Journal of Hydrology 523 (2015) 636–649 Contents lists available at ScienceDirect Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol A hydrograph separation method based on information from rainfall and runoff records Yiwen Mei, Emmanouil N. Anagnostou ⇑ Civil and Environmental Engineering, University of Connecticut, Storrs, CT, USA a r t i c l e i n f o Article history: Received 4 October 2014 Received in revised form 24 January 2015 Accepted 31 January 2015 Available online 9 February 2015 This manuscript was handled by Konstantine P. Georgakakos, Editor-in-Chief, with the assistance of Marco Borga, Associate Editor Keywords: Baseflow separation Flood event Hydrograph Rainfall record Digital filte s u m m a r y Hydrograph separation is considered as the first step to catchment-scale water balance analysis. A wide variety of hydrograph separation methods exists ranging from empirical to analytical and physical. This study discusses a physically-based approach that combines baseflow separation and event identification with minimal data requirement. The input datasets are basin-average rainfall and discharge time series. Outputs are baseflow time series, the timing of the runoff events, differentiated as single- or multi-peak, and the associated rainfall event time series. To assess the method’s feasibility, hydrograph properties are evaluated for both long-term (annual and monthly) and event-scale time series. Results show that the long-term derived baseflow indices are positive (negative) correlated with basin area (runoff coefficient). The event scale analysis shows that the timing-related parameters (i.e. durations of rainfall and flow events and time lag between rainfall to flow events) increase with basin area in terms of magnitude and variability. Similar dependence on basin scale is shown for the water balance-related parameters determined from this analysis, namely event rainfall and baseflow volumes and baseflow index. Water balance parameters are shown to be characterized with less degree of variability for single-peak events relative to multi-peak events. Ó 2015 Elsevier B.V. All rights reserved. 1. Introduction The separation of baseflow from direct flow has been a recurring theme in hydrology for more than four decades (Koskelo et al., 2012; Chen et al., 2008; Gustard et al., 1992; Chow et al., 1988; Lyne and Hollick, 1979; Hall, 1968). The essence of hydrograph separation is traditionally considered to render a deconstructive rationale of streamflow as a two-component or multi-component process. The most commonly used scheme is the two-component scenario that considers streamflow consisting of direct flow (i.e. quick surface or subsurface flow) and baseflow (i.e. flow that comes from groundwater storage or other delayed source) (Tallaksen, 1995; Hall, 1968). Direct flow is in general formed by surface precipitation, overland flow (i.e. infiltration excess or saturation excess), interflow (i.e. shallow subsurface flow), and rapid groundwater flow, while baseflow is the relatively stable flow between storms and includes contributions from groundwater and return flow (Hornberger, 1998; Tallaksen, 1995). There exists a wide variety of methods for baseflow separation, which are categorized into different types based on selected crite- ⇑ Corresponding author. Tel.: +1 (860) 486 6806. E-mail address: manos@engr.uconn.edu (E.N. Anagnostou). http://dx.doi.org/10.1016/j.jhydrol.2015.01.083 0022-1694/Ó 2015 Elsevier B.V. All rights reserved. ria, such as tracer-based method, graphical method, filtering method, digital filter and recession analysis (see Table 1 for a summary). Among the various methods, the tracer-based method yields the most realistic results (Buttle, 1994; Sklash and Farvolden, 1979); however, it is laborious and expensive; thus its application is restricted to small number of events, which prohibits statistical analysis. Graphical is the most intuitive method (Chow et al., 1988), but it is based on empirical assumptions and user’s speculations. Another technique is the filtering method which is typically designated for long-term, daily time scale, data records. Example filtering methods are the smooth minima baseflow separation method of the United Kingdom Institute of Hydrology (UKIH) and its subsequence versions and the Hydrograph Separation Program by the United States Geologic Survey (HYSEP) (Aksoy et al., 2009, 2008; Sloto and Crouse, 1996; Gustard et al., 1992). Digital filter is a commonly used baseflow separation method nowadays, and it can be sorted as one-, two- or multi-parameter filter depending on the number of parameters used (Lyne and Hollick, 1979; Jakeman and Hornberger, 1993; Chapman, 1999; Eckhardt, 2005). Common parameters for these filters are the recession coefficient and the maximum baseflow index (the longterm ratio of baseflow to total streamflow) (Eckhardt, 2005); the one-parameter filter has a predefined maximum baseflow index. 637 Y. Mei, E.N. Anagnostou / Journal of Hydrology 523 (2015) 636–649 Table 1 Properties of the baseflow separation methods. a Method Examples Data resolution Record length Physical basis In-situ experiment Tracer-based Buttle (1994) Sklash and Farvolden (1979) Sub-daily or higher Event Highest Required Graphical Straight line, fixed-base, variable slope method (Chow et al., 1988) Daily or higher Event Lowest No Filtering HYSEP; (Sloto and Crouse, 1996) UKIH (Gustard et al., 1992) Daily Long term Low No Digital filter Chapman-Maxwell Filter (Chapman and Maxwell, 1996) Recursive Digital Filter (Eckhardt, 2005) Jakeman and Hornberger Filter (Jakeman and Hornberger, 1993) Hourly or higher Long term or event Medium to high Optionala Recession analysis Constant-k method (Blume et al., 2007) Wittenberg and Aksoy Method (Wittenberg and Aksoy, 2010) Hourly or higher Event High No Degree of physical basis increase by running the in-situ experiment for baseflow index. The recession coefficient (rate of change of discharge depletion during periods of little or no precipitation) can be determined reasonably well from the recession limb of the hydrograph (Nathan and McMahon, 1990), while to get a value for the maximum baseflow index would require running in-situ measurements, or acquiring it from the literature. A three-parameter filter is rarely used since it was concluded to produce baseflow hydrographs with sharp peaks compared to observations (Chapman, 1999). The most physically based method without running field experiments could be the analytical solution of recession equation. This group of methods generally starts from assuming either a linear (Blume et al., 2007; Su, 1995) or nonlinear (Wittenberg and Aksoy, 2010) relationship between storage and flow rate. To ensure a reasonable recession coefficient for a digital filter, or the analytical solution of recession, fine temporal resolution flow data is required. Use of baseflow separation methods to study properties of hydrologic events requires determining the start and end times of these events in the streamflow record. Typically this is carried out manually by visual inspection of the time series data. However, visually inspecting the timing of events is cumbersome when it comes to long-term data records. Few studies on this topic have attempted to develop automatic event identification methods that can apply to large data records (Dhakal et al., 2012; Koskelo et al., 2012; Norbiato et al., 2009; Merz and Blöschl, 2009; Khanal, 2004). Merz et al. (2006) introduced an automatic event identification technique by using a calibrated lump hydrologic model. The study used the technique to identify 50,000 events from 337 Austrian catchments (areas ranged from 80 to 10,000 km2) over a 20 year period; Merz and Blöschl (2009) expanded the number of Austrian catchments to 459 (5–10,000 km2 basin areas) and provided a more comprehensive analysis on runoff coefficient. Norbiato et al. (2009) applied this technique on 14 mountainous catchments in the eastern Italian Alps (basin areas ranged from 7 to 608 km2) to extract 535 events over a 15-year period. In short, the Merz et al. (2006) is a reliable technique, but requires calibrating a hydrologic model, which limit it applicability in data poor regions (e.g. mountainous areas). Khanal (2004), on the other hand, proposed a semi-automatic approach based on the unit hydrograph method, which he applied on 90 mid-slope watersheds in Texas to extract 1737 single peak events over a 27-year period. The method required manual identification and extraction of the multi-peak events as well as events with un-wanted shapes. The event database was then used in several subsequent studies. Cleveland et al. (2006) compared the differences in peak discharge and time-to-peak between the observed events and their simulated counterparts from three different unit hydrograph models; Fang et al. (2007) studied the scale dependency of the time of concentration for the selected events and found a positive relationship between time of concentration and the drainage area; Dhakal et al. (2012) investigated the responses of event-based runoff coefficients to precipitation and percentages of impervious surface for more than 1600 events from that database. A simpler and more empirical method called SARR (Sliding Average with Rain Record) was recently developed by Koskelo et al. (2012) for daily flow data. The essence of SARR is to associate each rainfall event (i.e. a series of consecutive days with rain followed by at least one day with no rain) with a quickflow event (i.e. time period between the beginning of one quickflow cycle to the beginning of the next quickflow cycle) to form a rainfall-runoff event. In their study, Koskelo et al. (2012) found that the tracerbased method calculated about 1–4 times more baseflow than the SARR method for the same events, ascribing this to the dampening effect of using the daily temporal resolution flow data. Requirements of SARR are obviously less demanding, but the method itself is empirically based, and restricted to small basin scales (<50 km2) and coarse temporal resolutions (daily). In this study, we investigate an automatic hydrograph separation method that is based on long time series and hourly time scale data on basin rainfall and runoff. The new aspects of this technique are its physical basis, which requires less data to constrain the even separation algorithm. Specifically, a set of parameters (recession coefficient, maximum baseflow index, time lag between rainfall and runoff mass centers) are derived by mining the basin areal rainfall and runoff time series and used to drive the event separation algorithm. An important point to note is that the algorithm is designated for basins with clear recession period (this limitation is detailed in the conclusion part). In Section 2 below we describe the study area, rainfall and runoff data used to demonstrate the efficiency of the proposed technique. The technique’s procedures used for baseflow separation and event identification are described in Sections 3.1 and 3.2, respectively. The results are discussed in Section 4, while conclusions are summarized in Section 5. 2. Study area and data 2.1. Study area The study area is the Tar River basin in North Carolina, USA (Fig. 1 top left panel). Information about the basin can be found in Mei et al. (2013). The study area was divided into eight nested sub-basins, namely T1, T2, T3, T4, S, F1, F2 and TSF shown in Fig. 1, based on the available locations of stream gauges (each 638 Y. Mei, E.N. Anagnostou / Journal of Hydrology 523 (2015) 636–649 Fig. 1. Location (top left), drainage systems (top right) and geomorphology (bottom panel) of the Tar River Basin. Table 2 Main physical information of the study basins. Gauge codes T1 T2 T3 T4 S F1 F2 TSF Area (km2) 432 1125 2031 2406 429 461 1374 5848 Elevation (m) Slope (°) Mean Range Mean Max 148 128 106 99 98 83 81 76 88–225 56–225 27–225 17–225 41–163 38–143 25–158 3–225 2.7 3.2 2.9 2.7 2.8 2.8 2.8 2.2 21.3 28.3 28.3 28.3 25.5 20.8 21.3 28.3 steam gauge is regarded as the outlet of that sub-basin). Drainage areas for the eight sub-basins range from 400 to 5900 km2 (refer to Table 2 for details about the basins). There are three separate drainage systems (Fig. 1 top right panel): The main channel of Tar River, which runs through sub-basins T1, T2, T3 and T4; the Swift Creek, a tributary of the Tar River that flows across sub-basin S; and the Fishing Creek, another tributary of the Tar River, which flows across sub-basins F1 and F2. These three rivers join as the Tar River nears the basin outlet we name the entire basin as TSF using the first letter of each river’s name. The basin is characterized by low elevations (ranging between 4 and 225 m above sea level) and mild slopes (i.e. max slope is less than 30° with 3° of mean slopes). 2.2. Rainfall and flow data Rainfall dynamics and variability information for each basin is extracted from the US National Weather Service (NWS) Multisensor Precipitation Estimation (MPE) rainfall product available at 4 km/hourly spatiotemporal resolution. MPE data are derived from a combination of observations from satellite, the WSR-88D radar network and rain gauges (Breidenbach and Bradberry, 2001; Fulton, 2002). Eight years of data (2002–2009) were analyzed for this work. Mean annual precipitation for all sub-basins was over 1000 mm; among the study years, 2003 was the wettest with more than 1200 mm of annual cumulative precipitation for every sub- 639 Y. Mei, E.N. Anagnostou / Journal of Hydrology 523 (2015) 636–649 Table 3 Rainfall and runoff properties of the study period. Mean annual runoff (mm/year) Annual runoff ratio Mean maximum annual flow (m3/s) T1 T2 T3 T4 S F1 F2 TSF 1000 1015 1027 1038 1059 1080 1070 1074 302 298 300 311 326 280 279 310 0.30 0.29 0.29 0.30 0.31 0.26 0.26 0.29 162.7 166.6 174.1 206.2 55.5 56.2 104.1 347.0 (b) Event Identification Mean annual precipitation (mm/year) (a) Baseflow Separation Gauge codes Fig. 2. Flow charts of baseflow separation (left panel) and event identification (right panel) based on methods described in Section 3 (dashed lines standard for the iterations). basin, while 2005 and 2007 were comparatively drier years receiving less than 1000 mm of annual cumulative precipitation (Table 3). The streamflow datasets used in this study are hourly streamguage measurements from USGS that span the same eight-year period as the precipitation data (information regarding the streamflow datasets are listed in Table 3). The mean annual runoff volumes are around 300 mm for all sub-basins. Similarly to precipitation, 2003 was hydrologically the wettest with annual cumulative runoff volume over 500 mm (518–668 mm) for the different sub-basins, while 2007 and 2008 had relatively low (138– 211 mm) annual cumulative runoff volumes. Besides, values of the runoff ratio (mean annual runoff over mean annual precipitation) for the different sub-basins are nearly the same at 0.29 due to the similar annual precipitation and runoff volumes. sion (denoted below as bRCK and bFRCK). Timings of the analyzed events (i.e. their start, peak and end hours) are the outputs of the event identification part. Every process step and variable computed from this steps are labeled on the flow chart and the corresponding descriptions are documented in Sections 3.1 and 3.2. 3.1. Baseflow separation We considered the two-component streamflow scenario (baseflow and direct flow) in formulating this technique. In short, we revised the constant k method developed in Blume et al. (2007) (hereafter named revised constant k method, RCK) so as to adjust it for long term flow records. Also, we coupled the revised constant k method with the recursive digital filter (RDF) constructed by Eckhardt (2005) to compute the baseflow hydrograph, namely FRCK method. The two methods are described next. 3. Methodology This section describes the details on the proposed methodology including inputs, outputs, implemented steps and variables involved. Flow charts showing the connection of the various steps and flow of data and information are shown in Fig. 2 for the two main aspects of this algorithm, namely baseflow separation and event identification. As we can see from the flow charts, the required inputs are merely rainfall and flow time series. Outputs from the baseflow separation part are the baseflow time series constructed under the revised constant k method, and its filtered ver- 3.1.1. Revised constant k (RCK) method Blume et al. (2007) proposed the CK method to determine points on the hydrograph associated with negligible changes of the recession coefficient. By assuming the linear reservoir model, discharge at time t during recession is defined as: Q ¼ Q 0 ekt ð1Þ where Q is discharge at time t (mm/h), Q0 is discharge at the beginning of recession (mm/h), and k is the recession coefficient (h1). Based on the form of Eq. (1), k can be expressed as: 640 Y. Mei, E.N. Anagnostou / Journal of Hydrology 523 (2015) 636–649 k¼ d 1 dQ ln Q ¼  dt Q dt ð2Þ In the RCK method, we defined the change rate of k (k⁄, h2) analytically as:  kt ¼ kt  kt1 Dt ð3Þ where Dt is 1 h. Any time step with absolute k⁄ value smaller than a given constant were defined as recession points and were marked down on the flow time series. The specific steps of the RCK method are shown in the flow chart of Fig. 2 and described below: (1) Determine k from Eq. (2) by performing linear regression over a fixed-length time window (linear regression between dQ/dt and Q), namely regression window (LRW, set as 19 h to make sure there are enough points to guarantee the representativeness of the linear regression). Fig. 3 (top panel) indicates that k is negative/positive during the rising/recession limb but close to 0 during the crest and it tends to stabilize going to the recession. (2) Compute k⁄ by Eq. (3). Fig. 3 (middle panel) indicates that k⁄ value in most of the points during recession is stable, while it can vary within a large range around the crest. This is consistent with the behavior of k. (3) Select and record the time steps with positive k and |k⁄| < 5  105 h2. Value of 107 min2 is suggested in Blume et al. (2007) since it is small enough for quantifying ‘‘no changes’’, thus any value smaller than 104 h2 is accepted in this study. We named the value 5  105 h2 as null-change ratio, RNC. (4) Further exclude the selected recessing points associated with regression r2 values lower than a threshold, namely minimum acceptable r2 (r 2MA , refer to Table 4 for the values). The reason of this restriction is visualized in Fig. 3 (bottom panel); recession limb is characterized mostly with high r2 Table 4 Initial parameters of the FRCK method. Gauge codes r 2MA K (102 h1) a BFII LSP (h) T1 T2 T3 T4 S F1 F2 TSF 0.9 0.9 0.9 0.85 0.88 0.9 0.9 0.88 5.99 2.94 1.74 1.46 1.77 2.44 1.53 0.75 0.942 0.971 0.983 0.986 0.982 0.976 0.985 0.992 0.28 0.38 0.49 0.48 0.50 0.44 0.49 0.60 67 81 91 94 67 68 84 112 value while the crest and the period before the rising limb have low r2. This implies that quantifying recession limb with Eq. (1) is appropriate. (5) Find the time step that the flow rate is from recessing to rising. These points are named as rising points and should satisfy the following condition: ( r2 > r 2MA Q ðt  1Þ P Q ðtÞ < Q ðt þ 1Þ ð4Þ (6) An extra quality control criterion was put on for further selection of the rising and recessing points with flow rate greater than an envelope baseflow rate (ben) are excluded; the procedure for implementing this envelope baseflow rate is described in Section 3.1.2. The remaining rising and recessing points are named as turning points. (7) Connect the turning points with straight lines to form the baseflow hydrograph, bRCK. A quality control procedure used in the other studies is also implemented here; namely, baseflow is set as total flow when it is greater than total flow. This is valid not only for bRCK, but also for any baseflow time series in our study; thus, we use the symbol Qb here to represent any baseflow time series: Qb ¼  Qb Qb < Q Q Qb P Q ð5Þ 3.1.2. Envelope baseflow hydrograph As shown in the procedure (3) of RCK method, a null-change ratio is determined for every potential turning point from recession limbs. This leads to an issue; this ratio cannot satisfy every single recession limb due to the heterogeneity of temporal flow properties. That is although most of the turning points appear at the visually acceptable locations, a portion of them would show up at inappropriate locations, (e.g. near the peaks; this issue becomes more significant in flow data from larger basins). Therefore, envelope baseflow time series (denoted by ben) are constructed to limit the occurrences of turning points at the high flow rate locations. The envelope baseflow time series are simply the product between the flow rate maxima for every block (envelope flow time series, Qen) and the baseflow index determined for the entire study period (denoted by BFI). Therefore, Qen are constructed as following (also shown in the flowchart of Fig. 2): (i) The flow hydrograph is divided into a number of segments according to a searching period, LSP. This searching period should be able to capture most of the flow maxima associated with an event. We apply one of the classical empirical methods to determine the number of hours from the peak hour to the event ending hour (Hornberger, 1998; Chow et al., 1988): Fig. 3. Temporal dynamics of recession coefficient, k (top panel), change rate of recession coefficient, k⁄ (middle panel) and coefficient of determination, r2 (bottom panel) for a sample flow period of T1 basin. LSP ¼ 19:848A0:2 Values of LSP (in hours) are listed in Table 4. ð6Þ 641 Y. Mei, E.N. Anagnostou / Journal of Hydrology 523 (2015) 636–649 (ii) Find the time steps with maximum flow rate of every segment; these time steps are represented as (tM(i), QM(i)). (iii) Select the time steps that the maximum flow rates are the largest compared to their two outliers; that is: Q M ði  1Þ 6 Q M ðiÞ P Q M ði þ 1Þ ð7Þ (iv) For the selected time steps, fill the time period from tb(j) to te(j) with QM(j) to form the Qen; tb(j) and te(j) are defined as: t M ðj  1Þ þ t M ðjÞ 2 t M ðjÞ þ t M ðj þ 1Þ te ðjÞ ¼ 2 tb ðjÞ ¼ ð8Þ ð9Þ (v) Determine ben by taking the product between Qen and BFI as mentioned in Section 3.1.1. To limit the value range of ben, upper and lower limit of envelope baseflow rate, bu and bl are set. Thus, the final ben values are calculated as: ben 8 bu > < ¼ BFI  Q en > : bl R Q b dt BFI ¼ RT Qdt T ð12Þ BFI in Eq. (12) is determined from the entire flow record T. a in Eq. (11) is related to the recession coefficient as following: a ¼ ek ben P bu bl < ben < bu ð10Þ ben 6 bl bu and bl (in mm/h) are determined based on the mean flow rate over the study period according to the subsequent steps (vi and vii). (vi) Construct a CDF for Q and find the corresponding quantile for the mean flow rate. (vii) Find the baseflow envelope by taking the quantile range between 8% (bu) above and 2% below (bl) the mean flow rate quantile. Values of bu and bl and mean flow quantiles are determined from the CDF of the flow time series (step vi) and are basin scale dependent (refer to Table 5 for values). Fig. 4 shows a case of excluding turning points above the envelope baseflow time series by rendering an example segment of hydrograph from T3. As noted in the figure, turning points above the envelope baseflow rate are excluded. 3.1.3. Parameterization for RDF The recursive digital filter is used to pass bRCK attained after procedure (7) once forward. RDF has the following form (Eckhardt, 2005): bRDF ðtÞ ¼ Fig. 4. Visualization of the baseflow separation parameters for a sample period of T3 basin. að1  BFIÞ ð1  aÞBFI bRDF ðt  1Þ þ Q ðtÞ 1  aBFI 1  aBFI ð11Þ where bRDF is the baseflow time series (in mm/h). BFI is the baseflow index defined as the ratio of baseflow volume in a given time interval (e.g. a year, a month or an event) to the total streamflow volume at the same time interval: ð13Þ We use K instead of k to represent the recession coefficient in Eq. (13) because this is determined for the entire flow record, while k is evaluated at any time step. The parameterization process of RDF (see Fig. 2) is described as following: (8) Plot dQ/dt against Q for the time steps from recession limbs (characterized by positive dQ/dt value and r2 P r 2MA ) on a log–log scatter plot (see Fig. 5). (9) Fit a straight line for the eligible dQ/dt against Q with zerointersection; the slope is the recession coefficient K (Fig. 5) since Eq. (2) can be rewritten as:  dQ ¼ KQ dt ð14Þ Thus, for time steps from the recession limb the slope of linear regression defined by Eq. (14) should reflect the overall recession coefficient of the basin (see Table 4 for K). (10) Calculate a for every basin according to Eq. (13) (Table 4). (11) Apply UKIH to find the initial baseflow index for Eq. (11) since we cannot calibrate BFI solely based on RDF (Eckhardt, 2005). UKIH was designed for daily flow data (Gustard et al., 1992); hence, the hourly flow time series are aggregated to daily resolution before applying UKIH. The initial BFIs are calculated based on the entire 8-year period (see Table 4 for values). (12) Filter the bRCK time series forward by Eq. (11) once, name the new time series as bFRCK. Table 5 Quantiles and flow rate for construction of envelope baseflow hydrographs. Gauge codes T1 T2 T3 T4 S F1 F2 TSF Upper envelope baseflow Lower envelope baseflow Mean flow Quantile (%) Rate (102 mm/h) Quantile (%) Rate (102 mm/h) Quantile (%) Rate (102 mm/h) 87.0 84.0 80.7 78.9 79.9 80.4 79.4 76.2 5.01 4.52 4.66 4.66 4.75 4.02 4.01 4.67 77.5 74.5 71.2 69.4 70.4 70.9 69.9 66.7 3.14 3.11 3.19 3.29 3.54 3.03 3.02 3.31 79.5 76.5 73.1 71.4 72.4 72.9 71.9 68.7 3.45 3.40 3.42 3.55 3.72 3.20 3.18 3.54 642 Y. Mei, E.N. Anagnostou / Journal of Hydrology 523 (2015) 636–649 3.2.1. Flow events A flow event is defined with three characteristic points, the start, peak(s) and end. If these points are ensured, an event is established. Based on the concepts of rising and recessing points, it is seen that event start/end points on the flow time series could be found within the population of rising/recessing points. Hence, this section presents a method to locate the flow peak and then associate the peak flow points with the closest rising and recessing points. The technique steps (also shown in the flowchart of Fig. 2) are described below: (1) Replace the continuous time steps with equivalent flow rate by one time step. For example, time steps t to t + n have the same flow rate at Qs, then the point that will replace these time steps is (Ts, Qs) where Ts is the midpoint of t and t + n, and estimated as: l nm Ts ¼ t þ 2 ð15Þ Q s ðx  1Þ 6 Q s ðxÞ P Q s ðx þ 1Þ ð16Þ Time steps with unique flow rate to their two neighbors remain. (2) Find the maxima time steps for (Ts, Qs) as: Fig. 5. Recession analysis for basin overall recession coefficient K. The basin name is shown at the upper left corner of each panel. Procedures (1) through (12) document the entire process of baseflow separation. Among the involved parameters, K is derived based on recession analysis, LSP is determined empirically based on a classical method, RNC is reported in previous studies and the other parameters are arbitrarily selected. We may also accept the selections of LRW and r2MA since the temporal dynamics of k, k⁄ and r2 are reasonable as shown in Fig. 3. Thus, only the choices of BFI could be ambiguous to some extent. Aiming to reduce the arbitrary aspect of FRCK method, we add an iterative scheme in the technique, described below: (13) Calculate BFI based on bFRCK with Eq. (12). (14) With the new BFIs from step (13), rerun steps (6), (7) and (13) six times. Fig. 6 (left panel) shows the differences of two consecutive baseflow indices for successive iterations. As shown, the difference is decreasing exponentially with iteration, converging to nearly 0 (value below 107) after the sixth iteration, justifying the six iterations selected for use in this iterative scheme. 3.2. Event identification In this section we describe a method to identify single flow events from the stream flow record together with the information from the FRCK method. The flowchart of this method is presented in Fig. 2 right panel. Besides the hydrograph (Q) and hyetograph (p0), information needed for the FRCK method are the locations of rising and recessing points, the FRCK baseflow hydrograph (bFRCK), the baseflow index (BFI) and the searching period (LSP), which were derived in the baseflow separation procedure. In short, the essence of this method is to synthesize flow events with three characteristic points (start, peak(s) and end of the event) and then associate the flow event to a corresponding rainfall event from the rainfall time series; the method for rainfall event identification used here is based on a procedure used in Mei et al. (2014). This method is named as characteristic point method (CPM). Time steps satisfy this criterion form the maxima flow hydrograph, (Tm, Qm). (3) Exclude the time step from the maxima flow hydrograph if its baseflow index at that hour is higher than BFI or the product between its flow rate and BFI is lower than the mean of Q. This means that only the time steps that satisfy the following condition remain: Q m ðyÞ  BFI > max  Z 1 QðtÞdt; T T bFRCK ðyÞ  ð17Þ where y is the index of (Tm, Qm). This criterion is intended to remove low Qm. (4) Group the (Tm, Qm) pairs that are close to each other. The term ‘‘close’’ is quantified as: T m ðyÞ  T m ðy  1Þ 6 LSP ð18Þ The same number is assigned for any consecutive (Tm, Qm) that satisfy Eq. (18). (5) Select the maximum flow rate from each class assigned by the same number. These time steps are regarded as the peak flow points. (6) For each peak flow, use its closest rising/recessing hours as the event beginning/end. It is possible that some peak flow points share the same rising or recessing points or both, these peak flow points are grouped together as a multi-peak event. Peak flow points that have unique rising and recessing hours are termed as single-peak events. 3.2.2. Rainfall events We considered rainfall events as periods of non-zero basin-average rainfall intermitted by zero rainfall periods (Mei et al., 2014). Two parameters are included within this definition, the threshold of rainfall rate that defines existence rainfall and the minimum time length between two rainfall events (namely zerorain threshold, r0, and length of minimum gap, LMG, respectively); r0 is selected as 0 and LMG is set equal to 1 h by definition. The overall properties (mean duration of events, mean event rainfall volume, mean event rainfall intensity and mean maximum rainfall rate of events) are listed in Table 6. It is seen that smaller size basins have fewer number of events associated with shorter durations leading to higher basin-average rainfall intensities. This is expected given that larger basin areas have higher chance of 643 Y. Mei, E.N. Anagnostou / Journal of Hydrology 523 (2015) 636–649 Fig. 6. Behavior of baseflow index (left panel) and mean time lag (right panel) for each iteration. Table 6 Overall properties of rainfall events in the study period. Gauge codes Num. of events Duration (Dr, h) Volume (Vr, mm) Intensity (mm/h) Max rain rate (mm/h) T1 T2 T3 T4 S F1 F2 TSF 2033 2126 2289 2295 1986 1899 2060 2361 4.1 4.6 5.4 5.3 4.4 4.5 5.0 6.0 3.9 3.8 3.6 3.6 4.3 4.5 4.2 3.6 0.5 0.4 0.3 0.3 0.5 0.6 0.4 0.3 1.5 1.3 1.0 1.1 1.6 1.8 1.4 1.0 receiving rainfall (more events and longer duration). On the other hand, the event rainfall volume average values do not show clear basin scale dependency. Besides, the mean maximum event rainfall rates are smaller for larger size basins, pointing to the smoothing effects of basin area. 3.2.3. Events combination A method is introduced to associate rainfall with flow events. If the difference between the start time of a rainfall event and a flow event is less than a specified time length (the searching radius defined in Eq. (20)), the two events are considered coincident. We grouped this type of rainfall events as group A. If rainfall event start time is occurring close to the flow event centroid is counted as contributing rainfall event to that flow event. This type of rainfall events can in some cases trigger another peak flow or at least elongating the recession limb. They are termed as group B events. A rainfall event occurring after a flow event’s centroid with its centroid within the flow event is named as group C event. Flow events with only group A rainfall are typically characterized with a clear shape and peak, while multi-peak events or events with elongated recession limbs often have group B event within. Group C event is typically characterized by short duration and low volume. The event-based properties (e.g. event time lag, runoff coefficient, baseflow index) are also computed. Details of the event combination method are listed below (also included in the flowchart of Fig. 2): (7) Find the rainfall events that occur before the beginning of each flow event within a searching radius, RS in h, as: 0 6 t b  s b 6 Rs ð19Þ where tb and sb are the beginning hour of flow event and rainfall event, respectively. RS are determined differently for dry and wet seasons. For wet season, events are close to each other; thus, the radius is selected as the length of the gap between two consecutive events. For the dry season, where events are apart from each other, the mean of event time lag, tlag, is used as the radius. This is implemented as: Rs ðnÞ ¼ min " tb ðnÞ  t e ðn  1Þ; N 1X t lag ðnÞ; N n¼1 LSP # ð20Þ where te is the end hour of flow event; n is the index of flow event and N is the total number of events for the basin. It is noted that the mean of tlag needs to be initialized to values smaller than the LSP for each basin, since the purpose of using LSP is to maintain stability. Based on visual inspection of the rainfall and flow datasets, the initial mean tlag are selected as 30, 40, 70, 70, 60, 40, 60 and 100 h. The rainfall events being identified from this step belong to the group A. (8) Find the rainfall events having centroids between the centroid of the closest group A event and the centroid of the flow event itself. The concept of centroid is given as (Ehret and Zehe, 2011): R T t c ¼ Rf t  Qdt Tf Qdt ð21Þ where Tf stands for the period of flow event. If Q and Tf are replaced by p0 and Tr (period of rainfall event), centroid of rainfall event, sc, is yielded. This group of rainfall events belongs to group B. 644 Y. Mei, E.N. Anagnostou / Journal of Hydrology 523 (2015) 636–649 (9) Merge the corresponding group A and B event(s) as a whole rainfall event and calculate the time lag between this combined rainfall event to its matching flow event. The time lag here is different from that in Eq. (20) and thus, it is represented by tl for distinction. (10) Find the rainfall events after the flow event centroid satisfying the following conditions:  sc > t c t e  sc > t l ð22Þ These rainfall events are the group C events. The term rainfall event refers to the combination of group A, B and C rainfall event in the study. (11) Calculate the event time lag (difference between rainfall and flow event centroid) and runoff coefficient (RC). We applied one of the most classical definition of RC (Norbiato et al., 2009; Blume et al., 2007; Merz et al., 2006) as: RC ¼ R Tf ðQ  bFRCK Þdt R p dt Tr 0 4. Results and discussions ð23Þ (12) Exclude events with negative tlag or RC greater than 1. Average tlag with the rest events and plug it into Eq. (20). (13) Rerun from steps (7) to (13) until the mean of tlag remain the same. It is found that differences in two consecutive mean tlag are decreasing as the iteration time increase for all basins (Fig. 6 right panel). Also, it needs four times of iteration so as to attain constant mean tlag for every basin. The mean tlag differences become 0 after the 3rd iteration except for the F2 case. (14) Some extra event selection criteria are implemented to remove events with fairly low flow volume and high initial and final flow rate. For the first aspect, it can be determined mathematically as: 1 Df Z Qdt < Tf 1 D Z Qdt ð24Þ T where D and Df stands for the duration of the T and Tf periods, respectively. Eq. (24) indicates events with mean flow rate smaller than the mean flow rate of the entire record. This kind of events is disregarded from the analysis. For the second aspect, events with ratio between their beginning/end flow rate to their peak flow rate larger than the event-based BFI, BFIe, are also removed: max   Q ðtb Þ Q ðte Þ ; > BFIe Qðt p Þ Qðt p Þ sub-basin T1). It is seen that rainfall is only found around the first rising hour of the flow (i.e. group A events). Event in the top right panel is from the same sub-basin, but year 2004. Besides group A events, group B events are also identified in the rising limb and around the crest. The group B event located in the rising limb act as one of the flow-peak-triggering rainfall events similar to the previous group A events. Existence of the second group B event elongated the duration of recession by maintaining the flow rate until the beginning of July 16th. Contrast to the first two sample single-peak events, the bottom panel renders an example multipeak event from basin T1 in 2002. No points satisfy the requirements of recessing at the first recession limb and rainfall occur at the late period of the recession. This rainfall event (a group C event) acts as a flow-peak-triggering rainfall, which results in another peak flow and eventually end up as a multi-peak flow event. ð25Þ where tp is the peak flow hour. For event with multiple peaks, the tp associated with the largest peak flow is used. Three sample events are displayed in Fig. 7. Within the top left panel is an example exhibiting a clear recession limb (year 2003, 4.1. Temporal dynamics of baseflow We first evaluated the temporal dynamics of baseflow constructed under RCK (bRCK) and its RDF filtered version (bFRCK) by rendering an example sequence taking from sub-basin T3 in Fig. 8 left panel. It is seen that the two hydrographs are similar to each other in values but the temporal variability of Q has been propagated to bFRCK through the filter. By using the filter, some rapid droppings and risings from RCK are eliminated. Fig. 8 (right panel) shows a hydrograph segment containing four sample events. The start and end times of each event are associated with high BFIs (above 0.9). The third sample event has a long duration and four peaks, which each has a follow up recession limb. It cannot be further separated here since the first potential recession period is not long enough to let the flow rate drop below the ben while the second and third one are ambiguous, thus no points satisfy the recessing requirements. The first and second sample events are typical single peak events. The similarity between FRCK hydrograph to RCK and RDF hydrographs are quantified by the mean relative error (MRE) and correlation coefficient (CC) on both long term and event basis time scales (see Tables 7 and 8 for statistics, respectively). Both tables indicate few discrepancies between the RCK hydrographs to the FRCK ones, implying that the RDF does not change the temporal variability of RCK hydrograph significantly by passing the information from the stream flow to the RCK baseflow sequence. Magnitudes of the long-term based MREs/CCs are smaller/larger compared to those for the event basis; namely, highest CCs between RCK and FRCK are shown for the annual time scale, while high correlation between RDF and FRCK is found mostly at monthly time scale. Additionally, the mean of long term MREs between RCK/RDF and FRCK are always positive/negative, while the event MREs are negative/positive because the event quick flow dampens the filter’s diminishing effect (i.e. magnitude of the original Fig. 7. Illustration of events with group A (left panel), group A & B (middle panel) and group A, B & C rainfall events (right panel). 645 Y. Mei, E.N. Anagnostou / Journal of Hydrology 523 (2015) 636–649 Fig. 8. Visualization of baseflow hydrographs by RCK and FRCK method (left panel), and event identification under CPM (sample segments from T3) (right panel). sequence becomes smaller after the filter is applied). The eventbased MREs and CCs show positive basin-scale dependencies for every drainage systems (also seen for annual CCs). Table 8 Same as in Table 7, but for the event time scale. Gauge codes T1 T2 T3 T4 S F1 F2 TSF 4.2. Long term based baseflow properties Fig. 9 exhibits the long term (entire flow record) baseflow indices, determined after the 6th iteration according to FRCK method, plotted against the basin areas. It is noted that there exist positive basin-scale dependencies for every drainage system; pointing to one aspect of the basin dampening effect that rain water is recharging the subsurface flow during traveling downstream (Wainwright and Parsons, 2002). In addition, the positive correlations between BFI and area are more evident for the Tar River basin, which implies the differences in rainfall response for the three drainage systems. We focus on two lumped parameters that are intimately related to the catchment water budget (baseflow index and runoff coefficient) on an annual and monthly basis. Fig. 10 indicates a negative correlation between BFI and RC on both yearly and monthly basis (more pronounced for the yearly basis). This is reasonable since years or months with high BFIs are dry with fairly low quick flow rates defined as the nominator in Eq. (23). One may argue that both stream flow and baseflow should be low in dry years/months, which may not as well lead to low quick flow. This aspect can be understood considering the variation of stream flow and baseflow sequences during dry and wet periods; changes in baseflow among dry and wet periods are almost negligible compared to those in stream flow. Consequently, as wet periods have high stream flows their quick flows are also high since the main driver of quick flow is flow magnitude. Num. of events RCK vs. FRCK RDF vs. FRCK Single-peak Multi-peak MRE (%) CC MRE (%) CC 76 66 62 57 55 69 59 44 13 13 9 11 15 12 14 8 5.6 2.7 1.3 0.8 1.9 3.2 1.8 0.4 0.67 0.84 0.93 0.88 0.94 0.81 0.90 0.99 59 46 31 22 46 60 52 18 0.48 0.56 0.62 0.63 0.43 0.49 0.53 0.60 Fig. 9. Baseflow Index as a function of basin area for the entire flow record. Table 7 Mean of long-term time scale MRE and CC error metrics between RCK/RDF and FRCK. Gauge codes Annual basis Monthly basis RCK vs. FRCK T1 T2 T3 T4 S F1 F2 TSF RDF vs. FRCK RCK vs. FRCK RDF vs. FRCK MRE (%) CC MRE (%) CC MRE (%) CC MRE (%) CC 0.23 0.07 0.09 0.13 0.12 0.17 0.09 0.08 0.967 0.992 0.996 0.998 0.994 0.993 0.997 0.999 2.9 3.0 3.1 3.4 3.5 4.3 3.7 4.3 0.626 0.669 0.650 0.716 0.646 0.667 0.660 0.742 2.08 0.69 0.36 0.41 0.08 0.01 0.23 0.22 0.945 0.980 0.987 0.992 0.962 0.955 0.979 0.992 21.1 14.0 10.4 12.3 4.3 5.7 8.7 12.0 0.779 0.754 0.763 0.701 0.736 0.746 0.723 0.723 Values in italic represent better consistency between the two bases. 646 Y. Mei, E.N. Anagnostou / Journal of Hydrology 523 (2015) 636–649 Fig. 10. Baseflow index and runoff coefficient for the study sub-basins determined at annual (left panel) and monthly (right panel) time scales. For the annual time scales, the years with high BFI appear to have low rainfall input and vice versa (e.g. BFIs for 2003 and 2006 are low with cumulative rainfall volume at around 1200 mm and 1100 mm for every sub-basin while those for 2005 and 2007 are high with 800 mm yearly cumulative rainfall volume). This implies that the baseflow dominated total flow in dry years and quick flow dominated total flow in wet years. At the monthly time scale (in the bottom panel), months associated with high rainfall (June–September) are not always characterized with low BFIs. For example BFIs for June and September are moderate and low. A cause of this discrepancy in BFI vs. rainfall volume between yearly and monthly time scales could be the distinct evapotranspiration patterns of the two time scales. The evapotran- spiration losses for different years can be approximately the same but those of different months are significantly different. Two technical reports from NOAA show that the evapotranspiration rate for the North Carolina is peaked during June and July while it drops to a moderate level in September (Farnsworth and Thompson, 1982; Farnsworth et al., 1982). Therefore, although the rainfall accumulation for June and September are similarly high, they are associated with high and moderate evapotranspiration losses (according to the reports) which leads to low and moderate quick flow (implying high and moderate BFI) respectively. Moreover, lower RCs are likely to appear in rainier months but hydrologically drier years. This could be again ascribed to the differences in annual and monthly evapotranspiration patterns. Drier years are associated with lower Fig. 11. Distribution (box plots) of event-based timing-related properties for single-peak and multi-peak events determined for the three drainage systems. Y. Mei, E.N. Anagnostou / Journal of Hydrology 523 (2015) 636–649 647 Fig. 12. Same as in Fig. 11, but showing the event-based water balance-related properties. accumulation in quick flow but stable accumulation in baseflow (compared to wetter years) and thus, lead to lower annual RCs. On the other side, despite the high rainfall accumulations, rainy months of the study area are characterized by comparatively high evapotranspiration losses as well. This points to the fact that high rainfall accumulation may not lead to high quick flow accumulation during these months and hence lower RCs. 4.3. Properties of events We identified 583 events (488 single-peaks and 95 multi-peaks) for the study sub-basins (see Table 8). It is noted that the larger the basin, the smaller the number of identified events. This is because some events occurring in the smaller sub-basins were merged when cascading to the larger sub-basins. Also, due to the higher baseflow conditions for larger basins (Fig. 9), fewer potential recession limbs satisfy the recessing point requirements (number of recession limbs without recessing point(s) are larger) and thus more events are characterized by longer durations. Fig. 11 renders boxplots for three timing properties of the single- and multi-peak events for every drainage system (the circle and box indicate the median and 25th & 75th percentiles while the upper and lower whiskers and the outliers are marked by the dash lines and crosses); they are the durations of rainfall and flow events and time lag between them (Dr, Df and tlag, respectively). All of the multi-peak event timing properties are in general taking larger values and wider value ranges than those of the single-peak ones, which indicates that the variability of timing properties from single-peak events is smaller than those of the multi-peak ones. Also, there exists a positive scale dependency (refer to the median and quantile ranges) for these three timing related properties. Additionally, positive scale dependency of Dr is anticipated since rainfall events from larger basins have higher possibility of being detected and are overall longer (see Section 3.2.2). Durations of flow events are also longer in larger basins due to higher baseflow conditions as described in the previous paragraph. Moreover, as larger basins have longer flow paths (Table 2) longer time lags between rainfall and runoff are demonstrated. Interestingly, there exists a basin-scale dependency for a large portion of the quantile ranges; the two quantile ranges tend to be elongated as basin areas increase, implying events from smaller basins are marked with higher degree of homogeneity for the timing related event properties. Four water balance related parameters, water volume of rainfall and runoff events, the event baseflow index and runoff coefficient (Vr, Vb, BFI and RC, respectively) are displayed in Fig. 12. Similar to the timing properties in Fig. 11, the multi-peak event properties have higher medians and longer value ranges except for the BFI cases. The BFI medians of multi-peak events are lower than those of the single-peaks in most of the cases, and the tendency in value 648 Y. Mei, E.N. Anagnostou / Journal of Hydrology 523 (2015) 636–649 ranges is not clear. Positive correlation in terms of median and quantiles to the basin area can be found in most of the cases of Vr, Vb and BFI (no clear trend for the BFI value ranges with areas), while values and value ranges of RC tend to be negatively correlated to basin area. This pattern can be explained for the two volumerelated parameters (Vr and Vb), since events from larger sub-basins are characterized by longer durations, which implies higher amount of rainfall volume. In addition, condition as rain water is subjected to be lost when traveling downstream, Vb should be increase with areas. This also explains why larger basin scales have higher baseflow condition (indicated by BFI). Another important aspect within Fig. 12 could be a possible reasoning for the negative role of area to RC. On the one hand, by assuming that the event total flow volume remains unchanged with scale, larger basin scales are outlined with smaller amount of quick flow volume ascribing to the positive role of area to Vb; on the other hand, Vr is also positive with scale. According to Eq. (23), if the nominator decreases and the denominator increases with area, RC should decrease with area. 5. Conclusions In this study, two baseflow separation methods, namely revised constant k method (RCK) and filtered revised constant k method (FRCK), and an event identification method, termed as characteristic point method CPM, are proposed for processing hourly rainfall and streamflow time series. RCK is formed by connecting all turning points with straight lines while FRCK is a filtered version of RCK using the recursive digital filter to pass RCK forward once. The essence of CPM is to locate the start, peak and ending points of flow events in stream flow time series and then associate rainfall events to these flow events. Beginning and ending of flow events under CPM are found within the population of rising and recession points, respectively, according to the location of peak flow. Rainfall events extracted based on continuous rainfall time steps are associated to flow events according to timing considerations of the two events. Long term (monthly and annual) and event based analyses were conducted with the aim of investigating the feasibility of the scheme as well as studying relationships between parameters. Although the entire scheme seems cumbersome and inevitably involving some arbitrariness, it has potential in terms of practical application due to the low requirement for data (only rainfall and flow time series are needed), and that the entire scheme is physically based through the application of linear recession model in determining the end point of flow events and the recession coefficient. Results showed that although most of the variability of RCK baseflow hydrograph remained after applying the RDF once, the RDF is able to smooth out some sharp peaks and troughs in the RCK baseflow sequence introduced by the linear interpolation. This yields more steady changes in the baseflow sequence, which is considered to be more representative of natural processes. For the long-term scale analysis, it is concluded that the hybrid baseflow sequence FRCK shares a larger degree of consistency (in terms of magnitude and shape) with the RCK baseflow sequence than the RDF one; this consistency seems to be increasing with basin scale. Besides, the baseflow index determined based on the entire flow record is positively correlated with drainage area for the three drainage systems in this study. This confirmed the fact that larger basins have higher baseflow conditions due to the longer travel distances downstream. Furthermore, BFI is negatively correlated with RC at the long-term basis indicating that dry or wet basin background conditions represented by high or low BFI values are well correlated with low or high RC, as anticipated. For the event based analysis same results on baseflow sequence similarity are exhibited; the FRCK baseflow hydrographs take more features from the RCK technique, vs. the RDF one, with higher degree of agreeability as basin scale increases. However, the consistency between either RCK and FRCK or RDF and FRCK is the lowest in the event scale among the three time scales. Seven event-based properties (three on timing, four for water balance) were investigated for single and multiple peak events from the eight basin scales. Except for RC, which correlated negatively with basin scale, the other six properties are all positively dependent on basin scale by means of median and value ranges in most of the cases. The scale dependency of value ranges (larger areas have wider ranges) is more explicit for the three timing properties regardless it is single-peak or multi-peak event. Furthermore, besides the BFI case, value ranges of the other properties are longer for multi-peak event than single-peaks, especially for the Dr and Df cases. Overall, larger basins exhibit longer rainfall and flow event durations, longer event time lag, larger amount of cumulative rainfall and baseflow volume, higher BFI and lower RC. In addition, variability of event properties is increasing with basin area except for RC, which shows the opposite tendency, and BFI, which displays no preference with basin scale. Single-peak event properties are subjected with lower degree of variability compared to the multipeaks with reversed trend in BFI as an exception. Future research regarding the herein proposed method should focus on potential method expansions and hydrological applications. Specifically, one may attempt a more physically based way (apply the nonlinear recession model or other approaches) in determining the location(s) of the ending points of the hydrologic events. A possible way would be to get the timing of all the events based on the methods and then redefine the timing separately by utilizing different parameters. For coarse resolution data (e.g. daily or coarser), we recommend using the UKIH, or any of its modified versions, to determine the flow event beginning or ending, and then apply the event association method described in this paper to form the hydrologic events. This is because for the coarse temporal resolution, it is difficult to find points satisfied the requirements for recessing points. For the sub-hourly data the algorithm could be appropriate with minor modification in the parameters. Once the method is applied on long time series of stream flow and precipitation data can be used to decipher correlations among timing and water balance related parameters. 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