Hydrological water balance closure is a simple concept, yet in practice it is uncommon to measure every significant term independently in the field. Here we demonstrate the degree to which the field-scale water balance can be closed using only routine field observations in a seasonally frozen prairie pasture field site in Saskatchewan, Canada. Arrays of snow and soil moisture measurements were combined with a precipitation gauge and flux tower evapotranspiration estimates. We consider three hydrologically distinct periods: the snow accumulation period over the winter, the snowmelt period in spring, and the summer growing season. In each period, we attempt to quantify the residual between net precipitation (precipitation minus evaporation) and the change in field-scale storage (snow and soil moisture), while accounting for measurement uncertainties. When the residual is negligible, a simple 1-D water balance with no net drainage is adequate. When the residual is non-negligible, we must find additional processes to explain the result. We identify the hydrological fluxes which confound the 1-D water balance assumptions during different periods of the year, notably blowing snow and frozen soil moisture redistribution during the snow accumulation period, and snowmelt runoff and soil drainage during the melt period. Challenges associated with quantifying these processes, as well as uncertainties in the measurable quantities, caution against the common use of water balance residuals to estimate fluxes and constrain models in such a complex environment.
Water balance closure has been described as the holy grail of scientific hydrology (Beven, 2006). Beven suggests that the most important problem in hydrology in the 21st century is providing the techniques to measure integrated fluxes and storages on useful scales. In the current paper, we define the problem of water balance closure as that of independently quantifying each term in the water balance equation, such that the changes in storage within a specified domain and over some time interval are adequately balanced by the net fluxes into or out of that domain over the same time interval. As simple as this concept is, it has proven to be extremely hard to achieve in field studies. For example, Mazur et al. (2011) reported a water balance closure study for a well-characterized, intensively monitored artificial catchment and were unable to close the water balance due to their inability to quantify evapotranspiration and changes in storage. Natural heterogeneity of both water fluxes and moisture states, which can vary on spatial and temporal scales that are beyond (or beneath) our measurement capabilities, can make the task of observing complete water balance closure seem like an enigmatic pursuit.
In this paper we present a case study from a heterogeneous pasture site in the Canadian prairies, where we have quantified the various components of the water balance on the field scale, and critically examine some of the simplifying assumptions which are often invoked when applying water budget approaches in applied hydrology. The Canadian prairie region lies in the southern part of the provinces of Alberta, Saskatchewan, and Manitoba and makes up the northern portion of the Great Plains region of North America. The hydrology of this region is markedly influenced by the regional climate and geology and at first glance appears to have a relatively simple water balance. Much of the rainfall occurs during the growing season and is consumed by evapotranspiration, resulting in very little surface runoff. Extensive past glaciations have blanketed the region with a thick compacted till which has very low permeability (Keller et al., 1989), resulting in relatively small interactions between the surface water and the underlying groundwater regime (van der Kamp and Hayashi, 2009). As such, the water balance in this region is conceptualized to be dominated by vertical exchanges of precipitation and evapotranspiration between the soil and the atmosphere.
However, certain characteristics of the prairie region also make the hydrology complex and are likely to confound simple 1-D assumptions regarding the water budget. The region is seasonally frozen, with long winters (4–6 months), featuring many cryosphere-dominated hydrological processes. Approximately one-third of annual precipitation is snowfall, which is subject to extensive wind redistribution throughout the landscape (Pomeroy et al., 1993; Pomeroy and Li, 2000), resulting in a spatially variable water input. During the spring melt, spatially variable surface albedos and heat advection from snow-free to snow-covered areas can cause differential rates of snowmelt (Shook et al., 1993; Liston, 1995). Moreover, infiltration into frozen soil has complex dependencies upon the antecedent moisture, the rate of melt, and local topography (Gray et al., 2001), resulting in a highly variable spatial infiltration pattern (Hayashi et al., 2003; Lundberg et al., 2016). Due to these factors, the annual snowmelt event typically produces 80 % or more of the annual local surface runoff (Gray and Landine, 1988). The hydrological complexity of the landscape is also largely influenced by glacial and post-glacial geomorphological processes, which have imparted a tremendous degree of heterogeneity. Morainal deposits, comprised of a variable mix of soil textures, are often topographically indeterminate and consist of areas which are internally drained and infrequently contribute to stream flow (Zebarth and de Jong, 1989; Shaw et al., 2012).
While observations of all of the hydrological fluxes and states on large, i.e. useful (Beven, 2006), scales are desirable, current measurement approaches do not yet fully permit this. The evaporative flux can be measured over reasonably large scales (on the order of hundreds of metres) using the eddy covariance technique, whereas the soil moisture status and bottom drainage fluxes can generally only be measured on point scales. Recent advances in remotely sensed soil moisture, such as the ground-based cosmic ray neutron probe (Zreda et al., 2008) or satellite-based sensors such as those used by the Soil Moisture and Ocean Salinity (SMOS) mission (Kerr et al., 2010) or the Soil Moisture Active Passive (SMAP) mission (Entekhabi et al., 2010), can retrieve soil moisture estimates over hundreds of metres to tens of kilometres. However, these observations are limited to the near surface, and need to be depth-scaled to the root zone to be suitable for water balance studies (Peterson et al., 2016). Adequately capturing field-scale variability using point-scale measurement techniques requires a large number of samples (e.g. Grayson and Western, 1998; Famiglietti et al., 2008; Brocca et al., 2010).
The objective of this paper is to explore how well the water balance can be closed using only routine field observations in a seasonally frozen environment. We use a well-instrumented field site to quantify the magnitude of the water balance components as they vary across three distinct seasons in the prairies on field scale. We start with a conceptual model of all of the dominant hydrological processes active at the site, from which we construct a water balance equation. We designed a simple field experiment to measure the components of the water balance that can be measured in a routine, if labour-intensive, manner on field scale. We performed an uncertainty analysis on each measurement, accounting for instrument error and sampling error. We evaluate the validity of treating the problem as 1-D in different seasons, and the value of using water balance residuals to estimate fluxes and constrain models.
We consider field scale to represent an area on the order of
500 m
where all terms are in units of millimetres, and
The water table is located 3–5 m belowground surface depending on location (the water table is shallower in topographic depressions) and time of year (the water table is shallowest in the earlier summer after the melt period). Water table dynamics are modest, but there will be lateral saturated flow processes occurring. Since the saturated zone is well below the domain of our water balance, here we only consider vertical drainage from the base of our soil layer. Lateral unsaturated subsurface flow may occur on local scales due to changes in soil properties, but we do not expect these fluxes to be significant on field scale. Hence, lateral subsurface fluxes are neglected.
In seasonally frozen environments where winters are long and cold, processes
in the summer and winter are markedly different. A water year in this region
is typically defined as from November to October, such that snow accumulation
and melt occur within the same water year. Annual water balances are useful,
but do not elucidate the important seasonal processes – in particular the
storage dynamics. For a more rigorous analysis, here we examine the water
balance over three distinct seasons:
In each period the nature of the individual components of the water budget is different. For example, in the snow accumulation period, surface storage occurs as snow; in the growing season, if it exists at all, it is as ponded water in ephemeral ponds which tend to dry out in early summer; and in the melt period, it is a transition between these two. Snow drift, runoff, and evaporation are typically only significant in the snow accumulation season, the melt period, and the growing season, respectively. This will be discussed in detail in Sect. 4.
Brightwater Creek sub-basin in Saskatchewan River Basin (effective
drainage area shown by hatching) and locations of measurements.
The instrumented field site (51
This local study area (500 m
A variety of measurements were used to characterize the field-scale water
balance from 1 November 2012, reported here until 31 October 2014. The total
evaporation flux,
The available energy, consisting of the net radiation flux (
The energy balance closure ratio (EBR),
Precipitation (mm) was measured by a Geonor T200-B weighing gauge. Biases in solid precipitation (i.e. snow) measurements were corrected for undercatch using a catch efficiency relationship with wind speed (Smith, 2008), and for liquid precipitation (i.e. rain) we assume a catch efficiency of 95 % for all rainfall measurements (Devine and Mekis, 2008). Precipitation bias-correction leads to an increase in measured precipitation of 19 and 13 % in 2013 and 2014, respectively.
Root zone soil water content and snowpack depth and density were measured at
point locations in a crosshair pattern, comprising two perpendicular
transects, centered on the flux tower (shown in the upper right corner of
Fig. 1a). Water content was measured by a down-hole neutron moisture meter,
model CPN 503DR Hydroprobe (CPN International Inc., Concord, CA). The blue
pins are the neutron probe reading locations installed in June 2012, and the
yellow pins show new locations added in summer 2013. Volumetric soil moisture
content (liquid water
Water table depths were monitored using piezometers, screened (33 cm in length) at a depth of around 5.5 m belowground, with level loggers (Solinst, Model 3001) at three locations along the northwest–southeast transect (no. 1, no. 2 and no. 3 in Fig. 1b). The one closest to the flux tower started collecting data on 17 July 2012, and the other two started on October 7, 2013. The measured water table depth was corrected for changes in barometric pressure, measured at the flux tower, using the graphical method for estimation of barometric efficiency proposed by Gonthier (2007).
Soil temperature was measured using Stevens Hydro-probes at three profiles,
co-located with the piezometers. At profile no. 1 (Fig. 1b) five probes were
installed, at depths of 0.05, 0.2, 0.5, 1.0, and 1.5 m belowground, and at
the other two profiles seven probes were installed, at depths of 0.05, 0.2,
0.5, 0.75, 1.0, 1.3, and 1.6 m belowground. Measurements were recorded every
30 min. The depth of the freezing front as a function of time was
calculated by interpolating the 0
We performed a quantitative uncertainty analysis of all of the measured terms
in our water balance assessment. We expect uncertainties in our measurements
of precipitation and evapotranspiration to be dominated by measurement
errors. Conversely, we expect uncertainties in our measurements of soil
moisture and snowpack to be dominated by sampling errors. These four terms
make up a naïve, 1-D, water balance, where the net precipitation
(defined as
If
The error bounds for each measurement term are described in the following paragraphs. In all cases, we concentrate on quantifying the largest, most dominant, source of uncertainty.
Fluctuation of the major variables in vadose zone hydrology during
the years of 2013 and 2014.
Components of the water balance for each season in 2013 and 2014 (see Eq. 5 and related discussion in the text for symbols).
Spatio-temporal variation of snowpack depth along the snow survey
transect in 2013
Comparison of measured solid precipitation, bias-adjusted
precipitation, and measured snow on the ground during the snow accumulation
period in hydrological years of 2013
The hydrological conditions over the water years 2013 (1 November 2012 to
31 October 2013) and 2014 (1 November 2013 to 31 October 2014) are shown in
Fig. 2, and the quantified water balance components for each season are
presented in Table 1. Total annual precipitation was 302 (2013) and 386 mm
(2014). In both years, snow accumulation started around the beginning of
November and snowmelt was complete by the end of April. The
undercatch-adjusted snowfall was coincidentally the same in both years:
72 mm. Rainfall was 230 (2013) and 314 mm (2014). The sum of evaporation,
transpiration, and sublimation was 285 (2013) and 368 mm (2014). Both years
had low measured sublimation: 14 (2013) and 10 mm (2014). Most
evapotranspiration occurred in June, July and August. Water year 2013 was
typical for the region in that soil moisture was recharged following
snowmelt, and then experienced drying over the summer months as
Lateral exchange of blowing snow during the snow accumulation period is an
important characteristic of open prairie environments, and it is essential to
account for this in any water balance study. The sub-field-scale distribution
of snow within our instrumented field was strongly affected by trapping of
snow at the fenced tower (location M0) and within brush vegetation (e.g.
location S3). The spatiotemporal distribution of snow along the long transect
(Fig. 1) is shown in Fig. 3. Topographic effects can also play a role in snow
redistribution, but here they were negligible. The phenomenon also operates
on scales larger than our field site. Whether this results in a net influx or
efflux to a particular site generally depends on the relative height of the
local and surrounding vegetation, which can trap snow (Pomeroy et al., 1993).
Taking sublimation losses into account, Table 1 shows that in 2013 there was
markedly more snow on the ground (72 mm SWE) than there was
Over-winter change in water content with depth belowground.
Symbols indicate the mean over all measurement locations, and bars indicate
95 % confidence intervals. In water year 2013, the pre-freeze measurement
was taken on 1 November 2012, and the pre-snowmelt measurement on
22 April 2013. In water year 2014, the pre-freeze measurement was
taken on 7 November 2013, and the pre-snowmelt measurement on 3 April 2014. Note that the measurements were taken at 20 cm depth
intervals, but are plotted here as offset
During the snow accumulation period the soil freezes progressively from the
surface downwards. The maximum freezing depths were 1.3 (2013) and
> 1.6 m (2014), as shown in Fig. 2d. The reasons for the
differences in freezing depth are a combination of multiple factors, which
are beyond the scope of this study to determine. The important point from a
water balance perspective is that in both years there was a non-negligible
increase in soil water content over the winter (24
In terms of the total water balance residual,
Contrasting snowmelt processes in 2013 and 2014.
Spatio-temporal variations of soil water storage change in the
shallow vadose zone along the Neutron Probe transect during the melt period
(between black and red dashed lines in Fig. 2). SWE: measured maximum snow
storage; net precipitation: cumulative difference between precipitation and
evapotranspiration;
The observed timing and magnitude of snowmelt and discharge in Brightwater
Creek (measured at gauging station 05HG002) in 2013 and 2014 are compared in
Fig. 6. Runoff from our field site may or may not have directly contributed
to this watershed-scale discharge (see the effective area in Fig. 1a), but
the local infiltration and runoff behaviour can still explain the differences seen
on the larger scale. The timing of peak discharge in both years is consistent
with the timing of the depletion of the snowpack by melting. However, the
magnitude of the peak discharge in 2014 is much bigger than that in 2013.
Snowpack depths were comparable (Fig. 6), but field-average SWE was
significantly higher in 2013 (Table 1), which indicates there is some complex
behaviour in terms of the runoff generation mechanism, which we explore here.
In both years, there was a large negative water balance residual, meaning
melt from the snowpack exceeded the increase in soil moisture, and hence
water was lost from the domain, most likely as runoff,
Spatio-temporal variation of water content in shallow vadose zone
at different locations (Fig. 1b) along the Neutron Probe reading transect
during the pre-melt (red), post-snowmelt (black), and post-thaw (blue) in
2013
To explore the marked differences in snowmelt infiltration in the 2 years, soil water content profiles for pre-melt, post-snowmelt, and post-thaw conditions are shown in Fig. 8. These observations show the strikingly different antecedent soil moisture conditions in these 2 years, with dry antecedent conditions in 2013 and wet antecedent conditions in 2014. It is well understood (Gray and Landine, 1988; Ireson et al., 2013) that the infiltration capacity of frozen soils depends strongly on the antecedent soil moisture. When wetter soils freeze, ice-filled pores develop, giving the soil a relatively low infiltration capacity. Drier soils (or more specifically, soils where the largest significant pores, which may be macropores, remain air-filled) can maintain a high infiltration capacity when frozen and the snowmelt infiltration can be significant, whilst runoff may be negligible, as in 2013.
Comparison of net precipitation (
Figure 9 shows the observed water budget for the growing period in 2013 and
2014. There is a large, systematic bias in the raw net precipitation, which
is caused by the energy balance closure correction for the eddy flux
measurement of evaporation. This clearly highlights the importance of making
this correction, whereas the net precipitation was actually positive prior to
adjusting for the lack of energy balance closure. In both years, we see
Groundwater rise along the slope during the early growing period in 2014.
While we cannot directly measure soil drainage, we have measured the water
table response, 3–5 m belowground, which gives some qualitative indication
of the timing and relative amount of soil drainage. In 2013, the water table
in piezometer 1 (P1) rose steadily during the growing period, though the
amount of rise was small,
In this study we have used a suite of relatively standard instrumentation to explore the field-scale water balance. Our findings are of practical importance for those wishing to measure the field-scale water balance, to interpret water balance residuals or use such field-scale observations to calibrate and/or validate models. Due to the local climate, the year is split into three periods, each summarized in the following paragraphs.
During the winter, i.e. the snow accumulation period, we were unable to close the water balance because we did not directly measure the fluxes of blowing snow or upward soil moisture redistribution, both of which are shown to be significant. The results of this study emphasize three practical points that should be considered before using similar data to constrain or validate hydrological models: (1) it is critical that solid precipitation records should be adjusted to remove bias due to wind-induced undercatch; (2) a well-timed snow survey to reveal the peak SWE in the snowpack before melt can capture the pre-melt spatial variability, can help negate the requirement to capture blowing snow and sublimation, and can minimize uncertainties in the measured solid phase precipitation; and (3) measuring soil moisture prior to melt, if possible, can be extremely valuable to partition soil moisture increases due to over-winter upward redistribution, from increases due to infiltrating snowmelt.
The snowmelt period in the Canadian prairies, as illustrated by this field study, strongly dominates the subsequent hydrological processes. A fundamental challenge is to predict how the melting snowpack will be partitioned between runoff and infiltration, which is a strong determinant of flood risk and soil moisture availability. Our observations demonstrate nicely how SWE alone is a poor predictor of runoff, and are consistent with past studies that have highlighted the importance of antecedent soil moisture in generating runoff.
From a water balance perspective, the growing season was the least
problematic in this study. Here, the important question for agricultural
production is how much water is available for use by plants. A simple
vertical water balance (rainfall minus evaporation) seems to adequately
explain the changes in moisture. However, a significant admonition here is
that the errors in our water balance were substantially decreased by forcing
energy balance closure, which caused a sizeable increase (35–39 %) to the
evaporation amount. This approach is not universally accepted, but in this
instance it seems to be warranted. There were likely small amounts of
drainage in both years (more in 2014 due to large rainfall events), but even
neglecting these does not result in a large error in the water balance, which
is to say they are small compared with the observational errors in
All data is available upon request.
The authors declare that they have no conflict of interest.
The authors thank Amber Peterson, Bruce Johnson, Dell Bayne, Brenda Toth and Erica Tetlock, who participated in field data collection, as well as Craig Smith and Daqing Yang (National Hydrology Research Centre, Environmental Canada) for providing an unpublished empirical relationship for the Geonor gauge correction. Financial support was provided by the Canada Excellence Research Chair in Water Security, University of Saskatchewan. Edited by: Ross Woods Reviewed by: James Buttle, Miles Dyck, and two anonymous referees