Timescales of land surface evapotranspiration response in ...
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Timescales of land surface evapotranspiration response in the
PILPS phase 2(c)
Dag Lohmanna,*, Eric F. Woodb
aEnvironmental Modeling Center, NOAA/NWS/NCEP, 5200 Auth Road, Suitland, MD 20746, USAbDepartment of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544, USA
Received 12 December 2001; received in revised form 25 January 2002; accepted 26 May 2002
Abstract
Present-day land surface schemes used in weather prediction and climate models include parameterizations of physical
processes whose complex nonlinear interactions can lead to models of unknown spatial and temporal characteristics. This paper
describes the timescales of the evapotranspiration response of 16 land surface schemes which participated in the Project for
Intercomparison of Land-surface Parameterization Schemes (PILPS) Phase 2(c) Red-Arkansas River experiment. The basins
were represented by 61, 1j�1j grid boxes. Ten years of hourly meteorological data were used to force 16 land surface schemes
off line. The evapotranspiration responses of the models are characterized by an impulse response function (or unit kernel)
which is described by a two-parameter model, representing the fast response of evaporation from the canopy surface or bare soil
and a slower one due to transpiration. The analysis of the results shows significant differences among the various LSS in their
characteristic timescales across the basins.
D 2003 Elsevier Science B.V. All rights reserved.
Keywords: PILPS; evapotranspiration timescales; land surface schemes; Red-Arkansas River basin
1. Introduction
The aim of this paper is to describe the typical
timescales of evapotranspiration of 16 LSS which
participated in the Project for Intercomparison of
Land-surface Parameterization Schemes (PILPS)
Phase 2(c) Red-Arkansas River experiment. This is
done by calculating an impulse response function from
the given precipitation and the modeled evapotranspi-
ration for each of the LSS, which afterwards is fitted
with a two-parameter model. Although an approach of
simply describing the evapotranspiration timescales
with a conceptual model can be seen as a step back-
ward from a more ‘physically’ based approach, we
think that such a description of model results gives us a
valuable insight into the general behaviour of LSS, as
it is the only way to directly compare this aspect of
model results.
The only LSS with known evapotranspiration time-
scales is the bucket model. Delworth and Manabe
(1988) showed that the bucket model basically
behaves like a first-order Markov process, in which
white noise input (precipitation) yields an output
variable (soil moisture), where the redness of the
0921-8181/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0921-8181(03)00007-9
* Corresponding author.
E-mail address: [email protected] (D. Lohmann).
www.elsevier.com/locate/gloplacha
Global and Planetary Change 38 (2003) 81–91
spectrum is controlled by potential evapotranspiration
and field capacity. The typical timescale (under the
assumption of steady-state forcing) of the actual
evapotranspiration can then be described by the e-
folding time of an exponential.
For other non-bucket LSS, these timescales of
evapotranspiration cannot be derived analytically,
because of the complex nonlinear interactions in the
various parameterizations which control the evapo-
transpiration response. However, a number of publi-
cations have attempted to quantify the timescales of
evapotranspiration and the effect on an atmospheric
model. Koster and Suarez (1996) controlled the soil
moisture retention timescales in a coupled general
circulation model (GCM) simulation. They showed
that shorter retention timescales of the soil moisture
lead to increased daily precipitation variance and one-
day-lagged precipitation autocorrelations, but to
decreasing autocorrelations on longer timescales.
They also give an excellent overview of previous
studies.
Scott et al. (1995) found that a canopy interception
reservoir shortened the timescales of hydrological
persistence, as represented by a 1-month-lagged auto-
correlation of precipitation. In a subsequent paper,
Scott et al. (1997) described the timescales of land
surface evapotranspiration efficiency with impulse
response (or kernel) functions. They found typical
timescales of 0–5 days for non-bucket LSS scheme
and longer evaporation timescales for the bucket
model. The fundamental difference between non-
bucket LSS and the bucket model was attributed to
the presence of a canopy interception reservoir in the
SVAT scheme.
This paper surveys the timescales of evapotranspi-
ration of 16 different (LSS) which participated in the
PILPS Phase 2(c) experiment. The setup and the main
results of the Phase 2(c) are described in a series of
three papers by Wood et al. (1998), Liang et al. (1998)
and Lohmann et al. (1998). The PILPS Phase 2(c)
experimental design was, briefly, as follows. Partic-
ipants were provided with surface atmospheric forc-
ings, the soil and vegetation characteristics on a 1jscale for 61 grid cells that constitute the Red-Arkansas
River basin. Ten years of hourly meteorological data
were used to force the LSS off line. Model simula-
tions of surface energy and moisture fluxes (including
streamflow) were evaluated for three calibration and
three verification catchments as well as on the scale of
the entire Red-Arkansas basin.
The Red-Arkansas River basin has a strong east–
west gradient in precipitation from more than 100
mm/month in the east to less than 30 mm/month in the
west. The potential evapotranspiration, as calculated
with the Penman–Monteith equation (see, e.g. Shut-
tleworth, 1993), does not follow the same distribution
(see also figure of forcing data in Liang et al., 1998).
Fig. 1 shows the mean monthly precipitation, the
potential evapotranspiration (PET) and the quotient
of the two from May to September for the years
1980–1986. The high PET values in the ‘‘L’’ shape
(see Liang et al., 1998) around the grid cell 96.5Wand
36.5N and the grid cells at 93.5W, 94.5W and 33.5N
are caused by a low surface albedo and a high
roughness of the surface.
This study is motivated by results from the PILPS
Phase 2(c) data analysis. Lohmann et al. (1998) (Fig.
13) showed that the 16 LSS have a large range of soil
water storage use. For example, in July, the modeled
mean monthly storage change for the entire Red-
Arkansas basin had values between 3 and 38 mm/
month, and therefore resulted in significant differ-
ences in the modeled monthly evapotranspiration.
However, the question of evapotranspiration time-
scales on daily timesteps has not been addressed by
Liang et al. (1998) and Lohmann et al. (1998). Fig. 2
shows the modeled daily evapotranspiration for all
LSS in the year 1981 in the grid cell centered around
34.5N and 94.5W. Two differences are most impor-
tant. First, the models show maximum peak values of
evapotranspiration between 17 mm/day (BASE) and
4.5 mm/day (SPONSOR). Second, in the time period
in July without precipitation, some models have only
very little evapotranspiration (CLASS, PLACE) while
others still have significant contributions (CAPS,
IAP94, MOSAIC, NCEP, SEWAB, SPONSOR, see
also Fig. 13 in Lohmann et al., 1998). These two
results show that the LSS have differences in their
daily and monthly evapotranspiration response.
2. Analysis of timescales
The methods followed in this paper have been
outlined by Scott et al. (1997). However, their
approach was modified. We require non-negativity
D. Lohmann, E.F. Wood / Global and Planetary Change 38 (2003) 81–9182
in the calculation of the kernel function and fitted a
two-parameter model to the kernel function.
2.1. Convolution representation
The timescales of evapotranspiration response to a
precipitation event in a general circulation model
(GCM) have been described by Scott et al. (1997).
Although this relationship between precipitation and
evapotranspiration is known to be nonlinear, a simple
timescale analysis with kernel functions can provide
insight into the basic mechanisms and timing that
characterize the system.
A linear system can be characterized by its
impulse response function g(t), which in turn includes
all the necessary information about the response
timescales of the system. The theory of linear sys-
tems is well developed and impulse response func-
Fig. 1. Precipitation, potential evapotranspiration and the quotient for the months May–September, 1980–1986.
D. Lohmann, E.F. Wood / Global and Planetary Change 38 (2003) 81–91 83
tions are widely used to describe, for example, the
relationship between effective precipitation (part of
the precipitation which becomes streamflow) and the
streamflow itself (see Dooge, 1979; Duband et al.,
1993; Lohmann et al., 1998 and references in these
papers).
The output E(t) of any linear system is determined
by a convolution of the input signal Peff with the
impulse response function g(t).
EðtÞ ¼Z t
lgðt � sÞPeff ðsÞds ð1Þ
In this case, E(t) is the evapotranspiration and Peff
is the part of the precipitation which becomes eva-
potranspiration. There are a couple of methods to
solve this implicit mathematical problem in time-
space (Duband et al., 1993; Lohmann et al., 1996,
and references therein), or in Fourier-space (see Scott
et al., 1997 and references therein). In this paper, we
solve Eq. (1) (see Lohmann et al., 1996) by an
iterative deconvolution procedure to insure the non-
negativity of the impulse response function and the
effective precipitation.
We note, that Eq. (1) is different from the Eqs. (1),
(2) and 6 from Scott et al. (1997). We do not calculate
the timing of evapotranspiration efficiency, but of the
evapotranspiration itself. We do this for two reasons:
potential evapotranspiration is different for all the
LSS, as their surface temperatures, their albedos and
their aerodynamic resistences differ. Second, we are
interested in the timing of evapotranspiration itself,
Fig. 2. Daily evapotranspiration for the grid cell around 34.5N and 94.5W for all 16 LSS.
D. Lohmann, E.F. Wood / Global and Planetary Change 38 (2003) 81–9184
rather than evapotranspiration efficiency, as it is a
direct measure of the soil moisture timescale. Also
potential evapotranspiration was very inconsistent
among the models in the PILPS phase 2(c), varying
by an order of magnitude.
2.2. Fitting of the impulse response function
We used a simple two-parameter function to char-
acterize the impulse response function. Scott et al.
(1997) used a one-parameter decaying exponential
which is equivalent with the Antecedent Precipitation
Index (WMO, 1983). They suggested that due to a
multiplicity of timescales represented by the LSS, as
represented by different processes such as canopy
evaporation and transpiration, the appropriate func-
tional form would be a weighted combination of
several exponentials. We followed this approach, but
simplified it by fitting a weighted sum of a delta
function, d(t) and an exponential, exp� k t:
gðtÞ ¼ b*dðtÞ þ kexp�kt
b þ 1ð2Þ
where g(t) is the fitted impulse response function, b is
the weight for the delta function d, and 1/k is the e-
folding time. The reason for this functional form is
that it did fit the calculated impulse response function
well, because it reflects the typical model timescales
of a fast canopy evaporation response and slower
transpiration response. A one-parameter exponential
was not able to reproduce the basic shape of most
impulse response functions.
Fig. 3. Calculated and fitted impulse response function for the grid cell around 34.5N and 94.5W for all 16 LSS.
D. Lohmann, E.F. Wood / Global and Planetary Change 38 (2003) 81–91 85
3. Analysis of PILPS Phase 2(c) results
The evapotranspiration timescales from the 16 LSS
of the PILPS Phase 2(c) were analysed as follows. We
first calculated the impulse response function for the
months of May–September for a 7-year period from
1980 to 1986 for all 61 grid cells and all LSS. The
seven impulse response functions for the different
years were then averaged and afterwards fitted with
Eq. (2).
Fig. 3 shows the averaged impulse response func-
tion for the same grid cell (centered around 34.5jNand 94.5jW) as in Fig. 2. The impulse response
functions show a large range in their values at time
0 as well as large differences in their timescale
T1/2 = ln(2)/k. A comparison with Fig. 2 shows that
those schemes whose evapotranspiration values have
the highest peaks (ALSIS, BASE, BATS, CLASS,
IAP94, PLACE) also have the highest values of the
impulse response function at time 0. The bucket model
(BUCK) is clearly different from all other models
because of the absence of a canopy interception
reservoir. It therefore does not represent very short
timescales of evapotranspiration, which is reflected by
small values of the impulse response function at time
0. The fact that the impulse response function of the
BUCK model has its peak value at the day after the
precipitation event can be explained by two reasons.
The net radiation and the vapor pressure deficit have
often larger values the day after the precipitation event.
Also, the daily precipitation was given uniformly over
24 h from 5:00 am or 6:00 am in the morning to the
same time the next morning. The soil of the BUCK
model therefore was often more moist the day after the
Fig. 4. Spatial distribution of the parameter k [1/day].
D. Lohmann, E.F. Wood / Global and Planetary Change 38 (2003) 81–9186
precipitation event than at the day of the precipitation
itself. The LSS with the longest timescales (IAP94,
MOSAIC, NCEP, SEWAB and SPONSOR) clearly
show a longer evapotranspiration persistence in the
summer months, as reflected by a lower k. The three
LSS (MOSAIC, SSiB and VIC-3L) which include
parameterizations of fractional coverage of precipita-
tion have the lowest values of the impulse response
function beside BUCK at time 0. Their parameter-
izations lead basically to a smaller canopy interception
storage for the whole grid cell and therefore less water
to directly re-evaporate.
Fig. 4 shows the spatial distribution of the fitted
parameter k for all 61 grid cells and Fig. 5 shows the
values of the impulse response function at time 0. Most
LSS have shorter timescales (higher k values) in the dry
western part of the basin and longer timescales in the
eastern part. Eleven LSS (ALSIS, BASE, BATS,
BUCK, CAPS, CLASS, IAP94, ISBA, PLACE, SSiB
and VIC-3L) show the ‘‘L’’-shaped structure as given
by the potential evaporation in Fig. 1 (see also Liang et
al., 1998). A higher potential evapotranspiration seems
to be reflected by shorter timescales of evapotranspira-
tion for this area compared to the neighbouring grid
cells. Furthermore, three LSS (BASE, BATS, SEWAB)
havemuch shorter timescales on the grid cells with bare
soil. The shorter timescales of MOSAIC and SPON-
SOR in the grid cells around 104.5W and 35.5N and
36.5N may result from the shallow roots in these two
grid cells.
The evapotranspiration timescales of the bucket
(BUCK) model are only dependent on the PET and
bucket size. All LSS participating in the PILPS Phase
2(c) have different patterns of net-radiation, because
Fig. 5. Spatial distribution of g(0) [1/day].
D. Lohmann, E.F. Wood / Global and Planetary Change 38 (2003) 81–91 87
of differences in surface temperature and albedo
(Liang et al., 1998). They therefore have different
patterns of PET. BUCK, for example, has a much
higher surface temperature than any other model,
which in turn shortens the evapotranspiration time-
scales. From Fig. 1, we can estimate the e-folding
times (see Delworth and Manabe, 1988) of the BUCK
to be on the order of 20–40 days; however, the
analysis from Fig. 4 shows that the calculated time-
scales are between 6 and 20 days, which basically
resulted from an overestimation of PET compared to
the Penman–Monteith estimation by a factor of 2.5
from BUCK. The reasons for this overestimation are
unclear, but could be related to the abnormal high
surface temperature (Liang et al., 1998). Note that the
Penman–Monteith equation itself is known to under-
estimate PET (Teillet and Holben, 1960). The regres-
sion of the inverse timescale 1/k with PET should be a
straight line for the BUCK model in the case of
constant bucket depth. The relationship of timescales
to PET can be seen in Fig. 6, which is a scatterplot of
PET against k for all 61 grid cells. The plot also shows
the regression line and the error of the slope. ALSIS,
CLASS, ISBA, MOSAIC, NCEP, SEWAB, and
SPONSOR show a small negative slope, indicating
that they have longer timescales in areas with higher
potential evapotranspiration. However, the error of the
slope is on the order of the slope itself.
All other models show the opposite behaviour,
especially BATS, BUCK and VIC-3L shorten their
evapotranspiration timescales with increasing PET.
The two grid cells around 35.5jN and 103.5jW and
104.5jW with bare soil were not taken into account
for the regression analysis, as some LSS have much
Fig. 6. Relationship between mean monthly potential evapotranspiration (May–September, 1980–1986) and k for 61 grid cells.
D. Lohmann, E.F. Wood / Global and Planetary Change 38 (2003) 81–9188
shorter timescales there. These two points are shown
as triangles in the figures.
Fig. 7 shows a scatterplot of the mean monthly
precipitation (from May to September) compared with
k. The LSS results can be categorized in three groups.
Ten LSS (ALSIS, BASE, CAPS, CLASS, IAP94,
ISBA, MOSAIC, NCEP, SEWAB, SSiB) have a
negative slope, which means that their evapotranspi-
ration timescales are longer in the humid eastern part
of the basin. Five LSS (BATS, BUCK, PLACE,
SPONSOR, SWAP) have a slope of the regression
close to zero, with one standard deviation of the slope
as large as the slope itself. One LSS (VIC-3L) has
longer evapotranspiration timescales in the dry west-
ern part of the basin. The result for the BUCK model
is not surprising, as its evapotranspiration timescale is
not a function of precipitation. However, it is interest-
ing to observe, that most LSS have longer timescales
in humid regions and shorter timescales in the dry
region. These models therefore show a fundamentally
different behaviour in their spatial distribution of
evapotranspiration timescales than the bucket model.
It cannot be concluded whether one model shows a
more realistic spatial pattern than the other models.
The final analysis has to be done with measurements.
4. Summary
This paper discusses the evapotranspiration time-
scales of 16 different land surface schemes which
participated in the Project for Intercomparison of
Land-surface Parameterization Schemes (PILPS)
Phase 2(c) Red-Arkansas River experiment. Although
Fig. 7. Relationship between mean monthly precipitation (May–September, 1980–1986) and k for 61 grid cells.
D. Lohmann, E.F. Wood / Global and Planetary Change 38 (2003) 81–91 89
a simple analysis with a linear system can only approx-
imate the modeled timescales, we think that such an
analysis is a valuable tool for the comparison of LSS.
LSS are normally described with parameterizations ‘‘as
physical as possible’’ (with which they refer to detailed
descriptions of local scale bio-physical parameteriza-
tions) but do neglect the typical timescales of in-
teraction implicit to these parameterizations and
interactions with other parts of the LSS (e.g. vertical
transports of water with Richards equation, Hillel,
1982).
The 16 LSS have very different timescales across
the Red-Arkansas River basin. LSS have a tendency
to become more and more complicated over time.
Although many of the parameterizations seem to be
necessary to have a realistic description of the land
surface, we think that it is time to take a look at the
typical timescales inherent in the complex nonlinear
interactions.
The analysis in this paper showed that the LSS,
which participated in the PILPS Phase 2(c), have
differences in their timeseries of modeled evapotrans-
piration, up to a factor of 4 in their peak values after
precipitation events. The timing of evapotranspiration
was described by a two-parameter impulse response
(kernel) function. This kernel function resolves two
different timescales which are included in most param-
eterizations of land surface processes. We believe that
there are typical impulse response functions for differ-
ent climates and think that the knowledge of such a
function could yield to more simple descriptions of the
complex interactions within LSS. This is especially
important.
We did not have long-term evapotranspirationmeas-
urements in the basin, and therefore we cannot con-
clude which one of the LSS response timescales is more
realistic. Such a comparison might be interesting and
was already requested by Koster and Suarez (1996) and
Scott et al. (1995). The atmospheric budget as used by
Liang et al. (1998) and Lohmann et al. (1998) was too
noisy on a daily timescale to allow for the estimation of
an impulse response function for the whole basin.
Acknowledgements
The PILPS Phase 2(c) participants are gratefully
acknowledged: Aaron Boone, Sam Chang, Fei Chen,
Yongjiu Dai, Carl Desborough, Robert E. Dickinson,
Qingyun Duan, Michael Ek, Yeugeniy M. Gusev,
Florence Habets, Parviz Irannejad, Randy Koster,
Dennis P. Lettenmaier, Xu Liang, Kenneth E.
Mitchell, Olga N. Nasonova, Joel Noilhan, John
Schaake, Adam Schlosser, Yaping Shao, Andrey B.
Shmakin, Diana Verseghy, Kirsten Warrach, Peter
Wetzel, Yongkang Xue, Zong-Liang Yang and Qing-
cun Zeng.
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