Spatial delineation: crop plot boundaries

Crop field boundaries were provided by the Agricultural Geo-referenced Information System (AGIS) developed by the South African National Department of Agriculture (available online from www.agis.agric.za). These data were available for the provinces of Free State, Gauteng, Northwest and Mpumalanga. The field boundaries in this dataset were determined using the Producer Independent Crop Estimate System (PICES) which combines satellite imagery, Geographic Information System (GIS), point frame statistical platforms and aerial observations (Ferreira et al. Reference Ferreira, Newby, du Preez, Baruth, Royer and Genovese2006). Satellite imagery of crop field of cultivated fields was obtained from the SPOT 5 satellite at a 2·5-m resolution. Crop field boundaries were then digitized using GIS. When cloud-free satellite images were not available, field polygons hidden by clouds were removed before processing. This ensured a more accurate dataset. Over the four regions of interest, PICES distinguished c. 280 000 plots covering an area of c. 6·5 million hectares.

To approximately match the resolution of the crop growth indicator data described below, which were only available at the 250-m resolution, the analysis was limited to plots larger than 6·25 ha. This restricted the sample to 213 110 crop fields. A geographical representation of the crop fields’ location is presented in Fig. 1.

Fig. 1. Crop plot location in South Africa.

Crop types

Within each crop plot described above, AGIS provided information on the crop cultivated. Crop types were determined using the digitized satellite images described above. Sample points were selected randomly and surveyed by trained observers from a very light aircraft in order to determine crop type (Ferreira et al. Reference Ferreira, Newby, du Preez, Baruth, Royer and Genovese2006). Crop information collected during the aerial surveys on the sample points was used as a training set for crop type classification for each field and for accuracy assessment. For crops planted sparsely, field verification on certain sample points was not possible and therefore larger areas were considered to include these crops. These estimated crop classifications were checked against a producer based survey for the Gauteng region. The Gauteng census survey showed that less than 1·8% of crop types had been misclassified.

All in all, seven summer crops were distinguished (classification of winter crops was generated for the season 2007/08 only, therefore these crops were not considered in the analysis): cotton, dry beans, groundnuts, maize, sorghum, soya and sunflower. Given the small number of cotton observations (110 plots over only one province), these were excluded from the analysis. Although the data also identified fallow and pasture plots, these were also not considered given the focus of the analysis on cropland.

Crop classification data were available for the summer season 2006/07 for the provinces of Free State, Gauteng, Northwest and Mpumalanga, and for one province only, Free State, for the summer season 2007/08. A geographical representation of crop types for each season is provided in Fig. 2. Figure 3 provides a close-up representation of crop type change across seasons. As can be seen, crops showed patterns of alternation between crop types and fallow/pasture.

Fig. 2. Crop type location for the summer seasons 2006/07 and 2007/08.

Fig. 3. Crop type changes across the summer seasons 2006/07 and 2007/08.

Crop growth measure

Crop biomass production was estimated using the NDVI. Vegetation indices such as the NDVI are particularly attractive as they provide consistent spatial and temporal representations of vegetation conditions. As a matter of fact, numerous studies have demonstrated that NDVI values are significantly correlated with crop yields including wheat (Das et al. Reference Das, Mishra and Kalra1993; Gupta et al. Reference Gupta, Prasad, Rao and Nadham1993; Doraiswamy & Cook Reference Doraiswamy and Cook1995; Hochheim & Barber Reference Hochheim and Barber1998; Labus et al. Reference Labus, Nielsen, Lawrence, Engel and Long2002), sorghum (Potdar Reference Potdar1993), corn (Hayes & Decker Reference Hayes and Decker1996; Prasad et al. Reference Prasad, Chai, Singh and Kafatos2006), rice (Quarmby et al. Reference Quarmby, Milnes, Hindle and Silleos1993; Nuarsa et al. Reference Nuarsa, Nishio and Hongo2011), soybean (Prasad et al. Reference Prasad, Chai, Singh and Kafatos2006), barley (Weissteiner & Kühbauch Reference Weissteiner and Kühbauch2005), millet (Groten Reference Groten1993) and tomato (Koller & Upadhyaya Reference Koller and Upadhyaya2005). Moreover, NDVI has also been shown to provide a very good indicator of crop phenological development (Benedetti & Rossini Reference Benedetti and Rossini1993).

The NDVI index is calculated using ratios of vegetation spectral reflectance over incoming radiation in each spectral band. More specifically, NDVI can be formulated as:

where the difference between near-infrared reflectance (NIR) and visible reflectance (VIS) values are normalized by the total reflectance and vary between −1·0 and 1·0 (Eidenshink Reference Eidenshink1992). Negative and very low values corresponding to water and barren areas were excluded from the analysis by design. The NDVI data were extracted from the MOD13Q1 dataset (available online from: https://lpdaac.usgs.gov/lpdaac/content/view/full/6652), which regroups reflectance information collected by the MODerate-resolution Imaging Spectroradiometer (MODIS) instrument operating on NASA's Terra satellite (Huete et al. Reference Huete, Didan, Miura, Rodriguez, Gao and Ferreira2002). The NDVI estimates were available as 16-day composite indices at a resolution of 250 m. Area-weighted averages of the 16-day NDVI values for each crop field were calculated using the ‘zonal statistics’ tool in ArcGIS.

Growing season

Crop growing seasons are characterized by the planting date and the phenology cycle, which determine the length of the season. In South Africa, planting dates are spread from October to December in order to reduce the vulnerability to erratic rainfalls (Ferreira et al. Reference Ferreira, Newby, du Preez, Baruth, Royer and Genovese2006). At the same time, however, phenology cycles also differ among crops. The TIMESAT program (Jönsson & Eklundh Reference Jönsson and Eklundh2002, Reference Jönsson and Eklundh2004) was used to determine crop- and field-specific growing seasons. The algorithm within the software is commonly used to extract seasonality information from satellite time-series data. Within this context, it allows one to approximate the start and end of growing seasons based on distribution properties of NDVI. The repartition of growing season for each crop is presented in Fig. 4. This bar chart shows that within the area considered, groundnuts had the shortest growing season, whereas sunflower had the more widespread planting period.

Fig. 4. Crop growing season estimated using Timesat. Notes: Average growing season bars represent the average start and end of growing season for each crop. Start and End range bars represent respectively start and end dates of growing seasons comprised between the 10th and the 90th percentile.

Using these growing season estimates for each crop plot, it was also possible to determine the stage of the biomass development within the cropping season. In this exercise, the position of each 16-day period was determined relative to the length of the cropping season. For instance, the first 16-day period of a 160-day cropping season was assigned the value 0·1, and the last was assigned the value 1. This measure therefore accounts for the difference in growing season length of each crop plot.

Weather

Daily rainfall data were extracted from the rainfall estimation algorithm RFE (version 2.0) dataset implemented by the National Oceanic and Atmospheric Administration (NOAA) – Climate Prediction Center (CPC). These data, which were generated from a combination of rain gauges and satellite observations, were available at FEWS NET Africa Data Portal (available online from: http://earlywarning.usgs.gov/fews/africa/index.php) at the 0·1° resolution (c. 10 km).

Reference evapotranspiration (ETo), which represents the evaporative demand of the air, was calculated using the Penman–Monteith equation following the FAO methodology (Allen et al. Reference Allen, Pereira, Raes and Smith1998). These data are also available from: http://earlywarning.usgs.gov/fews/global/index.php: this source labels ETo as ‘potential evaporation’. However, as noted in Allen et al. (Reference Allen, Pereira, Raes and Smith1998), ‘the use of other denominations such as potential ET is strongly discouraged due to ambiguities in their definitions.’ Daily ETo data at 1° resolution were calculated using a 6-hourly assimilation of conventional and satellite observational data of air temperature, atmospheric pressure, wind speed, relative humidity and solar radiation extracted from the NOAA's Global Data Assimilation System.

Irrigation

The AGIS crop boundaries dataset also provides information regarding irrigation for each crop plot. As displayed on the left-hand side of Fig. 5, cropland in South Africa was mainly rain-fed. Moreover, the right-hand side of Fig. 5, which represents a detailed view of the crop plots, shows that irrigated crop plots were generally clustered around streams. It should be noted that the lines representing streams were not representative of the width of the actual streams, which may explain the ‘gap’ between the plots and the streams.

Fig. 5. Crop plots irrigation.

Other water sources

To account for water sources other than local precipitation, the proximity of crop plots to streams and the daily flow of these were calculated. The proximity of each crop plot to a river or stream (perennial and non-perennial) was estimated using the river network of the African continent from the HYDRO1K dataset (USGS 2011). Stream flow was estimated using the Geospatial Stream Flow Model (GeoSFM) (Artan et al. Reference Artan, Asante, Smith, Pervez, Entenmann, Verdin and Rowland2008 ), which simulates the dynamics of runoff processes using spatial information on river basin and network coverage, land cover type, soil characteristics, and daily precipitation and evapotranspiration data. River basins in South Africa were delineated using the HYDRO1K dataset, which provides drainage basin boundaries data derived from river network and flow direction data. Soil characteristics (water-holding capacity, hydrologically active soil depth, texture, average saturated hydraulic conductivity) were extracted from the Digital Soil Map of the World (FAO 2011). The GeoSFM model produced daily stream flow in terms of cubic meters per second (m³/s). Each crop plot was then assigned to a river basin and its corresponding river flow. For crop plots spreading over more than one river basin, the basin to which the plot belongs is determined by the largest area share located in the basin.

Summary statistics

Summary statistics of time-invariant plot characteristics for each crop are provided in Table 1. Maize was the most prevalent crop with nearly 50 000 plots in the 2006/07 season. Groundnuts plots were on average the largest (37 ha). Irrigation summary statistics indicate that the irrigation rate for crops ranged from 4 to 7% (i.e. lowest for sorghum and highest for sunflower). Dry beans and groundnuts plots were located the furthest from perennial rivers, with an average distance of 13 km.

Crop plot time-series statistics are presented by crop type in Table 2 for all provinces over the 2006/07 season. Table 3 provides similar statistics for the Free State province over both the 2006/07 and 2007/08 seasons. The NDVI index, showing daily biomass productivity, was the largest for soya. Productivity was generally slightly larger during the 2007/08 season. One may also note that although the NDVI index is theoretically bounded, it never actually came close to either bound within this dataset.

The growing season length was the longest for dry beans and the shortest for groundnuts, with an average of 172 and 141 days, respectively. Weather variables show that sorghum and soya were grown in the wettest conditions (i.e. the highest rainfalls and the lowest ETo rates) during the 2006/07 season. Dry beans and soya were cultivated within the basin having the lowest stream flows in both seasons.

The skewness statistics show that the Stream flow and Rain were positively skewed and may need to be transformed.

Regression specification

In the current analysis, a vector of various weather and irrigation factors was considered to estimate the determinants of crop growth. The base regression specification was formulated as follows:

where p and t are plot and time indicators, respectively, X represents a vector of explaining variables, δ are the estimated coefficients representing the marginal effects and ε a standard independent and identically distributed (i.i.d.) error term. The vector X includes weather variables, represented by rainfall and ETo, and irrigation-related variables such as the distance to perennial and non-perennial rivers, stream flow and irrigation application. Many factors explaining crop growth, such as soil fertility, ozone concentration, crop variety, nutrient application and other management practices, were not included in the analysis. The omission of these explaining factors was an important issue for this, and many other, studies but was unavoidable due to data limitation. However, in order to control for region-specific fixed effects, a set of province factors was also included in all specifications. This regional distinction was deemed the most appropriate as it captures the geographic and political unobservable specificities. Also, it may reflect data collection discrepancies across regions as the data were collected at the province level. As a sensitivity analysis, regression (6) was re-estimated for the full sample using alternatives to the province factors. Climatic zone factors were considered first. The study area spreads over three major climate zones defined by FAO (1996): warm Sub-Tropics, cool Sub-Tropics and cold Sub-Tropics. A second alternative considered agro-ecological zones (AEZ) developed by Monfreda et al. (Reference Monfreda, Ramankutty, Hertel, Hertel, Rose and Tol2009), who defines zones globally by overlaying six categories of growing length periods with climatic zones. In the study area, five AEZ categories are distinguished. However, neither of these alternative regional indicators changed the estimation results in any noticeable qualitative or quantitative manner. Detailed results are available from the authors upon request. It should be noted that, since the full set of these factors would be perfectly correlated if included together, the Free State factor was excluded so that any marginal effects on the others must be interpreted in terms of additional marginal productivity relative to this reference province. Additionally, as these fixed effects assume that the explanatory variables coefficients are similar across provinces, the interaction of the province factor variables with each determinant were also included to relax this condition.

The statistical analysis was performed using Stata 12.0 (StataCorp 2011). To investigate the possibility that crop growth is spatially correlated, a Moran's I test (Moran Reference Moran1950) was conducted. Since this test indicated that the crop growth measure was spatially correlated, the non-parametric covariance matrix estimator proposed by Driscoll & Kraay (Reference Driscoll and Kraay1998) was implemented to obtain robust s.e. for all estimations.

To account for the skewness of the Stream flow and Rain variables, the log of Stream flow and the square root of Rain, which were deemed the most appropriate at reducing the skewness, were also considered. However, the results indicated that the transformed variables did not improve the fit of the regression and the distribution of the residuals. Therefore, for ease of interpretation, the Stream flow and Rain variables were kept in levels.

Regression results

Regressions results at the crop level are presented in Tables 4–6. These regressions were obtained through a selection process to remove non-significant secondary variables (i.e. non-linear terms and interaction terms) from the most general specification of Eqn (1). In order to make the results more legible, the dependent variable was scaled by a factor of 10 000 in all specifications. The crop samples were pooled across the four provinces. Differences between provinces were accounted for by including a set of province factors (the reference case is Free State) and their interaction terms with explanatory variables.

Rainfall and evapotranspiration were considered in the model to represent the effect of weather on crop biomass productivity. The Rain coefficients suggest that precipitation had a direct beneficial impact on sorghum and soya biomass productivity in all provinces. For dry beans, the beneficial effect was observed in the Mpumalanga province only. Rainfall had no significant effect on sunflower and groundnuts. Increases in evapotranspiration had a negative effect on dry beans, except in the Mpumalanga province, where it was beneficial to biomass productivity growth. For groundnuts, the effect of increased evapotranspiration was detrimental in all provinces, whereas it was beneficial for maize, sorghum and sunflower. The largest evapotranspiration effect was observed for sorghum.

In order to investigate whether there may be non-linearities in the relationship between these weather factors and cropland biomass productivity, their squared terms were included. Accordingly, there is strong evidence that evapotranspiration had a non-linear relationship with biomass productivity of maize, sorghum and sunflower. For these crops, the regressions indicate that evapotranspiration had a biomass productivity enhancing effect up to a certain point. The coefficients suggest that this threshold was about 7·4 mm/day for maize, 8·3 mm/day for sunflower and 10·3 mm/day for sorghum. In contrast, the impact of rainfall was better modelled by simply including it in its linear form.

To account for the effect of other forms of water availability on crop biomass productivity, the effect of the presence of irrigation on the crop plot was investigated. The results show that irrigation enhanced cropland biomass productivity substantially for all crops except sorghum, which was the less irrigated crop of the sample (<0·02 of the plots). The size of the coefficients suggests that irrigation was the most important for maize in the Northwest. More specifically, the estimated coefficient indicates that, in the Northwest, an irrigated maize plot had a 0·2 greater NDVI than a non-irrigated plot. In contrast, irrigation of a sunflower plot in Mpumalanga only increased biomass productivity by 0·003 NDVI.

Stream-related factors such as stream flow and the distance of each plot from perennial and ephemeral rivers were also considered. Stream flow had a positive direct effect on biomass productivity for most crops, although the quantitative effect was very small (e.g. one sd of river flow entailed an increase of less than 0·00005 NDVI). In a few cases (i.e. dry beans in Mpumalanga, maize in Gauteng and soya and sunflower in Mpumalanga), however, the increased stream flow appears to have had a detrimental effect on biomass productivity. For sorghum, the direct effect of stream flow was not significant.

Distance to perennial and non-perennial rivers were also significant determinants of the dependent variable. Generally, being closer to a perennial river increased the biomass productivity of a plot but being closer to an ephemeral river decreased it. For instance, for each kilometre closer to a perennial river, sunflower biomass productivity increased by up to 0·02 NDVI in Gauteng. In Mpumalanga, productivity was slightly larger for dry beans and sunflower plots being farther away from a stream. No effect was estimated for groundnuts. In contrast, being farther away from ephemeral streams increased biomass productivity for maize, sorghum and soya in the Free State and sorghum in Gauteng only.

Thus far, it was assumed that each of the explanatory factors had potentially only isolated effects on the biomass productivity of crops. This may arguably be a rather restrictive and unrealistic assumption. For instance, the importance of rainfall in providing water to crops depends on the degree of evapotranspiration. Similarly, the effect of river flow will be related to the distance of the plot from rivers. Moreover, the existence of irrigation may make the dependence on other time-varying water resources less important. To investigate these factors, a set of interaction terms was included. As can be seen for the regressions, this unearthed some interesting features from the data. When considering the interaction effect between rainfall and evapotranspiration, the results indicate that evapotranspiration not only had a direct effect on sorghum, but also reduced the productivity enhancing impact of precipitation by about 20%. Similar impacts were found for dry beans in Mpumalanga and soya in Northwest.

As gauged by the interaction term between the Irrigation and Rain variables, irrigation also appeared to reduce the reliance on precipitation for most crops except dry beans and groundnuts. Irrigation reduced the importance of rainfall as a water source for sunflower biomass production the most. When considering the combined effect of Stream flow with Irrigation, stream flow increased sorghum biomass productivity only if the plots were irrigated. For maize in Gauteng, in contrast, the negative effect of stream flow on biomass productivity was exacerbated by irrigation. For groundnuts in the Northwest and dry beans, stream flow had a smaller beneficial impact on biomass productivity in irrigated plots. Finally, the distance to perennial and ephemeral rivers can reduce the impact of stream flow for some crops. More specifically, the interaction terms of these factors with the stream flow proxy show that being farther away from a perennial river reduced the impact of stream flow on soya and sunflower in all provinces and for maize in Free State and Northwest, sorghum in Mpumalanga, and groundnuts and dry beans in Northwest.

All regressions included the growing season length, growing season stage and its square term. The growing season length unsurprisingly reduced the biomass productivity of plots within South Africa, as crops having a longer cropping season grow more slowly and produce less biomass daily. The growing season stage coefficients indicate that crop biomass increased as the growing season advanced and then decreased past an optimal point in the growing season. This inverted U shape is representative of the biomass evolution of crops along the phenological cycle. These results are consistent across all specifications in Tables 4–6.

The inspection of the residual for each crop-specific regression confirmed that variances are constant over the fitted range and that the residuals have a normal distribution.