Landscape Structure and Climate Influences on Hydrologic Response

Abstract

Climate variability and catchment structure (topography, geology, vegetation) have a significant influence on the timing and quantity of water discharged from mountainous catchments. How these factors combine to influence runoff dynamics is poorly understood. In this study we linked differences in hydrologic response across catchments and across years to metrics of landscape structure and climate using a simple transfer function rainfall-runoff modeling approach. A transfer function represents the internal catchment properties that convert a measured input (rainfall/snowmelt) into an output (streamflow). We examined modeled mean response time, defined as the average time that it takes for a water input to leave the catchment outlet from the moment it reaches the ground surface. We combined 12 years of precipitation and streamflow data from seven catchments in the Tenderfoot Creek Experimental Forest (Little Belt Mountains, southwestern Montana) with landscape analyses to quantify the first-order controls on mean response times. Differences between responses across the seven catchments were related to the spatial variability in catchment structure (e.g., slope, flowpath lengths, tree height). Annual variability was largely a function of maximum snow water equivalent. Catchment averaged runoff ratios exhibited strong correlations with mean response time while annually averaged runoff ratios were not related to climatic metrics. These results suggest that runoff ratios in snowmelt dominated systems are mainly controlled by topography and not by climatic variability. This approach provides a simple tool for assessing differences in hydrologic response across diverse watersheds and climate conditions.

Full text

Landscape structure and climate influences on hydrologic response
Fabian Nippgen,
1
Brian L. McGlynn,
1
Lucy A. Marshall,
1
and Ryan E. Emanuel
2
Received 19 July 2011; revised 5 October 2011; accepted 30 October 2011; published 20 December 2011.
[1]Climate variability and catchment structure (topography, geology, vegetation) have a
significant influence on the timing and quantity of water discharged from mountainous
catchments. How these factors combine to influence runoff dynamics is poorly understood.
In this study we linked differences in hydrologic response across catchments and across
years to metrics of landscape structure and climate using a simple transfer function rainfall-
runoff modeling approach. A transfer function represents the internal catchment properties
that convert a measured input (rainfall/snowmelt) into an output (streamflow). We
examined modeled mean response time, defined as the average time that it takes for a water
input to leave the catchment outlet from the moment it reaches the ground surface. We
combined 12 years of precipitation and streamflow data from seven catchments in the
Tenderfoot Creek Experimental Forest (Little Belt Mountains, southwestern Montana) with
landscape analyses to quantify the first-order controls on mean response times. Differences
between responses across the seven catchments were related to the spatial variability in
catchment structure (e.g., slope, flowpath lengths, tree height). Annual variability was
largely a function of maximum snow water equivalent. Catchment averaged runoff ratios
exhibited strong correlations with mean response time while annually averaged runoff ratios
were not related to climatic metrics. These results suggest that runoff ratios in snowmelt
dominated systems are mainly controlled by topography and not by climatic variability.
This approach provides a simple tool for assessing differences in hydrologic response across
diverse watersheds and climate conditions.
Citation: Nippgen, F., B. L. McGlynn, L. A. Marshall, and R. E. Emanuel (2011), Landscape structure and climate influences on
hydrologic response, Water Resour. Res.,47, W12528, doi:10.1029/2011WR011161.
1. Introduction
[2] Catchment structure (topography, geology, vegetation
and soil patterns) has long been recognized as a first-order
control for soil moisture [Burt and Butcher, 1985; Western
et al., 1999], hydrologic response [Dunne and Black, 1970 ;
Jencso et al., 2009 ; Quinn et al., 1991] and biogeochemical
processes [Pacific et al., 2011; Riveros-Iregui and McGlynn,
2009] in forested mountain landscapes. At the same time, the
impact of climatic variability on hydrologic processes and
water resources has been intensively studied across various
temporal and spatial scales [e.g., Montgomery et al., 1997;
Nijssen et al., 2001; Niehoff et al., 2002]. However, the
extent to which the intersection of landscape structure and
climatic variability influences hydrologic response and the
timing of streamflow remains largely unknown. This raises
the question: Do climate variability and landscape character-
istics explain differences in the hydrologic responses among
catchments?
[3] A parsimonious way to assess the response of catch-
ments is through the use of transfer function models, which
often utilize only rainfall and catchment runoff. Transfer
functions are quantitative filters that describe the transla-
tion of a measured input (e.g., snowmelt/rainfall) into an
output (e.g., runoff). In hydrology, transfer function models
have been used to model solute transport through porous
media [Beven and Young, 1988; Jury, 1982; Maloszewski
and Zuber, 1982], river solute transport [Wallis et al.,
1989] and tracer residence time modeling and hydrograph
separation [Hrachowitz et al., 2009; McGuire et al., 2002;
Weiler et al., 2003]. Rainfall-runoff applications of transfer
functions date back to the unit hydrograph and its adapta-
tions [Dooge, 1959; Sherman, 1932] where an amount of
excess rainfall (i.e., effective rainfall) is convoluted with
the unit hydrograph and thus translated into catchment run-
off. Transfer function approaches usually assume linear
behavior between rainfall amount and the resulting runoff,
but they can contain nonlinear modules, as for the calcula-
tion of effective precipitation [Jakeman and Hornberger,
1993]. Transfer functions allow for qualitative and quanti-
tative analysis of the integrated processes in catchments
that translate inputs signals into output signals, subsuming
complex catchment characteristics into one parsimonious
function. Runoff transfer functions may differ among dif-
ferent catchments, and even for a single catchment the
transfer function may differ through time.
[4] In this study we use a simple transfer function rain-
fall-runoff model (modified from TRANSEP, see Weiler
et al. [2003]) to estimate mean response times. Mean
1
Department of Land Resources and Environmental Sciences, Montana
State University, Bozeman, Montana, USA
2
Department of Forestry and Environmental Resources, North Carolina
State University, Raleigh, North Carolina, USA
Copyright 2011 by the American Geophysical Union.
0043-1397/11/2011WR011161
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WATER RESOURCES RESEARCH, VOL. 47, W12528, doi:10.1029/2011WR011161, 2011

hydrologic response time is a measure of how long it takes
to discharge an amount of water equal to an effective pre-
cipitation input. Mean response time should not be con-
fused with mean residence time (or mean transit time),
terms that are often used in tracer based catchment model-
ing. Though seemingly similar, they are two very different
metrics of catchment hydrology. Mean response time as it
is used in this paper, refers to the transmission of an input
magnitude or pressure response, while mean residence or
transit time refers to the transmission of the water mole-
cules themselves and not the pressure response. A mean
residence time describes how long an individual water
input (or molecule) remains in the catchment, while mean
response time does not contain information about the age
of water.
[5] Using this simple transfer function model, we exam-
ine how catchment structural characteristics and climatic
variability affect the hydrologic response of mountain
catchments. We examined runoff and precipitation data
from seven adjacent catchments located in the mountains
of central Montana over a 12 year period in conjunction
with ten landscape metrics derived from high-resolution
lidar data.
[6] Focus on adjacent catchments reduces confounding
factors typically encountered when comparing catchments
across regions. The close proximity and similar elevation
range of the catchments also limit hydrologic process dif-
ferences and rainfall/snow variability. Differences in trans-
fer functions and the resulting mean response times are
therefore signatures that we expect to be related to distinct
catchment characteristics including structure and climate.
We address the following questions in this study: (1) What
is the role of landscape structure in determining intercatch-
ment differences in mean response time? ; (2) Can intra-
catchment (i.e., annual) variability in mean response time
be explained by climate variability?
2. Methods
2.1. Site Description
[7] The Tenderfoot Creek Experimental Forest (TCEF)
is located in the Lewis and Clark National Forest, which is
part of the Little Belt Mountains in the Northern Rocky
Mountains of central Montana (lat. 56.550N, long. 110.5200 W).
The total area of TCEF encompasses 2300 ha and includes
seven gauged catchments, Bubbling Creek (BUB), Lower
Stringer Creek (LSC), Middle Stringer Creek (MSC),
Lower Tenderfoot Creek (LTC), Spring Park Creek (SPC),
Sun Creek (SUN) and Upper Tenderfoot Creek (UTC),
with subcatchments ranging in size from 318 ha to 554 ha
(Figure 1). Tenderfoot Creek is a headwater of the Smith
River that drains into the Missouri River. In all subcatch-
ments the slope generally increases downstream with more
constrained and smaller riparian areas in a downstream
direction. Rock outcrops and steep talus slopes are most
frequent on lower portions of the catchment.
[8] The dominant tree species is lodgepole pine (Pinus
contorta), though the forest also includes subalpine fir
(Abies lasiocarpa), Engelmann spruce (Picea engelmannii)
and whitebark pine (Pinus albicaulis). Shrubs and grasses
dominate the riparian areas, which make up about 14% of
the study area. Two of the subcatchments, SPC and SUN,
were partially clearcut between 1999 and 2001 to investi-
gate the effect of different silvicultural treatments on water
yield and sediment export. Each watershed included two
different types of treatments: In one treatment the forest
was thinned and in the other treatment individual groups of
trees were left standing with clearcut corridors between
them; both treatment types removed approximately 50% of
the tree basal area with total treated area of 127 ha in
SPC (32% of the catchment area) and 162 ha in SUN
(45% of the catchment area).
[9] Soils at TCEF are loamy Typic Cryochrepts located
along hillslope positions and clayey Aquic Cryoboralfs in
riparian zones and parks [Holdorf, 1981]. Watershed soils
are 0.5–2 m deep. Average soil depths were found to be
approximately 1 m, based on the installation of >180 shal-
low groundwater wells and soil pits located on hillslopes
and in riparian areas [Jencso et al., 2009].
[10] The most dominant geologic layer is Flathead Sand-
stone. Granite gneiss underlies the sandstone and is preva-
lent toward the bottom of the watersheds. The highest
elevations of LSC and SPC are underlain by biotite horn-
blende quartz monzonite, which lies over a layer of shale
(Wolsey formation). The sandstone portions of TCEF tend
Figure 1. Tenderfoot Creek Experimental Forest with two
SNOTEL sites and seven gauged catchments. The color
coding remains the same for following figures. LTC, Lower
Tenderfoot Creek; LSC, Lower Stringer Creek; MSC, Mid-
dle Stringer Creek; SPC, Spring Park Creek; UTC, Upper
Tenderfoot Creek; SUN, Sun Creek; BUB, Bubbling
Creek.
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to have a gentler slope whereas the other formations gener-
ally coincide with steeper slopes.
[11] Climate at TCEF is predominantly continental. For
the 1961–1990 base period annual precipitation was about
880 mm [Farnes, 1995]. Approximately 70% of the precip-
itation volume falls as snow. Discharge usually peaks
between mid-April and the end of May. Stream discharge
peaks are generated by snowmelt and rain on snow events
during the spring melt period. Discharge typically reaches
its minimum in late September or October.
2.2. Landscape Analysis
[12] Topographic variables were derived from 1 m reso-
lution airborne laser swath mapping (ALSM) data. The
ALSM based digital elevation model (DEM) was
resampled to 10 m, a resolution high enough to capture the
actual topography but coarse enough not to introduce errant
behavior due to micro topographical features such as fallen
trees or individual boulders [see Jencso et al., 2009].
[13] We calculated catchment-wide means and medians
for 10 different landscape variables (Table 1). Topographic
variables were derived from the 10 m DEM, whereas tree
height (TH) was calculated by subtracting the last return
LIDAR coverage (bare earth) from the first returns (eleva-
tion of canopy) [see Emanuel et al., 2010]. Tree heights of
up to 2 m were then resampled to 0 m to avoid noise caused
by riparian vegetation and clear cut regrowth. Two sample
nonparametric Kolmogorov-Smirnov tests were performed
on pairs of watersheds to test for significant differences
between entire distributions of landscape variables, while
Kruskal-Wallis tests were performed on all seven water-
sheds to test for significant differences in the medians of
landscape variable distributions.
[14] To assess interdependency among the landscape
metrics, we also calculated a cross-correlation matrix for
Lower Tenderfoot Creek (LTC) with Pearson’s correlation
coefficients for all landscape metrics with distinct values
for each grid cell. Since TH was calculated based on the
original 1 m resolution LIDAR data, the remaining varia-
bles were resampled from 10 m resolution to 1 m resolution
in order to correlate them with the 1 m TH coverage. The
correlations are based on more than 20,000,000 grid cells
for each landscape variable.
2.3. Hydrologic Measurements
[15] Precipitation and discharge data were available for
years 1996–2002 and 2005–2009. The model simulation
period was from 1 March to the last day of February of the
following year instead of the conventional water year (e.g.,
year 1996 runs from 1 March 1996 to 28 February 1997).
This time period was selected to match the characteristic
timing of annual snowmelt and the event-based nature of
transfer function models, including a short ‘‘warm up’’ pe-
riod and a longer time following the annual event. Dis-
charge for the years 1996 through 2005 was made available
by the USDA Forest Service. Discharge for the period 1996
through 2001 was available in daily time steps. For the
years 2002 and 2005, stage was recorded every 15 min at
H-Flumes or Parshall Flumes located at the catchment out-
lets using a high-precision potentiometer (model 3540,
Bourns Inc., Riverside, CA) and later aggregated to a daily
time series. The USDA obtained missing data for individ-
ual catchments and years by regression with other catch-
ments. Data for the entire melt period was missing for the
following watersheds and years: UTC 1997, SUN 2000
and UTC 2000. Small portions (15%) of the falling limb
of the hydrograph were missing for SPC 2001, BUB 2001
and LTC 2001, small portions (10%) of the rising limb of
the hydrograph were missing for SUN 1997, MSC 1998
and LTC 1998. For the years 2006 through 2010, stage was
recorded every 30 min at the same flumes using capaci-
tance rods with 61 mm resolution (TruTrack Inc., Christ-
church, New Zealand) and later aggregated to a daily time
series. Precipitation and snowmelt were measured at two
Natural Resources Conservation Service (NRCS) SNOTEL
stations, one at Onion Park (2259 m) near the headwaters
of UTC and the other at Stringer Creek near the bottom of
the Experimental Forest next to the LSC flume (1996 m).
The calculations of liquid water input (comprising snow-
melt and rainfall) at the surface are based on four assump-
tions: (1) when both cumulative precipitation and SWE
increase, neither melt nor liquid precipitation is occurring,
Table 1. Landscape Metrics Used in the Analysis With Their Abbreviations and Definitions
Landscape Metric Abbreviation Definition
Slope () SLP Slope of a grid cell based on the greatest elevation difference with its eight
neighboring cells
Convergence (%) CON Convergence or divergence of a grid cell using the surrounding eight cells;
100% convergence means all surrounding grid cells flow into the center cell,
100% divergence means all surrounding cells face away from the center cell
[after Moore et al., 2001]
Distance from creek (m) DFC The distance from a grid cell to the stream along a flow path
Gradient to creek () GTC The gradient of a flow path
Local input (ha) LI Upslope accumulated area (UAA) of a grid cell bordering the stream [ Grabs
et al., 2010; Seibert and McGlynn, 2007]
Hillslope power () HP UAA of a grid cell multiplied by the slope of the contributing area
Riparian buffering () RP Ratio of riparian area to hillslope area [McGlynn and Seibert, 2003]
Tree height (m) TH Average pixel elevation (tree height) above ground surface including the silvi-
cultural treatment areas, calculated by subtracting the last return from the first
return LIDAR coverage
Potential solar insolation (kWh m
2
yr
1
) INS Potential annual solar insolation calculated for each grid cell [Böhner and
Antonic, 2009]
Geology GEO Different geologic strata [Reynolds and Brandt, 2006]
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(2) when SWE decreases and cumulative precipitation stays
the same, melt is occurring, (3) when cumulative precipita-
tion increases and SWE decreases, both melt and rain are
occurring and finally (4) when SWE is 0 and cumulative
precipitation increases, rain is occurring. We then sub-
tracted SWE from cumulative precipitation. This can be
expressed mathematically as
dI
dt ¼
0;dP
dt >0\dS
dt >0
dS
dt ;dP
dt ¼0\dS
dt <0
dP
dt dS
dt ;dP
dt >0\dS
dt <0
dP
dt ;dP
dt >0\S¼0
;
8
>
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
>
:
(1)
where Iis the amount of liquid water input to the ground, P
is cumulative precipitation (both liquid and solid), Sis
snow water equivalent, and tthe time step. Note that a
reduction of Sresults in the release of melt water from the
snow pack.
[16] This results in a time series of cumulative liquid
input, the numerical differentiation of which yields an input
per unit time. Precipitation and snowmelt data were aggre-
gated from 6 h time steps to a daily time series. Based on
observed differences in precipitation and SWE of up to
20% between the two SNOTEL stations, we weighted and
combined the input of the two SNOTEL sites by elevation.
We calculated a linear regression for the elevation range
between the Stringer and Onion Park SNOTEL sites and
assigned each DEM grid cell a precipitation value based on
the regression. All elevations >2259 m were assigned the
Onion Park precipitation. Since TRANSEP is a lumped
model the semidistributed precipitation was then averaged
to a single value per time step for each catchment. In addi-
tion total SWE was calculated for the Onion Park and
Stringer Creek SNOTEL sites for each of the 12 years.
Maximum precipitation and snowmelt intensities were cal-
culated with a moving average from one to 21 days.
2.4. Uncertainties Associated With the Use of Two
SNOTEL Sites
[17] Calculating response times to determine differences
between the catchments requires exact input time series for
each of the catchments. An important assumption for the
analysis is that differences in snow accumulation, the tim-
ing of melt and the magnitude of melt rates are adequately
reflected by the elevation weighting employed based on the
two SNOTEL sites. This is a strong but necessary assump-
tion due to the limitation to two precipitation measurement
sites. Multiple factors could play a role in determining
SWE characteristics across the landscape. However, we
believe that the elevation weighted input adequately
describes the snow accumulation and melt timing differen-
ces between the catchments. Smith and Marshall [2010]
quantified uncertainties for a predictive runoff model for
TCEF and found that elevation had a greater impact on
both runoff and melt than aspect. Personal observations of
the authors over the course of six winters corroborate the
assumption that elevation has a greater impact on snow
accumulation than aspect. In addition, the SNOTEL sites
are usually located on flat ground, not ‘‘favoring’’ a certain
aspect. We acknowledge that aspect could lead to slight
differences in the onset of snowmelt. However, considering
the duration of the whole melt period this initial uncertainty
is likley negligible. The general spatial variability of pre-
cipitation is, in our opinion, of less concern in contrast to
convective summer rain storm events, which can be small
in extent and therefore highly localized. Frontal snow
storms at TCEF are usually of a greater spatial extent and
easily cover the full extent of the experimental forest.
2.5. Hydrologic Model
[18] We used a simple rainfall-runoff transfer function
model, a module of the Transfer Function Hydrograph Sep-
aration Model (TRANSEP) developed by Weiler et al.
[2003]. A transfer function translates a measured input
(effective daily rainfall þsnowmelt) into an output (daily
discharge) (Figure 2).
[19] The rainfall-runoff module in TRANSEP includes a
nonlinear loss function, s(t), to first transform measured
precipitation into effective precipitation [Jakeman and
Hornberger, 1993]:
sðtÞ¼b1pðtÞþð1b1
2ÞsðttÞ;(2)
sðt¼0Þ¼b3;(3)
peff ðtÞ¼pðtÞsðtÞ;(4)
Figure 2. Flowchart representation of model implementation: (a) A measured input is transformed
into effective precipitation by the loss function; (b) convolution of a calibrated transfer function and the
effective precipitation results in (c) discharge. For our study, the parameters of the loss function and the
parameters of the transfer function were optimized in 150,000 Monte Carlo simulations.
W12528 NIPPGEN ET AL.: LANDSCAPE AND CLIMATE INFLUENCES ON HYDROLOGY W12528
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where sðtÞis the antecedent precipitation index, b1main-
tains the water balance that the total effective precipitation
equals the total runoff, b2determines the rate at which the
watershed dries out, b3sets the initial state of catchment
wetness at the beginning of the time series, peff the effec-
tive precipitation and pðtÞis the measured rainfall and
snowmelt input at time t.
[20] We applied the gamma distribution transfer function
to daily data
gðÞ¼ 1
ðÞexp 


;(5)
where gðÞis the value of the transfer function at a given
lag time between rainfall and runoff, ðÞis the gamma
function, is the shape parameter and a scale parameter.
Multiplying and yields the mean value of the gamma
distribution [Kirchner et al., 2000], which can be inter-
preted as the mean response time. Therefore mean response
time is defined as the average time that it takes for a given
amount of water input (liquid precipitation and/or snow-
melt) to leave the catchment through the outlet. The two-
parameter gamma function was selected for our analysis as
it is more flexible than an exponential function [Hrachowitz
et al., 2010] but does not require an additional splitting pa-
rameter as, for example, the two-parallel-linear-reservoir
transfer function.
[21] The parameters in equations (2) and (5) were cali-
brated with 150,000 Monte Carlo simulations. Convolution
of the transfer function (5) and the effective precipitation
(2) results in runoff:
QðtÞ¼Zt
0
gðÞpeff ðtÞd; (6)
where Q(t) is the runoff at time t.
[22] Correlations between TRANSEP calculated mean
response times and the catchment-averaged landscape and
annual climatic variables were calculated as Pearson corre-
lation coefficients. The means and medians of the land-
scape variables were tested for significant correlation with
the catchment averages of mean response times (each
catchment averaged over the 12 years of simulation). In
addition, maximum annual SWE (mm per year) and maxi-
mum input (mm per time step) were tested for correlation
with the annual averages of mean response time (each year
averaged over the seven catchments) in order to distinguish
between landscape controls on catchment hydrologic
response and the influence of climatic fluctuations on intra-
catchment variability. We also calculated the runoff ratios
for each catchment (averaged over 12 years) and each year
(averaged over seven catchments) and tested for correlation
with the corresponding mean response times.
3. Results
3.1. Catchment Hydrology
[23] Annual elevation-weighted precipitation for LTC
over the 12 years of simulation period averaged 790 mm
and was 110 mm less compared to the 1961–1990 base pe-
riod. The highest amount of precipitation and melt water
entered the catchments in 1997 with an average of 960 mm
among all catchments; 2001 had the least amount of input
with an average of only 621 mm (Figure 3a). The timing
and intensity of inputs varied from year to year but the av-
erage range among catchments was only 17 mm per year
(BUB 788 mm, UTC 805 mm). The interannual variability
in precipitation was much greater and hence more impor-
tant than the intercatchment variability of the precipitation
and melt inputs among the seven catchments.
[24] Runoff peaks varied strongly from year to year,
with up to 23 days between the annual maximum peaks and
peak magnitudes ranging from 4.2 to 15.1 mm d
1
at LTC.
Single peaks were the exception, and multiple peaks gener-
ally occurred between mid-April and late May (Figure 3b).
3.2. Catchment Transfer Functions
[25] Model results indicate strong differences in transfer
functions (Figure 4a). The greatest differences in catchment
response occurred over the first 10 to 15 day portion of the
transfer function (Figure 4b), with fractions of the input
leaving the catchments (response fraction) within the first
24 h ranging from 10.3% (LTC) to 4.4% (SPC) with an av-
erage of 7.6% over all seven catchments. Response frac-
tions for all catchments declined after the first day and
averaged 3.6% on the 10th day after an input and ranged
from 4.3% in BUB to 3.0% in SPC. Sixty days after the
input event, average runoff contribution decreased to 0.1%
of the original input with variations among catchments
from 0.05% for LTC to 0.25% for SPC (Figure 4c). After
132 days, nearly all inputs left the catchments with runoff
comprising less than 0.01% per day of original input. On
average, a single precipitation or snowmelt input sustained
runoff in the streams for about 132 days. The shortest com-
plete transfer function was LSC (96 days), while LTC and
SUN both maintained runoff for 153 days. Catchments
with greater early response proportions do not necessarily
maintain higher response through the season. For example
SPC relatively low early response fractions but greater
response than SUN by day 6 and greater than the other
catchments by day 14. Whereas the daily SUN water con-
tributions after 14 days exceed those of the other catch-
ments, it still lags behind in total amount of water that has
Figure 3. (a) Accumulated input (rainfall and snow melt)
and (b) variations in discharge from 1996 to 2009. Year
with max SWE (1997) denoted by black, bold line, year
with minimum SWE (2001) denoted by black, dashed line.
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left the outlet in the remaining catchments and remains lower
for the later parts of the transfer function. The cumulative
transfer functions (Figure 4d) show that on average 20.6% of
an input has left the catchments as streamflow after only
3 days, with individual catchments ranging from 12.8%
(SPC) to 25.7% (LTC). After 9 days an average of 50% of
the effective precipitation has left the catchments, with a
maximumof59.9%forLSCandaminimumof37%for
SPC. After 35 days an average of 90% of the input has left
the catchments, ranging from 96.1% in LSC to 82.9% in
SUN. After 85 days 99% of the original input has left the
catchments.
[26] Averaged over the 12 years of simulation, mean
response time for the seven catchments ranged from 9.56 days
for LSC to 18.67 days for SPC, with the average of all catch-
ments being 13.72 days (Table 2). Average Nash-Sutcliffe effi-
ciencies across catchments ranged from 0.80 to 0.90.
3.3. Annual Transfer Functions
[27] The averaged transfer functions for each year of the
12 year simulation period (averaged over seven catchments
for each year) exhibit strong differences (Figure 5a for
averaged transfer functions and Figure 5b for the averaged
cumulative transfer functions). The input was greatest in
1997 and smallest in 2001 (highlighted in Figure 5 as solid
black line and dashed black line, respectively). The mean
response times for each year averaged over the seven catch-
ments ranged from 7.16 days in 2006 to 24.95 days in 2001
(Table 3). Average Nash-Sutcliffe efficiencies across years
ranged from 0.72 to 0.92.
3.4. Landscape Analysis
[28] The means and medians for slope (SLP), distance
from creek (DFC), gradient to creek (GTC) and hillslope
power (HP) for all seven catchments indicate an identical
ranking for the catchments (i.e., the smallest mean corre-
sponds to the smallest median and the largest mean to the
largest median (Table 4)). Means and medians for conver-
gence (CON) differ in sign, denoting slight convergence in
the median but small divergence in the mean. The strongest
departure between mean and median was evident for local
input (LI), with the mean exceeding the median by up to an
order of magnitude. Maps for 8 of the 10 topographic pa-
rameters are shown in Figure 6.
[29] Both the Kolmogorov-Smirnov and the Kruskall-
Wallis tests resulted in pvalues << 0:01 and highlight the
significant difference for all the landscape metrics between
the catchments.
[30] The strongest cross-correlations between the land-
scape metrics for LTC are correlations between SLP and
Figure 4. (a) Transfer functions for each catchment averaged over 12 simulated years ; the yaxis
denotes the fraction of the input that left the watershed at a certain day; (b) short term behavior of the
transfer functions (first 15 days); (c) long term (base flow) behavior of the transfer functions (days 30
through 70). Note the order of magnitude difference on the yaxis as compared to the remaining panels ;
(d) cumulative distribution transfer functions for each catchment averaged over the 12 year simulation
period; the yaxis denotes the fraction of an input that left the watershed by a certain time (xaxis) ; the
steeper the curve at short times, the faster the precipitation to runoff response ; an elevated curve later on
indicates higher base flow contributions.
Table 2. Modeled Mean Response Times for the Seven TCEF
Catchments, Averaged Over the 12 Simulated Years
a
BUB LSC LTC MSC SPC SUN UTC
Days 13.23 9.56 11.00 10.72 18.67 18.27 14.56
a
Response times are in days.
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GTC (rp¼0:64), INS and SLP (rp¼0:58), GTC and
DFC (rp¼0:43) and SLP and DFC (rp¼0:30). The
metric with the weakest correlations was tree height (TH)
with no correlation stronger than rp¼60:08. The cross-
correlation matrix is shown in Figure 7.
3.5. Mean Response Time Correlations With
Topographic Parameters
[31] There were no significant correlations between the
landscape variables and modeled mean catchment response
times, with the exception of mean convergence with
rp¼0:94 (Table 5). However, when the two catchments
subjected to silvicultural harvesting (SUN and SPC) were
omitted from the correlation, several significant relation-
ships emerged. We excluded SUN and SPC from the corre-
lation analysis because the silvicultural treatments and
harvesting of more than 30% of the catchment areas have
wide-ranging effects on hydrological processes [Bosch and
Hewlett, 1982; Stednick, 1996]. We focus our analysis of
landscape variables on the five remaining catchments and
discuss the behavior of SUN and SPC in detail in the
section 3.6.
[32] The correlations for both the mean and median for
the majority of the landscape parameters were equally
strong (Table 5). However, both LI and RB showed strong
differences in mean and median in the correlations with
mean response time, with the medians showing the stronger/
significant correlations. The distributions for both LI and RB
are highly positively skewed. We thus focus on the medians
because they are more representative of the distributions of
LI and RB than the arithmetic mean, which is more suscepti-
ble to extreme outliers and skewness.
Figure 5. (a) Transfer functions and (b) cumulative dis-
tribution transfer functions averaged over all seven catch-
ments for each of the 12 years simulated; the black solid
lines denote the year with highest SWE (1997), the black
dotted lines denote the year with lowest SWE (2001).
Table 3. Modeled Mean Response Times for Each Individual Year, Averaged Over the Seven Catchments
a
1996 1997 1998 1999 2000 2001 2002 2005 2006 2007 2008 2009
Days 12.66 9.76 24.73 13.22 13.81 24.95 17.44 11.95 7.16 10.44 10.13 8.34
a
Response times are in days.
Table 4. Topographic Parameters for Each Catchment
a
BUB LSC LTC MSC SPC SUN UTC
SLP ()
Mean 6.5 9.5 8.0 8.6 9.5 6.5 5.4
Median 5.3 8.3 6.3 8.1 8.6 5.1 4.0
CON (%)
Mean 0.020 0.016 0.014 0.013 0.029 0.032 0.026
Median 0.344 0.601 0.511 0.550 0.712 0.256 0.231
DFC (m)
Mean 575 452 545 491 440 691 714
Median 515 396 466 439 394 642 614
GTC ()
Mean 0.135 0.168 0.142 0.140 0.153 0.104 0.088
Median 0.104 0.149 0.119 0.140 0.145 0.094 0.072
LI (m
2
)
Mean 6511 7280 7343 8480 6645 10,546 10,058
Median 3345 2357 2403 2367 1695 3326 3510
HP ()
Mean 517 595 547 594 552 563 450
Median 215 313 248 310 238 221 191
RB ()
Mean 0.69 0.045 0.465 0.053 0.115 0.044 0.043
Median 0.022 0.028 0.028 0.031 0.043 0.024 0.024
TH (m)
Mean 3.65 3.01 3.03 3.10 2.51 2.41 3.83
INS (kWh yr
1
)
Mean 3392 3428 3418 3442 3463 3401 3427
Median 3419 3461 3443 3461 3487 3430 3450
GEO (% Catchment Area)
Sandstone 92.9 56.2 70.3 54.7 31.2 91.4 97.6
Wolsey shale 0 19 9.8 19.9 26.7 0 2.2
Monzonite 0 15.3 10.8 23.8 40.4 0 0
a
Means and medians with percent of catchment area for geology. The
median for TH was 0 and is not shown here.
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[33] The landscape variables plotted versus the mean
response times of the different catchments indicate strong
correlations for multiple landscape metrics (Figures 8
and 9). Although excluded from the correlation analysis,
SPC and SUN are displayed in Figure 8 for completeness.
3.6. Mean Response Time Correlations With Climatic
Variables
[34] Maximum elevation weighted SWE for LTC ranged
from 282 mm in 2001 to 467 mm in 1997 (Table 6). The
correlation with the annually averaged mean response times
was significant (rp¼0:82); the greater the snowpack was
during a given year, the faster the mean response time aver-
aged among all seven catchments (Figure 10). From the
input intensities for temporal windows ranging from 1 to 21
days, the period with the greatest intensity over a 13 day
moving window exhibited the strongest and most significant
correlation with mean annual response time (rp¼0:76).
Maximum input intensities over 13 days ranged from 16.3
mm d
1
in 2001 and 1998 to 23.1 mm d
1
in 1997, result-
ing in 211.9 mm in 13 days in 2001 and 1998 to 300.3 mm
in 1997.
3.7. Mean Response Time Correlations With Runoff
Ratios
[35] There was a strong, significant correlation between
mean response time and the runoff ratio for each catchment
(Figure 11a) with rp<0:96 for both the modeled and
measured runoff ratios, omitting SUN and SPC. Larger run-
off ratios were generally associated with shorter mean
response times. However, with SUN and SPC included the
correlation decreased to rp¼0:74 for observed runoff
ratios and rp¼0:79 for simulated runoff ratios. In con-
trast, there was no significant correlation for averaged an-
nual response times and annual runoff ratios (rp¼0:41 for
the observed runoff ratios and rp¼0:42 for the simulated
runoff ratios) (Figure 11b).
4. Discussion
[36] The influence of topographic structure, geology,
vegetation distribution and climate on hydrologic response
is of intense interest. However, the independent and com-
bined influences of climatic variability and landscape char-
acteristics on stream response remain poorly understood.
Figure 6. Map representation of topographic parameters for seven TCEF catchments, including
(a) slope, (b) convergence, (c) distance from creek, (d) gradient to creek (e) local input, (f) hillslope
power, (g) insolation, and (h) geologic strata.
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We calculated mean response times, the average time it
takes for a liquid water input from the moment it hits the
ground surface to leave the catchment through the outlet,
for both catchment averages and annual averages for seven
catchments and 12 years. We analyzed the seven TCEF
subcatchments for a total of nine landscape structure met-
rics that can all be derived from airborne LIDAR data,
including tree height distributions and potential solar inso-
lation. We also calculated fractions of geologic strata types
for each catchment. In addition to stationary topographic
metrics we analyzed nonstationary climatic metrics, derived
from two NRCS SNOTEL sites within TCEF. These data
allowed us to independently examine the influence of both
topography and climate on modeled mean response time.
The following discussion focuses on the five more pristine
catchments BUB, LSC, LTC, MSC, and UTC. The two
catchments, which were subjected to silvicultural treatments,
SUN and SPC, will be discussed separately.
4.1. What Are the Interdependencies of the Selected
Landscape Metrics?
[37] Comparing the effect of different landscape metrics
on hydrologic response raises the question about redundan-
cies in the chosen metrics, i.e., whether two seemingly dif-
ferent metrics are effectively expressing the same
phenomenon due to strong cross correlation. To date, a few
studies focusing on landscape evolution have addressed
cross correlations between catchment characteristics, most
notably the effect of vegetation on landscape metrics such
as drainage density [Istanbulluoglu and Bras, 2005] and
the effect of drainage networks structure on vegetation dis-
tribution and plant water stress [Caylor et al., 2004]. To
our knowledge no studies have calculated grid cell based
correlations of LIDAR derived topographic metrics. We
investigated metric interdependencies by calculating cross
correlation between metrics for which values existed for
each cell.
[38] The correlation matrix calculated for LTC shows no
correlations stronger than rp¼60:64 and only four of the
21 correlations are stronger than rp¼60:30 (Figure 6).
However, some redundancy in the chosen landscape met-
rics is apparent with the most obvious being SLP (the slope
angle of an individual cell based on the surrounding eight
cells) and GTC (the gradient integrated over the flowpath
from a particular cell to the stream). Based on these defini-
tions SLP and GTC are not necessarily correlated with each
other (e.g., a low angle cell sits on top of a steep flowpath).
However, Figure 6 indicates that the steepest local slopes
of LTC correspond with the steepest gradients. This also
explains the negative correlations between DFC-GTC and
DFC-SLP: in general slope and gradients at TCEF increase
toward the outlet of each catchment and are therefore corre-
lated with DFC.
[39] The negative correlation between SLP and INS is a
result of how slope and insolation interact. Insolation is a
function of aspect and slope. In general south facing slopes
have a higher insolation than north facing slopes. However,
on south facing hillslopes a steeper slope increases solar
insolation, whereas a steeper slope on north facing areas
leads to a decrease in insolation.
[40]Florinsky and Kuryakova [1996] reported correlations
between vegetation type and topographic metrics, especially
those affecting solar insolation. However, no correlations
between TH and landscape metrics were observed at TCEF.
[41] Due to the lack of strong cross correlations between
the landscape variables, we can assume that potential sig-
nificant correlations between landscape variables and mean
response times are the result of individual but interacting
Figure 7. Cross-correlation matrix (Pearson’s correlation
coefficient) between seven landscape metrics. Correlations
were calculated on a grid cell-to-grid cell basis using each
1 m grid cell across coverage. Blue colors indicate positive
correlations, red colors indicate negative correlations. The
gray diagonal is the correlation of a landscape metric with
itself.
Table 5. Correlations Between the Modeled Mean Response
Time and the Topographic Parameters for Catchment Averages
over 7 and 5 Catchments Without SPC and SUN
a
All Catchments (n¼7) W/o SUN and SPC (n¼5)
SLP Mean Median Mean Median
r
p
0.25 0.23 1.00
b,c
0.95
b,c
CON Mean Median Mean Median
r
p
0.94 0.20 0.87 1.00
b,c
DFC Mean Median Mean Median
r
p
0.34 0.42 0.95
b
0.98
b,c
GTC Mean Median Mean Median
r
p
0.43 0.32 0.91
b
0.97
b,c
LI Mean Median Mean Median
r
p
0.30 0.10 0.46 0.96
b,c
HP Mean Median Mean Median
r
p
0.28 0.64 0.95
b
0.93
b
RB Mean Median Mean Median
r
p
0.46 0.27 0.07 0.81
TH Mean Mean
r
p
0.45 0.97
b,c
INS Mean Median Mean Median
r
p
0.11 0.10 0.39 0.53
GEO Shale Sandst. Monz. Shale Sandst. Monz.
r
p
0.13 0.04 0.11 0.89
b
0.95
b
0.83
a
Significance level for a two-tailed test with n¼7 and ¼0:01 equals
rp¼60:87, and with ¼0:05 the significance level equals rp¼60:75.
b
Significance level for a two-tailed test with n¼5 and ¼0:05 equals
rP¼60:88.
c
Significance level for a two-tailed test with n¼5 and ¼0:01 equals
rP¼60:96.
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effects, rather than a manifestation of one effect (one vari-
able) in several variables.
4.2. How Does Topography Explain the Observed
Differences in Average Catchment Response Times?
[42] For a majority of the landscape metrics considered
in this study, we found strong linear relationships with
mean response time (Figures 8 and 9). SLP and GTC both
exhibited a strong negative correlation with mean response
time. The similar strength of the correlations is a result of
the strong correlation of the two metrics with each other.
These results confirm the greater the slope or the gradient
to creek the faster the mean response time.
[43] Conversely, greater DFC increases the mean
response time, which is consistent with geomorphic instan-
taneous unit hydrograph theory [Gupta et al., 1980 ; Rodri-
guez-Iturbe and Valdes, 1979]. Simply stated, the greater
Figure 8. Regressions between mean response time (days) and topographic parameters. SUN and SPC
have been excluded from the regressions but are shown for completeness; each symbol represents the
averaged mean response time for one catchment over 12 years.
Figure 9. Regressions between the mean response time
for the five catchments (BUB, LSC, LTC, MSC, and UTC)
and the percentage of each geologic strata present in each
catchment.
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the distances that water or input signals must travel, the
longer it takes them to reach the catchment outlet. The pos-
itive relationship between DFC and mean response time is
likely amplified by the slight negative correlation between
SLP/GTC and DFC: short flow paths tend to have steeper
gradients while longer flow paths are often associated with
gentler gradients (Figures 6 and 7).
[44] The inverse relationship found for LI (positive corre-
lation with response time) and CON (negative correlation
with response time) seems counterintuitive at first since both
metrics are a measure of flow accumulation. The results for
local input are consistent with the findings of Jencso et al.
[2009] who found a strong relationship between LI size and
the duration of a hydrologic hillslope-riparian area-stream
hydrologic connection. Jencso et al. [2009, 2010] reported
that a larger LI does not necessarily mean that more water
gets transported from the hillslope to the streams at any
given time but rather that larger LI hillslopes contribute for a
longer period of time than smaller size LIs. It is the longev-
ity of the hillslope-stream connection that is mediated by LI
and not how fast water is being delivered to the stream. Note
that LI is the UAA size for grid cells bordering the stream,
whereas CON was calculated for every grid cell in each
catchment, resulting in a metric that is more suitable to
assess overall catchment concavity than LI, which describes
overall hillslope size and connectivity potential for near-
stream cells. Comparing CON and LI we found a significant
negative correlation between the means and medians of the
two metrics at the catchment scale, with rp¼0:98: the
larger the mean and median local input to the stream, the
smaller the overall catchment convergence. A higher catch-
ment convergence means that all catchment grid cells have
more neighboring cells draining into them than catchments
with a smaller convergence. CON can hence be considered
a measure of catchment complexity or dissection, with less
convergent catchments being less dissected, resulting in
larger hillslope UAAs while more convergent catchments
Table 6. Maximum SWE Elevation Weighted for LTC and Maxi-
mum Calculated Input Intensities Over 13 Consecutive Days and
rpWith the Averaged Response Time for Each Year
a
Year
Max SWE Elevation
Weighted (mm)
Max Input Intensity
Over 13 Days (mm d
1
)
1996 387 21.0
1997 467 23.1
1998 306 16.3
1999 319 19.2
2000 364 16.9
2001 282 16.3
2002 337 17.6
2005 375 17.2
2006 446 22.8
2007 352 20.5
2008 395 18.2
2009 408 21.5
Correlations with
mean response time
0.82 0.76
a
Significance level for n¼12 and ¼0:01 equals rp¼60:71.
Figure 10. Relationship between maximum annual SWE
(mm) and mean response time (days) averaged over all
seven catchments for each of the 12 years of simulation.
The gray dashed line is a power law regression (R2 ¼
0.75). The higher the maximum annual SWE, the faster the
response time. The blue symbol denotes the year with low-
est SWE (2001), the red symbol denotes the year with high-
est SWE (1997).
Figure 11. (a) Mean response time for catchment averages
plotted against catchment runoff ratios (each point represents
an average over 12 years). Omitting SUN and SPC there is a
strong negative correlation, with smaller runoff ratios associ-
ated to longer mean response times ; (b) Mean response time
for annual averages plotted against annual averaged runoff
ratios (each point represents an average of 7 catchments for
each year) with no significant correlation. The blue symbol
denotes the year with lowest SWE (2001), the red symbol
denotes the year with highest SWE (1997).
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exhibit a higher degree of topographic dissection. For
instance, the most convergent catchments at TCEF are also
the steepest catchments. Topographic dissection increases at
TCEF in a downstream direction. UTC, at the headwaters of
TCEF, consists of large, relatively planar hillslopes with
long flowpath lengths and can be considered relatively sim-
ple in terms of topographic dissection. However, in a down-
stream direction, slopes increase, the stream becomes more
incised, the riparian areas narrow, flowpath lengths become
shorter, local input decreases, and convergence increases
leading to greater landscape dissection.
[45] Another metric describing the potential for water
accumulation and the associated potential energy is hill-
slope power (HP). In contrast to CON, HP is highly related
to LI. In addition to upslope area, HP incorporates slope
and therefore the energy gradient associated with this
water. Therefore, HP can be related to the potential rate of
water movement. This may only apply to saturated soils
and not necessarily to unsaturated soils, where additional
forces (e.g., matric potential) influence water movement.
However, soils at TCEF are saturated or near saturation for
periods during snowmelt [Jencso et al., 2009]. The correla-
tion between HP and mean response time is negative, a
higher HP was correlated with a lower mean response time
(similar to SLP and GTC).
[46] The final topographic metric, riparian buffering (RB),
is also related to LI in that it is the dimensionless ratio of ri-
parian area and the corresponding hillslope area that drains
into it (riparian area/hillslope area). Its correlation with
mean response time is negative (rp¼0:81 for the median)
but below the significance threshold, the correlation for the
mean is even less strong (rp¼0:07, Table 5). A negative
correlation indicates that higher riparian buffering potentials
are associated with shorter mean response times, a result that
seems counterintuitive. One would expect a greater potential
for volumetric buffering as indicated by McGlynn and
McDonnell [2003], McGlynn and Seibert [2003] and Jencso
et al. [2010] with more riparian area in relation to hillslope
area. In fact, Jencso et al. [2010] observed a logarithmic
relationship between riparian buffering potential and the
turnover half-life time for the groundwater stored in riparian
areas (the time it takes to replace 50% of riparian water with
water from an adjacent hillslope). Based on the findings of
Jencso et al. [2010], a positive correlation between RB and
mean response time would have been expected. However,
RB is a good example why it is important to differentiate
between mean residence time (replacement of riparian water
by hillslope water) and mean response time (displacement of
water in the saturated riparian zone by hillslope water).
4.3. Do Vegetation and Energy Availability Have an
Impact on Mean Response Times?
[47] Vegetation affects watershed hydrology in many
ways and at all times during the hydrologic year. Two im-
portant hydrologic processes affected by vegetation in
snow-dominated catchments during the winter include snow
interception and subsequent sublimation from the canopy
[Hedstrom and Pomeroy, 1998; Pomeroy et al., 2002; Pom-
eroy et al., 1998]. During the growing season, vegetation
acts as loss mechanism for soil moisture because of evapo-
transpiration [Rodriguez-Iturbe et al., 1999]. However, for
snow-dominated systems, interception and sublimation are
likely the dominant processes that affect mean response
time at the annual scale.
[48] Our results indicate that tree height (TH) and mean
response time are positively correlated (rp¼0:97), with a
greater TH leading to a longer mean response time (Table 5
and Figure 8). TH was calculated by incorporating all grid
cells, including clear cuts, thins, parks, and cells absent of
trees in forests, which reduced the estimated catchment av-
erage tree height considerably but is a better surrogate for
‘‘tree-biomass’’ for a given catchment in a lodgepole pine
dominated landscape. Mean response time can be affected
by vegetation and TH in various ways, most notably in the
accumulation and melt of snow in snow dominated sys-
tems. Forests often accumulate less snow [Woods et al.,
2006], but they hold the snow longer than clearcut areas
and parks [Winkler et al., 2005]. This behavior is attributed
to attenuated energy input to the subcanopy snowpack and
enhanced canopy interception and sublimation. In hydro-
logic models attenuation of shortwave radiation by forest
canopies is often calculated by incorporating LAI [e.g.,
Wigmosta et al., 1994], with a greater LAI leading to less
shortwave radiation penetrating the canopy, resulting in
less energy to melt the subcanopy snowpack. LAI estimates
in coniferous forests are often made through allometric
relationships with tree height. Keane et al. [2005] estab-
lished tree height-LAI relationships for TCEF for ground
based LAI estimation methods and Jensen et al. [2008]
found a linear relationship between LIDAR derived tree
height and LAI for coniferous forests (among others con-
sisting of pine and spruce species) in northern Idaho. Based
on the relationship found by Jensen et al. [2008] and Keane
et al. [2005], TH corresponds to a greater LAI and there-
fore increased potential to reduce incoming shortwave radi-
ation received by the snowpack in forested areas, thus
slowing down snowmelt and mean response time. The
water input to the system as measured by the SNOTEL
sites is potentially biased in that the SNOTEL stations are
located in open areas and typically melt out earlier than for-
ested sites due to differences in snowpack energy balances
[Woods et al., 2006]. Personal observations by the authors
at TCEF during the last eight years corroborate that the for-
ests hold snow longer than open areas. Therefore, the TH-
mean response time relationship could be influenced by
delayed melt in forests as compared to the SNOTEL sites.
[49] In addition to the potential effect of TH on snow-
pack energy balances, topographically mediated potential
solar insolation also varies across the 7 catchments. Poten-
tial solar insolation (INS) is a function of aspect, slope, and
geographic latitude and describes the incoming shortwave
radiation for each grid cell accumulated over one year. In
snow dominated catchments increased solar radiation can
decrease snow accumulation by enhancing both sublima-
tion of the snowpack and vegetation intercepted snowfall
[Jost et al., 2007; Lopez-Moreno and Stahli, 2008]. There-
fore, INS can influence both the magnitude and timing of
snowmelt. In general north facing slopes receive less incom-
ing radiation, accumulate more snow, and release this water
later in the melt period [Murray and Buttle, 2003]. This
leads to a dampened yet sustained input through time, which
increases mean response time. South facing catchments
would exhibit the opposite behavior. Most catchments, how-
ever, contain a wide range of aspect and slope. Therefore,
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mixtures of catchment landscape attributes can effectively
work in opposition thereby muting the effect of INS. As
expected, the correlations between mean response time and
mean and median INS are negative (higher INS leads to
shorter mean response times) but with rp¼0:39 for the
mean and rp¼0:53 for the median, respectively, they are
both below the 95% significance threshold. INS is the poten-
tial solar insolation on the ground surface and does not
incorporate any attenuating factors, i.e., vegetation. The
effective insolation that reaches the ground surface may dif-
fer significantly from the calculated potential solar insolation
because of interception by the vegetation. The strong corre-
lation between TH and mean response time highlights the
importance of vegetation on hydrologic response and also
explains why solar radiation input to the ground surface as
single metric might be insufficient for prediction of hydro-
logic response.
4.4. What is the Role of Geology on Hydrologic
Response?
[50] Bedrock geology can influence water chemistry
[e.g., Gardner and McGlynn, 2009; Newton et al., 1987;
Gardner et al., 2011] and the routing of water downslope
and downstream [e.g., Freer et al., 2002; Onda et al.,
2001].
[51] We evaluated the influence of geologic strata at
TCEF to quantify the potential effect of different types of
bedrock on mean response time. Strong, significant correla-
tions between fraction of surficial bedrock geology and
mean response time were observed for three of the four geo-
logic layers at TCEF, with sandstone exhibiting the highest
correlation, rp¼0:95 (Table 5 and Figure 9). In contrast to
the sandstone layer, correlations between mean response
times and the shale and monzonite layers were negative.
While sandstone is a sedimentary rock with relatively high
hydraulic conductivities, both shale and monzonite (an igne-
ous intrusive rock), have hydraulic conductivities several
orders of magnitude lower than sandstone in unfractured
conditions [Freeze and Cherry, 1979], likely leading to less
recharge into deeper groundwater reservoirs. Potentially ele-
vated seepage occurring into the sandstone relative to the
shale and monzonite may reenter the shallow soil system
and/or stream network further downslope. Because of longer
travel times in the bedrock layer than in the (saturated) soil
system, base flow contributions in catchments with greater
sandstone fractions may be higher and mean response times
longer. Jencso and McGlynn, [2011] found that the intersec-
tion of hillslopes greater than 0.5 ha with the sandstone
layer extended flow duration curves for TCEF catchments.
This is consistent with our findings that the sandstone frac-
tion in a catchment is positively correlated with mean
response time.
4.5. Can Intracatchment (i.e., Interannual) Variability
be Explained by Climate Forcing?
[52] The transfer functions for both catchment averages
over time (Figure 4) and annual averages of mean response
time across catchments (Figure 5) exhibited considerable
variability. While catchment averages of mean response
time can be explained by topographic characteristics of
each catchment (Figures 8 and 9), the question remains :
what causes the differences observed in response time
between the individual years (Figure 5)? Higher rainfall
intensities generally lead to faster hydrologic response
[Montgomery et al., 1997], and antecedent moisture is often
a key factor for low-intensity events [Castillo et al., 2003 ;
Niehoff et al., 2002]. At TCEF, higher input intensities that
are typically a combination of snowmelt and rainfall, lead
to faster annual mean response times (Table 6). We eval-
uated input intensities for temporal windows ranging from
one to 21 days. We selected the period with the greatest
intensity for each temporal window and correlated them
with catchment mean response times. For these input inten-
sities, the correlation was strongest for the 13 day window
(rp¼0:76, Table 6). However, somewhat surprisingly the
simple metric of maximum annual snow water equivalent
(SWE) exhibited a slightly stronger correlation (rp¼0:82,
Table 6). A power law regression between maximum annual
SWE and mean response time indicated that that 75% of the
variability in annual mean response time could be explained
by maximum annual SWE alone (Figure 10).
[53] Since mean response time was calculated for each
input signal it is likely that the size of the snowpack affects
response times by shifting soils from unsaturated to satu-
rated, increasing hydraulic conductivity, increasing the sat-
urated thickness (higher water tables), and increasing
hydraulic gradients toward the stream. Greater SWE could
also lead to a greater number of consecutive melt inputs to
the ground (i.e., days with melt), increasing soil moisture
for the next input and maintaining higher perched water
tables above the bedrock-soil interface. This would suggest
that both the input intensities and the duration of melt
events have an effect on the rate of hydrologic response in
snow-dominated systems.
4.6. What is the Relationship Between Mean Response
Times and Runoff Ratios in the Context of Topographic
and Climatic Variability?
[54] In our study, runoff ratios exhibited different behav-
ior when they were calculated for catchment averages or
annual averages. There was a strong negative relationship
between runoff ratios and mean response time for catch-
ment averages (Figure 11a). However, there was no visible
pattern for annual runoff ratios versus annual mean
response time (Figure 11b), suggesting that runoff ratios in
a snowmelt dominated system like TCEF are determined
by topography and not by climatic variability. This result is
corroborated by nonsignificant relationships between maxi-
mum annual SWE and annual runoff ratios (Figure 12a) as
well as annual precipitation amounts and annual runoff
ratios (Figure 12b). This means that in general steeper
catchments will have a higher runoff ratio compared to flat-
ter watersheds but the ratio is independent of the amount of
snowmelt. These results are counter to previous research,
which indicated runoff ratios largely depended on local cli-
mate, i.e., the availability of energy and precipitation
[Arora, 2002; Budyko, 1974; Donohue et al., 2007; Hew-
lett and Hibbert, 1967; Pike, 1964 ; Zhang et al., 2001].
[55] We can assume that independent of the actual input
magnitudes the catchments wet up fairly quickly due to the
large melt input in even the low-precipitation years. SWE
magnitudes may therefore be secondary to topographic
influences in determining runoff ratios. However, this does
not contradict our finding that SWE impacts mean response
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times. While response time is controlled by input intensities
over longer time periods, annual runoff ratios appear to be
mostly independent of max SWE and max input intensities
due to the large magnitude of snowmelt events and the
effect of ET and other melt/precipitation characteristics.
These results suggest that even during small melt events,
the velocity of subsurface flow depends mostly on the to-
pography of each catchment, especially slope (i.e., Darcy’s
law), assuming homogenous soils with homogenous hy-
draulic conductivities across TCEF.
4.7. What Explains the Different Behavior of
SUN and SPC?
[56] We excluded both the SUN and SPC catchments ini-
tially because of the silvicultural treatments in 2001/2002
and the potential treatment impact on the hydrologic cycle.
Many studies have focused on the effect of silvicultural
treatments and disturbances on hydrologic response [Bosch
and Hewlett, 1982; Cheng, 1989 ; DeBano, 2000; Miller,
1984; Swank and Douglass, 1974] and most studies found
increased water yield and increased stormflow following
clear cutting.
[57] At TCEF, both SUN and SPC exhibited consider-
ably longer mean response times than the other catchments
and do not fit on any of the regressions shown in Figure 8.
The harvests occurred in 2001 and 2002. We compared the
mean response times of all catchments for both the pre and
post logging periods (Table 7). The mean response times of
SPC and SUN were longer than the mean response times of
the remaining catchments for both the pre and post logging
period, but more closely approached the response times of
the other catchments in the post logging period. In general,
mean response times decreased from the pre to post logging
period for all catchments, which was likely caused by
larger snowpacks in the post logging period, but the abso-
lute decline is greatest for SPC and SUN. Therefore, patch
cuts and thinned stands increased the responsiveness of the
two managed catchments, however, they remained less re-
sponsive (longer mean response times) than the other
catchments and less responsive than the landscape metric
regressions would predict.
[58] Longer mean response times in SPC and SUN sug-
gest that factors other than those derived from the digital
elevation model, vegetation, and fractional geology must
influence catchment runoff behavior in these two catch-
ments. LIDAR data capture surface topography in great
detail but are unable to detect subsurface topography. R. A.
Payn et al. (Shift from topographic to subsurface structural
controls on spatial patterns of stream baseflow during sea-
sonal recession, submitted to Water Resources Research,
2011) have shown that subsurface contributing area in
TCEF may differ from the contributing area derived from
LIDAR data during low-flow conditions. Also the fraction
of geologic strata for each catchment does not reveal infor-
mation about the dip of the layers, the thickness of the
layers, nor the location of geologic transitions relative to
runoff generation processes.
[59] SPC covers the full range of geologic variability in
TCEF with four different geologic layers. The transition
from Wolsey shale to Flathead sandstone in SPC coincides
with a noticeable break in slope (Figures 6a and 6h). The
forested and clearcut hillslopes transition into a wide, open
park (meadow). This park area is one of the wettest sites in
TCEF with water tables close to the surface even in the late
summer when most of TCEF has already dried down. R. A.
Payn et al. (submitted manuscript, 2011) analyzed spatial
patterns of stream base flow generation at TCEF and found
steady or increasing contributions relative to the overall
LTC runoff for the spring visible at the shale – sandstone
interface during the summer dry down period in 2006.
R. A. Payn et al. (submitted manuscript, 2011) suggest
extensive storage in the SPC ridge area, which would sus-
tain a higher runoff in the summer base flow period and
lead to longer mean response times. Interestingly, an equal
transition in MSC/LSC from shale to sandstone does not
produce visible springs or wet areas, suggesting differences
in the stratigraphic transition between the two catchments.
[60] On the other hand, SUN comprises mostly sand-
stone with a small fraction of granite gneiss and does not
Figure 12. (a) Maximum annual SWE versus average an-
nual runoff ratios, r
p
¼0.48 and pvalue ¼0.11. (b) Annual
precipitation versus average annual runoff ratios, r
p
and p
value ¼0.47. Both correlations are nonsignificant.
Table 7. Comparison of Mean Response Times for the Entire
Simulation Period and the Pre- and Post-Logging Periods
BUB LSC MSC LTC SPC SUN UTC Average
1996–2009 13.23 9.56 11.00 10.72 18.66 18.27 14.56 13.72
Pre-logging 15.52 10.58 14.76 13.64 23.34 22.60 15.21 16.52
Post-logging 10.93 8.55 7.23 7.81 13.99 13.94 13.92 10.91
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exhibit noticeable transitions that would favor the forma-
tion of springs. The most notable geologic feature in SUN
is a fault line (Quartzite ridge fault) that dissects SUN east
to west in approximately equal portions. Runoff generated
on the catchment portions above the fault could infiltrate
along the fault into deeper geologic layers and reenter the
system further downstream as return flow, thus increasing
hydrologic response times. The fault also runs through
BUB and UTC. However, the areas above the fault in these
two catchments are significantly less than in SUN.
[61] The tailing behavior of the transfer functions of SPC
and SUN also suggests higher base flow contributions as
compared to the remaining catchments, which may be a
combined result of sustained groundwater contributions
and reduced evapotranspiration (Figure 4c).
5. Conclusions
[62] The use of runoff transfer functions provides a sim-
ple tool for assessing the hydrologic response of catch-
ments and relating differences in response to landscape
structure and climate. Based on our correlations using mod-
eled mean response time and variables of landscape struc-
ture and climate we conclude the following.
[63] 1. Differences in mean response time among five of
the TCEF catchments were caused by differences in land-
scape structure. There were no strong cross correlations
among the TCEF landscape variables, suggesting that the
observed correlations are not just the effect of one or two
variables superimposed onto the others. However, it is in-
triguing that metrics that are seemingly independent from
each other show equally strong correlations with mean
response time. This raises questions of how independent
catchment characteristics are in fact related and form dur-
ing landscape evolution.
[64] 2. Vegetation has an effect on mean response time
most likely due to reduced snow accumulation, the shading
of the subcanopy snowpack and the attenuation of solar
radiation used to melt the snowpack.
[65] 3. The Sandstone layer at TCEF showed the strong-
est correlation with mean response time. Variable hydraulic
conductivities of the geologic strata at TCEF potentially
lead to differing recharge rates into deeper groundwater
layers, which also affected mean response time.
[66] 4. Interannual variability in mean response time was
a result of variable climatic conditions, i.e., the maximum
amount of annual snow water equivalent and differences in
melt intensities.
[67] 5. The two apparent outliers SPC and SUN suggest
controls on hydrologic response in these watersheds other
than metrics of surface topography, i.e., metrics than can
be derived from digital elevation models. Geology was
likely responsible for this unexpected behavior. However,
we were unable to ultimately answer the question of why
the two catchments show hydrologic response that does not
fall in line with the relationships established for the other
five catchments.
[68] 6. For these snow dominated systems runoff ratios
were largely a function of topography. This means that in
general steeper catchments had higher runoff ratios
compared to flatter watersheds. The runoff ratio was inde-
pendent of the amount of snowmelt.
[69] Some of the correlations shown in this study are
very strong and suggest that one single metric explains
catchment runoff behavior (e.g., SLP and CON with an
rp¼1:00). However, we emphasize that catchment het-
erogeneity is too complex to reduce the governing factors
of hydrologic response to individual landscape structural
metrics. It is rather the interaction of several metrics that
ultimately determines how a watershed responds to a pre-
cipitation input.
[70] We tested the transfer function rainfall-runoff mod-
eling framework in a snowmelt-dominated system of the
northern Rocky Mountains. Future applications of the
model and analysis approach could involve comparisons of
catchments in other places to test whether the relationships
we established at TCEF also hold for different landscapes,
climatic settings, and scales.
[71]Acknowledgments. This study was funded by NSF grants EAR-
0943640 to Marshall and McGlynn, EAR-0837937 to McGlynn, EAR-
0838193 to Emanuel through the Department of Geology at Appalachian
State University, and the Inland Northwest Research Alliance (INRA). The
authors would like to thank the U.S. Department of Agriculture, Forest
Service, Rocky Mountain Research Station for providing runoff data and
Kevin McGuire for providing his TRANSEP code.
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R. E. Emanuel, Department of Forestry and Environmental Resources,-
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L. A. Marshall, B. L. McGlynn, and F. Nippgen, Department of Land
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