Monitoring and Forecasting of Height and Area Variations on Urmia Lake Based on Markov Chain Monte Carlo Time Series Analysis

Study of local changes in wetlands is of great importance in hazard management of water resources and climate change prediction. According to the infiltration process of water on the ground surface and mixing with groundwater, there will always be a need for monitoring and quality control of surface waters to avoid horrible environmental hazards. Retreat of the coastlines can cause a hydrological concern, moreover, it can be a serious challenge to the quality of water resources followed by the consequences on living organisms.
Lake Urmia is the largest permanent salt water lake located in north-western part of Iran, between East and West Azerbaijan provinces, and the twentieth largest terminal lake in the world which stands in second place after the Great Salt Lake, located in the northern part of the U.S. state of Utah. Drought, heat, increased demand for irrigation water, construction of numerous dams and ecological changes due to construction of a causeway that divides the lake into south and north parts, have been steadily shrinking the salty Lake Urmia. By a continuation of this process, disturbance of the regional ecosystem is possible in the near future.
Sequential data over a long time interval is required to monitor fluctuations of the lake and form time series. For this reason, satellite data captured by radar and optical sensors in a 24-year interval from 1992 to 2016 were taken into account. Radar data was used to obtain surface water level fluctuations of the lake and a spectral process of the optical data was used to compute the surface water extent of the lake for the intended time interval. Surface water level (height) and surface water extent (area) are two important parameters that are directly correlated with the water balance of Lake Urmia. Normalized difference vegetation index (NDVI) was calculated from Landsat satellite imageries to obtain candidate wetland pixels followed by a multiplication of candidate wetland pixels and ground sampling distance (GSD) of Landsat scenes to calculate the area of the lake for any desired time interval. Then, classic and modern methods for modeling the time series of height and area data were studied and cross validated. Auto-regressive integrated moving average (ARIMA) and generalized auto-regressive conditional heteroscedasticity (GARCH) were selected as representatives of classic methods and Markov chain Monte Carlo (MCMC) was selected as a representative of modern methods.
A Markov chain is a discrete time stochastic process with the property that the distribution of any new value of the process, only depends on the pervious value of the chain. This chain needs to be aperiodic to stop Markov chain from oscillating between different sets of states in a regular periodic movement. Monte Carlo sampling technique was then used to avoid this problem. Periodic seasonal variation parameters were then added to the MCMC model using a combination of delayed rejection and adaptive metropolis sampling (DRAM). In this case, the solution to the problem that we are pursuing is to compute the probability of transition from current state to any other possible states. Finally, a comparison between results from classic models and MCMC based on root mean square error (RMSE) and R-squared measures was done to obtain goodness of fit in cross-validation section. For this purpose, classic and modern models were applied on the first 90 percent of input data and the efficiency of each model evaluated from comparison of predictions from the model and latter 10 percent of input data. Results from goodness of fit tests showed that ARIMA and GARCH are not able to model non-linear behavior of input data. However, Markov chain random sampling time series analysis using Monte Carlo algorithm showed good results in prediction of Lake Urmia height and area time series in comparison with classic methods.
Deployment of MCMC in monitoring and prediction of height and surface fluctuations of Lake Urmia can provide precise measurements with error intervals of about ±14 centimeter and ±1.66 square kilometer, respectively. Considering calculated error intervals and predictions from MCMC model, Lake Urmia fluctuations until 2020 were computed. Results showed a nearly stable state for drought conditions at Lake Urmia. According to the predictions from MCMC model, maximum height and surface fluctuations are limited between [-23 to ] centimeter and [-80 to ] square kilometer, respectively. Recent observations of height and surface in a six-year period from 2011 to 2016, showed a good stability in fluctuations which could be a cause of implementation of restoration policies for Lake Urmia, however, there is still a long way to full restoration of this lake. Strict plans for restoration policies are necessary in order to avoid an environmental disaster due to a possible decrease in height and surface of Lake Urmia based on future predictions.