Introduction
River discharge is an essential component of the earth's water cycles,
which can be used as an indicator of the hydrological cycle intensification
(Munier et al., 2012). It is important not only for water resources
management, climate studies and ecosystem health over land (Syed et al., 2010;
Sichangi et al., 2016) but also for providing freshwater inflow to ocean (Dai
and Trenberth, 2002). The freshwater flux at the sea surface has significant
influence on the climate system (e.g., ENSO, ocean dynamics) and on ocean
salinity (Kang et al., 2017). The fresh water inputs for ocean models usually
require high-frequency data (e.g., daily or 10-daily; Scherbakov and
Malakhova, 2011). Besides, as the ocean models with high spatial resolution
(e.g., < 10 km) demonstrate better skills than coarse resolution
model (Bricheno et al., 2014; Wang et al., 2018), there is also a requirement
of high-resolution fresh water fluxes. Although great efforts have been made
for gridded river discharge data at the global scale (e.g., RivDIS v1.1;
Vorosmarty et al., 1998; Dai and Trenberth, 2002; Fekete et al., 2002), these
data are usually at monthly or annual timescales and have not been updated with
time. Therefore, it is of great interest to estimate large-scale river
discharge over the long-term at high temporal and spatial resolutions and low
uncertainty.
Estimating the river discharge input to ocean is a difficult endeavor for
several reasons. First, there are many un-gauged rivers that are difficult
to evaluate. Second, most large rivers are gauged by national agencies, and
these data are difficult to access for public users. Besides, the number of
operational gauging stations is decreasing worldwide (Syed et al., 2010;
Sichangi et al., 2016). Third, even though the observations are available,
the observed river flow at the outlet is not well known because it is
difficult to get gauging stations close to the river mouth and many
observations are affected by human activities especially in semiarid
regions (Jordà et al., 2017).
One approach to estimate the freshwater inflow into ocean is based on the
observed water fluxes over data-rich regions and a simple annual water
balance model, precipitation inputs minus the evaporation, which ignore
human usage and other processes over un-gauged basins (e.g., Szczypta et al.,
2012; Peucker-Ehrenbrink, 2009; Mariotti et al., 2002; Struglia et al., 2004;
Boukthir and Barnier, 2000; Ludwig et al., 2009). This method is the basis
of most water balance studies and oceanic modeling activities but it has
several limitations. First, there are uncertainties in observations related
to the measurement method and post-processing method. These uncertainties are
difficult to quantify due to incomplete information (Jordà et al.,
2017). Second, only annual mean values are available over un-gauged basins
(about 40 % for the Mediterranean; 42 % over globe, excluding Greenland
and Antarctica; Clark et al., 2015) by simple runoff models, which are not
sufficient for oceanic modelings.
Riverine input can also be obtained through forcing a state-of-the-art land
surface model (LSM) or global hydrological model (GHM) with bias-corrected
atmospheric conditions (e.g., aus der Beek et al., 2012; Bouraoui et al.,
2010; Jin et al., 2010; Sevault et al., 2014). These numerical models can
estimate river discharge at higher frequency and over more un-gauged basins
(Jordà et al., 2017), but they are associated with modeling
uncertainties. First, models are designed and have proved the ability to
capture the natural water cycles, but relatively less progress has been made
in parameterizing human processes (Pokhrel et al., 2017). The water flow of
many catchments has been strongly regulated by humans through irrigation use,
dam operation, etc. (e.g., the southern shores of the Mediterranean).
Second, there are large discrepancies among models resulting from the
differences in model inputs, parameterizations and atmospheric forcing data
(Ngo-Duc et al., 2007; Wang et al., 2016; Liu et al., 2017).
The objective of the present study is to illustrate a novel approach based on
assimilation techniques applied to LSMs to estimate continental water cycles
(riverine fresh water). The data assimilation, a specific type of inverse
problem, is generally applied for different cases: (1) to correct initial
condition (correcting state variable) which is mostly used for numerical
weather prediction; (2) to correct the state variable during the data
assimilation period (i.e., in this case both the trajectory of the model and
the initial conditions are corrected) and (3) to correct the parameter of a
model by optimization. In the current study, the data assimilation refers to
the third case. This assimilation approach merges the data from the model
(ORCHIDEE LSM) and the observed river discharge from the Global Runoff Data
Centre (GRDC, 56068 Koblenz, Germany). This will allow us to compensate for
model systematic errors or missing processes and provide estimates of the
riverine input into the sea at high temporal and spatial resolutions.
Although previous works exist on assimilation of river discharge (e.g., Li et
al., 2015; Bauer-Gottwein et al., 2015; Pauwels and De Lannoy, 2009), these
studies mainly focus on the stream flow prediction over individual
catchments. They are difficult to extend to long-term timescales and large
catchments due to the observations and computing time limitations.
This paper focuses on the methodology and its illustration in a
Mediterranean region (the Iberian Peninsula) which is considered one of the
most vulnerable regions to climate change due to its geographic and
socio-economic characteristics (Vargas-Amelin and Pindado, 2014). Although
the amount of river discharge is relatively small (about one-third to half
of precipitation amount; Tixeront, 1970; Shaltout and Omstedt, 2015), it is
an important source of fresh water entering the Mediterranean Sea and it
plays an important role in sustaining the marine productivity (Bouraoui et
al., 2010) and overturning circulation (Verri et al., 2017). The river
discharges to the Mediterranean Sea underwent important changes during
recent decades. This variation is particularly important for this region
because of its scarce water resource with increasing water demand for
domestic, industrial, irrigation and tourism activities, as well as its
drier and warmer conditions under climate change (Romanou et al., 2010).
Considering the high stress on the water resources in the Mediterranean
region, accurate estimation of the actual resources is important.
The methods (including the model, datasets and numerical experiment) are
described in Sect. 2. The results and discussions are given in Sect. 3.
Conclusions are drawn in Sect. 4.
(a) Illustration of correcting river discharge (Q)
simulation (simulation in blue solid dot, observation in red star) by
applying correction factors (x) to runoff and drainage over different
basins. Basin 1 and basin 2 are represented in yellow and blue,
respectively. (b) The model framework of the river discharge
assimilation. The blue and red parts are run for “First Guess” and for
assimilation, respectively.
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Methods
The theoretical background
The theoretical basis of the LSM assimilation for the study is the vertical
and lateral water balance. The precipitation (P) input of a basin is
transferred into either evaporation, surface runoff (R), deep drainage (D)
(eventually the R and D reaching the channel and leaving in the form of river
discharge) or stored in the ground.
dWdt=P-R+D-E
Over a long period, the change in water storage
dWdt is small
dWdt≈0, thus
P-E≈R+D.
The lateral water balance over a basin (e.g., the sub-catchment 2 in blue in
Fig. 1a) is given by
dA2dt=∫S2(R2+D2)ds-Q2+Q1,
where S2 is the area of sub-catchment 2; A2 is the water stored in
the aquifers of area S2; Q2 and Q1 are the river
discharge at outlet of each sub-catchment, and they are calculated by the
integral of runoff and drainage over the sub-catchment area S1 and
S2. We assume the A2 variation at the annual timescale is small
dA2dt≈0 due to its slow
variability, although it can be nonzero due to human intervention (e.g., over
the Indo-Gangetic basin, MacDonald et al., 2016). The W and A terms refer
to water storage and water stored in the aquifers, respectively. The
Eqs. (1)–(3) describe the basic water cycle processes in the LSMs.
Despite the fact that the LSMs have developed rapidly during the last few
decades, few models take into account the human water usage processes. Due to
this limitation, LSMs are usually accompanied with errors in reproducing
discharge and evaporation in areas where these processes are dominant.
Assuming the P forcing is known in the LSM, the modeled water continuity
imposes a balance of errors between E, R and D. However, the R and
D are conceptual variables, and their errors are impossible to evaluate by
observations directly. The field measurements of E over large area are also
scarce due to land surface heterogeneity (Kalma et al., 2008). Fortunately,
the observations of river discharge (Qobs) are available.
By fitting modeled discharge with Qobs, we can correct
model intermediate variables in Eqs. (1)–(3) (e.g., correct R andD by a
correction factor x, Fig. 1a) in order to get bias-corrected river
discharge (Qcorr).
Qcorr=∫catchment(x⋅R+x⋅D)dS
Recalling the dWdt is small and P is known, we then transfer the
x into vertical water balance and close the horizontal water balance by the
corrected evaporation (Ecorr):
Ecorr≈P-x⋅R+D,
The impacts of assimilation on E (ΔE) can be derived from the optimal
x, R and D:
ΔE=Ecorr-E≈1-x⋅R+D.
The key problem remains to determine the optimal x (described in
Sect. 2.2.2). Each discharge observation station corresponds to an optimal
correction factor x since the discharge is the only representative of the
integral over the basin. The total number of x depends on the number of
available stations. The optimal x over each observation station is applied
to its entire upstream area. Over each upstream area (dashed box in Fig. 1a),
the optimal x of these model grid cells are the same. The “R+D” and
E are corrected at the same grid cell level by x and Eq. (5),
respectively.
The models
Assimilation strategy and ORCHIDAS
The optimal x is obtained from the ORCHIDEE Data Assimilation System
(ORCHIDAS; https://orchidas.lsce.ipsl.fr, last access: 4 July 2018).
It was designed to optimize the variables related to water, energy and carbon
cycles in ORCHIDEE (Organising Carbon and Hydrology in Dynamic Ecosystems;
Krinner et al., 2005; De Rosnay et al., 2002) LSM by using various
observations (in situ, satellite, etc.). The ORCHIDAS has been applied over
different regions for various variables and demonstrated good performance
(Santaren et al., 2007; Kuppel et al., 2012; MacBean et al., 2015). More
details of ORCHIDAS are presented by Peylin et al. (2016).
In this work, the ORCHIDAS drives the ORCHIDEE routing scheme which is
computationally less expensive than the full ORCHIDEE model (Fig. 1b). The
data assimilation approach relies on the minimization of a misfit
function J(x) (a.k.a. cost function) by successive calls to
“gradient-descent” minimization algorithm L-BFGS-B (Limited-memory
Broyden–Fletcher–Goldfarb–Shanno algorithm with simple box constraints;
Byrd et al., 1995).
A new vector of parameter values x is estimated at each iteration. The
J(x) measures the mismatch between the vector of observed river discharges
Qobs and corresponding simulated
values Qsim(x), as well as between the optimized
correction factors x and its prior information xprior:
Jx=Qobs-QsimxtR-1Qobs-Qsimx+x-xpriortB-1x-xprior,
where R and B represent the prior error
covariance matrices for observations and parameters, respectively. Diagonal
elements of the R matrix represent the data uncertainties, which
include both the measurement errors (systematic and random) and model errors,
we have defined it as the root mean squared error (RMSE) between the prior
model simulations and the observed river discharges. Non-diagonal elements
describe correlations between the data, which are difficult to presume
correctly, and are usually neglected. The prior parameter uncertainties
(matrix B) have been set to 40 % of the range of variation in
correction factors obtained from the ratio Qobs and first
guess value of river discharge simulation (Qfg) obtained
from xprior. The matrix B was determined based on
the expert knowledge of ORCHIDEE model (Kuppel et al., 2012; Santaren et al.,
2014). Correlations between prior parameter values have not been considered.
The gradient of the J(x) is calculated for all the parameters by a finite
difference approach at each iteration (Kuppel et al., 2012).
ORCHIDEE LSM with high-resolution river routing model
The ORCHIDEE LSM is the land component of Institut Pierre Simon Laplace
Climate Model (IPSL-CM), which simulates energy, water and carbon cycles
between the soil and atmosphere. The unsaturated water flow is described at
each land point by the one-dimensional Richards equation with 2 m soil
discretized to 11 levels. The surface runoff and deep drainage at bottom
layer are computed by Horton overland flow and free drainage (equals to
hydraulic conductivity), respectively. In other words, the ORCHIDEE LSM
assumes that the aquifer level is below the model bottom, and it neglects
the upward water flow through capillary forces from its underlying aquifer.
The evaporation is partitioned into transpiration, bare soil evaporation,
interception loss and snow sublimation.
The ORCHIDEE is coupled with the ocean model through the river routing scheme
(Polcher, 2003; Ducharne et al., 2003; Guimberteau et al., 2012), which
computes river discharge by integrating the surface runoff and deep drainage
over the basin. A high-resolution river routing scheme was developed
recently, which better describes catchment boundaries, flow direction and water residence time (Nguyen-Quang et
al., 2018; Zhou et al., 2018). It is based on the HydroSHED (Hydrological
data and maps based on SHuttle Elevation Derivatives at multiple Scales;
http://www.hydrosheds.org, last access: 4 July 2018; Lehner et al.,
2008) map with 1 km spatial resolution. There are several hydrological
transfer units (HTUs) in one ORCHIDEE grid-cell (e.g., 100 in the current
study). The HTU is constructed based on the Pfafstetter topological coding
system and user-defined size. Each HTU represents the section of the river
basin within the grid box, and many HTUs forms a river basin (Nguyen-Quang et
al., 2018). Therefore, the relative locations of HTUs in each grid cell are
not fixed.
In each HTU, the water is routed through a cascade of three linear reservoirs
characterized by their residence times: the groundwater, overland and stream
reservoirs. The runoff and drainage are the inputs into the overland
reservoir and groundwater reservoir, then they flowed into the stream
reservoir of the downstream sub-grid basin. The residence times are
determined by multiplying a constant reservoir factor (g) with a slope
index (k). The g for stream, overland and groundwater reservoirs are
0.24, 3 and 25 days km-1, respectively (Ngo-Duc et al., 2007). The
slope index is a function of distance (d) and slope (S) between a pixel
and its downstream pixel (k=d/S1/2 defined by Ducharne et al., 2003).
The water can flow either to the next HTU within the same grid cell or to the
neighboring cell. The river discharge is diagnosed at the HTU level in the
assimilation. The river discharge is linear with R and D at an annual
timescale over a small basin. In the case of more than one observation
station being assimilated in a river basin (e.g., x1 and
x2 in Fig. 1a), the river discharge downstream is affected by the
discharge of upstream, thus it is not a linear system anymore. Therefore, the
optimization is needed to deal with the x over the non-linear sub-basins.
The time steps for the ORCHIDEE model and routing scheme are 30 min and
3 h, respectively. The spatial resolution of the model depends on the
resolution of the atmospheric forcing, and it is 0.5∘ for the current
study (given in Sect. 2.3.2). The soil texture map is from United States
Department of Agriculture (USDA) with 12 soil textures (Reynolds et al.,
2000). The vegetation map is from the European Space Agency Climate Change
Initiative (ESA CCI, https://www.esa-landcover-cci.org, last access: 4
July 2018) reduced to the 13 plant functional types represented by the model.
The study domain and the datasets
Study domain
The assimilation system is applied over the Iberian Peninsula. This region is
dominated by two climate types: the oceanic climate in the Atlantic coastal
region and the Mediterranean climate over most of Portugal and Spain. The
annual precipitation is extremely unevenly distributed with more than
1500 mm over northeastern Portugal, much of coastal Galicia and along the
southern borders of the Pyrenees but less than 300 mm over southeast Spain
(Estrela et al., 2012). Over Spain, agriculture occupies approximately
50 % of the land area (e.g., year 2014,
https://data.worldbank.org/indicator/AG.LND.AGRI.ZS, last access: 4
July 2018), and with around 1200 large dams (European Working Group on Dams
and Floods, 2010).
The meteorology forcing
In order to study the sensitivity of the optimization results to different
forcing data, three meteorology forcings are used: WFDEI_GPCC, WFDEI_CRU
and CRU_NCEP. The WFDEI_GPCC and WFDEI_CRU (3-hourly, 0.5∘) are
based on the WFDEI meteorological forcing data which was produced using WATCH
(WATer and global CHange) Forcing Data (WFD) methodology applied to
ERA-Interim data at 0.5∘ (Weedon et al., 2014;
http://www.eu-watch.org/data_availability, last access: 4 July 2018).
The WFDEI is from 1979 and updates until now with eight meteorological
variables at 3-hourly time steps. The precipitation of WFDEI_GPCC and
WFDEI_CRU is corrected by GPCC (Global Precipitation Climatology Centre) and
CRU (Climatic Research Unit), respectively. The CRU_NCEP (6-hourly,
0.5∘) combines the CRU TS.3.1 (0.5∘, monthly) climatology
covering 1901–2012 and the NCEP (National Centers for Environmental
Prediction) reanalysis (2.5∘, 6 h) beginning in 1948
(https://vesgint-data.ipsl.upmc.fr/thredds/fileServer/IPSLFS/igcmg/IGCM/INIT/SRF/IPSLCM5CHS/METEO/CRU-NCEP/README_CRUNCEP.txt, last access: 4 July 2018). The precipitation
of the three forcings is compared with the IB02 which is a gridded daily
rainfall dataset for the Iberian Peninsula with 0.2∘ resolution and
covers 1950 to 2003 (Belo-Pereira et al., 2011). It is generated by using
ordinary kriging from more than 2400 quality-controlled stations.
The GRDC dataset
The Global Runoff Database collects the monthly river discharge from most
basin agencies around the world (more than 9300 stations) with an average
record length of 43 years. Although the quality of the observations is
unknown (e.g., monitoring the river transect, velocity measurements, etc.),
the GRDC datasets are the most complete river discharge dataset available
today. It is hosted by the German Federal Institute of Hydrology
(Bundesanstalt für Gewässerkunde or BfG; https://www.bafg.de/GRDC/EN/Home/homepage_node.html,
last access: 4 July 2018).
Integration of GRDC into ORCHIDEE
The location of some stations in the GRDC dataset might be incorrect for
either the longitude or latitude coordinate due to simple typos, logical
errors in the original coordinates or a swapped order of the coordinate
digits (Lehner, 2012). Due to this uncertainty, a quality control is applied
for GRDC when matching it with the corresponding HTUs in the river routing
model. For each GRDC station, the corresponding catchment surface in the
model is estimated. The matching process is stringent, and the GRDC
qualification is restricted by two matching criteria: (1) the difference in
upstream area between GRDC and the model is less than a pre-defined
percentage and (2) the distance between GRDC and the model is less than a
pre-defined distance. The higher the two thresholds are, the more the
matched GRDC stations can be positioned on the model's basin representation.
Meanwhile, the high threshold increases the uncertainties in the GRDC data
due to the errors in location and upstream area. By compromising between the
two contradictory requirements (the number of GRDC stations and the precision of the data),
we choose the threshold for upstream area difference and
distance to be 10 % and 25 km, respectively. Under this constraint, 27
GRDC stations are qualified among all 65 stations over the Iberian Peninsula
domain (34∘ N–45.5∘ N, 10∘ W–5.5∘ E; Fig. 2).
It should be noted that one GRDC station can
match with several model HTUs that locate in different model grids. In this
case, the HTU with the lowest upstream area difference is chosen. Therefore,
the GRDC station is not necessarily in the same model grid as the model HTU.
The river network (blue lines) and the GRDC stations (solid dots
represent the 27 qualified stations and the gray triangles represent
unqualified stations) over the study domain.
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The evaporation products
The bias-corrected evaporation deduced from the assimilation is compared with
the GLEAM (Global Land Evaporation Amsterdam Model; Martens et al., 2017;
https://www.gleam.eu, last access: 4 July 2018) product. GLEAM
provides daily evaporation from 1984 to 2011 at 0.25∘. The
evaporation is estimated by a minimalistic Priestley–Taylor potential
evaporation model with the majority of inputs estimated from remote sensing.
It uses the microwave-derived soil moisture, land surface temperature and
vegetation density, and the detailed estimation of rainfall interception
loss. The rainfall interception loss is estimated separately using the Gash
analytical model which considers the canopy storage capacity, coverage and
the ratio of mean evaporation rate from wet canopy. There are several
versions of GLEAM data available, and we choose the latest version v3.1a. The
precipitation forcing of GLEAM v3.1a is from the Multi-Source
Weighted-Ensemble Precipitation (v1.2).
Experiments design
An ORCHIDEE simulation is performed to obtain the Qfg and
the corresponding R and D. The ORCHIDAS with L-BFGS-B algorithm explores
the full space of x by perturbing a separate x (xi) over the
ith upstream catchment (i=1,2, … , Nopt;
Nopt is the total number of optimized x depending on the number
of observation stations) in each iteration. To save computing time, the river
routing parameterization (forced by corrected R and D) rather than the
full ORCHIDEE is executed. The total execution time depends on the number of
parameters to be optimized, the length of simulation years and the number of
iterations. Multi-level parallelisms of the assimilation are implemented to
achieve the high computational efficiency. In each iteration, the
assimilation can run with Nopt “river routing” simulations,
with each “river routing” model parallelized with Nrouting CPUs
(Nopt=27, Nrouting=16 over the study domain). Over
the Iberian Peninsula, the range of x is defined between 0 and 20 which is
determined by Qfg and Qobs.
In order to check the impacts of prior information xprior
on the optimization convergence time, the xprior is set to
a constant value “1” (xprior_1) or a “pre-estimated
prior” (xprior_ref, defined as the ratio of
Qobs/Qfg), separately. The optimal x
values are assigned over the whole study domain. The x of the sub-catchment
without the GRDC station available is set to 1 (no correction). The
climatology values (e.g., over 1979–2014) are applied to fill the missing
observation values over a certain period. In the case of more than one GRDC
station located in the same model grid, the averaged correction factor is
used.
(a) The variation in cost function J (unit: 1;
logarithmic y axis) with iterations for xprior_1
(“xprior=1”, in blue) and for
xprior_ref (“xprior= pre-estimated
prior”, in red). The iterations 6–15 are enlarged in the window (normal
y axis). The Norm_BIAS of optimized river discharge after 7 iterations
for xprior_1 (b) and for
xprior_ref (c).
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The setup of assimilation experiments for n years (n=10,
1980–1989) and k iterations (k=10) with m(m=27) correction factors
(x) each year (x is different over years). (a) The ith year
(Yi) optimization is initialized by the end of
Yi-1 optimization; (b) the initial condition of Yi
optimization is obtained by running Yi-1 optimization fed with the
same x as Yi; (c) optimizing n years together with 1-year
spin-up at the beginning of n years. The Y1SP0 and Y1SP1 perform the optimization year by year. The
blue and red colors mean optimization and spin-up simulations, respectively.
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The optimization results are not sensitive to the choice of
xprior, but the convergence time indeed depends on
xprior. Figure 3a shows that the
xprior_ref method requires less iteration to converge than
xprior_1 (7 and 15–20 iterations, respectively). The
value of the cost function of xprior_ref method is lower
than that of xprior_1 for all iteration steps. The
normalized bias (Norm_BIAS) of discharge after 7 iterations is less than
0.3 for the xprior_ref method, while it is larger than 0.6
over most southern regions for xprior_1 (Fig. 3b and c).
The oscillation of J at the steps 3 and 5 could be due to the fact that
the calculation of the gradient of J by finite difference is not optimal.
It is also possible because the L-BFGS-B partly explores the physical range
during the first few iterations to estimate the Hessian of the cost function
for convergence.
Norm_BIAS=Qsim-QobsQobs.
We choose xprior set by xprior_ref for
n years (n=10, 1980–1989) experiment with iteration number k being 15
and number of correction factor m (i.e., the number of GRDC station) being
27. The x values vary with different years. Due to the slow variation in
aquifer levels, a spin-up is necessary before optimization to get the
equilibrium of aquifer levels in the LSM. The spin-up creates the aquifer
initial states (Acorr0,Acorr1,Acorr2, … , Acorr10) at the start of
the assimilation cycles over each ORCHIDEE model grid (Fig. 4), making it
adapt to the bias-corrected aquifer states.
dAcorridt=∫Sx(R2+D2)-Qcorr,2+Qcorr,1,0≤i≤10
To test different assumptions of errors in initial conditions, we implemented
different optimization methods with each method results in a group
(m × n) of optimal x (Fig. 4, Table 1). In method 1, the
optimization is carried out year by year with 1-year spin-up for each
iteration (“Y1SP1” here after). The x of the optimization year is applied
during simulation. Method 2 is similar with Y1SP1 except that it uses
optimized aquifer levels from the previous year (“Y1SP0” here after). This
method assumes the final state variables (aquifer
levels) of the optimal solution at the current optimization year is the best
initial condition for the following assimilation year. In method 3, the
optimization is done continuously over 10 years with 1-year spin-up at the
beginning of each 10-year simulation (“Y10C” here after). The Y10C
optimizes 270 correction factor x over 10 years together, while the Y1SP1 and Y1SP0 optimize the
10 years separately with 27 x each year. The “river routing” model
running years required by the three methods are 8100
(=m × 2 × n × k), 4050
(=m × n × k) and 44 550
[=m × n × (n+1) × k], respectively. Take
the Y1SP0 for example, in each iteration the correction factor x is
perturbed by m times. For each perturbation, the ORCHIDEE river routing
model runs once with one x (e.g., xi at the ith sub-catchment)
being perturbed while the x of other sub-catchments are kept the same.
Therefore, the total number of years required for m stations, n
iterations and k years assimilation is m × n × k.
For all experiments, the optimization is carried out at daily timescale, and
the diagnostics are performed for annual averages where we assume the water
storage variation is neglectable.
The assimilation and simulation experiments.
Name
Atmospheric forcing
Method
FG(WFDEIG)
WFDEI_GPCC
no assimilation
FG(WFDEIC)
WFDEI_CRU
no assimilation
FG(CRUN)
CRU_NCEP
no assimilation
Y1SP0(WFDEIG)
WFDEI_GPCC
Y1SP0 assimilation
Y1SP1(WFDEIG)
WFDEI_GPCC
Y1SP1 assimilation
Y10C(WFDEIG)
WFDEI_GPCC
Y10C assimilation
Y1SP0(WFDEIC)
WFDEI_CRU
Y1SP0 assimilation
Y1SP0(CRUN)
CRU_NCEP
Y1SP0 assimilation
Note: all runs are from 1980 to 1989 with 0.5∘ spatial
resolution; FG stands for “First Guess”.
In order to further identify the impacts of atmospheric forcing on
optimizations (e.g., optimal correction factor x), we measure the
“Uncertainty” in the variable (“var” in equation; “var” refers to x, corrected
evaporation, etc.) by Eq. (10). The higher the “Uncertainty” is, the larger the
uncertainty is. The 0 value means that all three “var” values are equal.
Uncertainty(var)=var1-var2+var2-var3+var1-var33
The river discharge simulations from 1980 to 1989 using WFDEI_GPCC
(1st row), WFDEI_CRU (2nd row) and CRU_NCEP (3rd row) forcings. Left column: the
correlation coefficient of river discharge between observations and
simulations; Right column: the Norm_BIAS of simulated river discharge.
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Results and discussions
Evaluation of river discharge without assimilation
Figure 5 displays the first-guess simulation forced with different
atmospheric forcing: WFDEI_GPCC (Fig. 5a–b), WFDEI_CRU (Fig. 5c–d) and
CRU_NCEP (Fig. 5e–f). The Norm_BIAS and correlation coefficient
(computed by the annual mean values) are used to measure the qualities of the
simulated discharge. The diagnostics at each GRDC station are spread to the
entire upstream basin which contributes to the errors in discharge
downstream. The correlation coefficient between FG (forced by WFDEI_GPCC and
WFDEI_CRU) and observation is greater than 0.6 over most regions, but it is
less than 0.2 over certain regions (e.g., middle and southeast of the Iberian
Peninsula, Fig. 5a and c). The correlation coefficient obtained by using
CRU_NCEP forcing is less than 0.2 for most regions (middle and west of the
Iberian Peninsula), which is worse than the simulation from WFDEI_GPCC and
WFDEI_CRU. Wang et al. (2016) also show the relatively poor performance of
CRU_NCEP in simulating global land surface hydrology and heat fluxes by
using the the Community Land Model (CLM4.5). The spatial pattern of the
absolute bias in river discharge varies with the atmospheric forcing (not
shown). The normalized bias is then applied to measure the river discharge
simulation. The Norm_BIAS in discharge shows consistent spatial
distribution for simulations of the three forcings. The Norm_BIAS
(positive) is higher than a factor of 1.5 over the south and northeast of the
Iberian Peninsula, which means an overestimation of river
discharge. The Norm_BIAS is small
(within ±0.3) over the north, west and southeast of the region
(Fig. 5b, d and f).
The optimization results from 1980 to 1989 using the three methods
(1st row: Y1SP1; 2nd row: Y1SP0; 3rd row: Y10C) forced by WFDEI_GPCC. Left column:
the optimized correction factor x; Middle column: the correlation coefficient of
river discharge between observations and optimizations; Right column: the
Norm_BIAS of optimized river discharge.
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Comparison of the three optimization strategies forced by
WFDEI_GPCC
We apply the three assimilate approaches (Y1SP1, Y1SP0, Y10C) to ORCHIDEE
simulations to correct the bias in discharge simulation by
WFDEI_GPCC forcing. Figure 6 (left column) displays the geographical
distribution of the average correction factor x obtained after the
assimilation. The x values range between 0 and 1.5 over the study domain. The
perfect discharge simulation corresponds to x equal to 1. The x value lower than
1 means the discharge in FG (WFDEI_GPCC) is overestimated and
thus a decrease in R and D is required, and vice versa for x being higher than
1. The further x is away from 1, the larger the corrections of runoff and
drainage are. The three methods display similar spatial distribution pattern
with x being less than 0.5 over the south and east of the Iberian Peninsula and
x being higher than 1 over the north of the Iberian Peninsula. This spatial
distribution of x is highly consistent with the pattern of
Norm_BIAS in FG (discharge overestimated in south and northeast, underestimated in
north).
Figure 6 (central column) shows the correlation coefficient between corrected
discharge and GRDC observations. After assimilation, the correlation of the
optimized discharge and observations is larger than 0.8 over most regions.
The correlation coefficient for assimilated discharge and observation is less
than 0.6 (but higher than 0.4) over some regions and seems very dependent on
the forcing. This is probably because there is a contradiction of x between
the upstream and downstream stations and thus the method has difficulties
finding a compromise (e.g., over the Ebro Basin). In general, the regions
with low correlation coefficient are forcing dependent, while the regions
with high correlation coefficient are very consistent among different
forcing. Figure 6 (right column) gives the Norm_BIAS in discharge between
assimilations and observations. After assimilation, this positive bias in
river discharge has been significantly reduced (within ±0.3). It should
be mentioned that the xprior_ref is able to capture the
general distribution pattern of optimal x, but the performance of river
discharge estimation is significantly improved through optimization. The role
of optimization is to find an appropriate correction factor when there are
several basins (with observations) overlaps at upstream
The annual cycles of river discharge for “First Guess” (FG) forced
by WFDEI-GPCC (black), Y1SP1 (blue), Y1SP0 (green), Y10C (yellow) and GRDC
observations (red) over the Alcala Del Rio station (37.52∘ N, -5.98∘ W)
on the Guadalquivir river. The dotted lines show the
trend.
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A common validation approach is to compare the assimilated river discharge
with other independent data sources. However, the river discharge
observations are limited, and the GRDC is the only comprehensive river
discharge datasets at global scale so far. To overcome this limitation, the
assimilated river discharges are also validated over the catchments where the
GRDC stations are discarded during assimilation. Figure 7 shows the annual
mean of river discharge over the Alcala Del Rio station (37.52∘ N,
-5.98∘ W) on the
Guadalquivir river (located in the southwest of Spain) before and after
correction. The observation of this station is not assimilated due to its
large upstream area difference
(18.39 % > 10 %) between
model (55 635 km2) and GRDC (46 995 km2). The overestimated
discharge simulated by the model at this station is also corrected because it
benefits from the correction factor estimated at the Cantillana station
(37.59∘ N, -5.83∘ W; 44 871 km2) which is located
15.3 km upstream of Alcala Del Rio station of the Guadalquivir river
(southwest of the Iberian Peninsula). Between the two stations, there are
several tributaries that flow to Alcala Del Rio station, which leads to
different annual mean river discharges at Cantillana
(49.7 m3 year-1) and Alcala Del Rio stations
(94.8 m3 year-1). This result illustrates that this approach is
able to correct the river discharge over the entire basin. The discharges for
certain sub-basins without assimilated observations (e.g., observation
unavailable or GRDC stations discarded) are corrected by x as well.
Although the validation datasets are from the same GRDC source, they are from
other independent observation stations thus can be seen as an independent
validation (“first order validation”).
In summary, all three methods (Y1SP1, Y1SP0 and Y10C) are able to
improve the river discharge simulation by ORCHIDEE LSM. The correlation
coefficient and Norm_BIAS in discharge obtained from the three methods are generally
consistent. The correlation coefficient of the Y10C method in the northeast is lower
than that of Y1SP0 and Y1SP0, which is probably resulting from its poor
quality of atmospheric forcing. The Y1SP0 consumes less computing time than
Y1SP1 and Y10C, and it does not worsen the optimization results. By
compromising between the accuracy of results and the computing time, we
choose the Y1SP0 method for further assimilation.
The above assimilations are performed with the same forcing (WFDEI-GPCC) by
assuming the errors in discharge are caused by model defect (e.g., model
parameterization, model structure, etc.). The uncertainties in simulated
discharge also result from the atmospheric forcing. The role of atmospheric
forcing in assimilation is discussed in the following section.
The correction factor x obtained from Y1SP0 forced
by (a) WFDEI_CRU, (b) CRU_NCEP, (c) WFDEI_GPCC
and (d) the “Uncertainty” (defined by Eq. 10) of x by different
forcing. All values are averaged over the period 1980–1989.
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The sensitivity of the optimizations to atmospheric forcing
In order to understand the response of the optimizations to different
atmospheric forcing with different precipitation sources, the ORCHIDAS was
also run with WFDEI_CRU and CRU_NCEP forcing using the Y1SP0 optimization
strategy. Using two other different forcings for the assimilation can allows
us to understand how important the forcing uncertainty affects the correction
factor. The multi-year mean correction factor x obtained from WFDEI_CRU
(Fig. 8a), CRU_GPCC (Fig. 8b) and WFDEI_GPCC (Fig. 8c) displays quite
consistent spatial patterns. The coverage of low correction factor (blue in
Fig. 8a–c, corresponds to large correction) obtained from CRU-NCEP is larger
than that obtained from WFDEI_CRU and WFDEI_GPCC. This is because the
positive bias in discharge of the FG simulation forced by CRU-NCEP is larger
than that by WFDEI_CRU and WFDEI_GPCC. Besides the atmospheric forcing, the
uncertainties could also originate from boundary conditions (e.g.,
topographic or other land surface features), model parameter, model structure
or missing processes. For all forcing, the x is less than 0.3 (but greater
than 0) over the south, which implies that the error in discharge is probably
resulted from the missing model processes (human activity). Over the north,
the x values are close to 1 (discharge well simulated) for all three
forcings, which indicates the correction comes from model “random” error
(natural discharge) rather than the system error (e.g., missing processes).
The evaporation (E, in mm day-1) before assimilation (1st row),
change of evaporation (dE, in mm day-1) after and before
assimilation (2nd row) and the ratio of dE and runoff + drainage (3rd row)
for forcing WFDEI-GPCC (1st column), WFDEI-CRU (2nd column), CRU-NCEP
(3rd column) and the “Uncertainty” (defined by Eq. 10) in different
forcing (4th column) averaged from 1980 to 1989.
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The uncertainty in x by the three forcings is small for most regions
(Fig. 8d). The high uncertainty in x over the Adour (southwestern France) and
the Chelif (in Algeria) river basins correspond to the large uncertainty in
the different atmospheric forcing. This result demonstrates the obtained
correction factor x is robust in spite of using different atmospheric
forcing. This is also demonstrated by comparing the precipitations between
the three forcings and the IB02 dataset. Compared to the IB02, all the three
forcings overestimate rainfall in the Iberian Peninsula (Fig. S1a–c), but
none of these error patterns resembles that of the proposed E correction
(Fig. 9e–g). Unlike the pattern of the correction factor (Fig. 8a–c), the
ratios of annual mean precipitation between the three forcings and the IB02
are higher than 1 over most regions (Fig. S1d–f). Therefore, the
precipitation forcing error is likely not the dominant factor in determining
the correction factor distribution.
In summary, the assimilation approach is able to correct errors in lateral
water balance despite using different forcing. Recalling that the corrected
R+D (through x) and the precipitation are known, we then transfer the optimal
correction factor x to the vertical water balance equation (Eq. 5) to derive
the bias-corrected evaporation. This will enable us to understand the
impacts of assimilation on evaporation.
Evaporation estimations through the optimal correction factor
The evaporation of the FG simulation by different forcings show a quite consistent
spatial distribution (Fig. 9a–c) and small uncertainty (< 0.2 mm day-1,
Fig. 9d) with the value being higher over the north than south. The change
of evaporation (dE) induced by the correction is consistent for three forcings
(Fig. 9e–g) with low uncertainties (Fig. 9h). It should be mentioned that
the evaporation for the regions without GRDC stations are not corrected
(i.e., correction factor x equals 1) such as southern France, western
Portugal, and northwest, south and southeast of Spain (blank regions in Fig. 8).
The dE is positive (around 0.2 to 0.4 mm day-1) over the south and northeast where
the evaporation is underestimated in FG. Cazcarro et al. (2015) show a large
blue water footprint (volume of surface and groundwater consumed for
production of an item) of human activity over the south (Jaén, Sevilla, and
Malaga provinces), northeast (Palencia, Burgos, La Rioja, Navarra and
Valladolid provinces), north (Tarragona province) and middle (Toledo
province) of Spain (Map. 1 of that paper). The large dE over the south and
northeast obtained in the current study is consistent with the blue water
footprint of Cazcarro et al. (2015). Figure 9i–k plot the change of the ratio
of water demand (dE) and water supply (R+D). This ratio measures the degree of
water shortage. The greater the ratio, the higher the level of water shortage.
The ratio is larger over the south and northeast of Spain, which is consistent
with the results from other studies that measure the water deficits
(Rodríguez-Díaz et al., 2007) and water exploitation index
(Pedro-Monzonís et al., 2015) in Spain. Since we assume that the
missing human processes are the main error in ORCHIDEE, the dE and dE / (R+D)
indicate the changes induced by human processes. The spatial patterns of
dE and dE / (R+D) are quite consistent with human water exploitation, thus the
model missing processes (e.g., human water usage) is considered as the
dominant contribution to x.
We also tested the possibility of improving the river discharge estimation
by using an annual constant correction factor to evaporation (XEcorr),
which can be derived from Eq. (6).
XEcorr≈E+1-x⋅R+DE
Ecorr=XEcorr⋅E
Although Eqs. (11)–(12) are able to improve river discharge estimation by
modifying soil moisture, the energy and water balance are not conserved. One
solution could be to run the full ORCHIDEE LSM in the assimilation system
with the same cost function as Eq. (7). In this way, the intermediate
variables are adjusted towards optimal river discharge with the modification
of evaporation. This approach executes the full ORCHIDEE model, thus it is very
time consuming and is beyond the scope of the current study.
The interannual variation in correction factor and water cycle
The interannual cycles
All the results so far are obtained by averaging multi-year mean values
which provide us the bias correction information at spatial scale. To
understand the interannual cycles of the correction and its possible
contribution, we analyze the assimilation results over two stations in the south
of Spain where the discharge correction is large during the period of 1980–1989 (Fig. 8).
The optimization results by different atmospheric forcings
(WFDEI-GPCC in black, WFDEI-CRU in green and CRU-NCEP in blue) over the
Puente De Palmas station on the Guadiana River (a–c,
38.88∘ N, -6.97∘ W; 48 515 km2) and over the Masia
De Pompo station on the Júcar River (d–f, 39.15∘ N, -0.65∘ W;
17 876 km2): (a, d) annual river
discharges; (b, e) runoff coefficient; (c, f) optimized
correction factor x for the simulated/assimilated river discharge (First
Guess in dark color, Y1SP0 in light color) with respect to GRDC observations
(in red) from 1980 to 1989.
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The Puente De Palmas station is located on the Guadiana River (southwest of the
Iberian Peninsula) with an upstream area of 48 515 km2. The three FG
simulations (with different forcing) significantly overestimate the river
discharge and the runoff coefficient (ratio of discharge and precipitation),
while the FG(WFDEIG) and FG(WFDEIC) underestimate the interannual
variability comparing with observations (Fig. 10a–b). The
standard deviation of the annual means for observation, FG(WFDEIG),
FG(WFDEIC) and FG(CRUN), are 33.8, 28.8, 25.2
and 34.3 m3 s-1, respectively. One reason could be the variation in water
usage by irrigated agriculture which occupies 90 % of the blue water usage
(surface water and groundwater) in this semiarid basin (Aldaya and Llamas,
2008) or model errors. Besides, there are many interconnected wetlands and
structurally complex hydrogeological boundaries between the two
upper Guadiana aquifer in the upper Guadiana River basin (Van Loon and Van
Lanen, 2013). These complex features are difficult to represent in the model,
thus a large bias exists in river discharge of ORCHIDEE. The correction factor
corrects these model defects (Fig. 10c) and it demonstrates good skill in
correcting the interannual variability in discharge and runoff coefficient
(Fig. 10a–b).
The Masia De Pompo station (17 876 km2) is on the
Júcar River (southeast of Spain). The observations over the year 1983
and 1988–1989 are obtained from the climatology values due to the
unavailability of GRDC data during this period. During 1980–1989, the
interannual variation in observed discharge (and runoff coefficient) and FG
simulation is quite inconsistent (Fig. 10d–e). This is probably caused by
the surface water usage which occupies about 55 % over this basin (Kahil
et al., 2016). Most of them are used for agriculture (> 80 %)
and urban (> 10 %). Although the improvements in assimilated
discharge are small, the correction factor is able to capture the interannual
variability in observations (Fig. 10d and f).
In summary, the interannual variation in river discharge in the FG simulation
and observations do not agree with each other over the Guadiana River basin
and the Júcar River basin during 1980–1989. The human water usage (e.g., groundwater or surface water
extraction) process, which is neglected in current ORCHIDEE model, is likely
to play an important role in river discharge variation. The optimized
correction factor (varies each year) improves the interannual variability of
the modeled river discharge.
The interannual variation in correction factor x (σ(x)x‾; a, d, g), simulated river discharge without
assimilation (σQsimQsim‾; b, e, h) and optimized
river discharge (σQoptQopt‾; c, f, i) for
Y1SP0_WFDEIGPCC (1st row), Y1SP0_WFDEICRU (2nd row) and Y1SP0_CRUNCEP (3rd
row) averaged over 1980–1989.
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The geographical distribution
To further understand the interannual variability in corrections over the
entire Iberian Peninsula region, Fig. 11 plots the spatial distribution of
interannual variability in correction factor x and river discharge which is
quantified by the coefficient of variation as used by Déry et al. (2011) and
Siam and Eltahir Elfatih (2017). In the FG (WFDEI_GPCC)
simulation, the interannual variation in discharge is lower than 0.4 over
most regions, which indicates an underestimation of interannual variability
of river discharge in FG. The inter-annual variability in discharge is
increased after assimilation over the south and northeast. This change could be
attributed to the fluctuation of correction factor (human water usage) over
these regions. This result agrees with the results (Map. 6) of
Cazcarro et al. (2015) with more large dams in the south and northeast (natural discharge
greatly affected by human) than the northwest of Spain (natural discharge less
affected by human). The interannual variability in correction factor x and
discharge for Y1SP0 (CRUN) is different from others, which mainly results
from the different atmospheric forcing.
Comparison of evaporation (E, in mm day-1, 1st row) between
GLEAM (v3.1) and FG (First Guess), as well as E(2nd row), precipitation
(P, in mm day-1, 3rd line), P-E (in mm day-1, 4th row) and
P-E (relative value between 0 to 1, 5th line) between GLEAM (v3.1) and
assimilated values using different forcings (1st column: WFDEI-GPCC; 2nd
column: WFDEI-CRU; 3rd column: CRU-NCEP; 4th column: “Uncertainty” (defined
by Eq. 10) of using different forcing) averaged from 1980 to 1989.
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Comparison of bias-corrected evaporation with GLEAM data
In order to evaluate the bias-corrected evaporation, Fig. 12a–h compare the
GLEAM product (v3.1a) with FG and with bias-corrected E by assimilation
using WFDEI_GPCC, WFDEI_CRU and CRU_NCEP forcing. Due to the
unavailability of parts of GLEAM's atmospheric forcing (e.g., air pressure,
air humidity, air speed, etc.) and difficulty of maintaining a coherence with
other forcings, the assimilation system does not run with GLEAM's
precipitation input. We find a large difference between GLEAM and FG, which
indicates that the evaporation is quite uncertain for different estimations.
The geographical distribution and magnitude of difference in E between
GLEAM and FG is highly consistent with that between GLEAM and bias-corrected
values by using different forcings (Fig. 12a–c, and e–g). The systematic
negative difference is higher than the uncertainties in bias-corrected E
with different forcing (Fig. 12d and h). Parts of the differences are
explained by the lower P of GLEAM than the ORCHIDEE forcing (Fig. 12i–l).
Generally, the P-E (in mm day-1) of GLEAM is higher than the
bias-corrected value associated with small uncertainties (Fig. 12m–t).
Because the bias-corrected P-E are corrected by GRDC observed river
discharge, the P-E (≈ river discharge) of GLEAM is very likely to
be higher than GRDC observations over Iberia. This result indicates that some
processes are probably also missing in GLEAM v3.1. We also compared our
bias-corrected E with GLEAM v1 data (Miralles et al., 2011), and we find
the P-E between GLEAM v1 and bias-corrected values are quite consistent for
different forcings. The results are quite consistent when comparing the
corrected E with several other products which are obtained by using
different methodology and forcings (e.g., Jung et al., 2009; Vinukollu et
al., 2011; Mueller et al., 2013). Considering the availability of P-E for
GLEAM data which allows us to compare it with the bias-corrected value, only
the results of GLEAM are shown.
Conclusions
There has been several studies working on the estimation of fresh water input
from continent to ocean (e.g., the Mediterranean Sea) based on an observation
or modeling approach (e.g., Boukthir and Barnier, 2000; Mariotti et al.,
2002; Struglia et al., 2004; Peucker-Ehrenbrink, 2009; Ludwig et al., 2009;
Szczypta et al., 2012). However, these estimations are limited either by the
coarse temporal resolution for observation approach or by the
non-comprehensive representation of physical processes (e.g., human
activities) for the modeling approach. As a result, the fresh water estimations
are accompanied with large uncertainties among varies studies. This proposed
methodology aims to improve the estimation of continental water cycles by
merging the merits of observations and modeling approach through data
assimilation.
The basis of the method is the vertical and lateral water balance equations.
The method assumes that the precipitation minus evaporation from the model
simulation is an appropriate first guess so that all the errors in river
discharge end up with runoff and drainage. Under this assumption, the river
discharges simulation at river outlet are expected to be improved by
correcting the runoff and drainage (inputs for river routing model).
The idea is achieved by embedding a river routing scheme of ORCHIDEE LSM and
GRDC river discharge observations into a data assimilation system
(ORCHIDAS). The system can run in multi-level parallel computing mode
(both the routing model and the optimization are parallelized). The river
discharge is optimized through applying a correction factor x to model runoff
and drainage which translates errors in estimated P-E.
The method has been explained through its application over the Iberian
Peninsula with 27 GRDC stations during 1979–1989 with x values being
different each year. The main conclusions are the following: first, the
optimization results are not sensitive to x prior information
xprior and assimilation strategies, but the setting of
xprior by a “pre-estimated-prior” (defined as
Qobs/Qfg) indeed converges faster than
other xprior values. The method Y1SP0 (the model spin-up
uses the optimal aquifer levels of the previous optimization year)
demonstrates high computing efficiency and comparable discharge accuracy
comparing with the other two methods (Y1SP0, Y10C), thus the Y1SP0 is
recommended (e.g., over the full Mediterranean catchment). Second, the
largest correction of discharge is found over the south and northeast of the
Iberian Peninsula. These regions are characterized by large blue water
footprint with large groundwater and surface water usage by human activity.
It implies that most of the corrections by x represents the missing human
processes (at least in the south of the study domain). This is consistent
with the fact that the ORCHIDEE model neglects the human processes (e.g., dam
operation, irrigation, etc.). The discharge correction over north of the
Iberian Peninsula is relatively small, where it is mainly due to model
systematic error. The correction factor x can also cover errors in the
model structure, model parameter or boundary conditions (e.g., land surface
characteristics imposed to the model). Third, the assimilated discharges
reveal lower bias (from > 100 % to < 30 %) and higher
interannual variability (due to the fluctuation of water usage) than
uncorrected ones. Fourth, the bias-corrected evaporation are compared with
the GLEAM v3.1a product. The E of GLEAM is lower than the optimized E,
while the P-E of GLEAM is higher than the optimized values. This different
P-E could be caused by the different P forcing and the missing processes
in the GLEAM model.
The method takes into account both gauged rivers (usually large rivers) and
un-gauged rivers, and it provides discharge estimates at a daily timescale from
1980 to 2014 with the time range depending on atmospheric forcing. By using the
correction factor of an adjacent catchment, this method also improves the river
discharge simulation for the catchment without assimilating observations.
Besides, this method fills the gap of the missing data period (e.g., war,
instruments, etc.) by climatology values, thus the data are complete over
the whole period. The proposed method is supposed to be superior to the
simple water-balance methods, because a LSM estimates E at sub-diurnal timescales
with physically based equations and takes advantage of the spatial distribution
of the P and P-E.
The result implies the necessity of parameterizing the human water uptake
process in the ORCHIDEE LSM. Besides, the poor quality of the river
discharge observations (e.g., 68 % of stations are discarded over the Iberian
Peninsula) calls for high-quality data. The optimized correction factors
x are model and atmospheric forcing dependent. It is encouraged to apply this
assimilation method to other models, which will allow us to identify the
sources of errors (e.g., model missing process or forcing data). To improve
the calculation efficiency, this study uses annual mean correction factors
without considering its seasonal variation, thus the seasonal discharges are
not improved. One issue of the x optimization could be the equifinality with a
number of optimized x result in a similar river discharge downstream.
Future developments can be made towards generating ensemble optimal x to
better assess the uncertainties associated with each parameter x. This
assimilation method can be applied for water cycle studies, data
intercomparison and riverine fresh water estimation over other basins
(e.g., the full catchment of the Mediterranean Sea).