Taiwan is a mountainous island geographically located at the juncture between the Eurasian and Philippine tectonic plates and climatologically located in the corridor of typhoons. An active mountain belt with frequent typhoons shapes a steep and fractured landscape with verdant forests. The mean annual rainfall is about 2510 mm, and approx. 40 % of annual rainfall is brought by typhoons within a few days (Huang et al., 2014). The lowest mean annual temperature is approx. 4 ∘C in montane regions and 22 ∘C in the coastal plains. The mountains of Taiwan reach an elevation of 4000 m within a short horizontal distance (∼75 km) from the coast, creating a steep terrain (Huang et al., 2016). Specifically, the drainage area of most catchments is smaller than ∼500 km2, and stream lengths are less than ∼55 km (Fig. 1). The basic catchment descriptions, including landscape variables, can be found in Table S2 in the Supplement. Land cover inventories from the Taiwan Ministry of the Interior (https://www.moi.gov.tw, last access: 29 November 2023) were reclassified into three major categories, namely, water (CW), forest (CF), agriculture (CA), and others. The landscape metric was retrieved from the digital elevation model (DEM) with 20 m resolution: A is the drainage area [km2]; DD is the drainage density [kmkm-2], defined as the ratio of total stream length to drainage area; Sm is the gradient of the main stem [%]; HI is the hypsometric integral [–]; and ELO is the basin elongation [–], defined as the ratio of the diameter of the circle with the same area as the basin to basin length.

In addition to the primary landscape variables described above, we incorporated flow-path-associated variables into our study, as flow path is an explicit proxy for aquifer systems. Within a gridded DEM, the flow path is defined as the route followed by water from a grid cell, following the surface flow direction towards the channel cell (see details in Tetzlaff et al., 2009). Specifically, flow path length (lfp) is the route length from a cell to the nearest channel cell, flow path height (hfp) is the elevation difference between the specific cell to the nearest channel cell, and flow path gradient (gfp) is calculated as flow path height divided by flow path length. Each cell possesses its own value of lfp, hfp, gfp, and lfp/gfp. Since the velocity of gravity-driven flow is typically proportional to the gradient (v=lfp/T∼hfp/lfp), this implies that the time (T) is proportional to lfp/gfp: T∼lfp2/hfp=lfp/gfp. Consequently, lfp/gfp could serve as a potential proxy for residence time. Within a catchment, the medians of the lfp, hfp, and gfp distributions (L, H, and G) served as representative flow path characteristics. Please be aware that we defined the median of lfp/gfp (L/G) in our study, differing from the previous study by McGuire et al. (2005), which directly used the median lfp divided by the median gfp. In the hydrological context, lfp/gfp represents the residence time of each flow path, while the median of lfp/gfp reflects catchment-wide residence time. The detailed definition and calculation of the flow-path-associated variables are illustrated in Table S3 in the Supplement.

Streamflow in this steep mountainous island descends quickly after a typhoon invasion. Thus, hourly streamflow records are required to describe the entire streamflow recession since it only lasts a few days after the peak. This study collected hourly streamflow records during 1986–2014 from the Taiwan Water Resource Agency (https://www.wra.gov.tw, last access: 29 November 2023) and Tai-Power Company (https://www.taipower.com.tw, last access: 29 November 2023). Only the catchments without large water division infrastructures in the upstream area and with total rainfall greater than 30 mm were used to avoid human-manipulated streamflow data. Based on these criteria, 19 catchments and 291 events were included for further recession analysis. Commensurate with the hourly streamflow, the hourly rainfall dataset from the Taiwan Central Weather Bureau (https://www.cwb.gov.tw, last access: 29 November 2023) was collected, and the Thiessen weighted method was used to estimate areal rainfall in the corresponding catchments. The cumulative rainfall window was defined as the elapsed time from 6 h before the rising flow to the peak flow. We do not consider rainfall amount after peak flow because there is typically less rainfall occurring after the peak flow. Hydroclimate metrics of rainstorm and streamflow, including total precipitation (P), duration (D), average precipitation intensity (Iavg), total streamflow (Qtot), peak flow (Qp), antecedent streamflow (Qant), and runoff coefficient (Qtot/P), were extracted from these datasets (Tables S3 and S4 in the Supplement).

The storage–outflow relationship is typically described by a power law if treating the catchment as a black box. The representative storage is, in fact, composed of many aquifers and thus exhibits a nonlinear relationship: 1Q=mSn, where S is the storage volume within a catchment (in units of volume [L3] or depth [L]), Q is the rate of streamflow ([L3T-1] or [LT-1]), and m and n are constants (Vogel and Kroll, 1992). Since S is difficult to directly measure, the relationship between the rate of streamflow decline and streamflow could be derived to represent the recession behavior (Brutsaert and Nieber, 1977) in Eq. (2). 2-dQdt=nm1nQ2n-1n=a^Qb, where a^ is the recession rate, and b represents the nonlinearity of storage, which is also the slope of the regression line in the plot of log⁡(-dQ/dt) vs. log⁡(Q) (the recession plot). Both parameters can be estimated via different assumptions and fitting techniques. Notably, since nonlinearity is dimensionless, a^ is inherently strongly dependent on the units of Q and b via fitting (see details in Sect. 2.2.2). Although the recession plot enables the analysis of streamflow recession and facilitates the derivation of the storage–outflow relationship (Stölzle et al., 2013), the methods of recession segment extraction affect parameter estimation. For example, Stölzle et al. (2013) compared three extraction methods in conjunction with their corresponding parameter estimations. They found that recession characteristics, like recession time (1/a^), varied over 1–2 orders of magnitude, yet nonlinearity, b, varied rather narrowly. Their results suggested that the recession characteristics derived from different procedures have only limited comparability. Further, Dralle et al. (2017) found that the relationship between a^ and antecedent wetness was sensitive to the number of data points and thus the extraction method. Despite the estimated parameters being inconsistent among the procedures, applying the same procedure is still a feasible way to capture the recession responses in a region.

The streamflow recession plots of catchments W9, W5, and W8, as examples, are illustrated in Fig. 2. The three catchments have distinct differences in landscape, particularly in drainage area (A) and the ratio of flow-path length to gradient (L/G). Catchment W9 has a larger A and lower L/G, W5 has a smaller A and lower L/G, and W8 has a smaller A but higher L/G; see Table S2 for catchment details. Median b values, in descending order, were 2.34 in catchment W9, 1.96 in W5, and 1.63 in W8. The point-cloud-derived b values were 1.45 (W9), 1.37 (W5), and 0.88 (W8), showing that point-cloud-derived b values are smaller than median-derived values (Fig. 2c). Notably, the exponent b decreases with storm magnitude in W5 and W8 but increases with storm magnitude in W9 (Fig. 2b and c). The contradictory responses observed in these three catchments might be attributed to variations in their landscape structure and rainstorm characteristics. This apparent association is explored further in the Discussion section.

The frequency distributions of the fitted recession coefficients and nonlinearities from all catchments and event records are shown in Fig. 3a and b. Recession coefficient a ranged from 0.003 to 0.273 h-1 with a mean of 0.059 h-1 and median of 0.047 h-1. The large difference between the median and mean reflects a right-skewed distribution. Exponent b ranged from 0.90 to 4.39 with a mean of 1.76 and median of 1.69. The small difference between the median and mean suggests a relatively symmetric distribution. Spatial patterns of recession coefficient and exponent b are illustrated in Fig. 3c and d. Generally, larger recession coefficients were seen in the southwestern plain catchments (Fig. 3c), which have higher L/G ratios. Apart from this, no other distinct pattern can be found in other more mountainous catchments. Conversely, the plot of recession nonlinearity shows no clear connection to large-scale landscape features on the island (Fig. 3d).

The recession parameters derived from individual segments and aggregated point-cloud data are illustrated in Fig. 4. The variations of recession responses from individual segments differed greatly among catchments. For parameter a, point-cloud-derived values, which aggregate all recession segments in a catchment, are much larger than the coefficients from individual segments. Notably, when the catchment size exceeds approximately 500 km2 (W19), the point-cloud-derived coefficients become similar to the third quantile of the coefficient distribution from individual segments. For exponent b, the values derived from the point cloud are consistently close to the lower limit of the distribution of the individual segment-derived values and the median and interquartile range of exponent b derived from individual segments are not correlated with drainage area. These distinct differences between coefficients and exponent b from the two fitting methods make comparison and interpretation difficult. The details of the recession characteristics for each catchment can be found in Table S5 in the Supplement.

To capture how rainfall forcing affects streamflow recession, correlation analyses were performed. The correlation coefficients between recession parameters and event-associated variables are shown in Fig. 5 and Table 2. The total precipitation (P), duration (D), total streamflow (Qtot), antecedent streamflow (Qant), and runoff coefficient (Qtot/P) were negatively correlated with the recession coefficient, a. The average precipitation intensity (Iavg) and peak flow (Qp), both of which represent the rainstorm magnitude, were not significantly correlated to a. As for initial event conditions, the 7 d antecedent precipitation, AP7day, defined as the 7 d rainfall amount prior to a rainstorm, was not correlated to a nor were other AP period lengths (3, 5, 14, or 30 d). Unlike the recession coefficient, exponent b was only correlated with two, Qant and Qp, with positive and negative correlations, respectively. This indicates that higher antecedent flow could lead to higher nonlinearity and peak flow to lower. Overall, hydrometric forcing moderately controls the coefficient and only slightly affects nonlinearity.

Regarding landscape variables, the average height (H), length (L), and gradient (G) of the flow path were approx. 120 m, 252 m, and 0.47, respectively (Table S2). The mean L/G value for our catchments was approx. 951 m. Forest coverage (CF), ranging between 11.8 %–92.1 %, was the dominant landscape type for most mountainous catchments. Notably, the catchments in the western plain are characterized by gentle gradients of flow path, such as catchments W8, W9, W11, W12, W13, and W14, where agriculture is the dominant land cover. The correlations of recession parameters against landscape variables are illustrated in Fig. 5 and Table 2. Most landscape variables (H, L, G, L/G, DD, Sm, HI, CW, CF, and CA) are significantly correlated with the coefficient, particularly the flow-path-associated ones (H, L, G, L/G, and DD). Flow-path height (H), length (L), and gradient (G) were negatively correlated to the coefficient, but L/G and DD were positively correlated. Additionally, the coefficient increases as HI and Sm decrease. Looking at land cover, the coefficient increases with CW (proportion of water body land cover) and CA (proportion of agriculture land cover) and decreases with CF (proportion of forest land cover). Greater water-body or agricultural land area in a catchment lead to a faster recession, yet greater forested land area can slow recession. Correlations between b and the landscape variables were generally weaker and of the opposite sign than the correlations seen with a. There also were less significant correlations. In short, most landscape variables are moderately associated with the coefficient and low-to-moderately associated with exponent b. Perhaps, putting all catchments with various landscape features together would obscure the landscape's control in recession.

The point-cloud estimates are distinctly different from the estimates from the individual recessions (Fig. 4). The larger a and smaller b values derived from the point cloud compared to those derived from individual segments could be expected due to the influence of antecedent flow and superimposition of recession events (Jachens et al., 2020). Since a and b are inherently dependent and while the decorrelation method might be only valid for some specific cases (Biswal, 2021), the way (e.g., fixing b) to obtain the a or b of an individual event is still goal-dependent (Sharma and Biswal, 2022). Even so, using the median from individual segments is suggested, compared to the point-cloud derivation (Dralle et al., 2017; Jachens et al., 2020).

Higher median recession coefficients were found in W8, W11, W12, and W14, which we attributed to the landscape features of shorter and gentler flow paths, i.e., dense drainage networks. By contrast, catchments with longer and steeper flow paths, such as W7 and W15, have lower median recession coefficients. Taken together, these data demonstrate how drainage density and flow-path-associated variables can affect the recession coefficient. The findings presented in Table 2 corroborate this (discussed more in Sect. 4.2). On the other hand, the median of exponent b is approx. 1.69 (Fig. 3b) with a range of 0.90 to 4.39, which is also comparable to the ranges found in the literature. For example, values of b from 0.5 to 2.1 could be found in 220 Swedish catchments with low-flow data (Bogaart et al., 2016), 0.6 to 1.7 for 22 Taiwanese rivers derived from low-flow data (Yeh and Huang, 2019), and 1.5 to 3.2 for 67 US watersheds with event data (Biswal and Marani, 2010). Nonlinear storage–outflow relationships (b is not equal to 1.0) are prevalent for most catchments worldwide. In our cases, the highest and lowest median values of b were found in W7 and W19, respectively. Despite the fact that these two catchments have similar landscape structures, their exponent b exhibits distinct differences. Perhaps, other controlling factors, such as geological structure (i.e., connectivity between the deep aquifer and the stream, heterogeneous hydraulic properties, and/or the interface slope between the shallow and bedrock layers; see Roques et al., 2022) or land cover (Tague and Grant, 2004) might alter recession behavior as well.

Landscape structure aggregates catchment hydraulic properties, embodying recession parameters conceptually. Therefore, recession behaviors in a catchment could be interpreted from two perspectives, hillslope hydraulics and inter-hillslope heterogeneity (Harman et al., 2009), both of which could be represented by the flow-path-associated variables (e.g., H, L, G, L/G, and DD in Table 2) and drainage area. Notably, heterogeneity increases with drainage area because of the possibility of including a wider range of subsurface conditions. Recession nonlinearity also increases with drainage area since a larger area accommodates a higher possibility of superimposition of multiple linear reservoirs, which has been seen in the 68 km2 Mahurangi watershed, New Zealand (McMillan et al., 2014), and the 41 ha Panola Mountain Research Watershed, USA (Clark et al., 2009; Harman et al., 2009), though this does not appear to be the case in our study (Fig. 6a). Moreover, the correlation analysis showed that flow-path-associated variables (H, L, G, L/G, DD) only have a weak correlation with the recession nonlinearity (Table 2).

The weak correlation between recession nonlinearity and those variables may be attributed to two factors. First, there is the scale effect. Some of our catchments are much larger than 500 km2, which far exceeds the extent of rainstorms (usually less than 200 km2). In these large catchments, the limited extent of rainstorms would not bring about a comprehensive recession response in the outflow hydrograph (Huang et al., 2012). Second, the drainage area cannot reflect the unknown number of aquifers (Ajami et al., 2011), making it unclear whether a positive relationship exists between nonlinearity and drainage area in our study. Moreover, Karlsen et al. (2019) argued that the dependence of b on landscape variables would change with the streamflow rate. Specifically, flow path height, H, dominates the nonlinearity during high flow, whereas the drainage area, A, gains more importance during low flow. The relationship between flow-path-associated variables and drainage area and recession needs to be examined in our catchments.

Recession behavior is a convolutional response starting as rain falls within catchments. Thus, we separately examined the recession parameters against hydrometric variables for the three catchment types (Types A, B, and C) to rule out the influences (Fig. 8). This produced two significant findings: (1) the recession coefficient, a, decreases with the rainfall amount in all types, and (2) the exponent b shows contrasting responses in Types A and B (Type C is statistically insignificant). In heterogeneity-dominated (large) or hydraulics-dominated (small and steep) catchments, exponent b increases or decreases with rainfall amount, respectively.

The above two sections have demonstrated the influence of landscape and rainfall amount on streamflow recession behavior. Thus, a perceptual model which demonstrates the interactive regulation of landscape structure and rainfall amount on recession nonlinearity is introduced (Fig. 9). Landscape structure is considered in two contexts: spatial heterogeneity (drainage area) and hillslope hydraulics (L/G). The drainage area may correlate to the number of perched storages within the catchments, and the L/G ratio, encapsulating hillslope geometry, can indicate the dynamics of the contributing area associated with runoff generation. Along the spatial heterogeneity dimension (from Type B to A, with increasing drainage area), additional perched storages respond increasingly with rainfall amount and thus enhance the recession nonlinearity. Perched storages are expected to occur where the hydraulic conductivity abruptly decreases due to heterogeneous soil properties or geological structures. The existence of perched storages was found in an experimental forested catchment in Taiwan through an intensive soil water monitoring scheme (Liang, 2020). Large catchments may suffer uneven spatial rainfall, which activates perched storages locally; thus, the nonlinearity increases. On the other hand, along the L/G dimension (increasing from Type B to C), the heterogeneities of hydraulic conductivities decrease. Heavy rainfall, causing saturation and expansion of the saturation area, can mediate the heterogeneity of hydraulic conductivity and thereby reduce nonlinearity.