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420 S. Werth and A. Güntner
signal leakage from surrounding areas for a specific basin shape. The filter is of
degree- and order-dependency (anisotropic) and an a-priori given maximum of the
basin average satellite error
max
tunes the filter properties. The error is a-posteriori
propagated from the smoothed GRACE coefficient errors. (3) Another anisotropic
Swenson and Wahr (2002) technique minimizes the sum of GRACE error and sig-
nal leakage (MF). To estimate the latter, a synthesized signal of an exponential
design is parameterized by the auto-correlation length G
l
and standard deviation
s
0
of the expected signal. Both parameters determine the MF filter design. And (4)
the signal-to-noise ratio of each GRACE coefficient is optimized by the method of
Seo et al. (2006). We applied the method B
4
of their study, which uses monthly
GRACE coefficients as a signal estimate and calculate the filter from the variance of
the monthly coefficient errors (called SF below). For regulation of the filter intensity,
a dimensionless error factor f is introduced to the errors.
To ensure consistency in space for the filter evaluation, the same filtering was
applied to GRACE data (GFZ, data release RL04) and simulated hydrological model
results. For varying filter parameters, regionally averaged time series of TWSC for
the Amazon River basin were derived from both data sets and compared by the
correspondence criteria wNSC (see Werth et al., 2009b). This criterion measures
the agreement of both time series in signal amplitude and phase as well as the
filter induced leakage error by a comparison of filtered and unfiltered simulated
Fig. 1 Filter performance for the Amazon basin: wNSC correspondence between time series of
TWSC from GRACE and WGHM for different filter types and parameter values
Calibration of a Global Hydrological Model with GRACE Data 421
hydrological data. A perfect agreement corresponds to a wNSC of 1, whereas wNSC
decreases for lower agreement.
For the Amazon, high filter parameter sensitivities of GF, OF, SF and for s
0
of MF
were found (Fig. 1). Since the Amazon basin is located close to ocean to the east
and the west (inhering different signal properties) and at the equator to the north
(with shifted seasonality of water storage), basin averages for the Amazon are quite
sensitive to leaking signals for high filter intensities. The second MF parameter G
l
is comparatively insensitive in terms of wNSC values to correlation lengths greater
than 300 km which are typical values for continental-scale water storage patterns
(Güntner et al., 2007).
Among other features, basin shape and signal characteristics mostly determine
which filter type is optimal for a specific basin. The results vary widely between
different regions. The overall best results corresponding wNSC values for the
Amazon basin are provided by the OF filter with max = 13 mm and for MF with
σ
0
= 250 mm and G
l
= 200 km. For this study, we select OF filtered time
series of TWSC from GRACE gravity fields for the multi-objective calibration of
WGHM.
2.4 Calibration Approach
To retain the original station-based accuracy of WGHM in terms of river discharge
and gain from the integrative nature of the GRACE TWSC estimations, we expect
improved simulation results from a multi-objective calibration approach against
several observation data. Calibration denotes an iterative method of parameter
Fig. 2 Multi-objective calibration principle for the integration of GRACE data into WGHM
422 S. Werth and A. Güntner
testing and selection based on the evaluation of simulation results against obser-
vation data (see scheme in Fig. 2). In a multi-objective calibration, parameter values
are selected through the model performance against more than one objective. In this
study, two observation data sets were used as evaluation objectives for the Amazon
basin: (a) monthly mean river discharge from GRDC (Global Runoff Data Centre)
at the most downstream gauging station in Obidos and (b) TWSC derived from opti-
mal filtered GRACE data. For the period of 01/2003 until 12/2007, the evaluation of
the calibration objectives was done by computation of the Nash-Sutcliffe-efficiency
coefficient NSC (Nash and Sutcliffe, 1970) as a criterion of agreement between
modeled and measured time series.
The calibration of six WGHM parameters against two objectives depicts a non-
linear optimization problem. This requires a global optimization method, which
searches the whole parameter space. To handle also the computational demands
of WGHM we selected the efficient -Non-dominated-Sorting-Genetic-Algorithm-
II (ε-NSGAII, Kollat and Reed, 2006) which solves multi-objective problems using
the concept of evolutionary parameter variation (mutation, crossover and selection).
Its operators were parameterized as in the original version and a population size of
N = 8 and an -resolution of 0.05 for both objectives was used and the optimization
was stopped after 2,000 iterations.
The multi-objective approach leads to a Pareto set of optimal solutions (see
Fig. 2). Each Pareto optimum is an optimal solution from a multi-objective point
of view in the sense that no other solution exists that provides a better simula-
tion performance for both model output objectives. Hence, when moving from one
Pareto solution to another, simulation performance increases for one objective while
it decreases for the other objective. A ranking between the Pareto solutions is only
possible with additional information or decision about a weighting between the
objective functions.
3 Results
Calibration results of the Amazon provide an improved s imulation performance
for both TWSC and river discharge (Fig. 3). Improvement holds for all solutions
on the Pareto frontier compared to the original model simulation. An optimal fit
would give a simulation performance of 1 for each objective. A balanced improve-
ment between both objectives is given by the metrically closest Pareto solution to
an optimal fit (called the Pareto optimum in Fig. 3). The simulated TWSC time
series show that the underestimated TWSC variability of the original WGHM ver-
sion could be corrected in the recalibrated model (Fig. 3a). Furthermore, the phase
and amplitude of the seasonal water storage regime is improved in the recalibrated
model.
The better representation of TWSC simulations for the Amazon is mainly due to
a lower river flow velocity in the calibrated model version (see graph B in Fig. 3) as
well as a larger runoff coefficient. This causes a delay in river runoff and a longer-
Calibration of a Global Hydrological Model with GRACE Data 423
Fig. 3 Amazon calibration results in terms of simulation performance of discharge (y-axis) and
total water storage (x-axis). The Pareto solution closest to the optimal fit was selected for fur-
ther analyzes. Embedded graph A contains results for time series of water mass variations of
GRACE, the original model and the selected Pareto optimum model. Embedded graph B com-
pares normalized param eter values of the original model and the selected Pareto optimum
model
lasting storage of more surface water in the river network of the basin. The larger
river storage variability during the rainy season in the recalibrated model is also
revealed by the storage time series of all individual storage compartments (Fig. 4).
Furthermore , increased soil water storage is due to the larger rooting depth in the
recalibrated model (see also Fig. 3b). In contrast, the larger value of the parameter
wetland depth has nearly no effect on the storage variability in lakes and wetlands
in spite of the large importance of wetlands and floodplains for water storage in the
Amazon (e.g. Frappart et al., 2006). This may be an indication of structural model
errors in representing surface water exchange processes between floodplains and the
channel due to the conceptual model formulations and the cell-based simulation of
surface water bodies in WGHM.
424 S. Werth and A. Güntner
Fig. 4 Simulation of individual storage compartments of the Amazon basin by the original and
the recalibrated model
4 Conclusions
The presented calibration approach for large-scale hydrological models follows
three important steps: (1) selection of most sensitive and relevant process param-
eter of the model to be calibrated, (2) equal filtering of GRACE and hydrological
data and filter optimization to achieve the best possible separation of signal and error
in the GRACE data, and (3) multi-objective calibration against two observables that
represent different states of the hydrological system.
This approach results in a successful calibration of WGHM with regard to
both river discharge and GRACE water storage change for the Amazon basin.
Furthermore, the multi-objective strategy provides comprehensible results for single
storage compartments by adjusting parameter values and thus processes in a reason-
able manner. Such an improved process representation is required towards more
reliable simulations of the continental water cycle with regard to impacts of climate
variability and water resources management. The developed approach is applicable
for any large region worldwide to improve simulation performance of large-scale
hydrological models. Additionally, the multi-objective nature of the calibration
Calibration of a Global Hydrological Model with GRACE Data 425
technique sets a useful framework for the integration of other remote sensing data
into hydrological models, such as soil moisture, surface water volumes or snow
cover.
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Part VI
NRT-RO
Near-Real-Time Provision and Usage of Global
Atmospheric Data from CHAMP and GRACE
(NRT-RO): Motivation and Introduction
Jens Wickert
Global and precise atmospheric satellite-based measurements with high tempo-
ral and spatial resolution are especially suited to characterize global change
related atmospheric variations and to improve global numerical weather forecasts.
Atmospheric research cannot be imagined without satellite measurements since the
sixties, when the meteorological use of satellite data started. Especially data from
passive multi-spectral radiometers contributed substantially to the understanding of
global atmospheric processes. But these data from, e.g., MSU (Microwave Sounding
Unit) and AMSU (Advanced Microwave Sounding Unit) are influenced by instru-
ment and orbit changes, calibration problems, instrument drifts, and insufficient
vertical resolution. Because of these shortcomings, e.g., the reliability of the derived
temperature data and – in particular – its trends in the troposphere is under debate
(Foelsche et al., 2007; Anthes et al., 2000).
With the installation of the US-American GPS (Global Positioning System) in
the nineties an innovative technique has come up to complement the measurements
of the established satellite remote sensing systems with data of a new quality: GPS
radio occultation (RO) measurements (see Fig. 1). Thesedata are recorded aboard
Low Earth Orbiting satellites (LEOs) and have a number of favorable characteristics,
as global coverage, high accuracy and vertical resolution, all-weather capability and
long-term stability (Kursinski et al., 1997). Extensive validation studies with data,
generated by the classical methods, as, e.g., radiosonde measurements, and several
applications demonstrated the high potential of the new data for atmospheric remote
sensing on a global scale (Wickert et al., 2009, 2005; Anthes et al., 2008, 2000).
The method was successfully tested within the US-American GPS/MET-
experiment (1995–1997; Rocken et al., 1997) and is currently continuously applied
aboard the CHAMP and GRACE (Wickert et al., 2009, 2005), COSMIC (Anthes
et al., 2008) and Metop (v. Engeln et al., 2008) satellites.
The CHAMP measurements were for a long time (2001–2006) the only opera-
tionally available RO data world-wide. It was extensively used for various scientific
J. Wickert (B)
Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences,
Department 1: Geodesy and Remote Sensing, Telegrafenberg, 14473 Potsdam, Germany
e-mail: wickert@gfz-potsdam.de
429
F. Flechtner et al. (eds.), System Earth via Geodetic-Geophysical Space Techniques,
Advanced Technologies in Earth Sciences, DOI 10.1007/978-3-642-10228-8_37,
C
Springer-Verlag Berlin Heidelberg 2010
430 J. Wickert
Fig. 1 Principle of GPS radio occultation measurements. A key observable is the bending angle
α of the signal path between the GPS and LEO (here CHAMP) satellites. Globally distributed
vertical profiles of atmospheric parameters (e.g., here temperature and electron density) can be
derived from a time series (50 Hz) of bending angles, recorded during an occultation event (Figure
from Wickert, 2002)
investigations (Wickert et al., 2009, 2006; Schmidt et al., 2008) including initial
and very promising impact studies to improve global numeric weather forecasts
at the Met Office (Buontempo et al., 2008; Healy et al., 2005) and the ECMWF
(European Centre for Medium-Range Weather Forecasts; Healy, 2007; Healy et al.,
2007).
A major result of these impact studies was the conclusion of the weather centers,
that the GPS RO measurements would be operationally assimilated if they would
be available in near-real-time. A real assimilation (based on available near-real-
time data) would not only improve the forecasts, but also would reduce systematic
errors in the ECMWF and Met Office model and allow for other satellite data
(e.g. Atmospheric InfraRed Sounder) to be assimilated and therefore result in
supplementary improvement of the global forecasts.
The promising impact study results and the above mentioned statement of the
weather centers were the reasons to propose a research project, focused to pro-
vide GPS radio occultation data from CHAMP and GRACE in near-real time in
2005 (Wickert and Rothacher, 2005). It was recognized that the preconditions for
an operational use of GPS RO data in numerical weather forecasts were established
and is was time to push this important GPS RO application. It was the best time to
take an active and leading role and to push the international activities f or the opera-
tional application of the GPS RO data, based on the reliable CHAMP and GRACE
measurements and before the launches of COSMIC and Metop. The proposal
submission was led by GFZ, which also provided significant components of the
necessary infrastructure for the planned research project (see Wickert et al., 2009;
chapter “Global Atmospheric Data from CHAMP and GRACE-A: Overview and
Results” by Wickert et al., this issue). The related proposal NRT-RO (Near-real-time