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Ciência Rural

Print version ISSN 0103-8478On-line version ISSN 1678-4596

Cienc. Rural vol.46 no.9 Santa Maria Sept. 2016  Epub June 16, 2016 


Temporal variation of normalized difference vegetation index (NDVI) and calculation of the crop coefficient (Kc ) from NDVI in areas cultivated with irrigated soybean

Variação temporal do Índice de Vegetação por Diferença Normalizada (NDVI) e obtenção do coeficiente de cultura (Kc ) a partir do NDVI em áreas cultivadas com soja irrigada

Thálita Carrijo de Oliveira1  * 

Elizabeth Ferreira2 

Antônio Augusto Aguilar Dantas2 

1Instituto Federal Goiano (IFG), 75650-000, Morrinhos, GO, Brasil.

2Departamento de Engenharia, Faculdade de Engenharia Agrícola, Universidade Federal de Lavras (UFLA), Lavras, MG, Brasil.


Vegetation indices obtained by remote sensing products have various applications in agriculture. An important application of the Normalized Difference Vegetation Index (NDVI) is obtaining the crop coefficient (Kc). The aims of this study were to analyze NDVI temporal profiles and to obtain Kc from the NDVI vegetation index product MOD13Q1. The analysis is based on the phenological stages of irrigated soybean crops in the municipality of Planura/MG during the 2010/2011 growing season. Areas planted with irrigated soybean were identified through fieldwork. Temporal series of the MOD13Q1 products were used to analyze NDVI, allowing the extraction of NDVI values for all points in the period studied. The NDVI temporal profiles showed a similar pattern to each other and corresponded to the crop cycle. The KcNDVI values for the MOD13Q1 products were well correlated to the FAO Kc values (r2=0.72). Thus, NDVI can be used as an alternative for obtaining crop coefficient (Kc).

Key words: MOD13Q1; phenological stages; temporal profiles


Os índices de vegetação obtidos a partir de produtos de sensoriamento remoto apresentam várias aplicações na agricultura. Uma importante aplicação do índice de vegetação Normalized Difference Vegetation Index (NDVI) está relacionada à obtenção do coeficiente de cultura (Kc). Assim, o objetivo deste trabalho foi analisar os perfis temporais de NDVI e obter o Kc a partir do produto de índice de vegetação NDVI (MOD13Q1), baseado na análise dos estádios fenológicos da cultura de soja irrigada, no município de Planura/MG, safra 2010/2011. A identificação das áreas plantadas com soja irrigada foi feita através de pesquisa de campo. As séries temporais do produto MOD13Q1 foram utilizadas para analisar o NDVI, permitindo a extração dos valores de NDVI para todos os pontos no período estudado. Os perfis temporais de NDVI apresentaram um padrão semelhante entre si e quanto ao ciclo da cultura. Os valores de KcNDVI variaram, em média, de acordo com os valores de Kc FAO, representando uma correlação linear (r2) de 0,72 para o produto MOD13Q1. Assim, o NDVI pode ser usado como uma alternativa na obtenção do Kc.

Palavras-chave:  MOD13Q1; estádios fenológicos; perfis temporais


Agricultural surveys are conducted mainly by using conventional methods and information available from government agencies. However, with advances in remote sensing devices, including vegetation index-based sensors such as TERRA/MODIS, the data thus obtained can be used to monitor agricultural areas.

For agricultural applications, the high periodicity provided by these vegetation indices products is of fundamental importance for analysis and monitoring of the phenological cycle of crops such as soybean over large areas (ESQUERDO & ZULLO, 2007; RUDORFF et al., 2007; WARDLOW et al., 2007; EPIPHANIO et al., 2010; PENG et al., 2013), which could vary from 75 to 210 days depending on the cultivar (GARCIA et al., 2007). Nevertheless, because the images are produced with different spatial and temporal resolutions, further studies are needed to assess the influence of these resolutions in the behavior of indexes from planting to harvest.

The Brazilian Agricultural Research Corporation (Embrapa) makes available the vegetation index product called Normalized Difference Vegetation Index (NDVI) with the purpose of facilitating and disseminating the use of TERRA/MODIS products() (ESQUERDO et al., 2010).

An important application of NDVI is that it helps determine the crop coefficient (Kc). Thus, determination of the crop's evapotranspiration (ETc), which is based on Kc, on a daily basis is a key requirement for the adoption of agricultural management and for irrigation (BEZERRA et al., 2010).

Kc is related to phenological crop cycles and when it is associated to NDVI products, it provides an alternative in obtaining new Kc values (DUCHEMIN et al., 2006; SINGH & IRMAK, 2009; BERGSON et al., 2010; KAMBLE et al., 2013).

Therefore, the present study aimed to analyze the temporal NDVI profiles and obtain Kc values from the NDVI vegetation index product (MOD13Q1), based on analysis of the growth stages of irrigated soybean in the Municipality of Planura/MG, during the 2010/2011 harvest.


The study area selected was the municipality of Planura, located in the "Mineiro" Triangle region (19° 57′ 22″ and 20° 10′ 10″ S, 48° 44′ 39″ and 48° 30′ 45″ W; total area: 318 km²). The municipality has a plateau relief, covered by a savannah-like vegetation (Brazilian "cerrado") and irrigated agriculture is common. Climate is humid (B2) with a moisture index of 32.8, which is attributable to the aridity index (la) of 13.7, according to the climatic classification of Thornthwaite (CARVALHO et al., 2008).

Areas cultivated with irrigated soybean by center-pivot sprinkler have been previously identified by PEREIRA et al. (2011), who conducted field work for the identification and collection of 11 points (punctual geographic coordinates) by using a GNSS receiver (Table 1), in farms located within the study area. Each point represented data including dates of planting and harvesting, and duration of different crop cycles. This information was then compared with NDVI data obtained from the MODIS sensor.

Table 1 Specifications of points regarding areas cultivated with irrigated soybeans in the municipality of Planura/MG. 

MOD13Q1 products were obtained from September 2010 to April 2011 (i.e., the 2010/2011 harvest season). These products were obtained from the Bank of MODIS Products supplied by Embrapa, in the Brazilian state basis, for Minas Gerais (ESQUERDO et al., 2010). Technical specifications of the MOD13Q1 products are presented in table 2.

Table 2 Technical specifications of the product MOD13Q1. 

Source: Adapted from SHIMABUKURO & RUDORFF (2006).

The software Environment for Visualizing Images (ENVI), version 4.8 (VISUAL INFORMATION SOLUTIONS, 2008), was used to import the MOD13Q1 products. A time series of MOD13Q1 products was constructed for comprehensive description and analysis of NDVI, thereby allowing determination of NDVI values, for a 16-day composite.

The relationship between Kc and NDVI values was evaluated by analysis of KcNDVI and Kc FAO values obtained in the FAO56 manual (ALLEN et al., 1998). Thus, using the simple linear regression model (Equation 1) created by KAMBLE et al. (2013), it was obtained KcNDVI values, which were subsequently compared to Kc FAO data for the analysis of phenological stages of irrigated soybean crop. In addition, according to KAMBLE et al. (2013), the procedure for quantifying crop coefficients from NDVI data (Equation 1) could find applications in other regions worldwide to understand the regional consumption of water for irrigation.

KcNDVI = 1.457 NDVI - 0.1725 (1)

To evaluate the comparison between calculated (KcNDVI) and tabulated (Kc FAO) data, a simple linear regression was carried out to NDVI and Kc FAO. Statistical analyses involved using the t-test, at a 5% significance level (relative standard error, estimate, standard error, t-value, and p-value) for the parameters β0 and β1 of the regression equation, as well as for the coefficient determination (r2) analysis.


The NDVI temporal profiles of MOD13Q1 products for the irrigated soybean crop during the 2010/2011 harvest were grouped according to cycle duration (Figure 1). The soybean development period continued until November 17 for plots harvested on February 02, 2011, and February 18, 2011, with mean NDVI values of 0.77 and 0.84, respectively. As for the plot harvested on March 06, 2011, the mean NDVI value in the crop development period was 0.85, as on December 03, 2010. The maturation period started on January 01, 2011, for the plot harvested on February 02, 2011; and on January 17, 2011 for plots harvested on February 18, 2011 and March 06, 2011.

Figure 1 NDVI temporal profiles of the MOD13Q1 products used for monitoring irrigated soybean crop during the 2010/2011 harvest season. 

With regard to NDVI analysis of the MOD13Q1 products (Figure 1), it was reported that the duration of the soybean cycle was 109, 125, and 141 days, respectively, for the plots harvested on February 02, 2011; February 18, 2011; and March 06, 2011. According to GARCIA et al. (2007) the soybean cycles can range from 75 to 210 days depending on the crop, which indicated that the variation of soybean cycle observed in this study was within the expected period.

The dates of planting and harvest, and duration of the irrigated soybean cycle, based on the NDVI analysis of MOD13Q1 products were compared to field data collected by Pereira (2011), for the 2010/2011 harvest (Table 3). Thus, the field data analysis showed that planting occurred for most points at the end of the second fortnight of October, and NDVI/MOD13Q1 analysis revealed that planting occurred early in the second fortnight of October. The harvest occurred, for most points in February. However, even with the difference between the dates of planting and harvesting, the duration of the cycle was similar in both analyses.

Table 3 Comparison among dates of planting and harvesting, and duration of the irrigated soybean cycle in the analysis of field data and NDVI of the MOD13Q1 products. 

Analyses of NDVI temporal profiles of MOD13Q1 products (Figure 1) revealed little variation among the crops, which possibly indicates that the temporal profiles of the respective plantations showed a similar pattern with each other regardless of the difference between the harvest dates and type of crop adopted. This was observed by ESQUERDO & ZULLO (2007) in their analysis of NDVI temporal profiles that were generated using remote sensing data for the soybean crop in western Paraná.

Comparisons were made between KcNDVI and Kc FAO in the analysis of phenological stages of irrigated soybean crop for the MOD13Q1 products. Thus, the NDVI, KcNDVI and Kc FAO values (Table 4) are associated with the respective phenological stages of the irrigated soybean crop, based on the analysis of the MOD13Q1 product temporal profile, considering the planting from October 16, 2010 to February 02, 2011 (Figure 1). The stages were characterized on the basis of methodology proposed in the FAO-56 report (ALLEN et al., 1998). During the growth stage (stage II), Kc varied between 0.6 and 1.1, increasing up to stage III. After maturation (stage IV), Kc decreased until harvest (stage V), with values of 0.2 and 0.4, respectively, for KcNDVI, and Kc FAO. When NDVI showed high values, Kc values ranged between 1 and 1.2 on average, which showed that the maximum evaporation (ETc) can be higher than the reference evapotranspiration (ET0), defining the well irrigated crop condition. This was observed by KAMBLE et al. (2013) in the analysis of Kc for irrigated crops in the state of Nebraska-USA.

Table 4 Phenological stages of irrigated soybean and their values of NDVI, KcNDVI and Kc FAO, for the planting from October 16, 2010 to February 02, 2011, of the MOD13Q1 products. 

*VD: Vegetative Development.

Table 5 shows the statistics of the linear regression fit to NDVI and, Kc FAO, for the MOD13Q1 products.

Table 5 Statistics of the linear regression fit to NDVI and Kc FAO data, for the MOD13Q1 products. 

Analyses by the t-test revealed that all parameters were statistically significant P<0.05), although the standard deviation was relatively high. This can be explained by the existence of several factors that directly affect the determination of Kc, such as relative humidity, wind speed, type of cultivar used, as well as the conditions that affect soil evaporation (ALLEN et al., 1998).

The coefficient of determination (r2) was 0.79. This result corroborated those obtained by SINGH & IRMAK (2009) and KAMBLE et al. (2013), in the correlation between NDVI and Kc values for irrigated soybean with an r2 value of 0.9 and 0.81, respectively, which highlighted the adequacy of the method to represent NDVI variation in the Kc data set.


These results showed that despite the low spatial resolution of the MODIS sensor, it was possible to follow the phenological cycle of the irrigated soybean crop, based on the analysis of the NDVI temporal profiles of the vegetation index. Thus, the NDVI temporal profiles of the MOD13Q1 products showed similar patterns to each other and regarding crop cycle.

Comparing KcNDVI and Kc FAO values in the analysis of the phenological stages of the irrigated soybean crop, we reported that the calculated Kc values (KcNDVI) varied, on average, according to the tabulated values of Kc (Kc FAO) and the coefficient of determination (r2) has showed that variations in the Kc data set are explained by variations in NDVI. Therefore, NDVI may be used as an alternative tool for obtaining the crop coefficient (Kc).


In the Fundação de Amparo à Pesquisa de Minas Gerais (FAPEMIG), CAG-APQ 01560-12 process.


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Received: March 05, 2015; Accepted: November 21, 2015; Revised: May 25, 2016

*Corresponding author: Thálita Carrijo de Oliveira, email:

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