Error correction method of automatic monitoring soil moisture data based on differential equation

Abstract: In practical work of soil moisture monitoring, the automatic monitoring devices provide faster, more efficient and continuous observations compared with manual drying method. Thus, the automatic monitoring, which bases on Frequency Domain Reflectometry (FDR) or Time Domain Reflectometry (TDR), is becoming the main technical means to achieve the goal of fast and continuous monitoring. However, the automatic monitoring data is less stable and accurate because of installation and tuning situation, equipment aging and farm environment changing. Automatic monitoring data error can be divided into two categories: random error and systematic error. Random error complies normal distribution and its mean tends to zero. Systematic error does not have statistical characteristics, but it usually has certain regularity in value and continuity in time. For the time series data of automatic monitoring, error from one time point is relevant to the data errors of previous and subsequent time points. Thus, the random error can be reduced by averaging multiple measurements and the impact of systematic error can be reduced by differential equation correction. Soil moisture values measured by manual drying method are generally considered as the most accurate and reliable data, therefore it provides the possibility to correct the values measured by automatic monitor. The method proposed in this study is based on the numerical analysis of errors, regardless the specific causes. This scheme avoids the complex process of locating each error source and analyzing its numerical impact. The data analyzed in this paper included soil moisture values measured by manual drying method and automatic devices in the same period and same area but with different time intervals. The manual data was acquired every half-month and automatic data was acquired hourly. The daily means of automatic monitoring data were calculated to match manual data. Taking the manual data as true values, the errors of automatic monitoring data in corresponding days can be calculated. The error analysis results showed that the automatic monitoring soil moisture data contains apparent systematic error and the absolute mean error exceeded 5% of the operational requirement. The differential equations to correct the automatic monitoring data were established in forms of linear equation, quadratic equation and cubic equation. The argument of equations is measuring time and the dependent variable of equations is error estimation. The automatic monitoring data errors before and after correction were compared. The result indicated that the absolute mean error decreased 34% and 24% in 20 cm depth and decreased 67% and 54% in 40cm depth, and all the absolute mean errors satisfy the 5% of the operational requirement. Moreover, the error after correction is normally distributed. The residual error is mainly the simple random error which could be further reduced by calculating the monthly average and ten days average. Among the three equation forms, linear differential equation has the best correction performance altogether. The correction method using differential equation is easy to implement and can effectively improve the accuracy of automatic monitoring data. With this method, the synchronistical observation of soil moisture can give full play to the advantages of both manual and automatic data collecting methods and improve the overall performance of monitoring system.