Remote Sensing of Environment

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1 Remote Sensing of Environment 113 (2009) Contents lists available at ScienceDirect Remote Sensing of Environment journal homepage: Phenologically-tuned MODIS NDVI-based production anomaly estimates for Zimbabwe Chris Funk a,, Michael E. Budde b a U.S. Geological Survey and Climate Hazards Group, Department of Geography, University of California Santa Barbara, California, USA b U.S. Geological Survey Earth Resources Observation and Science (EROS) Center, Sioux Falls, SD, USA article info abstract Article history: Received 15 May 2007 Received in revised form 29 August 2008 Accepted 30 August 2008 Keywords: Crop production Yield Early warning Drought Africa Zimbabwe Timeseries Agricultural monitoring Phenology For thirty years, simple crop water balance models have been used by the early warning community to monitor agricultural drought. These models estimate and accumulate actual crop evapotranspiration, evaluating environmental conditions based on crop water requirements. Unlike seasonal rainfall totals, these models take into account the phenology of the crop, emphasizing conditions during the peak grain filling phase of crop growth. In this paper we describe an analogous metric of crop performance based on time series of Moderate Resolution Imaging Spectroradiometer (MODIS) Normalized Difference Vegetation Index (NDVI) imagery. A special temporal filter is used to screen for cloud contamination. Regional NDVI time series are then composited for cultivated areas, and adjusted temporally according to the timing of the rainy season. This adjustment standardizes the NDVI response vis-à-vis the expected phenological response of maize. A national time series index is then created by taking the cropped-area weighted average of the regional series. This national time series provides an effective summary of vegetation response in agricultural areas, and allows for the identification of NDVI green-up during grain filling. Onset-adjusted NDVI values following the grain filling period are well correlated with U.S. Department of Agriculture production figures, possess desirable linear characteristics, and perform better than more common indices such as maximum seasonal NDVI or seasonally averaged NDVI. Thus, just as appropriately calibrated crop water balance models can provide more information than seasonal rainfall totals, the appropriate agro-phenological filtering of NDVI can improve the utility and accuracy of space-based agricultural monitoring. Published by Elsevier Inc. 1. Introduction In food-insecure Africa, where two hundred million sub-saharan Africans were undernourished in 2002 (FAO, 2006), satellite-derived Normalized Difference Vegetation Index (NDVI) images are routinely used to identify poor pasture conditions (FEWS, 2000; Hutchinson, 1998), malaria (Hay et al., 2003), epizootic diseases (Linthicum et al., 1999), and damage caused by pests (Hielkema et al., 1986). NDVI, however, is not generally used to assess variations in crop yields or production. Atmospheric contamination, data continuity, and data latency limit the operational use of NDVI. This limited use may be contrasted with satellite observations of precipitation (Adler et al., 1994, Arkin et al., 1994; Huffman et al., 1995, 1997; Love et al., 2004; Xie & Arkin, 1996), which routinely drive crop yield and water requirement satisfaction index (WRSI) models. A well developed literature linking precipitation anomalies with agricultural impacts (FAO, 1977, 1979, 1986; Reynolds et al., 2000; Senay & Verdin, 2003; Verdin & Klaver, 2002) supports effective analysis and wide-spread Corresponding author. address: chris@geog.ucsb.edu (C. Funk). applications. In this paper, we present a general NDVI metric ( V ) that provides a WRSI-like metric of crop performance. V is used in combination with MODIS imagery and U.S. Department of Agriculture (USDA) production figures to estimate crop performance in Zimbabwe Background: early and recent NDVI-yield analyses Four results from the very extensive NDVI-crop literature are pertinent to this paper. First, a large number of studies document the close ties between vegetation indices and yields (Table 1). Taken together, these manuscripts suggest that mid-to-late season NDVI represents yields better than seasonal integrations or maximum NDVI values. Second, a smaller number of studies adjust NDVI time series or metrics phenologically. A third consideration involves the use of crop masks to isolate agricultural signals. A fourth aspect relates to the removal of pre-season noise. All four factors contribute to successful agricultural monitoring; we briefly review each in turn. A number of field studies have demonstrated strong relationships between corn and soy bean vegetation indices and plant phenology (Batista,1990; Daughtry et al.,1983; Ma et al., 2001; Rudorff & Ma et al., 1996; Shanahana et al., 2001; Tucker et al., 1979). Satellite remote /$ see front matter. Published by Elsevier Inc. doi: /j.rse

2 116 C. Funk, M.E. Budde / Remote Sensing of Environment 113 (2009) Table 1 Relevant yield/ndvi evaluation studies Year Authors/region/comments Metrics 1986 J.P. Malingreau Found that Max NDVI was a weak indicator of drought in Southeast Asia 1992 Maselli et al., Niger July NDVI 1992 p,r Rasmussen, Burkina Faso and Senegal NDVI integrated during the reproductive period 1997 Subtracted pre-growing season NDVI Max +10, 20, 3040 days until harvest 1996 Hayes and Decker, US Corn Belt Used post-maximum VI (week 34) 1998 p Hochheim and Barber, Western Canada MaxNDVI+3 weeks similar to V Maximum NDVI, Cumulative NDVI over season and average from Max NDVI+3 weeks 1998 Unganai and Kogan, Zimbabwe Used V CI =100 (N Nmax)/(Nmax Nmin) Found Jan Feb critical for temperature T CI =100 (Tmax T)/(Tmax Tmin) Late March critical for vegation index Yield V CI B 1 +T CI B S. M. E. Groten, Sahel End of season (September) NDVI 1993 N. A. Quarmby et al., Greece Cumulative NDVI 1993 Beneddetti and Rossini, Italy NDVI summed during the grain filling period 1995 Doraiswamy and Cook, Western U.S. Cumulative NDVI values for spring wheat during the grain-fill period 1998 Lewis et al. Maximum NDVI 1998 D. O. Fuller, Senegal End of season (September) NDVI Period of analysis (September) similar to April for Zimbabwe 2000 c Maselli et al., Sahel Found max correlation during mid-august to mid-september 2001 c Genovese et al., Spain Sum of NDVI between flowering and ripening Found best relationship for end of season NDVI Sum of NDVI over 60 days after maximum Used crop masking 2002 p J. F. Brown et al., United States Seasonal Greenness seasonally integrated NDVI Used NDVI-based start-of-season metric 2002 p Labus et al., Montana Fixed seasonal integrations (April September) Variable onset growth integrals r Variable onset NDVI growth integrals Strong NDVI relationship in August, about 1 1/2 months after peak NDVI Fixed 8-week growth periods End-of-month NDVI values 2005 Mkhabela et al., Swaziland 20-day NDVI average from February-to-March Strong performance except for Highveld 2005 c,r Freund, Kenya NDIF =N max N max,historic Crop smoothing, masking and averaging similar Metrics similar to Labus' growth integrals NDSUM=Sum(N N norm ) from onset to mid-season 2007 p,c Rojas, Kenya Cumulative NDVI from onset to end of season Crop masking/district averaging similar Maximum NDVI throughout the crop season Uses rainfall-based onset dates 30-day NDVI average around the NDVI Maximum Entries marked p used variable seasonal timing. Entries marked c used crop masking to make composites. Entries with r removed early season NDVI signals. sensing studies (Table 1) converge on similar results; yield-reflectance relationships are typically strongest after mid-season. For example, Rasmussen (1992) found that early season NDVI bore no significant relationship to millet yields in Burkina Faso (R 2 =0.1), while values from 30 days after the mid-season maxima until the end of season explained 93% of the variation in yields. Many of these studies were relevant to Africa, examining variations in the Sahel (Fuller, 1998; Groten, 1993; Maselli et al., 1992, 2000; Rasmussen, 1992, 1996) or Southern Africa (Unganai & Kogan, 1998; Mkhabela & Mashinini, 2005). Daughtry et al. (1983), Malingreau (1986) and Benedetti and Rossini (1993) commented on the weak relationships between seasonal maximum NDVI and yields. Rasmussen (1992) suggested that the mixture of herbaceous cover and millet blurred the NDVI maxima; looking 30 days beyond the NDVI maxima would yield the best results. Phenological adjustment can also assist in the analysis of NDVI. In their study of Canadian wheat yields, Hochheim and Barber (1998) utilized the timing of the NDVI maxima to phenologically adjust time series from different years. More recently, start-of-season has been used as a basis for adjustment. Start-of-season may be derived from characteristics of the seasonal NDVI curve (Brown et al., 2002; Reynolds et al., 2000; Rojas, in press) or precipitation data (Fruend, 2005). In the past, NDVI-based onset dates have been used to guide WRSI modeling (Reynolds et al., 2000). Conversely, precipitationbased onset dates have been used to inform NDVI analyses (Rojas, in press). Brown & de Beurs (submitted for publication) recently found a high level of correspondence between MODIS-based onset dates and field observations from Niger. Crop masking helps reduce the influence of non-agricultural vegetations signals. The earliest masking applications used NDVI thresholds to discard irrelevant locations (e.g. Maselli et al., 2000). Most recent masking operations are based on land use/land cover classifications derived from medium resolution optical satellite data (Freund, 2005; Genovese et al., 2001; Rojas, in press), and can improve yield estimation accuracies. Interestingly, Kastensa et al. (2005) have examined a different approach to masking that tailors masks based on the target signal being evaluated. Removing pre-season NDVI values is another means of isolating the agricultural vegetation signal. Rasmussen (1997) subtracted NDVI values from before the season, increasing estimation accuracy substantially. Labus et al. (2002) and Freund (2005) also implicitly removed pre-season NDVI by using metrics focused on NDVI growth. These parameters are based on NDVI changes, rather than raw NDVI values, and hence implicitly filter out pre-season conditions. Our present study advances previous applications of masking and phenological adjustment by developing and analyzing national, phenologically-adjusted, crop-weighted NVDI time series. These representative time series provide an easy to understand tool for visualizing and summarizing agricultural performance. We use precipitation-based start-of-season estimates, and remove pre-season NDVI signals. These phenologically-adjusted, crop-weighted NVDI time series show strong relationships to USDA production figures one month after peak grain filling Operational contexts: Zimbabwe the and seasons This work was carried out in and to address the US Agency for International Development's (USAID) need for information regarding agricultural conditions in Zimbabwe. In , a predicted drought (Brown et al., 2007; Funk et al., 2006, 2007), combined with reductions in cropped area and agricultural inputs, led to a 55% cereal production shortfall. An analysis of MODIS data, presented here, provided a clear, early and objective evaluation

3 C. Funk, M.E. Budde / Remote Sensing of Environment 113 (2009) of production anomalies. This was one factor contributing to an appropriate and timely international request for aid assistance in The study was carried out again in the spring of 2008, demonstrating the significant negative impacts of late seed dispersals and low February March rains. As we write, in the summer of Zimbabwe faces a 10,000% inflation rate and 80% unemployment rate. 2007/08 yields were the lowest on record, and the country faces a grain deficit of more than 1,400,000 MT, a quantity more than three times to the total 2007/08 crop production. In this context of high vulnerability, the early identification of production deficits have motivated timely humanitarian responses that will help mitigate famine conditions during the hunger season of Data 2.1. Data sources Three sources of data were used in this analysis: vegetation imagery, a regional landuse/landcover classification, and a time series of national maize production figures. We summarize each of these three data sources below. Moderate Resolution Imaging Spectroradiometer (MODIS) 500- meter 16-day maximum value NDVI composites (Huete et al., 1994) were used to evaluate surface vegetation conditions. These MODIS vegetation index data (MOD13A1) were derived from the Earth Observing System (EOS) Terra MODIS surface reflectances which have been corrected for molecular scattering, ozone absorption, and aerosols. The index is produced globally over land at 16-day compositing intervals and enables consistent spatial and temporal comparisons of vegetation condition. The regional land cover/land use database was produced by the Southern African Development Community (SADC) Council for Scientific and Industrial Research (CSIR, 2002). The 1-km resolution classification was based on a number of high resolution national land cover datasets that were merged together to produce a regional land use/land cover data layer. For Zimbabwe, the original dataset is a 1:250,000-scale map that was produced through a cooperative effort between the Forestry Commission and the German Development Cooperation using 1992 Landsat imagery. National maize production figures, produced by the U.S. Department of Agriculture (USDA) Production Estimates and Crop Assessment Division (PECAD), were used to train and evaluate regression models. USDA PECAD figures are routinely produced by best-ofscience approaches combining field assessments, crop model evaluation, and qualitative analysis of satellite imagery. The production figures used here are national grain production estimates taken from the PECAD Web portal ( aspx). While these assessments do include some remote sensing information, the estimation procedure used by PECAD is much different than that presented here. The International Production Assessment experts at PECAD evaluate crop model output, field assessments, crop tours, and national-level agro-meteorological reports, building an expert assessment through a collaborative process. These PECAD estimates are finalized after the end of the growing season. The production estimates shown here are empirically derived from NDVI alone, and are available at the close of the maize reproductive cycle. Finally, national/seasonal interpolated rainfall data ( , Funk et al., 2007) provided historical context for our study, and were used to estimate the seasonal start dates /08 onset date calculations Political and economic conditions in were substantially different than the previous through growing seasons. Large seed shortages limited farmer's ability to plant at the optimal onset of rains date (mid-november). At the provincial level, late seed distributions led to the following percent distributions of areas planted to maize in November, December and January: Mashonaland West: 15/20/65%, Mashonaland East: 22/63/15%, Mashonaland Central: 5/29/66%, Manicaland: 15/63/22%, Masvingo: 10/20/70%, Midlands: 21/35/44%, Matebeland South: 8/48/44% and Matebeland North: 1/66/33% (FEWS NET internal communication). To represent the various outcomes dependent on these planting dates, district level results were estimated for November, December and January start dates and then pooled based on the relative provincelevel maize area percentages. 3. Methodology 3.1. The V metric The V metric has been developed based on logic similar (but not identical) to the WRSI water balance metric. The seasonal WRSI is the accumulated ratio of actual versus optimal crop evapotranspiration from the onset of rains to the end of the season (Senay & Verdin, 2003; Verdin & Klaver, 2002). The onset of rains is typically estimated from satellite precipitation, and the end of season is determined by a cropspecific length of growing period (LGP). The crop water requirement is a function of potential evapotranspiration (PET, calculated via Penmann Monteith, Senay et al., 2007) and crop stage dependent plant growth coefficients. The WRSI identifies when plants tends to be most sensitive to water stress, and creates an index related the available water during that time period. In early warning applications, WRSI percent anomalies can identify areas experiencing crop water stress. In semi-arid regions of southern Africa, rainfall deficits are the primary cause of crop moisture stress (Unganai & Kogan, 1998). Although the WRSI estimates actual evapotranspiration (ET) by way of extended moisture balance considerations, it has also been shown that MODIS vegetation indices can be a good proxy for actual evapotranspiration (Chong et al., 1993; Nagler et al., 2005a,b). This suggests that the sum of NDVI increases during the mid-to-late season growing period should be a good indicator of crop evapotranspiration. In general, a broad range of phenologically-sensitive NDVI sums ( V ) can be written as: onsetþlgp onset ET i V ¼ onsetþlapþlag onsetþlag ðndvi t NDVI onset Þ: ð1þ The V calculation (Eq. (1)) incorporates a lag that combines delays associated with the temporal sensitivity associated with grain filling and the delayed response of vegetation to rainfall (Funk & Brown, 2005; Ji & Peters, 2003; Kerr et al.,1989; Potter et al., 1999; Richard & Poccard, 1998). We also include a length of accumulation period (LAP). LAP determines the length of the window over which the NDVI is summed. NDVI onset is subtracted from V to remove the pre-onset influences associated with the previous dry and rainy seasons. The dates used in this study for the onset of rains were based on a simple rainfall accounting method defined as the first 10- day period in which at least 25 mm of rain fell, followed by two 10- day accumulation periods with a total of at least 20 mm of rain. These onset periods were then linked to the closest 16-day MODIS composite period Space time MODIS filtering and pixel-to-nation averaging Although Eq. (1) is physically plausible, there are a number of contamination sources that can confound the potential NDVI/ET and crop productivity relationship. Temporally, cloud and moisture contamination can influence the NDVI signal. Furthermore, vegetation signals from before or after the season contain fluctuations not related to grain filling; an onset of rains temporal re-alignment helps remove some of these effects. Finally, spatial filtering was used to minimize the influences of non-agricultural vegetation on V.

4 118 C. Funk, M.E. Budde / Remote Sensing of Environment 113 (2009) Fig. 1. This time series NDVI plot, for a single 500-m pixel, shows unsmoothed data in blue and temporally smoothed NDVI in red. The smoothing algorithm effectively corrects these erroneous NDVI values based on characteristics of the valid NDVI curve. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Temporal and spatial MODIS processing NDVI data may be affected by a number of phenomena that contaminate the signal, including clouds, atmospheric perturbations, and variable illumination and viewing geometry. Each of these reduces NDVI values. A time series smoothing technique developed by Swets et al. (1999) was used to minimize these effects. The technique uses a weighted least squares linear regression approach to smooth observations that are of poor quality as a result of clouds or other atmospheric contamination. A temporal window is used to calculate a regression line for each point in a time series. The window is moved one 16-day period at a time, resulting in a family of regression lines associated with each point; this family of lines is then averaged at each point and interpolated between points to provide a continuous temporal NDVI signal (Fig. 1). The smoothing technique also incorporates various weighting parameters for peak, slope, and valley points in the series. Since most sources of contamination tend to lower the NDVI values, peak points are given a higher weight than either slope or valley points. The result is a smoothed NDVI time series that minimizes the influence of contaminants while maintaining seasonal characteristics of the original data series. In order to minimize the influence of non-agricultural land cover types on V we applied a mask to the NDVI time series using a cultivated areas map based on the SADC regional land cover database (Fig. 2). The mask was used to calculate NDVI time series statistics for only those areas classified as cultivated lands. The end result of the temporal spatial smoothing procedure was a set of 61 characteristic district level NDVI time series covering the season through the 16-day MODIS period beginning on day of year 81 (March 22 April 6) of Because this analysis was Fig. 3. National average NDVI (top) ands composited onset-adjusted NDVI time series from the onset of rains forward (bottom). Also shown are annual PECAD maize production estimates. conducted prior to the availability of complete late season 2008 data, composites beginning on day 97 (April 7), day 113 (April 23), and day 129 (May 9) were filled by assuming seven-season average NDVI change, estimated from data Temporal re-alignment procedures NDVI changes that occur outside of the primary rain vegetation response period may not relate positively to increased crop productivity. For example, early in the season the clearing of agricultural lands (reducing NDVI) may be positively related to increased production at season's end. Similarly, once the NDVI responses associated with grain filling are complete, increasing greenness may represent late season cyclonic activity, which can hamper seed drying and harvesting activity. Late season greenness may also represent continued green-up in non-cultivated regions. Focusing on the mid- Fig. 2. Cultivated areas from the SADC land cover/land use database and MODIS masking procedure.

5 C. Funk, M.E. Budde / Remote Sensing of Environment 113 (2009) to-late season NDVI response helps identify crop-specific vegetation changes. This focus was achieved by estimating V over a set of dates indexed by the onset of rains, and specified by the lag and LAP coefficients in Eq. (1) National averaging and production anomaly regressions The space time filtering and onset-specific V calculations produce an 8 by 61 matrix of V values, representing the eight seasons ( to ) and 61 districts analyzed. District V percent anomalies were then calculated by dividing by the district mean and scaling by 100. District level weighted averages, based on cultivated area, were then used to develop national-level V percent anomalies. These values were then regressed against USDA PECAD maize production anomalies for a range of lag and LAP specifications. The season was screened from the regression process to limit the influence of the large structural changes that occurred within the agricultural system in This topic is discussed further in Section Results After temporally smoothing the NDVI data and building district and national-level time series, we visually examined time series of both NDVI and NDVI growth since the date of onset (Fig. 3). These time series have been derived using the cultivated area weighted average of the onset-adjusted district level data. The top panel in Fig. 3 shows the national average NDVI. At the onset of rains (about November 15th, on average for the through seasons), these NDVI time series have a substantial degree of variability (about 0.1 NDVI). These pre-season variations, which are fairly substantial in magnitude, should be unrelated to moisture availability during grain filling. Removing this component, by subtracting out the NDVI at onset date, produces time series that begin at 0 (bottom panel, Fig. 3). When averaged across the Zimbabwe districts, then onset date calculated from rainfall values varied little from season-to-season, with the average onset date being mid-november. The V calculation subtracts the first NDVI value at the onset date, so the time series begins at 0 and increases with vegetation green-up. Note the dramatic interannual variability in the dates of peak NDVI. These large variations suggest problems with using this indicator as a phenologic guide as used by Rojas (in press). The vigorous performance of is readily apparent, as is the poor productivity of the growing season. Mid-to-late season increases in NDVI are generally related to final vegetation status, but several seasons ( and ) begin with strong performance and then decline dramatically toward the latter part of the season. However, the converse does not hold; poor early season NDVI growth is generally not overcome by later season increases. This suggests similarities with the WRSI calculation: moisture deficits can occur early or late, but late moisture surpluses cannot replace early deficits. Seasonal maximum NDVI can isolate these strong early NDVI peaks, ignoring reductions occurring later in the season. The left-hand box in the bottom panel of Fig. 3 shows the time period (January February) during which rainfall most strongly predicts end-of-season WRSI (R 2 =0.7, ). The combination of typical late October /early November rainfall onset dates and the specific crop growth phenology of 90-to-120 day maize produces strong rainfall-crop performance sensitivity during this period. Given the 1-to-2 month lag between rainfall and vegetation response in this region (Funk & Brown, 2005; Richard & Poccard, 1998), V measures taken immediately after this period (right hand box, Fig. 3) would presumably give good results. This assertion is validated in the next section. Note that the onset date, modified to reflect abnormal seed distributions (cf. Section 2.2), was almost 48 days late, falling in late December. Late rains (February March of 2008) were poor, and the overall NDVI curve was quite low, on par with the poor and crop seasons (Fig. 3, top). Onset adjustment, factoring in the impact of late planting (Fig. 3, bottom) suggests a dramatic reduction in crop performance. Late planting, missing the bulk of the rains and NDVI increase, is clearly reflected in the onset-adjusted NDVI time series for V performance as a function of lag and LAP In order to explore the accuracy of the V metric, a set of experiments was conducted across a range of lag and LAP periods (Fig. 4). In all cases, a take-one-away cross-validated coefficient of determination (R 2 ) was used as our accuracy statistic. It is important to note that this statistic does not correct for the skill bias associated with the selection of model parameters. Given the short period of record available and the large number of parameters controlling the V metric, the accuracy levels presented are likely to overstate the true level of performance. These tests we calculated using the through seasons as inputs with USDA PECAD crop production values used our target. Increasing the lag and LAP values tended to increase the coefficients of determination (Fig. 4B), and these were high (greater than 0.85) across a broad array of lag and LAP combinations. This suggests that the V metric is representative and fairly tolerant of small changes in parameter settings. Of the two, lag (the number of 16-day periods since the onset of rains) appears much more important. The weak significance of the LAP setting may be caused by the smoothing of the NDVI data (Section 3.2.1). The combination of lag and LAP Fig. 4. Cross-validated V R 2 values based on comparison with , , , , and USDA PECAD national maize production figures. Panel A shows the cross-validated R 2 as a function of the last date used in the V calculation. Panel B shows the R 2 as a function of the length of accumulation period and the first date of the accumulation period (lag), measured from the onset of rains. The white dot in panel B denotes the lag/lap values (10, 2) used in the final production estimation.

6 120 C. Funk, M.E. Budde / Remote Sensing of Environment 113 (2009) Table 2 Comparison of V, NDVI maximum, and seasonal NDVI average metric correlations with PECAD production estimates Statistics calculated for each district and then averaged nationally Statistic based on national average NDVI time series R 2 /cross-validated R 2 Stdev B1 100 (%) Cross-validated R 2 Stdev 100 B1 (%) B 1 B 1 V s 0.95/ / NDVI Max 0.27/ / Seasonal NDVI Avg 0.47/ / Statistics are based on take-one-away cross-validation for 2001/02 through 2006/07 data. This table shows coefficient of determination (R 2 ) and the regression slope variability, expressed as a percentage of the mean slope. parameters can be used to identify the last 16-day period incorporated into V, and the summation through this date is strongly related to the model R 2, up to a maximum of twelve 16-day periods after onset. Given a typical late October/early November onset of rains, this is equivalent to a date falling in early April. Thus, grain filling in December January February relates strongly to February March early April NDVI. Inclusion of NDVI observations after this date can actually decrease the accuracy modestly. A lag of 10 and LAP of 2 were used in our analysis of the growing season. Among the class of good lag-lap combinations with R 2 values of greater than 0.85 in Fig. 4B, this combination had the earliest final date used in the V calculation, eleven 16-day periods after the onset of rains. This is important because we wanted to maximize the use of actual NDVI values available for the season (Section 3.2.1). For a typical onset date, the corresponding final MODIS period would composite observations from April 7 to April 22. As we shall describe below, the was atypical, having much later planting dates than normal V performance compared to maximum NDVI, seasonal NDVI and WRSI This section compares (Table 2) three seasonal metrics: V, seasonal maximum NDVI, and seasonally averaged NDVI. V was estimated per Eq. (1), with an offset of 10 and a LAP of 2. Seasonal maximum NDVI used the peak NDVI value between MODIS periods indexed by day 305 and day 129. Seasonally averaged NDVI utilized observations between MODIS periods indexed by day 305 and day 97 for each year. Two approaches were used to compute these statistics. In the first approach, district-based analysis, the NDVI performance metric was calculated for each season and sub-national district. Each district's cultivated area was then used to derive a national weighted average performance metric for each season. The second class of performance metrics was determined using the national time series of NDVI (cf. Fig. 3). This produced six sets of performance metrics, each composed of seven estimates. Take-oneaway cross-validated regression with PECAD production was then used to provide estimates of skill and stability (Table 2). The coefficient of determination (R 2 ) was used as a measure of estimation skill. The stability of the regressions was determined by the cross-validation standard deviation of the slope (B 1 ), coefficient, expressed as a percentage: 100 Stdev ð B 1Þ. For each season, that year's data was removed, B 1 the regression coefficients recalculated, and the withheld year's production estimated. As expected, given the linear nature of the operations involved, district level and national V metrics were highly correlated (R 2 =0.95), as were the seasonally averaged NDVI values (R 2 =0.99). The V performance, however, was much better than seasonal averaged NDVI, with cross-validated R 2 values of 0.87 at the district level and 0.86 at the national level (Table 2). In addition, the year-toyear variability in the cross-validated slope coefficients for this metric was small (7%). This suggests that using the spatial and temporal information contained in onset of rains imagery can improve results. This process tends to focus on the latter part of the growing season, consistent with numerous previous studies (See Section 1.1). Seasonally averaged NDVI performance was scale invariant: bad at both national and regional levels, only explaining 7 20% of the PECAD variance under cross-validation (Table 2). This result highlights the need to cross-validate short time series. This uncertainty is further reflected in the large year-to-year variability in the cross-validated slope coefficients; 16% of the average slope for the seasonally averaged NDVI. The very poor performance of the seasonally averaged NDVI metric is surprising. We would suggest three plausible explanations. The first probable cause stems from the fact that most NDVI growth occurs early in the season, in response to early (October November) rains (Funk & Brown, 2005), and is linked to growth during the vegetative stage of the plant. This large quantity of early vegetation growth has very little relationship to yields in semi-arid Africa (Rasmussen, 1992). Including this large NDVI growth in the seasonal accumulation actually degrades performance. Soil background signatures mixed with early season vegetation in the NDVI could impact this result as well. Another difference between V and seasonal averages or integrals involves the subtraction of pre-season NDVI. This nuance can help remove impacts from off-season weather, climate trends, alterations in land cover, and non-cultivated regions (Rassmussen, 1997). Fig. 5. National onset-adjusted NDVI curves constrained to begin within November, December and January. Also shown is a combination of these curves based on district level estimates of seed availability. The NDVI curve for 2006/2007 used the first available onset of rains date.

7 C. Funk, M.E. Budde / Remote Sensing of Environment 113 (2009) Fig. 6. Planting/onset date and V anomalies for Interestingly, performance of the seasonal maximum NDVI varied dramatically based on the means of calculation. This scale effect has been documented and discussed in De Cola (1997). De Cola evaluates the scale effects on various statistical relationships, evaluating their commutative properties. Aggregation (and averaging) commute across scales, maxima calculations do not. Metrics derived along the lines of V, which include various seasonal integrations with a fixed period of accumulation, can operate meaningfully across scales. Maxima estimates performed at a given spatial scale cannot be aggregated transparently. Criteria such as these should be considered when evaluating metrics for wide-area agricultural drought monitoring. Maxima calculated from the nationally averaged NDVI time series performed reasonably well (cross-validated R 2 of 0.55). On the other hand, when NDVI maxima were calculated on district level data and then averaged nationally, the correspondence with PECAD figures was very low (R 2 =0.0, Table 2). Examination of the aggregated district level NDVI maximum estimates shows that this approach performed poorly during the , , and seasons. These years stand out as having early ( ) or late ( , ) maxima (Fig. 3). One contributing factor may be the tendency for rainfall performance to reverse between the early and mid-growing season periods. For example, Husak et al. (2002) found that El Niño seasons with a wet October typically had below normal January March rains. Similarly, early season forecasts for (Funk et al., 2002b) and (Brown et al., 2007; Funk et al., 2006, 2007) accurately predicted a transition to mid-season deficits, while a forecast for anticipated the opposite transition (Funk et al., 2003). Such intra-seasonal variations could confound district level maxima calculations and seasonal NDVI averages. Note, as already mentioned, that the poor performance of NDVI maxima has been Fig. 7. PECAD (light gray boxes) and V (dark gray boxes) estimates of Zimbabwe national maize production. Fig. 8. Scatterplot of the seven seasonal MODIS and PECAD national maize production estimates. The season isshownwith 95% confidence intervals, based on thecrossvalidated standard error of 57,000 tons, this results in an estimate of 0.33±0.11 millions of tons.

8 122 C. Funk, M.E. Budde / Remote Sensing of Environment 113 (2009) documented previously (Benedetti and Rossini, 1993; Daughtry et al., 1986; Malingreau 1986). In summary, V performed well, even under cross-validation. Furthermore, the V metric is a linear computation, giving similar results whether calculated at the district level and averaged nationally, or calculated directly based on the national averages. This property lends scale-invariance to the metric, assisting analysis on both national and district scales. Maximum NDVI, on the other hand, is a non-linear function, providing substantially different results depending on the order of operations used Spatial and temporal variations in V productions estimates One advantage of the V heuristic is that it allows the NDVI analysis to represent agricultural practices such as planting dates. This turned out to be very important in the 2007/08 season, since economic and political disruptions within Zimbabwe resulted in dramatic seed shortages, with a bulk of the actual planting occurring in many districts as much as two months beyond typical start dates. These late starts combined with far below normal February/March rainfall to produce large reductions in nationally composited onset-adjusted NDVI (Fig. 5). Using November onset dates in the V calculation (Eq. (1)) produces a time series slightly higher than series. Unfortunately, limited seed availability caused many fields to be planted in December, January, or even in February. The V time series constrained by these late onset dates are substantially lower, indicating much lower yields indicated by NDVI decreases during the main period of crop biomass gain. Blending these results by the spatial distribution of estimated planting dates (see section 2.2) produces a national NDVI curve much below the 2006/07 season. Fig. 6 shows the spatial distribution of onset date anomalies, highlighting the very late starts in the productive southeast and north-east parts of the country. These late-starting districts are associated with very dramatic V anomalies, with V values of less than 40% of the to average. Many, if not all, of these districts are likely to experience substantial production deficits. Fig. 7 shows USDA PECAD production anomalies, together V regression estimates. The drop between and is precipitous, reflecting dramatic changes in agrarian management practices. Crop production during the season may be as poor as the lowest season on record: the 1991/92 drought. Fig. 8 shows a scatterplot of recent PECAD and V production anomalies, expressed in units of millions of tons. The V estimate (0.33±0.1 millions of tons) is approximately half of the poor season, on par with the worst drought year within the recent record: (Fig. 7). Recent (August, 2008) USAID yield assessments confirm this result, with maize yields estimated at 0.27 MT/ha, the lowest on record. Fig. 9 shows spatial plots of V totals and anomalies for through These images have been placed in order with the seasonal PECAD totals, from lowest to highest. Even in the raw V imagery the variation between low and high production years is apparent. 5. Discussion 5.1. Summary of results Consistent with numerous studies (Section 1.1), this paper demonstrates that national-level crop production anomalies in semi-arid Africa may be successfully monitored via vegetation index time series, assuming that appropriate spatial and temporal filters are applied to the data, and pre-season non-agricultural signals are removed. Using a priori cultivated Fig. 9. V and V anomalies for all seven seasons, 2001/02 through 2007/08, ranked from worst to best based on PECAD production estimates.

9 C. Funk, M.E. Budde / Remote Sensing of Environment 113 (2009) within this window (Rassmussen, 1992). With 500-meter data, it is difficult to completely mask out non-cultivated lands and considerable sub-pixel mixing may occur. Especially problematic may be grassland, fallow fields, or other natural vegetation that responds strongly to early season rains. This vegetation may green vigorously upon receipt of October November rains, yet mid-season rains and production may be low (cf in Fig. 3). In general, Zimbabwe vegetation responds more vigorously to early season rains (Funk & Brown, 2005). This creates a discrepancy between rainfall receipts and NDVI green-up. At coarse (1 ) scales, moderate October November rains are associated with strong NDVI increases (Fig. 10). On the other hand, heavier December January rains are associated with smaller large-scale NDVI increases. The cultivated area NDVI traces examined here (Fig. 3) suggest that these late season NDVI increases may be the most important. This result is consistent with some of our previous food security studies which traced the observed El Niño-crop production deficits relationship (Cane et al., 1994) to December January rainfall shortages (Funk et al., 2002a,b) and February March NDVI decreases (Verdin et al., 1999). Future extensions of this research should pursue closer linkages between satellite observed vegetation and crop water balance modeling techniques. It may also be possible to leverage rainfallbased NDVI projection techniques (Funk and Brown, 2005) to provide earlier warning of drought conditions. While this work has focused on the pragmatic needs of agricultural monitoring and early warning, the analysis presented here also underscores the rather obvious, but important, role that planting/ onset dates play in agricultural production. We have argued elsewhere (Brown & Funk, 2008; Funk et al., 2008) that improved seed and fertilizer inputs will be needed to overcome the food shortfalls caused by Africa's population growth and changing climate. As the Zimbabwe season forcefully demonstrates, resource mismanagement can be just as devastating as the worst drought. Conversely, improved management practices can leverage existing resources more effectively, increasing human welfare and wealth. 6. Summary Fig. 10. Average NDVI, precipitation, and month-to-month NDVI change for a 1 test site in central Zimbabwe, centered at 19.5 S, 30.5 E. These data have not been masked for cultivated areas. area masks and cloud contamination removal procedures we eliminated sources of crop signal error. This procedure can provide time series of vegetation greenness that correspond visually with independent production estimates (Fig. 3). Interestingly, this figure suggests that late season post-maxima NDVI values tend to correspond most strongly with maize production, a result confirmed by our sensitivity analysis (Fig. 4). This result is quite interesting, differing from several current operational analyses (Brown et al., 2002; Rojas, in press) which tend to focus on mid-season and/or maximum NDVI responses. There are three likely explanations for this late season correspondence, which has been observed in previous studies (Section 1.1). First, and most importantly, this is the response window indicated by phenological analyses guided by commonly used crop water requirement models. Empirical analysis of climatological crop water requirements shows peaks in December January, when monthly rainfall receipts are typically highest (Fig. 10). Since vegetation greening typically lags rainfall events by one month or more, late March/early April NDVI should correspond well with crop production. Late season cloud free observations may also enhance the NDVI-production relationship. A third contributing factor may be a better distinction between natural and crop vegetation Current state-of-the-science monitoring tools in the United States (Brown et al., 2002) and Kenya (Rojas, in press) utilize temporal smoothing to reduce atmospheric contamination, apply masks to limit non-agricultural vegetation signals, and are phenologically adjusted based on year-to-year variations in seasonality. However, these operational implementations use integrated NDVI or averages clustered about the time of peak NDVI. In addition to smoothing, masking and phenological adjustment, the work described here removes pre-season signals and uses simple linear operators tuned to specific crop phenologies. The combination of these techniques provides scale-invariant results that are consistent across sub-national and national spatial aggregations. Unlike maximum value computations, aggregation operations are commutative across scales (De Cola, 1997). Hence, estimates based on small regions can be scaled meaningfully to a national level. This allows for the quantitative and visual evaluation of characteristic NDVI curves for a country, assisting in the identification of drought. The combination of space time compositing and the V metric should be a useful addition to early warning systems in food-insecure Africa. When combined with the high repeat rate and high resolution of MODIS and reliable production statistics for training, these techniques allow us to accurately track crop production from space. The use of appropriate temporal smoothing to remove the effects of clouds, atmospheric perturbations, variable illumination, and viewing geometry is critical. These sources of contamination continue to plague the operational use of satellite vegetation imagery by the early warning community. Smoothed NDVI, averaged over cultivated areas, provides a concise visual summary of seasonal performance. At national levels,

10 124 C. Funk, M.E. Budde / Remote Sensing of Environment 113 (2009) both seasonal maximum NDVI and V correspond well with PECAD production figures, but the latter appears more robust. One way of understanding this increase in skill is that V incorporates additional information (onset of rains dates) not contained in NDVI maxima. Furthermore, the linearity of V gives the metric a scale-invariance that NDVI maxima do not possess. V is probably less influenced by aggressive early greening that does not contribute dramatically to mid-season grain filling. The scale-invariance of V also supports the mapping and analysis of sub-national totals and anomalies, since these district level quantities should be related to crop production. Accurate and easy to interpret visually, V can enhance our ability to monitor and mitigate production extremes. The lag between rainfall and vegetation response, however, makes it difficult to estimate production in early growing stages. 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