Recession analysis is a classical method in hydrology to
assess watersheds' hydrological properties by means of the receding limb of
a hydrograph, frequently expressed as the rate of change in discharge
(

Accurate representations of watershed-scale hydrological processes are
urgent in a global- and anthropogenic-change perspective. Streamflow
recession analysis has been routinely used for about half a century to
assess watershed properties (e.g.,
Brutsaert and Nieber, 1977; Kirchner, 2009; Mcmillan et al., 2014) and more
recently their vulnerability to climatic and anthropogenic factors (Berghuijs
et al., 2016; Brooks et al., 2015; Buttle, 2018; Fan et al., 2019).
Recession analysis is commonly done by plotting the time rate of change in
discharge

Two categories of parameter estimation methods are based on: (1) the
aggregation of all observations in the space of

When Brutseart and Nieber (1977) first proposed their recession analysis
method, aquifer recession behavior was identified by fitting a lower
envelope to the point cloud, thus assuming small values of

In contrast, the variability in watershed response to individual recharge
events can be depicted by fitting recession parameters to individual
recession events. Several authors have observed that individual recessions
had greater

Recession analysis plot in log–log space for Lookout
Creek (USGS no. 14161500). Individual recession fits are displayed with
color scale differencing by values following a discretization according to
decile groups. This discretization allows for the description of the
organization of individual recessions where recessions with similar

For a given discharge range in Fig. 1, there appears to be multiple
individual recessions with similar values of

This paper explores the source of the offset (ln(

This section presents methods for (1) the definition of three synthetic hydrographs, (2) the description of recession extraction from the hydrograph, and (3) the comparisons between four fitting methods for parameter estimation applied to a discharge time series for Lookout Creek.

This paper makes use of synthetic hydrographs to explore factors that change

The falling limb of the hydrograph is assumed to follow a power law
following Eq. (2) (Dewandel et
al., 2003; Drogue, 1972; Rupp and Woods, 2008):

Conceptual model of identical recession events only
dependent on the initial dimensionless flow (

Holding

Recession analysis for Lookout Creek to aid in the
comparison of four different fitting methods and the dependency on parameter
estimation shown visually (lower envelope – LE, central tendency – CT, and
binning average – BA) and individual recessions parameters (median
individual recession – MI). Depending on the fitting method, the parameter
estimation for

A pulse recharge amount corresponding to a given

We compared three hypothetical time series generated with different
assumptions about the distribution of the magnitudes and inter-arrival times
of recharge events and the superposition of recession events (Table 1). The
inter-arrival times are distributed log-normally (Cases 1 and 3) or
uniformly (Case 2). Event magnitudes (as defined by

Synthetic-hydrograph scenarios.

To generate the time series for Cases 1 and 3, independent recessions were
created using a random-number generator for a log-normal distribution for
event peak magnitude and duration for a total of 10 years of time series
data. The log-normal distributions for event magnitude and duration are
chosen for the synthetic hydrographs because the distributions for Lookout
Creek are skewed right and roughly log-normal (Supplement Fig. S1), which is also consistent with
other skewed-right precipitation distributions in previous studies (Begueria et al., 2009; Selker and Haith,
1990). Recharge events were created with log-normally distributed
inter-arrival times (

For Case 1, the individual recessions were combined to make a time series
such that each event was concatenated onto the last event disregarding the
antecedent flows. For Cases 2 and 3, individual recessions were superimposed
on antecedent flows, appealing to the simplest model presented by the
instantaneous unit hydrograph method (Dooge, 1973). We
acknowledge that the framework for the instantaneous unit hydrograph as
described in Dooge (1973) does not consider non-linear reservoirs, but we use
it as a simple representation to produce variability between recessions. We
discuss the implicit assumptions of this model in the Discussions and
Conclusions section. From Fig. 2, the baseflow from the first event,

As a result, Case 1 looks specifically at a time series events where the
falling limb of each event maintains the same decay constant and the effect
of having no antecedent baseflow influence on streamflow. By including
baseflow to Case 2 but maintaining equal inter-arrival times and event
magnitudes, we look specifically at the effect of antecedent conditions on
individual recessions and the point cloud. Case 3 combines the distribution
of event inter-arrival times and magnitudes of Case 1 with the baseflow
conditions of Case 2, best representing the variability and inter-arrival
times of individual recession events seen in Fig. 1 for data from Lookout
Creek. Each case will address how the controls on the hydrograph affect the
recession analysis plot and the estimates of

Recession extraction from observed hydrographs and the associated
sensitivities to different criteria have been explored by Dralle et al. (2017), including minimum recession length and the definition of the
beginning and the end of the event. For Lookout Creek, we used extraction
criteria similar to those of other studies (e.g.,
Chen and Krajewski, 2016; Dralle et al., 2017; Stoelzle et al., 2013) and
applied the same criteria prior to all fitting methods presented in Sect. 2.3 to isolate differences in calculated

For the synthetic hydrographs used in Sect. 3.2, events of any length were included; the recession start was selected at peak discharge because overland flow was not a factor; and the end of the recession was chosen as the time immediately before the next generated discharge peak.

Four methods of estimating representative recession parameters were evaluated: lower envelope, central tendency, binning average (Kirchner, 2009), and the median individual recessions (MI) (Roques et al., 2017). Linear regression in bi-logarithmic space was used with each method for consistency across methods.

Because a change of hydraulic regime was suggestive in Fig. 1 between high-flow ranges and low-flow ranges, recession analysis parameters were
estimated for two flow ranges, early time and late time. Early time and
late time describe a theoretical transition of flow regimes between
high-flow and low-flow ranges (Brutsaert and Nieber, 1977). To reduce the
subjectivity of distinguishing between high and low flows, a breakpoint in
discharge separating high- from low-flow behavior was optimized to best
represent the analytical solution. By separating the data into two
subgroups, either smaller or larger than a defined breakpoint discharge, the
best-fit line was determined for each subgroup. The location of the
breakpoint is defined so the error between the observed ratio of

For each of the four estimated methods, parameters were estimated for the
early-time and late-time behavior separately. For the LE method,

In Fig. 3 we display the recession plot stacking all individual recessions
resulting in the formation of the point cloud. The different fitting
strategies revealed that the LE, CT, and BA methods all fit to the point
cloud and result in different values of

Comparison of recession analysis parameters

More importantly, parameter estimation differs greatly whether the point
cloud or individual recessions are used. The late-time

Based on the similar results from BA and CT methods discussed above, and the
questionable practice of setting an early- and late-time

The recession decay exponent

The

Recession analysis of a hydrograph with log-normally distributed event
inter-arrival times and peak discharge with a constant falling-limb decay
constant (no baseflow represented) results in individual recession events
with the same

To examine the sensitivity of parameter estimation to recession extraction
criteria, we evaluated how choosing the start of the recession (i.e., the
time elapsed since peak discharge) affects the value of

The superposition of recession events accounts for the effects of antecedent
baseflow. The superposition changes the effective

A hydrograph more representative of real-case conditions includes variable
inter-arrival times and event magnitudes from Case 1 and baseflow antecedent
conditions from Case 2 (Fig. 6a). These complexities result in a recession
plot where the individual recessions represent the variability in watershed
response represented by the hydrograph (Fig. 6b), where

In the 42 years since Brutsaert and Nieber (1977) proposed their recession analysis, it has provided a seemingly simple analytical method for estimating basin-scale hydrologic properties. However, recent studies have highlighted the sensitivity to estimation methods on the recession parameter values and to the resulting interpretation of average watershed behavior. This paper explores the effect of the distribution (in time and in magnitude) of individual recessions on parameter estimation and compares that to the parameter estimation from collective recessions (i.e., the point cloud). The four estimation methods considered were the lower envelope, central tendency, binning, and individual recession method. Because of the poorer apparent fit and problems pointed out from previous studies when using the lower envelope and central tendency methods, we chose to use the binning method to compare with results from the individual recessions method for a set of synthetic case studies.

We hypothesize that the climate controls the distribution of individual
recessions in bi-logarithmic plots of

We conclude that recession analysis performed on collective recessions does
not capture average watershed behavior, regardless of the fitting method.
The point cloud is an artifact of the variability of the individual
recessions, including the event inter-arrival times and distribution of
magnitudes. Individual recessions with the same

For Case 1, the recession analysis parameter

While the mean

An additional important simplifying assumption of this study is the use of a
constant timescale

We show how the point cloud pattern does not arise from watershed properties
alone. The consequence is that parameters estimated from the point cloud do
not represent watershed properties. In all three synthetic-hydrograph
representations, the median individual recession

A strength of the critical-zone community is the ability to create a global
analysis by comparing across studies (Brooks
et al., 2015; Fan et al., 2019). However, a lack of consensus for a standard
method for recession analysis procedures exists and thus inhibits recession
analysis studies from being widely compared. If streamflow analysis is to be
included in a global analysis, results need to be comparable across scales
and observatories. There is a need for a common method employed to compare
the average and variability in watershed responses. Because estimated
parameters may differ greatly by estimation method, misinterpretation of
hydrological properties and incorrect predictions within the critical zone
are possible. When using the point cloud in particular, a smaller recession
parameter

The streamflow record for Lookout Creek is freely available from the USGS
website (

The supplement related to this article is available online at:

ERJ, DER, and JSS were involved in conceptualization. ERJ and CR developed the methodology and performed the analysis. ERJ prepared the paper with contributions from all co-authors.

The authors declare that they have no conflict of interest.

This work was supported by the National Science Foundation awards to the Center for Transformative Environmental Monitoring Programs (nos. 1551483 and 1440506).

This paper was edited by Daniel Viviroli and reviewed by Michael Stoelzle and one anonymous referee.