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2.2 The Rice Model


The cultivation of rice surely depicts the most important enterprise on Philippine small-scale farms. Rice represents not only the major basic foodstuff for the farmers but also serves as a market product and as a currency for paying the land rental. It is the major income source for the farmers and the rice fields often claim more than 70 % of the whole farm area.

As a rice model ORYZA_0, developed by the Research Institute for Agrobiology and Soil Fertility (AB-DLO), Wageningen, NE and the International Rice Research Institute (IRRI), Los Banos, Philippines, was selected (ORYZA, 1994). A few adaptations have been made concerning the modeling of fertilizer application and the connections between the other compartments. This became necessary in order to reflect the fertilizer application schemes of Philippine farmers and the integration into a whole-farm model. All values for constants, parameters and initial values of ORYZA_0 are taken from the Forum of Simulation and Systems Analysis for Rice Production (SARP) (SARP Research Proceedings 1995). This set of parameters was measured in the Philippines and is calibrated to Philippine conditions concerning soil types and rice varieties.

Description of the Rice Model

ORYZA_0 is basically a simple light use efficiency based model which also incorporates the role of nitrogen in the plant. Therefore it is also possible to model the effects of N-fertilization.

Naturally, one of the major stocks in this dynamic model is the total crop weight (CropWeight, kg DM/ha). This contains the shoot weight as well as the roots. It is calculated by integration of the growth rate (GrowthRate, kg DM/(ha*d)) over time. For a complete list of the acronyms used in the model see appendix 2.

GrowthRate = FSV*LNuseCoef*LeafN*[1 - e - epsilon*Radiation/(LNuseCoef*LeafN*0.1) ]

The growth rate depends on the incident global radiation (Radiation, MJ/(m²*d)) and the amount of nitrogen contained in the leaf canopy (LeafN, kg leaf nitrogen per hectar ground surface area). LNuseCoef (g dry matter/(g leaf N*d)) is the inital leaf nitrogen use coefficient and epsilon (g dry matter/ MJ incident global radiation) is the initial global radiation use coefficient. The leaf nitrogen is the 'production capital' for converting radiation into dry matter. This is a simplification of various processes of producing dry matter. As a consequence, the parameter LNuseCoeff represents the efficiency by which leaf nitrogen is used for producing dry matter. The adjective 'initial' indicates that the overall efficiency of

Fig. 4: Overall global radiation use coefficient (GRUC, g dry matter MJ-1 incident global radiation) as a function of amount of leaf nitrogen (LeafN, g N m-2 ground surface area), for selected levels of global radiation (MJ m-2 d-1). Reproduced according to SARP, 1994.

Fig. 5: Overall global radiation use coefficient (GRUC, g dry matter MJ-1 incident global radiation) as a function of incident global radiation (MJ m-2 d-1) for selected levels of leaf nitrogen (LeafN, g N m-2 ground surface area). Reproduced according to SARP, 1994.

Fig. 6: Overall leaf nitrogen use coefficient (LNuseCoef, g dry matter g-1 leaf nitrogen) as a function of the amount of leaf nitrogen (LeafN, g N m-2 ground surface area), for selected levels of global radiation (MJ m-2 d-1). Reproduced according to SARP, 1994.

Fig. 7: Overall leaf nitrogen use coefficient (LNuseCoef, g dry matter g-1 leaf nitrogen) as a function of incident global raduation (MJ m-2 d-1), for selected levels of leaf nitrogen (LeafN, g N m-2 ground surface area). Reproduced according to SARP, 1994.

leaf nitrogen use GrowthRate/LeafN (LNUC) approaches LNuseCoef for low levels of LeafN. Likewise, the overall global radiation use coefficient GrowthRate/Radiation (GRUC)approaches epsilon for low radiation. epsilon and LNuseCoeff are found as mean values across a range of data sets: epsilon = 2.5 g/MJ and LNuseCoeff = 10 g/g*d (Fig. 4-7). FSV is a calibration factor wich is site specific. Here site-variety interactions can be merged into one single factor. SARP scientists often observed a sudden shift of this parameter around flowering stage (SARP, 1994). An especially calibrated parameter for the rice variety cultivated on the considered farm (IR 74, see Tab.1) could not be found.

Radiation is implemented in two ways (Radiation and avRadiation,MJ/(m²*d)). Radiation is the tabulated daily incident global radiation as observed by the IRRI weather station (extracted from CLICOM database, 1991), whereas avRadiation is the average radiation of the years 1990-1993 observed at the same weather station. This weather station is located near IRRI (Longitude 121° 15' E , Latitude 14° 11' N, Altitude 21 m) and therefore represents a good picture of the actual climate on the considered farms which, in fact, are situated in the same area.

CropWeight(t) = CropWeight(t - dt) + (GrowthRate - cut) * dt

GrowthRate = IF (DAT <= 0) OR (DATEH=1) THEN 0


FSV*LNuseCoef*LeafN* (1-EXP(-(epsilon*avRadiation)/(LNuseCoef*LeafN*0.1)))

cut = IF (DATEH=1) THEN CropWeight Else 0

Rice growth starts after rice transplanting, i.e. if the days after transplanting (DAT) are positive, and ends with the harvest of the rice, i.e. if the day of harvest is reached (DATEH = 1). At day of harvest the stock Cropweight is emptied (cut, kg DM/(ha*d)) and the shoots are divided into grains (Yield, kg DM/ha) and straw (Ricestraw, kg DM/ha).

Yield(t) = Yield(t - dt) + (Harvest) * dt

Harvest = IF (DATEH=1) THEN WSHT*0.4 ELSE 0

Ricestraw(t) = Ricestraw(t - dt) + (strawrate) * dt

strawrate = IF (DATEH=1) THEN WSHT-Harvest ELSE 0

Yield comrises the grains and hulls. This is the usual measure of the total rice yield. Grains and hulls amount to about 40 % of all dry matter harvested. The rest is rice straw.

The shoot weight (WSHT, kg DM/ha) must be considered if there is no data available about the root weight. The root-shoot ratio (RSR) is a function of crop age (RELTIME).

WSHT = CropWeight/(1+RSR)

RSR = IF (RELTIME<1) THEN 0.4-(0.4-0.15)*RELTIME ELSE 0.15

RELTIME = IF (DAT<=0) THEN 0 ELSE DAT/flowering

RELTIME is the relative time from transplanting to flowering, which is about 67 days after transplanting. Before flowering the root-shoot ratio changes in time. Here an initial value of 0.4 is assumed. That means that root weight measures 40 % of the shoot weight. This ratio decreases linearly until flowering to a value of 15 %. After flowering this ratio is fixed. That means that after flowering no further root development takes place.

The leaf nitrogen (LeafN, kg/ha) is a function of the total crop nitrogen uptake (TCNUptake, kg/(ha*d)). A fraction of the total crop nitrogen uptake (FNL = 0.5), i.e. 50 %, is allocated in the leaves. The initial value is also this fraction from the initial total crop nitrogen.

After the date of first flowering (DATEFF = 1), which is usually 7 days before flowering, leaf nitrogen is reallocated to the panicles.

LeafN(t) = LeafN(t - dt) + (LNUptake) * dt

LNUptake = IF(DATEFF=0) THEN (TCNUptake*FNL) ELSE (FNL*(TCNUptake-PNUptake))

After the start of flowering, all crop growth is invested into panicles (PanicleN, kg/ha) since this represents a strong sink for nitrogen.

PanicleN(t) = PanicleN(t - dt) + (PNUptake) * dt

PNUptake = IF(DATEFF=1) THEN 0.01*GrowthRate ELSE 0.0

The total crop nitrogen uptake (TotalCropN, kg/(ha*d)) is limited by various assumptions. First of all it seems plausible that it is the minimum of the nitrogen demand of the plant (NDemand, kg/(ha*d)) and of what is available to the plant (NAvail, kg/(ha*d)).

TotalCropN(t) = TotalCropN(t - dt) + (TCNUptake) * dt

TCNUptake = NUptake

NUptake = MAX(0.0,MIN(NAvail,NDemand))

What is available to the plant is determined by fertilization, i.e. the nitrogen application rate (NAppl, kg N/(ha*d)) plus the nitrogen that is naturally supplied by the soil (SoilSupply, kg/(ha*d)). Only a fraction (Recovery, g/g) of the applied fertilizers can actually be taken up by the roots. This reflects the competition between loss processes and uptake by the roots that determines the actual amount of fertilizers available to the plant. In the early growth period nutrient loss processes like, e.g. through percolation and seepage have an advantage because the root system is not yet fully developed and cannot cover the whole potentially available root space. Depending on environmental conditions and possibly also on crop characteristics the maximum recovery fraction is reached around panicle initiation (PI) up to flowering. Here it is implemented as a tabulated function which can be obtained by field trials by evaluating effects of nitrogen split applications given at different times. A first approximation for good rice soils shows a linear increase from 0.0 at transplanting to 0.4-0.7 at PI or even 0.8 around first flowering stage and then a linear decrease to 0.0-0.2 over a time span of three weeks (SARP, 1994). It is an empirical tabulated function of the size of the root system.

NAvail = NAppl*Recovery+SoilSupply

Nitrogen application (NAppl, kg N/(ha*d)) is modified from ORYZA_0 to suit the actual applications schemes traditionally realized by the farmers. Philippine farmers often apply fertilizers two times per season. The first time is around the second week after transplanting and the second time is shortly before flowering. Fertilizer application is modelled as an 'impulse response function'. It is a reflection of the delayed penetration of fertilizers into the soil (Fig. 8) and their trespassing into the soil solution. The user of the model can determine the first date (DAT1) and the second date (DAT2) of application, each with a specified amount of fertilizer (Appl1 and Appl2, kg N/ha). The integration of the slope of fertilizer application (NAppl, kg N/(ha*d)) cumulates to the actual amount of nitrogen applied in one season (Apcum, kg N/ha). In Fig. 8 it is assumed that the commercial fertilizer is a so-called 14-14-14 fertilizer. That is that the nitrogen-phosphor-potassium content is 14 %, respectivley. 58 % are fillers such as sand etc. (see chapter 1.1). In the model the user has to differentiate between different types of fertilizer and state only the nitrogen input.

Apcum(t) = Apcum(t - dt) + APSLOP * dt

Fig. 8: Fertilizer application scheme: at 30 DAT and 60 DAT 100 kg 14-14-14 fertilizer/ha (i.e. 14 kg N/ha) are applied respectively (NAppl). At 30 DAT less fertilizer is actually available for the plant as at 60 DAT (Navail) because the root system cannot yet utilize all of what is in the soil solution (Recovery). The nitrogen demand of the plants (NDemand) cannot be satisfied over the growth period. At 60 DAT there is more nitrogen available than is actually applied because the soil supply of 0.6 kg N/(ha*d) adds to the available amount as well.

NAppl = step(FertAppl1*0.12,DAT1+offset)*(1/0.3) *(exp(-0.2*(time-DAT1-offset)) -exp(-0.4*(time-DAT1-offset)))+ step(FertAppl2*0.12,DAT2+offset)*(1/0.3) *(exp(-0.2*(time-DAT2-offset)) -exp(-0.4*(time-DAT2-offset)))+NtoSoil/Hectar

SoilSupply is set to 0.6 kg N/ha*d (SARP, 1995). The value is estimated from nitrogen uptake of unfertilized plants by dividing the full season's total nitrogen uptake by the number of field days. NtoSoil (kg N/d) is the nitrogen contained in the applied buffalo manure (see chapter 2.5 and 2.6). Soil nitrogen supply of the soil only takes place during the rice growth period. It is set to zero otherwise.

The variable offset measures the time from the starting-day of the simulation (StartDOY) until rice transplanting. This allows the running of the rice model rather independently from the rest of the farm simulation. The actual model time is measured by TIME [days], whereas the time relevant for the rice model is determined by the days after transplanting (DAT). It is

DAT = TIME - offset.

The amount of nitrogen needed by the plant is calculated on the basis of several assumptions. Naturally, there is no demand for nitrogen after harvest (DATEH = 1) and before transplanting (DAT<=0). During the first 20 DAT the demand is governed by the relative uptake coefficient (RUR, 0.2/d). This phase ends before completion of the 20 days period if the total crop nitrogen exceeds 35.0 kg/ha. After the exponential phase other uptake limitations exist.

NDemand = IF(DATEH = 1) THEN 0


ELSE(IF(TotalCropN<35.0)AND(DAT<20)THEN (RUR*TotalCropN)


MIN(5,0.035*GrowthRate, (MaxNCon*(CropWeight+GrowthRate*DT)- TotalCropN)/DT,

IF(LeafN>=100) THEN 0 ELSE 9999.9,

IF (DATEHF=1) THEN 0 ELSE 9999.9 ) ) )

These limitations are:

These assumptions concerning nitrogen-demand and nitrogen-availability were all established by SARP (1994). The parameter values are determined by field trials and experiments by IRRI or mean values from literature (SARP 1994,1995).

Further information and a more accurate explanation of the assumptions made here can be obtained from 'SARP Research Proceedings' (1994).

Verification and long-term stability

This model has been verified by IRRI and Wageningen. So testing of the internal logic of the model was omitted. The implementation used here was verified by running the model with different sets of the same input parameters as the implementation of ORYZA_0 as realized in the MANAGE-N2 software (SARP, 1995) and comparing the outputs of both implementations. After mistakes of the implementation were erased and both implementations produced the same outputs, verification was considered executed.

Since the model concept only intends simulation for one rice growth period, i.e. one season, all growth of rice is stopped after the first harvest (see implementation of GrowthRate p. 12). After the end of the growth period all main driving variables are set to zero and therefore no further change of the outputs takes place. The rice submodel is stable in the long run. Simulation only makes sense for one season. All external parameters and forcing functions have to be reconsidered and set for another half year of simulation after the first harvest.

Sensitivity analysis

In the SARP publications no sensitivity analysis for the ORYZA_0 model was found. For the sensitivity analysis the state variable, whose deviation in relation to the variation of certain parameters is compared, is the simulated crop weight (CropWeight). In order to obtain a standard value of the crop weight to which the deviation of the results can be compared, a standard situation has to be declared. In the case of this rice model only the 'external' parameters such as fertilizer input and rice growth period have to be defined. Initial values are no subjects of the sensitivity analysis here. Taking initial values and all other constants from SARP (1994), assuming a medium nitrogen application of 14 kg N/ha at 7 DAT and 45 DAT, respectively (those are usual fertilization dates in the Philippines), setting the rice growth period to one hundred days and taking the average radiation of the years 1990 - 1993 as input, we obtain a standard crop weight of 8625.63 kg DM/ha. The critical parameters were identified as the 'external' parameters which are user-defined, such as amount of fertilizer application, rice growth period, start DOY, radiation and internal growth constants, such as the radiation use coefficient (epsilon)and the leaf nitrogen use coefficient (LNuseCoef).).

Tab. 3: Sensitivity analysis of the rice model. For each level and each parameter only the larger sensitivity S of the two model runs is tabulated.
Model Sector Parameter
20 % deviation 50 % deviation
external fertilizer per session
parameters growth period
start DOY
growth epsilon (radiation)
constants LNuseCoef
D Demand RUR
max. uptake
max. growth rate
max Leaf N
N Availability SoilSupply
Standard value: 8625.63 kg DM/ha. Standard situation: Start DOY = 153, Fertilization: 14 kg N/ha at 7 DAT and 45 DAT respectively. Growth period = 100 days. Radiation: average radiation of the years 1990 - 1993.

Furthermore, the parameters concerning the nitrogen demand and the nitrogen availability of the crop were taken into consideration. In the sensitivity analysis only one parameter at a time is varied. The range of variation was set to 20 % and 50 % of the standard value, requiring two model runs for each parameter. If the parameter was not a single value but a graph, for instance, like in the case of the maximal nitrogen concentration in the plant or the average radiation throughout the year, a factor of 0.8 or 1.2 was multiplied. The sensitivity index S was calculated as described in chapter 2.0. The results are listed in Tab. 3.


To test the validity of this implementation for the small-scale farms, environment data of yields in relation to applied fertilizers was compared to simulated results. Unfortunately, there were only four cases available where yields of the considered farms were recorded with their respective fertilizer inputs (Dalsgaard, 1996). Dalsgaard conducted productivity and efficiency analysis on four different smallholder rice farms which were considered to represent different stages of integration. The data used here is presented in Table 4.

Tab. 4: Agroecological productivity for four different rice farms; measured and simulated results. Productivity data taken from Dalsgaard (1996).
Farm A Farm B Farm C Farm D
Farm area (ha) 1.36 1.512.76 2.75
Ricefield area (ha) 1.34 1.112.55 1.99
crops (no.) 2 2.331 1
net yield (kg/ha) 6007.5 6982 3588.2 2839.2
net yield (kg/ha/crop) 3003.75 2996.57 3588.2 2839.2
Fertilizer input
commercial Fertilizer (kgN/ha) 32 12.60 0
Urea (kg N/ha) 46.34 62.2 19.126.6
net N input (kg/ha/crop) 39.17 32.1 19.126.6
growth period: 97 days
simulated yield (kg/ha/crop) 3011.17 2919.34 2790.55 2876.79
N content of Urea 46%
Commercial Fertilitzer:
N content of 14-14-14 Fertilizer 14%
N content of NH3PO4 12.50%

It was assumed that for the farms where the net yields of different crops was summarized each yield had an equal share.

The growth period is also an important factor which determines the final net yield in the model. Since this parameter was not stated in Dalsgaard (1996), a growth period of 97 days was assumed. Another assumption was a typical split fertilizer application scheme on 7 DAT and 45 DAT as is usual in the Philippines. The day of transplanting was set to May 22.


For the farms A, B and C, simulated results reflect the real situation quite well. The recorded data for these farms also support the notion that increasing fertilizer input also increases net yields. This is an assumption which, naturally, also found an entry in the models equations formulation and is therefore mirrored in the simulated outputs as well. The results of farm C do not support this thesis. Although having the least fertilizer inputs farm C has the highest yields and its simulated value is totally underestimated. The reason for the extraordinary high yields on farm C, despite relatively low fertilizer input are not clear and give rise to various speculations. They might be due to improved rice varieties or good soil or interactions between both. The water availability might be better or rice pests could have had a lesser impact on the crop.

Nevertheless, experiments conducted by IRRI support the notion of the positive correlation between nitrogen input and grain yields. Model evaluations showed good results for Philippine conditions, too (SARP, 1994), despite the relatively simple simulation approach. The good simulation results for three of four farms where this model is to be applied are promising. To make this submodel more trustworthy, more evaluations with on-farm data have to be made.

Sensitivity analysis showed that in a standard situation the most influencing parameters are the growth period, the leaf nitrogen use coefficient and the soil nitrogen supply. The latter two regulate the nitrogen uptake of the plant. Still they are far from being critical because a 20 % and a 50 % variation resulted in almost all cases in a less than 20 % or 50 % deviation from the standard value. Some parameters which determine the nitrogen demand of the crop did not influence the outcome at all. They become limiting factors in situations of high fertilizer input, i.e. far from the standard situation. It can be stated that in the usual situation of Philippine small-scale farms no critical parameters were found. Although nonlinear growth was assumed the model behaves well within the ranges that are of primary interest. The critical parameters are normally subjected to a thorough calibration. This was already carried out by SARP (1994).

Many aspects which influence the sustainability of farms were not considered. For instance, negative long-term effects of inorganic commercial fertilizers on the fertility of the topsoil, as mentioned in the introduction, could not be quantified. The use of pesticides has, of course, also a negative impact on ecosystem health and water quality. On the other hand, integration of more aspects and processes leads to a higher complexity of the model. This makes the model more dependent on input data which might be difficult or even impossible to determine. More complexity does not necessarily mean more accuracy of model predictions, as more uncertainties are incorporated as well.

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