Recent advancements in catchment hydrology (such as understanding catchment
similarity, accessing new data sources, and refining methods for parameter
constraints) make it possible to apply catchment models for ungauged basins
over large domains. Here we present a cutting-edge case study applying
catchment-modelling techniques with evaluation against river flow at the
global scale for the first time. The modelling procedure was challenging but
doable, and even the first model version showed better performance than
traditional gridded global models of river flow. We used the open-source
code of the HYPE model and applied it for >130 000 catchments
(with an average resolution of 1000 km2), delineated to cover the
Earth's landmass (except Antarctica). The catchments were characterized using
20 open databases on physiographical variables, to account for spatial and
temporal variability of the global freshwater resources, based on exchange
with the atmosphere (e.g. precipitation and evapotranspiration) and related
budgets in all compartments of the land (e.g. soil, rivers, lakes, glaciers,
and floodplains), including water stocks, residence times, and the pathways
between various compartments. Global parameter values were estimated using a
stepwise approach for groups of parameters regulating specific processes and
catchment characteristics in representative gauged catchments. Daily and
monthly time series (>10 years) from 5338 gauges of river flow
across the globe were used for model evaluation (half for calibration and
half for independent validation), resulting in a median monthly KGE of 0.4.
However, the World-Wide HYPE (WWH) model shows large variation in model
performance, both between geographical domains and between various flow
signatures. The model performs best (KGE >0.6) in the eastern USA,
Europe, South-East Asia, and Japan, as well as in parts of Russia, Canada,
and South America. The model shows overall good potential to capture flow
signatures of monthly high flows, spatial variability of high flows,
duration of low flows, and constancy of daily flow. Nevertheless, there
remains large potential for model improvements, and we suggest both redoing
the parameter estimation and reconsidering parts of the model structure for
the next WWH version. This first model version clearly indicates challenges
in large-scale modelling, usefulness of open data, and current gaps in
process understanding. However, we also found that catchment modelling
techniques can contribute to advance global hydrological predictions.
Setting up a global catchment model has to be a long-term commitment as it
demands many iterations; this paper shows a first version, which will be
subjected to continuous model refinements in the future. WWH is
currently shared with regional/local modellers to appreciate local
knowledge.
Introduction
Global hydrological models with various properties and structures are
provided by several modelling communities (see reviews by e.g. Bierkens et
al., 2015, and Sood and Smakhtin, 2015), although it is well recognized that
uncertainties associated with existing models are high when simulating the
water cycle at the global scale (e.g. Wood et al., 2011). To overcome this,
some communities suggest hyper-resolution (Bierkens et al., 2015), while
others propose better coupling with Earth observations (Sood and Smakhtin,
2015). In this paper, we argue for improving global hydrological-model
performance by applying methods from the catchment modelling community.
In catchment modelling the water balance and fluxes are calculated within
water divides. The geographic unit for process descriptions is thus a
polygon defined by topography instead of a grid cell defined by size,
without physical boundaries. Recently, new topographic data with high
resolution (Yamazaki et al., 2017) have enabled definition of catchments
globally. Having catchments as a calculation unit makes it possible to apply
an ecosystem approach and account for co-evolution of processes at the
landscape scale (e.g. Bloeschl et al., 2013). Model parameters can thus be
linked to catchment state from interacting entities and not only to
aggregation of separated building blocks (grids) of the catchment. The
structure of the catchment model is usually a function of the modellers'
hydrological understanding, and it is admitted that model parameters cannot
be measured directly in many cases, but have to be estimated (Wagener,
2003).
Catchment modellers have a long tradition of evaluating model performance
against observations of river flow (e.g. Bergström and Forsman, 1973;
Beven and Kirkby, 1979; Lindström et al., 1997) as this is the
integrated result of hydrological processes at the catchment scale and,
moreover, is relatively easy to monitor. In the early 1970s, model
parameters were calibrated using rather simple curve fitting towards
observed time series of river flow in a specific catchment outlet (e.g.
Bergström and Forsman, 1973). Since then the methods for parameter
estimation have become more sophisticated, with the focus on uncertainties in
parameter values. The catchment models themselves are normally quick to run
even on a personal computer, which has allowed the methods for evaluating
and calibrating catchment models to become computationally heavy, such as
GLUE (Beven and Binley, 1992), DREAM (Laloy and Vrugt, 2012), or methods in
the SAFE toolbox (Pianosi et al., 2015). Nevertheless, with increasing
computational capacity, these methods should be possible to apply also
across large domains with numerous river gauges.
The catchment community advocates the potential to advance science by
addressing a larger domain with multiple gauged catchments than just
exploring one single catchment at a time (Falkenmark and Chapman, 1989;
Bloeschl et al., 2013; Hrachowitz et al., 2013; Gupta et al., 2014). One
current trend among catchment modellers is thus to test their methods also
at the continental scale (e.g. Pechlivanidis and Arheimer, 2015; Abbaspour
et al., 2015; Donnelly et al., 2016), where traditionally other types of
hydrological models were applied, using other modelling procedures and
showing other advantages than the methods used by the catchment modelling
community (see e.g. Archfield et al., 2015). Traditional global hydrological
models are for instance water-balance and water-allocation models (e.g. Arnell,
1999; Vörösmarty et al., 2000; Döll et al., 2003; Mulligan,
2013) or meteorological land-surface models (e.g. Liang et al., 1994; Woods
et al., 1998; Pitman, 2003; Lawrence et al., 2011), sometimes with more
advanced routing schemes (e.g. Alferi et al., 2013). With the current evolution
of catchment models, their performance can now be compared to more
traditional global and continental modelling approaches in the large-scale
applications (Fig. 1).
Different modelling communities who can now start comparing their
results.
Bierkens et al. (2015) pose the question “how, if at all, it is possible
to calibrate models at the global scale”. In fact, the catchment modelling
community has developed several approaches to regionalize parameter values
for large domains, for instance by using (i) the same parameters based on
geographic proximity (e.g. Merz and Blöschl, 2004; Oudin et al., 2008);
(ii) regression models between parameter values and catchment
characteristics (Hundecha and Bárdossy, 2004; Samaniego et al., 2010;
Hundecha et al., 2016); and (iii) simultaneous calibration in multiple
representative catchments with similar climatic and/or physiographic
characteristics (e.g. Arheimer and Brandt, 1998; Fernandez et al., 2000;
Parajka et al., 2007). Theoretically, these methods should be possible to
apply also on the global scale.
In this paper we test a variety of the latter method, using a stepwise
approach (e.g. Strömqvist et al., 2012; Pechlivanidis and Arheimer,
2015; Donnelly et al., 2016; Andersson et al., 2017a) trying to isolate
hydrological processes and calibrate them separately against observed river
flow in selected representative basins across the entire globe (although
some hydrological features such as large lakes and floodplains were
calibrated individually). This is an example of how to use the catchment
ecosystem approach assuming that hydrological processes are similar across
the globe wherever the catchments have evolved under similar conditions and
have similar physiographic conditions.
The hypothesis tested in the present study states that it is now possible
and timely to apply catchment modelling techniques at the global scale, for
which only gridded approaches have been reported so far (Bierkens et al.,
2015; Sood and Smakhtin, 2015). We address this hypothesis by applying a
catchment model world-wide and then evaluating the results, using
statistical metrics for streamflow time series and signatures. To our
knowledge, this is the first time a catchment model was applied world-wide
and evaluated against river flow across the globe. The catchments were
delineated and routed based on high-resolution topography (90 m), resulting
in an average size of ∼1000 km2 (WWH version 1.3). Our specific
objective is to provide a harmonized way to predict hydrological variables
(especially river flow and the water balance) globally, and then the model
set-up can be shared for further regional refinement to assist in water
management wherever hydrological models are currently lacking. To address
this objective, we (i) compile open global data from >30
sources, including for instance topography and river routing, meteorological
forcing, physiographic land characteristics, and in total some 20 000
time series of river flow world-wide, (ii) apply the open-source code of the
Hydrological Predictions for the Environment, HYPE model (Lindström et
al., 2010), (iii) estimate model parameter values using a new stepwise
calibration technique addressing the major hydrological processes and
features world-wide, and (iv) compute metrics and flow signatures, and
compare model performance with physiographic variables to judge model
usefulness. We then pose the scientific question: how far can we reach in
predicting river flow globally, using integrated catchment modelling, open
global data, and readily available time series for calibration?
The HYPE model
The development of the HYPE model was initiated in 2002, primarily to support
the implementation of the EU Water Framework Directive in Sweden (Arheimer
and Lindström, 2013). It was originally designed to estimate water
quality status, but is now also used operationally at the Swedish
hydrological warning service at SMHI for flood and drought forecasting (e.g.
Pechlivanidis et al., 2014). The water and nutrient model is applied
nationally for Sweden (Strömqvist et al., 2012), the Baltic Sea basin
(Arheimer et al., 2012), and Europe (Donnelly et al., 2013). It also provides
operational hydrological forecasts for Europe at short-term and seasonal
scales and has been subjected to several large-scale applications across
the world, e.g. the Indian subcontinent (Pechlivanidis and Arheimer, 2015)
and the Niger River (Andersson et al., 2017a). One of the main drivers for
HYPE applications has been climate-change impact assessments, for which its
results have been compared to other models in selected catchments across the
globe (Gelfan et al., 2017; Gosling et al., 2017; Donnelly et al., 2017).
The HYPE model code (Lindström et al., 2010) represents a rather
traditional integrated catchment model, describing major water pathways and
fluxes in a catchment ensuring that the mass of water is conserved at each
time step. Parameters are often linked to physiographic properties and the
values regulate the fluxes between water storages in the landscape and
interaction with boundary conditions of the atmosphere, the oceans, and
outlets of endorheic catchments, so-called sinks (see Sect. 4.1 and
detailed model documentation at https://hypeweb.smhi.se/model-water/, last access: 20 January 2020; SMHI, 2020b). It is forced by
precipitation and temperature at a daily or hourly time step and starts by
calculating the water balance of hydrological response units (HRUs), which
is the finest calculation unit in each catchment. In the WWH set-up, the
HRUs were defined by land cover, elevation, and climate, without specific
consideration of further definition of soil properties. This was guided by
recent studies indicating that soil water storage and fluxes related better to
vegetation type and climate conditions rather than soil properties (e.g.
Troch et al., 2009; Gao et al., 2014). HYPE has a maximum of three layers of soil
and these were all applied in WWH, with a different hydrological
response from each one for each HRU. The first layer corresponds to some 25 cm, the second to some 1–2 m, and the third can be deep also accounting
for groundwater. A specific routine can account for deep aquifers, but this
was not applied in WWH due to a lack of local or regional information of
aquifer behaviour. HYPE has a snow routine to account for snow storage and
melt, while a glacier routine accounts for ice storage and melt. Mass
balances of glaciers were based on the observations provided in the Randolph
Glacier Inventory (RGI Consortium, 2015) and fixed separately in the model
set-up.
There are a number of algorithms available to calculate potential
evapotranspiration (PET) in HYPE. For WWH we used the algorithms that
had been judged most appropriate in previous HYPE applications, giving
Jensen–Haise (Jensen and Haise, 1963) in temperate areas, modified
Hargreaves (Hargreaves and Samani, 1982) in arid and equatorial areas, and
Priestly–Taylor (Priestly and Taylor, 1972) in polar and snow-/ice-dominated
areas. River flow is routed from upstream catchments to downstream along the
river network, where lakes and reservoirs may dampen the flow according to a
rating curve. A specific routine is used for floodplains to allow the
formation of temporary lakes, which may be crucial especially in inland
deltas (Andersson et al., 2017a). Evaporation takes place from all water
surfaces, including snow and canopy. The HYPE source code, documentation, and
user guidance are freely available at https://hypeweb.smhi.se/model-water/.
DataPhysiographic data
For catchment delineation and routing, topographical data are needed, but
none of the hydrologically refined databases covers the entire land surface
of Earth, and therefore we had to merge several sources of information (Table 1). Most of the globe (from 60∘ S to 80∘ N) is covered by GWD-LR (Global Width
Database of Large Rivers) 3 arcsec (Yamazaki et al., 2014), apart from the
very northern part close to the Arctic Sea, for which HYDRO1K 30 arcsec
(USGS) is used. For Greenland, we used GIMP-DEM (Greenland Ice Mapping
Project) 3 arcsec (Howat et al., 2014) and for Iceland the national data
from the meteorological office. For the latter we merged the catchments to
better fit the overall resolution, going from 27 000 catchments to 253. Each
of the above datasets was used independently in the delineation.
Databases used for catchment delineation, routing, and elevation in
WWH version 1.3.
TypeDataset/link (last access: 20 January 2020)Provider/referencesTopography (flow accumulation, flow direction, digital elevation, river width)GWD-LR (3 arcsec) http://hydro.iis.u-tokyo.ac.jp/~yamadai/GWD-LR/ GIMP-DEM (3 arcsec) https://nsidc.org/data/measures/gimp HYDRO1K (30 arcsec) 10.5066/F77P8WN0 SRTM (3 arcsec) https://www.usgs.gov/centers/eros/science/usgs-eros-archive- digital-elevation-shuttle-radar-topography-mission-srtmYamazaki et al. (2014), Howat et al. (2014), United State Geological Survey (USGS, 2020), USGSNon-contributing areas in CanadaAreas of Non-Contributing Drainage (AAFC Watersheds Project – 2013) https://open.canada.ca/data/dataset/67c8352d-d362-43dc-9255-21e2b0cf466cGovernment CanadaWatershed delineation (Iceland)IMO subbasins and main river basins http://en.vedur.is/hydrology/Icelandic Met Office (IMO)KarstWorld Map of Carbonate Rock Outcrops v3.0 http://digital.lib.usf.edu/SFS0055342/00001Ford (2006)Global Flood RiskGlobal estimated risk index for flood hazard http://ihp-wins.unesco.org/layers/geonode:fl1010irmtUNEP/GRID-EuropeFloodplainsGlobal Lake and Wetland Database (GLWD) https://www.worldwildlife.org/publications/global-lakes-and-wetlands-database-lakes-and-wetlands-grid-level-3Lehner and Döll (2004)Desert areasWorld Land-Based Polygon Features https://earthworks.stanford.edu/catalog/stanford-bh326sc0899University of New York
Additional data were gathered to help with defining catchments as the
delineation of catchments can be difficult in some environments. In flat
areas we consulted previous mapping and hydrographical information of
floodplains, prairies, and deserts (Table 1). Karstic areas are unpredictable
due to lack of subsurface information of underground channels crossing
surface topography and thus needed to be defined and evaluated separately.
Finally, flood risk areas (UNEP/GRID-Europe; Table 1) were recognized as
potentially important, enabling the use of model results in combination with
hydraulic models, and thus also had to be identified so that model results
can be extracted for such applications.
Databases used to assign land cover, waterbodies, and climate to
catchments in WWH version 1.3.
TypeDataset/link (last access: 20 January 2020)Provider/referencesLand-cover characteristicsESA CCI Landcover v 1.6.1 epoch 2010 (300 m) https://www.esa-landcover-cci.org/?q=node/169ESA Climate Change Initiative – Land Cover projectGlaciersRandolph Glacier Inventory (RGI) v 5.0 https://www.glims.org/RGI/randolph50.htmlRGI ConsortiumGreenland ice sheetGreenland Glacier InventoryRastner et al. (2012)LakesESA CCI-LC waterbodies 150 m 2000 v 4.0 https://www.esa-landcover-cci.org/?q=node/169ESA Climate Change Initiative – Land Cover projectLakesGlobal Lake and Wetland Database 1.1 (GLWD) https://www.worldwildlife.org/publications/global-lakes-and-wetlands-database-large-lake-polygons-level-1Lehner and Döll (2004)Lake depthsGlobal Lake Database v2(GLDB) http://www.flake.igb-berlin.de/site/external-datasetKourzeneva (2010), Choulga et al. (2014)Reservoirs and damsGlobal Reservoir and Dam database v 1.1 (GRanD) http://globaldamwatch.org/grand/Lehner et al. (2011)IrrigationGMIA v5.0 http://www.fao.org/nr/water/aquastat/irrigationmap/index10.stm MIRCA v1.1 http://www.uni-frankfurt.de/45218031/data_downloadSiebert et al. (2013a, b), Portmann et al. (2010)Climate classificationKöppen-Geiger Climate classification, 1976–2000, v June 2006 http://koeppen-geiger.vu-wien.ac.at/Kottek et al. (2006)
For catchment characteristics governing the hydrological processes in HYPE,
the ESA CCI Landcover version 1.6.1 epoch 2010 (300 m) was the baseline for
HRUs, but several other data sources were used to adjust and add information
to some hydrologically important features, such as glaciers, lakes,
reservoirs, irrigated crops, and climate zone (Table 2).
Meteorological data
The WWH model uses time series of daily precipitation and temperature to
make calculations on a daily time step. All catchment models require
initializations of the current state of the snow, soil, and lake (and
sometimes river) storages. At the global scale, a seamless dataset for
several decades is necessary for consistent model forcing, to also cover
hydrological features with large storage volumes. For WWH version 1.3
precipitation and temperature were achieved from the Hydrological Global
Forcing Data (HydroGFD; Berg et al., 2018), which is an in-house product of
SMHI that combines different climatological data products across the globe.
This global dataset spans a long climatological period up to near-real time
and forecasts (from 1961 to 6 months ahead). The period used in this study
is primarily based on the ERA-Interim global (50 km grid) re-analysis product
(Dee et al., 2011) from ECMWF, which is further bias adjusted
vs. other products using observations, e.g. versions of CRU (Harris and
Jones, 2014) and GPCC (Schneider et al., 2014). The HydroGFD dataset is
produced using a method for bias adjustment, which is similar to the method
by Weedon et al. (2014) but additionally uses updated climatological
observations, and, for the near-real time, interim products that apply
similar methods. This means that it can run operationally in near-real time.
The dataset is continuously upgraded and, in the present study, we used
HydroGFD version 2.0.
Observed river flow
Catchment models need time series of hydrological variables for parameter
estimation and model evaluation. Metadata and daily and monthly time series
from gauging stations were collected from readily available open data
sources globally (Table 3). In total, information from 21 704 gauging
stations could be assigned to a catchment outlet. Of these, time series
could be downloaded for 11 369, while 10 336 could only assist with metadata,
such as upstream area, river name, elevation, or natural or regulated flow.
The time series were screened for missing values, inconsistency, skewness,
trends, inhomogeneity, and outliers (Crochemore et al., 2019). Stations
representing the resolution of the model (≥1000 km2) and with
records of at least 10 consecutive years between 1981 and 2012 were
considered for model evaluation. With these criteria, 5338 time series were
used for evaluating overall model performance, of which 2863 represented
independent model validation and 2475 were also involved in the stepwise
model calibration (see Sect. 4.2). In addition, 1181 stations not
fulfilling the criteria were added to increase the number of representative
gauges to capture spatial variability when estimating parameter values. In
total, 6519 gauging stations were used for model calibration and validation.
Databases used for time series of water discharge and location of
gauging station when estimating parameters and evaluating the model
performance of WWH version 1.3.
Data typeShort name/link (last access: 20 January 2020)CoverageProvider/referencesTime series + metadataGRDC https://www.bafg.de/GRDC/EN/Home/homepage_node.htmlGlobalGlobal Runoff Data CenterEWA https://www.bafg.de/GRDC/EN/04_spcldtbss/42_EWA/ewa.htmlEuropeGRDC – EURO-FRIEND-WaterRussian River data by Bodo, ds553.2 https://rda.ucar.edu/datasets/ds553.2/Former Soviet UnionBodo (2000)R-ArcticNet v 4.0 http://www.r-arcticnet.sr.unh.edu/v4.0/index.htmlArctic regionPan-Arctic Project ConsortiumRIVDIS v 1.1 https://daac.ornl.gov/RIVDIS/guides/rivdis_guide.htmlGlobalVörösmarty et al. (1998)USGS https://waterdata.usgs.gov/nwis/swUSAU.S. Geological SurveyHYDAT https://www.canada.ca/en/environment-climate-change/services/water-overview/quantity/monitoring/survey/data-products-services/national-archive-hydat.htmlCanadaWater Survey of Canada (WSC)Chinese Hydrology Data Project http://www2.oberlin.edu/faculty/aschmidt/chdp/summary.htmlChinaHenck et al. (2011)Spanish Water Authorities https://www.miteco.gob.es/es/ministerio/funciones-estructura/organismos-publicos/confederaciones-hidrograficas/default.aspxSpainEcological Transition MinistryWISKI https://vattenwebb.smhi.se/station/SwedenSwedish Meteorological and Hydrological InstituteMetadataCLARIS-project http://www.claris-eu.org/La Plata BasinCLARIS LPB- project FP7 Grant agreement 212492CWC handbook http://cwc.gov.in/get-hydrological-dataIndiaCentral Water Commission (CWC)SIEREM http://www.hydrosciences.fr/sierem/AfricaBoyer et al. (2006)Regional data https://uia.org/s/or/en/1100058436Congo BasinInternational Commission for Congo-Ubangui-Sangha Basin (CICOS)National data http://www.bom.gov.au/water/hrs/AustraliaBOM (Bureau of Meteorology)Red Hidrometrica SNHN 2013 http://geo.gob.bo/geonetwork/srv/dut/catalog.search#/metadata/ff98cf17-f9a8-4a8d-b96c-bf623dd6b13bBoliviaServicio Nacional de Hidrografía NavalEstacoes Fluviometrica http://www.snirh.gov.br/hidroweb/BrazilANA (Agencia Nacional de Aguas)Red Hidrometrica http://www.dga.cl/Paginas/default.aspxChileDGA (Direccion General de Aguas)Catalogo Nacional de Estaciones de Monitoreo Ambiental http://www.ideam.gov.co/geoportalColombiaIDEAM (Instituto de Hidrologia, Meteorologia y Estudios Ambientales)Estaciones_Hidrologicas http://www.serviciometeorologico.gob.ec/geoinformacion-hidrometeorologica/EcuadorINAMHI (Instituto Nacional de Meteorología e Hidrología)National data http://www.senamhi.gob.pe/?p=0300PeruSENAMHI (Servicio Nacional de Meteorologia e Hidologia del Peru)National data http://www.inameh.gob.ve/web/VenezuelaIGVSB (Instituto Geográfico de Venezuela Simon Bolivar)Conabio 2008 http://www.conabio.gob.mx/informacion/metadata/gis/esthidgw.xml?_httpcache=yes&_xsl=/db/metadata/xsl/fgdc_html.xsl&_indent=noMexicoInstituto Mexicano de Tecnología del Agua/CONABIONiger HYCOS http://nigerhycos.abn.ne/user-anon/htm/Niger RiverWorld Hydrological Service System (WHYCOS)National data http://www.dwa.gov.za/Hydrology/South AfricaDepartment Water & Sanitation, Republic of South AfricaNational data http://publicutilities.govmu.org/English/Pages/Hydrology-Data-Book-2006---2010.aspxMauritiusMauritius Ministry of Energy and Public UtilitiesModel set-up
WWH is developed incrementally, and the current version 1.3 was based on
previous versions, where version 1.0 only included the most basic functions
to run a HYPE model and was forced by MSWEP (Beck et al., 2017) and CRU
(Harris and Jones, 2014). Version 1.2 included distributed geophysical and
hydrographical features, and finally, version 1.3 (described below) included
estimated parameter values and was forced by the
Hydro-GFD meteorological dataset, which also provides operational forecasts at a 50 km grid (Berg
et al., 2018). Gridded forcing data were linked to catchments using the grid
point nearest to the catchment centroid. Dynamic catchment models need to be
initialized to account for adequate storage volumes, which may, for
instance, dampen or supply the river flow based on catchment memory (e.g.
Iliopoulou et al., 2019). WWH was initialized by running for a 15-year
warm-up period 1965–1980, which was judged to be enough for more than 90 %
of the catchments by checking the time it takes for runs initialized 20 years apart to converge. Long initialization periods are needed for large
lakes with small catchments, large glaciers, and sinks or
rarely contributing areas.
The current model runs at a Linux cluster (using nodes of 8 processors and
16 threads) with calculations in approximately 1 800 000 HRUs and 130 000
catchments covering the world's land surface, except for Antarctica. The
model runs in parallel in 32 hydrologically independent geographical domains
with a run time of about 3 h for 30-year daily simulations. The methods
applied for modelling and evaluation mostly follow common procedures used by
the catchment modelling community, as described below.
Catchment delineation and characteristics
Catchment borders were delineated using the World Hydrological Input Set-up
Tool (WHIST; https://hypeweb.smhi.se/model-water/hype-tools/, last access: 20 January 2020), software
developed at SMHI that is linked to the Geographic Information System (GIS)
Arc-GIS from ESRI. By defining force points for catchment outlets in the
resulting topographic database (cf. Table 1) and criteria for minimum and
maximum ranges in catchment size, the tool delineates catchments and the
link (routing) between them. By adding information from other types of
databases, WHIST also aggregates data or uses the nearest grid for assigning
characteristics to each catchment. WHIST handles both gridded data and
polygons and was used to link all data described in Sect. 2, such as
land cover, river width, precipitation, temperature, and elevation, to each
delineated catchment. WHIST then compiles the input data files into a format
that can be read by the HYPE source code. The software runs automatically,
but also has a visual interface for manual corrections and adjustments. It
may also adjust the position of the gauging stations to match the river
network of a specific topographic database.
When setting up WWH, force points for catchment delineation were defined
according to the following.
Locations of gauging stations in the river network: in total, catchments were defined for all 21 704 gauging stations which
had an upstream area greater than 1000 km2, except for data-sparse
regions (500–1000 km2). Their coordinates were corrected to fit with
the river network of the topographic data, using WHIST and manually. Quality
checks of catchment delineation were done towards station metadata and
88 % of the estimated catchment areas were within ±10 % discrepancy
towards metadata. These catchments were used in further analysis for
parameter estimation or model evaluation; however, not all of these sites
provided open access to time series (see Sect. 2.3).
Outlets of large lakes/reservoirs: new lake delineation was done to solve the spatial mismatch between data
of the waterbodies from various sources (cf. Table 2). The centroid of the
lakes included in GLWD and GRanD was used as initialization points for a
flood-fill algorithm, applied over the ESA CCI Water Bodies, followed by
manual quality checks. The outlet location was defined using the maximum
upstream area for each lake. In total, around 13 000 lakes and 2500
reservoirs >10 km2 were identified globally. The new
dataset was tested against detailed lake information for Sweden, which
represents one of the most lake-dense regions globally. Merging data from
the two databases and adjusting to the topographic data used were judged to be more
realistic for the global hydrological modelling than only using one dataset.
Large cities and cities with high flood risk: the UNEP/GRID-Europe database (Table 1) was used to define flood-prone
areas for which the model may be useful in the future. The criteria for
assigning a force point were city areas of >100 km2
(regardless of the risks on the UNEP scale) or city areas of 10–100 km2
with risk 3–5 and an upstream area >1000 km2. This was only
considered if there was no gauging station within 10 km of the city. This
gave another 2439 forcing points to the global model.
Catchment size: the goal was to reach an average size of some 1000 km2, for practical
(computational) and scientific reasons, reflecting uncertainty in input
data. Criteria in WHIST were set to reach maximum catchment sizes of 3000 km2 in general and 500 km2 in coastal areas with <1000 m
elevation (to avoid crossing from one side to another of a narrow and high
island or peninsula). Post-processing was then done for the largest lakes,
deserts, and floodplains, following specific information on their character
(see data sources in Table 2).
Using this approach, the land surface of the Earth (i.e. 135 million km2 when excluding Antarctica) was divided into 131 296 catchments with
a mean size of 1020 km2 (5th percentile: 64 km2; 50th
percentile: 770 km2; 95th percentile: 2185 km2). Flat land
areas of deserts and floodplains ended up with somewhat larger catchments,
about 4500 and 3500 km2, respectively. Around 23.8 % of the
land surface did not drain to the sea but to sinks (Fig. 2), the largest
single one being the Caspian Sea. This water was evaporated from water
surfaces but also percolated to groundwater reservoirs. Moreover, several
areas across the globe are of karstic geology with wide underground
channels, which does not follow the land-surface topography. Sinks within
karst areas according to the World Map of Carbonate Rock outcrops (Table 1)
were linked to the “best neighbour” and inserted into the river network. The
Canadian prairie also encompasses a large number of sinks due to climate and
topography, and there existed a national dataset from Canada with
well-defined non-contributing areas to adjust the routing in this area.
Major river basins and areas not contributing to river flow from
land to the sea.
The land-cover data from ESA CCI LC v1.6 (Table 2) were used as the baseline
for HRUs. They have 36 classes and subclasses, and 3 of these were adjusted
using additional data to improve the quality; (i) by using glacier
delineated by the RGI v5 and comparing spatially the outlines of both
sources, we avoided overestimation of the glacier area; (ii) by using GMIA
and MIRCA in a data fusion algorithm to create a more robust new irrigation
database, we added irrigation information where this was missing and
underestimated; (iii) by combining several sources of waterbodies (see
Table 2) and spatial analyses (e.g. a flood fill algorithm and geospatial
tools), we differentiated one general class of waterbodies into four: large
lakes, small lakes, rivers, and coastal sea, which makes more sense in
catchment modelling. Five elevation zones were derived to differentiate
land-cover classes with altitude (0–500, 500–1000, 1000–2000,
2000–4000, and 4000–8900 m) as the hydrological response may be very
different at different altitudes due to vegetation growth and soil
properties. The land cover at these elevations was thus treated as a
specific HRU globally. In total, this resulted in 169 HRUs.
All catchments were characterized according to Köppen–Geiger (Table 2)
to assign a PET algorithm (see Sect. 3.2), but the characteristics did not
include soil properties, which is common in catchment hydrology. The
approach when setting up HYPE was to use the possibility of assigning
hydrologically active soil depth for the HRUs instead (see Sect. 2 on the HYPE
model), based on the variability in vegetation, climate, and elevation they
represent as suggested by Troch et al. (2009) and Gao et al. (2014).
However, a few distinct soil properties were unavoidable besides the general
soil to describe the hydrological processes; these were impermeable
conditions of urban and rock environments and infiltration under water and
rice fields.
Stepwise parameter estimation
The method to assign parameter values for the global model domain aimed at
finding (i) robust values also valid for ungauged basins as well as (ii) reliable process description of dominating flow-generation processes and
water storage along the flow paths. The first aim was addressed by
simultaneous calibration in multiple representative catchments world-wide.
Spatial heterogeneity was accounted for by separate calibration of
catchments representing different climate, elevation, and land cover
globally. The second aim was addressed by applying a stepwise approach
following the HYPE process description along the flow paths, only
calibrating a few parameters governing a specific process at a time
(Arheimer and Lindström, 2013). The estimated parameter values were then
applied wherever relevant in the whole geographical domain, i.e. world-wide.
We estimated parameters for 11 hydrological processes separately, where each
process description includes between 2 and 20 parameters (Table A1 in the
Appendix). Some processes were calibrated for specific categories, for
instance different soil types, land use, and elevation zones.
Number of gauging stations and their locations that were used in
each step of the stepwise parameter estimation procedure and evaluation
against in situ observations world-wide.
Aggregated land covers used for calibrating HRUs, their
representation in the upstream catchment, and the number of gauges available
for each land cover when estimating parameter values of WWH v1.3.
AggregatedOriginal land cover from ESA CCI 1.6 (model HRUs)LandNo. of gaugesNo. of gaugesland covercover(snow area)(no snow)BareBare areas Consolidated bare areas Unconsolidated bare areas35 %732CropCropland, rain fed Herbaceous cover Tree or shrub cover Cropland, irrigated or post-flooding irrigated rice50 %5230GrassGrass50 %–1MosaicMosaic cropland (>50 %)/natural vegetation (tree, shrub, herbaceous cover) (<50 %) Mosaic natural vegetation (tree, shrub, herbaceous cover) (>50 %)/cropland (<50 %) Mosaic tree and shrub (>50 %)/herbaceous cover (<50 %) Mosaic herbaceous cover (>50 %)/tree and shrub (<50 %)50 %3929ShrubShrubland Shrubland evergreen Shrubland deciduous Shrub or herbaceous cover, flooded, fresh/saline/brackish water50 %5417SparseLichens and mosses Sparse vegetation (tree, shrub, herbaceous cover) (<15 %) Sparse shrub (<15 %) Sparse herbaceous cover (<15 %)35 %4011TreeBrDecMixTree cover, broadleaved, deciduous, closed to open (>15 %) Tree cover, broadleaved, deciduous, closed (>40 %) Tree cover, broadleaved, deciduous, open (15 %–40 %) Tree cover, mixed leaf type (broadleaved and needle-leaved)50 %2628TreeBrEvFloodTree cover, broadleaved, evergreen, closed to open (>15 %) Tree cover, flooded, fresh or brackish water Tree cover, flooded, saline water50 %3730TreeNeDecTree cover, needle-leaved, deciduous, closed to open (>15 %) Tree cover, needle-leaved, deciduous, closed (>40 %) Tree cover, needle-leaved, deciduous, open (15 %–40 %)50 %46–TreeNeEvTree cover, needle-leaved, evergreen, closed to open (>15 %) Tree cover, needle-leaved, evergreen, closed (>40 %) Tree cover, needle-leaved, evergreen, open (15 %–40 %)50 %–10UrbanUrban50 %2130
Different catchments were selected globally to best represent each process
calibrated (Fig. 3). Processes were assumed to be linked to different
physiographic characteristics (Kuentz et al., 2017) and catchments with
gauging stations where these characteristics were most prominent in the
upstream area were selected (i.e. the representative gauged basin method).
For HRUs, separate calibration was done for the snow-dominated areas
(>10 % of precipitation falling as snow), as the snow
processes give such a strong character to the runoff response and simultaneous
calibration with catchments lacking snow may thus underestimate other
flow-controlling processes. The HRUs based on the ESA CCI 1.6 data were
aggregated from 36 classes into 10 (Table 4) for more efficient calibration
and to ensure that some gauged catchments represented the appointed
land cover. Some local hydrological features such as large lakes and
floodplains were calibrated individually. When evaluating the effect of
this, we discovered some major bias for the Great Lakes in North America and
Malawi and Victoria lakes in Africa. Finally, we introduced the 11th
step to calibrate the evaporation of these separately (Fig. 3).
In total, 6519 river gauges were used for evaluating model performance.
Among these, 3656 were used in the calibration, but each gauge only affected
a few model parameters in the stepwise procedure. Automatic calibration was
applied for each subset of parameters and representative catchments in each
step, using the differential evolution Markov chain (DEMC) approach (Ter
Braak, 2006) to obtain the optimum parameter value in each case. The
advantage of DEMC vs. plain DE is both the possibility of getting a
probability-based uncertainty estimate of the global optimum and a better
convergence towards it. The DEMC requires several parameters to be fixed and
the choice of these parameters was based on a compromise between convergence
speed and the accuracy of the resulting parameter set. Global PET parameter
values were fixed first, before starting the stepwise procedure, using the
MODIS global evapotranspiration product (MOD16) by Mu et al. (2011) for
parameter constraints. The parameter ranges were defined as the median and
the 3rd quartile of the 10 % best agreements between HYPE and MODIS
in terms of RE. The first selection was done with 400 runs and then repeated
for a second round. In addition, a priori parameters (Table A1 in the
Appendix) were set for glaciers and soils without calibration, taken from
previous applications (e.g. Donnelly et al., 2016; MacDonald et al., 2018).
The bare deserts soil was manually calibrated only using four stations in the
Sahara. The area and volume of glaciers were evaluated in 296
glaciers and soil parameters in some 30 catchments. The root zone storage of
soils was further calibrated in the parameter setting of each HRU (in step
nos. 4 and 5).
While the calibration period was 1981–2012, it was always preceded by 15 years of initialization. Different metrics were chosen as calibration
criteria, depending on the character of the parameter and how it influences
the model. For instance, relative error (RE) was used as a metric in the
calibration of precipitation and PET parameters, since the aim was to
correctly represent water volumes. By contrast, a correlation coefficient
(CC) was used when the timing was the main goal (i.e. for river routing or
dampening in lakes). If both water volume and timing were required,
Kling–Gupta efficiency (KGE; Gupta et al., 2009) was used (i.e. for soil
discharge from HRUs). Wherever possible, calibration was made using a daily
time step, while overall model evaluation on the global scale was made on a
monthly time step.
Model evaluation
The model was evaluated against independent observed river flow by using
remaining gauges which were not chosen for the calibration procedure. The
agreement between modelled and observed time series was evaluated using the
statistical metric KGE and its components r, β, and α, which
are directly linked with CC (Pearson correlation coefficient), RE, and RESD (relative error of standard deviation), respectively (Gupta
et al., 2009). KGE is defined as
KGE=1-r-12+α-12+β-12,
where
2r=CC=covxo,xsσsσo,3β=μsμo;RE=β-1×100,4α=σsσo;RESD=α-1×100.x represents the discharge time series, μ the mean value of the
discharge time series, and σ the standard deviation of the discharge
time series. The sub-indexes o and s represent observed and simulated
discharge time series, respectively. Thus CC represents how well the model
dynamics agree between observations and simulations, i.e. the timing of
events but not the magnitude; RE represents the agreement in volume over
time; RESD represents how well the model captures the amplitude of the
hydrograph. KGE was chosen as the performance metric to analyse all these
aspects and because it has been found to be good in capturing both mean and
extremes during calibration (Mizukami et al., 2019). We used the original
version so that our results can easily be compared to other studies reported
in the literature, even though non-standard variants may be more efficient
(e.g. Mathevet et al., 2006; Mizukami et al., 2019).
Flow signatures (FS) from observed time series and physiographic
descriptors (T: topography; LC: land cover; C: climate) from databases in
Sect. 2.1.
Variable nameDescriptionRangeskew (FS)Skewness = mean/median of daily flows[0.63–70 000]MeanQ (FS)Mean specific flow in mm[0–1024.41]CVQ (FS)Coef. of variation = standard deviation/mean of daily flows[0.01–46.4]BFI (FS)Base flow index: 7 d minimum flow divided by mean annual daily flow averaged across years[0–0.84]Q5 (FS)5th percentile of daily specific flow in mm[0–218.04]HFD (FS)High flow discharge: 10th percentile of daily flow divided by median daily flow[0–1]Q95 (FS)95th percentile of daily specific flow in mm[0–2654.81]LowFr (FS)Total number of low flow spells (threshold equal to 5 % of mean daily flow) divided by the record length[0–1]HighFrVar (FS)Coef. of variation in annual number of high flow occurrences (threshold 75th percentile)[0–5.48]LowDurVar (FS)Coef. of variation in the annual mean duration of low flows (threshold 25th percentile)[0–3.78]Mean30dMax (FS)Mean annual 30 d maximum divided by median flow[0–29.49]Const (FS)Constancy of daily flow (see Colwell, 1974)[0.01–1]RevVar (FS)Coef. of variation in annual number of reversals (change in sign in the day-to-day change time series)[0–5.48]RBFlash (FS)Richards–Baker flashiness: sum of absolute values of day-to-day changes in mean daily flow divided by the sum of all daily flows[0–2]RunoffCo (FS)Runoff ratio: mean annual flow (in mm yr-1) divided by mean annual precipitation[0–1362.52]ActET (FS)Actual evapotranspiration: mean annual precipitation minus mean annual flow (in mm yr-1)[-100–2660.03]Area (T)Total upstream area of catchment outlet in km2[13.5–4 671 536.7]meanElev (T)Mean elevation of the catchment in metres[3.63–5046.16]stdElev (T)Standard deviation of the elevation of the catchment in m[1.66–1595.89]Meanslope (T)Mean slope of the catchment[0–224.24]Drainage density (T)Total length of all streams in the catchment divided by the area of the catchment[2.19–259 798.14]13 land-cover variables (LC)% of the catchment area covered by the following land-cover types (see Table 4): Water, Urban, Snow & Ice, Bare, Crop, Mosaic, TreeBrEvFlood, TreeBrdecMix, TreeNeEv, TreeNeDec, Shrub, Grass and Sparse[0–1]Pmean (C)Mean annual precipitation in mm yr-1[51.5–5894.86]SI.Precip (C)Seasonality index for precipitation: SI=1R‾⋅∑n=112x‾n-R‾12x‾n: mean rainfall of month n; R‾: mean annual rainfall[-16.93–31]Tmean (C)Mean annual temperature in degrees[0.08–50.06]AI (C)Aridity index: PET/P, where PET is the mean annual potential evapotranspiration and P the mean annual precipitation[0.05–1.28]5 Köppen regions (C)% of the catchment area within the following Köppen regions: A (Tropical), B (Arid), C (Temperate), D (Cold-continental), and E (Polar)[0–1]
In addition, a number of flow signatures (Table 5) was calculated to explore
which part of the hydrograph is well captured by the model. Flow signatures
are used by the catchment modelling community to condense the hydrological
information from time series (Sivapalan, 2005) and the choice of flow
signatures was guided by previous studies by Olden and Poff (2003) and
Kuentz et al. (2017). In this study, flow signatures were calculated at 5338
gauging stations globally, based on catchment size and at least 10 years of
continuous time series (see Sect. 2.3).
The model capability in capturing observed flow signatures was then related
to upstream physiographical and climatological factors, such as area, mean
elevation, drainage density, land cover, climatic region, or aridity index.
Catchment modellers tend to study differences and similarities in flow
signatures as well as in catchment characteristics to improve understanding
of hydrological processes (e.g. Sawicz et al., 2014; Berghuijs et al., 2014;
Pechlivanidis and Arheimer, 2015; Rice et al., 2015). In large-sample
hydrology it is not possible to examine each hydrograph individually using
inspection. As the flow signatures aggregate information about the
hydrograph, the model capability to simulate signatures will tell the
modeller which part of the hydrograph is better or worse. Linking catchment
descriptors to the performance in flow signatures helps the modeller to
examine whether the process description and model structure are valid across
the landscape or whether the regionalization of parameter values must be
reconsidered for some parts of a large domain. In addition, this exercise
will guide the users to judge under which conditions the model is reliable
and thus of any use for decision making. In the present study, the
physiographic characteristics of catchments were all extracted from the
input data files of WWH version 1.3. For each gauging station with
calculated flow signatures, the catchment characteristics were accumulated
for all upstream catchments to account for any potential physiographical
influence on the flow signal at the observation site (Table 3). Gauging
stations were grouped according to the distribution of each physiographic
characteristic and model performances in flow signature representation were
computed for each of these groups.
ResultsGlobal river flow and general model performance
To some extent WWH version 1.3 describes hydrological features globally and
spatial variability in factors controlling the runoff mechanisms, although
there is still substantial room for improvements over the coming decade(s).
The catchment modelling approach with careful consideration to hydrography
resulted in a new database with delineated hydrographical features (e.g.
Fig. 4) of major importance for hydrological modelling. The merging of
several data sources resulted in consistency between available information
on waterbodies, topographic data, and the river network (e.g. for glaciers,
floodplains, lakes, and gauging stations), so that this information can be
used in catchment modelling and provide results of river flow at a
resolution of some 1000 km2 globally.
Some examples of WWH version 1.3 details in describing hydrography
at local and regional scale from supporting GIS layers: (a) subbasins of the Orinoco River defined as a connected floodplain; (b) adjustment of lake areas (New) from merging several data sources (see Sects. 2.1 and 3.1) and the original GLWD in the Canadian Prairie; (c) river routing and access to flow gauges in the Congo River basin.
Annual mean of river discharge across the globe for the period
1981–2015 estimated with the WWH version 1.3 catchment model (on average
1020 km2 resolution).
WWH version 1.3 resulted in a realistic spatial pattern of river flow
world-wide, clearly identifying desert areas and the largest rivers (Fig. 5). Compared to other global estimates of average water flow in major
rivers, HYPE gives results of the same order of magnitude, but of course,
comparisons should be based on the same time period to account for natural
variability due to climate oscillations. The Amazon, Congo, and Orinoco
rivers came out as the three largest ones, where the river flow of the
Amazon River is almost 6 times larger than any other river. Compared to
recent estimates by Milliman and Farnsworth (2011), HYPE estimated a higher
annual average of river flow in Mississippi, St Lawrence, Amur, and Ob but
less in the rest of the top 10 largest rivers of the world; especially
relatively lower values were noted for Ganges–Bahamaputra. For World-Wide
HYPE, the Yangtze River came out as no. 11 and Mekong as no. 12, and it should be
noted that the river flow to the Río de la Plata was separated into
the Paraná River and the Uruguay River (the former ranked no. 13 of the
largest rivers).
Model performance of WWH version 1.3 using the KGE metric of
monthly values of ≥10 years in each of the 5338 gauging sites for the
period 1981–2012. Blue and green indicate that the model provides more
information than the long-term observed mean value.
On average, for the whole globe and 5338 gauging stations with validated
catchment areas and at least 10 years of data, the model performance was
estimated to a median monthly KGE of 0.40 (Fig. 6). When decomposing the
KGE, we found a median correlation coefficient of 0.76 and a median relative
error of -15 %. This means that the model captures the temporal dynamics
of the hydrographs reasonably well in many sites, while it generally
underestimates the river flow. This underestimation could result from
using MODIS when setting calibration ranges. The bluer the colour in Fig. 6, the
better the model performance is; hence, the model performs best in central
Europe, north-eastern America, the Upper Amazon, and northern Russia (KGE >0.6). These regions are mostly lowlands and one explanation for good model
performance could be that the precipitation from the global meteorological
dataset is more correct at lower altitudes with smooth orography. It could
also be that the seasonality is more regular and easier to capture.
Model performance was surprisingly similar for the gauges used in parameter
estimation and independent ones, with a median KGE of 0.41 (2475 stations) and
0.39 (2863 stations), respectively. Among the validation stations, 498 were
completely independent without any influence from calibration in any branch
of the upstream river network. Also here the model showed similar
performance (median KGE =0.45; median CC =0.79; median RE =-17).
This indicates that the model results are robust and similar model
performance can be assumed also in ungauged basins.
If KGE is below -0.41, the model does not contribute with more information
than the long-term average of observations (Knoben et al., 2019); however, to
judge whether the model performance is good or bad, the model purpose and
use of results must be considered. Most catchment modellers who come from
engineering would probably judge the KGE of 0.40 as poor, but given that
global open input data were used for model set-up and rough assumptions were
made when generalizing hydrological processes across the globe, the overall
model performance meets the expectations of a first version.
Global hydrological modellers rarely compare their results to gauged river
flow (e.g. Zhao et al., 2017), but similar results were recently reported
when Beck et al. (2016) were testing a scheme for global parameter
regionalization world-wide; in an ensemble of 10 global water allocation or
land-surface models, the median performance of monthly KGE was found to be
0.22 using 1113 river gauges for mesoscale catchments globally (median size
500 km2). The best median monthly KGE was then 0.32 for catchment-scale
calibration of regionalized parameters, using a gridded HBV model with a
daily time step globally (Beck et al., 2016). It is difficult to compare results
when not using the same validation sites or time period, and more concerted
actions for model inter-comparison are needed at this scale. Nevertheless,
the catchment modelling approach of the present study seems to have better
performance than other gridded global modelling concepts of river flow (see
results from more models in Beck et al., 2016).
The red spots in Fig. 6 indicate where the HYPE model fails (KGE <-1), such as in the US Midwest (especially Kansas), the north-east of Brazil,
and parts of Africa, Australia, and central Asia. When decomposing the KGE,
it was found that the correlation was in general fine. However, the relative
error in standard deviation was causing the main problems, showing that the
HYPE model does not capture the variations of the hydrograph and, instead,
generates a too even flow. The relative error also seemed problematic, which
indicates problems with the water balance. The model has severe problems
with dry regions and areas with large impact from human alteration and water
management, where the model underestimates the river flow. Such regions are
known to be more difficult for hydrological modelling in general (Bloeschl
et al., 2013), but in addition, precipitation data do not seem to fully
capture the influence of topography and mountain ranges. The patterns in
model performance were further investigated in the analysis of model
performance vs. flow signatures and physiographic factors (Sect. 4.3).
Global parameter values from stepwise calibration
Both model performance in representative catchments and improvement achieved
through calibration varied a lot for each hydrological process considered in
the stepwise parameter estimation (Table 6). Although a large number of
river gauges was collected for parameter estimation, only a few could be
considered to be representative with enough quality assurance. More gauges in
the calibration procedure would probably have given another result.
Nevertheless, the results show promising potential in applying the process
descriptions of catchment models, also at the global scale.
Metrics of model performance before and after calibrating various
hydrological processes simultaneously at a number of selected river gauges,
using the stepwise parameter-estimation procedure globally. Parameter values
and names in the HYPE model are given in the Appendix.
Hydrological processNo. of gaugesMedian value of metric(s) BeforeAfterPotential evapotranspiration (three PET algorithms: median of ranges constrained with MODIS)0RE: 11.5 %RE: 0.5 %Glaciers (only evaluated vs. mass balance data)296RE: 0.38 % CC: 0.51–Soils (average, rock, urban, water, rice)25RE: -14.1 % KGE: 0.2Bare soils in deserts (calibrated manually)4RE: 236.1 %RE: -18.91. Precipitation: catchment elevation147RE: -6.7 %RE: 4.4 %2. Precipitation: land-cover altitude1041RE: 24.3 %RE: 10.1 %3. HRUs in areas without snow318KGE: 0.16KGE: 0.274. HRUs in areas with snow: ET, recession, and active soil depth225KGE: 0.16KGE: 0.245. Upstream lakes731CC: 0.71CC: 0.726. Regionalized ET (in 12 Köppen climate regions)458KGE: 0.58KGE: 0.627. River routing302CC: 0.70CC: 0.718. Lake rating curve945CC: 0.50CC: 0.599. Floodplains (partly calibrated manually)32KGE: -0.03KGE: 0.0310. Evaporation from water surface201RE: -20.7 %RE: -12.2 %11. Specific lake evaporation16RE: 24.8 %RE: 4.8 %
In spite of the wide spread in geographical locations across the globe, a
priori values were reasonable for hydrological processes describing glaciers
and soils. As shown in Table 6, the water balance (RE) was improved
considerably by first calibrating PET globally and then precipitation vs.
altitude of catchment and land-cover type. Simultaneous calibration of soil
storage and discharge in HRUs increased the KGE both in areas with and
without snow by 0.1 on average. For calibration of river routing and rating
curves of lake outflows, the correlation coefficient was used to avoid
erroneous compensation of the water balance, as the parameters involved
should only set the dynamics of flow and not volume. Especially lake
processes benefited from calibration. Less convincing were the metrics from
calibration of the floodplains, which were not always improved by the
floodplain routine applied. Overall, the results indicate that global
parameters are to some extent possible for describing hydrological processes
world-wide, using a catchment model and globally available data of
physiographic characteristics to describe spatial variability. Nevertheless,
the WWH v.1.3 model still has considerable potential for improvements and, to
really make use of more advanced calibration techniques, the water balance
needs to be improved first as too much volume error makes the tuning of
dynamics difficult.
Model evaluation against flow signatures
WWH1.3 is more prone to success or failure in simulating specific flow
signatures than to specific physiographic conditions, which is visualized by
vertical rather than horizontal stripes in Fig. 7. In general, the model
shows reasonable KGE and CC for spatial variability of flow signatures
across the globe (i.e. a lot of blue in the two panels to the left in Fig. 7). However, the RE and the standard deviation of the RE (RESD) are less
convincing (i.e. the two panels to the right). This means that the model can
capture the relative difference in flow signature and the spatial pattern
globally, but not always the magnitudes or the spread between the highest and
lowest values. The relative errors are mostly due to underestimations,
except for skewness, low flows, and actual potential evapotranspiration; the
latter two are always overestimated when not within ±25 % bias.
Overall, the model shows good potential to capture spatial variability of
high flows (Q95), duration of low flows (LowDurVar), monthly high flows
(Mean30dMax), and constancy of daily flows (Const). These results were found
to be robust and independent of metrics or physiography. The results imply that
the overall process understanding behind the HYPE model structure and the
assumptions of catchment similarities in the set-up may be relevant at the
global scale but that the estimation of parameter values or the quality of
forcing data are not optimal for capturing the flow dynamics.
Matrix showing the relation between model capacity to capture flow
signatures (colours, where blue is good and yellow/red/purple is poor
performance) and physiography of catchments, divided into quartiles (Q1–Q4)
for characteristics of the total area upstream of each gauging station with
more than 10 years of continuous data (5338 catchments). Descriptions of flow
signatures and physiographic characteristics are found in Tables 4–5 and
metrics used for model performance in Eqs. (1)–(4).
The model shows the most difficulties in capturing skewness in observed
time series (skew), the number of high-flow occurrences (HighFrVar),
base flow as average (BFI), or absolute low flows (Q5). Short-term
fluctuations (RevVar and RBFlash) are also rather difficult for the model to
capture. Some results are not consistent between metrics; for the coefficient of
variation (CVQ) the RE was good, while the RESD was poor. This indicates that
the model does not capture the amplitude in variation between sites even if
the bias is small. The opposite was found for high-flow discharge (HFD) and
low-flow spells (LowFr), i.e. poor performance in volumes but RESD showing
that the variability is captured.
For the remaining flow signatures studied, it was interesting to note that
the model performance could be linked to physiographic characteristics,
indicating that the model structure and global parameters are valid for some
environments but not for others. For instance, the volume of mean specific
flow (RE of MeanQ) is especially difficult to capture in regions with
needle-leaved, deciduous trees (TreeNeDec) and for medium and large flows in
Köppen region B (Arid), large flows in D (Cold-continental), and
small flows in E (Polar). Moreover, the analysis shows that the model tends
to fail with the mean flow in catchments with high elevation, high slope,
small fraction water and urban land cover, and little or much of snow and
ice. This shows where efforts need to be taken to improve the model in its
next version.
For other water-balance indices, it was interesting to note that the ratio
between precipitation and river flow (RunoffCo) show good results (RE
±25 %) all over Köppen region C (Temperate) but is otherwise
often underestimated for some parts of the quartile range of the physiographic
variables studied. By contrast, precipitation minus flow (ActET) is
overestimated in parts of the quartile range, except for the good results
in Köppen region C, needle-leaved, deciduous trees (TreeNeDec), and
regions with snow and ice (i.e. where mean specific runoff failed). Figure 7
clearly shows the compensating errors between processes governing the runoff
coefficient and actual evapotranspiration, with one being overestimated
when the other is underestimated for the same specific physiographic
conditions. This indicates the need for recalibrating the HRUs of WWH in its
next version but also reconsidering the initial parameters for
evapotranspiration and the quality of the precipitation grid and its linkage
with the catchments. It is rather common to use Köppen when evaluating
ET (e.g. Liu et al., 2016), but it may not be the best separator
hydrologically (Knoben et al., 2018), so model performance should preferably
be evaluated and calibrated in clusters based on other characteristics in
the future.
Discussion
This experiment of whether it is now possible and timely to apply catchment
modelling techniques to advance global hydrological modelling gave some
diverse results. Regarding physiographic data, it is now possible to
delineate catchments thanks to high-resolution topographic data (Yamazaki et
al., 2017), and there are many global datasets readily available with
necessary physiographic input data for catchment modelling also including
local hydrological features and waterbodies (e.g. sinks and floodplains)
that are normally not included in the traditional global models (e.g. Zhao
et al., 2017). Nevertheless, before merging the databases we found that they
need to be harmonized and quality assured, which has already been noted in
previous studies (e.g. Kauffeldt et al., 2013). For meteorological data,
global precipitation from re-analysis products are well known to contribute
a lot to the output uncertainty in traditional global modelling (e.g.
Döll and Fiedler, 2008; Biemans et al., 2009), and this was still the
case when applying catchment modelling; although the precipitation grid was
bias adjusted against observations (Berg et al., 2018) and further adjusted
with elevation during calibration, the density of stations at the global
scale was not sufficient for the resolution of the catchments. New
high-resolution products from the meteorological community have the potential to
become a game changer in global hydrological modelling.
The test whether parameter estimation methods from the catchment modelling
community could improve model performance in global hydrological predictions
resulted in better metrics than previously reported by e.g. Beck et al. (2016). Despite the large sample of river gauges, however, we experienced
that it was not distributed well enough to cover the large domain. Screening
of the gauged data quality showed that most regions worldwide have access to
some high-quality time series of river flow (Crochemore et al., 2019), but
for the stepwise procedure applied here this was still not enough for many
of the pre-defined calibration steps. Even when merging the original ESA
land-cover classes before calibration (Table 4) sufficient gauged data were
missing. As the structure of the catchment model reflects the modellers'
process understanding and as parameters must be estimated (Wagener, 2003), a
better compromise must be made between the HYPE structure or set-up and flow
gauges available for the global calibration scheme. Hence, the ecosystem
approach needs to be elaborated with better defined clusters for catchment
similarity across the globe to be truly helpful at this scale.
With current computational resources it was possible to use automatic
iterative calibration techniques from the catchment community (i.e. DEMC,
Ter Braak, 2016) to obtain the optimum parameter values from several
iterations, also across large samples of gauges. However, enough
computational resources were still lacking for advanced uncertainty
analysis, such as using GLUE (Beven and Binley, 1992).
To sum up, we found that the catchment model application at global scale
could be considered timely because it was doable, and now there is potential
for improvements, although even at this stage the model might be useful for
some purposes in some regions, as discussed below.
Potential for improvements
The results from evaluating model performance using several metrics, several
thousand gauges, and numerous flow signatures gave a clear indication of
regions where the model most urgently needs improvements. A thorough
analysis would also benefit from evaluation against independent data of
spatial patterns of hydrological variables, for instance from Earth
observations. In general, the WWH model has severe problems with dry regions
and base flow conditions where the flow is sporadic (e.g. red areas in Fig. 5). The flow-generating processes in such areas are known to be difficult to
model (Bloeschl et al., 2013). For instance, most model concepts, and also
WWH, have problems with the Great Plains of the USA (e.g. Mizukami et al.,
2017; Newman et al., 2017), where the terrain is complex with prairie
potholes, which are disconnected from the rivers, and where precipitation comprises
a major source of hydrologic model error (e.g. Clark and Slater, 2006). Poor
model performance was also found for the tundra and deserts, but it should
then be recognized that the parameters for these regions were estimated
using only four time series for bare soils (Table 6); including more gauging
stations would be a way to improve the model here. In large parts of Africa,
however, model errors could be linked to the soil-runoff parameters, and
local calibration based on catchment similarities has already been found to
improve the performance a lot in western Africa.
In the snow-dominated part of the globe, extensive hydropower regulation
changes the natural variability of river discharge (Déry et al., 2016;
Arheimer et al., 2017), but the global databases miss out on all medium and
small dams that may affect discharge along these river networks. A general
problem with modelling river regulation is that reservoirs can have
multiple purposes and must be examined individually to understand the
regulation schemes applied. Such analyses have started and shown the potential
to improve the global model a lot as the poorest model results are often
linked to river regulations. However, individual reservoir calibration will
be very time-consuming, so instead, we suggest starting with improvements
that can be undertaken relatively quickly and easily. These mainly focus on
the overall water balance. Firstly, the global water balance can be improved
through re-calibration, but some basic concepts need to be adjusted
accordingly: (i) more careful analyses indicate that the choice of climate
regions based on Köppen's classification for applying the different PET
algorithms was not optimal and needs some adjustments, (ii) linking the
centroid of the catchments to the nearest precipitation grid seems to remove
a lot of the spatial variation, and instead an average of the nearest grids
should be tried. Secondly, the HRUs can be recalibrated and reconsidered,
and we suggest (i) testing a calibration scheme based on regionalized
parameters rather than global ones, using clustering based on physiographic
similarities (e.g. Hundecha et al., 2016), (ii) including soil properties in
the HRU concept again (as in the original version of HYPE; see Lindström
et al., 2010) to account for spatial variability in soil-water discharge
linked to porosity in addition to vegetation and elevation. Thirdly, the
behaviour of hydrological features, such as lakes, reservoirs, glaciers, and
floodplains, can be evaluated and calibrated separately, after categorizing
them more carefully or from individual tuning. Finally, more observations
can be included, both in situ by adding more gauges to the system and from
global Earth observation products, for instance on water levels and storage.
Hence, each step in Fig. 3 still has the potential for model improvements.
Discrepancy between the idealized procedure for stepwise
calibration (a) and the numerous iterations between the steps that appear in reality (b), leading to overall model corrections.
The stepwise parameter-estimation approach should ideally be cycled a couple
of times to find robust values under new fixed parameter conditions.
However, as the model was carefully evaluated during the calibration, there
were a lot of bug fixing, corrections, and additional improvements resulting
between the steps, and time was rather spent on this than on several
fulfilled iterations. Therefore, the stepwise calibration was subjected to
several re-takes and shifts between steps until it eventually could
fulfill all the calibration steps in one entire sequence (Fig. 8). Hence,
only one loop was done for parameter estimations in this study. The
procedure was judged to be very useful for the model to be potentially right
for the right reason, but was also very time-consuming. However, applying a
catchment modeller's approach, this is inevitable for reliably integrated
catchment modelling, and both the stepwise calibration and iterative model
corrections will continue with new model versions.
Another important next step in model evaluation and improvement would be to
initiate a concerted model inter-comparison study at the global scale with
benchmarking (e.g. Newman et al., 2017), as we currently lack such studies
for global modelling of river flow. The focus should then be on comparing model
performance in general but also on input data and performance of specific
hydrological processes to understand differences between various model
concepts. The latter could be done by using the representative gauged basin
approach, as in this study, to evaluate model performance for sites where
flow is dominated by certain processes or by analysing specific parts of the
hydrograph (or flow signatures) that represents time periods when specific
processes dominate the flow generation. In addition to river gauges, other
data sources should be used for model evaluation of spatial patterns, e.g.
Earth observations. Specific areas that are intensively managed and impacted
by humans should also be distinguished and evaluated separately to better
understand process variability vs. human impacts. Various sources of input
data (from which errors may propagate) should also be evaluated to improve
global hydrological modelling.
Model usefulness
Catchment models are often applied by water managers and the usefulness is
part of the concept; however, to provide global hydrological data that are
relevant locally is far from trivial (e.g. Wood et al., 2011; Bierkens et
al., 2015). The result analysis of this first version of the WWH model shows
that it can only to some extent be useful for water managers in some regions
globally. For instance, long-term averages are rather reliable in the eastern
USA, Europe, South-East Asia, Japan, as well as most of Russia, Canada, and
South America. Here the model could thus be used for e.g. analysing shifts
in water resources between different climate periods. For high flows,
monthly values show good performance as well as the spatial pattern of
relative values. This implies that the model could be used for seasonal
forecasting of recharge to hydropower reservoirs, for which these variables
are often used. Accordingly, the model has already been applied for
producing water-related climate impact indicators, and it is set up
operationally to provide monthly river-flow forecasts for 6 months ahead
(https://hypeweb.smhi.se/explore-water/; SMHI, 2020a).
In many areas, HYPE should still be considered a scientific tool and
cannot be used locally by water managers because of poor performance.
However, the model provides a first platform for catchment modelling to be
further refined and experimented with at the global, regional, and local
scales. Parts of the model can be extracted (e.g. specific catchments or
countries) and used as infrastructure when starting the time-consuming
process of setting up a catchment model. The model can then be improved for
the selected catchments by exchanging the global input data with local data
and knowledge, as well as parameters estimated to fit with local
observations. Significant improvements in model performance from such a
procedure have already been noted for western Africa (Andersson et al., 2017a).
In Sweden the operational HYPE model runs with national data and adjusted
parameter values, providing an average daily NSE (Nash and Sutcliffe, 1970)
of 0.83 for 222 stations with ≤5 % regulation and an average relative
volume error of ±5 % for the period 1999–2008. For all gauging
sites (some 400) with both regulated and unregulated rivers, the mean
monthly NSE is 0.80. The Swedish HYPE model also started with poor
performance in its first version, but has been improved incrementally during
more than 10 years and has proven very useful in providing decision support
to society. It supports a national warning service with operational
forecasting of floods and droughts (e.g. Pechlivanidis et al., 2014) and
the water framework directive with plans and measures to improve water quality
(e.g. Arheimer et al., 2015). Moreover, it has been used in assessments of
hydro-morphological impact (e.g. Arheimer and Lindström, 2014),
climate-change impact analysis (e.g. Arheimer and Lindström, 2015), and
combined effects from multiple drivers on water resources in a changing
environment (e.g. Arheimer et al., 2017, 2018; Arheimer and
Lindström, 2019).
Thus, we found it to be very useful to have a national multi-catchment model to
support society in water-related issues. This should be encouraging for
other countries who do not yet have a national model set-up and also for
international river basin authorities searching for a more harmonized way to
predict river flow across administrative borders. Using WWH as a
starting point would be a quick and low-cost alternative for getting started
with more detailed catchment modelling for decision support in water
management. Parts of the model are therefore shared and can be requested at
https://hypeweb.smhi.se/model-water/ (SMHI, 2020b). Using a common framework for
catchment modelling by many research groups and practitioners will probably
advance science as it enables a critical mass and better communication when
sharing experiences. Only when using the same methods or data is there full
transparency in the research process so that scientific progress and
failures can be clearly understood, shared, and learnt from. WWH could be
one stepping stone in such a collaborative process between catchment
modellers across the globe. Therefore, SMHI has annually offered a free training
course since 2011, accompanied by travel grants for participants from
developing countries since 2013. Every year about 30 new persons are trained
in HYPE and get access to a piece of the modelled world, resulting in model
refinements and various regional assessments around the globe, e.g.
climate-change impact on Hudson Bay (MacDonald et al., 2018), flow forecasts
in the Niger River (Andersson et al., 2017b), hydromorphological evolution of
the Mackenzie delta (Vesakoski et al., 2017), and water quality in South Africa
(Namugize et al., 2017) or England (Hankin et al., 2019).
Conclusions
This study shows the usefulness of applying catchment modelling methods
(topographic catchment delineation, stepwise calibration, performance
evaluation against a large sample of observations using several metrics and
flow signatures) to help advance global hydrological modelling. The
catchment modelling approach resulted in better performance (median monthly
KGE =0.4) than what has been reported so far from more traditional
gridded modelling of river flow at the global scale. Major variability in
hydrological processes could be recognized world-wide using global
parameters, as these were linked to physiographical variables to describe
spatial variability and calibrated in a stepwise manner. Clearly, the
community of catchment modellers' can contribute to research also at the
global scale nowadays with the numerous open data available and advanced
processing facilities.
However, the WWH resulting from this first model version should be used with
caution (especially in dry regions) as the performance may still be of low
quality for local or regional applications in water management.
Geographically, the model performs best in the eastern USA, Europe, South-East
Asia, and Japan, as well as parts of Russia, Canada, and South America. The
model shows overall good potential to capture flow signatures of monthly
high flows, spatial variability of high flows, duration of low flows, and
constancy of daily flow. Nevertheless, there remains large potential for
model improvements, and it is suggested both to redo the calibration and
reconsider parts of the model structure for the next WWH version.
The stepwise calibration procedure was judged as very useful for the model
to be potentially right for the right reason, but also very time-consuming
and data demanding. The calibration cycle is suggested to be repeated a
couple of times to find robust values under new fixed parameter conditions,
which is a long-term commitment of continuous model refinement. The model
set-up will be released in new model versions during this incremental
improvement. For the next version, special focus will be given to the water
balance (i.e. precipitation and evapotranspiration), soil storage, and
dynamics from hydrological features, such as lakes, reservoirs, and
floodplains.
The model is shared by providing a piece of the world to modellers working
at the regional scale to appreciate local knowledge, establish a critical
mass of experts from different parts of the world, and improve the model in a
collaborative manner. The model can serve as a fast track to a model
environment for users who do not have this ready at hand, and in return
WWH can be improved from feedback on hydrological processes from local
experts across the world. Potentially it will accelerate scientific
advancement if more researchers start using the same tools and data, which
makes it easier to be transparent when evaluating and comparing scientific
results. SMHI is committed to long-term management, continuous refinement,
supporting tools, training, and documentation of the WWH model.
The table below shows additional information to Table A1 regarding which HYPE
parameters were calibrated for each process during the model set-up and
the range of resulting parameter values. A description of each parameter can
be found in the HYPE wiki at https://hypeweb.smhi.se/model-water/ (SMHI, 2020b).
Metrics and parameter values from the stepwise
parameter estimation globally. Parameter names and values are given in the
same order of appearance (columns 2 and 6).
Hydrological processHYPE parametersNo. of gaugesMedian value of metric(s) Parameter value(s)https://hypeweb.smhi.se/model-water/BeforeAfterPotential evapotranspiration (three PET algorithms: median of ranges constrained with MODIS)Jhtadd, jhtscale, kc2, kc3, kc4, krs, alb, alfapt0RE: 11.5 %RE: 0.5 %5; 100; [0.7–1.7]; [0.15–1.7]; [0.8–1.6]; 0.16; [0.3–0.8]; 1.26Glaciers (only evaluated vs. mass balance data)glacvexp, glacvcoef, glacvexp1, glacvcoef, glac2arlim, glacannmb, glacttmp, glaccmlt, glaccmrad, glaccmrefr, glacalb, fepotglac296RE: 0.38 % CC: 0.51–1.38, 0.17 1.25, 12.88, 25 000 000, 0, 0, 1.58, 0.19, 0.06, 0.35, 0Soils (average, rock, urban, water, rice)5 soils: rrcs1, rrcs2, rrcs3, trrcs, mperc1, mperc2, macrate, mactrinf, mactrsm, srrate, wcwp1-3, wcfc1-3, wcep1-325RE: -14.1 % KGE: 0.2Ranges: [0.20–0.5]; [0.01–0.45]; [0.01–0.1]; [0.05–0.35]; [30–100]; [10–60]; [0.05–0.7]; [12–30]; [0.3–0.9]; [0.01–0.3]; [0.01–0.6]; [0.2–0.6]; [0.01–0.5]Bare soils in deserts (calibrated manually)rrcs1, rrcs2, rrcs3, trrcs, mperc1, mperc2, macrate, mactrinf, mactrsm, sfrost, srrate, wcwp1-3, wcfc1-3, wcep1-34RE: 236.1 %RE: -18.90.6, 0.3, 0.0002, 0.15, 10, 0.1, 10, 0.8, 1, 0.01, 0.01, 0.0001, 0.0001, 0.3, 0.3, 0.0001, 0.03, 0.03, 0.00031. Precipitation: catchment elevationPcelevth, Pcelevadd, Pcelevmax147RE: -6.7 %RE: 4.4 %500; 0.01; 0.72. Precipitation: land-cover altitude5 elevation zones: pcluse1041RE: 24.3 %RE: 10.1 %0.05; 0.2; 0.25; 0.25; 0.353. HRUs in areas without snow10 HRUs: kc2, kc3, kc4, alb, soilcorr, srrcs, soilcorr318KGE: 0.16KGE: 0.27Range: [0.90–1.54]; [0.40–1.77]; [0.20–1.90]; [0.20–0.80]; [1.00–10.55]; [0.03–0.50]4. HRUs in areas with snow: ET, recession, and active soil depth10 HRUs: ttmp, cmlt, cmrad, fscdist0, fepotsnow225KGE: 0.16KGE: 0.24Ranges: [-2.67–1.80]; [1.10–4.00]; [0.16–1.5]; [0.20–0.75]; [0.09–0.98]5. Upstream lakesIlratk, ilratp731CC: 0.71CC: 0.721.8; 1.4 (depth: 5 m; icatch: 0.3)6. Regionalized ET (in 12 Köppen climate regions)12 climates: cevpcorr458KGE: 0.58KGE: 0.62Ranges: [-0.43–0.38]7. River routingrivvel, damp302CC: 0.70CC: 0.710.6; 1.08. Lake rating curve888 Lakes: rate; exp (LakeData.txt)945CC: 0.50CC: 0.59Ranges: [0.001–1013]; [1.002–3.0]9. Floodplains (partly calibrated manually)13 Floodplains: rclfp; rclpl; rcrfp; rcfpr (FloodData.txt)32KGE: -0.03KGE: 0.03Ranges: [0.05–0.99]; [0.15–0.90]; [0.05–0.99]; [0.15–0.90]10. Evaporation from water surfacekc2water, kc3water, kc4water201RE: -20.7 %RE: -12.2 %1.36; 0.65; 1.2511. Specific lake evaporation2 regions: cevpcorr16RE: 24.8 %RE: 4.8 %Ranges: [0.375–0.5]Code and data availability
Time series and maps from the World-Wide HYPE model are
available for free downloading at https://hypeweb.smhi.se/explore-water/ (SMHI, 2020a) and
documentation and open-source code of the HYPE model are available at
https://hypeweb.smhi.se/model-water/ (SMHI, 2020b).
Author contributions
All the authors contributed to the model development behind this article through weekly team meetings led by BA, KI, and JCMA. The main contribution by the authors to the work tasks are as follows: experimental design by BA and JCMA,
data collection and preparation by KI, LC, LP, RP, and AH,
catchment delineation by KI and AH,
model calibration by LC, RP, and AH,
model evaluation by RP, LC, BA, JCMA, KI, LP, and AH,
figure creation by RP, KI, BA, and LC,
manuscript writing by BA, and
manuscript refinement by LC, RP, KI, and JA.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
We would like to thank all the data providers listed in Tables 1–3 who made their
results and observations readily available for re-purposing; without you any
global hydrological modelling would not have been possible at all. Especially we
would like to express our gratitude to Dai Yamazaki, University of
Tokyo, for developing and sharing the global width database for large
rivers, which we found very useful. WWH was developed at the SMHI
hydrological research unit, where much work is done in common, taking
advantage of previous work and several projects running in parallel in
the group. It was indeed a team effort. We would especially like to
acknowledge contributions from our colleagues Jörgen Rosberg, Lotta Pers, David Gustafsson, and Peter Berg, who provided much of the model
infrastructure.
Review statement
This paper was edited by Jim Freer and reviewed by two anonymous referees.
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