PUBLICATIONS
Journal of Geophysical Research: Atmospheres
RESEARCH ARTICLE
10.1002/2013JD020597
Key Points:
• We propose a simple framework for
predicting soil temperature
• The model generates soil temperature
at high spatio-temporal resolutions
• The model is ideal for remote areas
where measurements are scarce
Correspondence to:
L. L. Liang and D. A. Riveros-Iregui,
[email protected];
[email protected]
Citation:
Liang, L. L., D. A. Riveros-Iregui, R. E.
Emanuel, and B. L. McGlynn (2014), A
simple framework to estimate distributed soil temperature from discrete air
temperature measurements in datascarce regions, J. Geophys. Res. Atmos.,
119, doi:10.1002/2013JD020597.
Received 22 JUL 2013
Accepted 17 DEC 2013
Accepted article online 20 DEC 2013
A simple framework to estimate distributed soil
temperature from discrete air temperature
measurements in data-scarce regions
L. L. Liang1,2, D. A. Riveros-Iregui1,3, R. E. Emanuel4, and B. L. McGlynn5
1
School of Natural Resources, University of Nebraska–Lincoln, Lincoln, Nebraska, USA, 2Now at Botany and Plant Sciences,
University of California, Riverside, California, USA, 3Now at Department of Geography, University of North Carolina at Chapel
Hill, Chapel Hill, North Carolina, USA, 4Department of Forestry and Environmental Resources, North Carolina State University at
Raleigh, Raleigh, North Carolina, USA, 5Nicholas School of the Environment, Duke University, Durham, North Carolina, USA
Abstract
Soil temperature is a key control on belowground chemical and biological processes. Typically,
models of soil temperature are developed and validated for large geographic regions. However, modeling
frameworks intended for higher spatial resolutions (much finer than 1 km2) are lacking across areas of complex
topography. Here we propose a simple modeling framework for predicting distributed soil temperature at high
temporal (i.e., 1 h steps) and spatial (i.e., 5 ! 5 m) resolutions in mountainous terrain, based on a few discrete air
temperature measurements. In this context, two steps were necessary to estimate the soil temperature. First, we
applied the potential temperature equation to generate the air temperature distribution from a 5 m digital
elevation model and Inverse Distance Weighting interpolation. Second, we applied a hybrid model to estimate
the distribution of soil temperature based on the generated air temperature surfaces. Our results show that this
approach simulated the spatial distribution of soil temperature well, with a root-mean-square error ranging from
~2.1 to 2.9°C. Furthermore, our approach predicted the daily and monthly variability of soil temperature well. The
proposed framework can be applied to estimate the spatial variability of soil temperature in mountainous regions
where direct observations are scarce.
1. Introduction
Temperature is an important variable affecting chemical and biological processes such as oxidation-reduction
reactions [Krause and Weis, 1991], primary productivity [Farquhar et al., 1980; Bernacchi et al., 2001], ecosystem
respiration [Luo et al., 2001; Piao et al., 2010], and microbial decomposition of organic matter [Davidson and
Janssens, 2006]. In the soil, temperature is widely regarded as a key control on nutrient cycling in terrestrial ecosystems [Canadell et al., 2007] for both aboveground and belowground processes [Raich et al., 2002; Zhou et al.,
2009; Bond-Lamberty and Thomson, 2010]. Recent years have seen an increase in approaches directed at modeling
air temperature over large geographic regions at resolutions of 1 km2 or greater [Courault and Monestiez, 1999;
Daly et al., 2002; Jolly et al., 2005; Huld and Dunlop, 2006; Lundquist et al., 2008; Wloczyk et al., 2011; Zhu et al., 2013].
Such studies have implemented interpolation algorithms for air temperature at regional to continental scales, but
their usefulness to capture and simulate the variability of air temperature at finer scales has not been assessed.
Around the world, meteorological stations record point measurements of variables such as air temperature, relative
humidity, precipitation, and/or solar radiation [Toy et al., 1978]. Many researchers use these point measurements to
estimate the variability of air temperature over large areas [Shen et al., 2001; Stahl et al., 2006] using approaches such
as Inverse Distance Weighting (IDW) [Shepard, 1968; Dodson and Marks, 1997], truncated Gaussian filters[Thornton
and Running, 1997], Kriging-based geostatistical methods [Hudson, 1994], and other mechanistic approaches [Daly
et al., 2002]. The IDW algorithm is one of the most useful methods to generate continuous air temperature surfaces
at large spatial scales (i.e., 1 km2 or greater) given its simplicity of implementation and comparable accuracy to other
interpolation methods [Dodson and Marks, 1997]. However, this and other algorithms are typically applied at large
spatial scales (i.e., 1 km2 or greater) and their potential to investigate fine-scale variability of air temperature (i.e., at
the scale of one to tens of m2) in ecological studies has not been fully explored. While air temperature measurements may be available from meteorological stations, direct soil temperature measurements, or the information
that allows estimation of the spatial variability of soil temperature, are usually scarce. This lack of information limits
the use of meteorological stations as a viable source of data for landscape-oriented studies of soil processes
LIANG ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Atmospheres
10.1002/2013JD020597
[Zheng et al., 1993]. As a result, a methodology for using available air temperature measurements to predict the
spatiotemporal dynamics of soil temperature is needed.
Modeling soil temperature can be achieved based on (1) physical approaches, which are founded on the mechanism of heat transfer in soil [Bhumralkar, 1975; Horton and Wierenga, 1983; Gao et al., 2003; Wang et al., 2010]; (2)
empirical approaches, which expand upon regression-based relationships between air and soil temperature, or
elevation and soil temperature [Zheng et al., 1993; Plauborg, 2002]; and (3) hybrid approaches, which combine
physical and empirical approaches [Kang et al., 2000]. Physical approaches typically focus on bare soil surfaces
[Shao and Horton, 1998; Gao et al., 2003, 2008; Gao, 2005] and depend strongly upon initial and boundary conditions—not always available in areas where measurements are scarce [Kang et al., 2000]. Differences in direct,
incoming solar radiation as it reaches the land surface complicate the accurate estimation of boundary conditions
[Thornton and Running, 1997; Kang et al., 2000]. Further complications include the parameterization of variables
such as soil heat diffusivity, which is influenced by soil texture and soil moisture content [Gao et al., 2003, 2008;
Gao, 2005]. At the same time, empirical approaches tend to be site specific and have limited applicability over
large regions [Kang et al., 2000]. As a result, hybrid approaches have emerged as effective solutions that combine
the strengths of both physical and empirical approaches to overcome the weaknesses of each [Kang et al., 2000;
Riveros-Iregui et al., 2011].
We propose a modeling approach for predicting distributed soil temperature in mountainous terrain and apply
it at hourly frequencies and over 5 ! 5 m grid cells. In this approach, two steps have been adopted to estimate
spatial and temporal soil temperature distributions. First, we applied the potential temperature equation,
known as the neutral stability algorithm (NSA) or Poisson’s equation [Dodson and Marks, 1997], to generate air
temperature surfaces using discrete air temperature measurements made at five weather stations. These surfaces were generated based on a 5 m digital elevation model (DEM) and Inverse Distance Weighting (IDW) interpolation. Second, we applied a hybrid model to estimate the distribution of soil temperature based on the
generated air temperature surfaces. Soil thermal properties and vegetation-driven extinction coefficients were
determined by a Monte Carlo analysis and the Nash-Sutcliffe coefficient of model efficiency [Nash and Sutcliffe,
1970]. Air temperature was validated using measured air temperature at three stations located within the site of
interest. Modeled soil temperature was validated using continuous soil temperature measurements collected at
5 cm depths in 10 locations distributed across the site. Based on this framework, we report the predicted spatial
and temporal distribution of soil temperature at 5 m resolution and 1 h time steps across a small watershed
(~22 km2) of the northern Rocky Mountains.
2. Methods
2.1. Study Area
This study was performed in Tenderfoot Creek Experimental Forest (TCEF, Figure 1), which is located in the Little
Belt Mountains of central Montana (46°55″N, 110°54″W), in the United States. The TCEF has an area of ~22 km2
and an elevation range between 1963 m and 2426 m. Mean annual temperature is 0°C [Farnes et al., 1995].
Growing season at TCEF varies from 45 to 75 days, depending on elevation. This study was performed over one
growing season, from 18 July to 7 September 2006. Air temperature was measured at an eddy covariance tower
at the TCEF site. Mean air temperature at the tower was 13.7°C over the study period (minimum air temperature
was "4°C and maximum air temperature was 30°C). The dominant landscapes in TCEF are riparian meadows
and upland forests, which are mostly covered with Calamagrostis canadensis (blue joint reed grass) and Pinus
contorta (lodgepole pine), respectively [Farnes et al., 1995]. Measured precipitation during the study period
totaled 38.1 mm across four precipitation events (12, 16, 31 August, and 2 September). Measured leaf area index
(LAI) ranged from 1.1 to 1.35 m2 m"2 in the forest and from 0.8 to 2.0 m2 m"2 in riparian areas of TCEF [RiverosIregui et al., 2011].
2.2. Distributed Air Temperature Estimation in Mountainous Terrain
It is well established that air temperature is highly heterogeneous over mountainous terrain due to the effects of
elevation, and therefore, it is difficult to estimate accurately [Willmott and Robeson, 1995; Dodson and Marks,
1997]. In addition, the rate of temperature change with elevation, or the lapse rate, varies as a function of vapor
pressure of air and can be highly variable across space and time [Barry and Chorley, 1998]. There are several
methods in the literature to address the variation of the lapse rate, including climatologically aided interpolation
(CAI) [Willmott and Robeson, 1995], linear lapse rate adjustment (LLRA) [Leemans and Cramer, 1991; Willmott and
LIANG ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Atmospheres
10.1002/2013JD020597
Figure 1. Location of Tenderfoot Creek Experimental Forest (TCEF), SNOTEL stations, and eddy covariance tower. The air temperature surface is originated from five sites outside the TCEF site, as indicated by the arrows.
Matsuura, 1995], and the neutral stability algorithm (NSA) [Marks, 1990; Dodson and Marks, 1997]. The CAI
approach involves computing temperature anomalies and interpolation of such anomalies [Dodson and
Marks, 1997] to generate complete temperature surfaces; however, this approach requires long-term observations (e.g., multidecadal trends [Legates and Willmott, 1990]), which are not always available in remote
areas. On the other hand, the LLRA and NSA approaches do not require long-term observations yet they
differ in that the LLRA approach implements a constant lapse rate equation whereas the NSA approach
implements the potential temperature equation [Dodson and Marks, 1997]. Because the NSA approach
assumes that the atmosphere has a neutral stability profile in the vicinity of the data collection site, the NSA
is less sensitive to the specific lapse rate and can lead to low uncertainties (for example, lower than 0.5°C
across elevation reliefs no greater than ~1500 m [Dodson and Marks, 1997]). While it is known that lapse
rates vary across space and time, the elevation range at TCEF is fairly narrow (1963 m to 2462 m) and this
makes the site suitable for the NSA approach.
In addition, we apply the NSA approach [Dodson and Marks, 1997] because (1) it can be applied across different
sites without knowing site-specific lapse rates; (2) it provides results on the basis of physical processes; therefore, results are easier to calibrate, validate, and describe on the basis of field observations; and (3) this algorithm
is less sensitive to the changes and assumptions of the variability in temperature gradients in space and time
[Dodson and Marks, 1997].
The basic implementation of the NSA includes three steps. First, air temperature (Ta) was converted to potential
temperature θa at sea level surface using the potential temperature equation, as follows:
! "m!cR
p
P0
(1)
θa ¼ T a !
Pz
where P0 (Pa) and Pz (Pa) are the pressures at sea level and at the elevation z (m) of stations, respectively. The
parameters R, m, and Cp are the gas constant (8.3143 J mol"1 K"1), the molecular weight of dry air (0.02897 kg
mol"1), and the specific heat capacity of dry air (1005 J kg"1 K"1), respectively. In this paper, the Pz is calculated according to a commonly used empirical relationship [Allen et al., 1998] using the standard temperature
lapse rate for the continental U.S. of "0.0065°C m"1 [NOAA, 1976]:
!
"
293 " 0:0065 ! z 5:26
:
(2)
Pz ¼ 101:3 !
293
Second, the calculated potential temperature from discrete stations is interpolated to a distributed potential air
temperature surface, using an interpolation algorithm such as Inverse Distance Weighting (IDW) or similar Kriging
LIANG ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Atmospheres
10.1002/2013JD020597
algorithm. Here we adopted the IDW algorithm because it is simpler to implement compared to other
geostatistical methods. Third, the distributed potential air temperature is then converted to distributed
air temperature according to equation (1). Pz in equation (1) represents the distributed pressure, and z is the grid
cell elevation, which was derived from a 5 m digital elevation model (DEM) (courtesy of the National Center for
Airborne Laser Mapping (NCALM)). When employing the NSA to estimate air distribution at large scales
(~105 km2), Dodson and Marks [1997] suggested a bias correction factor was needed to adjust the estimated air
temperature to interpolation errors produced by the difference between grid cell elevation and the weighted
mean station elevation (ΔZ; for further details, see original paper by Dodson and Marks [1997]). According to
Dodson and Marks [1997], the interpolation error is clearly dependent on ΔZ, at a rate of 4.49°C for every 1000 m
in ΔZ. Our study takes place at a much smaller scale (study area is ~22 km2), with an estimated magnitude of ΔZ
ranging between "2.0 m and 2.4 m. Thus, the interpolation error highlighted by Dodson and Marks [1997] is
lower than 0.01°C and can be considered negligible. Moving forward, however, care must be taken to account
for potential artifacts introduced by scale.
2.3. Soil Temperature Model
Temperature in the soil is modified via two physical processes, thermal conductivity and heat capacity, which
are driven by changes in environmental variables such as solar radiation, latent heat of condensation, or soil
water evaporation [Bonan, 2008]. These properties determine the thermal conductivity in the soil profile, which
obeys Fourier’s law [Gao et al., 2003]:
F ¼ "λ
∂T
∂z
(3)
where F (W m"2) is the heat flux at depth z (m), λ represents soil thermal conductivity (W m"2 K"1), and ∂T
∂z is
the temperature gradient along the depth (K m"1). Assuming that soil properties are homogenous and that
heat conduction occurs primarily in vertical direction along the steepest temperature gradient, the change of
soil temperature over time can be given as follows [Bhumralkar, 1975]:
∂T
λ ∂2 T
∂2 T
¼
¼ ks 2
2
∂t ρc ∂z
∂z
(4)
where ρ is the soil bulk density (g m"3) and c is the specific heat capacity of soil (J g"1 K"1). The term ρcλ is
known as thermal diffusivity ks (cm2 s"1). Thus, under known initial and boundary conditions [Hillel, 1982;
Gao et al., 2003], the variation of soil temperature at a given depth and time can be described as a sinusoidal
curve that represents both diurnal and annual cycles of temperature as follows:
! "1=2 !
1=2
ω
"z ð2kωs Þ
T s ðz; tÞ ¼ T 0 þ A0 e
sin ωt " z
(5)
2k s
where ω is the angular velocity of the Earth’s rotation, T 0 is the average temperature at the soil surface, and A0
is the amplitude of the soil surface temperature variation. It is important to note that equation (5) can be used
to model Ts from diel to annual time scales.
In addition to the thermal properties of the soil, vegetation cover and litter also affect soil temperature by
intercepting solar radiation [Lewis, 1998]. The fraction of radiation that arrives at the soil surface is given by
Beer-Lambert law as e" kLAI, where LAI is the leaf area index (m2 m"2) and k is the extinction coefficient. Zheng
et al. [1993] developed an empirical model to estimate soil temperature at depth based on air temperature
and is shown below:
If Taj > Ts"1,
else if Taj ≤ Ts"1,
#
$
T s ¼ T s"1 þ T aj " T s"1 ! M ! e"kðLAIj þLitterj Þ
#
$
T s ¼ T s"1 þ T aj " T s"1 ! M
(6)
(7)
where Ts and Ts"1 represent the mean soil temperature on the present day and the previous day, respectively.
LIANG ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Atmospheres
10.1002/2013JD020597
Taj is the air temperature on the present day, and M is a scaling factor that originated from a regression
between the average air temperature and the observed soil temperature.
Combining equations (6) and (7), M can be substituted by a damping ratio for any given depth (DRZ)
[Kang et al., 2000]:
DRz ≡
ω 1=2
Az
¼ e"zð2ks Þ
A0
(8)
where A0 is the amplitude of the soil surface temperature variation and Az is the amplitude of the soil temperature variation at a depth z. This leads to the following:
If Taj > Ts"1,
else if Taj ≤ Ts"1,
#
$
T s ¼ T s"1 þ T aj " T s"1 ! DRz ! e"k ðLAIj þLitterj Þ
#
$
T s ¼ T s"1 þ T aj " T s"1 ! DRz ! e"k!Litterj :
(9)
(10)
In our study case, Ts and Ts"1 represent the soil temperature at the present hour and the previous hour, respectively, whereas Taj is the air temperature at the present hour. The values of model parameters, including thermal
diffusivity (ks), extinction coefficient (k), LAI, and litter were set to be static across space and time. These parameters
were derived from a 25,000-iteration Monte Carlo optimization [Riveros-Iregui et al., 2011], and in each step, the
parameters were used to calculate the Nash-Sutcliffe coefficient [Nash and Sutcliffe, 1970] of model efficiency (E);
optimal parameters were selected by choosing those with the highest E. The values of ks, k, LAI, and litter were
1.54 ! 10"3 cm2 s"1, 0.45, 1.2 m2 m"2, and 1.5 m2 m"2, respectively. Thus, the soil temperature model shown in
equations (9) and (10) was applied to calculate the soil temperature of every cell for the entire TCEF watershed
using the air temperature estimated in section 2.2.
2.4. Observed Air and Soil Temperature
The air temperature data used for interpolation were retrieved from five Snowpack Telemetry (SNOTEL) sites,
designed to collect snow, precipitation, and related climatic data in the Western United States and Alaska at
hourly time scales and maintained by the Natural Resources Conservation Service (NRCS) (http://www.wcc.
nrcs.usda.gov/snow). At these sites, air temperatures are measured via a shielded thermistor about 1.5 m
above the ground (actual thermistor height was accounted for and varied from site to site depending on sitedependent snow depth) [Finklin and Fischer, 1990]. The five SNOTEL sites selected were Rocky Boy, Wood
Creek, Daisy Creek, Spur Park, and Dead Man Creek, as they represent some of the few sources of air temperature data in the surrounding vicinity of TCEF. The five sites are located at horizontal distances ranging
from 23 km to 264 km, and in the NW, NE, and SE directions from a flux tower located within TCEF (Figure 1).
We intentionally chose to work with SNOTEL stations that were distant from our study site to evaluate the
feasibility of using remote stations for this type of analysis. At the same time, we deliberately excluded the
stations that were within the study site so that (1) they would not influence the IDW interpolation and (2)
they could be used during validation. Our results show that our approach can yield realistic air temperature
estimations, even when direct observations are made and available at distant locations (see section 3). All the
hourly records from these five stations were checked before being used. If data points were missing for a given
hour, linear interpolation was applied to fill the gap. No gaps longer than a day were observed. Combined, these
sites represent an appropriate case scenario to assess the usefulness of a framework designed to model soil
temperature in data-scarce regions. In addition, two SNOTEL sites within TCEF (Stringer Creek and Onion Park) and
a flux tower provided 1 h real-time observations of air temperature for validation of the interpolated air temperature (see section 3.1).
Soil temperature was measured every 4 h at 10 sites distributed across the watershed by installing temperature
Data Loggers (iButton Thermochron, Maxim, Sunnyvale, California) at a 5 cm depth. The locations of the iButtons
were selected with the intent to capture as many different landscape positions as possible, including the range in
elevations, aspects, vegetation cover, and soil water conditions. The study targeted the snow-free season, 18 July
to 7 September 2006. The estimations of soil temperature were compared to observations, which were collected
at 4 h intervals from the iButtons.
LIANG ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Atmospheres
10.1002/2013JD020597
Figure 2. A schematic diagram of the modeling framework, including an air temperature component (Step 1) and soil temperature component (Step 2).
2.5. Modeling Approach: Estimating Distributed Soil Temperature in Data-Scarce Regions
Two steps were necessary to estimate the spatial and temporal distribution of soil temperature (summarized
in Figure 2). First, air temperature measurements from five distant SNOTEL stations were used to model the
spatial distribution of air temperature for a 5 m DEM and following the NSA approach (Step 1 in Figure 2). This
step included the calculation of potential air temperature and interpolation using the IDW algorithm. Second,
a hybrid, soil temperature model was applied to generate distributed soil temperature based on distributed
air temperature (Step 2 in Figure 2). A Monte Carlo parameter optimization was applied to retrieve parameters for the hybrid soil temperature model. Modeled soil temperature was validated using existing observations taken using temperature data loggers (section 2.4).
3. Results
3.1. Interpolating Air Temperature Measurements
Based on climatological information from five SNOTEL sites and the NSA approach, we modeled air temperature
and validated these results using observations from three sites within TCEF (Figure 3). Both modeled and observed
air temperature ranged from ~ "3°C to ~ 32°C, and there was, in general, good agreement between these
two data sets. Using the NSA approach (Figures 3a–3c), the coefficient of determination (R2) of the regression
between observed and modeled air temperature ranged from 0.93 to 0.96, with a root-mean-square error (RMSE)
c)
b)
Modeled Ta (˚C)
a)
Observed Ta (˚C)
Figure 3. Validation of modeled air temperature shows the difference in air temperature from modeled results and observation from Stringer Creek, Onion Park, and flux tower.
LIANG ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Atmospheres
10.1002/2013JD020597
Table 1. Summary of Recent Studies That Model Air Temperature (Ta), Including Spatial Resolution and Root-Mean-Square Error (RMSE) or
Mean Absolute Error (MAE)
Location
Tibetan Plateau, China
Northern Germany
Northern Rocky Mountains, USA
California Sierra Nevada, USA
Pyrenees, France
Colorado Rocky Mountains, USA
Senegal, West Africa
Continental United States
China
Central California, USA
England and Wales, UK
Southeast France, France
Pacific Northwest, USA
Central Montana, USA
Spatial Resolution (m)
RMSE/MAE (°C/ K)
Reference
500–1000
60
10
100
100
50
3000
8000
1000
4000
1000
1000
1000
5
3.43
3
1.96–3.84
2.5–3.6
1.5–2.5
0.6–1.2
2.55–2.99
1.6–2.0
0.42–0.83
1.6
0.85–1.22
0.9–1.95
1.2–1.3
1.37–1.71
Zhu et al. [2013]
Wloczyk et al. [2011]
Emanuel et al. [2010]
Lundquist et al. [2008]
Lundquist et al. [2008]
Lundquist et al. [2008]
Stisen et al. [2007]
Jolly et al. [2005]
Hong et al. [2005]
Daly et al. [2002]
Jarvis and Stuart [2001]
Courault and Monestiez [1999]
Dodson and Marks [1997]
This study
ranging from 1.37°C to 1.71°C across three sites. Comparing with the previous studies (Table 1), our modeled air
temperature meets the criteria in air temperature estimation, suggesting that our air temperature output is reliable for further usage, i.e., calculating soil temperature in our case.
3.2. Performance of the Soil Temperature Model
A comparison between modeled and observed soil temperature showed good agreement for the 10 different
locations across the entire watershed (Figure 4). RMSE values ranged from 2.07°C to 2.9°C depending on site
location, with an average value of 2.4°C among all sites. The soil temperature model performed better (average
RMSE = 2.4°C) at upland sites (i.e., sites 1, 2, 4, 5, 7, 8, and 9) than it did at riparian sites (i.e., sites 3, 6, and 10;
average RMSE = 2.6°C). In general, the model performed well in the range of soil temperatures between 7°C and
15°C among all sites, with roughly 68.2% of the observations (i.e., 1 standard deviation from the mean) falling in
this range. However, the model showed poor agreement toward the extremes of observed soil temperature (i.e.,
lower than 7°C or greater than 15°C). While there is variability in the agreement between observations and
modeling results across sites, the soil temperature model captured the temporal and spatial variability of soil
temperature across the entire watershed (Figure 5).
A spatiotemporal estimate of soil temperature at 5 cm for the entire TCEF watershed (~22 km2) is presented in
Figure 5. The daily progression of soil temperature is highlighted for 2 days, 29 July (Figure 5a) and 31 August
Site1
35
Modelled Ts (°C)
25
RMSE=2.14
n=312
Site2
35
25
RMSE=2.69
n=312
Site3
35
25
RMSE=2.87
n=313
Site4
35
25
RMSE=2.78
n=312
Site5
35
25
15
15
15
15
15
5
5
5
5
5
−5
−5
5 15 25 35
−5
−5
Site6
35
25
RMSE=2.38
n=312
5 15 25 35
−5
−5
Site7
35
25
RMSE=2.43
n=312
5 15 25 35
−5
−5
Site8
35
25
RMSE=2.58
n=312
5 15 25 35
−5
−5
Site9
35
25
RMSE=2.07
n=312
25
15
15
15
15
5
5
5
5
5
5 15 25 35
−5
−5
5 15 25 35
−5
−5
5 15 25 35
−5
−5
5 15 25 35
5 15 25 35
Site10
35
15
−5
−5
RMSE=2.21
n=312
RMSE=2.51
n=312
−5
−5
5 15 25 35
Measured Ts (°C)
Figure 4. Comparison of modeled and observed soil temperatures at 10 sites within TCEF, between 18 July and 7 September 2006.
Modeled soil temperature (Ts) is shown as a mean value (black dots) ± 1 standard deviation (μ ± 1σ; error bars) from a 1000-run Monte
Carlo simulation.
LIANG ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Atmospheres
10.1002/2013JD020597
Figure 5. The spatial-temporal distribution of 5 cm soil temperature in the whole TCEF across two different days of the 2006 growing season: (a) 29 July and (b) 31 August. The frequency
distribution (probability density function) of selected soil temperature maps is shown to the right of each map. The soil temperature ranging from μ " 1σ to μ + 1σ (where μ is the mean and
σ is 1 standard deviation) is shaded. (c) Time series of modeled soil temperature at tower location. Two selected time segments (T1 and T2) are highlighted to show daily variation of soil
temperature at one site.
(Figure 5b). The frequency distribution of modeled soil temperature from six snapshots shows a similar pattern,
indicating that the majority of soil temperature (shaded areas) is distributed around the mean and extremes are
rare. Note that these snapshots include whole watershed estimates. Model output includes 1 h intervals across 5 m
grid cells across the entire ~22 km2 watershed. The highest daily soil temperature was commonly observed
and modeled between 16:00 and 20:00 local time, commonly 2–3 h later than the highest air temperature
of the day. Across the watershed, lower elevations showed higher soil temperatures (Figure 5). These results suggest that modeling soil temperature based on a few single air temperature observations can yield
realistic temporal and spatial dynamics of soil temperature, when used in combination with knowledge of
the physical characteristics of the landscape (Figure 5).
4. Discussion
4.1. Air Temperature
Despite the need to evaluate the variability of air temperature across mountainous terrain, accurate interpolation of air temperature based on available observations remains a significant challenge due to the mechanistic
effects imposed by elevation and the spatiotemporal variability of lapse rates [Barry and Chorley, 1998; Stahl et al.,
2006]. Additional challenges arise when considering the need of high spatial and temporal resolution models.
Combining the NSA approach and a widely used interpolation method (IDW), our results showed that a simple
modeling framework based on topography can provide reliable air temperature distributions.
In addition to elevation, factors such as aspect, slope, vegetation, and wind can impose significant effects
on air temperature at regional scales [Schroeder and Buck, 1970]. While the implementation of each of
these factors would result in a more realistic model, it would also complicate the application of the model
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©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Atmospheres
10.1002/2013JD020597
especially in areas where such parameters are poorly characterized. Our results indicate that the NSA
approach performs well for the TCEF site, with RMSE values close to 1.6°C for modeled air temperature.
This error is comparable to previous studies and models applied at much greater spatial scales and across
multiple regions around the world (Table 1). Thus, our findings suggest that this modeling approach is a
feasible option to develop a physically based understanding of air temperature variability for regions
where direct observations are scarce (Figure 3).
4.2. Soil Temperature
The comparison between modeled and measured soil temperature can be summarized in three important
points. First, our soil temperature model performed better in upland locations (i.e., sites 1, 2, 4, 5, 7, 8, and 9;
Figure 4) than in riparian locations (i.e., sites 3, 6, and 10), likely as a result of upland locations having low soil
water content. Upland areas are drier due to gravitational drainage, and as a result, the thermal capacity of
these soils is also lower. Static LAI and litter values applied across the watershed can also lead to the observed
discrepancies. Nonetheless, for mountainous landscapes such as TCEF, roughly 98% of the total landscape is
considered forested upland with a fairly uniform vegetation cover [Riveros-Iregui and McGlynn, 2009; Emanuel
et al., 2011]; thus, the prediction from the proposed modeling framework captures the spatial and temporal
variability of soil temperature for most of the watershed (Figure 5).
Second, the soil temperature model did not fully capture the extremes (i.e., low and high ends) of the observed soil
temperature range. Accurate prediction of daily temperature fluctuations near the soil surface also remains a
challenge due to the high variability of shallow soil conditions. Better predictions of these dynamics could be
achieved using greater parameterization at single sites, yet this approach would likely lead to overparameterization
at the watershed scale, hindering interpretation of landscape-level results. Furthermore, the discrepancy between a
discrete number of measurement sites and the heterogeneity of the terrain will still exist even if a higher number of
parameters were used at single sites. Thus, striking the right balance between realistic parameterization, model
simplicity, and model applicability remains a difficulty not only here but in any modeling study. Our proposed
framework offers a practical approach that provides both reasonable detail at single sites and realistic spatial and
temporal patterns at the landscape level.
Third, the discrepancies between modeled and measured soil temperature were also due to the parameterization
of the soil temperature model. The current parameters, including thermal diffusivity (ks), extinction coefficient (k),
and leaf area index (LAI), were previously estimated using a 25,000-iterations Monte Carlo optimization [RiverosIregui et al., 2011] and based on the Nash-Sutcliffe coefficient of model efficiency. However, the heterogeneity of
these parameters in nature is high and at the same time difficult to estimate in a distributed manner. For example,
previous studies by Kang et al. [2000] used distributed LAI values derived from Landsat thematic mapper at a 30 m
spatial resolution, yet their model performance was not considerably higher (i.e., MAE = 1.05°C) than our proposed
framework with a fixed LAI (LAI = 1.2 m2 m"2; MAE = 2.37°C), given their added complexity. A higher MAE value in
our study can also be the result of higher spatial resolution (5 m) with respect to Kang et al. [2000] (30 m) and a
higher number of validation sites in our study 10 with respect to the number of validation sites in the previous
study (two forested sites). In our study, thermal diffusivity (ks) was assumed to be static, while it is well known that
ks is related to soil water content [Hopmans et al., 2002; Gao et al., 2003; Gao, 2005], which is highly variable across
mountainous regions due to differences in precipitation, evapotranspiration, and the lateral redistribution
of water [Jencso et al., 2009]. Nonetheless, the simplicity of our proposed framework allows for probing the
potential of our approach to predict spatiotemporal patterns of soil temperature in data-scarce regions. We
suggest that the strengths and utility of a simple modeling framework far outweigh the deficiencies of the
model and the proposed modeling framework can be particularly useful in regions where observations are
scarce. Future studies should focus on the spatial effects introduced by variability in the distribution of
solar radiation (i.e., aspect), soil moisture content, heterogeneous vegetation cover, and the heterogeneity
of soil characteristics.
5. Summary
Soil temperature is an important control on physical, chemical, and biological processes across terrestrial
ecosystems. It is one of basic inputs of process-based, ecological models used to estimate carbon, water, or
nutrient balances along the soil-plant-atmosphere continuum [Parton et al., 1987; Running and Coughlan, 1988;
Potter et al., 1993; Randerson et al., 1996; Thornton et al., 2002; Niu et al., 2011; Riveros-Iregui et al., 2011]. To date,
LIANG ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Atmospheres
10.1002/2013JD020597
long-term observations of soil temperature are not available despite the common availability of air temperature
measurements. We developed a framework to estimate distributed soil temperature from mountainous regions
using discrete air temperature measurements, an interpolation algorithm, a digital elevation model, and
mechanistic understanding of radiation attenuation. Our framework predicted both distributed air and soil
temperatures well based on validations performed using data available at this site. Furthermore, we suggest this
approach is useful to generate spatiotemporal information of the variability of soil temperature across large
areas in complex terrain, in particular areas with limited or no observations available.
Finally, and at a more basic level, our study characterizes the spatial variability of soil temperature distribution,
which is highly mediated by topography in complex terrain. Our findings suggest that terrain should be used as
an important parameter to model soil temperature over large spatial scales. Thus, whether in a large-scale study
or a plot-scale experiment, this study suggests considering the effects of terrain heterogeneity on soil temperature at any given point as well as the variability of soil temperature across the landscape. Improving our capacity
to predict soil temperature may be particularly beneficial in regions where ground observations are scarce and
can be useful to multiple disciplines from soil science to hydrology to ecology.
Acknowledgments
This research was supported by the U.S.
Department of Agriculture under grant
2012-67019-19360. Additional funding
was provided by NSF Nebraska EPSCoR
and the Layman Foundation at the
University of Nebraska. The SNOTEL
network is maintained by the Natural
Resources Conservation Service (NRCS)
(http://www.wcc.nrcs.usda.gov/snow).
Soil temperature observations were
collected under NSF EAR-0404130.
Airborne laser mapping was provided
by the NSF supported National Center
for Airborne Laser Mapping (NCALM) at
the University of California, Berkeley. We
thank the Tenderfoot Creek
Experimental Forest and the USDA,
Forest Service, Rocky Mountain
Research Station for logistical support.
Randall Mullen, two anonymous
reviewers, and the Associate Editor
provided valuable suggestions for the
improvement of this manuscript. The
soil temperature model and computer
code from this paper are available for
use in other data scarce regions. Please
contact Diego Riveros-Iregui (diegori@unc.
edu) for further information.
LIANG ET AL.
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