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Dissertation presented at Uppsala University to be publicly examined in Hambergsalen, Earth Sciences
Centre, Villavägen 16, Uppsala, Wednesday, April 28, 2010 at 10:00 for the degree of Doctor of
Philosophy. The examination will be conducted in English.
Abstract
Gong, L. 2010. Large-scale Runoff Generation and Routing. – Efficient Parameterisation using Highresolution Topography and Hydrography. Acta Universitatis Upsaliensis. Digital Comprehensive
Summaries of Uppsala Dissertations from the Faculty of Science and Technology 725. 79 pp. Uppsala.
ISBN 978-91-554-7757-8.
Water has always had a controlling influence on the earth’s evolution. Understanding and modelling the
large-scale hydrological cycle is important for climate prediction and water-resources studies. In recent
years large-scale hydrological models, including the WASMOD-M evaluated in the thesis, have
increasingly become a main assessment tool for global water resources.
The monthly version of WASMOD-M, the starting point of the thesis, revealed restraints imposed by
limited hydrological and climate data quality and the need to reduce model-structure uncertainties. The
model simulated the global water balance with a small volume error but was less successful in capturing
the dynamics. In the last years, global high-quality, high-resolution topographies and hydrographies
have become available. The main thrust of the thesis was the development of a daily WASMOD-M
making use of these data to better capture the global water dynamics and to parameterise local nonlinear processes into the large-scale model. Scale independency, parsimonious model structure, and
computational efficiency were main concerns throughout the model development.
A new scale-independent routing algorithm, named NRF for network-response function, using two
aggregated high-resolution hydrographies, HYDRO1k and HydroSHEDS, was developed and tested in
three river basins with different climates in China and North America. The algorithm preserves the
spatially distributed time-delay information in the form of simple network-response functions for any
low-resolution grid cell in a large-scale hydrological model.
A distributed runoff-generation algorithm, named TRG for topography-derived runoff generation,
was developed to represent the highly non-linear process at large scales. The algorithm, when inserted
into the daily WASMOD-M and tested in same three basins, led to the same or a slightly improved
performance compared to a one-layer VIC model, with one parameter less to be calibrated. The TRG
algorithm also offered a more realistic spatial pattern for runoff generation.
The thesis identified significant improvements in model performance when 1) local instead of global
climate data were used, and 2) when the scale-independent NRF routing algorithm was used instead of a
traditional storage-based routing algorithm. In the same time, spatial resolution of climate input and
choice of high-resolution hydrography have secondary effects on model performance.
Two high-resolution topographies and hydrographies were used and compared, and new techniques
were developed to aggregate their information for use at large scales. The advantages and numerical
efficiency of feeding high-resolution information into low-resolution global models were highlighted.
Keywords: Parameterisation, runoff generation, routing, WASMOD-M, hydrography, data uncertainty,
topographic index, scale, river network, response function, HydroSHEDS, HYDRO1k, Dongjiang basin.
Lebing Gong, Department of Earth Sciences, Air, Water and Landscape Science, Villavägen 16,
Uppsala University, SE-75236 Uppsala, Sweden
© Lebing Gong 2010
ISSN 1651-6214
ISBN 978-91-554-7757-8
urn:nbn:se:uu:diva-121310 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121310)
Akademisk avhandling som för avläggande av filosofie doktorsexamen i hydrologi vid Uppsala
universitet kommer att offentligen försvaras i Hambergsalen, Geocentrum, Villavägen 16, Uppsala,
onsdagen den 28 april 2010 kl. 10:00. Professor Thorsten Wagener från Pennsylvania State
University är fakultetsopponent. Disputationen sker på engelska.
Referat
Gong, L. 2010. Storskalig modellering av flödessvarstid ochavrinningsbildning – Effektiv
parametrisering baserad på högupplöst topografi och hydrografi. Acta Universitatis Upsaliensis. Digital
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 725.
79 sid. Uppsala. ISBN 978-91-554-7757-8.
Vatten har alltid varit en nyckelfaktor för jordens utveckling. Att förstå och kunna modellera det storskaliga
vattenkretsloppet är betydelsefullt såväl för klimatförutsägelser som för studier av vattenresurser. På senare
år har storskaliga hydrologiska modeller, däribland WASMOD-M som utvärderas i denna avhandling, i
ökande utsträckning kommit att användas som huvudverktyg för utvärdering av globala vattenresurser.
Den månatliga versionen av WASMOD-M, avhandlingens startpunkt, användes för att påvisa
inskränkningar som låg i begränsande hydrologi- och klimatdata liksom behovet av att minska modellens
strukturella osäkerheter. Modellen simulerade den globala vattenbalansen med ett mycket litet volymfel
(avrinningens långtidsmedelvärde) men var mindre lyckosam att efterlikna dynamiken. Under senare tid
har globala topografiska och hydrografiska data med hög rumslig upplösning och kvalitet blivit
tillgängliga. Avhandlingens huvudsakliga drivkraft var att utveckla WASMOD-M med hjälp av dessa
data i syfte att bättre fånga den globala vattendynamiken och för att parametrisera lokala ickelinjära
processer i den storskaliga modellen. Under hela modellutvecklingen har skaloberoende, lågparametriserad modellstruktur och numerisk beräkningseffektivitet varit viktiga bivillkor.
En ny skaloberoende svarstidsalgoritm, benämnd NRF (network-response function), som utnyttjar
två aggregerade högupplösta hydrografier, HYDRO1k och HydroSHEDS, utvecklades och provades i
tre avrinningsområden med olika klimat i Kina och Nordamerika. Algoritmen bevarar den rumsligt
fördelade informationen om koncentrationstider i form av enkla responsfunktioner för vattendragsnätet
för godtyckliga lågupplösta beräkningsrutor in en storskalig hydrologisk modell.
En distribuerad algoritm för avrinningsbildning, benämnd TRG (topography-derived runoff generation), utvecklades för att representera den höggradigt ickelinjära processen i större skalor. Algoritmen
användes i den dagliga WASMOD-M och provades i samma tre avrinningsområden som ovan.
Modellprestanda blev lika bra eller bättre än en enlagers VIC-modell fast med en parameter mindre att
kalibrera. TRG-algoritmen gav ett rimligare rumsligt mönster för avrinningsbildningen.
Avhandlingen har identifierat påtagliga förbättringar i modellprestanda när 1) lokala i stället för
globala klimatdata användes och 2) när NRF, den skaloberoende svarstidsalgoritmen användes i stället
för en traditionell magasinsbaserad svarstidsalgoritm. Samtidigt har klimatdatas rumsliga upplösning
och val av högupplöst hydrografi en andra ordningens inverkan på modellprestanda.
Två högupplösta topografier och hydrografier användes och jämfördes, och nya tekniker utvecklades
för att aggregera deras informationsinnehåll i stora skalor. Fördelarna och den numeriska beräkningseffektiviteten av högupplöst information i lågupplösta globala modeller har belysts.
Nyckelord: Parametrisering, avrinningsbildning, flödessvarstid, WASMOD-M, hydrografi, topografiskt
index, dataosäkerhet, skala, flödesnät, svarstidssfunktion, HYDRO1k, HydroSHEDS, Dongjiang
Lebing Gong, Institutionen för geovetenskaper, Luft-, vatten- och landskapslära, Villavägen 16, Uppsala
universitet, 752 36 UPPSALA.
© Lebing Gong 2010
ISSN 1651-6214
ISBN 978-91-554-7757-8
urn:nbn:se:uu:diva-121310 (http://urn.kb.se/resolve?urn= urn:nbn:se:uu:diva-121310)
List of Papers
This thesis is based on the following papers, which are referred to in the text
by their Roman numerals.
I.
Widén-Nilsson, E., L. Gong, S. Halldin, and C.-Y. Xu. 2009. Model
performance and parameter behavior for varying time aggregations and
evaluation criteria in the WASMOD-M global water balance model.
Water Resources Research. 45, W05418, doi:10.1029/2007WR006695.
Copyright 2009 by the American Geophysical Union, reprinted with
permission.
II. Gong L., E. Widén-Nilsson, S. Halldin, C.-Y. Xu, 2009. Large-scale
runoff routing with an aggregated network-response function. Journal
of Hydrology, Volume 368, Issues 1-4, Pages 237-250,
doi: 10.1016/j.jhydrol.2009.02.007. Copyright 2009 by Elsevier,
reprinted with permission.
III. Gong L., S. Halldin, C.-Y. Xu, 2010. Global-scale river routing – An
efficient time-delay algorithm based on HydroSHEDS high-resolution
hydrography. Hydrological Process, accepted on 27 March 2010 with
only minor revisions.
IV. Gong L., S. Halldin, C.-Y. Xu, 2010. Large-scale runoff generation –
Parsimonious parameterisation of runoff generation using highresolution topography data. Manuscript.
Reprints were made with permission from the respective publishers.
In Paper I, I took the main responsibility for developing the model code. In
papers II, III and IV, I was responsible in modifying and/or developing the
model structure, programming the code of the models, running the model,
analyzing the result, and writing the first version of the papers.
In addition, the following papers, related to this thesis but not appended to it,
have been published during the PhD study:
Xu, C.-Y., L. Gong, T. Jiang, D. Chen and V. P. Singh, 2006. Analysis
of spatial distribution and temporal trend of reference evapotranspiration
in Changjiang (Yangtze River) catchment. Journal of Hydrology,
Volume 327, Issues 1-2, Pages 81-93,
doi:10.1016/j.jhydrol.2005.11.029
Xu, C.-Y., L. Gong, T. Jiang and D. Chen, 2006. Decreasing reference
evapotranspiration in a warming climate – a case of Changjiang
(Yangtze River) catchment during 1970-2000. Advances in Atmospheric
Sciences 23(4), 513-520. doi:10.1007/s00376-006-0513-4
Gong, L., C.-Y. Xu, D. Chen, S. Halldin and Y. D. Chen, 2006.
Sensitivity analyses of the Penman-Monteith reference evapotranspiration
estimates in Changjiang (Yangtze River) catchment and its sub-regions.
Journal of Hydrology, 329 (3-4), pp. 620-629.
doi: 10.1016/j.jhydrol.2006.03.027
Chen, D., L. Gong, C.-Y. Xu and S. Halldin, 2007. A high-resolution,
gridded dataset for monthly temperature normals (1971–2000) in
Sweden. Geografiska Annaler: Series A, Physical Geography, Volume
89, Number 4, pp. 249-261(13), doi: 10.1111/j.1468-0459.2007.00324.x
Chen, D. L. Gong, T. Ou, C.-Y. Xu, W. Li, C.-H. Ho, and W. Qian, 2010.
Spatial interpolation of daily precipitation in China: 1951-2005. Advances
in Atmospheric Sciences doi: 10.1007/s00376-010-9151-y, in press.
Contents
Introduction...................................................................................................11
Hydrological processes and modelling at large scale ..................................13
The global hydrological cycle ..................................................................13
Global hydrological models .....................................................................15
Land-surface models ................................................................................16
Hydrological processes at large scales .....................................................17
Runoff generation ................................................................................17
Evapotranspiration...............................................................................19
Snow and glacier .................................................................................20
Routing at the large scale.....................................................................22
Uncertainties, equifinality and scale issues ..............................................25
WASMOD-M, the Topography-derived Runoff Generation algorithm (TRG)
and NRF routing algorithm...........................................................................28
Global simulation with monthly WASMOD-M.......................................28
Regional simulation with daily WASMOD-M ........................................30
The NRF routing method .........................................................................30
The Topography-derived Runoff Generation algorithm (TRG)...............33
Datasets, basins and simulation setup ...........................................................35
Global datasets for monthly WASMOD-M .............................................35
Global datasets for daily WASMOD-M...................................................35
Global dataset for the TRG algorithm......................................................36
Global datasets for the NRF routing algorithm ........................................36
Test basins and local climate data ............................................................36
Model setup and evaluation......................................................................37
Results...........................................................................................................39
Performance of monthly WASMOD-M at global scale ...........................39
Performance of daily WASMOD-M and NRF routing algorithm in
the Dongjiang basin..................................................................................41
HydroSHEDS and HYDRO1k comparison .............................................44
Global and local dataset comparison........................................................47
Sub-grid distribution of storage capacity derived from topography.........48
Simulated cell-average storage capacity ..................................................51
Performance of the TRG-based model .....................................................53
Discussion .....................................................................................................54
Equifinality and parsimonious model structure........................................54
The non-linearity of runoff generation at large scale ...............................54
Importance of river identification at large scale.......................................55
LRR algorithm vs. NRF algorithm...........................................................56
Distributed climate input vs. distributed delay dynamics ........................56
HYDRO1k vs. HydroSHEDS ..................................................................57
Interaction between routing algorithm and runoff-generation
parameters ................................................................................................58
Computational efficiency .........................................................................58
Conclusions...................................................................................................60
Acknowledgements.......................................................................................62
Sammanfattning på svenska (Summary in Swedish) ....................................64
Ё᭛ᨬ㽕 (Summary in Chinese) .................................................................68
References.....................................................................................................71
Abbreviations
1DD
CIT
CRU
DEM
FAO
GCM
GLUE
GPCP
GRDC
HBV
HydroSHEDS
LRR
NRF
PDM
SCA
SMR
STN
TOPLATS
TRG
TRMM
VIC
WASMOD-M
WaterGAP
WBM
WGHM
WTM
1-Degree Daily
Channel Initiation Threshold
Climate Research Unit
Digital Elevation Model
Food and Agriculture Organization
General Circulation Model
Generalised Likelihood Uncertainty Estimation
Global Precipitation Climatology Project
Global Runoff Data Centre
Hydrologiska Byråns Vattenbalansavdelning
Hydrological data and maps based
on SHuttle Elevation Derivatives at
multiple Scales
Linear Reservoir Routing
Network Response Function
Probability-Distributed Moisture model
Snow Covered Area
SnowMelt Runoff model
Simulated Topological Network
TOPMODEL-Based Land Surface-Atmosphere
Transfer Scheme
Topography-derived Runoff Generation
Tropical Rainfall Measurement Mission
Variable Infiltration Capacity
Water And Snow balance MODelling system at
Macro scale
Water - Global Analysis and Prognosis
Water Balance Model
WaterGap Global Hydrological Model
Water Transport Model
Introduction
Water has always had a controlling influence on earth’s evolution.
Understanding and modelling of the large-scale hydrological cycle is
important for climate prediction and water resources studies. Measurement
techniques, either ground-based or remote-sensing, provide a basis for
understanding of the large-scale hydrological system and validating our
knowledge, but they cannot provide a consistent description of the dynamics
of the system in space and time. Quantitative estimation and prediction of
the hydrological regime variations and the hydrological consequences of
anthropogenic impact requires modelling. In recent years, large-scale
hydrological models have increasingly been used as a main assessment tool
for global water resources. Land-surface models, which also provide waterresources information, have been used as lower boundary condition for
global climate models.
Large-scale modellers face several practical and theoretical challenges.
Firstly, much of the earth’s land surface is covered with ungauged basins.
This makes regionalisation central to large-scale hydrological modelling.
Secondly, uncertainties in hydrological and climate data are assumed to be
one of the main reasons for the simulated discharge uncertainties. Low data
quality sometimes force model parameter values outside of their physical
ranges, or force the usage of large runoff-correction factors when it has not
been possible to reproduce measured discharge (Döll et al., 2003; Fekete et
al., 2002). Those challenges have led to a number of theoretical
considerations for both current large-scale models and issues that should be
improved in future models. Thirdly, there is a need to bridge the gap
between small-scale heterogeneities and large-scale model formulations.
Fourthly, there exist many large-scale models with different spatial
resolutions. Scale dependency has been introduced by the use of different
non-compatible flow networks. Fifthly, although the complexity of largescale models is limited by lack of global data, equifinality still exists for
many model parameters.
Scale is a central issue when it comes to large-scale modelling. Currently,
many large-scale models use model equations developed at the catchment
scale. For instance, WBM (Vörösmarty et al., 1989, 1996, 1998) is rooted
back to the Thorntwaite method (Thorntwaite and Mather 1957); MacroPDM (Arnell, 1999, 2003) is a large-scale application of PDM, the
probability-distributed moisture model (Moore, 1985); the runoff generation
11
algorithm of WGHM (Döll et al., 2003) is adopted from HBV (Bergström,
1995); the VIC model (Wood et al., 1992, Liang et al., 1994) is developed
from the Xinanjiang (Zhao and Liu, 1995) and Arno models (Francini and
Pacciani 1991; Todini, 1996); TOPLATS (Famiglietti and Wood, 1991) is
based on TOPMODEL concepts (Beven and Kirkby 1997); WASMOD-M
(Widén-Nilsson et al., 2007) essentially uses the same algorithms as
WASMOD (Xu, 2002). There are no simple ways to transfer knowledge of
model structure across scales but some model structures might be easy to
transfer from catchment to larger scales if the algorithm can easily be
adapted to use the same input data at different scales. For example, runoffgeneration algorithms at different scales can be based on distribution
function of topographic indexes aggregated from a given high resolution
DEM. The TOPLATS (Famiglietti and Wood, 1991) is one example. A
similar approach is implemented by Sivapalan et al. (1997), but with the
TOPMODEL assumption relaxed so topographic index is used only as
indicator of relative storage capacity. The model of Sivapalan et al. (1997),
however, was only tested in a small catchment (26.1 km2).
Kirkby (1976) and Beven and Wood (1993) demonstrated that time
delays in small catchments tend to be dominated by the routing of hillslope
flows while in large catchments routing in the channel network plays a
dominant role in shaping the hydrographs. There is a lack of scaleindependent routing algorithms which preserve small-scale delay dynamics
at large scales, partly because lateral water transport is sometimes considered
less important than the vertical land-surface exchange that dominates runoff
generation in many global-scale models (e.g., Olivera et al., 2000).
The further progress of large-scale hydrological models relies on highquality data, and model development should adapt to new such data. Global
topographical and hydrographical data are currently available with high
resolution and quality. The aim of this PhD thesis was to find an efficient
way to parameterise small-scale hydrological processes, such as runoff
generation and routing, based on such high-quality global datasets, and to
use the result of these parameterisations in the form of distribution functions
which summarise the underlying physical dynamics. The thesis also aimed at
examining to what degree a large-scale hydrological model, when driven
with aggregated small-scale dynamics, could resemble the performance of
small-scale models, to what degree scale dependency could be avoided, and
how much large-scale models would benefit from using high-resolution
topographical and hydrographical datasets. The technical-applicability and
computational-efficiency issues related to using high-resolution data at large
scales were also challenged.
12
Hydrological processes and modelling
at large scale
The global hydrological cycle
The global hydrological cycle plays an important role in the earth system.
Water exists in all three phases in the climate system and determines the
scale and patterns of large-scale oceanic and atmospheric circulations.
Transitions between the three water phases act as a stabilizer which restricts
the earth’s climate to remain within a unique, narrow bound (Webster,
1994). From a broader sense, the term “global hydrology” includes clouds
and radiation, atmospheric moisture, precipitation process, land and ocean
fluxes and state variables. In the context of classic surface hydrology,
“global hydrology” often refers to presence, transfer and storage of water
between the land surface and atmosphere, i.e. precipitation, snow and ice
storage, evaporation, soil water storage, runoff generation and river routing.
The global hydrological cycle explains the distribution of water resources for
all life on the earth. Currently only a small percentage of the earth’s fresh
water is withdrawn by human beings; however the uneven distribution of the
fresh water recourses in space and time has caused about 2 billion people
lacking access to sufficient drinking water (Oki and Kanae, 2006). The
global hydrological cycle also plays an important role for the future climate
regime. For instance, water vapour is radiatively active and is also the most
variable component of the atmosphere. The presence of water vapour
enhances the radiative effect of any increase of concentration of other
greenhouse gases such as CO2 (Chahine, 1992a). On the other hand,
cloudiness would also get increased from a warmer and wetter atmosphere
which in turn reduces the incoming solar radiation (Webster, 1994). Better
understanding of such competing and conflicting processes would help
achieving better prediction of the future climate.
The hydrological cycle circulates from plot to global scales. Continents,
oceans and atmosphere exchange water through various hydrological
processes at different scales with mean residence time ranges from around
10 days in the atmosphere to over 3,000 years in the oceans. Over the
oceans, evaporation exceeds precipitation and the difference contributes to
precipitation over land. Over land, about 35% of the rainfall comes from
marine evaporation driven by winds, and 65% comes from evaporation from
13
the land (Chahine, 1992b). As precipitation exceeds evaporation over land,
the excess must return to the oceans as gravity-driven runoff. Oki and Kanae
(2006) supplied quantitative descriptions of the global hydrological cycle
(the terrestrial part does not include Antarctica) in terms of water fluxes and
storages. The oceans hold about 1,338,000,000 km3 water (97%), followed
by deep groundwater 23,400,000 km3 (1.7%). The majority of fresh water on
the land surface is locked as glaciers, snow and permafrost, summing up to
around 24,364,000 km3. Water stored in lakes, wetlands, rivers and soils are
only around 211,000 km3, merely 0.015% of the total. The atmospheric
water vapour is around 13,000 km3. In terms of fluxes, over the oceans, more
evaporation (436,500 km3year-1) than precipitation (391,000 km3year-1)
occurs. The surplus (45,500 km3year-1) is transported to the land as net water
vapour flux, magnitude of which equals to the difference between terrestrial
precipitation (111,000 km3year-1) and evapotranspiration (65,500 km3year-1),
and also equals to the global discharge returning to the oceans (45,500
km3year-1). The total global discharge is normally higher than 45,500
km3year-1 when endorheic (river flow and groundwater flow into inland
basins) discharge is also included. It is worth noting that isotope studies
(e.g., Moore, 1996; Church, 1996) show that approximately 10% of the total
global discharge goes directly into costal water system as submarine
groundwater discharge. Conventionally, water withdrawn from surface and
groundwater was considered as water recourse, or “blue water”;
evapotranspiration (or soil moisture that remains and contributes to
evapotranspiration) from non-irrigated (rain-fed) agriculture is also a water
resource that is beneficial to the society (Oki and Kanae, 2006; Jewitt, 2006;
Rost et al., 2008). The evapotranspiration flux is named “green water”.
Currently, about 10% of the blue water resources and 30% of the green
water are being used by irrigation, industry and domestic usages (Oki and
Kanae, 2006).
Before the introduction of the first global hydrological model, global
water resources were originally assessed from gauged discharge data (e.g.,
L’vovich, 1973; Baumgartner and Reichel, 1975; Korzun et al., 1978;
Shiklomanov, 1997). Discharge data are still the bases for global water
resources assessment today. For example, estimates of long-term surface
freshwater fluxes into the oceans were compared with literature by GRDC
recently (GRDC, 2004). However, the homogeneity of pure data-based
assessments is often limited by the fact that many of such data come from
country statistics (Widén-Nilsson et al., 2009), and the usage of different
continental boundaries (e.g., Nijssen et al., 2001a; Döll et al., 2003) and
different time periods (Widén-Nilsson et al., 2007). Remote sensing
technologies offered new opportunities of measuring global river flows from
the space (Calmant and Seyler, 2006), although it is still hard to achieve high
spatial and temporal resolution at the same time (e.g., Calmant and Seyler,
2006; Wagner et al., 2007). The area of surface water extent is also
14
measured and combined with altimetry measurements (Alsdorf and
Lettenmaier, 2003). River discharge can be calculated from a combination of
several remotely sensed river hydraulic data (Bjerklie et al., 2003). More
recently variations in the total terrestrial water storage are related to
observed changes in earth’s monthly gravity field in the GRACE (Gravity
Recovery and Climate Experiment) project (Güntner et al., 2007).
Global hydrological models
Global hydrological models are increasingly used to estimate present and
future water resources at large scales for purposes of, e.g., climate impact
studies, freshwater assessment, transboundary water management, and
virtual water trade (Arnell, 2004; Islam et al., 2007; Lehner et al., 2006;
Nijssen et al., 2001a; Vörösmarty et al., 2000a). MacPDM (Arnell, 1999;
2003), WBM (Vörösmarty et al., 1998), WGHM/WaterGAP (Alcamo et al.,
2003; Döll et al., 2003), and WASMOD-M (Widén-Nilsson et al., 2007)
were developed from conceptual catchment models. VIC (Liang et al.,
1994), TOPLATS (Famiglietti and Wood, 1991; Famiglietti et al., 1992) and
the integrated global water resources model of Hanasaki et al., (2008a, b) are
macroscale hydrological models designed for coupling with General
circulation models (GCMs). Global runoff is also calculated by dynamic
vegetation models (e.g., Gerten et al., 2004; Kucharik et al., 2000).
Performance of global hydrological models has received attention in
recent years. Global models differ from regional models by the fact that a
substantial part of the land surface is ungauged. Most modelers agree that
global model parameters should preferably not be calibrated (Arnell, 1999;
Hanasaki et al., 2008a) to allow an easier regionalisation. However, because
of data and model structure uncertainty, Döll et al. (2003) argued that
calibration is necessary and they calibrated the runoff regulation parameter
of WGHM against measured long term average values. In WBM
(Vörösmarty et al., 1998) soil storage parameters were set from vegetation
and soil properties, even though WBM’s routing module is calibrated. Arnell
(1999; 2003) also avoided calibration as much as possible, although when
developing the model, Arnell (1999) did some tuning to set values and test
model sensitivity. WASMOD-M (Widén-Nilsson et al., 2007) and VIC
(Liang et al., 1994) are calibrated. On the global scale, the uncertainty of
input and validation data, and the difficulty of including all relevant
processes, for instance glaciers, permafrost, lakes, wetlands, dams and
reservoirs all adds up to the uncertainty of model prediction. Calibration
techniques that optimise model parameters against one or more measured
datasets do not always give useful result. Any performance measure, for
example the commonly used Nash-efficiency (Nash and Sutcliffe, 1970),
reflects both model performance and uncertainty of input and validation
15
data. No single model, even the one that gives the best performance measure,
is able to bracket the possible range of prediction under the influence of
uncertainty. Monte Carlo simulation techniques are often used to reveal the
uncertainty of model prediction and model parameters. Prediction bounds
could be produced by weighting the accepted Monte Carlo simulation as was
used in the GLUE method (Beven and Binley, 1992).
Many of the large rivers in the world are regulated, for example, a lot of
dams and reservoirs were constructed in the middle of the 20th century in the
Unites States (Vörösmarty et al., 2004). More dams and reservoirs are still
being constructed today which further changes the regime of natural water
system globally. For heavily regulated river basins, validation of global
water balance models against measured discharge time series is only
meaningful if not only the natural water cycle, but also evaporative loss,
water abstraction and delay from dams and reservoirs are taken into account
(Vörösmarty et al., 1997; Nilsson et al., 2005; Döll et al., 2003). Otherwise,
validation must primarily be done on long-term average of annual runoff
data.
Land-surface models
Global water resources are commonly assessed with global hydrological
models, whereas the interaction between the terrestrial hydrological cycle
and the atmosphere is commonly studied with land-surface schemes. These
two approaches differ in complexity and in land-surface parameterisation.
Global hydrological models are commonly simpler than land-surface
schemes, requiring less input data and computational resources. However,
their lack of feedback mechanisms and their weaker physical foundation
lower their ability to predict changes in the hydrological system under
changing land use or changing climate. Land-surface schemes, on the other
hand, commonly lack ability to represent direct anthropogenic influence on
the water cycle, are computationally more demanding and have seldom, if
ever, been tested for equifinality or parameter and model-structure
uncertainty.
In general, energy and hydrology in the climate system are linked by
many atmospheric and surface processes. Energy is needed to convert soil
water to vapour. Most of this energy comes from radiation absorbed by the
surface. Surface albedo is governed, among others, by snow, vegetation and
bare soil conditions. Changes in vegetation and soil moisture alter the
partition between evaporation and runoff which, in turn, changes surface
conditions. On the global average, at annual level, radiation energy is
unbalanced between the atmosphere and the land surface, with a surplus for
the land surface and a deficit for the atmosphere. When an energy imbalance
occurs in the atmosphere or at the surface, the atmosphere-surface system
16
reacts to re-establish the balance by a number of atmospheric and hydrologic
processes, among which, balance is most efficiently re-established by means
of transport of latent heat through evaporation and condensation. The
hydrological part of the GCMs provides a lower boundary condition for the
fluxes of energy and water vapour between the land surface and the
atmosphere. These models are also commonly known as land surface
parameterisation schemes or soil-vegetation-atmosphere transfer schemes
(SVATs).
In the Manabe’s bucket model (1969), evaporation occurs at potential rate
until a critical value of soil moisture is reached, and then continues at a rate
linearly proportional to the soil moisture ratio. This simple concept still
keeps its popularity in modelling evaporation in today’s catchment and
global scale models. The Xiananjiang model (Zhao and Liu, 1995) and its
further developed variants, the Arno model (Todini, 1996) and the VIC
model (Wood et al., 1992; Liang et al., 1994) are good examples. Sharing
similarities with the probability distributed moisture model (PDM) (Moore,
1985) and Macro-PDM (Arnell, 1999), the VIC model modified the original
bucket model idea to allow a variable infiltration capacity, and the spatial
distribution of the infiltration capacity follows a power law with one shape
parameter. The two-layer VIC model (VIC-2L) was designed for use within
general circulation models. The VIC-2L has an independent water-balance
part, which simulates canopy evaporation, transpiration and bare soil
evaporation separately based on surface resistance and aerodynamic
resistance, and then uses the variable infiltration capacity concept to generate
direct runoff, and uses the Arno model concept to formulate subsurface
runoff for the second soil layer. The VIC-2L also has an energy balance part,
linked with the water balance by the latent heat flux (evapotranspiration) to
calculate the surface temperature and the fluxes of sensible heat and ground
heat which depend on surface temperature. The VIC model has been applied
globally (Nijssen et al., 2001a, 2001b), and been compared to several global
hydrological models.
Hydrological processes at large scales
Runoff generation
Fully distributed runoff generation models are in general difficult to apply
because much of their demand on input data is not readily available. Semidistributed models simplify the model structure by grouping parts of a basin
that behave in a hydrologically similar way. Variations in soil, vegetation
and topography play a significant role in the spatial variation of storage
deficit and in setting up initial conditions for runoff generation and
evaporation. It is however difficult to get explicit spatial descriptions of the
17
land surface at global scale. Instead it would be practically sufficient to use a
simplified model based on the statistical representation of the heterogeneities
(e.g., Wood and Lakshmi, 1993). The basic idea of a statistical approach is
that beyond a certain spatial scale, sometimes referred to as Representative
Elementary Area (REA) (Wood et al., 1988), the dynamics of runoff
generation can be represented by probability distributions of conceptual
stores without an explicit representation of the stores in space, nor of the
explicit physics that control the distribution. For example, VIC model (Liang
et al., 1994; Nijssen et al., 1997; Wood et al., 1992) assumes that soil
infiltration and moisture capacity properties vary across the grid following a
defined probability distribution. Macro-PDM (Arnell, 1999, 2003),
developed from PDM (Moore and Clarke, 1981), assumes that the sub-grid
distribution of storage capacity is following a power distribution. At large
scale, the parameters defining variability of storage deficit are normally
fixed, implying the same type of response from different parts of the basin.
Another way of grouping hydrologically similar areas is to use data-based
methods. Compared with pure statistical approaches, date-based methods are
based on physical data and require more assumptions to be made. For
example, TOPMODEL (Beven and Kirkby, 1979) is based on a topographic
index derived from soil and topography data. Under the assumption of
kinematic wave and successive steady-states, points with the same
topographic index behave in a hydrologically similar manner. TOPMODEL
is able to map spatially the soil moisture deficit, which allows the prediction
of saturated areas to be truly spatially distributed rather than a lumped
percentage as derived from statistical approaches.
The VIC model and the TOPMODEL concept are interesting candidates
to simulate global hydrology because they combine the computational
efficiency of the distribution function approach and the catchment physics.
Global scale applications include VIC (Nijssen et al., 1997, 2001a, b) and
TOPLATS (Famiglietti and Wood, 1991; Famiglietti et al., 1992).
Increasingly, models based on the topographic index are considered as basis
for efficient parameterisation of land-surface hydrological processes at the
scale of the GCMs grid square (Famiglietti and Wood, 1991). On the other
hand, the application of TOPMODEL concept on large scales has received
criticism because TOPMODEL was originally designed for small
catchments with moderate to steep slope and with relatively shallow soils
overlaying impermeable bedrocks. Under such conditions topography does
play an important role in runoff generation, at least under wet conditions. In
places with dry climate, flat terrain or deep groundwater system, the validity
of the TOPMODEL assumptions is questionable. The VIC model, on the
other hand, is built on fewer assumptions and is easier to be generalised
(Kavetski et al., 2003 ).
Conceptualisation of soil layers is a central part in a runoff generation
algorithm. Single-soil-layer models are simpler but generally underestimate
18
surface evapotranspiration during dry seasons. Stamm et al. (1994) reported,
in their study of the sensitivity of GCM simulated global climate to the
representation of land-surface hydrology, that the storage capacity of the
VIC model has relatively little influence on the simulated climate in northern
Eurasia and north America. They attributed this finding to the fact that the
soil moisture is not utilised for evaporation, due to dry period drainage to
base flow. An alternative method will be the addition of a root zone that is
only depleted by evaporation and an unsaturated zone which delays the
infiltration of rain water to the saturated zone, or like Liang et al. (1994), the
addition of a deep groundwater layer. If more than one soil layer is
considered, the recharge from the unsaturated zone to groundwater should be
accounted. This recharge rate is important for the partitioning of surface and
subsurface flow, and can be simulated by a simple, conceptual or more
physically based method. In TOPMODEL (Beven, 2001), for example,
recharge from the unsaturated zone is treated as a linear function of the
deficit of the groundwater store. This method effectively allows the
conductivity of the unsaturated zone to decrease linearly as groundwater
table falls.
Evapotranspiration
It has long been known that it is not possible to determine the actual
transpiration or evaporation from land surface by simply measuring the rate
of loss of water from an exposed pan (Thornthwaite and Holzman, 1939).
Factors other than meteorological conditions affect evapotranspiration, for
example, growth of vegetation and water content of surface soil. There exist
different ways to interpret the physical mechanism of evapotranspiration.
Dalton (1802) was the first to point out that evaporation is proportional to
the difference between the vapour pressure of the air at the water surface and
that of the overlaying air; the aerodynamic approach was later developed
from this idea to treat evaporation as turbulent transport due to the gradient
of vapour pressure between evaporating surface and overpassing air.
Another approach is to derive the amount of evaporation by energy balance
between the net radiation absorbed by water and the energy exchange due to
convection, conduction and latent heat of evaporation. The combination of
the aerodynamic methods and the energy balance approaches was introduced
by Penman (1948), and further developed into the Penman-Monteith
combination method for estimating reference evapotranspiration rate, which
was later used as the basis by FAO (Allen et al., 1998) as the standard
method for estimating reference and actual crop evapotranspiration.
The Penman-Monteith combination method assumes that the boundary
layer at the surface is well mixed with a logarithmic vertical wind profile.
Under this condition the aerodynamic resistance ra can be derived from wind
speed and vegetation height. The method lumps the surface of
19
evapotranspiration, which consists of soil surface (evaporation), stomata
openings (transpiration) and the total leaf area (canopy evaporation), into a
big leaf which has a bulk surface resistance rc. The application of the
Penman-Monteith equation for actual evapotranspiration requires
temperature, humidity, radiation and wind speed data (and the height of
measurement), vegetation parameters like the active leaf area index (LAI),
the minimal canopy resistance, the height of the vegetation or zero plan
displacement height, and surface albedo. A soil moisture stress factor,
normally linearly related to the moisture storage, is also needed to determine
the surface resistance. On one hand, the Penman-Monteith equation requires
a large amount of data, on the other hand, it has the advantage of reflecting
the influence of the climate and land use on evapotranspiration. Under a
changing climate and land use, one may not be able to extrapolate those
evaporation models to make prediction into the future. The PenmanMonteith equation is constructed for describing processes at very small
spatial scale. At regional scale, the assumption for the well-mixed boundary
layer may not hold everywhere, and the aggregation of different atmospheric
and surface conditions may be very difficult. The complementary
relationship method (Bouchet, 1963) for estimating regional
evapotranspiration is based on the idea that when evaporation is limited by
the availability of soil moisture resultant changes in temperature and
humidity of overpassing air are reflected in the magnitude of potential
evaporation. Thus, at regional scale, the potential evaporation reflects the
effect rather than the cause of evaporation (Morton, 1971; Monteith, 1981).
A number of complementary relationship methods (Morton, 1983; Brutsaert
and Stricker, 1979; Granger and Gray, 1989) were developed to estimate
actual evapotranspiration from potential evaporation and evaporation under
equilibrium condition.
Snow and glacier
Global warming, melting of glaciers and thawing of permafrost, may change
the hydrological regime of the cold regions. In the same time, snow melt
contributes substantially to the global river discharge. Glacier ice contains
75% of the available freshwater on the earth. Although 99.5% of the ice is
contained in the form of ice sheets in the Greenland and Antarctic, smaller
glaciers and ice caps in the alpine catchments are important supplies and
regulators for regional water resources. Response of alpine glaciers to global
warming can significantly influence the hydrology of river basins: the loss of
the temporary storage in glaciers, if they disappear, will change the seasonal
runoff pattern and reduce river flow during warm and dry period of the year.
Accumulation and melting of ice and snow are dependent on
climatological factors and surface albedo of ice and snow. Compared to
snow-free catchments, where runoff generation is dominated by precipitation
20
and current state of soil moisture storage, glacier and snow melt runoff is
determined by the amount of energy supply. The energy consumed by
melting is mainly supplied by net radiation and sensible and latent heat
fluxes from the atmosphere.
Melting models exist at different complexities, from simple temperature
index methods (degree-day methods), to full energy balance methods. On
large scales a model that could sufficiently reflect the underlying physics,
but remains a simple form, is needed. Temperature index methods have the
advantage of simplicity and data availability. The simplest temperature index
method is the degree-day method (Bergström, 1995), assuming a linear
relationship between the melting and the deviation of the mean air
temperature from a threshold temperature. Different degree-day factors
could be assigned for different land cover types, for example, for forest and
open land in the HBV model (Bergström, 1995). At sub-daily scale, the
degree-day factor shows pronounced diurnal cycle which follows the course
of the radiation cycle. The degree-day factor also shows long term variation,
for example, in the end of a melting season there can often be an increasing
trend of the degree-day factor as a result of the increasing supply of solar
radiation and the deceasing of the albedo. Rango (1995) showed that the
degree-day factor, even averaged over large basins (for example Durance in
France, 2170 km2), showed significant increase from 0.4 to 0.6 cmoC-1day-1
during the melting season, indicating the gradual increasing contribution of
the net short wave radiation, which is less temperature-correlated.
On the catchment scale, the temperature index methods show a competing
performance (Hock, 2003) compared with the energy balance methods. The
well-performing of the temperature index methods can be explained by the
high correlation of temperature with several energy balance components that
control melting, especially when considering lumped spatial and temporal
extent (Hock, 2003). Several authors (e.g., Rango and Martinec, 1995; Hock,
2003) reported a modification of the temperature-based methods by adding a
radiation component. This modification needs the radiation to be measured,
and a model for energy balance at the snow surface taking into account the
varying snow albedo.
On the global scale a typical 0.5º grid covers a wide range of elevations,
thus it is necessary to divide the grid into elevation zones and use the lapse
rate to derive temperature for each zone. However, it is still difficult to
simulate the snow covered area (SCA) by explicit snow pack counting
methods like the degree-day method used in HBV. This is because the
roughness of the surface, e.g., hollows and valleys, trap more snow than
elsewhere; and the uneven distribution of energy due to, for example
topographic effects such as shading, slope and aspect angles (Hock, 2003).
To overcome this deficiency in the snowmelt runoff model SMR, Rango
(1995) used the remotely sensed snow covered area as an input, and the melt
21
runoff in each elevation zone was obtained by multiplying the snow covered
area by the melt rate.
Routing at the large scale
On the global scale it is difficult to calibrate a model against discharge time
series if the model does not include routing delays from rivers, lakes,
wetlands, as well as dam regulations. The problem is exacerbated since
estimation of water resources is required at finer temporal resolution, and
due to the fact that many of the large river basins in the world are regulated.
Most previous studies have used long-term average discharge when
evaluating the results or selecting behavioural parameter value sets. Some
global models, e.g., WGHM (Döll et al., 2003) and WBM/WTM
(Vörösmarty and Moore, 1991; Vörösmarty et al., 1996), include routing
delay. Many global rivers have regulation delays of 1–3 months (Vörösmarty
et al., 1997), but regulation data are often unavailable (Brakenridge et al.,
2005). Algorithms for dam operation schemes are emerging (Haddeland et
al., 2006; Hanasaki et al., 2006) but are not widely used. At monthly time
steps river routing is only necessary for a few very large rivers (Sausen et al.,
1994; Kleinen and Petschel-Held, 2007), where lakes, wetlands and dams are
much more important for the delays (Vörösmarty et al., 1997; Coe, 2000).
WBM uses a flow network but only has routing with the additional WTM
water transport model. Macro-PDM has within-cell routing only. WGHM
calculates routing in rivers as well as in lakes, wetlands and reservoirs.
Water withdrawal is also simulated with WaterGAP.
Large-scale routing algorithms transfer runoff to discharge in global and
continental water-balance (Vörösmarty, 1989; Döll et al., 2003) and landsurface models (Russell and Miller, 1990; Liston et al., 1994; Coe, 2000;
Arora, 2001; Hagemann and Dümenil, 1998). Runoff routing at large scales
normally involves development of low-resolution flow networks, the spatial
resolutions of which range from 1 km (HYDRO1k, USGS, 1996a) to 4°×5°
latitude-longitude (Miller et al., 1994). Many global water-balance models
use a 0.5°×0.5° latitude-longitude grid (Fekete et al., 2002; Arnell, 2003;
Döll et al., 2003) since this has been found suitable for a broad range of
global water-resources and water-quality studies (Vörösmarty et al., 2000a).
There exist at least 5 global routing networks with this resolution (Hageman
and Dümenil, 1998; Graham et al., 1999; Renssen and Knoop, 2000;
Vörösmarty et al., 2000b; Döll and Lehner, 2002). The lack of a common
network complicates inter-comparison of global models, which is regrettable
because of the large differences in model predictions that are seen even
when runoff predictions are aggregated to global and continental scales
(Widén-Nilsson et al., 2007; Hanasaki et al., 2008a).
Most large-scale routing models apply storage-based routing algorithms
on low-resolution flow networks. Such algorithms are based on mass
22
conservation and relationships between river-channel storage and river
inflows and outflows. In the Muskingum method (McCarthy, 1939), the
storage S is a function of both inflow I and outflow O:
S = K ⋅ [ x ⋅ I + (1 − x) ⋅ O]
The mean residence time K can be approximated by the time needed by
the wave to travel through the reach, whereas x is a shape parameter
controlling the relative importance of inflow on the outflow hydrograph. For
most rivers, x takes values in the range between 0 and 0.3 with average
around 0.2 (Linsley et al., 1982). The parameters of the Muskingum equation
can be estimated graphically from inflow and outflow hydrographs or, as
shown by Cunge (1969), from flow hydraulics. Since the estimation of x
requires local knowledge for each river reach, it is always set to zero in
global-scale applications. This zero-x simplification implies that wedge
storage in the channel is unimportant (e.g. Linsley el al., 1982) and that there
are no wave-velocity delays. With this simplification, the Muskingum
method reduces to the linear-reservoir-routing method (LRR), used widely
on large-scale networks because of its simplicity. Examples are the routing
models by Sausen (1994), Miller et al. (1994), Liston et al. (1994), the HD
model (Hagemann and Dümenil, 1998), TRIP (Oki et al., 1999) and its
applications (Oki et al., 2001; Falloon et al., 2007; Decharme and Douville,
2007), HYDRA (Coe, 2000) and its application (Li et al., 2005), WTM
(Vörösmarty et al., 1998) and its application (Fekete et al., 2006), RTM
(Branstetter and Erickson, 2003), and the routing model of WGHM (Döll et
al., 2003). Although all are based on similar principles, they are named
differently, e.g., linear routing, linear Muskingum routing (Arora and Boer,
1999), and simple advection algorithm (Falloon et al., 2007). The number of
linear reservoirs sometimes exceeds unity, e.g., two (Arnell, 1999) or more
(Hagemann and Dumenil, 1998). Wave velocity is an important parameter in
most LRR algorithms and is normally obtained by calibration to a
downstream discharge time series. The velocity can be fixed globally (Coe,
1998; Döll et al., 2003) but model performance is improved if it is varied
between basins (Miller et al., 1994; Arora et al., 1999; Döll et al., 2003).
Vörösmarty and Moore (1991) assign a transfer coefficient to each cell on
the basis of geometric considerations, implying a constant wave velocity that
should be calibrated. Fekete et al. (2006) use a temporally uniform but
spatially varying velocity field derived from an empirical relation between
mean annual discharge, slope, and flow characteristics after Bjerklie et al.
(2003). Spatially variable velocities were first introduced by Arora et al.,
(1999), and further developed by Arora and Boer (1999) to allow for
temporally variable velocity. Hydraulic equations can be used to relate
modelled wave velocities to river-channel geometry. Such velocities require
real river segments that can be derived from large-scale flow-net segments
23
after multiplication with a meandering factor (Arora and Boer, 1999; LucasPicher et al., 2003).
The question of the suitability of storage-based routing algorithms for
large-scale river routing is raised in Paper II. The critique is based on two
arguments. The first is that storage-based routing methods, even
sophisticated ones like the Muskingum-Cunge method, lack a convective
time delay (Beven and Wood, 1993) such that an upstream input will have
an immediate effect on the downstream output. The convective delay
increases with the length of the reach, so ignoring it may not work well at
scales where both network segments and river lengths are very long. The
second argument is that storage-based routing algorithms are inherently
scale-dependent since they rely on flow networks that change with spatial
resolution. On one hand, lower resolution leads to a decrease of derived
slope resulting in longer travel times and lower peak flows; on the other
hand, lower resolution also leads to a decrease of flow paths resulting in
shorter travel times and high peak flows, and these two effects may
compensate each other to some extent. Another effect of lower DEM
resolution is the change in optimal channel threshold values, pertaining
relative to the channel length. In short, a low-resolution network smoothes
the spatial-delay pattern on large scales. Together with neglecting the
convective delay this may decrease routing accuracy at large scales. Du et al.
(2009) presented the effect of grid size on the simulation of a small
catchment (259 km2) in the humid region in China. They showed that
changes in the spatial model resolution affected the simulation because of
different values of GIS-derived slopes, flow directions, and spatial
distributions of flow paths. Three types of DEMs with grid sizes of 100 m,
200 m, and 300 m were used to simulate storm discharge in their study. They
concluded that results are poor when grid size is larger than 200 m. Arora
(2001) compared runoff routing at 350-km and 25-km scales with the same
runoff input and concluded that discharge is biased at large scales and also
more error-prone at high and low flows. The method of Guo et al. (2004) to
scale up contributing area and flow directions was designed to improve
decreasing model performance with decreasing spatial resolution. Although
the overall performance improves and reaches a maximum at 7.5', model
performance decreases continuously at increasingly lower resolutions. Yildiz
and Barros (2005) found a strong dependency of the simulated runoff
components on flow-network resolution in the Monongahela River basin, in
particular when a 5-km resolution was used instead of a 1-km resolution.
Less sub-surface and more surface runoff was simulated as a result of the
lower hydraulic gradients. The runoff-generation mechanism was
inconsistent with observations at the lower spatial resolution, and not only
resulted in a bad fit to observed discharge, but also in the hydraulicconductivity parameter that had to be given non-realistic values to
compensate the lower gradients at this resolution (Yildiz and Barros, 2005).
24
A valid routing algorithm requires that the wave crest should not travel
through a cell within one routing time step. This gives a practical
disadvantage to storage-based routing methods at large scales since they
require a time step much shorter than the time step of the runoff-generation
model (Coe, 1998; Liston et al., 1994; Sushama et al., 2004; Kaspar, 2004).
This requirement means that computational demand may be too great when
global water-balance models are built on a finer spatial grid than commonly
used today. Storage-based routing algorithms are computationally expensive
also because they must route the discharge cell-to-cell. However, when the
reproduction of discharge dynamics at a basin outlet is an important
objective, cell-to-cell methods can be replaced by source-to-sink methods
(Naden et al., 1999; Olivera et al., 2000) that only simulate delays at predefined cells, normally co-registered to a runoff gauge or a river mouth.
Such methods enable more efficient computation, which allows the use of
higher-resolution flow networks (Olivera et al., 2000) and more
sophisticated routing methods. This computational efficiency allows Naden
et al. (1999) to use the convective-diffusive approximation of the Saint
Venant equations (Beven and Wood, 1993) at the continental scale.
Uncertainties, equifinality and scale issues
Global models rely on global data sets and are confined by their availability
and often limited quality. All global models suffer from data uncertainties,
which are often assumed to be a main cause of simulated runoff
uncertainties. Gerten et al. (2004) showed large differences between runoff
simulated with the LPJ, WBM, Macro-PDM, and WGHM models. Kleinen
and Petschel-Held (2007) compared simulation volume for 31 world large
river basins calculated with the VIC model (Nijssen et al., 2001b) and the
land-surface GCM component of Russell and Miller (1990). They found
volume differences to vary from -70% to over +2000% with an average of
+10%. Internationally coordinated efforts have been made in recent years to
improve both the data sets and evaluation techniques for global hydrological
models. The multi-model ensemble techniques are suggested as a way to
improve global assessments (Dirmeyer et al., 2006). There is, however, still
a large uncertainty in global discharge estimation. The reported annual
global fluctuations commonly vary between 34,500 and 44,000 km3 a-1,
(Probst and Tardy, 1987). A more recent study showed that the total global
discharge estimates range between 36,500 km3 a-1 and 44,500 km3 a-1
(Widén-Nilsson et al., 2007). Continental discharge estimates differ much
more (Widén-Nilsson et al., 2007). The difference between the largest and
smallest global runoff estimates exceeds the highest continental runoff
estimate (Widén-Nilsson et al., 2007).
25
The practice of hydrological science is supposed to work towards a single
correct description of the reality. However, empirical evidences have
revealed that in many cases a number of different parameter sets may yield
similar model results (Beven and Binley, 1992). The problem of equifinality
arises as a result of insufficient knowledge of the hydrological processes,
and limited techniques for measuring and modelling the characteristics of the
hydrological system. A number of reactions to the equifinality have been
proposed, for example, to use parsimonious models and to search for
calibration methods that better use information of available data series of,
e.g., discharge, groundwater levels, and snow cover (Wagener et al., 2003).
The Monte Carlo simulation technique is also useful to reveal over
parameterisation and equifinality. Behavioral models from Monte Carlo
simulations could be identified with a GLUE type of approach (Beven and
Binley, 1992) with the use of limit of acceptability (Beven, 2006). Instead of
searching for the model producing the highest Nash efficiency value, the
GLUE methodology looks for a set of models producing acceptable results
and weighs them according to their likelihood. The GLUE-type of
calibration exercise has received critics as a subjective method, because the
modeller himself should decide the limit for discriminate behavioural models
from non-behavioural ones. The idea of limit of acceptability introduced by
Beven (2006) offered ways to determine the limit with support of data and
previous experience.
Large-scale hydrologic and atmospheric modellers put much effort on the
scale dependency of their algorithms. Different processes take place at
different spatial and temporal scales. For example, precipitation is normally
supplied as area average but runoff is not measured until it becomes
downstream discharge at some points. Topographic control on the moisture
distribution should be calculated at a very small hillslope scale, while the
same control on river routing can sometimes be performed at very coarse
global scales. Evapotranspiration is commonly measured, and equations
derived, for point scale but regional evapotranspiration is required for
hydrological models. The coupling of land-surface models with atmosphere
and ocean models introduces gaps in the scales at which those models
operate. To accomplish this coupling we face many conceptual and
computational difficulties to learn how to combine the dynamic effects of
hydrological processes on different space and time scales in the presence of
the enormous natural heterogeneity. One of the difficulties of scaling of
nonlinear behaviour could be demonstrated with this simple example: 10 cm
of precipitation falling during 1 hour of a day may produce a very different
response from 10 cm uniformly falling during 1 day. Similarly, 10 cm of
precipitation falling on 10% of a model grid cell may produce a very
different response from 1 cm uniformly falling over the entire cell. The
situation becomes more complicated if the sub-grid variation of soil
infiltration capacity is considered, or if the antecedent moisture condition
26
varies. Hydrological processes that are integrated to, e.g., a 0.5° global cell
are nonlinear over widely different smaller scales. The use of average values
of climate forcing and land-surface properties reduces the spatial variation of
those inputs, which in turn reduces the chance of the simulated discharge to
cover low and high extremes in space and time. Most global hydrological
models currently calculate the water balance on daily or sub-daily scales,
whereas validation is carried out over latitude bands, and continental and
global totals at monthly or annual time scales. Uncertainties at finer scales
are seldom dealt with.
27
WASMOD-M, the Topography-derived
Runoff Generation algorithm (TRG) and NRF
routing algorithm
A number of global and large-scale algorithms were developed during the
PhD work. The monthly WASMOD-M was used in Paper I to investigate
data and model uncertainty on the global scale. WASMOD-M, among all
other global hydrological models has the most parsimonious structure. The
monthly version was developed to investigate how well a simple model with
minimum data demand can perform compared with more sophisticated
models, and how much data and model structure uncertainties can be
revealed by various calibration techniques. The daily WASMOD-M and the
network-response-function (NRF) routing algorithm were developed in
Papers II III. The newly developed Topography-derived Runoff Generation
algorithm (TRG) described in the following sections combines the
advantages of statistical and data-based semi-distributed modelling, and is a
new attempt to use more physical data and less parameters for large-scale
runoff generation models.
Global simulation with monthly WASMOD-M
The monthly global water-balance model WASMOD-M (Widén-Nilsson et
al., 2007) is a distributed version of the monthly catchment model
WASMOD by Xu (2002). The WASMOD and its earlier versions
(Vandewiele et al., 1992; Xu and Vandewiele, 1995; Xu et al., 1996; Xu,
2002) have been proved to be simple and satisfactory for many catchments
around the world under different climate. The WASMOD-M calculates snow
accumulation and melt, actual evapotranspiration, and separates runoff into
fast and slow component (Figure 1) for each grid cell with a time step of one
month. WASMOD was originally derived physically from catchment
geometry, soil hydraulic properties, groundwater flow equation (Darcy’s
law), variable source area with saturation excess assumption, and recession
analysis (Xu, 1988). In practice, however, WASMOD-M lumps physical
parameters into a few conceptual parameters. The model has five parameters
that need to be calibrated (Table 1 of Paper I). The major advantage of
28
WASMOD-M is its minimal requirement for data; the model is driven by
precipitation and temperature. Additional measurements for relative
humidity, wind speed, and sunshine duration would improve the estimation
of potential evaporation for the model. The snow routine in WASMOD-M is
developed with lumping in both time and space domains. The air
temperature used by the snow routine is an average for a catchment or grid
square for an entire day or month, without the explicit knowledge of the subcatchment and sub-time-step temperature distribution. The snow routine of
WASMOD differs from the degree-day method in such a way that both
snowmelt and snowfall are allowed to occur simultaneously within a range
of air temperature around zero. This range is determined by two threshold
temperatures considered as model parameters (Table 1 of Paper I). This
snow routing is simple and well performed when calibrated against spatially
lumped snow cover observations (Xu et al., 1996). The evapotranspiration in
the WASMOD-M is simulated as a function of potential evaporation and
available water. Detailed model equations for the monthly WASMOD-M
were described in Paper I.
Figure 1. The structure of the WASMOD model system (Xu, 2002).
29
Regional simulation with daily WASMOD-M
The daily WASMOD-M was developed from the monthly version and was
validated in a number of basins located in China (Papers II and III), and
North America (Papers III). A major difference between the daily and
monthly WASMOD-M is the modification of the runoff generation
algorithm and, most importantly, the introduction of a scale-independent
routing algorithm using high-resolution hydrography data. The same snow
routine as in the monthly WASMOD-M was be used for the daily model.
Detailed model equations for the daily WASMOD-M can be found in Paper
II.
The NRF routing method
Two central ideas of the network-response-function (NRF) routing method
are (1) to achieve a scale-independent routing by up-scaling dynamics from
the best available resolution rather than relying on river-flow network at
coarser resolution; and (2) to achieve a high computational efficiency when
routing runoff in a large-scale hydrological model. High resolution routing
dynamics was first parameterised in the form of linear response functions,
which could be aggregated to the desired lower spatial resolution.
Parameterisation and aggregation were done once to derive NRF for each
resolution. The final routing can then be used for any given time period and
runoff model, by the convolution of runoff time series with derived NRF.
Two different high-resolution global hydrographies, the 1-km HYDRO1k
and the 3-arc-second HydroSHEDS, were tested with the NRF algorithm.
The basic NRF algorithm remains the same for both hydrographies. The
algorithm starts with calculating a 24-h response function (Paper II) at a
downstream gauging station for all upstream pixels of a basin, with either
full or simplified diffusion wave solution. The 24-h response functions were
then integrated in time to derive a daily response function for each pixel. The
daily response function, which contains detailed delay dynamics at high
resolution, could be parameterised with a number of percentages of runoff
arriving on corresponding days after runoff generation. This parameterised
delay dynamic was then integrated spatially to a low resolution global cell,
knowing the sub-cell distribution of runoff generation. In the simplest case,
uniform runoff generation within a cell was assumed. The aggregation from
pixel response function to cell response function transfers distributed delay
information at 1-km scale, in the form of a daily network response function,
to any lower resolutions as defined by the size of the cell. This is analogous
to the spatial integration of time delay by Beven and Kirkby (1979) to form a
time-delay histogram for an entire sub-basin.
30
The NRF is analogous to the network width function (e.g., Surkan, 1969),
which is obtained by counting the number of channel reaches at a given
distance away from the outlet (e.g., Kirkby, 1993). The application of a
width function requires detailed river-network data (e.g., Naden et al., 1999)
that are not always available on the global scale. Because stream length
decreases with coarser-resolution network, width functions obtained from
global flow networks are systematically shorter than those derived from
high-resolution networks, although the bias can be adjusted with a length
correction (Fekete et al., 2001). Paper II showed that the aggregated NRF for
global cells still contains delay information from pixel level. This is
equivalent to directly using contribution area instead of the number of
channel reaches at a given distance away from the outlet. The construction of
NRF for the Dongjiang River basin is shown in Figure 2.
Because HydroSHEDS contains a vast amount of data, a new technique
was developed in Paper III to process its 3-arc-second hydrography data to
make it possible to apply NRF on it.
31
Figure 2. Time-delay distribution for the Dongjiang basin derived with V45 = 8 ms-1 (Paper II), i.e., the times taken for runoff generated in a
given 1-km pixel to reach the reference point, in this case the down-most discharge station in Boluo (marked by an open circle). Aggregated
cell-response functions at 5' resolution (b), and at 0.5o resolution (c). The x-axes (scale 0–8 days) in the cell-response function (bar graphs in
each cell) shown in (b) and (c) represent delay and the y-axes (scale 0–1) first-day fraction of arrived discharge. (Paper II)
The Topography-derived Runoff Generation algorithm
(TRG)
The TRG algorithm represents the sub-cell distribution of the storage
capacity through topographic analysis. The storage distribution function is
the basis for the nonlinear partitioning of fast and slow runoff responses. The
complete hydrological model is constructed by coupling the TRG algorithm
with the NRF routing algorithm.
Figure 3 shows a typical sectional view of a hillslope element. The
successive steady states assumption of TOPMODEL states that within each
time step, the response from the groundwater system to the change of
recharge rate (i.e., changing of water table and discharge rate) reaches a
steady state, so the temporal dynamics can be represented by a succession of
such steady states. The kinematic wave assumption, on the other hand, states
that at every point the effective hydraulic gradient equals the local surface
slope. The combination of the two assumptions means that the groundwater
table moves up and down always in parallel.
The parallel water table indicates that, at any point, the deviation of
storage deficit from catchment average is always fixed, except under surface
saturation. This feature offers a nice way to distribute the mean catchment
storage deficit to every point in the catchment. In another word, the
distribution of topography determines the distribution of water table and thus
the storage deficit. When the catchment wets up or dries out the spatial
distribution of the storage deficit determines the partition between fast
runoff, baseflow and evapotranspiration.
The steady state assumption of groundwater discharge in TOPMODEL
basically leads to a simple mathematical form that allows the average
groundwater discharge to be an exponential decay function of the average
storage deficit. It means that groundwater discharge to river channels is
strictly derived from topographic analysis and the successive steady states
assumption. Consequently, the evolvement of saturated area, storages and
other water balance components is also strongly influenced by topography.
The new model based on the TRG algorithm relaxes the assumptions in
TOPMODEL and only uses topographic analysis as a way to derive the
distribution of storage capacity, but avoids a strict formulation of steadystate groundwater discharge as in TOPMODEL.
33
ce
urfa
nd s
Grou
Dmax
Zi
Dmax
d
on
tc
ies
r
D
itio
ψc
e
ry fring
Capilla
n2
n1
itio
ond
c
t
es
Dri
Figure 3. Typical sectional view of a hillslope element. (Paper IV)
The TOPMODEL concept allows the storage deficit profile (Di) to be
determined by knowledge at any point on the profile plus topography. River
channel is often used as a boundary condition. If a catchment has a
continuous discharge, part of the catchment is always saturated, or has zero
storage capacity even under the driest condition (“driest condition 2” in
Figure 3). When the catchment is represented by cells, some upstream cells
may have seasonal channel or no channel at all, implying positive storage
capacity everywhere in the cell. There will be a certain area in the catchment
that is saturated just to the surface under the driest condition. If this area
corresponds to a certain critical topographic index value TI C , areas with
values larger than TI C are always saturated. In the VIC model, a
simplification is made that the river channels are just saturated under driest
condition, so TI C = max(TI ) , as illustrated by the “driest condition 1” in
Figure 3.
Paper IV showed that the profile represents the maximum storage deficit,
and thus the storage capacity, which can be obtained with topographic
analysis and the use of only one scaling parameter. A complete hydrological
model was developed using the sub-cell distribution of storage capacity,
derived from topographic analysis based on HydroSHEDS, to derive runoff
generation and evapotranspiration. Full description of the method was
provided in Paper IV.
34
Datasets, basins and simulation setup
Global datasets for monthly WASMOD-M
The monthly WASMOD-M requires time series of monthly precipitation,
temperature, and potential evaporation on a regular 0.5o by 0.5o latitudelongitude grid as inputs. Precipitation, temperature, and water vapour
pressure used to calculate potential evaporation were taken from the CRU
TS 2.10 climate data (Mitchell and Jones, 2005). Gridded potential
evaporation was pre-processed from air temperature Ta and water vapour
pressure (Paper I). The required flow network and areas of global cells and
basins by the monthly WASMOD-M were taken from STN-30p
(Vörösmarty et al., 2000b). Monthly discharge time series were taken from
654 GRDC (GRDC, 2010) stations, in 254 basins, co-registered in 2007 to
the STN-30p network in the UNH/GRDC composite runoff fields version
1.0 (Fekete et al., 1999a, 1999b, 2002). The Northern Hemisphere 0.5o
monthly snow cover extent data set by R. L. Armstrong (available at http://
islscp2.sesda.com/ISLSCP2_1/html_pages/groups/snow/snow_cover_xdeg.h
tml)), provided temporal snow-cover data (percentage of weeks in a month
for which a cell is snow covered to more than 50%) for 344 of the 654
GRDC basins for 1986–1995.
Global datasets for daily WASMOD-M
Three global remotely-sensed or reanalysis datasets were combined as
climate input for the daily WASMOD-M. Precipitation data were
constructed by combining a 0.25° and a 1° dataset: The TRMM 3B42 dataset
(Huffman et al., 2007), which has a coverage between 50°S and 50°N, and
the GPCD 1DD V1.1 dataset (Huffman et al., 2001) which covers the whole
globe. Air and dew-point temperatures were obtained from the ERA-Interim
reanalysis dataset (Simmons et al., 2007) to derive potential evaporation.
Daily discharge time series for test basins were taken from the GRDC
(GRDC, 2010) database. Although only used in test basins, the complete
global dataset was compiled for future global scale applications.
35
Global dataset for the TRG algorithm
The same climate input as in the daily WASMOD-M was used by the TRG
based model. The TRG-based model also uses high-resolution topography
and hydrography data from HydroSHEDS (Lehner et al., 2008) to derive
topographic indexes (Paper IV).
Global datasets for the NRF routing algorithm
Two global hydrographies: HYDRO1k (USGS, 1996a) and HydroSHEDS
(Lehner et al., 2008) were used for the NRF routing algorithm. HYDRO1k is
derived from the GTOPO30 30'' global-elevation dataset (USGS, 1996b) and
has a spatial resolution of 1 km. HydroSHEDS, an even more detailed
hydrography than HYDRO1k, was published soon after publication of Paper
II. HydroSHEDS, derived from elevation data of the Shuttle Radar
Topography Mission (SRTM), has a spatial resolution of 3-arc-seconds and
covers the globe approximately within ±60° latitude. Few studies (e.g.,
Getirana et al., 2009; Li et al., 2009) using HydroSHEDS have been reported
since the data have been available only for a short time.
Test basins and local climate data
Large-scale hydrological models have primarily been evaluated on the
largest river basins in the world. Such evaluations are subject to problems
because river-flow dynamics may be influenced by insufficient climatic and
hydrological data, regulations by dams and reservoirs, and water abstraction.
Under this consideration, the NRF routing and the TRG runoff generation
algorithm were tested in three medium-sized basins.
The well-documented Dongjiang medium-size basin was used as the main
test basin in the study to ascertain that the runoff generation and routing
properties are not too disturbed by unknown influences. The Dongjiang (East
River) basin is a tributary of the Pearl River in southern China. Its 25,325
km2 drainage area above the Boluo gauging station is large enough to retain
generality of the results in a study of global hydrology. The basin has a
dense network of meteorological and hydrological gauging stations and its
hydrology is well studied (e.g., Jiang et al., 2007; Chen et al., 2006, 2007;
Jin et al., 2009, 2010). The climate is sub-tropical with an average annual
temperature of around 21oC and only occasionally the winter temperature
goes below zero in the mountains. Daily hydro-meteorological data for
Dongjiang basin were obtained for 1960–1988. The National Climate Centre
of the China Meteorological Administration provided data on air
temperature, sunshine duration, relative humidity, and wind speed from
36
seven weather stations. Precipitation data from 51 gauges and discharge data
from 15 gauging stations were retrieved from the Hydrological Yearbooks of
China issued by the Ministry of Water Resources. Potential evaporation was
calculated from air temperature, sunshine duration, relative humidity, and
wind speed with the Penman–Monteith equation in the form recommended
by FAO (Allen et al., 1998).
Two North America basins (The Eel River basin and The Willamette
River basin) were also used to validate the TRG algorithm. The Eel River
enters the Pacific Ocean just north of Cape Mendicino, in Northern
California. Above the Scotia gauging station it has a drainage area of 8,062
km2. Its discharge is generally low, but it usually has one or more large
flows, lasting for several days during the passage of winter storms (Brown
and Ritter, 1971). The Willamette River is located upstream of the Columbia
River at Portland. The basin has an area of 29,008 km2 above the Portland
gauging station. The Willamette Valley lies roughly 80 km from the Pacific
Ocean, and prevailing westerly marine winds give it a Mediterranean-type
climate (Taylor et al., 1994). Winters are cool and wet, summers warm and
dry. Most runoff and flooding is caused by winter rains. Winter rainfall on
melting snow is the primary mechanism for generation of flood flows
(Waananen et al., 1971; Hubbard et al., 1993). Melting snow at high
elevations at the Cascade Range adds a seasonal runoff component during
April and May.
Model setup and evaluation
The monthly WASMOD-M was calibrated and validated with the splitsample method, i.e., the first half of each discharge time series was used for
calibration and the second was used for validation. Snow calibration of the
monthly WASMOD-M was made for the entire period and validated by
comparison with a benchmark snow calibration driven by the long-term
mean climatology. The daily WASMOD-M, the TRG based model and the
NRF routing method were calibrated using the entire discharge data due to
the limited length of discharge and daily precipitation data.
Calibration was made against monthly snow observations and monthly
and annual discharge observations (Paper I) and also daily discharge
observations (Papers II, III and IV). Calibration was carried out in the GLUE
framework (Beven and Binley, 1992). Behavioural parameter value sets
were selected from Monte Carlo simulations according to a number of
likelihood functions. Parameter values were sampled from uniform and
logarithmic distributions within initial ranges and were randomly combined
to generate parameter value sets. The likelihood functions used in the thesis
include the Nash efficiency, the volume error and the limit of acceptability
(Beven, 2006) criteria. The limit of acceptability criterion requires a
37
modeller to predefine acceptable simulation errors on the basis of effective
observation errors of input data and discharge measurements. Simulated
runoff that falls within the acceptable limits at a given point in time is
weighted with a triangular or a trapezoidal function where a simulation close
to the measured value is given 100% weight whereas a simulation outside
the limits is given zero weight.
HYDRO1k was used to construct a series of grids with gradually lower
spatial resolution to study the scale dependency of routing. Grid-cell sizes
were varied from 5' to 60' in steps of 1' to form 56 different basin network
representations. The performance of the NRF routing algorithm was
evaluated against the LRR and a benchmark NRF algorithm. First, the
network response functions were aggregated from the 1-km HYDRO1k
resolution to each of the 56 resolutions with the NRF method. A LRR
algorithm and a benchmark NRF algorithm were also derived at each of the
56 spatial resolutions. The benchmark routing calculated delay as a function
of cell-to-cell distance and a velocity parameter. Then, all three algorithms
were run with runoff generation derived from both spatially uniform and
distributed climate input data, and similar calibration procedures were used
to identify the best velocities. The best Nash efficiency for discharge at
Dongjiang basin was chosen as a performance indicator across spatial
resolutions and methods. The uniform run was done to guarantee that only
scale-dependent routing effects influenced the result. The benchmark
algorithm was constructed to guarantee that the difference between the TRG
and the “traditional” algorithms could be attributed to the algorithm
differences, rather than to their different network resolutions.
38
Results
Performance of monthly WASMOD-M at global scale
The performance of the monthly WASMOD-M, while calibrated against
observed monthly discharge time series of the GRDC stations, showed a
wide range of results from poor to excellent (Paper I Table 2). Only a small
percentage (24%) of GRDC stations showed satisfactory (>0.8) Nash
efficiency measure (NC, Paper I Table 2). If input data have no serious
systematic error, the long term average discharge could always be precisely
reproduced during the calibration periods, as shown by the fact that 96% of
GRDC stations has a volume error (VE) less than 1%. A few basins that
could not meet this criterion have a runoff-coefficient larger than 1.
Comparison of WASMOD-M and other major global water-balance models
at major river basins showed that the volume errors of WASMOD-M were
the smallest. Calibration of the WASMOD-M against monthly, annual and
long-term average runoff revealed that equifinality of the evaporation
parameter, and the slow and fast runoff generation parameters increased
when the validation data were aggregated temporally (Figure 4).
The best parameter value sets identified during the calibration period
always produced among the best validation results for all criteria (Figure 5).
The average validation performance could be better or worse, and the
performance relation was seldom one to one even if good calibrations led to
good validations (Figure 5). It was also common, especially for the volume
error, that the 1% best calibrations were not found among the 1% best
validations. The overlap between the best parameter value sets between
calibrations of the two periods was on average 80% for the sets selected
from the best 20% monthly NC values and 44% for the best 1% monthly NC
values. The overlap was better for monthly than for annual calibration.
Common sets were found for all basins among the best 20% NC values,
while the 1% best had total misses for 11% of the basins.
39
NC, mon
1
1
1
0.5
0.5
0.5
NC, yr
0
0
0.5
1
0 −6
10
0
1
0.5
0.5
0.5
VE
0.5
1
0 −6
10
−3
10
0
0
10
0
0
5
5
5
1
10 −6
10
c
−3
10
Ps
0
10
10
1
1
0.5
0.5
0.5
0.5
1
0 −6
10
−3
10
0
0
10
1
1
0.5
0.5
0.5
VE
0.5
1
0 −6
10
−3
10
0
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5
5
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0.5
A
c
1
10 −6
10
−3
10
P
s
0
10
−6
10
0
10
0
−6
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1
0
0
−6
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1
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−6
10
0
0.5
A
−6
10
1
10
0
NC, mon
0
10
1
0
0
NC, yr
−3
10
10
−6
10
−3
10
−3
10
−3
10
Pf
−3
10
−3
10
−3
10
P
0
10
0
10
0
10
0
10
0
10
0
10
f
Figure 4. Runoff performance for River Sénégal at Bakel (up) River Ob at
Salekhard (down) and for combinations of values of the evaporation (Ac), slow-flow
(Ps), and fast-flow (Pf) parameters. Calibration was made with the Nash criterion
(NC) against observed monthly (mon) and annual (yr) observations and with the
absolute value of the volume error (%) for the calibration time period (1904 – 1951
at Bakel, 1930-1961 at Salekhard). Values for the 500 (3.3%) best sets are shown as
large dots. (Paper I)
40
Figure 5. Modeled runoff performance for validation (second half) versus
calibration (first half of observation) periods for three evaluation criteria (Nash
(NC), limit of acceptability (LA), and volume error (VE)). Shown are performance
for (top) River Sénégal at Bakel (observations 1904–1989) and (bottom) River Ob at
Salekhard (observations 1930–1999). Simulations based on the best 150 (1%)
calibrated parameter value sets are highlighted, and the thin line gives the one-to-one
relation. The best calibrated parameter value sets for Ob River not fulfilling the 95%
limit for LA75 during the calibration period are marked with crosses. (Paper I)
Performance of daily WASMOD-M and NRF routing
algorithm in the Dongjiang basin
The daily WASMOD-M, while coupled to different routing methods
including the LRR, NRF and benchmark NRF algorithms, showed different
performances for the Dongjiang basin, as represented by the multiple
resolution spatial grid from 5' to 60'. Because the runoff generation parts, as
well as the climate input at each resolution, were the same, different
performances reflect differences in routing algorithms. The overall
performance also reflects the performance of the runoff generation
algorithm. For a given routing algorithm, variation of performance over
scale reflects different input information content and the quality of flow
network or aggregated NRF at each scale. The performance was similar
between all three routing methods at the 5' resolution, i.e., about 9 km cell
size (Figure 6). The performance of the LRR routing decreased linearly with
a fine-scale zigzag pattern when moving towards larger scales. The
benchmark routing had a slower performance decrease and a similar zigzag
41
pattern. The NRF routing performed equally well at all resolutions without a
zigzag pattern. The NRF routing was apparently scale-independent both
theoretically and practically. A comparison between the LRR and the
benchmark NRF routings indicated that the linear-storage-release function
performed increasingly worse for coarser scales. It also proved that both
methods based on aggregated cell information performed worse when
gradually losing hydrographical information. It was clear from Figure 6 that
extra information in a distributed versus a uniform climate input could only
be meaningful when the NRF method was used to route the runoff.
However, the increase in performance is small when distributed instead of
uniform climate input is used, indicating that for Dongjiang basin distributed
flow network is more important than distributed climate input in reproducing
downstream discharge dynamics.
0.9
0.85
Nash efficiency
0.8
0.75
0.7
NRF, V45 = 8 m/s
NRFuni, V45 = 8 m/s
LRR, V = 0.4 m/s
LRRuni, V= 0.4 m/s
Bench, V = 0.45 m/s
Bench , V = 0.45 m/s
uni
0.65
10
20
30
Cell size in arc−minutes
40
50
60
Figure 6. Nash efficiencies for three routing models at spatial resolutions varying
from 5' to 60' in steps of 1'. The models are NRF: Network-response function, LRR:
Linear-reservoir routing, and Bench: Benchmark model using NRF with averaged
hydrographic data from cells at each aggregated resolution. Each model was
calibrated to one flow velocity (V45) for all scales and each model was run with
spatially distributed as well as uniform (subscript “uni”) climate-input data. (Paper II)
42
7000
(a)
Discharge (m3/s)
6000
5000
4000
3000
2000
1000
0
J
F
M
A
M
J
J
1983
A
S
O
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0
0.94
0.96
0.98
D
J
F(x)
1
F(x)
1
F(x)
1
N
0
0
1
1
A4
2
0
0
3
c1
2
4
c2
−3
x 10
6
−4
x 10
7000
(b)
5000
3
Discharge (m /s)
6000
4000
3000
2000
1000
0
J
F
M
A
M
J
J
1983
A
S
O
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0
0.94
0.96
0.98
A
4
1
D
J
F(x)
1
F(x)
1
F(x)
1
N
0
0
1
2
c
1
3
−3
x 10
0
0
2
4
c
2
6
−4
x 10
Figure 7. Observed (black line) and modelled discharge (grey area) in 1983 for the
Dongjiang basin at Boluo. Runoff generation was modelled with WASMOD and
routed by the LRR method (a) and NRF functions (b). The three graphs below each
hydrograph show the posterior cumulative density functions (F(x)) for the three
WASMOD parameters (A4 governing evaporation, c1 governing fast runoff (mm-1),
and c2 governing slow runoff (mm-1)) after 250 Monte-Carlo simulations for spatial
resolutions ranging from 5' to 60' in steps of 1'. The grey areas represent the best
simulations at each of the 56 spatial resolutions. (Paper II)
43
Another difference between the routing methods could be seen in the
hydrographs for 1983 (Figure 7). The result from year 1983 is presented for
illustrative purposes. The NRF method helped to maintain similar posterior
cumulative density functions for the three WASMOD parameters over all
spatial resolutions. The aggregated network methods were unable to achieve
this. The best hydrograph simulations consequently got much less spread
over scales for the NRF method and closer to the observed discharge. A
model structure which produces similar posterior parameter distribution over
scales allows small scale parameters to be tested on larger scale with less
trouble. The stable posterior parameter distribution of WASMOD-M over a
wide range of spatial scales is due to 1) the scale independency of the
aggregated NRF algorithm, and 2) the fact that downstream discharge of
Dongjiang basin is not sensitive to the spatial variability of the climate input,
as long as the spatial average remains the same.
HydroSHEDS and HYDRO1k comparison
The downstream Boluo station of the Dongjiang basin was registered to the
HydroSHEDS pixel (211814, 203809). In this study 21 upstream cells were
identified, each of which partly or fully contributed to the drainage area of
the downstream station. The complete upstream area was identified as
25,381 km2 with HydroSHEDS as a basis but as 25,886 km2 with HYDRO1k
as a basis (Paper III). There were 3,234,541 HydroSHEDS pixels identified
as upstream of the Boluo station, about 125 times more than the number of
pixels identified in HYDRO1k. The 3,234,541 flow paths were constructed
to represent the complete flow dynamics, which included transport both at
hillslope scale and in river channels. The use of combined local (within-cell)
and global-scale (between-cells) flow paths allowed a great degree of
simplification (Figure 8) for the global-scale flow accumulation. Only
12,922 global flow paths, i.e., 0.4% of the complete number of flow paths
were needed to derive pixel upstream area and time-delay distribution by the
continuous updating procedure that added upstream-cell values to
downstream cells. The resolution of the flow network had a considerable
effect on the slope. The spatial distribution of pixel slope showed large
differences when based on HYDRO1k compared to that based on
HydroSHEDS data in both studied basins (Paper III Figure 4). The spatial
variation pattern agreed but the range differed between the two slope maps.
The maximum slope for the Dongjiang basin increased from 18 to 50
degrees, and for the Willamette basin from 27 to 57, when using
HydroSHEDS instead of HYDRO1k.
44
Figure 8. The connection of global-scale flows through downstream pixels of border
pixels for (a) the Dongjiang River basin and (b) the Willamette River basin. The
global flow paths are used to connect flows between cells and to update upstream
areas. The global flow paths derived only from pixels at the low-resolution-cell
borders greatly simplify the flow-structure complexity, which is used for the basinscale flow accumulation. (Paper III)
45
6000
(a)
Discharge (m3/s)
4000
2000
6000
(b)
4000
Simulated
discharge quantiles (m3/s)
2000
1982
6000
1983
(c)
4000
2000
0
0
1000
2000
3000
4000
5000
6000
3
Best model efficiency
Observed discharge quantiles (m /s)
0.9
0.8
0.7
0.6
(d)
0.5
5
10
15
20
25
30
V45 (m/s)
Figure 9. Observed (black line) and modelled discharge (grey lines) in 1982–1983
for the Dongjiang basin at Boluo. Runoff generation is modelled with WASMOD-M
with local weather input, and routed with network-response functions derived from
HYDRO1k (a), and HydroSHEDS (b); (c) quantile-quantile plot of observed versus
simulated discharge using HYDRO1k (filled dots) and HydroSHEDS (open squares);
(d) V45 wave velocity and corresponding best Nash efficiency of simulated discharge
using HYDRO1k (filled dots) and HydroSHEDS (open squares). (Paper III)
The aggregated network-response functions (NRFs) showed clear differences
when based on HYDRO1k and HydroSHEDS (Paper III Figure 6). The
HYDRO1k-based NRFs had a wider range, indicating a slower basin
response. This behaviour was the same for both Dongjiang and Willamette
basins. With a normalised wave velocity, V45, of 5 ms-1, the maximum time
delays were 37 days for Dongjiang and 15 days for Willamette when
HYDRO1k was used, but only 7 and 6 days respectively when HydroSHEDS
was used.
46
For illustrative purpose, a comparison of the difference caused by using
HYDRO1k and HydroSHEDS for the Dongjiang basin is shown in Figure 9
Routing performance showed less difference in the simulated discharges
between the two datasets. The top 2% simulation results using NRFs derived
from HYDRO1k and HydroSHEDS gave the best fit during the recession
period in early spring of 1982 and during the wetting-up period of 1983
when using HydroSHEDS (Figure 9a,b). A comparison between HYDRO1k
and HydroSHEDS for one randomly picked behavioural discharge time
series showed that both routing models underestimated low flows.
HYDRO1k significantly overestimated high flows whereas HydroSHEDS
showed less bias (Figure 9c).
The trends and most efficient V45 values differed considerably between
HYDRO1k and HydroSHEDS (Figure 9d). Calibration against observed
discharge forced HYDRO1k-based routing to very large V45 values with a
best value of 26 ms-1, corresponding to a maximum Nash efficiency of 0.85.
A different trend was observed with HydroSHEDS which showed a welldefined peak around 5 ms-1 with a maximum efficiency of 0.86. The basinaverage velocities were 1.6 ms-1 for HydroSHEDS and 7 ms-1 for HYDRO1k
when the optimum V45 values were converted to actual average wave
velocity by the average slopes. The HYDRO1k value was clearly less
realistic when compared to other global routing schemes (e.g., Döll et al.,
2003; Oki et al., 1999).
Global and local dataset comparison
Simulations in Dongjiang with global weather data gave lower Nash
efficiency and more scattered discharge simulations than those with the
local-weather-data case (Paper III Figures 7a,b; 8a,b). The HYDRO1k
routing overestimated high flows. Both HYDRO1k and HydroSHEDS based
routings underestimated low flows and slightly overestimated flows in the
range 1000–2000 m3s-1 (Paper III Figure 8c). When local-weather data and
HydroSHEDS were used (Paper III Figure 7c), the simulated flow showed
little bias for flow magnitude above 1000 m3s-1. This may indicate a bias
caused by using the global-weather data. Distinctly different wave velocities
were obtained also when global-weather data were used to drive the model
(Paper III Figure 8d). The HYDRO1k-derived basin velocity again showed
an unrealistic optimal value, 30 ms-1, with a Nash efficiency of 0.76. The
HydroSHEDS-derived velocity of 5 ms-1 was the same as when driven by
local data. The corresponding maximum Nash efficiency was 0.77 in this
case. The advantage of HydroSHEDS was clearer for the Willamette basin
than for the Dongjiang basin (Figure 9 Paper III). The steeper topography of
the Willamette basin was better represented with HydroSHEDS, reflected in
the significant differences of the model efficiency (Paper III Figure 9d).
47
The sensitivity of the runoff-generation parameters a4, c1 and c2 of
WASMOD-M (Paper III) was overall moderate with respect both to
hydrography and weather input (Paper III Figure 10). The difference in
probability-density functions for the two hydrographies was small for the
fast- (c1) and slow-flow (c2) parameter values, whereas some deviation was
seen for the evaporation parameter (a4). The difference was much larger
when global weather data were used instead of local. The use of global
weather data forced a4 and c1 to large values for both hydrographies. When
HYDRO1k was used, the slow-flow parameter c2 reacted differently to
global than to local data, while the HydroSHEDS response remained the
same.
Sub-grid distribution of storage capacity derived from
topography
The frequency distributions of the effective storage capacity for the whole
basins and for each individual cell derived from topographic analysis are
shown in Figures 10 a-c for the Willamette River basin, the Eel River basin
and the Dongjiang River basin, respectively. The range of the distribution is
derived from the range of the topographic index scaled by parameter m, and
the shape of the distribution is obtained through the distribution of the
topographic index itself. From the figure we see that the frequency
distributions of the storage capacity generally follow the inversed
distribution of the topographic index (e.g., Paper IV Figure 2a), except for
the left tail where the river channel has been set to allow parts of the basin to
be always saturated to the surface. As opposed to the distributions of the
topographic index, the distributions of the storage capacity are negatively
skewed, indicating a rapid increase of the storage capacity from river
channel to hillslope in the basins where topography makes a certain control
on the hydrological system. A major difference from the VIC model, where
the frequency always monotonically increases as a function of the storage
capacity, is that there exists a sharply deceasing right tail of the frequency
distribution. The significance of this right tail is discussed in the discussion
section. The Eel River basin shows a less spatial variation of the storage
distribution as compared with the Willamette River basin and the Dongjiang
River basin, where the cell distribution function varies a lot from the average
basin distribution. This is partly because the Eel River basin is much smaller
in size than the other two; on the other hand, the Willamette River basin and
the Dongjiang River basin have a more heterogeneous topography. The
spatial variability of the storage distribution function means that both the
cell-average storage capacity, which determines the general partitioning
between fast and slow response in different parts of the basins, and the
48
shapes of the distribution function, which define the dynamics of the
partitioning, are spatially varying. As showed by the figure, the existing
large spatial variability between cells justifies the use of the TRG based
model which accounts for this variability explicitly in its calculation.
49
Figure 10. Frequency distribution of effective storage capacity for the whole basin (thick line) and for each individual cell (dashed lines)
derived from topographic analysis for (a) Willamette River basin (b) Eel River basin and (c) Dongjiang River basin. (Paper IV)
Simulated cell-average storage capacity
The spatial distributions of the cell-average storage capacity are shown in
Figures 11a,b,c for the Eel River basin, the Willamette River basin and the
Dongjiang basin, respectively. Compared with the topography map and the
topographic index map (Paper IV Figure 3), it reveals that generally
speaking, the cell-average storage capacity shows a smaller variation along
the river valley and an increase towards headwater regions. It also shows that
(1) a significant spatial variation is seen in all three river basins, and (2)
going from the temperate North American basins to the warm and humid
southern Chinese basin, there is a large increase in the average basin storage
capacity. In general, the TRG based model shows a better ability to reflect
the actual spatial variation of the cell-average storage capacity, both within
the river basin and between different climate regions as compared with the
VIC model where the storage is dependent on the predefined statistical
distribution with calibrated model parameters.
51
39
39.5
40
40.5
41
−125
(a)
−124
−123
Longitude (degrees)
−122
255
260
265
270
mm
−125
43
43.5
44
44.5
45
45.5
46
46.5
(b)
−124
−123
−122
Longitude (degrees)
−121
150
160
170
180
190
200
mm
22
22.5
23
23.5
24
24.5
25
25.5
26
113
(c)
114
115
116
Longitude (degrees)
117
mm
720
740
760
780
800
820
840
860
880
Figure 11. Spatial distribution of average cell-storage capacity derived from topographic analysis for (a) Eel River basin (b) Willamette River
basin (c) Dongjiang River basin.
Latitude (degrees)
Performance of the TRG-based model
The performance of the TRG-based model for the Willamette River basin,
the Eel River basin, the and the Dongjiang basin are shown in Paper IV
(Figures 7 and 8), respectively. The snow parameters a1 and a2 show a strong
equifinality in all cases. The evapotranspiration parameter Be, the baseflow
parameter Kb, and the storage scaling parameter m all show a well defined
parameter range. We also run the VIC model with the same range of Be and
Kb, and another two parameters im and B for the three basins. To summarise,
when the VIC model is used the best Nash efficiency obtained in the Eel
River basin, the Willamette River basin and the Dongjiang River basin are
0.92, 0.84, and 0.88, respectively and when the TRG based model is used,
the corresponding efficiency are 0.92, 0.85, and 0.89, respectively. We see
that the TRG based model with one less parameter is able to perform as good
as the VIC model.
53
Discussion
Equifinality and parsimonious model structure
Beven (1989, p. 159) concluded that it ‘‘appears that three to five parameters
should be sufficient to reproduce most of the information in a hydrological
record’’. The complexity of monthly and daily WASMOD-M and the TRG
based model follows well this philosophy. Given the uncertainty of global
input and validation data, simple models that capture the essence of the
hydrological system are more preferred than complex models at large scales.
One conclusion from Paper I was that even the parsimonious WASMOD-M
showed a sign of being overparameterised. Most global hydrological models
are less parsimony in terms of total number of parameters compared to
WASMOD-M, however with considerable number of non-calibrated
parameters. Those pre-fixed parameters often suffer from errors introduced
by physiographic dataset (e.g., Hannerz and Lotsch, 2006; Peer et al., 2007).
Among a few ways to reduce equifinality, data-driven parameterisation is
one of the approaches. The TRG based model developed in Paper IV
demonstrated how the reliable physiographic dataset could be used to
parameterise storage distribution, and consequently the partition, between
fast runoff, baseflow and evapotranspiration, and to reduce the number of
parameters. In general, the TRG based model shows a better ability to reflect
the actual spatial variation of the storage capacity, both within the river basin
and between different climate regions, as compared with the VIC model.
This could be explained by the reduced equifinality between the two
parameters, the maximum storage capacity im and the shape parameter B,
which together define the statistical distribution of the storage.
The non-linearity of runoff generation at large scale
The proper representation of the uneven distribution of the storage capacity
is crucial for the simulation of the non-linear runoff generation processes. In
doing so, the TRG based model differs from the VIC model by a more
flexible and a more physically-based shape of the storage distribution
function. The frequency distribution of the storage capacity in the VIC
model is a monotonically increasing function, i.e., the larger the storage
capacity, the larger area it occupies in a basin. Under this setting, the
54
response of the basin would get faster and faster as the water table of the
basin rises, meaning that with the same amount of rainfall input, more area
will get saturated and more fast runoff will be produced. When the frequency
distribution is derived from topographic analysis, there is always a right tail
of the distribution function, indicating that the most remote headwater area
occupies a smaller area of the basin. A comparison of the cumulative
distribution of the storage capacity between the TRG based model and the
VIC model (Paper IV, Figure 9) showed that for the Eel River basin and the
Dongjiang River basin, the topography-derived distribution always rises
faster than the VIC model distribution curve, indicating a larger non-linearity
for the runoff generation. Using the Dongjiang basin as an example,
according to the topography-derived distribution curves, as the basin
gradually wets up, a very small amount of fast response will be observed in
the beginning before around 800 mm of storage is filled, and after this
turning point a very fast response will occur. According to the VIC model
concept (dotted curve in Figure 9 of Paper IV) the basin will response in a
much more linear way.
Importance of river identification at large scale
Most large-scale runoff generation models use low resolution flow network
to accumulate runoff. However, results from Papers III and IV suggest the
possibility and benefit of using a high-resolution hydrography and the
importance of river identification. The definition of river channel, or
effectively, the part of the basin that is always saturated, is one important
issue in the original TOPMODEL. It is commonly done by assuming a CIT
(channel initiation threshold) value and applying a cut-off. Effectively, this
means that the parts of the basin with the largest topographic index values
will be classified as river channels, so the distribution of the topographic
index will get less positively skewed. Quinn (1995) pointed out that the
optimal CIT value is a function of the grid resolution and it has a significant
effect on the simulated catchment dynamics. A common way to identify the
CIT value is to manually find a value that lies in the critical turning point
when a large number of river channels extend into the hillslope.
Paper III concluded that the NRF routing algorithm has a wide tolerance
on the CIT value. The identification of river channels is important for the
implementation of the TRG based runoff generation model. The maximum
storage capacity of a cell is directly proportional to the range of the
topographic index in the unsaturated hillslope area, so, as the identified river
channel area expands both the maximum and the average storage capacities
will reduce. It also means that less part of the left tail of the storage
frequency distribution function will be used in simulating the basin
dynamics.
55
LRR algorithm vs. NRF algorithm
A comparison between a LRR algorithm and a diffusion-wave (NRF)
algorithm showed that the inherent LRR assumption of instantaneous
reaction to an input at the up-stream cell border created too early arrival of
discharge at the outlet. This assumption is equivalent to neglecting the
convective delay in a river reach. The delay problem grew with cell size and
became significant for cell sizes used in most global water-balance models.
The diffusion-wave algorithm, on the other hand, gave delay times that were
more consistent with real-world travel times. This algorithm could be
drastically simplified by assuming near-zero diffusivity when applied in
large-scale global models. This simplification was quite good for small
diffusivities and, when compared to LRR, showed much better performance
for the medium-sized Dongjiang basin. The strength of the NRF algorithm
presented in this study was clearly shown as a high and constant efficiency
across all studied spatial resolutions, whereas the algorithms based on
spatially averaged properties (LRR) got impaired performance at coarser
scales (Paper II Figure 7). The NRF routing shares some assumptions with
existing large-scale routing algorithms. The most important one is that the
wave velocity does not change as a function of discharge. When only the
down-most gauging station is chosen as a reference point, the method
furthermore collapses to a simple source-to-sink algorithm, which is good
enough for most large-scale models. An interesting finding of Paper II is that
routing efficiency is sensitive to flow-path topology, primarily determined
by the relative position of the downstream station. A given river basin will
be assigned a good or bad downstream flow-path topology by chance when
global-scale grids are constructed on the latitude–longitude system. This
could influence global-scale routing results and complicate performance
comparisons.
Distributed climate input vs. distributed delay dynamics
Paper II showed that the network-based routing (LRR) algorithms did not
perform better than the NRF algorithm even at a spatial resolution of 5' , in
spite of their much higher computational cost. When moving towards larger
cell sizes, the spatial variability in the input climate field decreased and as a
result, the spatial variability of WASMOD-M-generated runoff also
decreased. The influence on model performance of spatial resolution in the
climate input was easier to analyse in the NRF case, since the delay
dynamics were preserved over all spatial scales. It was shown that the
network-based models performed equally good/bad with uniform and
distributed climate inputs, whereas the NRF model could take the advantage
of the extra information in the distributed field, even though the
56
improvement was small in this particular case study. The representation of
spatially distributed delay might thus be more important than spatially
distributed climate, as long as discharge is the main performance indicator.
Since a main objective for most global-scale water-balance models is to
reproduce discharge at large river outlets, a correct and accurate delay
distribution should be a high priority.
The importance of having high quality climate data was noted in Paper
III. The comparison between local precipitation data and the combined
TRMM-GPCP data showed that the routing performance was much more
sensitive to the quality of precipitation input than to the choice of spatial
resolution in the hydrography. Both input-data errors and routingparameterisation errors influenced the distribution of behavioural parameter
values. This can be a problem in a global water-balance model because its
parameters must be extrapolated spatially into ungauged areas and
temporally into the future for water-resources predictions and assessments.
The sensitivity study of the runoff-generation parameters showed that they
were more sensitive to the quality of input precipitation data than to the
hydrography. On the other hand, a good routing algorithm is always crucial.
For example, Paper II showed that if LRR algorithm is used for the
Dongjiang basin, a maximum Nash efficiency of only 0.75 can be achieved
at 0.5° resolution even with high-quality local precipitation input. This is as
poor as the result obtained with the global TRMM-GPCP data in Paper III.
HYDRO1k vs. HydroSHEDS
Paper III demonstrated the added value of using the high-resolution dataset
HydroSHEDS at a global scale, given all other uncertainties in global waterbalance models. The comparison of routing algorithms based on HYDRO1k
(1-km resolution) and HydroSHEDS (90-m resolution at the equator) gave
insight into the costs and benefits of using hydrographies with different
spatial resolutions. The use of HydroSHEDS instead of HYDRO1k to derive
network-response functions did not significantly improve overall model
efficiency when calibrated against observed discharge. The use of the lowerresolution HYDRO1k however resulted in too high wave velocities and a
positive bias for simulated high flows. The bias for the HYDRO1k-derived
wave velocity could be explained by comparing the cell-response function of
the two routing models for the same wave velocity value (Paper III). A much
larger spread of behavioural models was seen for HYDRO1k compared to
HydroSHEDS (Paper III, Figures 7c, 8c, 9c).
The scaling of flow-path lengths when using hydrographies with different
spatial resolutions may be reflected in the network meandering factor. This
was found to take a small value of 1.2 for the Dongjiang basin (Paper II)
when based on HYDRO1k or 1.4 globally when based on TRIP (Oki et al.,
57
1999). The significant delay of cell-response function for HYDRO1k
indicated that the lower resolution of HYDRO1k led to a decrease in derived
slope resulting in longer travel times which was not compensated by the
decrease of flow path. The underestimation of the slope was likely the main
reason for the unrealistically large V45 value obtained for HYDRO1k-based
algorithm. The good basin-area agreement between both hydrographies came
from our explicit accounting of sub-cell area. Other algorithms commonly
use the whole area of a cell. The STN-30p network, e.g., only identifies ten
0.5°×0.5° cells for the Dongjiang basin upstream of Boluo compared to
twenty one in this study.
Interaction between routing algorithm and runoffgeneration parameters
Transfer of knowledge between scales is always a difficult task, both
because physical processes depend on scale and because modellers
sometimes use scale-inconsistent approaches. Yildiz and Barros (2005)
pointed out that simulated runoff generation is considerably deteriorated
when flow-network resolution decreases from 1-km to 5-km while other
input data are the same. Our study provided a simple solution as shown by
the scale independence of the posterior distribution of runoff model
parameter values (Paper II Figure 8). This scale independence indicated that
runoff-generation models might use the same parameter values across scales,
and that both runoff generation and discharge dynamics will be scaleinvariant. In contrary, a scale dependent routing approach would also imply
strong scale-dependency on the runoff generation parameter, i.e., when the
runoff generation and routing models are coupled and calibrated together,
runoff generation parameters would try to compensate errors introduced by
inaccurate routing dynamics (Paper II).
Computational efficiency
Computational efficiency is of central importance for any kind of global
models. The efficiency was addressed in Paper III by separating the total
amount of calculation into two stages, the preparation stage and the
simulation stage. The computational time was recorded on a 2005 Windows
XP PC. The NRF algorithm allows the most computation-intensive tasks,
resulting in the network-response function for the given area and spatial
resolution to be accomplished in the preparation stage, which is a one-time
effort. Routing during the simulation stage is done by the convolution of
runoff into the network-response functions. The computational demand at
58
this stage is 4–5 orders of magnitude smaller than during the preparation
stage. The convolution algorithm is fast enough to allow using calibration
techniques based on Monte-Carlo methods on the global scale. The twostage computational strategy not only separates heavy from light
computation but also avoids the fine-scale data dependency at the simulation
stage. Once the network-response function is constructed for global cells, it
can easily be coupled to runoff generation output from any other global or
regional water-balance model.
59
Conclusions
Performance of large-scale hydrological models remains to be improved to
better represent spatial and temporal dynamics. To a certain extent, the
improvement depends on the quality of the global dataset. Comparison of a
combined remotely sensed and reanalysis climate datasets to local data
indicated insufficient quality of the global climate dataset. New algorithms
for runoff generation and routing were developed with reliable highresolution global topography and hydrography datasets to reduce model
uncertainty and improve model prediction.
The newly developed TRG-based model provided a simple physical basis
for runoff generation at sub-cell level for global hydrological modelling.
Comparing the model performance of the VIC model and the TRG based
model, it can be concluded that in all tested basins the new model performs
equally well and sometimes slightly better. The fact that the TRG based
model requires one less parameter and derives the storage capacity
distribution curve from topographic data indicates the potential application
of the method in ungauged areas. The equifinality problem existing between
the maximum storage capacity parameter im and the shape parameter B of the
VIC model can be potentially solved by using the TRG based approach. A
more realistic spatial pattern of runoff generation can also be expected with
the application of the TRG based method. Confirmation of these advantages
requires more intensive validation at the global scale.
The new NRF routing algorithm showed better performance in several
aspects when compared with the LRR method. The inherent LRR
assumption creates too early arrival of discharge at the outlet. The delay
problem grew with cell size and became significant for sizes used in most
global water-balance models. The NRF algorithm, on the other hand, gave
delay times that were more consistent with observed response times.
High resolution topography and hydrography are of central importance in
the application of the TRG and NRF algorithm. The use of the high-resolution
HydroSHEDS instead of HYDRO1k to derive network response functions did
not significantly improve the overall model efficiency. However, the use of
HYDRO1k resulted in a too high wave velocity and a positive bias for
simulated high flows. Simulation of runoff generation and routing can benefit
from the possibility of river identification offered by HydroSHEDS. The
importance of keeping aggregated high-resolution topographic and
60
hydrographic information at large scale, given the uncertainty of other input
data, was shown by a number of comparative studies.
When it comes to computational efficiency, the HydroSHEDS-based
TRG and NRF algorithms allow the most computation-intensive tasks to be
accomplished in the preparation stage as a one-time effort. The
computational demand at simulation stage for the NRF algorithm, for
instance, is 4–5 orders of magnitude smaller than during the preparation
stage. The algorithms are fast enough to allow using calibration techniques
based on Monte-Carlo methods on the global scale.
61
Acknowledgements
First of all I would like to thank my main supervisor Sven Halldin for all the
scientific support and advices during my time as a PhD student. I am grateful
for the opportunity he offered and the belief he has in me, and also for the
effort he made in helping me developing my research interests while keeping
the thesis work in a promising direction. I appreciate his strict scientific
attitude even in small aspects and his patience in explaining things in detail.
Sven is also thanked for having solved many practical and administrative
matters and leave my life easy. I am really lucky to also have Chong-yu Xu
as my supervisor. Ever since the first class I took from him, I have never
stopped working with him. He is always available to solve practical
problems I have or to motivate research interests. It is indeed impossible to
cover all the advices and help I received from him during these years in a
few lines. I also like to thank Allan Rodhe for your encouragement and good
suggestions at all formal meetings and informal occasions. Especially I thank
him for carefully reading the manuscript of the thesis several times and
being very helpful at final stage of the thesis preparation. I thank Deliang
Chen for giving me the opportunity to start my first ever project, and all the
effort he put in helping me finalising it. I enjoyed working with Auli Niemi
in my very first days in Uppsala. It was a surprise to me, thanks to all my
supervisors, that I stayed here so long and had the pleasure to teach in her
course and projects, which turns out to be a continuous inspiration for my
own research work. This thesis work was also made possible by the excellent
earlier work from my former colleague and nice officemate Elin WidénNilsson. Ida Westerberg is also thanked for being a nice colleague and for
sharing lots of work and discussions; also you have been a nice travel
companion on conferences and courses. I also like to thank Alvaro Semedo
for your really fast and reliable help in providing data in the end of my PhD
study. Although Keith Beven has only been in Uppsala part time, every talk
with him is inspiring and requires days even months to digest. The mastery
and passion he has in the science of hydrology certainly has an impact to all
hydrologists in Uppsala. I also thank him for his comments to Paper I and II
which greatly improved their qualities. Paper IV was also a result from a
short conversation with him. I thank Fritjof Fagerlund, my mentor and friend,
who has given me a lot of help from scientific discussion to personal mattes.
This thesis work was funded by the Swedish Research Council grants
629-2002-287 and 621-2002-4352, grant 214-2005-911 from the Swedish
62
Research Council for Environment, Agricultural Sciences and Spatial
Planning, grant SWE-2005-296 from the Swedish International
Development Cooperation Agency Department for Research Cooperation,
SAREC, and grant CUHK4627/05H from the Research Grants Council of
the Hong Kong. Parts of the computations were performed on Uppsala
University UPPMAX resources under Project p2006015. The Global Runoff
Data Centre in Koblenz, Germany is acknowledged for providing global
discharge data.
I thank all staff at LUVAL, Uppsala University, especially all my
previous and present fellow PhD students, for the great time we have had
together. Thanks for the nice company, and the friendship from José-Luis,
Zhibing, Agnes, Diana, Martin, Liang, José, Estuardo, Elias, Maria N, Maria
R and Kristina, Michael, Dan, Anna K, Cicci, Denis, Carlos, Peng Y and
Peng H, Can, Fengjiao, Patrice, Beatriz, Carmen, Zairis, Ann-Marie, Fredrik,
Hanna, Björn, Erik S, Erik N, John, Andreas, Julia, ...... I am looking
forward for a continued collaboration with many of you. Taher, Anna C, Leif
are thanked for various practical help. Tomas is thanked for his quick, robust
help every time my computer is going wrong.
I thank my friends, those who scattered in different parts of the world but
are always there when I need their voice. I thank my relatives, and my
parents for all you love and support.
63
Sammanfattning på svenska
(Summary in Swedish)
Storskalig modellering av flödessvarstid och avrinningsbildning
– Effektiv parametrisering baserad på högupplöst topografi och hydrografi
Vatten har alltid varit en nyckelfaktor för jordens utveckling. Att förstå och
kunna modellera det storskaliga vattenkretsloppet är betydelsefullt såväl för
klimatförutsägelser som för studier av vattenresurser. Studier med den
lågparametriserade månatliga globala vattenbalansmodellen WASMOD-M
påvisade konsekvenser av kvalitetsbegränsningar hos indata och behovet av
att begränsa osäkerheten i modellstruktur. Även om den månatliga
WASMOD-M alltid kunde kalibreras till ett mycket litet volymfel (avrinningens långtidsmedelvärde) för avrinningsområden där indata och antaganden bakom modellen båda var godtagbara, fanns möjligheter att förbättra
dess dynamiska egenskaper.
Huvudparten av avhandlingsarbetet har fokuserats på utvecklingen av
storskaliga hydrologiska modeller med daglig upplösning. Förbättringar i
modellprestanda beror på kvaliteten hos globala data. Indata byggda på en
kombination av satellitbaserade fjärranalysdata och s.k. återanalysdata för
klimatet användes och ledde till rimliga modellprestanda. Avhandlingens
huvudbidrag är de nya algoritmer för parametrisering av flödessvarstid och
avrinningsbildning som utvecklats på grundval av tillförlitliga högupplösta
globala data i syfte att minska modellosäkerhet och förbättra en modells
förmåga att förutsäga och förklara.
Den dagliga WASMOD-M utvecklades för att bättre efterlikna dynamiken hos storskaliga hydrologiska system. En distribuerad algoritm för
avrinningsbildning, benämnd TRG (Topography-derived Runoff Generation), utvecklades för att parametrisera ickelinjära egenskaper i storskaliga
hydrologiska modeller. Algoritmen mildrar antagandena i TOPMODEL och
använder dess topografiska index som ett verktyg för att distribuera den
genomsnittliga vattenlagringsförmågan för varje indexklass för att möjliggöra en rumslig fördelning inom varje beräkningsruta. Den nya algoritmen
erbjuder också ett mera realistiskt rumsligt mönster för avrinningsbildningen
och tillhandahåller en rimlig fysikalisk beskrivning av avrinningsbildning
inne i beräkningsrutor i globala hydrologiska modeller. Den teoretiska likheten mellan TOPMODEL och VIC-modellen gjorde det möjligt att bygga in
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en topografiskt härledd fördelningsfunktion för vattnets lagringskapacitet i
VIC-modellens ramverk. Algoritmen provades i tre avrinningsområden i
Kina och Nordamerika med olika klimat. Vid jämförelse mellan en modell
med TRG-algoritmen och en enlagers VIC-modell kunde man observera att
den nya modellen presterade lika bra eller aningen bättre i alla tre
avrinningsområden. Det faktum att den nya algoritmen kräver en parameter
mindre och härleder en fördelningsfunktion för vattenlagringskapaciteten
från topografiska data påvisar potentialen för tillämpning i avrinningsområden som saknar vattenföringsdata. Det ekvifinalitetsproblem (att flera olika
modellrealiseringar presterar lika väl) som råder mellan VIC-modellens
parameter im för maximal vattenlagringsförmåga och dess formparameter B
kunde potentiellt lösas genom det nya databaserade angreppssättet. Ett rimligt rumsligt mönster för avrinningsbildningen, som kan vara viktigt för
simulering av vattenbalansen i stora avrinningsområden, kan förväntas vid
tillämpning av TRG-algoritmen. Bekräftelse av dessa fördelar kräver ytterligare valideringsstudier i global skala.
En ny skaloberoende svarstidssalgoritm baserad på högupplösta hydrografiska data utvecklades och provades för samma avrinningsområden som
ovan. Algoritmen bevarar information om den rumsligt fördelade tidsfördröjningen i form av enkla svarsfunktioner för vattendragsnät i godtyckligt
lågupplösta beräkningsrutor. Den nya svarstidssalgoritmen, benämnd NRF
(Network-Response Function), visade bättre prestanda i flera avseenden än
den traditionella LRR-metoden (Linear-Reservoir Routing) i en flerskalestudie. De magasinbaserade cell till cell-algoritmer (LRR) som provades
föreföll allt mindre tillämpbara ju större den rumsliga skalan blev. En jämförelse mellan en LRR-algoritm och en diffusionsvågsalgoritm visade att LRRantagandet om omedelbar reaktion på ett inflöde från en beräkningsruta uppströms ledde till en alltför tidig ankomst vid avrinningsområdets utlopp.
Antagandet innebär att man försummar den konvektiva fördröjningen i en
rinnsträcka. Fördröjningsproblemet växte med storlek på beräkningsrutan
och blev signifikant för de storlekar som används i många globala
vattenbalansmodeller. Diffusionsvågsalgoritmen gav å andra sidan fördröjningar som stämde bättre överens med verkliga flödessvarstider. NRFalgoritmen, som baserades på diffusionsvågsalgoritmen, kunde förenklas
kraftigt genom att anta diffusivitet nära noll i storskaliga, globala modeller.
NRF-algoritmen provades med två högupplösta hydrografier, HYDRO1k
med 1 km upplösning och HydroSHEDS med 3 bågsekunders (ca 90 m vid
ekvatorn) upplösning. Det var viktigt att demonstrera det extra värdet av den
detaljerade informationen i HydroSHEDS i global skala i ljuset av alla andra
osäkerheter vid modellering av den globala vattenbalansen. Användningen
av HydroSHEDS i stället för HYDRO1k för att härleda svarsfunktioner för
vattendragsnät förbättrade inte signifikant några övergripande modellprestanda vid kalibrering mot observerad avrinning. Däremot resulterade
HYDRO1k-funktionerna, med lägre upplösning, i orealistiskt höga
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våghastigheter och överdrivna simuleringar av högvattenflöden. HydroSHEDS-data erbjuder möjligheten att identifiera bildpunkter (pixlar) med
individuella rinnsträckor. Denna möjlighet har flera konsekvenser för
modellering av flödessvarstider och avrinningsbildning. NRF-algoritmen
som konstruerats för rinnsträckor förblir så gott som oförändrad för
tröskelvärden för vattendragsidentifiering inom intervallet 0,5–100 km2.
Även om många fler rinnsträckspixlar identifierades vid den högre upplösningen förblev vattenföringsnätets topologi oförändrad. Denna egenskap
möjliggör förenkling av algoritmen eftersom kvaliteten i svarstidsberäkningen inte sjunker signifikant när man använder ett större tröskelvärde,
d.v.s. när man endast beräknar svarstiden för stora vattendrag. För beräkning
av avrinningsbildningen är modellprestanda troligen mera känsliga för valet
av tröskelvärde. Användningen av HydroSHEDS-data ger möjlighet att
modellera uppdelning av vattenflödets fördröjning genom landytor och i
vattendrag, något som måste klumpas ihop vid användning av HYDRO1k.
Den explicita identifieringen av vattendragspixlar kan också förenkla
registreringen av dammar och vattenmagasin i vattendragsnät och deras
införlivande i en svarstidsmodell. Noggranna bestämningar av avrinningsområdens vattendelare och högupplösta vattendragstopologier kan förenkla
jämförelser och valideringar mellan globala och regionala hydrologiska
modeller.
Numerisk beräkningseffektivitet är viktig för varje global modell.
Effektivitetsproblemet behandlades genom att
den totala mängden
svarstidssberäkningar separerades i två steg, förberedelsesteget och
simuleringssteget. Den HydroSHEDS-baserade NRF-algoritmen hanterar de
mest beräkningsintensiva uppgifterna, beräkningen av svarsfunktionen för
vattenföringsnät för ett givet avrinningsområde och rumslig upplösning i
förberedelsesteget, vilket endast behöver genomföras en gång.
Svarstidsberäkningar under en simulering görs genom faltning av avrinning i
svarsfunktionen. Behovet av beräkningskapacitet i detta steg är 4–5
storleksordningar mindre än under förberedelsesteget. Faltningsalgoritmen är
tillräckligt snabb för att möjliggöra kalibreringstekniker baserade på Monte
Carlo-metodik i global skala. Tvåstegsstrategin för de numeriska
beräkningarna skiljer inte bara tunga från lätta beräkningar utan frikopplar
också beräkningar i simuleringsstadiet från beroendet av finskaliga data. Så
snart svarsfunktionen är konstruerad för en godtycklig global eller regional
hydrologisk modells beräkningsrutor är det lätt att koppla funktionen till
avrinningsbildning från denna modell.
Denna avhandling har identifierat signifikanta förbättringar i hydrologiska
modellprestanda när 1) lokala i stället för globala klimatdata användes och 2)
en algoritm baserad på en skaloberoende svarsfunktion för vattenföringsnät
användes i stället för en magasinsbaserad svarstidssalgoritm. Samtidigt har
upplösning på klimatdata och val av högupplöst hydrografi bara en andra
ordningens effekt på modellprestanda. Två högupplösta topografier och
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hydrografier, HYDRO1k och HydroSHEDS användes och jämfördes, nya
algoritmer utvecklades för att aggregera information från dem för
användning i storskaliga hydrologiska modeller. Fördelarna och effektiviteten i att behålla information från dem för användning i lågupplösta globala
modeller har belysts.
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Ё᭛ᨬ㽕 (Summary in Chinese)
໻ሎᑺߚᏗᓣѻ⌕੠∛⌕῵ᢳ –ܼ⧗催ߚ䕼⥛ഄᔶ੠∈᭛ഄ⧚᭄᥂ⱘᑨ
⫼ঞ݊ᇍ໻ሎᑺ∈᭛῵ᢳ㊒ᑺⱘᕅડⷨお
∈ᇍഄ⧗ⱘⓨ࣪ϔⳈ᳝ⴔ‫އ‬ᅮᗻⱘᕅડDŽ⧚㾷੠῵ᢳ໻ሎᑺ∈ᕾ⦃
ᇍѢ∈䌘⑤੠⇨‫׭‬乘᡹ⷨお‫݋‬᳝䞡㽕ᛣНDŽᇍѢㅔ㑺ᓣ᳜ሎᑺܼ⧗∈
᭛῵ൟ WASMOD-M ⱘⷨお㸼ᯢˈܼ⧗໻ሎᑺ᭄᥂ⱘ䋼䞣᳝ᕙᦤ催ˈ
῵ൟ㒧ᵘⱘϡ⹂ᅮᗻ᳝ᕙᬍ䖯DŽ㱑✊೼᭄᥂䋼䞣䕗ད੠῵ൟⱘ‫؛‬䆒ᴵ
ӊ䗖⫼ⱘऎඳˈ᳜ሎᑺ WASMOD-M ῵ൟ῵ᢳⱘ໮ᑈᑇഛᕘ⌕ⱘ䇃Ꮒ
ৃҹ᥻ࠊ೼ᕜᇣⱘ㣗ೈˈԚᇍᇣⱘᯊ䯈ሎᑺ⌕䞣ⱘࡼᗕ῵ᢳҡ᳝ᕙᬍ
䖯DŽ
ᴀ䆎᭛ⴔ䞡䖯㸠໻ሎᑺ᮹∈᭛῵ൟⱘᓎゟǃখ᭄⥛ᅮ੠῵ൟᑨ⫼ㄝ
ᮍ䴶ⱘⷨおDŽ໻ሎᑺ∈᭛῵ൟ῵ᢳ䋼䞣ⱘᦤ催೼ᕜ໻⿟ᑺϞձ䌪Ѣ催
䋼䞣ⱘ໻ሎᑺ᭄᥂DŽՓ⫼䘹ᛳ੠‫ߚݡ‬ᵤ⇨‫׭‬᭄᥂ˈ᮹∈᭛῵ൟӮᕫࠄ
ৃҹ᥹ফⱘ῵ᢳ㒧ᵰˈԚᰃˈ੠߽⫼ᅲ⌟᭄᥂԰Ў䕧ܹⱘ῵ᢳ㒧ᵰⳌ
↨ˈ໻ሎᑺ‫ߚݡ‬ᵤ⇨‫׭‬᭄᥂ⱘ䋼䞣ҡᕙᦤ催DŽᴀ䆎᭛ⱘЏ㽕䋵⤂Пϔ
ᰃᦤߎњϔ⾡ᮄⱘ᳝ᬜ߽⫼催ߚ䕼⥛ഄᔶ੠∈᭛ഄ⧚᭄᥂䖯㸠໻ሎᑺ
ߚᏗᓣѻ⌕੠∛⌕῵ᢳⱘὖᗉ੠ᮍ⊩DŽ䆹ㅫ⊩ⱘ⡍⚍ᰃˈ೼ϡ๲ࡴ῵
ൟ໡ᴖ⿟ᑺ੠䅵ㅫ䲒ᑺⱘࠡᦤϟˈ䖯ϔℹ䰡Ԣ῵ൟ㒧ᵰⱘϡ⹂ᅮᗻ੠
ᦤ催῵ൟ㾷䞞੠乘⌟໻ሎᑺ∈ᕾ⦃ⱘ㛑࡯DŽ
ᴀ ⷨ お 佪 ‫ ܜ‬೼ WASMOD-M ᳜ ῵ ൟ ⱘ ෎ ⸔ Ϟ ᓎ ゟ њ ᮹ ሎ ᑺ ⱘ
WASMOD-M ῵ൟˈ੠᳜ሎᑺ⠜ᴀⳌ↨ˈ᮹ሎᑺ᳈㊒㒚ഄ῵ᢳњ∈᭛
㋏㒳ⱘࡼᗕব࣪DŽЎњ䖯ϔℹᦤ催໻ሎᑺߚᏗᓣ῵ൟ῵ᢳ䴲㒓ᗻ∈᭛
㋏㒳ⱘ㛑࡯ˈᴀⷨおᓎゟњ෎Ѣܼ⧗催ߚ䕼⥛ഄᔶ੠∈᭛ഄ⧚᭄᥂ⱘ
ѻ⌕ㅫ⊩˄TRG˅DŽ䆹ㅫ⊩ᬒᆑњ TOPMODEL ⱘ‫؛‬䆒ᴵӊˈҹഄᔶᣛ
ᷛЎᎹ‫ˈ݋‬Ў໻ሎᑺ῵ൟⱘ㔥Ḑ‫ݙ‬䚼੠㔥Ḑ䯈ߚᏗᓣѻ⌕䅵ㅫᦤկњ
⠽⧚෎⸔੠ড়⧚ㅫ⊩DŽ䆹ㅫ⊩߽⫼ TOPMODEL ੠ VIC ῵ൟ೼⧚䆎Ϟ
ⱘⳌԐᗻˈᇚ TOPMODEL Ё෎Ѣഄᔶⱘ‫∈ټ‬㛑࡯ߚᏗߑ᭄㵡ܹ VIC
῵ൟḚᶊDŽᮄᓎゟⱘ TRG ㅫ⊩೼ԡѢЁ೑੠࣫㕢ⱘϝϾϡৠ⇨‫㉏׭‬ൟ
ⱘ⌕ඳ䖯㸠њ偠䆕DŽᇍ TRG ੠ऩሖ VIC ῵ൟⱘ῵ᢳᬜⲞ㋏᭄ⱘᇍ↨ߚ
ᵤথ⦄ᮄ῵ൟ೼᠔᳝ⱘᇍ↨⌕ඳ㸼⦄⿡ད៪ⳌᔧDŽৠᯊˈᮄㅫ⊩Ңഄ
ᔶ᭄᥂Ё㦋প‫∈ټ‬㛑࡯ߚᏗߑ᭄Ң㗠↨ VIC ῵ൟᇥϔϾখ᭄ˈ䖭䇈ᯢ
ᅗ᳈‫݋‬᳝೼᮴䌘᭭⌕ඳЁᑨ⫼ⱘ┰࡯DŽ‫ݡ‬㗙ˈᮄㅫ⊩ৃҹ㾷‫ އ‬VIC ῵
ൟⱘ᳔໻‫∈ټ‬㛑࡯খ᭄ im ੠ᔶᗕখ᭄ B П䯈ⱘѦ㸹ᗻDŽᮄ῵ൟ㛑᳈ড়
⧚ഄ῵ᢳ໻⌕ඳѻ⌕ⱘぎ䯈ߚᏗ㾘ᕟDŽᔧ✊ˈҹϞ䖭ѯ↨䕗㒧ᵰ䖬䳔
㽕೼᳈໮໻ሎᑺ⌕ඳᑨ⫼Ё䖯㸠䖯ϔℹ偠䆕DŽ
68
ᇍѢ໻ሎᑺ῵ൟⱘ∛⌕䅵ㅫˈᴀⷨおᓎゟњϔϾ෎Ѣܼ⧗催ߚ䕼⥛
ഄᔶ੠∈᭛ഄ⧚᭄᥂ⱘ䎼ሎᑺ∛⌕ㅫ⊩˄NRF˅ˈᑊ೼Ⳍৠⱘ⌕ඳ䖯
㸠њẔ偠DŽ䆹ㅫ⊩ҹㅔऩ㔥㒰ડᑨߑ᭄ⱘᔶᓣˈ೼ӏԩ໻ሎᑺԢߚ䕼
⥛㔥ḐЁֱ⬭⬅ᇣሎᑺ催ߚ䕼⥛ഄᔶ᭄᥂䅵ㅫⱘ∛⌕ᓊᯊⱘぎ䯈ߚ
ᏗDŽᇍ↨ⷨおሩ⼎њᮄⱘ NRF ㅫ⊩↨Ӵ㒳ⱘḐ⚍㟇Ḑ⚍㒓ᗻ∛⌕ⓨㅫ
⊩˄LRR˅೼৘Ͼᮍ䴶䛑᳝њ䕗໻ⱘᬍ୘ˈᑊᰒ⼎њᮄㅫ⊩ⱘ〇ᅮ
ᗻDŽ㒧ᵰ㸼ᯢ LRR ㅫ⊩ⱘ䗖⫼ᗻ੠῵ᢳ㊒ᑺ䱣ሎᑺⱘ๲໻㗠ϟ䰡ˈ㗠
Ϩ LRR ㅫ⊩᠔೎᳝ⱘᇍϞ␌䕧ܹⶀᯊডᑨⱘ‫؛‬䆒䗴៤њ⌕䞣䖛ᮽࠄ䖒
⌕ඳߎষDŽ䖭Ͼ‫؛‬䆒ㄝৠѢᗑ⬹Ӵ䗕ᓊᯊˈ㗠䆹ᓊᯊ䯂乬䱣ⴔ㔥Ḑ໻
ᇣⱘ๲ࡴ㗠๲ᔎˈ಴㗠䆹䯂乬ᇍᕜ໮໻ሎᑺ῵ൟⱘᕅડ䛑ᰃᰒ㨫ⱘDŽ
෎Ѣᠽᬷ⊶⧚䆎ⱘ NRF ㅫ⊩ᕫࠄⱘᓊᯊ߭᳈ЎⳳᅲDŽ㗠Ϩ䆹ㅫ⊩ৃҹ
೼䳊ᠽᬷ㋏᭄‫؛‬䆒ϟ㹿ᵕ໻ㅔ࣪ˈҹ֓Ѣᑨ⫼೼໻ሎᑺ῵ൟЁDŽ
ᴀ䆎᭛Փ⫼ϸϾ催ߚ䕼⥛ⱘܼ⧗∈᭛ഄ⧚᭄᥂ᑧˈेߚ䕼⥛Ў 1 ݀
䞠 ⱘ Hydro1k ੠ ߚ 䕼 ⥛ Ў 3 ᓻ ⾦ ( 䌸 䘧 䰘 䖥 ໻ 㑺 90 ㉇ ) ⱘ
HydroSHEDSˈᇍ NRF ㅫ⊩䖯㸠њẔ偠ˈৠᯊ䯤䞞੠䆕ᯢњܼ⧗ሎᑺ
催ߚ䕼⥛∈᭛ഄ⧚᭄᥂ᑧⱘӋؐDŽ㱑✊᳈催ߚ䕼⥛ⱘ HydroSHEDS ੠
Hydro1k Ⳍ↨≵᳝ᯢᰒᦤ催῵ൟᬜ⥛㋏᭄˗ԚᰃˈՓ⫼䕗Ԣߚ䕼⥛ⱘ
Hydro1k ᯊ䗴៤䖛催ⱘ⊶䗳੠ᇍ໻⌕䞣῵ᢳⱘℷ‫أ‬ᏂDŽHydroSHEDS ᭄
᥂ᑧᦤկњ㊒⹂䆚߿⊇䘧ⱘৃ㛑ᗻDŽ䖭⾡ৃ㛑ᗻᇍѢ῵ᢳѻ⌕੠∛⌕
᳝޴⚍䞡㽕ᛣНDŽ佪‫ˈܜ‬ᔧ⊇䘧䆚߿ⱘ䯔ؐ䴶⿃೼ 0.5–100 km2 П䯈ᯊ
Ў⊇䘧䆚߿㗠ᓎゟⱘ⊇㔥ડᑨߑ᭄෎ᴀֱᣕϡবDŽ㱑✊೼催ߚ䕼⥛ϟ
᳈໮ⱘϞ␌⊇䘧㛑㹿䆚߿ˈ⊇㔥ⱘᘏԧᔶᗕֱᣕⳌԐDŽ䖭Ͼ⡍ᗻ‫އ‬ᅮ
њᔧՓ⫼໻ⱘ䯔ؐ䴶⿃ᯊ῵ൟⱘᬜ⥛ϡӮᰒ㨫䰡ԢˈҢ㗠Փ∛⌕ㅫ⊩
ᕫҹㅔ࣪ˈेা䳔೼Џ㽕⊇䘧Ϟ䖯㸠∛⌕䅵ㅫDŽᇍѢѻ⌕㗠㿔ˈ῵ᢳ
㒧ᵰ߭প‫އ‬Ѣ䯔ؐ䴶⿃ⱘ䗝ᢽDŽ঺໪ˈHydroSHEDS ᦤկњߚ⾏വ䴶⓿
⌕੠⊇䘧ᓊᯊⱘৃ㛑ᗻˈ㗠བᵰՓ⫼ Hydro1k 䖭ϸ㗙߭ᖙ乏㹿ড়ᑊDŽ
‫ݡ‬㗙ˈHydroSHEDS ᇍ⊇䘧ⱘ㊒⹂ᅮԡㅔ࣪њᇍ∈റ∈ᑧⱘᅮԡ῵ᢳDŽ
᳔ৢˈHydroSHEDS ᠔ᦤկⱘ㊒⹂ⱘ⌕ඳ䖍⬠ߦߚ੠催ߚ䕼⥛⊇㔥ϡԚ
ᦤ催њऎඳ῵ᢳⱘᬜ⥛ˈгՓᕫ䗮䖛ऎඳ῵ൟ偠䆕ܼ⧗῵ൟ᳈ࡴᮍ
֓DŽ
䅵ㅫᬜ⥛੠⫼ᯊᇍѢӏԩ໻ሎᑺ῵ൟ˄ࣙᣀܼ⧗῵ൟ˅䛑ᕜ䞡㽕DŽ
ᴀⷨおᦤկⱘᦤ催䅵ㅫᬜ⥛ⱘᮍ⊩ᰃᡞ∛⌕䅵ㅫߚЎ᭄᥂‫ޚ‬໛੠῵ᢳ
ϸϾ䰊↉DŽ՟བˈ᳔㐕䞡ⱘ䅵ㅫӏࡵ˄བ⊇㔥ડᑨߑ᭄ⱘ䅵ㅫ˅ˈ⬅
෎Ѣ HydroSHEDS ⱘ NRF ㅫ⊩೼᭄᥂‫ޚ‬໛䰊↉ᅠ៤໛⫼˗ᑊϨᇍӏԩ
ϔϾ⌕ඳা䳔䅵ㅫϔ⃵DŽ೼῵ᢳ䰊↉ˈ∛⌕ᰃ䗮䖛ᇍѻ⌕ⱘो⿃ᅲ⦄
ⱘDŽ῵ᢳ䰊↉ⱘ䅵ㅫ䞣↨‫ޚ‬໛䰊↉ᇣ 4 ࠄ 5 Ͼ᭄䞣㑻DŽ催ᬜ⥛ⱘो⿃䅵
ㅫՓᕫ㩭⡍व⋯ㅫ⊩ৃҹᑨ⫼೼ܼ⧗ሎᑺ∈᭛῵ൟЁDŽߚ䰊↉ⱘ䅵ㅫ
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