# A Forecast Model Applied to Monitor Crops Dynamics Using Vegetation Indices (NDVI)
## 1 Introduction  
Vegetation dynamic is very sensitive to environmental changes, particularly in arid zones where climate change is more prominent. Therefore, it is very important to investigate the response of this dynamics to those changes and understand its evolution according to different climatic factors. Pointed out as a cumulative effect on vegetation in combination with environmental changes that generates a temporary delay in the response of plants, this must be considered in order to understand the variations in vegetation and predict its changing characteristics under future climate changes [1, 2, 3, 4, 5]. According to this, several studies claim that the main factors that determine the relationship between vegetation and climate change are temperature and precipitation [6]. Therefore, the water content of the unsaturated zone determines the optimal development of vegetation. The availability of water in the soil over a period of time (year, month and day) is conditioned by the inflows of water, the effective precipitation reaching the soil and the water reserves accumulated in the soil itself [7,8]. However, the loss of moisture in the soil occurs as a consequence of the direct evaporation of water from the soil and the transpiration of the plants, which are direct functions of the ambient temperature and soil temperature [9, 10, 11, 12]. Remote sensing techniques provide an effective system to monitor vegetation dynamics on multiple scales using vegetation indices (IV) that are based on the difference of near infrared (NIR) and red visible (R) spectral reflectance [13]. The normalized difference vegetation index (NDVI) is the most widely used because it quantifies vegetation health by measuring the difference between near infrared (strongly reflected) and red light (absorbed). This index (Equation (1)) is calculated from remote sensing measurements in the visible and infrared bands as:  
\[\text{NDVI}\;=\;\frac{(\sigma\text{NIR}\;-\;\sigma\text{R})}{(\sigma\text{NIR }\;+\;\sigma\text{R})} \tag{1}\]  
where \(\rho\)NIR is the surface reflectance in the near infrared region and \(\rho\)R is the surface reflectance in the red visible region of the electromagnetic spectrum. The NDVI of a vegetated area tends toward positive values, whereas water and urban areas are represented by near zero or negative values [14]. This relationship between NDVI with vegetation health is well known and used, among other studies, for vegetation mapping, as a crop state indicator, as a biomass estimator and for drought or evapotranspiration monitoring [15, 16, 17, 18, 19, 20, 21, 22]. In accordance with the above time series, vegetation indices with high spatial resolution and high temporal frequency are important to describe and analyze the spatial patterns for vegetation monitoring and management [23]. Additionally, important issues, such as the prediction of vegetation response induced for climatic factors, are based on forecasting models of NDVI [24]. NDVI series have been studied in different ways applying several analyses. [PERSON] et al. (2010) proposed ARIMA models to simulate the vegetation temperature condition index (VTCI) series, and forecast their changes in the future [25]. In addition, the (2010) MODIS LAI (Leaf Area Index) model proposed by [PERSON] et al. applies three models that can characterize the non-stationary time series data and predict the future values, including Dynamic Harmonics Regression (DHR), Seasonal-Trend Decomposition Procedure based on Loess (STL) and seasonal autoregressive integrated moving average (SARIMA) [26]. [PERSON] et al. (2011) developed a method for forecasting the short-term response of forest vegetation on the basis of an autoregressive integrated moving average (ARIMA) [27]. [PERSON] et al.