There are several models that monitor movement of nitrogen in the soil. Most of these models have not been widely used in southern Africa because of sophisticated equipment required to collect data and the data needed to run the model are intensive. Nitrogen Distribution Model (NDM) has been developed to ensure that it responds to increasing need of managing nitrogen in agricultural systems characterized by smallholder farmers who do not have adequate resources to collect intensive data for modeling. NDM has parameters that are explicit and mostly intuitive and maintains good balance of simplicity and robustness. With the nature of smallholder farming in Malawi where over 85% of population are rural-based smallholder farmers, the model has also be designed so that it can acts as database to keep track of farmers and farms so that were given farm-specific nitrogen and water management advice.
Nitrogen (N) is the most important determinant of plant growth and crop yield. Plants lacking N show stunted growth and yellowish leaves. Plant growth and crop yield usually increase when N is added [
This mathematical expression has all three factors that influence the movement of nitrogen in the soil and these are advection, dispersion and plant nitrogen uptake.
This paper presents the work and steps used to develop NDM. NDM has been developed to ensure that it re- sponds to increasing need of managing nitrogen in agricultural systems characterized by smallholder farmers who do not have adequate resources to collect intensive data for modeling. NDM has parameters that are explicit and mostly intuitive and maintains good balance of simplicity and robustness.
The modes of nitrogen transport in soil are predominantly governed by advection and dispersion [
where, t is time, c is the N concentration in the liquid phase, xi and
Advection is defined as the flux of solute due to flow of water containing the solute. It is a product of water flux and the solute concentration
1) Determination of N concentration of solute in the soil
The following equation was used to calculate concentration of nitrogen in the soil.
where:
・ C is concentration of solute (kg/L3 of soil);
・ ar is N application per hectare (kg/ha);
・ bd is bulk density (g/m3);
・ dlayer is depth of layer (mm).
Solute is substance dissolved in a liquid. Concentration is measured in [mass/length3] (mg/L). Concentration is function of time, directions,
2) Determination of water flux
Triscan Sensor was used to collect soil water content in (d) depth of water in each layer (L of water/L of soil). This water depth was multiplied by row spacing (r) and planting spacing (s) to have (q) volume of water availa- ble within each layer of maize root zone as presented in below equation:
The water flux qw was determined by considering volume of water (q) crossing the cross-section area of maize rootzone (mm3), lateral conductivity (Kh in mm/day), and ground surface slope (m/m) as presented in equation below:
where:
Kh = horizontal conductivity (mm/day);
q = soil volumetric water content;
s = surface slope (m/m).
Dispersion is the spreading out of solute due to variations in water velocity within individual pores, across pores with differing sizes and shapes, and across interconnected pore pathways with different geometries. It allows solute to come to an equilibrium concentration within the soil solution and between regions where the soil solu- tion is mobile or immobile [
where
where:
・ D is the diffusion coefficient in water filling the pores (for N in water is 1.88 × 10−5 m2∙s−1);
・ τ is the tortuosity of soil (dimensionless), values are between 0.21 to 0.35 for unsaturated sandy loam soils, and between 0.59 to 0.84 for saturated sandy loam soil by [
・ θ is soil volumetric moisture content.
Another influence that will determine nitrogen movement in the soil is plant uptake. The uptake of water and nutrients by plant roots will create a gradient in regions surrounding the roots. With the general principle of hy- draulic gradient influencing water movement, then water and nitrogen will move towards plant roots where there is a negative gradient. Plant nitrogen uptake, Nu, is the function of time and coordinates. It is related to water uptake in that the nutrient gets taken up by the plants with the water. The Nu is governed by the following equa- tion:
where
Smax is the potential water uptake rate which equal to crop evapotransipiration (Smax = ETc).
The left graph of
The following assumptions have been drawn from
1) At the time of fertilizer application, the soil where fertilizer is applied has highest concentration of nitrogen than the surroundings;
2) Movement of nitrogen is from the point of application to the surrounding;
3) Concentration is mass of nitrogen/volume of soil (to be calculated by bulk density);
4) All NH4-N in fertilizer is converted to NO3-N immediately upon fertilizer application, and is completely dissolved in applied water;
5) There is no capillary rise, and water table lies far below the surface.
NDM has been developed by including all three factors that influence solute transport in the soil and these are advection, dispersion and plant uptake. It would have been difficult to use the model if the input parameters were soil moisture content, rate of nitrogen uptake by maize plant, concentration of nitrogen in the soil because cost associated with equipment need to capture such type of data. In order to simplify the model, the input pa- rameters have been simplified to volume of water applied in m3 and the model is then generating the depth of water in mm. The depth of applied water in the soil is linked to calculation of soil moisture content. The input parameter of the model is quantity of fertilizer applied in kg/ha and the model is generating quantity of nitrogen applied presented in N kg/ha. This input parameter is linked to the nitrogen concentration in the soil, which is an integral component of both advection and dispersion equations present in Equation (1). The other input parame- ter that has been used in the model is maize growth stage. The maize growth stage such as emergence, develop- ment, mid- and late-stages is generating crop coefficient (Kc) which is being used to calculate actual crop evapo- transpiration (ETc). The ETc has been assumed as potential water uptake rate (Smax) in the uptake component of the equation.
The model has included two other input parameters of farmer and farm. The input parameters under farmer consists of name of a farmer, district, Traditional Authority (TA), village and his/her mobile number. The farm
input parameters consists of land under cultivation, general slope of the farm, general soil type, irrigation me- thod, and district where the farm is ( here the model has assumed that some farmers might have two or more farms in different districts). These input parameters have been included to ensure that the model is farmer-center- ed that will enable them to have specific recommendations as per their specific agricultural production require- ments.
The NDM has five input data files namely Farmer Date file, Farm Data file, Water Data file, Fertilizer Data file, and Crop Data file. Within each data file, there are more than three input parameters that need to be entered in the model. These input parameters have been designed in such way that they are not difficult for users to collect and input them in the model. If the data input requires sophisticated equipment to collect them in the field, it may limit the wider application of the model [
The NDM is written in programming language of C++. The model used this programming language because NDM was developed so that it can be incorporated in the Soil Water Module of APSIM model as subroutine. The programming language of APSIM is C++; hence to ensure compatibility, the NDM had to be developed in the same programming language.
When clicked on Farmer file, the four operations will appear and these are New farmer, Update Farmer De- tails, Delete Farmer or Add Farm. The user will select the operation that he/she want to operate. Another advan- tage of this model is that it also acts as database to keep information of farmers and their farms; hence it is easy to track and give advice to farmers.
After data is entered under farmer file, the next step is to enter details of the farm. The model has assumed that one farmer might have different farms with different characteristics. In fact, the agricultural production sys- tem of most of the smallholder farmers is that they have several patches of land which they for crop production. This model has taken this agricultural production system into consideration. The model would provide informa- tion to farm specific.
The conceptual framework, design, structure and key algorithms of the NDM have been described to highlight the distinctive features and peculiarities of the model. The model requires low number of parameters and input data to simulate movement and distribution of nitrogen in the soil under irrigation. Unlike other previous similar models, the strength of this model is that input parameters are very minimum and easy to capture and enter in the interface. To capture the input parameters of water and nitrogen does not sophiscated equipment and hence smallholder farmers. The parameters of the model are explicit and maintain good balance of accuracy, simplicity and to some extent robustness. The model is aimed at ensuring that informed decisions are made on proper management of water and nitrogen resources on a farm. Another important application of the model is that it can be used as database for smallholder farmers so that they easily be tracked be advised on good agricultural practices. The model is still under development but will be tested under different soil types and crops so that it can be widely used by users.