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2 DEVELOPMENT OF THE FARM MODEL


2.0 The Modelling Procedure

The development of the farm model, including the several submodels, followed the usual modeling procedure as, e.g. described in Bossel (1992, p. 41f) and Joergensen (1994, p. 20f). This procedure comprises the subsequent steps of

  1. definition of the problem,
  2. making the conceptual model,
  3. formulating the mathematical equations,
  4. verification and long-term stability,
  5. sensitivity analysis,
  6. calibration,
  7. validation.

After the problem is defined in terms of time, space, subsystems and complexity, its main features such as state variables, internal connections, forcing functions and processes are selected and determined. Ideally, the data requirement to develop a model should be determined after the conceptual model (in the form of a diagram, for instance) has been formulated (Joergensen, 1994). In this case the development of the conceptual model and the imbedded submodels are biased in advance by the data availability. So each model can be considered as a compromise between the scope of the model and data availability.

The next step, the mathematical formulation, also resulted in compromises, mainly between the intended features of the (sub)model, data availability, desired complexity and the amount of time given for the development of this thesis.

Verification and long-term stability were carried out for all submodels to answer the following questions: 1. Does the model react as expected ? 2. Is the model stable in the long term ? (Joergensen, 1994). The logic of the internal structure was checked by implementing the model's equations and comparing the outcomes to the expected results under a range of conditions.

Afterwards follows a sensitivity analysis which gives an impression of the most sensitive and crucial parameters of each model. This will tell us which parameters have to be determined with higher accuracy or have to be handled with care. In practice, the sensitivity analysis is carried out by changing parameters, forcing functions or submodels and observing the corresponding change of selected state variables. Thus, the sensitivity, S, of a parameter, P, is defined as

S = [dx/x ] / [ dP/P ],

where x is the selected state variable.

The relative change of the parameters is based on our knowledge of the uncertainty of the parameter. It can be appropriate to vary the parameter at more than one level because the response of the reference state variable might not be linear (Joergensen, 1994).

When possible or sensible a calibration of certain parameters was conducted in order to fit the model to Philippine conditions. Validation was difficult to carry through in most cases, due to the lack of appropriate data. This task will surely be up to future possible users of the model.

This typical procedure of developing a mathematical ecological model is, of course, always adapted to the specific problem and type of model and not always every step can be taken as recommended. Moreover, 'the sequence of verification, sensitivity analysis and calibration must consequently not be considered a rigid step-by-step procedure, but rather as an iterative operation, which must be repeated a few times' (Joergensen, 1994 p. 48). This also applies to the first three steps.

The definition of the problem was already given in the introduction. In the following the conceptual model is developed and the resulting steps are the development and formulation of the submodels. For each submodel the described modeling procedure is applied as far as necessary or possible.

2.1 The Conceptual Model

Introduction

As a first step towards the development of a dynamic farm model and taking into account the definition of the problem in chapter 1.4, the biophysical level was considered to be most important. All aspects of sustainability, e.g. efficiency, recycling, productivity, economy, politics and social questions, are based on the biophysical layer, i.e. nutrient flows and yields. Biophysical phenomena can often be modeled satisfyingly with differential equations. Therefore STELLA 3.0.7. Authoring Version was chosen as the modeling environment. Biophysical differential equations that model, like in this case, the relations between different biophysical compartments, i.e. the farm enterprises, are characterized by flows and stocks.

Stocks comprise those entities that are relevant for the description of all states of the system. The state of the system is determined by the assignment of a certain value to each of these entities, like, e.g. grain yield, amount of manure, crop by-products, etc. Flows describe the relations and interactions of those entities among each other quantitatively and therefore determine the change of their values within time. In fact, if each stock is assigned a value at the beginning of the simulation, the so-called initial value, and if the flows are described by mathematical equations, the state of the system is determined for all times. These models are therefore called deterministic models.

Data and Methods

In order to identify the most important stocks and the flows between them for a typical Philippine small-scale farm, a preliminary study was conducted. The RESTORE data where data from thirteen smallholder rice farms was collected via monitoring and recall was analyzed. Moreover, several farms were visited and in conversation with the farmers important information about major nutrient flows and stocks in relation to seasonal changes and cropping patterns was attained.

Collection of the RESTORE data was achieved in the following way; staff from ICLARM and NGO's prepared bioresource flow diagrams together with the farmers. Bioresource flow diagrams (Fig.1) are drawn by first sketching cross-sections of each 'natural resource type' that is used by the household and/or cultivated by the farmer. Natural resource types comprise, e.g. lowlands, sloping uplands, ponds, streams, etc. Those are rather spatial entities which have different significance concerning the whole farmland cultivation. Next, on each resource type icons of the species used there are drawn (e.g. rice, grass, fruits, vegetable, fishpond, livestock, etc.) Finally, the arrows that connect the different enterprises and recycle resources are drawn on the diagram and complete it (Bimboa et al., 1995). Those diagrams build the basis not only for making kite-diagrams but also for quantification of farm stocks and flows and, last but not least, sustainability indicators. Naturally, flows and resources used on the farm change with seasons and years, still, in general, the availability of land resources stays more or less the same for several years. Therefore spreadsheets for the collection of quantitative data about farm use, farm performance and resource flows could be developed and stored in large data tables (for the full description of these data tables see appendix 8.3). The quantification of data started on most of the thirteen farms mentioned in the wet season (WS) 1989 and ended in the dry season (DS) 1994, whereas data before WS 1991 was obtained from farmers' recall. The quantities are aggregated over one season, respectively. This gives a fairly good average picture of the performance of a considered farm for a certain season, but to develop a dynamic model there is much more information needed concerning the course of events and processes throughout a season.

To be provided with this kind of information farmers were visited and conversations with involved scientists and researchers were held. Additionally, by consulting the appropriate literature a good picture of the run or flow of events and processes within time could be obtained. This includes information about

Provided with this information the conceptual model of an average Philippine rice farm can be established. Major stocks and flows were identified and at least roughly quantified.

Tab. 1: As a first step towards formulating the conceptual model, the considered farm is defined in space. Also the main submodels are identified.
Compartments and enterprises considered
for an average small-scale Philippine farm (WS)
Compartments (ha)Enterprises (ha/no.)
Homestead 0.375 ha buffalos 3
poulty 15
pigs 2
(fruit)trees 19
ricefield 1.5 ha rice variety IR 74
rice-fish 0.1 ha rice variety IR 74
Tilapia
fishpond Tilapia
total size: 2 ha
Compartments and enterprises considered
for an average small-scale Philippine farm (DS)
Compartments (ha)Enterprises (ha/no.)
Homestead 0.475 ha buffalos 2
poulty 25
pigs 2
vegetable 0.125 ha
(fruit)trees 27
ricefield 1.5 ha rice variety IR 74
fallow land 0.025 ha
rice.fish 0.1 ha rice variety IR 74
Tilapia
fishpond Tilapia
total size: 2 ha

Results

The most important stocks (enterprises) according to their natural resource type (compartments) are listed in Tab.1. On the homestead, which is the area around the farmers house where the family lives and most activities directly related to the household and every day life take place, four or five main enterprises are identified; buffalos, poultry, pigs and fruittrees. In dry season (DS) vegetables are cultivated, too. This is because in DS climatic conditions are more favorable to vegetable growth in WS. Secondly the rice field with rice as a major stock is listed. This is naturally the most important farm product.

Tab. 2:
The flows of the considered enterprises for an average small-scale farm (WS/DS)
inflows enterprise outflows
rice residues/ leaves
grass from
ricefields bunds
buffalomanure
golden snail
often no special inputs
padddy rice
broken rice/rice hulls
poultrymanure
poultry
golden snail
rice bran
broken rice
pigs manure
pig
buffalo manure
pond water
(fruit)trees leaves
fruits
wood
fertilizer
buffalo manure
pondmud
rice field rice bran
rice
bundweeds
chicken manure
pig manure
leaves (ipil, spinach>
buffalo manure
rice-fish rice
fish
rice bran
pig manure
leaves (ipil, spinach)
poultry manure td align=center>fishhpond
fish
pondmud
buffalo manure
chicken manure
leaves
fertilizer
rice straw
pond water
vegetables
(DS)
vegetable
fallowgrass
Tab.2: Flows and stocks in italics are quantified and modelled in this first version of FARMSIM.



Sometimes a part of the rice field is used for rice-cum-fish culture. The fishpond with Nile Tilapia as a main culture crop is assumed to present a farm compartment, too. Although not yet established on all farms it is taken into account for testing its impact on overall farm performance. In DS a large portion of the rice field cannot be cultured due to the lack of water. This also often affects the use of a fishpond.

All potential inflows and outflows which typically characterize the Philippine small-scale farm compartments are listed in Tab. 2. Since the cultivation of rice dictates the rhythm of life and the course of events on a Philippine small-scale farm, the time span considered here was set to one season, i.e. half a year. The main farm management strategies are concerned with the cultivation of rice,, or at least are connected with it. All other enterprises are of 'minor' importance.

After the identification of the main compartments of the model, and therefore of the main state variables and their connections, after the definitions of the bounds of the model in time and space, the conceptual model was set up. The next step was the determination of the internal structure of the several compartments, i.e. the formulation of their response to the identified forcing functions. This means the change of the stock values in relation to the quantity of in- and outflows.

To achieve this a number of existing models was surveyed with regard to their usefulness for the incorporation into a whole farm model. These models should be as simple as possible, and yet have all features necessary to describe the desired relations in an accurate manner. Simplicity was necessary for future validation with on-farm data. In the RESTORE project only data of the major flows and stocks is collected and consequently only those properties can be calibrated and validated.

Either due to the lack of appropriate data and/or the lack of models, not all identified enterprises and flows could be quantified. In the following sections those submodels are described for which either existing models could be found or enough data was available to derive statistical input-output relationships.



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