Spatial Variability of Crops in Sampling Units and its Effect on Sampling Extrapolation Efficiency

Abstract

Timely and accurate acquisition of crop area is of great significance for monitoring crop growth and estimation of crop yields. And it's important for strengthening agricultural management, ensuring food security and supply of agricultural products. The combination of remote sensing data with traditional sampling methods is an effective way to monitor and estimate crop area on a large scale. The traditional sampling method, on the basis of traditional statistics theory which studies the laws of random variables, requires that the sampling units should satisfy the principle of mutual independence. However, the regional crops, which are affected by natural conditions and socioeconomic factors, are often spatial variable. There is no report on whether and how spatial variability will influence the sampling efficiency of crop acreage. Therefor the further improvement of sampling efficiency is limited. To solve this problem, a variation function model was constructed with the area ratio between maize or rice and sampling units as object variable on 10 sampling unit scales combining remote sensing data, spatial analysis and traditional sampling methods with Dehui, Jilin as study area. Selecting base value as index for spatial variability within the sampling unit, the effect of sampling unit scales on spatial variability of maize and rice were quantitatively analyzed. Three commonly used sampling schemes (random sampling, systematic sampling and stratified sampling) were selected for sample selection, overall extrapolation and error estimation. The sampling efficiency was quantitatively evaluated using overall relative error (r) of the sampling extrapolation, the coefficient of variation (CV) of the total estimate and the sample size (n) on different sampling unit scales. The results show that the spatial variability of maize and rice decreases with the increase of the sampling unit scale. The range of base value is [0.15, 0.20] and [0.05, 0.14] for maize and wheat respectively. Using the three sampling methods to extrapolate the maize and rice area separately: 1) Under the same sampling ratio, the relative sampling errors of the two crops' area estimations gradually increase with the decrease of spatial variability (the sampling unit size increases), the coefficient of variation also shows an increasing trend, and the sampling accuracy and extrapolation stability is affected by spatial variability; 2) The relative error in estimation of the two crop areas varies with the sampling method, when using simple random sampling and systematic sampling, the relative error of the two crops was within the range of (1 %, 50%) and (0.5%, 40%), and the coefficient of variation was limited to (1 %, 75%) and In the range of (1 %, 88 %), the relative errors at all scales were limited to 10% or less with stratified sampling, and the fluctuations of the coefficient of variation were small (both within 0.3 % and 20%). Therefore, the stratification was selected. Sampling is the best sampling method; 3) When the sampling method is determined, the sampling ratio is the main factor determining the sampling efficiency. As the sampling ratio increases, the rate of change of the relative error of the two crop area estimators gradually decreases, when the sampling fraction reaches 5%, The relative error is basically limited to 5%, and the coefficient of variation is stable within 12 %. On this basis, the effect of increasing the sampling ratio to increase the sampling progress is minimal; 4) According to the conclusions of 2) and 3), Stratified sampling method is used to extrapolate crop area by 5% sampling ratio. The sampling efficiency decreases with the increase of sampling unit size. When the sampling unit size is limited within 3500m×3500m, the overall sampling satisfies 95% sampling accuracy requirements., And the coefficient of variation is stable within 7%, the stability of the extrapolation of the area is also high; 5) Based on the above research conclusions, the quantitative evaluation sampling efficiency scheme and the optimal sampling model composed of the combination of sampling unit scale (spatial variability), sampling fraction, extrapolated total relative error, and variation coefficient were finally obtained. This study provides a reference for the design of a rational spatial sampling schemes of spatial variable crops.