using remotely sensed and ancillary data to predict spatial variability of rainfed crop yield

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Using remotely sensed and ancillarydata to predict spatial variability ofrainfed crop yieldAhmed Musa shamseddin a & Ali Mohamed Adeeb aa Water Management and Irrigation Institute, University ofGezira , Wadmedani , SudanPublished online: 08 Dec 2011.

To cite this article: Ahmed Musa shamseddin & Ali Mohamed Adeeb (2012) Using remotely sensedand ancillary data to predict spatial variability of rainfed crop yield, International Journal ofRemote Sensing, 33:12, 3798-3815, DOI: 10.1080/01431161.2011.635162

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International Journal of Remote SensingVol. 33, No. 12, 20 June 2012, 3798–3815

Using remotely sensed and ancillary data to predict spatial variability ofrainfed crop yield

AHMED MUSA SHAMSEDDIN* and ALI MOHAMED ADEEBWater Management and Irrigation Institute, University of Gezira, Wadmedani, Sudan

(Received 25 February 2010; in final form 22 August 2011)

Rainfed agriculture is dominant in Sudan. The current methods for crop yieldestimation are based on taking random cutting samples during harvesting time.This is ineffective in terms of cost of information and time. The general objec-tive of this study is to highlight the potential role of remote-sensing techniques inupgrading methods of monitoring rainfed agricultural performance. The specificobjective is to develop a relationship between satellite-derived crop data and yieldof rainfed sorghum. The normalized difference vegetation index (NDVI), rainfall,air temperature (AT) and soil moisture (SM) are used as independent variablesand yield as a dependent variable. To determine the uncertainty associated withthe independent variables, a sensitivity analysis (SA) is conducted. Multiple mod-els are developed using different combinations of data sets. The temporal imagestaken during sorghum’s mid-season growth stage give a better prediction thanthose taken during its development growth stage. Among predictor variables, SMis associated with the highest uncertainty.

1. Introduction

Globally, rainfed agriculture is practiced on about 80% of cultivated land (Rockströmet al. 2003). It also dominates world food supply (De Fraiture et al. 2010, Rockströmet al. 2010), especially in developing regions such as sub-Saharan Africa (Fox andRockström 2003, Ngigi 2003).

Agriculture is the backbone of Sudan’s economy in terms of its contribution togross domestic product (GDP), and it also remains the main source of employmentand household income, especially in rural areas (Food and Agriculture Organization(FAO) of the United Nations, 2006). About 85% of Sudan’s cultivated land is underrainfed agriculture (Mohammed 1998, Ayoub 1999, FAO 2006). Sudan has expandedits agricultural production through an increase in rainfed cultivated areas (Ayoub1999). Two main sectors of rainfed agriculture are practised in Sudan: small-scaletraditional agriculture, which covers about 60% of rainfed cultivated areas, andlarge-scale mechanized agriculture, which forms the remainder.

The lack of a database for rainfed agriculture makes it difficult to construct devel-opmental plans, in Sudan. For instance, the FAO estimation of annual cultivated area,yield, production and cost for rainfed agriculture depends on sending survey teamsto the fields where the yield is estimated by taking random cutting samples. Suchmethods provide the final estimation of yield 2 or 3 months after harvesting. Such

*Corresponding author. Email: [email protected]

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online © 2012 Taylor & Francis

http://www.tandf.co.uk/journalshttp://dx.doi.org/10.1080/01431161.2011.635162

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Yield prediction 3799

traditional procedures of estimating crop yield have been widely criticized as tedious,laborious and time consuming (Murthy et al. 1996, Singh et al. 2002, Prasad et al.2007). However, FAO crop yield records are the only available data for calibratingcrop yield prediction models. Few studies on crop yield modelling are carried out inSudan. Fudl Elmoula (2004) attempted to directly correlate the yield of sorghum torainfall amount. Poor correlations were obtained when the FAO water requirementssatisfaction index for predicting rainfed crop yield was applied (Fudl Elmoula 2004).Another attempt was made by Ayoub (1999), who directly correlated rainfall to yieldof crops under rainfed conditions. The obtained correlation values were 0.5, 0.5 and0.4 for millet, sorghum and sesame, respectively.

Empirical statistical calculations and deterministic crop growth simulation are twowidely used approaches for modelling crop yield (Dourado et al. 1998, Bannayanet al. 2003, Kutner et al. 2004). The functional model, which is a relative relation-ship between the yield and evapotranspiration, is a famous example for the statisticalapproach (Hargreaves 1984, Doorenbos et al. 1986). However, Raes et al. (2006) statedthat the linear relationship in the functional crop yield model is valid only as long asthe water stress is less than 50%. This condition is very difficult to meet under rainfedagriculture conditions in arid climatic zones due to dry spells and mismanagementaspects (Ahmed 2009). The empirical growth simulation models require a large num-ber of parameters, which are very difficult to obtain, especially in developing countries(Ruget et al. 2002, Wallach et al. 2002, Mo et al. 2005, Prasad et al. 2007), and thelarge number of parameters makes them complicated. Hargreaves (1984) mentionedthat the emphasis should be on simplicity and ease of application of crop yield modelswithout sacrificing the reliability of estimation.

Recently, remote-sensing techniques have been widely used for monitoring weatherconditions, estimating evapotranspiration, monitoring vegetation cover, estimatingwater productivity, predicting crop yields and managing natural resources (Groten1993, Basstiaanssen et al. 1999, Singh et al. 2002, Jiyul et al. 2003, Domenikiotis et al.2004, Doraiswamy et al. 2004, Prasad et al. 2006, Ngigi et al. 2007, Prasad et al. 2007,De Wit and Van Diepen 2008, Cai and Sharma 2010). The remotely sensed param-eter known as the normalized difference vegetation index (NDVI) has been widelyused in predicting crop yield (Groten 1993, Quarmby et al. 1993, Murthy et al. 1996,Singh et al. 2002, Prasad et al. 2006, 2007, Wall et al. 2008, Cai and Sharma 2010).Wall et al. (2008) found that the NDVI possesses explanatory power 4 weeks earlier inthe season than the cumulative moisture index (Wall et al. 2008). Singh et al. (2002)found that, for small areas, post-stratification based on the NDVI provides a moreefficient estimate of crop yield than the ratio vegetation index. Prasad et al. (2007)have developed a model to predict wheat and rice yield by using NDVI, soil mois-ture (SM), surface temperature and rainfall and obtained high correlation coefficientvalues.

In arid and semi-arid zones, the spatial and temporal variability of rainfall is high(Ayoub 1999, Modarres and Silva 2007, Rockström et al. 2010). This variability affectsthe infiltrated volume of rainfall which forms SM in the root zone; ultimately, theproduction of rainfed crops will be affected (Ayoub 1999, Fox and Rockström 2003,Mati 2005, Tilahun 2006, Rockström et al. 2010). SM can be derived by partitioningrainfall into infiltration and runoff, as well as partitioning net radiation into sensibleheat and latent heat (Hupet and Vanclooster 2002, Fu et al. 2003, Tao et al. 2003).However, SM possesses fast temporal and spatial variability (Qiu et al. 2001, Hupetand Vanclooster 2002, Fu et al. 2003, Western et al. 2004).

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3800 A. M. Shamseddin and A. M. Adeeb

Many non-water factors limit production in rainfed agriculture (Raes et al. 2006,Van Keulen 2007, Rockström et al. 2010). Aggarwal and Kalra (1994) classifiedfactors influencing crop yield into weather factors (radiation and temperature), soilfactors (water and nutrition) and management factors (pests and diseases). Reliableweather data are scarce in developing nations (Droogers and Allen 2002). Air temper-ature (AT) data are often the only reliable data that are available over long periods oftime. This may justify why many evapotranspiration equations, such as the Hargreavesequation, are based on temperature (Droogers and Allen 2002, Hargreaves and Allen2003).

The general objective of this study was is to highlight the potential role ofremote-sensing techniques in upgrading methods of monitoring rainfed agriculturalperformance in Sudan. The specific objective was to develop a relationship betweensatellite-derived crop data, that is NDVI, and yield of rainfed sorghum.

2. Materials and methods

2.1 Characteristics of the study area

The study area is located between 11.5–13.1◦ N and 32.6–36.2◦ E and includes thethree states of Sennar, Blue Nile and Gedarif. These states are the most importantsorghum-producing areas of the country. The climate is semi-arid. Rainfall and lengthof the dry season are the most significant climate variables (FAO 2006). The rain-fall season extends for 5 months (June–October) with peak rainfall in August. Theannual rainfall average is 420 mm. The annual average reference evapotranspiration is2100 mm. Generally, the land is flat with a gentle slope of 10 cm km–1. The site is sit-uated in the central clay plains of Sudan, which are dominated by vertisols (Blokhuis1993) where cracks develop due to changes in SM, that is swelling–shrinkage phenom-ena. Rainfed agriculture and forest are the main land uses. Generally, two problemsare associated with this type of soil: low nitrogen and water stagnation or high runoffduring heavy rainfall storms. The livestock sector contributes appreciably to the liveli-hood of local communities and to GDP. From the hydrological point of view, there aremany minor streams (known locally as ‘Khors’); among them, Alatshan is famous.

2.2 Selection of crop, data and construction of models

Sorghum is the selected crop. FAO (2006) stated that, ‘If the trend of expansion in thearea of sorghum continues, it is likely to have serious consequences on the sustainabil-ity of crop yields in the traditional farming systems and for farm incomes’. Owing todifferent onsets of seasonal rainfall, the sowing dates of sorghum vary from year toyear and from one region to another. Farmers are used to sowing sorghum when theywitness sufficient rainfall and adequate SM. Generally, sowing dates of sorghum arein July. The optimum AT for sorghum growth is 24–30◦C, and its water requirementduring the growing period (100–140 days) is 450–650 mm (Doorenbos et al. 1986).According to the study’s experimental field observations, the length of the sorghumgrowth period under the study area conditions was found to be 105 days, with themid-season growth stage starting 50 days after sowing (50 DAS) and extending for37 days.

Four predictor variables were used for sorghum yield modelling. These are NDVI,SM, AT and rainfall (PPT). A linear model on the basis of the procedure of leastsquares error was used to model sorghum yield:

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Q =N∑

i=1

(yi − β0 − β1xi1 . . . βp−1xi, p−1

)2, (1)

such that the values of β . . . βp–1 minimize the sum of squares errors (Q). The errorswere assumed to be independent and to have a normal distribution N(0, σ 2). Theβ i variables (PPT, NDVI SM and AT) are considered to be independent and cropyield is a dependent variable. The relationship of sorghum yield to these four pre-dictor variables was obtained using historical climate data for 7 years (2000–2006).In order to study how the model depends upon parameters introduced into it as wellas to determine the uncertainty associated with the independent variables, a sensitivityanalysis (SA) was used (Crosetto et al. 2000, Ruget et al. 2002, Wallach et al. 2002).SA was carried out as described in Ruget et al. (2002), where, first, the output vari-ability was generated by varying input parameters and, second, the simulated outputvariability was assigned to the factors which are responsible. Figure 1 shows the dis-tribution of the four predictor variables. The simulated PPT values were calculated fortwo cases: cumulative and probability of exceedance. For the first case, the p-quantileof the distribution was used and in the second one, the probability of exceedance, wascalculated using the cumulative values. For the remaining data sets, computerized ran-dom numbers were calculated based on ‘b and a’ values (b > a). The resultant sensitiveparameters, that is SM and AT, were produced for a record of 11 years (1996–2006)(hereafter referred to as model 3). The interaction between SM and AT was tested(hereafter referred to as model 4). In terms of data collection, PPT and AT are rela-tively the easiest and can be collected at low cost. Thus, in developing countries, theexistence of a relationship between these two predictor variables (PPT and AT) andyield might be useful (hereafter referred to as model 5). The data for these variableswere available for 17 years (1990–2006). The comparison of models was carried outusing two statistical estimators (the root mean square error (RMSE) and the deter-mination coefficient, R2) as described in Durand et al. (2002), Kutner et al. (2004),Rodriguez et al. (2004), Tremblay and Wallach (2004) and Raes et al. (2006).

2.3 Data collection

The data sources for the four variables existed in different spatial and temporalresolutions, as depicted in table 1. The data sets were spatially averaged over thestudy area as monthly averages (see Prasad et al. 2007). The NDVI values werecalculated using Moderate Resolution Imaging Spectroradiometer (MODIS) imagesdownloaded with a resolution of 1 km × 1 km. Table 2 shows the image acquisitiondates. The main problem associated with the collection of images is the cloud noise,especially during August. The selection of the images was based on the crop calendarand on the avoidance of cloud noise. The images were geo-referenced and atmospher-ically corrected using the Environment for Visualizing Images (ENVI) version 3.5.The red and infrared bands were used to calculate the NDVI values. A surveyingtrip was carried out in order to identify sorghum fields using a Global PositioningSystem (GPS). The signature of an experimental sorghum field (5 ha) during season2006 was used as training samples for detecting sorghum fields during 2000–2009.The monthly SM data were downloaded in a columnar format from the NationalOceanic and Atmospheric Administration (NOAA) sites using the online viewerand the Distributed Oceanographic Data System. SM is estimated by a one-layer

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2000 2002 2004 200640

60

80

(a)

(c)

Rai

nfal

l (m

m)

Year

2000 2002 2004 2006

240

280

Soil

moi

stur

e (m

m)

Year

(d)

2000 2002 2004 2006

27

28

Air

tem

pera

ture

(°C

)

Year

Year

(b)

2000 2002 2004 20060

0.4

0.8N

DV

I

Figure 1. Distribution of the predictor variables during September in the study area, where(a), (b), (c) and (d) represent rainfall, air temperature, soil moisture and normalized differencevegetation index, respectively.

hydrological model. The model takes observed PPT and temperature and calculatesSM. The SM data were cleaned and adjusted according to the soil type of the studyarea where maximum SM is 230 mm m–1 depth. The AT data were downloaded ina columnar format using the online viewer and the Distributed Oceanographic DataSystem. PPT values were measured using a rain gauge. In order to obtain the data ofthe available meteorological stations in the desired area (see table 3), the online viewerand the Distributed Oceanographic Data System were specified to the required area.Then, spatial monthly averages were obtained. The yield data were downloaded fromFAO (2006) and the Ministry of Agriculture, Sennar State documents.

2.4 Temporal variability of the predictor variables

Figures 2–5 show the temporal variability of the four predictor variables during someselected months. Usually, the agricultural season extends between July and November.The lowest and highest NDVI values were found to be 0.2 and 0.7 in May and

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Table 1. Crop yield model data, source, spatial–temporal characteristic and spatial coverage.

Variable

Spatialresolution(at source)

Temporalresolution(at source) Source

Spatialcoverage

Rainfall Rain gaugebased

Monthly http://iridl.ldeo.columbia.edu/SOURCES/.NOAA/.NCDC/.GHCN/.v2beta/.prcp

Global

Air temperature 2.5◦ × 2.5◦ Monthly http://iridl.ldeo.columbia.edu/SOURCES/.NOAA/.NCEP-NCAR/.CDAS-1/.MONTHLY/.Diagnostic/.surface/.temp/

Global

Soil moisture 0.5◦ × 0.5◦ Monthly http://www.cpc.ncep.noaa.gov/soilmst/

Global

NDVI 1 km × 1 km Daily http://ladsweb.nascom.nasa.gov/data/search.html

Global

Note: NDVI is the normalized difference vegetation index.

Table 2. List of MODIS image acquisition dates (Julian dates).

2000 2001 2002 2003 2004 2005 2007 2008 2009

123 121 222 255 125 280 250 260 265254 241 278 210 261 269

263 256272289

Table 3. Location and characteristics of some selected weather stations in the study area.

Station Latitude Longitude Altitude Climatic zone

Gedarif 14.03 35.40 600 Semi-drySennar 13.55 33.56 420 Semi-dryAbu Naama 12.73 34.13 445 Semi-dryEl Renk 11.75 32.78 380 Semi-dryDamazine 11.82 34.40 470 Semi-humid

September, respectively. Normally vigorous vegetation does not exist in May, dueto low rainfall amounts. The maximum NDVI values for sorghum were found to beduring August and September. These values are about 45 and 75 DAS. However, some-times the maximum NDVI value was obtained in October. This might be attributedto the delay of sowing date as stated for season 2006 in the Crop Monitoring Bulletinfor Sudan (2006) and FAO (2007). The rainfall coefficient of variation is consideredhigh at 25%. It extends for 5 months (June–October), with the peak rainfall in August.The annual standardized departure from the 1970–2000 mean rainfall is demonstratedin figure 6. Although rainfall does not follow a constant pattern, there is a generaldecreasing trend from the mean rainfall. May shows the lowest monthly SM values.This is expected since the sole source of water, rainfall, is negligible in this month;

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2000 2002 2004 20060

0.4

0.8

May August

September October

ND

VI

Year

Figure 2. The temporal variability of the normalized difference vegetation index (NDVI).

2000 2002 2004 2006100

200

300

JulyAugustSeptemberOctober

Soil

moi

stur

e co

nten

t (m

m)

Year

Figure 3. The temporal variability of soil moisture content.

add to this a deep groundwater table which does not permit capillary rise from thegroundwater to the root zone. The SM value accumulates gradually to reach its max-imum in September. During the growing season, the monthly mean AT values rangefrom 24.7◦C to 28.5◦C. The proper temporal resolution was tested using the data of45 and 75 DAS as the sorghum crop reaches its peak growth stage (mid-season growthstage). Building a model on the basis of mid-season growth stage data will enable earlyestimation of crop yield about 2–3 months before harvesting.

3. Results and discussion

A single variable linear statistical relationship between observed yield and each pre-dictor variable was tested, that is a single variable analysis on the basis of monthly and

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2000 2002 2004 200624

26

28

July August

September OctoberAir

tem

pera

ture

(°C

)

Year

Figure 4. The temporal variability of air temperature.

2000 2002 2004 20060

100

200JulyAugustSeptemberOctober

Rai

nfal

l (m

m)

Year

Figure 5. The temporal variability of rainfall.

seasonal averages. The results in table 4 indicate that AT and PPT during Septembershowed the highest correlations as their coefficients of determination were 0.76 and0.37, respectively. The empirical correlations between crop yield and NDVI were foundto be very low under the semi-arid conditions of Sudan. With regard to seasonal aver-age, rainfall showed the highest correlation (0.36), which is statistically considered apoor correlation. Thus, monthly averages were more powerful than seasonal averagesin predicting crop yield. In this case, September average AT (a single variable), whichmay represent a mid-season growth stage (depending on the sowing date), can be usedto predict sorghum yield.

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1980 1990 2000

−2

0

2

Year

Rai

nfal

l ann

ual s

tand

ardi

zed

depa

rtur

e (z

)

Figure 6. Rainfall annual standardized departure (Z) from 1970 to 2000 mean. The smoothedline shows the trend of the rainfall time series.

Table 4. Values of sorghum yield correlation (R2) with monthly and seasonal valuesof each variable.

Variable July August September October Seasonal

NDVI – 0.1 0.001 0.03 0.02Rainfall 0.08 0.02 0.37 0.28 0.36Air temperature 0.03 0.14 0.76 0.12 0.03Soil moisture 0.003 0.005 0.03 0.1 0.008

Note: NDVI is the normalized difference vegetation index.

Sections 3.1–3.4 show the results of constructing a multivariate linear model withdifferent combinations of predictor variables. The resultant models are model 1,model 2, model 3, model 4 and model 5 as shown in table 5.

3.1 Model 1

This model was derived using data collected at the development stage of sorghum cropgrowth (≈45 DAS). The general equation of this model is

Y = [b + (a1 PPT) + (a2 AT) + (a3 SM) + (a4 NDVI)] , (2)

where Y stands for sorghum yield (kg ha–1), PPT is the rainfall (mm), AT is the airtemperature (◦C), SM is the soil moisture content (mm 1.6 m–1) and NDVI is the nor-malized difference vegetation index. Table 5 shows the values of the coefficients, R2

and results of analysis of variance (ANOVA). According to the F-test (see table 5),the alternative theory, that is there is a linear statistical relation between the depen-dent and independent variables, would be accepted within 50% probability. This lowprobability might be attributed to the small sample data (n ≈ 7 years). Using this 50%probability, model 1 gave an uncertainty factor of ± 34.1 kg ha–1. Figure 7(a) shows

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Tab

le5.

Var

iabl

esus

ed,

valu

esof

coef

ficie

nts,

sam

ple

size

(N),

dete

rmin

atio

nco

effic

ient

(R2),

Fca

lcul

ated

(Fca

l),F

tabu

late

d(F

tab)

and

stat

isti

cal

sign

ifica

nce

(p-v

alue

)of

the

prod

uced

mod

els.

Mod

elV

aria

bles

ba 1

a 2a 3

a 4a 5

NR

2R

MSE

(kg

ha–1

)F

cal

Fta

bp-

Val

ue

1A

T,P

PT,

SM,N

DV

I−8

523

353

0.1

−4.0

0782

0.0

70.

7612

3.9

1.55

1.21

(p≈

0.5)

0.43

2A

T,P

PT,

SM,N

DV

I9

137

−279

0.3

−1.3

−361

0.0

70.

9461

.27.

891.

21(p

≈0.

5)0.

123

AT,

SM9

097.

4−3

06.6

0.0

0.9

0.0

0.0

110.

5826

6.8

5.53

4.46

(p≈

0.95

)0.

034

AT,

SM,(

AT

SM)

4640

8−1

661

0.0

−138

.50.

05.

011

0.61

256.

13.

673.

07(p

≈0.

90)

0.07

5A

T,P

PT

1176

7.5

−392

.3−0

.98

0.0

0.0

0.0

170.

5926

3.3

5.80

4.46

(p≈

0.95

)0.

01

Not

e:A

T,ai

rte

mpe

ratu

re;P

PT,

rain

fall;

SM,s

oilm

oist

ure

cont

ent;

ND

VI

isth

eno

rmal

ized

diff

eren

ceve

geta

tion

inde

x.

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800 1000

800

1000

R2 = 0.76

(a)

Pred

icte

d yi

eld

(kg

ha−

1 )

Observed yield (kg ha−1)

(b)

(c)

800 1000

800

1000

R2 = 0.94

Pred

icte

d yi

eld

(kg

ha−

1 )


800 1000

800

1000

R2 = 0.58

Pred

icte

d yi

eld

(kg

ha−

1 )


Figure 7. Relationship between the observed and predicted yields. The letters (a), (b) and (c)refer to model 1, model 2 and model 3, respectively.

the comparison between the predicted and the actual yields. It is clear that there isgood agreement between the predicted and the actual values, except for season 2003.This season experienced the highest rainfall amount than other years, and the discrep-ancy might result from a problem associated with linear models, collinearity, wherethe estimated parameter values can have great changes with small changes of the data(Wallach et al. 2002). The correlation in model 1 between dependent and independentvariables is statistically not significant (see table 5, column p-value). This indicatesthat using the data of the development growth stage for predicting sorghum yield isnot worthy.

3.2 Model 2

This model was derived using data collected at the mid-season stage of sorghum cropgrowth (≈ 75 DAS), using the same parameters (PPT, AT, SM and NDVI) as includedin model 1 (equation (2)). Such a model will enable early estimation of crop yieldby at least 60 days prior to harvest. The general equation of this model is similar to

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equation (2). The R2 and ANOVA results of model 2 are shown in table 5. On thebasis of the F-test, the probability of accepting this model is 50%, which concludes anuncertainty of ±16.8 kg ha–1. About 94% of the outputs (prediction) were found dueto the model structure (R2 = 0.94). Figure 7(b) indicates the good agreement betweenthe predicted and the actual yields, except for season 2002. There was no evidence ofexistence of outlier values in the data sets. This explains the difficulty of interpretationwith regard to the results obtained using a regression model. The resultant p-valueof model 2 was improved compared to model 1 (see table 5, column p-value). Thisindicates that using the data of the mid-season growth stage (model 2) is more appro-priate than using the data of the development growth stage (model 1). This findingwas in conformity with that of Murthy et al. (1994, 1996), who found that the rela-tionship between yield and NDVI became weak when moved away from the headingstage of the paddy crop. However, Groten (1993) found significantly higher correla-tion between NDVI and yield towards the end of the season in the semi-arid regionsof Burkina Faso. This study examined the possibility of using October data (end ofthe season). The F-test resulted in the refusal of such possibility. This may strengthenthe argument against the use of crop growth stages that are away from the crop mid-season growth stage (peak stage) under the semi-arid conditions of Sudan. It is worthmentioning that after the plant reaches its mid-season growth stage, the later pheno-logical development (flowering, seed development, etc.) is more dependent on plantgenotype than weather conditions (Allen et al. 1998). This may justify the differenceof results obtained by this study and the study by Groten (1993).

NDVI data were obtained from the MODIS satellite with a spatial resolution of1 km × 1 km. In spite of this coarse resolution, the correlations obtained betweenthe observed and predicted yields in model 1 and model 2 were high (0.76–0.94). Thisis coupled with the lowest RMSE (table 5). The individual holding of mechanizedrainfed agriculture in Sudan is characterized by its large area; for example, the field sizeof one agricultural scheme (the same crop type) is 450 ha (≈4.5 km2). Therefore, in theabsence of images with fine resolution, the accuracy of the prediction model will not bestrongly affected. The single statistical correlation between NDVI and sorghum yieldwas very low (table 4). Thus, the power of NDVI to predict sorghum yield appearsto increase when it was included with other agro-meteorological parameters such asAT, rainfall and SM, as shown in model 1 and model 2. The rate and time of thecrop to reach its full cover depends on weather conditions, particularly AT (Allenet al. 1998). Hence, it is useful to include weather parameters in order to predict cropyield using weather data taken at the mid-season growth stage. Quarmby et al. (1993)estimated yields of wheat, cotton, rice and maize with a high degree of accuracy using asimpler relationship between NDVI and yield, in Greece. However, they recommendedmodification of their model, using agro-meteorological data during the grain-fillingperiod of the wheat crop. It is worth noting that other factors such as pests, plantdiseases and cultural practices will still cause deviations in predicted crop yield and, inturn, limit forecasting accuracy (Prasad et al. 2007).

3.3 Model 3 and model 4

These models include the independent variables that associated with the highestobtained uncertainty, using the SA test. The general equation of model 3 is

Y = [b + (a1 AT) + (a3 SM)] . (3)

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Figure 7(c) shows a comparison between the predicted and the observed yields. Thecorrelation between the dependent (sorghum yield) and independent variables (ATand SM) of this model was found to be statistically significant (α = 0.05), as depictedin table 5. In spite of this significant correlation, the resulting RMSE (266.8 kg ha–1)was higher than that obtained in model 1 and model 2. Generally, model 3 showedclear overestimated and underestimated values during years that had the lowest andhighest observed yields, respectively.

There is an expected interaction between AT and SM since SM partitions the latentand sensible heat (Hupet and Vanclooster 2002). This interaction was considered andgave model 4 with the following general equation:

Y = [b + (a1 AT) + (a3 SM) + (a5 ATSM)] . (4)

The incorporation of the interaction decreases the RMSE by 4% from that obtainedin model 3, but this incorporation decreased the significance of the statistical correla-tion (p-value) and the level of confidence, compared to model 3 (table 5). These resultsstate that the study’s assumption that AT and SM are independent variables can beaccepted. Accordingly, model 3 is statistically more appropriate than model 4 (albeitwith the low RMSE associated with model 4). Moreover, the outlier yield data inmodel 4 show a problem (1997, 1999 and 2001).

3.4 Model 5

This model represents data which are easily available in developing countries suchas Sudan. The independent variables used here included AT and PPT. The generalequation of this model is

Y = [b + (a1 AT) + (a2 PPT)] . (5)

The confidence level of this model is 95%. The resulting RMSE was 263.3 kg ha–1.Actually, model 5 shows the highest significant statistical correlation between depen-dent and independent variables among the developed models (table 5). This may beattributed to its sample size (17 years). The interaction between rainfall and AT pro-duced an insignificant effect in terms of R2 and RMSE. This states that the usedvariables (AT and rainfall) are independent.

3.5 The uncertainties associated with the predictor variables

According to SA, the RMSEs associated with each predictor variable in model 1 were33.1, 61.9, 79.5 and 44.5 for PPT, AT, SM and NDVI, respectively. Thus, the high-est uncertainty was associated with SM data. Thus, model 1 is more sensitive to theuncertainty in SM data. This is because of the large heterogeneity associated with SMdata. This is attributed to two reasons. (1) topography (e.g. soil slope), soil properties(e.g. texture), land use and cover (e.g. agriculture and vegetation), rainfall distribution,antecedent SM and field water management play controlling roles in the spatial vari-ability of SM (Qiu et al. 2001, Hupet and Vanclooster 2002, Xu and Mermoud 2002,Qiu et al. 2003). Increase of SM variability is observed with soil depth from 10 to15 cm (Qiu et al. 2001). It was noticed that heavier rainfall and higher mean SM areoften associated with lower spatial variability under the semi-arid conditions of the

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Loess plateau, China (Qiu et al. 2001). The spatial variability of vegetation within thefield, through the processes of evapotranspiration and root water uptake, was found tobe playing a non-negligible role in the temporal dynamics of SM patterns (Hupet andVanclooster 2002). Also, Hupet and Vanclooster (2002) found a negative correlationbetween the spatial variability and the mean SM. They attributed this to insufficientsamples for the drier conditions, that is, about 8000 SM measurements were used.(2) SM content has been calculated indirectly (on the basis of a water balance model).The spatio-temporal variability of SM has been studied using different spatial andtemporal scales, that is, 1 m2 to a few square kilometres and a few days to a few yearswith different monitoring techniques such as the Time Domain Reflectometer (TDR)(Qiu et al. 2001, Hupet and Vanclooster 2002). In this study, the used spatial (0.5◦ ×0.5◦) and temporal (month) resolutions for SM are large. Thus, different crops, vege-tation and land cover existed with regard to the results of the surveying trip (collectionof ground truth data) carried out. Subsequently, SM variability is expected to be high.Succinctly, collection of SM data, relative to other predictors, needs more effort andcare. Thus, research is needed to develop models that minimize error in SM deter-mination under Sudanese rainfed conditions. Because SM is a control factor for thelatent and sensible heat partitioning (Hupet and Vanclooster 2002), the uncertaintyof SM is directly reflected on the uncertainty associated with AT, which is ranked sec-ond with regard to the SA test. In contrast, rainfall data show low sensitivity. This isbecause the calculation of rainfall was based on a network of meteorological stationmeasurements. Using remote sensing (NDVI) to evaluate vegetation cover resulted ina reduction in the uncertainty related to plant phenological characteristics. However,difference in sowing dates should be considered when using multi-temporal images.

4. Conclusion

This study aimed to produce accurate, simple and low-cost crop yield prediction mod-els, which can fit the Sudanese rainfed agricultural conditions. Remote sensing andancillary data were used to construct such models. The remotely sensed data used weredownloaded from the MODIS satellite (free of charge). However, its data availabilityis limited (from the year 2000 onward). In addition, clouds, especially in August, haveconstrained the acquisition of clear remotely sensed images.

Five models were constructed. The availability of the data sets in different res-olutions, however, was found as the main obstacle. This can be easily solved if asufficient fund is available for acquiring images with fine resolutions (spatially andtemporally). Besides that, it was very difficult to find accurate data for the Sudaneserainfed agriculture. Thus, remotely sensed images remain the inevitable path to followfor monitoring and building up of a database. The most accurate modelling of rainfedsorghum based on NDVI data can be obtained using data taken during the mid-seasonsorghum growth stage, which often occurs in September under the Sudanese semi-aridconditions. The model based on AT and rainfall (model 5) shows the highest statisticalcorrelation with sorghum yield. Remote sensing can be used to monitor both AT andrainfall. Therefore, the spatial and temporal variability of these two data sets would beminimized. Generally, the produced models show successful results. However, insuffi-cient funds have hindered collection of long records of data. The study, thus, suggestssecuring funds in order to obtain long data records from other satellite sources orobtaining free imagery such as Landsat, which provides fine resolutions, and then

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re-construct these models. The procedures used here for sorghum yield modelling canbe used for other crops grown under the Sudanese rainfed conditions, as well.

Among the data sets used, SM shows the highest uncertainty. The procedure ofusing remote sensing (NDVI) for evaluating the vegetation cover has resulted in reduc-tion in the uncertainty related to plant phenological characteristics. Accordingly, thestudy suggests conducting in-depth studies of spatio-temporal variability of SM underthe semi-arid conditions of Sudan.

AcknowledgementsThis study is part of a PhD study funded by DAAD. The authors would like toacknowledge the ITT, Germany, for hosting the first author in Germany, with specialthanks to Prof. Gease (the dean of the institute). They also appreciate the role of Prof.Adam H. Suliman, Prof. Seifeddin A. Hamad, Prof. Adam Ibrahim and Mr AmmarM. Ahmed for their valuable advice. The authors are thankful to the anonymousreviewers, whose comments improved the quality of this article.

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using remotely sensed and ancillary data to predict spatial variability of rainfed crop yield

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