Data Analysis
Kendall’s correlation τ was used to quantify the monotonic relationships
between independent and dependent variables. The Kendall correlation
utilized a two-sided p-value, which we accepted as statistically
significant below an α value of 0.05. We also conducted a multivariate
analysis utilizing multiple linear regression in order to quantify
multivariate relationships with the dependent variables. All dependent
and independent variables, and their equivalent base 10 log, were tested
for normality using a Shapiro-Wilk test. If the non-transformed variable
was deemed normal by having a p-value of greater than 0.05, it was used.
If it was non-normal, the log transformed variable was used only of it
was deemed to be more normal than the non-transformed variable. We used
Bayesian Information Criterion (BIC) to choose the best combination of
variables driving the relationships (Burnham and Anderson 2004) and
accepted a p-value of 0.05 to be statistically significant.
RESULTS
Assessing
the Algorithm
We visually assessed the accuracy of the algorithm by plotting the
algorithm-generated chemograph characteristics with the actual
precipitation and SC data. Each analyzed storm was evaluated
graphically, including the distribution of estimated FSCand DSC values (Figures 5 and 6). The median values of
the slopes of both the PST and RSC were matched with
their median intercepts so that each could be plotted. This resulted in
a total of 34 days on which a storm began, 29 of which showed a flushing
response and 28 showed a dilution and recovery. For one storm event, the
algorithm did not detect the chemograph responses which we were
assessing. Each of the remaining 33 storms had either a flush or
dilution and subsequent recovery, or both.
Univariate
Correlations
The correlations between the FSC and the independent
variables revealed statistically significant relationships with
IP, IP,max, and PT(Table 2, Figure 7). These 3 relationships were drawn from 27
algorithm-identified flushes in response to precipitation events. This
number differed from the 29 available flushes due to a gap in the VPD
data record. The Kendall’s τ value for IP was 0.502
(p<0.001), for IP,max was 0.486
(p<0.001), and for PT was 0.422 (p=0.001).
The correlations between the DSC and the independent
variables also showed statistically significant relationships with
IP, IP,max, and PT(Figure 8). These 3 relationships were drawn from 28
algorithm-identified dilutions in response to precipitation events. The
Kendall’s τ value for IP was 0.407 (p=0.003), for
IP,max was 0.38 (p=0.006), and for PTwas 0.628 (p<0.001).
The correlations between the RSC and the independent
variables resulted in a statistically significant relationship with
PT (Figure 9). This relationship was drawn from 28
algorithm-identified recoveries in response to precipitation events. The
Kendall’s τ value for PT was 0.564 (p<0.001).
There was also a significant relationship with another dependent
variable: DSC (τ=0.45; p<0.001).
Multiple Linear
Regressions
The multiple linear regression between the log transformed
FSC and the independent variables showed three variables
driving the relationship (Table 3). The correlation with log transformed
IP, log transformed IP,Max, and log
transformed ΣVPD resulted in p<0.001 and an adjusted
R2 of 0.54. The equation of the regression was
The multiple linear regression between the DSC and the
independent variables showed two variables driving the relationship. The
correlation with log transformed PT and the slope of the
PST resulted in p<0.001 and an adjusted R2of 0.78. The equation of the regression was
The multiple linear regression between RSC and the
independent variables showed a single variable driving the relationship.
The correlation with log transformed PT resulted in a
p<0.001 and an adjusted R2 of 0.39. The
equation of the regression was .
DISCUSSION
The algorithm was effective at extracting patterns of solute flushing,
dilution, and recovery. Quantifying these chemograph characteristics and
comparing them to the environmental variables revealed that the three
precipitation variables exerted the greatest influence on these
patterns. The methodology we used here can be expanded to other
catchments in order to characterize and compare them using the easily
obtained, high-frequency data sources that have been produced and
collected in recent years. Given the ability of the algorithm to extract
both solute flush and dilution characteristics, we expect that other
temporal behaviors that occur in other streams could be extracted with
the general approach that we used.
Efficacy of the
Algorithm
There has been a major increase in in situ sensor-obtained
streamwater data (e.g., Pellerin et al. 2010, Rode et al. 2016, Duncan
et al. 2018, Fovet et al. 2018), creating a need for automated analyses
that explore the data, reveal patterns, and aid in interpretation. There
are numerous methods to analyze water quality time series (Hirch et al.
1982, Cun and Vilagines 1997, Faruk 2009), however these were not
well-suited to extracting the characteristic hydrologic patterns which
were our focus, due to the thresholds and conditional decisions needed
to identify each pattern. Our methodology presents a novel way to
extract useful information from the deluge of data provided by modern
high-yield sensors. While we demonstrate the approach for SC, the
general approach may be useful for data from other types of water
quality sensors. Our algorithm’s extraction of SC patterns was assessed
to be accurate and similar to what would be obtained from human
estimation (Figures 5 and 6). The rare instances in which the algorithm
was not accurate are acceptable, given the beneficial nature of the
automation; essentially that the process is highly robust due to the
Monte Carlo approach, which has previously been shown to accurately
extract complicated patterns from time series (e.g., Contosta et al.
2016). Similar approaches using machine learning would possibly
outperform our algorithm, and we see this as a likely next step in
analyzing streamwater sensing data.
Environmental Controls on Chemograph
Characteristics
Both flushing and dilution are strongly correlated with rainfall-based
variables. This leads to the assessment that both are primarily driven
by the mixing of different sources of water, rather than more nuanced
controls like seasonality of solute generation or variation in storage
(as represented by antecedent moisture indicators). The importance of
source water mixing, and the relative contributions of new and old water
to streamflow, has been previously discussed at length (Pinder and Jones
1969, Sklash and Farvolden 1979, Kirchner 2003) and are consistent with
our results involving SC dilution. However, the functional relationships
we show (Figure 8), obtained solely from SC and precipitation data, may
be useful in characterizing hydrologic systems for comparison.
In the case of flushing events, our results suggest that a third source
of solute-laden water (aside from the typically assumed two members:
groundwater and rainwater) is entering the stream system before
precipitation is transported to the stream, resulting in SC dilution
(Robson et al. 1992, Creed and Band 1998, Inamdar et al. 2009). This
third source, however, may quickly exhaust its supply, resulting in
water following the same pathway but exhibiting a lower concentration as
a storm progresses. For example, at the nearby Hubbard Brook
Experimental Forest, the upper intermittent stream reaches are
characterized by high dissolved organic carbon and aluminum, and low pH,
due to eluvial processes in the bedrock controlled soils that
predominate the upper catchment (Bailey et al. 2019). As the catchment
wets up, the active portion of the stream network may quickly expand
into the upper catchment, causing a flush of solutes from near-stream
soils , that may then be quickly diluted by precipitation or from lower
SC water as deeper soils lower in the catchment increase their
contribution to runoff. Analyses of flushing would benefit from
three-end member mixing models being used in future studies, requiring
sensing of additional chemical tracers (Burns et al. 2001, Hooper 2003).
SC has been an effective catchment hydrology tracer in the past (Davis
et al. 1980, Pellerin et al. 2008, Cox et al. 2007), however, the role
of the solute flushing in mixing analysis needs to be addressed more
thoroughly.
The univariate results indicate that this third source of water is
driven into the system not simply by the amount of rainwater added, but
maybe more importantly by the intensity at which it is added. Rainwater
can cause flushing events in two ways. First, it can displace stored
high SC water into the stream during precipitation events, or second, it
can reach the stream as high SC water after gaining solutes via mixing
during transport (Robson et al. 1992). Because FSC is
more correlated with IP and IP,max than
PT, we hypothesize that the flush of high SC water is
from either near-stream soils, ephemeral streambeds, or development of
saturated conditions in shallow to bedrock soils: pathways which allow
more rapid movement of water to the watershed outlet, whether that water
is precipitation that picked up solutes or is the displacement of
ionically enriched stored water.
If this is the case, we predict that the solutes responsible for this
flush are those which are shallow (e.g. dissolved organic C and nitrate)
rather than those which are weathering-derived (e.g. Ca, Na). If piston
flow later takes over as the major contributor of high SC water, as has
been shown to be the case in systems without flushing events (Sklash and
Farvolden 1979), then we hypothesize that the solutes responsible would
be from deeper, weathering-derived sources. Sample collection during
precipitation events would indicate which specific solutes are entering
the stream system and allow an evaluation of which of these processes
drives SC dynamics.
The RSC relationship with PT is expected
given it is driven by the dissipation of a pulse of low SC rainwater
through higher SC stored water, however we see potential to further
explore this chemograph characteristic to understand catchment
hydrologic function. As more rainwater enters the system and increases
the deviation from the catchment’s normal, high-SC state (shown by a
higher DSC), the system responds by recovering more
quickly. As the new water leaves the system, the SC will move towards
pre-event concentrations. The rate at which this rebound occurs may be
used to characterize the catchment’s export of new water. It may be
possible to derive hydrogeologic characteristics using
RSC, similar to previous hydrograph recession analysis
(Brutsaert and Nieber 1977).
The best multiple linear regression models we produced for
DSC and RSC ended up with
PT as a primary driver, accompanied in the case of
DSC with PST, which is due to the manner in which the
algorithm quantifies the DSC. The current analysis for
these two SC patterns suggests that the system was so influenced by
precipitation that the importance of other controls, while physically
relevant, were either very difficult to detect, were relatively
unimportant, or were restricted by the constraints of available data.
Similarly, no seasonal variables significantly influenced flushing,
dilution, or recovery behaviors, suggesting that seasonal variation of
runoff generation was similarly masked by precipitation characteristics
or due to us limiting our analysis to the snow-free season.
The lack of correlation between antecedent conditions (ΣVPD and ISP) and
DSC does not agree with previous studies, and
accordingly is unexpected, as the drying pressure exerted on a catchment
influences the hydrologic storage capacity of its soils, and thus runoff
generation (Biron et al. 1999, Detty and McGuire 2010, Grand-Clement et
al. 2014). It is possible that there is a threshold system response to
drying, rather than a gradient response, thus revealing no correlations
in our analyses pertaining to ΣVPD or ISP. Or, drying pressure’s effect
may be masked by the importance of precipitation amount and intensity.
We expect that this result may change if we had more storms to analyze
and could then apply data-intensive, non-parametric multivariate models
(e.g., regression trees) due to the complex nature of hydrologic
systems.
Cumulative vapor pressure deficit did, however, emerge as a driving
factor in our multiple linear regression model for FSC,
indicating that the drying pressure exerted on the catchment is a factor
in flushing responses. The antecedent conditions here likely influence
the connectivity of soil water to the stream, becoming more disconnected
with greater ΣVPD. As rainfall connects soils to the stream, a stronger
pathway is formed, allowing ions to more freely mobilize. Again, this
relationship may become stronger and more clearly important to
FSC with the study of additional storms.
Climate change is causing more intense precipitation events with longer
inter-storm periods (Allan and Soden 2008, Yu et al. 2016). Our results
indicate a likelihood of higher variability in streamwater SC as these
climate-driven effects take hold. The greater precipitation amounts and
intensities will cause higher spikes in the concentration of solutes at
the beginning of a precipitation event and higher dilution of stream
solutes later in events. This may have a negative effect on lotic
organisms that rely on certain ranges of SC, or concentrations of the
ions that SC represents, to carry out biologic functions (Daley et al.
2009). And, depending on the solutes making up the ionic composition of
the streamwater, these may impact the waters used for human consumption.
Thus monitoring of SC and automated detection of responses provides an
effective tool for surface water assessments.
CONCLUSION
Our algorithm extracted three chemograph patterns, which routinely
appear in response to rain events. Our comparison of these patterns to
independent environmental conditions suggested that the major factors
driving the variability in flushing, dilution, and recovery behavior
were the precipitation amount and intensity. Seasonal variables were
largely unimportant at this catchment or overshadowed by the heavy
influence of rainfall. When analyzed using multiple linear regression,
antecedent moisture was shown to be a factor in driving flushing
responses, but not in driving dilution or recovery responses. Our
methodology can be useful for analysis of other catchments, revealing
functional relationships between independent, environmental variables
and streamwater SC responses. The results of such investigations could
help characterize catchments in a robust, objective, and repeatable
manner, with implications for guiding water resource management
decisions.