## 1 Introduction  
_Nilaparuta lugens_ (brown planthopper; hereafter BPH) is one of the most damaging rice insect pests in the temperate and tropical regions of East and Southeast Asia [1]. It causes serious crop loss directly by sucking the sap of plants, causing the plants to wilt (known as hopper burn), as well as indirectly by transmitting viral diseases [2]. The life cycle of the BPH lasts around 30 to 40 days, consisting of an egg stage, five nymphal instar stages, and an adult stage. In the tropics, the egg stage lasts 7 to 11 days. The nymphal stage takes about 10 to 18 days from the hatching of the first-instar nymph to the adult stage, and adult planthoppers live for 18 to 20 days [3]. Both BPH nymphs and adults can damage rice plants [4]. For short duration rice varieties, BPH can feed on rice plants throughout the cropping season and reproduce continuously for three to four generations. From 2010 to 2013, BPH infestation in Thailand was estimated to have affected at least 800,000 hectares of rice and caused a 60% loss in production costing $800 million per year, especially in the central plain and lower northern regions [5]. This damage was partly a result of the rapid increase in insect populations, with farmers being unable to forecast outbreaks. Continual monitoring and accurate forecasting of pest population during the crop growing period could be useful in protecting rice crops against BPH. Both abiotic and biotic factors are believed to be responsible for changes in BPH populations [6]. The influence of abiotic factors such as weather variables has been well documented. [PERSON], [PERSON], and [PERSON] [7] found that temperature and evening relative humidity were key factors influencing BPH light trap catches. In addition, [PERSON] et al. [6] found that temperature, rainfall, and relative humidity influenced populations of both BPH and white-backed planthoppers during the rainy and summer seasons. [PERSON] and [PERSON] [8] similarly observed that weekly maximum temperature, rainfall, and evening humidity were significant factors that affected BPH light trap catches in the rainy season. Thus, climatic factors can be expected to be indicators of BPH attacks [9]. Biotic factors such as host plant phenology can also affect BPH populations [10]. [PERSON] [11] found that crop age has a highly significant effect on populations. In addition, BPH tends to be more numerous after 60 days' post-transplantation when crops are close to maturity, as well as between the heading and harvesting stages during dry seasons [12; 13]. [PERSON] et al. [14] found that BPH is a monophasous insect whose occurrence depends on host rice plants. Therefore, the temporal and spatial patterns of rice cultivation in the region should affect BPH incidence. Satellite images present an alternative approach for investigating the spatiotemporal pattern of rice phenology by providing information on phenological stages on a large scale. Vegetation indices derived from satellite images are used as an essential parameter for crop growth information detection, especially the normalized difference vegetation index (NDVI). A time series of NDVI data has been popularly used in continuous monitoring of land cover characteristics and vegetation phenology [15; 16; 17; 18; 19; 20; 21]. Among optical satellite data, the moderate resolution imaging spectroradiometer (MODIS) is advantageous in that it provides broad coverage, high spectral and temporal resolution, and free access to data. Therefore, many researchers in remote sensing have applied MODIS NDVI-time series data to study the growth stages of rice [22; 23; 24; 25]. To date, however, remote sensing data have not been used to model BPH fluctuations in Thailand. Statistical modelling for early prediction of pest risks is one strategy that has been widely adopted. The multiple linear regression model (MLR) is a statistical method used to investigate the relationship between one response variable (the dependent variable) with two or more variables (independent variables).