The study of single streamflow recession events is receiving increasing attention following the presentation of novel theoretical explanations for the emergence of power law forms of the recession relationship, and drivers of its variability. Individually characterizing streamflow recessions often involves describing the similarities and differences between model parameters fitted to each recession time series. Significant methodological sensitivity has been identified in the fitting and parameterization of models that describe populations of many recessions, but the dependence of estimated model parameters on methodological choices has not been evaluated for event-by-event forms of analysis. Here, we use daily streamflow data from 16 catchments in northern California and southern Oregon to investigate how combinations of commonly used streamflow recession definitions and fitting techniques impact parameter estimates of a widely used power law recession model. Results are relevant to watersheds that are relatively steep, forested, and rain-dominated. The highly seasonal mediterranean climate of northern California and southern Oregon ensures study catchments explore a wide range of recession behaviors and wetness states, ideal for a sensitivity analysis. In such catchments, we show the following: (i) methodological decisions, including ones that have received little attention in the literature, can impact parameter value estimates and model goodness of fit; (ii) the central tendencies of event-scale recession parameter probability distributions are largely robust to methodological choices, in the sense that differing methods rank catchments similarly according to the medians of these distributions; (iii) recession parameter distributions are method-dependent, but roughly catchment-independent, such that changing the choices made about a particular method affects a given parameter in similar ways across most catchments; and (iv) the observed correlative relationship between the power-law recession scale parameter and catchment antecedent wetness varies depending on recession definition and fitting choices. Considering study results, we recommend a combination of four key methodological decisions to maximize the quality of fitted recession curves, and to minimize bias in the related populations of fitted recession parameters.

Streamflow recession analysis has the goal of characterizing recession
behavior in terms of phenomenological models of decreases in flow (

Classical recession seeks a single, effective parameterization of the power
law recession model. With some exceptions

Recently, several authors have attributed physical meaning to observed
variability

Among the many issues associated with event-scale analysis

Despite the growing number of event-scale recession studies, it remains
unclear to what extent the particular method of recession extraction and
fitting could alter features of the computed populations of recession
parameters. If uncertainty due to methodological choices exceeds
physically derived variations in the recession parameters, new and less
ambiguous methods will be needed to allow empirical comparative analyses, and
to test hypotheses derived from novel theories

Analogously to

Research question 1 – how do methodological choices impact fit quality of the power law recession model?

Research question 2 – when catchments are ranked by fitted recession parameter statistics, is the rank order dependent on methodological choices?

Research question 3 – how do methodological choices affect the empirical frequency distributions (over the period of record) of recession parameter values?

Research question 4 – how might methodological choices affect relationships between a given recession parameter and other physical measures of catchment state, such as catchment wetness?

Green lines correspond to periods during which streamflow data were available for each catchment.

In seeking answers to these questions, we recognize that, unlike lumped
recession analysis

In this work, we select two end-member settings that define realistic methodological limits for each of the above four choices. The resulting 16 combinations of method choices, as applied to a broad flow dataset, provide a basis for constraining method-dependent uncertainty in the populations of recession parameters.

Typical, highly erratic runoff time series for northern California coastal mediterranean watersheds.

The analyses in this study are performed using United States Geologic Survey
daily streamflow data for the set of 16 US catchments from northern
California and southern Oregon summarized in Table

The study catchments are relatively steep, forested, and situated within the
US western coastal mediterranean climate region

Study catchments.

Presumably there is an unbounded range of methodological choices that could be made regarding event-scale recession analysis. To constrain the problem, we address, in the simplest manner possible, the decisions that all analyses must confront: (i) the selection of a minimum duration of time for any candidate recession, (ii) the selection of a time point signifying the recession start (peak selection), (iii) the selection of criteria to confirm the continuation of a hydrograph segment that merits analysis (e.g., a slope or concavity requirement), (iv) the selection of a fitting methodology by which to analyze a chosen recession. While other choices undoubtedly have impacts on the characteristics of a population of analyzed recessions, the selection of these four criteria represents the most constrained and fundamental set of methodological choices to explore.

To concisely describe the combinations of methods tested here, we first
represent the four methodological choices with four binary (taking values of 0
or 1) variables:

minimum recession length (

peak selectivity (

recession concavity (

fitting method (

Graphical illustration of the 16 method choices. Minimum
recession length (

Owing to the derivative-based methods developed by

To logically examine sensitivity to minimum recession length, the “liberal”
and “restrictive” end-member values should be chosen to be consistent with
typical recession timescales of the study catchments. By fitting a linear
recession model (d

Ideally, rainfall data would be used to identify periods of recession.
However, high-quality precipitation records are often unavailable, and so the
majority of event-scale recession analyses rely on flow data alone for
recession identification. We therefore only consider methods of recession
analysis that can be applied to any daily streamflow record, with or without
rainfall data. More stringent extraction methods that require rainfall data
would be expected to reduce uncertainty in recession analysis, as extracted
recession periods

Without rainfall data, recession starts are typically identified by locating
days with discharge peaks – that is, times when d

To test the effect of peak filtering decisions on recession analysis, we
implement a peak selection procedure that is sensitive to the
“distinctness” of any given peak relative to the data around it

Illustration of the peak extraction algorithm. The square represents
the most recent recession peak identified for selection. The empty star
identifies a local maximum that will not be selected due to the fact that the
subsequent recession does not decay by an amount

In most studies, once a significant discharge peak has been identified, a
recession start time, which is often lagged from the discharge peak, is
chosen. The most commonly cited rationale for this lagged recession start is
to ensure the dominance of groundwater dynamics in the recession signal,
rather than overland flow processes

A number of criteria have been used to determine the end of a recession
event. Without a reliable rainfall record, many event-scale analyses halt
recession extraction upon the first day where flow does not decrease, that
is, as soon as d

The first (

Fitting methods can be broken down into one of three categories: (i) linear
regression or enveloping of a binned collection of

For event-scale recession fitting, the most popular method is to find a
regression line through raw

For the purposes of the present study, we again frame the problem in terms of
the most fundamental methodological dichotomy between linear and nonlinear
fitting. Linear fitting (

In general, only fitted exponents can be reliably compared between different
recession events

The scale correction procedure begins by first fitting each recession curve
to obtain an initial population (of size

With this in mind, we choose three primary

To see how methodological choices might impact the interpretation of

Fit quality is one measure of confidence in the estimated value for each
recession measure. Testing event-scale recession theories that predict
specific values for recession measures

We report two measures of the overall quality of recession fits as a function
of combinations of method choices. First we compute the mean average percent
error (abbreviated as MAPE and denoted mathematically as

That is, do catchments rank in a similar order according to different
statistical measures (in the present study, the median and interquartile
range) of the populations of

While

Even if the absolute magnitudes of the values of

Event-scale theories of the streamflow recession suggest that, beyond
measures of central tendency, higher-order moments of recession parameter
distributions (such as the variance) should vary in systematic ways,
depending on climate or catchment physiographic properties

While shifts in the Spearman rank correlation between method combinations
allow a comparative analysis of the effects of method choice, they do not
provide information about variations in the specific values of the recession
parameters obtained by each method. To address the specific values of the
recession parameters, which is important for testing theories that make such
specific predictions

Example recession extraction from the hydrograph

We first illustrate general patterns of

One way to isolate the absolute effect of a given method choice is to compare
recessions that are

We compare shared and unshared recession measure distributions in two ways.
First, for a high-level overview, we show Tukey box plots of shared
vs. unshared distributions of the recession exponent (

For each catchment, we then rank the four method choices by the number of
Mann–Whitney

Overall, few studies have attempted to tease apart the convergent predictions
of power law recession theories. Some works informed by

While the lengths of record for study catchments vary from 35 to 99 years, we
find that subsetting flow records and re-performing analyses does not
significantly impact our findings. We also find that, at confidence level

The box plots in Fig.

Mean absolute percentage error (MAPE) lumped across catchments by three groups: concave only recessions with nonlinear fitting; concave recessions or nonlinear fitting but not both (denoted using the logical “exclusive or” operator, “xor”); and decreasing recessions (without the concavity requirement) and linear fitting procedures.

Catchments were ranked by the values of six recession characteristics – median(

Figure

Figure

Box and whisker plots of Spearman rank correlations for all six
descriptive measures of the distributions of

Box plots for

The results from Fig.

Figure

Box plots comparing recession exponent shared vs. unshared
distributions for minimum recession length and concavity method choices for
Elder Creek. Each subplot corresponds to a particular method choice; the
shared boxes are generated with the

Results of Mann–Whitney

The pattern in Fig.

The finding that concavity and linearity play primary roles in determining
the quality of recession fits is notable in light of the fact that minimum
recession length and minimum recession peak size are more commonly emphasized
as the most important methodological choices made during event-scale
recession analysis

The recession scale parameter plotted against antecedent catchment wetness for three method combinations, together with a linear fit for each point cloud, and a 95 % confidence interval for each fitted slope.

Beyond the tendency to produce lower-quality fits, the linear fitting
procedures applied in the majority of recession studies have other
well-documented drawbacks. Linear regression on log-transformed flow values
disproportionately weights errors for smaller model values, creating a risk
of bias in the fit

We find that the medians and IQRs of

The relatively stable ranking of catchments by recession measures has
potential implications for testing event-scale recession theory. Recent work
by

Results also provide support for application of the recession scale parameter
scale-correction procedure presented by

Patterns in the recession measures for Elder Creek plotted in Fig.

Fraction of recessions with non-physical recession exponent (

The recession scale parameter (

A pattern of shorter whiskers from left to right in Fig.

Patterns displayed in Fig.

Whereas Fig.

Despite moderate sensitivity to concavity and linearity in the Elder Creek
data (catchment 11475560) displayed in Fig.

Results demonstrate that nonlinear fitting and concavity significantly
increase recession fit quality, while minimum length and peak selectivity do
not adversely affect it. The recession measure

This study quantified the sensitivity of the power law streamflow recession
parameters

All streamflow data used for this study can be found on the website for
United States Geological Survey (

David N. Dralle conceived of the study, performed analysis, and was the primary author. Nathaniel J. Karst conceived of the study, performed analysis, and contributed to writing. Kyriakos Charalampous curated recession parameter datasets and performed analysis. Andrew Veenstra performed analysis and developed recession analysis software. Sally E. Thompson contributed to writing and editing.

The authors would like to thank Davit Khachatryan and Laurel Larsen for helpful conversations concerning some aspects of the statistical and sensitivity analyses presented here. Edited by: J. Seibert Reviewed by: M. Stoelzle and one anonymous referee