## 2 Materials and Methods
### Description of the Three-Phase Approach  
We have designed a three-phase approach which is a multivariate approach and through which descriptive factors of river health can be compounded to guide in developing management strategies for complex rivers at a temporal-spatial scale. The approach can be summarized as follows:  
* Phase I: Assessing current health status  
In the first phase, the current health status is evaluated via conducting a single-perspective or multi-perspective assessment. In general, most assessment approaches have been developed with multiple indicators, based on the experience and expertise of the team and drawing on scientific literature. In routine assessment, some of these commonly used indicators are water quality, biotic parameters, or a comprehensive index. Similarly, we have also established a water quality index (WQI) [29], index of biotic integrity (IBI) [30; 31], and health index (HI) [11] as the assessment indicators to evaluate the health status. Among these three indicators, WQI and IBI are considered single-objective indicators with which water quality and biotic features can be characterized and quantified. HI has been developed as a multi-perspective indicator to assess the comprehensive health status. WQI is composed of six variables, such as pH, temperature (T), total nitrogen (TN), total phosphorus (TP), dissolved oxygen (DO), and turbidity (Tur) [29], and the fish index of biotic integrity (FIBI), zooplankton index of biotic integrity (ZIBI), phytoplankton index of biotic integrity (PIBI), and benthic index of biotic integrity (BIBI) are compounded into the IBI [30; 31]. On the other hand, HI has been constructed with structural and functional variables and is evaluated using the order degree method, which could be found in detail in [PERSON] et al. (2013) [11]. Subsequently, when WQI, IBI, and HI are calculated and compared with the threshold value of each health grade, the current health status is graded. * Phase II: Forecasting health trends  
Given the current health status, the second phase, forecasting health trends, may be carried out, which yields a remarkable advance by forecasting upcoming severe short-term or long-term situations earlier than the original measurements. In this phase, WQI, IBI, and HI are used as the predictors, among which HI is considered as comprehensive objective predictor, while WQI and IBI are categorized as single objective predictors. Basically, after relationships between dependent and independent variables are projected into a new space, a linear regression combination can be constructed. When the residual error \(\hat{\varepsilon}_{P}(t)\) is very small, the ideal value \(Y_{P}(t)\) of predictor \(P\) can be interpreted with its predictive value \(\hat{Y}_{P}(t)\). Without loss of generality, the predictive model can be described by Equation (1). \[Y_{P}(t)=\hat{Y}_{P}(t)+\hat{\varepsilon}_{P}(t) \tag{1}\]  
where \(Y_{P}(t)\), \(\hat{Y}_{P}(t)\), and \(\hat{\varepsilon}_{P}(t)\), respectively, are the ideal value, predictive value, and predictive residual error of predictor \(P\) at time \(t\). \(P\) is a predictor such as IBI, WQI, or HI. \(\hat{Y}_{P}(t)\) and \(\hat{\varepsilon}_{P}(t)\) can be calculated via Equation (2) [32]. \[\hat{Y}(t)=f\Big{(}\hat{Y}(t-1),\ \hat{Y}(t-2),\dots,\hat{Y}(t-d);x_{1}(t),x_{2} (t),\dots,x_{n}(t)\Big{)} \tag{2}\]  
where \(\hat{Y}(t-1),\ \hat{Y}(t-2),\dots,\hat{Y}(t-d)\) are the predicted values of \(\hat{Y}_{P}\) or \(\hat{\varepsilon}_{P}\) at time \(t-1\), \(t-2\),..., \(t-d\) of the time series, respectively; \(x_{1}(t),x_{2}(t),\dots,x_{n}(t)\) are the values of monitoring variables at time \(t\), respectively; and \(d\) is the input and feedback delay time interval. * Phase III: Identifying causal factors  
If it is inferred that degradation exists according to the predictive trends, the next phase should be conducted to identify the main causal factors. Generally, river health may be threatened by natural, anthropogenic, or urgent stressors.