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\begin{document}

\title{Curating 62 years of Walnut Gulch Experimental Watershed dataset:
Improving QAQC methods of rainfall and runoff measurements.}



\author[1]{Menberu Bitew}%
\author[2]{Eleonora M. C. Demaria}%
\author[1]{Philip Heilman}%
\author[2]{David C. Goodrich}%
\author[1]{Mark Kautz}%
\author[1]{Gerardo Armendariz}%
\author[1]{Carl Unkrich}%
\author[3]{Haiyan Wei}%
\author[3]{Anandraj  Perumal}%
\affil[1]{USDA Agricultural Research Services}%
\affil[2]{USDA-ARS}%
\affil[3]{University of Arizona}%


\vspace{-1em}



  
  \date{May 24, 2024}


\begingroup
\let\center\flushleft
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\selectlanguage{english}
\begin{abstract}
The Walnut Gulch Experimental Watershed (WGEW) is the primary outdoor
hydrologic laboratory for the USDA-ARS' Southwest Watershed Research
Center (SWRC). This site represents the Southwest semiarid environment
within the Long-term Agroecosystem Research (LTAR) network. The SWRC
maintains a collection of long-term hydro-climatic measurements from
WGEW, featuring an extensive archive of rainfall and runoff observations
from an ephemeral network of streams within the 149 km2 watershed. The
WGEW was established in 1953, and has continually developed and improved
quality assurance and quality control procedures to aid in the accuracy
and curation of the constantly growing datasets obtained from more than
100 rain gauges and 18 flumes, weirs, and gauged ponds. These efforts
have led to the development of a state-of-the-art database and data
visualization tools to aid in the curation of research-grade
hydrometeorologic datasets. This required development of automated
quality assurance and quality control tools to check and maintain the
data for 21st century research needs. We developed five tools to improve
the quality of rainfall and runoff database based on conventional
hydrologic principles and the relationships between them: 1)
precipitation is spatially correlated; 2) there is a temporal relation
between rainfall and runoff; 3) runoff is only a limit portion of
rainfall; and, 4) closer took of extreme events. Hence, we developed the
following methods that included the analysis of interpolated rainfall
maps at a daily time step, the association between rainfall and runoff
events, lag time, runoff coefficients, and multiple regression methods
to identify problematic events in the data archive. To visually inspect
and verify the errors, we developed a graphical tool that displays
relevant event hyetographs and hydrographs within a specific time
window. After flagging anomalous events, we evaluated the types of
errors using the original records and metadata information. The
implementation of these approaches resulted in developing a suite of
semi-automated QAQC tools that correctly detected 813 rainfall and 24
runoff events with erroneous timestamps that had passed all previous
quality checks.%
\end{abstract}%



\sloppy


Curating 62 years of Walnut Gulch Experimental Watershed dataset:
Improving QAQC methods of rainfall and runoff measurements.

\textbf{Menberu B. Meles\textsuperscript{1,2}, Eleonora M.C.
Demaria\textsuperscript{1}, Philip Heilman\textsuperscript{1}, David C.
Goodrich\textsuperscript{1}, Mark A. Kautz\textsuperscript{1}, Gerardo
Armendariz\textsuperscript{1}, Carl Unkrich\textsuperscript{1}, Haiyan
Wei\textsuperscript{2}, Anandraj Thiyagaraja Perumal}

\textsuperscript{1}USDA-ARS, Southwest Watershed Research Center,
Tucson, AZ, USA.

\textsuperscript{2} University of Arizona, School of Natural Resources
and the Environment, Tucson, AZ, U.S.A

Corresponding author: Menberu B. Meles (mbmeles@email.arizona.edu)

Key Points:

\begin{itemize}
\tightlist
\item
  Long-term rainfall and runoff observations require continual quality
  checking and curation to improve fidelity.
\item
  Evaluating the relationships of conventional hydrologic principles
  plays a paramount role in the development of new QAQC tools to flag
  questionable rainfall and runoff events.
\item
  Quality hydrologic data reduces the uncertainty in hydrologic analyses
  and model predictions.
\end{itemize}

Abstract

The Walnut Gulch Experimental Watershed (WGEW) is the primary outdoor
hydrologic laboratory for the USDA-ARS' Southwest Watershed Research
Center (SWRC). This site represents the semiarid environment of the
Southwest U.S. within the Long-term Agroecosystem Research (LTAR)
network. The SWRC maintains a collection of long-term hydro-climatic
measurements from WGEW, featuring an extensive archive of rainfall and
runoff observations from an ephemeral network of streams within the 149
km\textsuperscript{2} watershed. The WGEW was established in 1953, and
has continually developed and improved quality assurance and quality
control (QAGC) procedures to aid in the accuracy and curation of the
constantly growing datasets obtained from more than 100 rain gauges and
18 flumes, weirs, and gauged ponds. These efforts have led to the
development of a state-of-the-art database and data visualization tools
to aid in the curation of research grade hydrometeorologic datasets.
This required development of automated quality assurance and quality
control (QAQC) tools to check and maintain the data for
21\textsuperscript{st} century research needs. To improve the integrity
of the historical rainfall and runoff database, five independent tools
were developed to identify questionable events based on the following
conventional hydrologic principles and the relationships between them:
1) precipitation is spatially correlated; 2) there is a temporal
relation between rainfall and runoff; 3) there is an upper limit to the
amount of runoff generated from a given rainfall event; and, 4) it is
always important to verify extreme events. Hence, we developed and
applied the following methods that included the analysis of interpolated
rainfall maps at a daily time step, the association between paired
rainfall and runoff events, the computation of runoff lag time, runoff
coefficients, and the analysis of multiple regression methods to
identify problematic events in the data archive. To visually inspect and
verify the errors, we developed a graphical tool that displays relevant
event hyetographs and hydrographs within a specific window of time.
After flagging anomalous events, we evaluated the types of errors using
the information in the original records and metadata. The implementation
of these approaches resulted in the development of a suite of
semi-automated QAQC tools that correctly detected 813 rainfall and 24
runoff events with erroneous timestamps that had passed all previous
quality checks.

Keywords: QAQC, hydrologic database, long-term data curation, rainfall
and runoff measurements, Walnut Gulch, Quality hydrologic data

1. Introduction

Long-term observations are the foundation for understanding earth system
processes for sustainable water and natural resource management under
current and future climate and management conditions (\emph{Tetzlaff et
al., 2017} ). As the uncertainty in water supply increases with warmer
temperatures and growing human population, the need for quality,
long-term hydrometeorological observations has increased. Data collected
in experimental watersheds and natural research observatories across the
U.S., such as the USDA-ARS Long-Term Agroecosystem Research (LTAR)
network \emph{(Kleinman et al., 2019; Spiegal et al., 2018; Walbridge
and Shafer, 2011} ), the Critical Zone Observatories (CZO)
(\emph{Brantley et al., 2017} ), the Long-term Ecological Research
(LTER) network, (\emph{Knapp et al., 2012} ), and the National
Ecological Observatory Network (NEON) sites (\emph{Collinge, 2018} ) are
critical for research, analyses, and planning (\emph{Tetzlaff et al.,
2017} ). Ensuring that the accuracy of these measurements are suitable
for scientific analysis and long-term monitoring requires a large
investment in time and money. Furthermore, these efforts need to be
operationally feasible and address the biophysical diversity of the
locations within these research networks. Common methods to ensure the
integrity of these data, referred to as quality assurance and quality
control (QAQC) procedures, include outlier checks using thresholds,
comparisons with neighboring stations, and fitting to theoretical
probability distribution functions to flag outliers (\emph{Kunkel et
al., 2005; You et al., 2007} ). QAQC procedures reflect improvements to
the quality of a dataset through a combination of steps that prevent
errors from occurring, quality assurance (QA), through improved data
collection and management practices, and the identification and
resolution of errors within the recorded dataset, quality control (QC).

Such efforts have been under continuous development at the Walnut Gulch
Experimental Watershed (WGEW) in southern Arizona. This site is operated
by the USDA Agricultural Research Service (ARS) Southwest Watershed
Research Center (SWRC) and is an LTAR site representing the semiarid
grazing lands of the southwestern United States. The SWRC has invested
millions of dollars since the establishment of WGEW in both QA, through
regular sensor calibrations, site maintenance, installation of
consistent instrumentation across networks, thorough testing of new
instrumentation prior to adoption, and redundant sensors to compare
observations (e.g., \emph{Fiebrich and Crawford, 2001} ), and QC through
regular data inspection and analysis conducted by SWRC scientists and
technicians.

In semiarid regions in the Southwestern U.S., where natural and human
systems compete for already over-allocated water resources, accurate
hydrologic measurements are essential. The WGEW was established during
the mid-1950s (\emph{Renard et al., 1993; Moran et al.. 2008a} ) to
measure high resolution rainfall, runoff and other hydro-climatic
variables within in a semiarid, ephemeral network of streams. QAQC
procedures at WGEW have evolved to accommodate the observations made by
retired analog instrumentation (\emph{Brakensiek et al., 1979} ) and
current digital instrumentation (\emph{Moran et al., 2008a} ). The
long-term record of measurements from the WGEW are archived in the Data
Access Project (DAP - https://www.tucson.ars.ag.gov/dap/) database which
was initiated in the year 2000 when analog instrumentation was replaced
with digital instrumentation (\emph{Nichols and Anson, 2008} ). Rainfall
and runoff observations in the WGEW are routinely checked for
inconsistencies and errors such as problematic recession curves on
runoff hydrographs or timing errors in measurement. Despite the past
QAQC efforts, several errors including human mistakes and instrument
malfunctions remain in the data, largely due to time stamp errors
associated with analog clocks that were used prior to 2000. QC efforts
have historically been performed on rainfall and runoff observations
independently, however, given the causality between these measurements,
a new QAQC procedure was needed that considered their relationships in
order to identify inconsistencies in the data and further improve the
overall quality of DAP.

From an ecosystem analysis standpoint, errors in rainfall or runoff
observations could lead to inconsistencies in model parameterization, in
model predictions, and errors in water balance partitioning. In this
paper, we initially used watershed-wide interpolated rainfall maps to
isolate observations that are inconsistent in space and time, which is
expanded to include the relations between the long-term data records to
execute a series of spatial and temporal comparisons to evaluate data
inconsistency. The goals of this study were: 1) to design and implement
systematic methods for identifying erroneous rainfall and runoff data in
DAP using relationships between the two datasets based on conventional
hydrologic principles for semiarid regions; and, 2) to identify, verify,
and remove the inconsistent rainfall and runoff observations in the DAP
database.

2. Data description and quality control methodology

2.1. WGEW data and site description

The study was conducted in three sub-watersheds at WGEW, WS-04, WS-011,
and WS-06 (Figure 1a) with 2.3, 8.2, and 95.1
km\textsuperscript{2}contributing areas respectively. In each of the
sub-watersheds, there are 5, 12, and 56 rain gauges and a runoff
recording flume at each outlet. Average summer rainfall, defined as the
rainfall observed in the period May through September, over the
watershed for the 1961-2017 period has been measured at approximately
293 mm (112 to 370 mm range), which represents approximately 60\% of the
annual total (Demaria et al., 2019). Summer rainfall is important in
this environment, as almost 100\% or the runoff is generated during this
period. To accurately measure the rainfall from spatially isolated
thunderstorms and the resulting runoff during the summer season, WGEW is
equipped with a dense network of rain gauges and runoff measurement
structures. Based on experiences from eastern and mid-western
watersheds, 20 rain gauges were initially installed across the WGEW
which increased to 99 rain gauges over time to capture the high
spatiotemporal variability of rainfall generated from highly localized
air-mass convective storms during the summer monsoon season.
(\emph{Goodrich et al., 1997} ). Rain gauge density per area is about
one gauge per 1.7 km\textsuperscript{2}, making the WGEW the densest
rainfall network on a semiarid experimental watershed in the world
(\emph{Garcia et al., 2008; Goodrich et al. 2008a;} ). Since the
establishment of ARS experimental watersheds and ranges in other regions
of the country starting in the mid-1930s, the primary precipitation
gauges employed have been a Belfort 8-inch (0.2032 m) unshielded
weighing-bucket gauge (Figure 1b). If well calibrated, these gauges have
a measuring resolution of 0.01 inches (0.254 mm). Runoff response has
been recorded at 18 nested sub-watersheds at WGEW using v-notch weirs, H
flumes, and supercritical flumes designed for Walnut Gulch channel
environment (\emph{Stone et al., 2008;}Smith et al.\emph{~1982)} (see.
Figure 1c for supercritical flume photo). The WGEW watershed and its
surrounding area are equipped with a total of 132 rain gauges, 18 runoff
measurement flumes and weirs, three meteorological stations, two eddy
covariance flux towers, soil moisture sensors at various depths, and
eight gauged tanks/ponds. The temporal frequency of the recordings
varies based on the type of sensor, with rainfall and runoff
observations being recorded at a maximum frequency of one minute. In
addition to the observations representing hydrology, climate, and
sediment, the SWRC has extensively collected datasets related to
vegetation abundance and diversity and conducted extensive research in
geology, soils, hydrology, ecology, and rangeland studies which provide
a broad set of data and proxies to investigate changes in water
resources of this semiarid environment. Common instrumentation
monitoring, calibration, and maintenance procedures have been followed
through time (\emph{Brakensiek et al., 1979} ). All WGEW data (current
and historical) are available through the web-based portal for the DAP
database~(https://www.tucson.ars.ag.gov/dap/).

With evolving digital technology, in the mid-1990s, the mechanical chart
recorders on instruments were replaced with electromechanical components
and digital recorders, eliminating the labor-intensive weekly rain
gauges visits, often over rough roads, to wind clocks, add ink to
recording pens, and change charts. After field collection of the paper
charts, they must be manually digitized to convert the pen trace to
breakpoint digital format (\emph{Goodrich et al., 2008} ). Both rainfall
and runoff observations are archived at sub-hourly frequency using
breakpoint format, which consists the times of change from one steady
rate to another with a minimum time step of 1 minute. In the breakpoint
data, the stream of data pairs consists of time and rainfall or runoff
depth with zero values at the beginning and end of the event recordings.
A side-by-side direct comparison of events before and after the change
from analog to digital gauges using pairs of co-located analog/digital
rain gauges was conducted for a 5year period for nine (9) 24 hour gauges
from 2000-2004. This analysis concluded that no measurement
discontinuities of a number of raw and derived quantities (e.g. peak 30
min rainfall intensity) were introduced by the switch in the weighing
and recording systems (\emph{Keefer et al., 2008} ). In general, we
observed that the analog period produced more errors than the digital
period, which could be attributed to mechanical clocks slowing down,
speeding up, or stopping between visits as well as expansion or
contraction of paper charts, and the manual digitizing process.

The DAP database has been used extensively in several hydro-ecological
modeling studies (\emph{Costa et al., 2012; Duan et al., 2006; Goodrich
et al., 2004; Goodrich et al., 2012; Niu et al., 2014; Scott and
Biederman, 2017} ) and in remote sensing studies as a critical ground
validation site for retrieval algorithms, including soil moisture and
vegetation measuring platforms (\emph{Morin et al., 2003; Moran et al.,
2008b; Amitai et al., 2012; Das et al., 2012; Knipper et al., 2017;
Kolassa et al., 2018} ). Therefore, the DAP observational database must
be as free of errors as possible. A special section of~20 papers in
Water Resources Research provides WGEW history, data collection,
metadata, data access and recent results of WGEW data analysis
(\emph{Moran et al., 2008a} -- all the papers in the special section can
be found at https://www.tucson.ars.ag.gov/dap/wrr.html).

2.2. Existing QAQC processes

The objective of the existing QAQC procedure is to prevent erroneous
information from getting into the database and to facilitate maintenance
of equipment efficiently. Substantial effort has been invested over the
years to ensure the quality of the WGEW rainfall and runoff datasets.
Rainfall depth and runoff stage measurements are calibrated and adjusted
annually prior to the monsoon season. Processing workflow from field
measurement to storage in the database and public access through a
web-interface requires several steps to ensure consistent quality. The
raw data and its summary report are transmitted to a central location
daily and are internally accessible for monitoring, identifying
malfunctions, and deployment of maintenance technicians. The data then
undergoes a QC processes including visual inspection of the hyetographs
and hydrographs, and geospatial representation of rain gauge locations
with associated rainfall amounts at the field office for approval every
2-3 weeks. Using these procedures, a significant portion of the errors
are removed, however, given the difficulty of identifying numerous
electromechanical errors or malfunctions, environmental issues (e.g.
bird nests in gauge orifice), technician errors, and operational
changes, maintaining quality data acquisition and storage faces
significant challenges. There have been several instances in which the
existing approach has not detected errors such as inaccurate base flow
values over a long period of time, incorrect time stamps of the
recordings, and falsely generated data from electromechanical failure of
sensors. Moreover, the analog system in use until 2000 required a
labor-intensive workflow resulting in increased chance of human errors
and the inability to identify anomalous recordings for almost five
decades worth of data. Within the 2 million gauge-day records, some
errors are to be expected. Errors might have occurred due to the changes
in the equipment used for data reading, storage, and digitizing recorded
charts. The current challenge is to find new ways to improve data
quality by identifying and correcting errors within the extensive
database (\emph{Bitew, et al., 2019} ). In addition to the potential
errors listed, there were other problems such as decommissioning a large
number of rain gauges between 1982 to 1989 during the winter season (DAP
provides complete metadata for these dates), when frontal rainfall
dominates and is more spatially uniform, due to budgetary constraints.
In this period, only nine gauges on the watershed were operated
year-round (\emph{Nichols et al., 2002} ).

2.3. Methods

Fundamental hydrologic principles and relationships were used to develop
the new QAQC tools for auto-flagging the inconsistencies and errors in
the WGEW data. These are:

1) Precipitation is spatially correlated;

2) Precipitation can be linked temporally to runoff:

3) There is a limit to the amount of precipitation converted to runoff;
and, 4) Extremes events require additional examination.

\textbf{Spatial correlation of rainfall:} Even though the summer rain in
WGEW is characterized by localized and short-lived events
(\emph{Goodrich et al., 1997} ), the dense rain gauge network in the
watershed is assumed to capture the spatial structure of the rainfall at
the event scale (\emph{Osborn et al., 1980} ). Rainfall observations
from rain gauges close to one another show strong spatial correlation,
which weakens as the separation distance increases. \emph{Keefer et al.
(2015)} identified correlation decreases significantly as the spatial
distance increases more than 2 km between rain gauges using 59 rain
gauges 1961--2013 in WGEW. This principle necessitates the application
of interpolation techniques in the context of identifying erroneous
events.

\textbf{Correlation of rainfall and runoff:} There is a temporal
correlation between rainfall and runoff observations. Based on this, two
relationships were utilized: 1) a one-to-one association of rainfall and
runoff (Association Method) by searching for the amount of rain observed
within a given window of time for each runoff observations, and 2)
computing the value of delay time between the runoff and the time of
precipitation occurrence (Lag Time Method). For each runoff event, there
exists a corresponding rainfall event that caused the runoff, and the
delay time should not be too early or too late.

\textbf{Runoff is a small portion of precipitation:} Not all rainfall is
converted to runoff. All or a portion of the rainfall is usually
abstracted in the landscape resulting in small runoff to rainfall ratio.
The abstraction is usually large in arid and semiarid regions
(\emph{Goodrich et al., 1997} ) resulting in only a small portion of the
rainfall converted into the runoff. The runoff amount is the result of
complex integrated hydrologic functions based on the rainfall and
watershed properties. These include rainfall attributes (spatial extent,
depth, intensity, duration, etc.) and the watershed properties,
including ephemeral channels, ground cover, soil, slope shape, etc. This
principle was applied in two forms: To evaluate the temporal
relationship between runoff and precipitation and watershed properties
and antecedent condition (Regression Method; \emph{Bitew et al., 2019}
); and, To calculate an index that accounts for the ratio of runoff to
rainfall amount (Runoff Coefficient Method).

\emph{2.3.1. Rainfall Interpolation method}

To improve process understanding and produce visually intuitive gridded
maps of rainfall, we performed a 100 m X 100 m gridded spatial
interpolation across the entire WGEW rainfall dataset for the period
1954-2014 at the daily scale. The interpolation method is based on a
Multiquadric-Biharmonic (MQ-B) interpolation, as described
in\emph{Garcia et al. (2008)} and \emph{Syed et al., (2002)} . By
visually inspecting each map, we identified rain gauges with anomalously
high/low rainfall amounts and flagged them. The interpolated maps were
used as a first step to narrow the focus on potentially erroneous
events.

The analysis of the interpolated rainfall maps identified two types of
errors: 1) Type I Error: the result of rain gauges being turned off
without any designation in the database or missing gauge data due to
other reasons; and, 2) Type II Error: the result of date coding errors
(i.e., the wrong date was recorded when digitizing the analog recording
chart). For Type I Error cases, rainfall totals for a rain gauge are
recorded as zero in the database due to equipment malfunction, human
error, or the gauge being turned off without notation. Causes of Type II
Errors include: an erroneous date recorded for the rainfall (i.e., the
rainfall was marked as occurring on a different date), false data
produced from electromechanical failure or environmental interference,
and human error in interpreting the analog data. For each gauge-rainfall
day, we evaluated the map of interpolated observations to determine if
inconsistencies on the rainfall field associated with the errors were
verifiable or not. The date of each flagged rainfall event and the rain
gauge number were stored for further verification and correction in the
database (Figure 2). The first step in verifying the flagged
interpolated daily rainfall inconsistencies is to identify if they
belonged to the periods when the gauges were turned off for budgetary
reasons. Those dates are usually available in the database metadata. In
the case of the flagged dates outside the period when gauges were turned
off, the field notes and paper charts were used in the verification
processes.

\emph{2.3.2. Rainfall-runoff association method}

The association method (Figure 3a) was designed based on the fact that
in ephemeral channels, any runoff generation is always triggered by an
associated precipitation event. If a given runoff event had no
associated rainfall within a reasonable time window, it was flagged for
further investigation. It was important that we considered timing errors
for runoff events that did not have associated rainfall due to
instrument time-keeping limitations during the period of analog
recording. During this period there was no way to synchronize clocks
other than to manually adjust to a wrist watch. Furthermore, attempts to
correct data with known timing issues were often made by adjusting to
the measurement of a nearby instrument.

In this method, we followed four steps to identify the erroneous events:
1) We generated continuous hourly rainfall and runoff data from the
breakpoint data format in the database; 2) We then calculated the
spatial sub-watershed average of the aggregated hourly rainfall using
only those rain gauges within the sub-watershed boundary and only
included the gauges that recorded rain, i.e., only non-zero values were
included in the average. This approach was used to account for instances
of relatively intense rain recorded in a small number of rain gauges
within the sub-watershed that could have resulted in runoff, but if
averaged over all the rain gauges could have resulted in a very small
depth; 3) The hourly runoff data and the spatial hourly average rainfall
data are then merged and summarized into total runoff volume within
seven (7) hours windows and total rainfall depth within a 4-hr window;
and, 4) Finally, we searched for a one-to-one association between the
runoff volume and the corresponding rainfall depth, which resulted in
flagging those events with insufficient (\textless{} 1 mm) or no
recorded rainfall as problematic data. The event-based summary using the
seven-hour window for the runoff and the four-hour window for rainfall
were selected through trial and error across several sub-watersheds in
WGEW. In summary, we accumulated the runoff depth within the seven-hour
window; 3-hour preceding and 3-hour following the hour at which the
maximum runoff was observed. The event-based rainfall depth was
calculated as the sum of all rainfall accumulated 3-hours proceeding and
1-hour succeeding the hour of maximum runoff observation for all rain
gauges in for near the sub-watershshed (Figure 3a).

\emph{2.3.3. Lag time method}

The lag time method relies on the relationship between the temporal
properties of the rainfall hyetographs and the corresponding runoff. The
lag time is defined as the time interval between the center of mass of
the hyetograph for a given rainfall event\(\ {(CM}_{f})\) and the time
of the peak runoff rate in the hydrograph for the associated runoff
event \((t_{\text{peak}})\) (Figure3b). The center of mass of excess
rainfall \({(CM}_{f})\) was estimated as the median of excess
rainfall time, i.e., rainfall duration after the starting time of the
runoff (equation 1). In long-duration rainfall events where only
rainfall in a certain portion of the duration has resulted in runoff,
equation 1 may not provide representative \(\text{CM}_{f}\) value. In
such cases, the use of equation 2 provides a better estimate of
\(\text{CM}_{f}\)values. In most cases, the center of mass calculation
based on the median of excess rainfall duration (equation 1) and time of
maximum rainfall (equation 2) yielded similar results. Lag time was then
calculated using equation 3. The lag time related parameters used in
this analysis are the rainfall start time \((t_{\text{oprecp}})\), runoff
start time (\(t_{\text{oRunoff}}\)), time of peak runoff
rate\((t_{\text{peak}})\), time of maximum rainfall intensity
(\(t_{max\_int}\)), and rainfall duration (D) ( Figure 3b).

In watersheds with multiple rain gauges, the hyetograph of the rain
gauge with the minimum succeeding time difference
i.e.,\(t_{\text{oprecp}}{-\ t}_{\text{oRunoff}}\) was used to calculate\(\text{CM}_{f}\).
Rainfall events with unrealistically long lag times could be due to
errors in the rainfall or runoff data timestamps and were flagged.

\begin{equation}
\text{CM}_{f}=\frac{D-\ \left(t_{\text{oprecp}}-t_{\text{oRunoff}}\right)}{2}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\left(1\right)\nonumber \\
 \end{equation}

\(\text{CM}_{f}=t_{max\_int}\) (2)

\(Lag\ Time=\text{CM}_{f}-t_{\text{peak}}\ \) (3)

The maximum threshold for lag times ranged from 1-2 hours and was
defined for each sub-watershed based on the size of the drainage area.
The estimated travel time, from the storm center to the outlet of the
watershed, was determined by simple routing equations. Lag time was
plotted against mean runoff rate for each event for visual
identification of the possible thresholds. An example of the visual aid
for threshold identification is given in Figure 4.

\emph{2.3.4 Runoff coefficient method}

The runoff coefficient (C) is computed as the total event runoff volume
divided by the total sub-watershed-averaged rainfall volume accumulated
between the 3-hours preceding the beginning of runoff observations and
the end of the runoff event (Figure 3c). The C values range from 0 to 1;
0 for no runoff generation from the rainfall and 1 when all rainfall
over the sub-watershed is converted to runoff. In WGEW the runoff
coefficient values range between roughly 0.065 at the hillslope scale
and 0.006 over the entire watershed (\emph{Renard et al., 2008} ). This
method was designed to identify two cases of rainfall-runoff relations:
Case 1) C equal to infinity, which shows the condition of a runoff event
without associated rainfall; and Case 2) an exceptionally large C
approaching 1, which can raise concerns about the quality and accuracy
of the rainfall and resulting runoff measurements. In Case 1, where C
equals infinity, the error is likely related to the runoff data as in
the case of the association method, but in Case 2 it is important to
flag both runoff and rainfall for further investigation.

\emph{2.3.5. Regression method}

We selected several hydrometeorological predictors from DAP with the
potential to influence rainfall-runoff relations to develop a
multi-parameter regression model (Figure 3d). The predictors that
influence rainfall-runoff relationship in WGEW were evaluated using a
multi-model inference approach that used the Akaike Information Criteria
(AIC; Akaike 1973). In this approach, we developed a regression equation
using the 18 predictors that describe rainfall properties, watershed
properties, and the antecedent soil moisture conditions related to the
contributing area and channel system. The simulated runoff depth
predicted by the regression model was then compared with the measured
runoff to identify events with questionable rainfall-runoff relations
based on the following three conditions. The first condition was the
identification of substantial rainfall events (\textgreater{}20 mm
depth) that did not produce runoff. The second condition identified
rainfall events with observed runoff (\textgreater{}0.5 mm depth), but
zero predicted runoff. The third condition identified those rainfall
events with observed runoff, but no predicted flow. For details of the
development and performance of the regression model in QAQC application
in the WGEW case, see \emph{Bitew et al. (2019)} .

2.4. Verification/Validation

Once the questionable rainfall and runoff events were flagged using the
test methods described above, the flagged events were further
investigated by visual inspection using a plotting tool that displays
the runoff event and corresponding rainfall. The plotting tool displays
cumulative runoff volume, the runoff rate, the corresponding cumulative
rainfall as the spatial mean of the watershed, and the cumulative
rainfall from each of the rain gauges in the sub-watershsed (see Figure
3e). In addition to using the plots for verification of the flagged
events, historical metadata were also used to gain insight to the cause
of the error. These data included: the original field notes and
maintenance logs kept by technicians, note on the original paper charts
from the analog instrumentation, and the use of information available
from the neighboring sensors.

3. Results and Discussion

3.1 Rainfall observation errors

Using the rainfall interpolation method, two types of errors were
identified. The Type I error is visually observed as isolated points
with no measured rainfall surrounded by gauges reporting rainfall on the
maps (Figure 5a). Type II errors (Figure 5b) can be identified on the
rainfall maps when a single gauge reports rain or suspicious subset of
gauges report rainfall while no other rainfall is detected in the
watershed. Often times these gauges show Type 1 error on previous or
subsequent days. Another relatively common error in the analog era was
the clock stopping. If ink was still in the recording pen, partial data
could sometimes be salvaged. In these cases, an estimated hyetograph was
constructed using the temporal storm distribution of adjacent gauges.
These instances are documented in the metadata for the gauge.

For each day with observed rainfall, a total of 6004 days in the 62-year
period, we visually inspected each map and identified the number of
occurrences of each type of error. Figure 6 a and b show temporal
changes in error type as cumulative relative frequency (\%) for daily
rainfall during the period 1954-2014. Type I Errors are primarily
associated with rain gauges not being operational for intentional and
unintended reasons. From the total number of cases, n = 641, 28\%
occurred during the summer months (July -September) while 72\% were
observed during the winter months (October -- March). The number of
occurrences of Type I errors was largest in the 1980s and mainly during
the winter months, a period when rain gauges were turned off due to
budgetary restrictions. The percentage of reported Type I errors
increased from 34\% in 1978 to 76\% in 1988. Type II errors totaled 160
cases during the 62-yr study period and were uniformly distributed
through time except in 1962 and 1970 that showed 17 and 25 cases,
respectively. For both error types, the majority of cases were reported
during the analog recording period (pre-2000) indicating that despite
the technical expertise of the WGEW technicians and the QAQC in place,
human and mechanical equipment errors are sometimes difficult to detect
and avoid. Of all the Type I errors, 49\% of the cases were
uncorrectable (unknown sources or lost information, etc.) while 41\%
were correctable cases (information available in the original charts or
maintenance log) (see Figure 6 c and d). For Type II errors, the largest
contribution to total error was correctable (56\%) while the false alarm
cases (33\%) were not errors but identified as errors due to visual
limitations in inspection of the maps.

3.2. Runoff observation errors

We applied the four QAQC runoff tests to all runoff-producing events on
the 3 sub-watersheds. The analysis found a total of 102 questionable
events flagged by one or more of the tests: 40 events in WS-04 (12\% of
events), 28 events in WS-11 (6\% of events), and 40 events in WS-06 (6\%
of events). The tests identified runoff events that were assigned
erroneous time stamps that occurred due to malfunctions in the analog
clocks, and human error when digitizing the charts. The errors in the
runoff time stamps resulted, in some instances, as runoff occurring
before the onset of the rainfall, in other instances it resulted from
excessively large lag times or in excess of the threshold time used in
the association and runoff coefficient methods. We also identified
runoff events with excessively long recession curves that commonly occur
in WGEW due to the functionality of the measurement flumes. These long,
low-flow periods, initiated at the recession of the hydrograph, are a
result of sediment deposition within the stilling well of the flume.
This accumulation of sediment slows the drainage from the stilling well
and consequently affects the measurement of the water level made by a
floatation mechanism. These erroneous events are typically adjusted in
the existing QAQC protocol by fitting a theoretical curve to the end of
the recession in the hydrograph and noting in the metadata.
Unfortunately, some of these types of errors have slipped into the
database over the years. These errors were easy to identify with the
association method due to the excessively long period of artificial low
flow following the recession of the hydrograph. The association method
identified these events because the 7-hr window breaks the long runoff
duration data into multiple 7-hr runoff events where only the first
window will have associated rainfall.

Overall, there were few instances where the four methods simultaneously
flagged runoff events. The Lag time method flagged the largest
percentage of events ranging from 51 to 80\% for the 3 sub-watersheds,
followed by the Regression method that identified between 40 and 50 \%
of the total number of events flagged (Figure 7 a). The Runoff
Coefficient method flagged the smallest number of events and also showed
the largest variability between the watersheds. We did not find a direct
relationship between the efficiency of any of the four methods and the
area of the sub-watershed. Each method, regardless of which one is used,
can identify between 50-75\% of the total number of flagged runoff
events, but that percentage decreases to 7-26\% for all the methods to
detect the error simultaneously (Figure 7b).

The number of questionable events flagged depends on the threshold
values selected in each of the methods. These thresholds require expert
knowledge of the watershed being examined, and will vary depending on
biophysical characteristics of the watershed. It is also important to
note that the threshold values (7-hr window in the association method,
1-2-hr lag time, etc.) were determined iteratively based on detailed
observation of the data analysis in this study. Examples of specific
problematic events that were not previously identified as errors in the
database were flagged by these tools and confirmed using the record
information associated with the database (Figure 8). The figure includes
a longer lag time than anticipated (Figure 8a and c), an excessive low
flow duration (Figure 8b) that showed a false baseflow over more than 14
hours, and errors where runoff occurred before the rainfall (Figure 8e
and f). Closer examination of the database and the inspection of analog
charts for the questionable data points identified revealed different
problems related to the timestamp of the data recording and storage. The
events in Figure 8 (except b) were flagged using lag time, showing a
significant delay of the rainfall that possibly resulted in the runoff.
The association method flagged all events except e and f as all the
runoff events did not have associated rainfall within the 4hr window
leading to the maximum runoff hours. The main hydrograph of the event in
Figure 8b (7/28/1966 on watershed WS11) does not seem to have a problem,
but the fact that the runoff baseflow component in the recession side
continued over 14 hours with the runoff rate value close to 0.2 cfs
which appeared as a sequence of runoff events with no associated
rainfall. The runoff coefficient method identified the events in a, c,
and d, and the events in e and f were flagged by the regression method
(see more on \emph{Bitew et al., 2019} ). We applied the plotting tool
on about 90\% of the 102 flagged events for which clock issues on
rainfall/runoff were the reason for inconsistencies in the data. From
the visual inspection, 72\% of the flagged events were problematic while
the rest required more than visual inspection to verify the error. The
verified events had no rain corresponding to the runoff or the rainfall
that appeared to have happened before the runoff event started. About
7\% of the flagged events seem to be false alarms, which were identified
mainly by the lag time and association method. The examples of the false
alarms were dominantly runoff events created by long-duration variable
rainfall across the watershed, which resulted in big lag time. There
were instances in which runoff with multiple peaks or separate runoff
events for the same long-duration rain occurred. In some cases, flow is
recorded on the flumes after the contributing area is saturated
sufficiently, resulting in large lag time. In the event where the data
showed that runoff recording before the rainfall in a few minute delay,
the inspection was not very clear, which needed to compare the start
time of the runoff and rainfall from all rain gauges in the watershed.

3.3. Strengths and weaknesses of the QAQC methods

Evaluations of the formulation of each of the methods and evaluating the
list of flagged events have different strengths and weaknesses. For
instance, in the interpolation method, the visual inspection of the
daily interpolated rainfall maps clearly shows the expected spatial
correlation between the rain gauges located close to each other. But
this does not mean the maps that showed consistent spatial rainfall
field are free of errors. The method misses errors related to sub-daily
time steps. In the lag time method, the fact that start times, peak rate
time, and duration are registered for all event rainfall and runoff
makes it possible to evaluate the lag time at 1-minute time resolution.
Using this method, we have identified errors that are very difficult to
identify using other methods. Such errors include errors like when the
runoff came 1-min before the start of the rainfall in the watershed. It
is also important to note that runoff that appears to happen before the
start of the rainfall could be related to runoff events triggered by
heavy rain on the flumes. The representation of the center of mass of
the rainfall and lag time computation using in the equations is a
simplified version of the lag time. This representation, especially in
long-duration rainfall and storms moving across the contributing areas,
may result in erroneous lag time. The other limitation is a threshold
lag time value, which usually depends on the watershed size. The
accuracy of the arbitrary definition of the threshold lag time values is
one of the limitations. The strengths and weaknesses of each of the
methods are summarized in the Table 1 below.

4. Conclusions

Given the challenges facing natural resource management, every effort
should be made to ensure that long-term datasets are used to their
fullest potential. Implementation of carefully curated datasets, will
ensure that future investigations will gain the benefits of reliable and
trustworthy data. The methods used in this study were developed and
applied to evaluate the quality of exceptional set of
hydrometeorological data in a semi-arid environment that comprises the
sub-hourly and high-density spatial observations. The use of
relationships based on conventional hydrologic principles allows using
the same principles in other regions. However, the application in
different areas requires understanding of the unique features of
rainfall-runoff responses in line with observation time steps and the
observations' spatial density. Therefore, one can say this QAQC strategy
can be potentially applied in similar networks with rainfall and runoff
observations to improve the quality of their long-term databases with
some modifications depending on specific meteorological and hydrological
processes related to the watershed.

Prior to this study, there had not been a systematic linkage of rainfall
to runoff for all of the nested sub-watersheds on WGEW. Inconsistencies
in the database were successfully flagged due to mainly date/time code
errors, events with unreasonably long low-flow periods, small runoff
events generated with rainfall on flumes when it did not rain enough
elsewhere in the watershed, maintenance flow mistakenly left in the
database, etc. So far, the five tools were designed and applied in such
a way to auto flag the problematic events separately. These tools can be
combined into a single partially automated workflow process, but
verification through visual inspection by a trained technician or
scientist is still necessary. The agreement between the four methods was
minimal, highlighting the importance of using more than one tool to flag
possible errors in rainfall-runoff observations. Due to the assumptions
in each of the methods, some errors are better identified by specific
methods while they miss certain types of errors. Therefore, it is vital
to apply all events and flag as many events as possible and go through
one by one to confirm the errors using the information available about
the events. These analyses for runoff QAQC included only 3
sub-watersheds, which will be expanded to all sub-watersheds in the
future. So far, these approaches brought to light 813 rainfall and 24
runoff events with erroneous timestamps or magnitude of observations
etc.

Acknowledgments

We thank the group of USDA-ARS dedicated technicians that for more than
60 years have professionally maintained the network of rain gauges,
runoff structures, and general experimental watershed infrastructure
used in this study and numerous research projects. Rainfall, runoff,
sediment, meteorology and watershed characterization data are freely
available from https://www.tucson.ars.ag.gov/dap/. This research was a
contribution from the Long-Term Agroecosystem Research (LTAR) network.

Data Availability Statement: The data that support the findings of this
study are publicly available https://www.tucson.ars.ag.gov/dap/.

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Tables

Table 1. Pros and cons of the four methods implemented for the runoff
QA-QC

\textbf{Figures}

\textbf{Figure 1} . a) Geographical location of WGEW. Average total
summer rainfall for the period 2000-2017 and spatial distribution of the
99 rain gauges operational in the watershed. The thicker lines show the
drainage boundaries for sub-watersheds WS-04, WS-06, and WS-011. Finer
lines show the boundaries for other larger sub-watersheds b) USDA
digital weighting rain gauge, c) sub-watershed WS-06 flume.

\textbf{Figure 2} . Flow chart used to flag inconsistencies in daily,
interpolated rainfall maps. Type I Errors are errors due to turned off
rain gauges or missing gauge while Type II Errors are errors resulting
from incorrect date coding.

\textbf{Figure 3} . Schematic description of the four approaches used
for runoff QAQC. a) Rainfall-runoff association method, b) Lag time, c)
Runoff coefficient, d) Regression method, and e) plots of runoff and
corresponding rainfall.

\textbf{Figure 4:} The example above shows questionable events
identified by lag time method and visual aid to identify the value of
threshold lag time for WS-11. The questionable events are identified as
the events having outlier lag time values. 70 min is considered as a
threshold lag time for this particular watershed where it showed clear
separation from the rest of computed values.

\textbf{Figure 5.} Rainfall errors identified with the aid of rainfall
maps, a) Type I and b) Type II.

\textbf{Figure 6.} Cumulative relative frequency of days with errors in
the rainfall dataset from 1954 to 2014 (a and b) and the percentage
contribution of each source of error to total error (c and d). The
horizontal line in a and b indicates the date when the analog system was
replaced by the digital system.

\textbf{Figure 7. a)} Percentage of events flagged by the four methods
for the three sub-watersheds, b) percentage of the total number of
flagged events identified by 1 to 4 methods simultaneously.

\textbf{Figure 8.} Selected runoff (black line) and rainfall from
multiple gauges (gray lines) within the watershed of interest on
inverted y-axis. The solid blue line represents conditional mean of the
different rain gauges in the watersheds. The figure shows excessively
delayed runoff in a and c, runoff events not associated with the
corresponding rainfall in d and b, and runoff occurring before the
rainfall was being recorded in f and e.

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