Agronomy is the science of crop management. It proceeds from a physiological understanding of the crop through to the prediction and verification of better management techniques. One possible means of achieving better agronomic management is the use of crop models. A crop model can be defined as a quantitative means of predicting the growth, development and yield of a crop, given a set of genetic coefficients and relevant environmental variables (Monteith, 1996). A model has two important and related purposes: to improve our understanding of the crop and to predict how a crop will perform in defined agricultural environments, thereby aiding tactical and strategic decision-making.
This study examines how well sites across the globe satisfy potential biomass requirements for bambara groundnut and their likely yield thresholds in terms of pod production. In overview, there are two major analytical procedures in this study:
BAMnut needs information and data on the most important factors that affect crop yields - the model inputs. After passing `through' BAMnut, the inputs are converted to a number of outputs, such as maps and statistics of crop yields. A schematic diagram summarising the methodological framework developed in this study is shown in Figure 1.
BAMnut is a process-oriented model developed at the University of Nottingham as a tool to simulate crop growth and yield in bambara groundnut. The model has been written in Visual Pascal, it simulates dry matter production and pod yield through numerical integration with a daily time-step. On each day, the resources of light and water are `captured' and `converted' into assimilated dry matter. Depending on the availability of these resources and the crop's ability to sequester them, growth (dW/dt) is considered as either light limited or water limited. Figure 2 summarises the relations between the different modules within BAMnut, which are further described below. Radiation limited growth (LLG) is calculated from incoming radiation and the fraction of radiation intercepted by green leaves. Water limited growth (WLG) is calculated from potential water uptake rates and the amount of available water in the rooting zone. LLG and WLG are then compared to take the minimum of the two as the actual growth.
dW/dt = minimum of (LLG, WLG)
Where:
W = total dry matter (g m-2)
LLG = radiation limited growth rate (g m-2 d-1)
WLG = water limited growth rate (g m-2 d-1)
Finally, pod yield is determined at crop maturity as the product of accumulated dry matter and a harvest index taken as a constant landrace-specific value.
Under optimal conditions (potential growth) a high proportion of variation in biomass production can be explained from intercepted radiation with a simple equation:
LLG = 
* Radiation * Fi * Tfactor
Fi = 1- e-(K*L)
Where:
LLG = radiation limited growth
= radiation use efficiency (g MJ-1)
Radiation = incoming solar radiation above canopy (MJ m-2 d-1)
Fi = fraction of radiation intercepted by canopy
Tfactor = growth correction factor for temperature
K = light extinction coefficient
L = leaf area index
The approach described above was first defined by Monteith (1977) and Gallagher and Biscoe (1978). BAMnut follows the same approach with growth as the product of intercepted radiation and a conversion factor (radiation use efficiency, ). The fraction, Fi, of radiation intercepted is calculated from the leaf area index, L, and the canopy extinction coefficient, K, using the Beer's Law approach (Squire, 1990), which states that fractional interception is related to the leaf area index of a canopy. Radiation limited growth (LLG) is calculated from solar radiation intercepted by leaves. BAMnut assumes a constant radiation use efficiency, ( =1.2 g MJ-1). This provides a conversion factor for radiant energy to plant biomass i.e. the ratio of dry matter produced to solar radiation intercepted during a defined period of growth.
The experimental data from the Nottingham glasshouse experiments showed that for bambara groundnut, remained constant across all experiments. The literature suggests that photosynthetic rate depends on the ambient temperature i.e. a temperature factor for the photosynthesis/light response (Goudriaan and van Laar, 1994). This concept is incorporated in BAMnut and a temperature factor (Tfactor) is calculated according to the temperature relation shown in Figure 3. The value of is reduced by Tfactor at temperatures outside the optimum temperature range (Tfactor = 1) from Topt1 to Topt2 and falls to zero above the maximum temperature for photosynthesis (Tfactor = 0). BAMnut uses this temperature factor to adjust the crop growth response to temperature.
The water balance in BAMnut considers three soil layers (Figure 4). Changes in water content are calculated for each layer separately, from rainfall, drainage, soil evaporation and water uptake by roots. Water limited growth (WLG) is the maximum growth rate that the water uptake potential of roots allows for. When growth is water limited, transpiration equals potential water uptake (Upot) and:
Where:
WLG = water limited growth
Upot = potential transpiration (maximum uptake by roots)
= transpiration equivalent (g kPa kg-1)
D = drainage (mm d-1)
Drainage (D) occurs when the net flow of water into a certain layer is more than the amount required for that layer to reach Field Capacity (FC). The surplus water then drains to the deeper layer.
Where:
D = drainage (mm d-1)
= actual soil moisture (volume %)
FC = soil moisture % at field capacity (volume %)
z = thickness of the soil layer (mm)
PET is calculated using an equilibrium evaporation concept as modified by Priestley and Taylor (1972). This allows the calculation of approximate daytime net radiation and equilibrium evaporation, assuming that the stomata are closed at night and therefore that no PET occurs during this period. PET is calculated as 1.1 times the equilibrium evaporation to account for the effects of unsaturated air. The multiplier is increased above 1.1 to allow for advection when the maximum temperature is greater than 35°C, and reduced for temperatures below 5°C, to account for the influence of low temperatures.
Potential soil evaporation is the potential evaporation minus transpiration. The actual soil evaporation is the lowest of two values; potential soil evaporation and soil evaporation calculated for a soil that dries within the time period. This consideration is consistent with the two-stage concept of Ritchie (1972).
Soil evaporation = ESO (potential soil evaporation) if Ecum < Upot
Otherwise:
Soil evaporation = 
Where:
Ecum = accumulated soil evaporation (mm d-1)
Upot = potential transpiration (maximum uptake by roots)
DAR = days after the last rain (d)
Evaporative demand is defined as the amount of water transpired in order to realise a certain light limited growth rate. As both photosynthesis and transpiration are based on canopy gas exchange, BAMnut assumes a close relationship between transpiration and dry matter production. This is because changes in stomatal resistance will equally affect both carbon assimilation and transpiration.
Water limited growth is often calculated as the product of potential water uptake and a crop specific (constant) water use efficiency (WUE). BAMnut uses the transpiration equivalent, W (g kPa kg-1), according to Azam-Ali et al, (1994). Water use efficiency is not treated as a crop specific constant but a variable that responds negatively to changes in atmospheric saturation deficit. Azam-Ali et al, (1994) defined W as a crop specific constant that relates to water use efficiency as follows:
WLG = Upot * WUE
Where:
WUE = water use efficiency (g kg-1)
= transpiration equivalent (g kPa kg-1)
D = atmospheric saturation deficit (kPa)
WLG = water limited growth
Upot = potential transpiration (maximum uptake by roots)
Roots tend to adopt a distribution that exponentially reduces with depth. This is similar to the inverse square root function used by Monteith et al., (1989). BAMnut calculates a total root length from the root biomass using a specific root length factor, RLfactor. Root density is calculated as an exponential function of depth.
Before dealing with the actual water uptake, the potential water uptake must be known to determine whether growth is light limited or water limited. The water uptake by roots can then be calculated from the actual growth rate.
Potential transpiration equals potential water extraction from the soil by roots. Its magnitude depends on the depth and density of the root system and on the available soil water. A maximum uptake rate Umax in mm(water) per mm (soil) is defined with a given value dependent on crop and soil properties. This maximum uptake rate can be realised in a soil that is at field capacity and is fully exploited by roots. When either soil moisture or root density is below optimum the potential water uptake is reduced. The relative potential uptake rate U at a certain depth in the soil is calculated as:
Where:
Upot = relative water uptake rate (mm (water) mm-1 (soil) d-1)
Umax = maximum relative water uptake rate (mm (water) mm-1 (soil) d-1)
AW = available water above permanent wilting point (mm)
AWmax = available water at field capacity (mm)
RD = root density (m m-3)
RDsat = maximum effective root density (m (roots) m-3)
Finally, the actual water extraction (U) in layers 1 and 2 can be calculated from the potential water uptake and the ratio of actual to potential transpiration.
An unstressed crop is one that grows at a rate limited only by the availability of light. If water supply cannot match the transpirational demand, then the crop is said to be stressed and growth proceeds at a rate dictated by water availability. Water stress in the model is defined as the ratio of actual available water to potential available water in the soil. Water stress in the model affects L and shoot production. Another stress concept is defined in the model as the ratio of water limited growth to light limited growth. This correction factor affects the harvest index and fraction of dry weight allocated to roots.
Table 1 shows the observed values of harvest index, pod yield and total above ground biomass across all the experiments involved in the development of BAMnut (Bannayan et al., 2000). Due to yet unquantified genotype/environment interactions bambara groundnut, particularly in rainfed growing conditions, shows a high individual plant variability in harvest index and subsequently in pod yield. The simulated harvest index includes the range 0.01 to 0.58. The Root Mean Square Difference (RMSD) of harvest index simulation in this study is 0.19. However, ignoring the experiments (3 out of 11) with unexplained variability in harvest index would improve the RMSD of harvest index to 0.07 and P values would decline to 0.04. Figure 5 shows the comparison of simulated against observed values of harvest index across all experiments shown in Table 1.
Figures 6 and 7 show the comparison of observed and simulated pod yield and shoot weight respectively. The model is able to simulate pod yield and shoot weight with reasonable accuracy, with RMSD of 23.9 and 180.7 g m-2 respectively. However, it is expected that with more experiments that examine crop partitioning during the reproductive stage and close monitoring of soil water, there is scope to substantially improve model simulation in all aspect of growth.
Shoot biomass, pod yield and harvest index of bambara groundnut
across all experiments used in the development of the BAMnut model (Bannayan et al., 2000)
Site |
Landrace |
Irrigated / Rainfed |
Shoot biomass (g m-2) |
Pod yield (g m-2) |
Harvest index |
Tanzania |
DodR |
Rainfed |
279 |
55.6 |
0.20 |
Tanzania |
DodR |
Rainfed |
215 |
29.7 |
0.14 |
Tanzania |
DodR |
Rainfed |
61 |
2.4 |
0.04 |
Tanzania |
DodR |
Rainfed |
144.6 |
35.9 |
0.13 |
Tanzania |
DodR |
Rainfed |
121.2 |
47.4 |
0.39 |
Tanzania |
DodR |
Rainfed |
78.8 |
5.4 |
0.05 |
Tanzania |
DodR |
Rainfed |
192.5 |
77.8 |
0.17 |
Tanzania |
DodR |
Irrigated |
575.3 |
332.9 |
0.19 |
Nottingham |
DodR |
Irrigated |
535.8 |
284.4 |
0.53 |
Nottingham |
DodR |
Irrigated |
661.6 |
310.9 |
0.46 |
Nottingham |
DodR |
Rainfed |
118 |
3.8 |
0.03 |
Nottingham |
DodR |
Rainfed |
111.9 |
0.3 |
0.0 |
Nottingham |
DipC |
Irrigated |
761.9 |
443.4 |
0.58 |
Nottingham |
DipC |
Irrigated |
565.3 |
274.8 |
0.48 |
Nottingham |
DipC |
Rainfed |
105.4 |
12.4 |
0.12 |
Nottingham |
DipC |
Rainfed |
156.9 |
18.4 |
0.12 |
Agronomic models are traditionally used for point or site-specific applications. This is often because of limitations in data availability and computer technologies. Most process-based models have examined temporal variation using point data from specific sites and, again, provide outputs that are site specific. Because agriculture is a spatial activity, there is growing interest in placing site specific information into spatial and long-term perspectives. GIS facilitates the storage, manipulation, analysis and visualisation of spatial data (Hartkamp et al., 1999). Therefore linking GIS with agronomic crop models is attractive because it permits the simultaneous examination of spatial and temporal phenomena. Spatial visualisation of the results from models significantly enhances our understanding and interpretation of simulation results (Engle et al., 1997) and provides an opportunity for complex spatial analyses of the model results (Campbell et al., 1989; Stoorvogel, 1995). By analysing the spatial patterns of simulated yield there is an opportunity to improve production estimates and highlight vulnerable areas, for example those that are prone to drought (Carbone et al., 1996). However, the major drawback with such work is the limited availability of input climate and soil data that precludes the use of the more sophisticated simulation models.
To integrate BAMnut into a Geographical Information System (GIS) it was first necessary to select and evaluate the data required as inputs to the model. Two important limitations were placed in this study to save costs. First, only already digitised or computer ready data could be used for the analysis and, second, the data had to be comparable world-wide.
Note: The relatively poor fit of the model (Figures 5, 6 and 7) illustrates the difficulties involved in modelling an underutilised crop for which there is little supporting data. Future studies will aim at identifying and modelling the causes of the variability which are likely to be genetic, i.e. within and between landrace variation.
To adapt the model for this study it is assumed that the crop does not begin to grow until the accumulated rainfall from the first day of the year is more than 10mm. Another assumption is that frost killing of the crop would occur at -10 °C, i.e. total absence of the crop in the areas where this temperature may occur. Unlike many major crops for which experimental evidence is available, the above assumptions on bambara groundnut growth were based on subjective interpretation and similar experimental evidence for pearl millet - a crop which grows in agro-ecological zones that are typical for bambara groundnut. In this study, the phenological characteristics of the Tanzanian bambara groundnut landrace Dodoma Red were used for model development. Therefore, total crop duration is assumed to be equivalent to a thermal time of 1900 °Cd.
According to the GIS dictionary, maintained by the Association for Geographic Information (AGI), and the Web page of Edinburgh University Department of Geography (www.geo.ed.ac.uk/agidict/welcome.html), a GIS is a computer system for capturing, storing, checking, integrating, manipulating, analysing and displaying data related to positions on the Earth's surface. Typically, a GIS is used for handling maps of one kind or another. These might be represented as several different layers where each layer holds data about a particular feature. Each feature is linked to a position on the graphical image of a map.
Layers of data are organised to be studied and to perform statistical analyses. Uses are primarily government related, e.g. town planning, local authority and public utility management, environmental, resource management, engineering, business, marketing and distribution.
GIS portrays the real world. A view of the world as depicted on a map surface reveals that the surface consists of either points, lines or polygons. Thus roads would be lines, houses are usually points, and gardens or fields polygons. In a GIS there are two basic methods which the computer may use to store and display spatial data - `vectors' or `rasters'. These methods differ in the manner by which spatial data are stored and represented. FAO's Environment and Natural Resources Service of the Sustainable Development Department (SDRN) (www.fao.org/sd/eidirect/gis/chap3.htm) provide useful comparisons of vector and raster systems in summary form.
One of the powerful features of GIS packages is that statistical summaries of layers/coverages, model stages or outcomes can easily be obtained. Statistical data can include area, perimeter and other quantitative estimates, including reports of variance and comparisons among images. A further powerful analytical tool that aids understanding of outcomes is visualisation of outcomes through graphical representation in the form of 2D and 3D maps. For example, entire landscapes and watersheds can be viewed in three dimensions, which is very valuable in terms of evaluating spatial impacts of alternative decisions. Also, techniques have been developed to integrate GIS with additional tools such as group support systems, that allow interactive scenario development and evaluation and support communication among stakeholders via a local area network (LAN) (e.g. Faber et al., 1997). Currently, there is also rapid development and deployment of Internet-enabled GIS tools, that allows a wider community of decision-makers to have instant access to spatial data. All of these tools are constantly being added to GIS packages and can be of great value.
Weather has a major influence on a wide range of biological processes including agricultural production. The weather data often needed in relation to crop growth and yield include rainfall, maximum and minimum temperature, solar radiation, some measure of atmospheric humidity and wind. However, daily records that include all these elements are rare or are of insufficient duration for desired applications. In particular, in many regions of the world, distances between meteorological stations mean that it is difficult to assess the likely weather conditions at intermediate locations. Therefore, weather generator programs that are able to generate long series of weather records from limited existing data are useful. BAMnut requires daily weather data. However, these data are not available across the world. To solve this problem, a daily data weather generator (Matthews and Stephens, 1996) was used. Stochastic weather generators (Richardson, 1981; Geng et al., 1986; Hutchinson, 1991; Racsko et al., 1991) can use historical weather data from a site to provide daily sequences of the main weather parameters that are statistically similar to the observed data from which they were derived. This approach can then be used to provide weather inputs for crop growth models (Bannayan and Crout, 1999).
In this study, the Turbo Pascal version of the weather data generator developed by Matthews and Stephens (1996) was adapted in Visual Pascal to generate the required daily weather data (Figure 8).
The observed climate data from the University of East Anglia Climate Research Unit (CRU) (www.cru.uea.ac.uk/) available through the Intergovernmental Panel on Climate Change (IPCC) Data Distribution
(http://ipcc-ddc.cru.uea.ac.uk/cru_data/examine/have_index.html) was found to be the most comprehensive world climate data available and provided the main inputs to the weather generator. Data from the CRU included mean monthly climate data for global land areas, excluding Antarctica, for the period 1961-1990. The mean 1961-1990 climatology of seven variables were selected as inputs for the model developed in this study: Rainfall (mm d-1), Radiation (W m-2), Wet Day Frequency (Days), Maximum Temperature (°C), Minimum Temperature (°C), Vapour Pressure (kPa) and Wind speed (m s-1). For full details of these variables please refer to the Data Description Pages - Climate Baselines - CRU Global Climate Dataset (http://ipcc-ddc.cru.uea.ac.uk/cru_data/examine/cru_climate.html). The procedure to import these files into Arc/Info (GIS software) is presented in the Appendix.
Based on the format of the Observed Climate Download files
(http://ipcc-ddc.cru.uea.ac.uk/cru_data/datadownload/observed/climatology_download.html), the world is represented on a map in rectangular form as a GIS raster comprising 720 columns and 360 rows. Each raster cell has a resolution of 0.5º latitude by 0.5º longitude i.e. equivalent to 50 km x 50 km at the equator.
Based on the number of columns and rows, the total number of raster cells that comprise a single climate map are 259,200 i.e. 720 x 360 cells. Of these, 62,482 cells correspond to the land areas and the rest (196,718 cells) to missing values in the climate data (Antarctica, oceans and major inland water bodies).
Since most of the study was based on the CRU data, the cell size and geographic projection of one of these parameters was chosen as the base map to standardise map extensions. Thus, all map outputs derived from the model, have the same CRU map extensions.
Data inputs and outputs for the weather generator are based on the CRU climate map extensions. CRU climate data in ASCII form were downloaded, imported, converted to raster form and prepared using UNIX Arc/Info GRID i.e. the raster module of Arc/Info. Once prepared, the data were reconverted to ASCII form (see Appendix for details). The prepared ASCII data reside in a single directory in a PC. The adapted weather generator is able to create data by user-defined coordinates by defining the latitude and longitude values for the top left and bottom right corners of the desired area. For example, the settings for an area comprising the United Republic of Tanzania and adjacent land areas, would be top left latitude 0, longitude 28, and bottom right latitude -12, longitude 41. Computer memory problems were encountered due to the number of files that the generator had to create (i.e. 62,482). However, because the model comprised user-defined coordinates, the desired results were obtained by splitting the world into 30 sections.
The weather generator only processed those rasters that represented land areas. Missing values in the climate data (Antarctica, oceans and major inland water bodies) that were assigned integer values of -9999 were not processed and thus retained their original value. For each raster containing a single monthly climate value, the generator creates a file with 365 daily weather records. Each record is automatically labelled with an ID (e.g. 90001) that corresponds to its geographical location in the CRU map, and each contains daily data on solar radiation (SRAD), maximum temperature (TMAX), minimum temperature (TMIN), rainfall (RAIN), evapotranspiration (EVAP), vapour pressure (MNVP), windspeed (WIND) and CO2 ( ACO2) (see Appendix). As an example,Figure 9 shows the comparison of one year simulated weather data for Sutton Bonington in the UK with observed weather data at that site, for radiation, minimum and maximum temperature and rainfall. The general pattern of both generated and observed data is similar.
