GENERALIZED SPACE TIME AUTOREGRESSIVE MODEL FOR PHYSICAL PROPERTIES OF PEATLAND - Prastoro, Tarasinta
Indonesia has one of the largest peatlands in the world. One of the peatland’s function is carbon storage. In a stable condition peatlands net absorb carbon. Meanwhile in an unstable or dry condition, peatlands emit more CO2 gas because of aeration and increased risk of peatland fire. Studies showed that peatlands’ stabilization is influenced by its physical properties such as groundwater level and soil moisture. If groundwater level reaches more than 0.4 m undergound, peatlands’ cultivation function can be disturbed. In order to anticipate the unstable condition, a model is needed to predict the physical properties of peatlands in the future. Because peatlands’ physical properties change from time to time and is influenced by the environment around it, a space-time model is used. Because of the heterogenicity of lands in Indonesia, the suitable space-time model is model Generalized Space Time Autoregressive (GSTAR). GSTAR Modelling can be divided into six stages. In the first stage, identification of GSTAR models is done using the movements of space time autocorrelation function (STACF) dan space time partial autocorrelation function (STPACF) through different time lags and spatial lags. In the second stage, parameters from the identified models from the first stage is estimated using least squares method. In the third stage, diagnostic tests are done to test the stationarity using Inverse of Autocovariance Matrix (IAcM) and the fulfilment of white noise assumption of the residuals which are independent in time using Ljung-Box test and normally distributed with zero mean and constant variance using Kolmogorov-Smirnov of the identified models. In the fourth stage, the best model is chosen based on the mean squared residual (MSR) for in-sample and mean squared error (MSE). In the fifth stage, parameter signification test is done using the F statistic to detect significant parameters to the model. In the sixth stage, prediction is done using the best model for some time in the future. Spatial weight matrix as one of the important components in GSTAR model is a matrix which consists of influence weights of the neighbouring locations towards the observed location. In constructing a spatial weight matrix, it is needed to determine the spatial lag order definition and the type of spatial weight matrix used. This paper develops a spatial lag order definition which resembles a layered diamond shape. The usual types of spatial weight matrix are uniform matrix and inverse distance matrix. This paper used spatial weight matrix in three-dimensional space. However, because difference in height of the neighbouring locations and the observed location may have a different weight distribution from the difference in two-dimensional space, Hadamard product is used to combine the two-dimensional inverse distance spatial weight matrix with the difference in height spatial weight matrix. This paper named this matrix as modified spatial weight matrix. This paper used Pulang Pisau Regency of Central Kalimantan Province as the focused study area. The observed location points in this paper are six locations in Pulang Pisau Regency which are named Jabiren, Jabiren2, Jabiren5, Jabiren7, Kahayan Hilir, and Pandih Batu. The period of the data used are from 20 February 2021 until 18 March 2023 with difference of seven days. For groundwater level, six locations are used, for soil moisture, four locations are used which are Jabiren, Jabiren2, Jabiren5, dan Pandih Batu, and for rainfall, four locations are used which are Jabiren, Jabiren2, Jabiren5, Jabiren7. Modelling results showed that GSTAR(2;0,1) with modified spatial weight matrix a = 0.1 and b = 1.1 is suitable for groundwater level, AR(1) is suitable for soil moisture, and GSTAR(2;1,2) with modified spatial weight matrix a = 0 dan b = 1.0001 is suitable for rainfall. This indicates that groundwater level of a location is influenced by its neighbours with a different weight distribution for difference in height. Meanwhile, soil moisture of a location is only influenced by its own value in the past. On the other hand, rainfall of a location is also influenced by its neighbours but with the same weight distribution for difference in height. For the next five weeks, based on the contour maps using ordinary kriging interpolation, it was predicted that groundwater level and soil moisture in most areas of Pulang Pisau Regency will decrease. Meanwhile, rainfall in most areas of Pulang Pisau regency will be stable.