پیش‌بینی سطح آب‌زیرزمینی با استفاده از مدل شبکه‌های بیزین پویا مبتنی بر تحلیل حساسیت (مطالعه موردی: دشت بیرجند)

نویسندگان

چکیده

پیش‌بینی سطح آب زیرزمینی، نقش مهمی در مدیریت منابع آب زیرزمینی دارد. در این پژوهش، با استفاده از شبکه‌های بیزین پویای احتمالاتی و در نظر گرفتن ?? رویکرد پیش‌بینی ماهانه، با استفاده از داده‌های واسنجی ?? سال آبی، سطح ایستابی آبخوان بیرجند، در یک دورة آبی ? ساله و در دو رویکرد صریح (پیوسته) و خوشه‌بندی (دسته‌بندی) صحت‌سنجی و پیش‌بینی شد. در رویکرد پیش‌بینی صریح، از داده‌های صریح ماهانه استفاده و در رویکرد خوشه‌بندی با استفاده از شاخص عرض سیلهوت تعداد خوشه‌های بهینه تعیین و با خوشه‌بندی داده‌ها، از داده‌های خوشه‌بندی شده برای آموزش مدل بیزین استفاده و پیش‌بینی مدل با استفاده از داده‌های خوشه‌بندی انجام شد. با اعمال واسنجی در مدل بیزین و بررسی نتایج سناریوهای تحلیل حساسیت مختلف، کارایی بالای شبکه‌های بیزین پویا به‌ویژه در رویکرد صریح، مشاهده شد. با بررسی ?? رویکرد تحلیل حساسیت اعمال شده برای پیش‌بینی سطح ایستابی آبخوان، مشاهده شد که از بین عوامل پیش‌بینی کننده، پارامتر سطح آب زیرزمینی در ماه فعلی اثرگذاری بالایی را در افزایش دقت مدل برای پیش‌بینی سطح ایستابی آبخوان ماه بعدی دارد؛ به گونه‌ای که با حذف این پارامتر در مدل بیزین، ضریب تبیین از ????/? به ????/? کاهش یافت و میانگین مجذور مربعات خطا نیز از ????/? به ????/?متر افزایش یافت. همچنین بالاترین ضریب تبیین در بین سناریوهای پیش‌بینی ???/? است.

کلیدواژه‌ها


عنوان مقاله [English]

Groundwater Level Prediction Using Dynamic Bayesian Networks Based on Sensitivity Analysis (Case Study: Birjand Plain)

نویسندگان [English]

  • Abbas Roozbahani
  • Ebrahim Ebrahimi
  • Mohammad Ebrahim Banihabib
چکیده [English]

The aquifers are about four percent of the water on the earth, but they are considered as the best and most accessible source of fresh water. In recent years, they have been faced with severe water withdrawal, therefore some plains was considered as forbidden plains that it means the water withdrawal from these aquifers is unauthorized. At some point, plains have been faced with land subsidence that showed the severity of the disaster. Given such a critical situation in aquifers, management of groundwater resources in the form of tools such as monitoring the level of the aquifers is essential. One of the plains in Iran that has a critical groundwater resource is Birjand plain which requires management measures to be protected from future water resources crisis. Prediction of groundwater level in future periods is a useful tool to enforce management measures before a crisis occurs. Thus, in this study, groundwater level was predicted in Birjand aquifer taking ?? monthly forecasting scenarios in a period of ? years and in both crisp (continues) and clustering approaches using probabilistic Dynamic Bayesian Networks (DBNs). Nowadays, various tools are used to predict the aquifer level including mathematical models, artificial neural network, neuro-fuzzy, Bayesian networks, and time series and so on. In recent years, due to the flexible and simple structure, Bayesian networks have been used for predictions of different parameters, especially in forecasting of hydrological parameters. Bayesian network as a modern forecasting probabilistic method shows probabilistic relationships between a set of variables by graphical model. It represents the dependence structure among several factors, that affecting on each other, and is based on Bayesian theory. Dynamic Bayesian Networks have been extended from Bayesian Networks which are created for two purposes: first, as the cycle of dependency detector over the time, quite similar to Markov model; second, as the fixed process which is repeated in fixed-time interval. Another feature of Dynamic Bayesian network is their willingness to approximately structured changing. In this study, the input data (predictor parameters) of the model includes: temperature, rain, evaporation, monthly aquifer recharge in each Thiessen Polygon (Recharge), monthly withdrawals of groundwater in each aquifer Thiessen Polygon (discharge), groundwater levels in the current month and the groundwater level in the next month (predicted parameter).
The first step in modeling by the dynamic Bayesian network is determining the dependent and independent data for calibration and validation. Model calibration data in both crisp and clustering approach include a ??-year period (???? to ????) and data validation include ?-year period (???? to ????), in monthly time step. Depending on the type of input data, both crisp and clustering approach was used. In the crisp approach, the probability functions were used and the predicted data were obtained by using the training data. In the clustering approach, by assigning each of the numbers to the right cluster, the modeling was done. A cluster is collection of objects that their relative distance to each other is low and relative to other members is high. In the first approach by using crisp data and NPC training structure in confidence level of ?%, the training was applied. In the second approach, the Silhouette index was calculated by using MATLAB software and by using the validation Silhouette index, and then, the number of clusters was determined. Finally, the clustering was performed by using k average method. Then, training was done in the second approach, using clustered data and NPC training structure in confidence level of ?%. Considering ?? different scenarios to predict groundwater level in the next month, the uncertainty of predicted parameters in both crisp and clustering approach were assessed.
In fact, using these scenarios, sensitivity analysis was performed to check the accuracy of the model with respect to the existence or absence of different predictor parameters. In addition, the uncertainty of the model output is evaluated using dynamic Bayesian network probabilistic analysis. The results of the selected scenario in crisp approach showed the high prediction accuracy of Bayesian networks. For example, in piezometers ? and ?, the coefficient of determination was estimated about ?.??. According to the results, crisp dynamic Bayesian networks approach predicted hydrograph aquifer more accurate than clustering approach. Due to the low efficiency of clustering approach in predicting groundwater hydrograph, to obtain the accuracy of ?? scenarios predictions in this approach, instead of coefficient of determination (R^?) and root-mean-square error (RMSE), the percentage of correct predicted clusters was determined. According to the results, the clustering approach predicts clusters with high accuracy for different piezometers. The scenario ? had the best prediction which all predictor parameters except evaporation were used for the prediction. In this scenario, R^? and RMSE were showed good accuracy as ?.???? and ?.????, respectively. The other scenarios had also the accuracy in their predictions very close to scenario ?, except scenario ? which the groundwater levels were not used as input. Thus, in the crisp approach, the groundwater levels have a substantial impact on the accuracy of the prediction. Generally, in crisp approach, all predictor scenarios have acceptable accuracy of over than ??% except scenario ?. In clustering approach, by examining the accuracy of the scenarios in predicting clusters, most scenarios were accurate except scenario ?. Dynamic Bayesian Network model in clustering approach correctly predicted clusters but, unlike the crisp approach in predicting hydrograph, it was not able to present acceptable results.
The results showed the ability of the proposed model in planning and management of groundwater resources, reducing the risk of aquifer level declining by applying short term management scenarios and predict its effects on rehabilitation. Moreover, this model can be used in the similar plains for aquifer management.

کلیدواژه‌ها [English]

  • Bayes' Theorem
  • Clustering
  • Groundwater management
  • Sensitivity analysis