Higher Order Markov Chain Model for Synthetic Generation of Daily Streamflows

ABSTRACT The aim of this study is to further investigate the two-state Markov chain model for synthetic generation of daily streamflows. The model presented in (4) to determine the state of the stream and later studied in (2) and (3) is based on two Markov chains, both of order one. In some areas of Hydrology, where Markov chains of order one have been successfully used to model events such as daily rainfall, researchers are concerned about the optimal order of the Markov chain (10). In this paper, an answer to a similar concern about the model developed in (4) is given using the Bayesian Information Criterion (BIC) to establish the order of the Markov chain which best fits the data. The methodology is applied to daily flow series from seven Brazilian sites. It is seen that the data generated using the optimal order are closer to the real data than when compared to the model proposed in (4) with the exception of two sites, which exhibit the shortest time series and are located in the driest regions.摘要 本研究旨在进一步探究用于逐日径流量合成生成的两态马尔可夫链（Markov Chain）模型。文献(4)中提出的用于确定径流状态的模型，后续在文献(2)与(3)中得到进一步研究，该模型基于两个一阶马尔可夫链。在水文学的部分研究领域中，一阶马尔可夫链已被成功用于模拟逐日降雨等水文事件，但研究者们仍关注马尔可夫链的最优阶数问题(10)。本文针对文献(4)所提模型的同类关切问题，采用贝叶斯信息准则（Bayesian Information Criterion, BIC）确定最适配数据集的马尔可夫链阶数，进而给出解决方案。本研究将该方法应用于7个巴西站点的逐日流量序列。结果表明，相较于文献(4)所提模型，采用最优阶数生成的径流量数据更贴近真实观测数据；仅两个站点例外——这两个站点的时间序列最短且地处最干旱区域。