pplication of Time-series Modeling to Predict Infiltration of Different Soil Textures

Infiltration is one of the most important parameters affecting irrigation. For this reason, measuring and estimating this parameter is very important, particularly when designing and managing irrigation systems. Infiltration affects water flow and solute transport in the soil surface and subsurface. Due to temporal and spatial variability, Many measurements are needed to explain the average soil infiltration characteristics under field conditions. Stochastic characteristics of the different natural phenomena led to the application of random variables and time series in predicting the performance of these phenomena. Time-series analysis is a simple and efficient method for prediction, which is widely used in various sciences. However, a few researches have investigated the time-series modeling to predict soil infiltration characteristics. In this study, capability of time series in estimating infiltration rate for different soil textures was evaluated.
For this purpose, the 60 and 120 minutes data of double ring infiltrometer test in Lali plain, Khuzestan, Iran, with its proposed time intervals (0, 1, 3, 5, 10, 15, 20, 30, 45, 60, 80, 100, 120, 150, 180, 210, 240 minutes) were used to predict cumulative infiltration until the end of the experiment time for heavy (clay), medium (loam) and light (sand) soil textures. Moreover, used parameters of Kostiakov-Lewis equation recommended by NRCS, 24 hours cumulative infiltration curves were applied in time-series modeling for six different soil textures (clay, clay loam, silty, silty loam, sandy loam and sand). Different time-series models including Autoregressive (AR), Moving Average (MA), Autoregressive Moving Average (ARMA), autoregressive integrated moving average (ARIMA), ARMA model with eXogenous variables (ARMAX) and AR model with eXogenous variables (ARX) were evaluated in predicting cumulative infiltration. Autocorrelation and partial autocorrelation charts for each variable time-series models were investigated. The evaluation indices were the coefficient of determination (R2), root of mean square error (RMSE) and standard error (SE).
The results showed that the AR(p), ARX(p,x) and ARMAX(p,q,x) time series models with various degrees 1, 2, 3 successfully predicted infiltration rates for duration of the test in different soils. Significant correlation between actual and estimated values of cumulative infiltration was almost obtained. The values of SE varied between 2 and 5 percent for three soil textures in Lali plain. Reducing input data from two hours to one hour did not have major impact on infiltration prediction. The results of 24 hours cumulative infiltration also indicated standard error of estimated infiltration varied between 2 and 21% for six different soil textures. Similarly, there was a very good correlation between the actual and predicted values of 24 hours cumulative infiltration. The prediction error increased with increasing prediction time (4 hours vs. 24 hours). The time-series models had accurate performances to predict cumulative infiltration until 12 hours, therefore, they would be as a useful tool to predict soil infiltration characteristics for irrigation purposes. The RMSE values for predicting 24 hours cumulative infiltration were 0.5, 2.6, 4.1, 4.9, 7.5 and 11.8 cm for clay, clay loam, silt, silty loam, sandy loam and sand, respectively. The SE values also were 2.6, 11.7, 13.9, 14.9, 17.2 and 21.6 % for clay, clay loam, silt, silty loam, sandy loam and sand, respectively. Time-series modeling showed better performance in heavy and moderate soils than in light soils. However, the performance of the time-series modeling for predicting infiltration for the double ring test with four hours experiment time was better for light soil textures as compared to heavy and moderate soil textures. Therefore, more studies are needed to investigate the capability of time series modeling to predict infiltration with more experiment data, particularly for heavy and moderate soil textures.
The results indicated that the experiment time of the double ring test could be reduced from four to one hour by using time series models in various soil textures and consequently the cost of soil infiltration measurements would be decreased. Using initial 120 min infiltration data, the time-series models could successfully predict the 12 hours cumulative infiltration. Comparison between the results of times-series models and actual data indicated the application of time-series models in predicting soil infiltration characteristics was efficient.