#### 2.1. Study Region

We conducted the study on the Nan River, located in Shengnongjia (31,015′–31,075′ N, 109,056′–110,058′ E), the western mountainous region in Hubei province of China. Elevation in this region varies from 420 to 3015 m (with a mean elevation >1500 m), resulting in an altitudinal climate gradient. The annual mean air temperature ranges from 7.1 °C in the western region to 14.5 °C in the eastern region, with the coldest and warmest months in January and July, respectively [

34]. The annual precipitation commonly varies between 800 and 2500 mm, in which more than 85% of rainfall occurs in April to October with December to February accounting for <8% [

34]. Karst terrain is a typical geomorphological characteristic in Shengnongjia where ~30% of bedrock is limestone. Due to the high solubility of this type of rock, there are enormous underground rivers, karst caves, swallow holes, groove, and springs in this region [

34,

35].

We surveyed four reaches in the headwaters of Nan River (

Figure 1). The streambed substrate is dominated by gravels, pebbles, and cobbles, with bedrock of limestone [

34]. Sheng Nong Yuan (SNY) and Da Long Tan (DLT) are two first-order reaches with elevation of 2320 m and 2220 m, respectively (

Table 1). SNY is located in the mainstream, while DLT is in an adjacent tributary (

Figure 1). Swallow holes are common along the 1-km-long stream channel just downstream of the confluence of DLT tributary (

Figure 1). Surface water seeps into swallow holes, leading to reduced flow in the reaches immediately downstream. The downwelling reaches (i.e., sections with swallow holes), which were not surveyed in this study, have been observed to dry up from late December to February when rainfall is minimal (personal observation). Groundwater recharges to the surface channel through discrete springs in reaches downstream of the swallow holes and ensure sufficient base flow to maintain surface water during dry periods. Hong Shi Zi (HSZ) is a second-order downstream reach approximately 2 km downstream from the confluence point of DLT with an elevation of 1950 m. Several visible springs can be observed along this reach; indicating that this reach is influenced by groundwater discharge. Ji Zi Gou (JZG) is another second-order reach about 4 km downstream HSZ, located at an elevation of 1820 m. All the four study reaches have permanent surface flow. The DLT tributary reach had the narrowest wetted width and the shallowest water depth during the study (

Table 1). As for the three mainstream reaches, mean wetted width and water depth both increased longitudinally among reaches from SNY to JZG. All the four reaches had closed riparian canopy and low degree of human disturbance because of effective protection of this region.

#### 2.2. Data Collection and Preparation

The four reaches were surveyed monthly from July 2011 to June 2017; however, data was not collected in April and July of 2015 due to large floods. We monitored stream discharge, air temperature, and water temperature for each reach on all sampling occasions. Mean reach discharge was calculated from measurements at three randomly selected cross-sections along a 50-m reach. At every 50-cm interval along each cross-section, flow velocity was measured using a Global Water Flow Probe Hand-Held Flowmeter (Xylem Inc., White Plains, NY, USA) and water depth was recorded using a tape. The wetted width of each cross section was also measured with a tape. Discharge (m

^{3} s

^{−1}) was calculated using the velocity-area method for each cross-section [

36]. Air and water temperature were measured and averaged from the same three cross-sections with an YSI Pro Plus multimeter (YSI Inc., Yellow Springs, OH, USA). Although we did not sample all the reaches at the same time on each occasion, fieldwork in all reaches was completed within a 2 to 3-hour period to minimize variation due to time of sampling.

Benthic algae were sampled at the same aforementioned three cross-sections for each reach during each occasion. Five stones of 10–20 cm diameter were randomly selected at each cross-section, with a total of 15 stones for each reach. We defined the sampling area for each stone with a circular lid of 2.7 cm radius. The stone surface within the lid was vigorously scrubbed using a nylon brush and rinsed 3–4 times with distilled water. All subsamples from the same cross-section were combined into one composited sample and the volume was recorded [

37]. Algal sample was passed through a glass fiber filter (Whatman GF/F) in the field and kept dark and cool. In the laboratory chlorophyll

a was extracted with 90% acetone and absorbance values at 630, 645, 665 and 750 nm were measured using a Shimadzu UV-1601 spectrophotometer (Shimadzu Corp., Kyto, Japan), following a standard analysis procedure [

38]. Benthic Chl.

a concentration for each cross-section was calculated as mg per stone surface area (mg m

^{−2}). Chl.

a concentration for each reach was averaged from the three cross-section replicates.

#### 2.3. Statistical Analysis

Although our data did not allow us to directly quantify variation in groundwater-surface water exchange among the study reaches and over time, we made use of long-term (six years) measurements to infer spatial and temporal variation in the relative influence of groundwater. This approach has been employed elsewhere [

7,

16,

19,

25]. We then relate this understanding of the relative variation in groundwater influence to the observed spatial and temporal variation in the physical and biotic parameters that we assessed.

We performed bivariate linear regression by using water temperature as the response variable and air temperature the predictor to investigate the degree of groundwater influence for each reach. Since monthly water temperature data is not generally autocorrelated, simple linear regression is effective in modeling such a relationship [

28]. We expect that the reach most influenced by groundwater (i.e., HSZ) would have a greater intercept and a lesser slope for the regression equation than reaches not influenced by groundwater [

39].

We calculated nine metrics characterizing stream water temperature and discharge regimes during the study period for each reach. These metrics represent the water temperature and discharge regime magnitude, variability, frequency, and timing. Magnitude was described with the total mean value, the maximum monthly mean value (Mean_max), and the minimum monthly mean value (Mean_min) of water temperature and discharge. Variability was represented by the range and coefficient of variation (CV) of the two variables. We counted the number of months with water temperature >10 °C for delineating temperature frequency because 10 °C is an important temperature threshold for many aquatic metabolic processes [

40,

41]. For instance, algal biomass was greatest when water temperature was at or below 10 °C in several forested streams [

41]. We also selected 3 °C as another threshold for calculating water temperature frequency because we observed that the study reaches displayed substantial differences among the reaches when temperature was lower than this value. For discharge frequency, we counted number of months with discharge <0.02 or >0.20 m

^{3} s

^{−1} which represents approximately the 25th and 75th percentiles of the distribution of discharge across all reaches. For the timing metrics, we identified specific months when the maximum (M_mean_max) and minimum (M_mean_min) monthly mean water temperature or discharge was reached. We also calculated all the aforementioned nine metrics for Chl.

a, because algal biomass also varies temporally [

42].

We used wavelet analysis to describe regime periodicities in water temperature, discharge, and Chl.

a for each reach. Wavelet analysis is especially effective in detecting and differentiating scale-specific dynamics from noisy, complex and usually nonstationary time series data that violates assumptions of many other statistical methods [

43,

44]. This method performs a local time-scale decomposition (i.e., local wavelet transform) of the time series by estimating its spectral characteristics as a function of time [

43]. Significance of local wavelet spectrum was tested by comparing against a background red noise spectrum (representing low-frequency/long-period cycles of the time series with autocorrelated residuals) simulated with Monte Carlo procedure [

45,

46]. Wavelet analysis was conducted by using ‘wt’ function in R package ‘biwavelet’, with continuous Morlet wavelet transforming as the base function due to its good balance in time and frequency localization [

45]. To further determine which periodicities were most important throughout the study duration, we calculated time-averaged wavelet spectrum for temperature, discharge, and Chl.

a with ‘analyze.wavelet’ function in package ‘WaveletComp’. For each site, there was a total of 3–4 missing data during the study period. Since missing data are not allowed in wavelet analysis, for each time series, we interpolated missing values with the mean of all available data from the same month adjusted for that year’s mean value using the decomposition method described by Cloern and Jassby [

42,

47].

We conducted convergent cross-mapping (CCM) to identify influences of water temperature and discharge on temporal fluctuations of Chl.

a. This novel nonparametric method has been described in detail elsewhere [

48,

49,

50], so we provide only a brief introduction here. Based on state space reconstruction, CCM measures the skill of cross-mapping (i.e., prediction) between two variables (e.g., x and y) as test for causality. Following Takens’ Theorem, it is assumed that if x influences y, then y would contain unique information from x. Therefore, historical values of x can be reconstructed from y alone. Conversely, x does not contain information from y, hence will be incapable of cross-mapping y [

50]. To accomplish the test, Simplex projection with a time delay embedding from y is first used to predict historical values of x [

48]. Then, Pearson’s correlation coefficient (ρ) between predicted x and measured x values is calculated to indicate the ability of y cross-mapping x. The ability of x cross-mapping y is also estimated with similar procedures. It is determined that x influences y if ρ value for y cross-mapping x is higher than that of x cross-mapping y, and vice versa [

51]. Significance of the result was tested with Ebisuzaki phase-shift null model. This randomizing procedure removes dynamic correlations between time series, but preserves most of short-term behaviors [

52]. A CCM result is considered significant if the ρ value for x cross-mapping y exceeds the range of the 5th and 95th percentiles of corresponding estimates for the null model. In the present study, we estimated reach-specific effects of stream water temperature and discharge on Chl.

a. If temporal dynamics of Chl.

a was driven by water temperature or discharge, Chl.

a would be more effective in cross-mapping the other two variables than using the other two variables to cross map Chl.

a. We applied simplex projection to calculate the optimal embedding dimension for individual time series, and set library size varying from 1 to 60 in steps of 6 with 100 bootstrapped library samples. CCM was performed with time lags of ±3 months to account for possible time delayed effects [

53]. For the time lag with the highest cross map skill, we further tested the significance of the results by generating a null distribution with 100 surrogate data. All the time series were first-differenced to remove any trends, and normalized to zero mean and unit variance for allowing time series comparisons [

48]. CCM was performed with package ‘rEDM’.

Additionally, to investigate whether contrasting seasonal hydrological conditions may influence water temperature, discharge, and Chl.

a, we calculated the mean values (± standard deviation) of these parameters for each reach during a typically low-flow (December to February) and high-flow (May to July) period in this region [

34]. We assessed whether these parameters differed among reaches within seasons using Kruskal–Wallis test by ranks, with pairwise comparisons by Mann–Whitney tests with Bonferroni correction.