DOI: 10.6078/d1ch64
title: Data from: The utility of information flow in formulating discharge forecast models: a case study from an arid snow-dominated catchment

description: These data accompany the manuscript “The utility of information flow in
 formulating discharge forecast models: a case study from an arid
 snow-dominated catchment”, in review at WRR. They were compiled from Boise
 State’s University’s Dry Creek Experimental Watershed (DCEW) web site, and
 consist of measurements of climatic data and discharge at various stations
 in the watershed from 1 January 2001 through 19 July 2017. The data
 quality-controlled, gap-filled, and aggregated at scales varying from 1
 day to 6 months. For each aggregation scale, anomalies with respect to the
 day of water year (DOWY) were also calculated. These data were then used
 to compute an information-theoretic measure, transfer entropy (TE), which
 quantifies the information flow from each variable (at each scale) to
 discharge.
description: Collection and pre-processing:
 Raw hourly data for the Tree-Line (TL) and Lower-Gauge (LG)
 meteorological stations (see manuscript for exact locations) from 1
 January 2001 through 19 July 2017 were obtained from Boise State
 University (https://earth.boisestate.edu/drycreek/data/) for the following
 set of variables measured in the Dry Creek Experimental Watershed (DCEW):
 air temperature, precipitation, relative humidity, solar radiation, snow
 water equivalent (SWE), wind speed and wind direction. Hourly soil
 moisture and soil temperature were also obtained from north-facing soil
 pits at both the LG and TL station at depths that range from 5cm to 100cm.
 Hourly discharge for the DCEW catchment was obtained for the same period
 as the meteorological and soil moisture time series from a station just
 downstream of the LG meteorological station. All data
 were carefully quality controlled and any outliers or spurious patterns in
 the data were identified and removed by hand. Gaps in the data were filled
 using interpolation, multiple linear regression, and autoregressive
 models. When possible, multiple linear regression was used to fill gaps as
 this provided a synthetic record based on observations from within the
 catchment. When gaps occurred over small time scales at both
 meteorological stations (LG and TL) autoregressive or linear interpolation
 was used to in-fill the records. Overall, only a small portion of the time
 series (&lt; 6% on average) required gap infilling.
 Snowmelt was computed from decreases in SWE and a temperature
 threshold of 0 °C was used to parse precipitation into rainfall or
 snowfall. We also estimated evaporation at the LG and TL gauges using the
 Priestley-Taylor method (Priestley & Taylor, 1972), which is based
 on radiation and is a simplification of the Penman-Monteith combination
 equation (Monteith, 1981; Penman, 1948). An α of 1.72 was used instead of
 the commonly used 1.26 to reflect the higher moisture stress of the arid
 conditions within the catchment. We compared mean monthly estimates of
 evaporation between the Priestley-Taylor and Penman-Monteith methods with
 long term (1916 - 2005) pan observations from the nearby Arrowrock Dam,
 Boise River, Idaho
 (https://wrcc.dri.edu/Climate/comp_table_show.php?stype=pan_evap_avg), and
 found better qualitative agreement with the Priestly-Taylor
 estimates. The quality-controlled data and derived
 parameters were aggregated to 1, 7, 14, 30, 60, 90, and 183 day time
 scales. The 1-day time scale was the minimum time stamp evaluated in this
 study and was computed by taking the daily mean of all meteorological
 variables except for evapotranspiration, precipitation, rainfall,
 snowfall, and snowmelt which were computed as a daily total. The 7, 14,
 30, 60, 90, and 183 day aggregation scales were computed with a
 back-looking moving mean. To remove periodic/seasonal trends from the time
 series we computed an anomaly for each variable at each aggregation length
 by taking the day of water year (DOWY) mean (based on the full period of
 record) and then differencing the DOWY mean from the aggregated values.
 These anomaly time series were used for our transfer entropy analysis and
 allowed us to detect interactions between hydrologic variables that were
 not driven by synoptic changes in seasonal conditions. Thus the full suite
 of candidate variables includes the 61 primary meteorological variables
 between the two weather stations and four soil pits, with each of these
 variables having six aggregated time series (1-day, 1-week, 2-week,
 1-month, etc.) for a total of 427 time series. Example time series are
 provided for the LG and TL stations in Figs. S5 and S6.
 TE analysis: To evaluate
 information transfers from meteorological and hydrological predictor
 variables to discharge (and for their anomalies to the discharge anomaly),
 we computed equation 1 for τ ranging from lags of 1 day up to 183 days,
 using block lengths (k and l) of one. The reduction in uncertainty from a
 meteorological variable to discharge was deemed statistically significant
 when the TE value exceeded the 95th percentile of a distribution of TE
 values computed from 500 randomly shuffled versions of the input data
 matrices (Ruddell & Kumar, 2009a and b). The full length of the
 time series used for calculating TE was 6044 days (~16.5 years). Thus, at
 the maximum lag of 183 days there were still &gt;5800 overlapping data
 points with which to compute the joint and marginal entropy values for
 estimating TE. We quantified the relative significance in TE at each lag τ
 as:
 T'<sub>rel,τ</sub>=(T-T<sub>0</sub>,τ)/H<sub>Q</sub>, where T<sub>0,τ</sub> is the significance threshold at that time lag and H<sub>Q</sub> is the total uncertainty (Shannon entropy; Shannon, 1948) in the sink variable, discharge. T'<sub>rel,τ</sub> is a normalized version of the TE that quantifies the significant reduction in the uncertainty of discharge relative to the total uncertainty in discharge. The τ associated with the highest T'<sub>rel,τ</sub> within the first 183 lags was selected as the critical timescale (i.e., most significant lag) to be used in the forecasting models.
description: The directory contains a Readme file, and each Matlab data file
 corresponds to an Excel file with the description of the variables and
 their structure.