran, M. and Tanji, K.K., 1974. Computer modeling of nitrogen transformations in soils. J. Environ. Qual., 3: 391-396. Meyer, L.D. and Wischrneier, W.H., 1969. Mathematical simulation of the process of soil erosion by water. Trans. ASAE, 12: 754-758. Moltz, F.J. and Remson, I., 1972. Extraction term models of soil moisture use by transpiring plants. Water Resour. Res., 6: 1346-1356. Negev, M., 1967. A sediment model on digital computer. Tech. Rep. 76, Department of Civil Engineering, Stanford University, Stanford, CA, 109 pp. Oberlin, G., 1973. Modrle pluie-d6bit. Dep. Hydraulique, Enseignement Hydrologie, Ecole Nationale Grnie Rural Eaux et For&s (ENGREF), Paris, 39 pp. Onstad, C.A. and Foster, G.R., 1975. Erosion modeling on a watershed. Trans. ASAE, 18: 288-292. Prat, M., 1982. Simulation num6rique du transfert de produits rractifs darts les sols. Cas de l'azote dans les relations bassin-versant rivi~re. Th~se Docteur-Ingrnieur, INP, Toulouse, 330 pp. Rao, P.S.C., Davidson, J.M. and Hammond, L.C., 1976. Estimation of non-reactive solute front locations in soils. In: Proc. Hazardous Waste Research Symp. EPA-600/9-76-015, Solid and Hazardous Waste Research Division, U.S. Environmental Protection Agency, pp. 235-242. Recan, M., 1982. Simulation du comportement thermique et hydrique d'un sol nu. Application ~ l'&ude de l'rvaporation par t~l~drtection. Th~se de Docteur Ingrnieur, INP, Toulouse, 307 pp. Roche, M., 1971. Les divers types de modules drterministes. Houille Blanche, 2: pp. 111-129. Roche, P.A. and Thiery, D., 1985. Mod6lisation des grands bassins versants: adaptation des modrles hydrologiques et analyse de sensibilitY. Application aux bassins de la Moselle. Rapport du BRGM 85 SGN 290 EAU, Bureau des Recherches G6ologiques et Minirres, Orl6ans, 23 pp. Selim, H.M., Mansell, R.S. and Zelazny, L.W., 1976. Modeling reactions and transport of potassium in soils. Soil Sci., 122: 77-84. Steenhuis, H., 1979. Cornell pesticide model. Internal report, Cornell University, Ithaca, NY. Tanji, K.K. and Gupta, S.K., 1978. Computer simulation modeling for nitrogen in irrigated croplands. In: D.R. Nielsen and J.G. MacDonald (Editors), Nitrogen in the Environment, 1. Nitrogen Behavior in Field Soil. Academic Press, New York, pp. 79-130. Thiery, D., 1983. Description du module C R E A C H I M . Note Tech. S G N / E A U 83/15, Bureau de Recherches Grologiques et Minirres, Orlrans, 53 pp. Tubbs, L.J. and Haith, D.A., 1981. Simulation model for agricultural non-point-source pollution. J. Water Pollut. Control, 53: 1425-1433. USDA, 1984. User's guide for the CREAMS computer model. Tech. rep. 72, Soil Conservation Service, U.S. Department of Agriculture, Washington, DC.

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Vauclin, M., Imbernon, J. and Vachaud, G., 1981. Spatial variability of some physical properties over one hectare field plot. A.G.U. Chapman Conf., Fort Collins, CO. Williams, J.R., 1975. Sediment yield prediction with universal equation using runoff energy factor. ARS-S-40, USDA Agricultural Research Service, Washington, DC, pp. 240-252. Williams, J.R. and Berndt, H.D., 1977. Determining the universal soil loss equations' length slope factor for watersheds. In: Soil Erosion: Prediction and Control. Spec. Publ. 21, Soil Conservation Society of America, Ankeny, 1A, pp. 217-225. Williams, J.R. and Hann, R.W., 1978. Optimal operation of large agricultural watersheds with water quality constraints. TR-96, Texas Water Resources Institute, Texas A&M University, 152 pp. Williams, J.R. and Lafleur, W.V., 1976. Water yield model using SCS curve numbers. J. Hydraul. Div. ASCE, 102: 1241-1253. Wischmeier, W.H. and Smith, D.D., 1978. Predicting rainfall erosion losses. A guide to conservation planning. Agriculture Handbook 537, U.S. Department of Agriculture, Washington, DC, 58 pp. WMO, 1983. Meteorological aspects of certain processes affecting soil degradation, especially erosion. Tech. Note 178, WMO 591, World Meteorological Organization, Geneva, 149 pp. Yalin, S., 1963. An expression of bed-load transportation. J. Hydraul. Div. ASCE, 89(HY3): 221-250.

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IN WATERSHEDS

8. APPENDIX ACTMO

A G R I C U L T U R A L CHEMICAL TRANSPORT MODEL

Fr~re et al. (1975) Reference Sediments, pesticides and nutrients (N) Objectives Organisation 3 sub-models USDAHL model (Holtan and Lopez, 1971) with dividing-up into sub-watersheds

Hydrology

1

USLE model (Onstad and Foster, 1975)

Erosion

Nitrogen Pesticides}

1 (Frare, 1975)

[Chemistry

Notes Usable on small watersheds because the USDAHL model only considers a uniform distribution of rain.

S E D I M E N T - P H O S P H O R U S - N I T R O G E N MODEL Williams and Hann (1978) Reference Sediments, nutrients (N and P); large watersheds ( < 2500 km 2) Objectives Organisation 4 sub-models Hydrology ] '

Erosion

SCSCN model (Williams and Lafleur, 1976) with dividing-up into subwatersheds

,

Modified USLE model (Williams, 1975)

~ Nitrogen

]

[ Phosphorus ] ,

Note Only one example in use published.

Estimation of the flux at the outlet (p-particulate)

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A N D M. P R A T

A G R I C U L T U R A L R U N O F F M A N A G E M E N T MODEL Donigian and Crawford (1976) References Objectives Sediments, pesticides, nutrients (N and P); small rural watersheds Organisation 4 sub-models

Pesticides

Hydrology

~

Stanford watershed model (Crawford and Linsley, 1966)

Erosion

,

Variation of Negev's model (1967) Nutrients N,P

Models inspired from research by: Mehran and Tanji (1974), Hagin and Amberger (1974)

Notes Largest surface ,-~ 5 kin2; limited to five types of soil use. The complete model was applied to two experimental watersheds; the results are good for hydrology and erosion, mediocre for chemistry.

T R A N S P O R T M O D E L L I N G IN W A T E R S H E D S

173

CORNELL N U T R I E N T SIMULATION MODEL

References Objectives Organisation

Haith and Loehr (1979), Tubbs and Haith (1981) Sediments, nutrients (N and P); small rural watersheds 3 sub-models

Hydrology

SCSCN model (Williams and Lafleur, 1976) modified

1 Erosion

USLE model (Williams, 1975) modified

1 Nutrients N and P

Notes Applicable to homogeneous watersheds of a limited size --- 5 km2. This model does not require calibration. Application of the model to two watersheds gave good results for hydrology and erosion; the results for nutrients are mediocre.

174

B. CAUSSADE AND M. PRAT

CORNELL PESTICIDE M()DEL

References Objectives Organisation

Steenhuis (1979), Haith and Loehr (1979), Haith (1982) Pesticides (dissolved and particulate); small rural watersheds 4 sub-models

f three choices for run-off

f i" ModifiedSCSCN model Green and Ampt's (1911 ) equation USDAHL's infiltration sub-model when the soil is frozen

Hydrology

Variation of NEGEV's model

,

r

Erosion

,

[ emperatore ]

1 Pesticides _

_

Division into threeparts: 1. Loss through run-off 2. Vertical displacement (Garner, 1965 ; Rao et al., 1976) 3. Volatilization and deterioration

Notes Applicable to small homogeneous watersheds ~ 5 km2. No calibration. Tested on two watersheds. The results are barely acceptable. Lorber and Mulkey (1982) tested it successfully after model calibration.

TRANSPORT MODELLING

CREAMS

References Objectives Organisation

CHEMICALS, R U N O F F AND EROSION FROM AGRICULTURAL M A N A G E M E N T SYSTEMS Knisel (1980), USDA (1984) Study of the changes of agricultural practices on: sediments, nutrients (N and P), pesticides. Scale of the field. 3 sub-models

Hydrology

I

175

1N W A T E R S H E D S

rosion

{ two options for infiltration

,

(

{12" SCSCN m°del if the daily rainfall is known . Green and Ampt model if you have the amount of rainfall

USLE model (Onstad and Foster, 1975) + transport equation (Yalin, 1963)

l l Chemicals N, P, Pesticides

Notes No calibration (in theory). Homogeneous watershed, one type of crop, of soil, of agricultural practice. In the case of nutrients: good results according to the researchers. For a group of Engineers (1985, paper without reference) mediocre results for N. For Lorber and Mulkey (1982) good results for the pesticide losses over the year less good over the daily losses.

176

B. CAUSSADE A N D M. PRAT

H Y D R O L O G I C A L SIMULATION P R O G R A M - FORTRAN

References Objectives Organisation

Donigian et al. (1984) Hydrological cycle, sediments, nutrients, pesticides, salts; rural and urban watersheds 3 modules applied to homogeneous sub-watersheds

Snow

Module 1

Water Sediments Pesticides Nutrients

Transport on a porous section

Module 2 Snow

Water Sediments

Hydraulic ] Temperature ] Sediments Nutrients / Oxygen Chlorophyl

,

Transport on a waterproof section

Stanford watershed model (variation) (Crawford and Linsley, 1966) Erosion + Chemical (cf. ARM model)

cf. algorithms of module 1 without hypodermic and underground run-off

Module 3

,

Transport in the hydrographic network

Notes Model applicable to large watersheds. The most complete and the most sophisticated. The calibration is very heavy (1000 parameters). Tried out on three watersheds; the 1st, 52 km / gave good results overall; 2nd, 7240 km 2 gave encouraging result

TRANSPORT

MODELLING

177

IN WATERSHEDS

WATERSHED MODEL References Prat (1982), Caussade et al. (1984) Objectives Nitrates at the outlet of small polycultivation watersheds Organisation 3 sub-models

~

Plant Absorption

Hydril°gy ] '

CREC model (Guilbot, 1975) Global conceptual type

Chemical Transformations

T Kinetics Michaelis-Menten

Transfer Nitrates Outlet

Notes Usable on small homogeneous polycultivation watersheds (a few km2). Tested on the

Vermeil (7 km2) watershed: good results. Tested on the Girou watershed (520 km2): mediocre results.

178

B. C A U S S A D E

BICHE

A N D M. P R A T

CHEMICAL BALANCE OF WATERS

Reference Objectives

Thiery (1983) Nitrates at the outlet of small watersheds or at a point in the underground water Organisation 3 sub-models Hydrology

I

GARDENIA model (Roche and Thiery, 1984) Global conceptual model

1 Chemistry

Nitrate Transfer

Note Good results at the application level.

SWRRB ] References Objectives Organisation

Hydrology

SIMULATOR FOR WATER RESOURCES IN RURAL BASINS Arnold and Williams (1985) Effect of agricultural practices on hydrology and on the sediments in large rural basins 2 sub-models. Variation of the CREAMS model, at the level of the hydrologic sub-model (1), to make the model applicable to big rural basins after dividingup into sub-basins Discretization into sub-basins For infiltration : SCSCN model For hypodermic run-off Chow's model (1964)

1 Erosion

USLE model (Williams and Berndt, 1977)

Notes No parameter calibration (as a rule). Tested on eleven watersheds ( < 500 km2). Annual soil losses are well simulated, the monthly ones less.

TRANSPORT

MODELLING

MNTHS

IN

179

WATERSHEDS

MODELLING OF NITRATE TRANSFER IN A HYDROLOGICAL SYSTEM

Reference Geng (1988) Objectives Nitrates in hydrological systems Organisation 3 sub-models Hydrology

Coupled model (Ledoux, 1980)

Chemistry

Plant Absorption

Nitrate Transfer

MORELN model (Geng, 1988)

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

LEACHING

Kinetics Michaelis-Menten Nitrate Transfer .....................................

in aquiferous

NEWSAMmodel (Ledoux, 1975; Ledoux and Tillie, 1987)

Notes Good results at the application levels (several km2, several hundred km2).